Academic Appointments


Administrative Appointments


  • Staff Scientist, Institute of Mathematics and Mechanics, Kazan State University, Kazan, Russia (1990 - 1993)
  • Technical Staff Member, Computer Research and Applications Group, CCS Division, Los Alamos National Laboratory (1999 - 2000)
  • Technical Staff Member and Team Leader (Multiscale Analysis Team, since 9/2004), Mathematical Modeling and Analysis Group, Theoretical Division, Los Alamos National Laboratory (2000 - 2007)
  • Adjunct Associate Professor, Department of Hydrology and Water Resources, The University of Arizona, Tucson (2001 - 2004)
  • Associate Professor, Department of Mechanical and Aerospace Engineering, University of California, San Diego (2004 - 2008)
  • Professor, Department of Mechanical and Aerospace Engineering, University of California, San Diego (2008 - 2016)
  • Professor, Department of Energy Resources Engineering, Stanford University (2016 - Present)

Honors & Awards


  • Foreign Member, Accademia delle Scienze, Istituto di Bologna (Sezione: Scienze Tecniche), Italy (2015)
  • Chutian Scholar Chair Professor, Three Gorges University, People’s Republic of China (PRC) (2012)
  • Travel award, State Administration of Foreign Expert Affairs, PRC (2010)
  • The 1999 Editors’ Citation for Excellence in Refereeing for Water Resources Research, EOS, 81(49), p. 598, December 5, 2000 (2000)
  • Travel award - The framework of the short-term mobility program, Italy, Italian Centro Nazionale delle Ricerche (CNR), (1999 & 2000)
  • Award, Special Fund for the Award of Personal Scholarships and Grants to Gifted Young Academics, Novosibirsk, Russia (1993)
  • Award, All-Union Student Research Conference in Mathematics and Mechanics, Moscow, USSR (1991)

Boards, Advisory Committees, Professional Organizations


  • Associate Editor, SIAM/ASA Journal on Uncertainty Quantification (2012 - Present)
  • Associate Editor, SIAM Journal on Scientific Computing (SISC) (2012 - 2017)
  • Member of Editorial Board, International Journal for Uncertainty Quantification (2010 - Present)
  • Associate Editor, Water Resources Research (2010 - 2017)
  • Associate Editor, Stochastic Environmental Research and Risk Assessment (2007 - Present)
  • Guest Editor, Computing in Science and Engineering (2007 - 2007)
  • Guest Editor, Computing in Science and Engineering (2005 - 2005)
  • Member of Editorial Board, Advances in Water Resources (2004 - Present)
  • Editor, Reviews of Geophysics (2001 - 2010)

Professional Education


  • Ph.D., Department of Hydrology and Water Resources, The University of Arizona, Tucson, Hydrology (1996)
  • M.Sc., Department of Mathematics and Mechanics, Kazan State University, Russia (Summa Cum Laude), Applied Mathematics/Fluid Mechanics (1991)

Current Research and Scholarly Interests


Environmental fluid mechanics:
Subsurface flow and contaminant transport, multiphase flow, groundwater hydrology, reservoir simulations, well hydraulics, surface-water/groundwater interactions, inverse modeling, subsurface imaging, decisions under uncertainty, geothermal energy.

Applied and computational mathematics:
Mathematical modeling of complex systems (electrochemistryfor energy storage, design of nano-porous materials), uncertainty quantification, probabilistic risk assessment, stochastic partial differential equations, hybrid numerical algorithms, spatial statistics, data assimilation.

Biomedical modeling:
Blood flow, microcirculation, intracellular and intercellular transport, bioinformatics, computational cell biology, hemodynamics, chemotaxis.

All Publications


  • Posttransfusion Increase of Hematocrit per se Does Not Improve Circulatory Oxygen Delivery due to Increased Blood Viscosity ANESTHESIA AND ANALGESIA Zimmerman, R., Tsai, A. G., Vazquez, B. Y., Cabrales, P., Hofmann, A., Meier, J., Shander, A., Spahn, D. R., Friedman, J. M., Tartakovsky, D. M., Intaglietta, M. 2017; 124 (5): 1547-1554

    Abstract

    Blood transfusion is used to treat acute anemia with the goal of increasing blood oxygen-carrying capacity as determined by hematocrit (Hct) and oxygen delivery (DO2). However, increasing Hct also increases blood viscosity, which may thus lower DO2 if the arterial circulation is a rigid hydraulic system as the resistance to blood flow will increase. The net effect of transfusion on DO2 in this system can be analyzed by using the relationship between Hct and systemic blood viscosity of circulating blood at the posttransfusion Hct to calculate DO2 and comparing this value with pretransfusion DO2. We hypothesized that increasing Hct would increase DO2 and tested our hypothesis by mathematically modeling DO2 in the circulation.Calculations were made assuming a normal cardiac output (5 L/min) with degrees of anemia ranging from 5% to 80% Hct deficit. We analyzed the effects of transfusing 0.5 or more units of 300 cc of packed red blood cells (PRBCs) at an Hct of 65% and calculated microcirculatory DO2 after accounting for increased blood viscosity and assuming no change in blood pressure. Our model accounts for O2 diffusion out of the circulation before blood arriving to the nutritional circulation and for changes in blood flow velocity. The immediate posttransfusion DO2 was also compared with DO2 after the transient increase in volume due to transfusion has subsided.Blood transfusion of up to 3 units of PRBCs increased DO2 when Hct (or hemoglobin) was 60% lower than normal, but did not increase DO2 when administered before this threshold.After accounting for the effect of increasing blood viscosity on blood flow owing to increasing Hct, we found in a mathematical simulation of DO2 that transfusion of up to 3 units of PRBCs does not increase DO2, unless anemia is the result of an Hct deficit greater than 60%. Observations that transfusions occasionally result in clinical improvement suggest that other mechanisms possibly related to increased blood viscosity may compensate for the absence of increase in DO2.

    View details for DOI 10.1213/ANE.0000000000002008

    View details for Web of Science ID 000400206800028

    View details for PubMedID 28328758

  • Optimal design of nanoporous materials for electrochemical devices APPLIED PHYSICS LETTERS Zhang, X., Tartakovsky, D. M. 2017; 110 (14)

    View details for DOI 10.1063/1.4979466

    View details for Web of Science ID 000399162100043

  • An analytical model for carrier-facilitated solute transport in weakly heterogeneous porous media APPLIED MATHEMATICAL MODELLING Severino, G., Campagna, R., Tartakovsky, D. M. 2017; 44: 261-273
  • On the use of reverse Brownian motion to accelerate hybrid simulations JOURNAL OF COMPUTATIONAL PHYSICS Bakarji, J., Tartakovsky, D. M. 2017; 334: 68-80
  • Doubly Penalized LASSO for Reconstruction of Biological Networks PROCEEDINGS OF THE IEEE Asadi, B., Maurya, M. R., Tartakovsky, D. M., Subramaniam, S. 2017; 105 (2): 319-329
  • A tightly-coupled domain-decomposition approach for highly nonlinear stochastic multiphysics systems JOURNAL OF COMPUTATIONAL PHYSICS Taverniers, S., Tartakovsky, D. M. 2017; 330: 884-901
  • Effective Ion Diffusion in Charged Nanoporous Materials JOURNAL OF THE ELECTROCHEMICAL SOCIETY Zhang, X., Tartakovsky, D. M. 2017; 164 (4): E53-E61
  • Noise-driven interfaces and their macroscopic representation PHYSICAL REVIEW E Dentz, M., Neuweiler, I., Meheust, Y., Tartakovsky, D. M. 2016; 94 (5)
  • Particle Methods for Heat Transfer in Fractured Media TRANSPORT IN POROUS MEDIA Gisladottir, V. R., Roubinet, D., Tartakovsky, D. M. 2016; 115 (2): 311-326
  • Noise-driven interfaces and their macroscopic representation. Physical review. E Dentz, M., Neuweiler, I., Méheust, Y., Tartakovsky, D. M. 2016; 94 (5-1): 052802-?

    Abstract

    We study the macroscopic representation of noise-driven interfaces in stochastic interface growth models in (1+1) dimensions. The interface is characterized macroscopically by saturation, which represents the fluctuating sharp interface by a smoothly varying phase field with values between 0 and 1. We determine the one-point interface height statistics for the Edwards-Wilkinson (EW) and Kadar-Paris-Zhang (KPZ) models in order to determine explicit deterministic equations for the phase saturation for each of them. While we obtain exact results for the EW model, we develop a Gaussian closure approximation for the KPZ model. We identify an interface compression term, which is related to mass transfer perpendicular to the growth direction, and a diffusion term that tends to increase the interface width. The interface compression rate depends on the mesoscopic mass transfer process along the interface and in this sense provides a relation between meso- and macroscopic interface dynamics. These results shed light on the relation between mesoscale and macroscale interface models, and provide a systematic framework for the upscaling of stochastic interface dynamics.

    View details for PubMedID 27967189

  • Analytical models of axisymmetric reaction-diffusion phenomena in composite media INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER Zimmerman, R. A., Jankowski, T. A., Tartakovsky, D. M. 2016; 99: 425-431
  • Efficient Multiscale Models of Polymer Assembly BIOPHYSICAL JOURNAL Ruiz-Martinez, A., Bartol, T. M., Sejnowski, T. J., Tartakovsky, D. M. 2016; 111 (1): 185-196

    Abstract

    Protein polymerization and bundling play a central role in cell physiology. Predictive modeling of these processes remains an open challenge, especially when the proteins involved become large and their concentrations high. We present an effective kinetics model of filament formation, bundling, and depolymerization after GTP hydrolysis, which involves a relatively small number of species and reactions, and remains robust over a wide range of concentrations and timescales. We apply this general model to study assembly of FtsZ protein, a basic element in the division process of prokaryotic cells such as Escherichia coli, Bacillus subtilis, or Caulobacter crescentus. This analysis demonstrates that our model outperforms its counterparts in terms of both accuracy and computational efficiency. Because our model comprises only 17 ordinary differential equations, its computational cost is orders-of-magnitude smaller than the current alternatives consisting of up to 1000 ordinary differential equations. It also provides, to our knowledge, a new insight into the characteristics and functioning of FtsZ proteins at high concentrations. The simplicity and versatility of our model render it a powerful computational tool, which can be used either as a standalone descriptor of other biopolymers' assembly or as a component in more complete kinetic models.

    View details for DOI 10.1016/j.bpj.2016.05.022

    View details for Web of Science ID 000380371400021

    View details for PubMedID 27410746

  • Shear-Induced Nitric Oxide Production by Endothelial Cells BIOPHYSICAL JOURNAL Sriram, K., Laughlin, J. G., Rangamani, P., Tartakovsky, D. M. 2016; 111 (1): 208-221

    Abstract

    We present a biochemical model of the wall shear stress-induced activation of endothelial nitric oxide synthase (eNOS) in an endothelial cell. The model includes three key mechanotransducers: mechanosensing ion channels, integrins, and G protein-coupled receptors. The reaction cascade consists of two interconnected parts. The first is rapid activation of calcium, which results in formation of calcium-calmodulin complexes, followed by recruitment of eNOS from caveolae. The second is phosphorylation of eNOS by protein kinases PKC and AKT. The model also includes a negative feedback loop due to inhibition of calcium influx into the cell by cyclic guanosine monophosphate (cGMP). In this feedback, increased nitric oxide (NO) levels cause an increase in cGMP levels, so that cGMP inhibition of calcium influx can limit NO production. The model was used to predict the dynamics of NO production by an endothelial cell subjected to a step increase of wall shear stress from zero to a finite physiologically relevant value. Among several experimentally observed features, the model predicts a highly nonlinear, biphasic transient behavior of eNOS activation and NO production: a rapid initial activation due to the very rapid influx of calcium into the cytosol (occurring within 1-5 min) is followed by a sustained period of activation due to protein kinases.

    View details for DOI 10.1016/j.bpj.2016.05.034

    View details for Web of Science ID 000380371400023

    View details for PubMedID 27410748

  • The method of distributions for dispersive transport in porous media with uncertain hydraulic properties WATER RESOURCES RESEARCH Boso, F., Tartakovsky, D. M. 2016; 52 (6): 4700-4712
  • Conservative tightly-coupled simulations of stochastic multiscale systems JOURNAL OF COMPUTATIONAL PHYSICS Taverniers, S., Pigarov, A. Y., Tartakovsky, D. M. 2016; 313: 400-414
  • Simulating social-ecological systems: the Island Digital Ecosystem Avatars (IDEA) consortium GIGASCIENCE Davies, N., Field, D., Gavaghan, D., Holbrook, S. J., Planes, S., Troyer, M., Bonsall, M., Claudet, J., Roderick, G., Schmitt, R. J., Zettler, L. A., Berteaux, V., Bossin, H. C., Cabasse, C., Collin, A., Deck, J., Dell, T., Dunne, J., Gates, R., Harfoot, M., Hench, J. L., Hopuare, M., Kirch, P., Kotoulas, G., Kosenkov, A., Kusenko, A., Leichter, J. J., Lenihan, H., Magoulas, A., Martinez, N., Meyer, C., Stoll, B., Swalla, B., Tartakovsky, D. M., Murphy, H. T., Turyshev, S., Valdvinos, F., Williams, R., Wood, S. 2016; 5

    Abstract

    Systems biology promises to revolutionize medicine, yet human wellbeing is also inherently linked to healthy societies and environments (sustainability). The IDEA Consortium is a systems ecology open science initiative to conduct the basic scientific research needed to build use-oriented simulations (avatars) of entire social-ecological systems. Islands are the most scientifically tractable places for these studies and we begin with one of the best known: Moorea, French Polynesia. The Moorea IDEA will be a sustainability simulator modeling links and feedbacks between climate, environment, biodiversity, and human activities across a coupled marine-terrestrial landscape. As a model system, the resulting knowledge and tools will improve our ability to predict human and natural change on Moorea and elsewhere at scales relevant to management/conservation actions.

    View details for DOI 10.1186/s13742-016-0118-5

    View details for Web of Science ID 000372428100001

    View details for PubMedID 26998258

  • Temperature fields induced by geothermal devices ENERGY Ciriello, V., Bottarelli, M., Di Federico, V., Tartakovsky, D. M. 2015; 93: 1896-1903
  • Data-driven models of groundwater salinization in coastal plains JOURNAL OF HYDROLOGY Felisa, G., Ciriello, V., Antonellini, M., Di Federico, V., Tartakovsky, D. M. 2015; 531: 187-197
  • Coexistence of short- and long-range ferromagnetic order in nanocrystalline Fe2Mn1-xCuxAl (x=0.0, 0.1 and 0.3) synthesized by high-energy ball milling JOURNAL OF MAGNETISM AND MAGNETIC MATERIALS Tran Dang Thanh, T. D., Nanto, D., Ngo Thi Uyen Tuyen, N. T., Nan, W., Yu, Y., Tartakovsky, D. M., Yu, S. C. 2015; 394: 37-43
  • Critical Behavior in Double-Exchange Ferromagnets of Pr0.6Sr0.4MnO3 Nanoparticles IEEE TRANSACTIONS ON MAGNETICS Tran Dang Thanh, T. D., YiKyung, Y., Ho, T. A., Manh, T. V., The Long Phan, T. L., Tartakovsky, D. M., Yu, S. C. 2015; 51 (11)
  • Impact of stochastic fluctuations in the cell free layer on nitric oxide bioavailability FRONTIERS IN COMPUTATIONAL NEUROSCIENCE Park, S., Intaglietta, M., Tartakovsky, D. M. 2015; 9

    Abstract

    A plasma stratum (cell free layer or CFL) generated by flowing blood interposed between the red blood cell (RBC) core and the endothelium affects generation, consumption, and transport of nitric oxide (NO) in the microcirculation. CFL width is a principal factor modulating NO diffusion and vessel wall shears stress development, thus significantly affecting NO bioavailability. Since the CFL is bounded by the surface formed by the chaotically moving RBCs and the stationary but spatially non-uniform endothelial surface, its width fluctuates randomly in time and space. We analyze how these stochastic fluctuations affect NO transport in the CFL and NO bioavailability. We show that effects due to random boundaries do not average to zero and lead to an increase of NO bioavailability. Since endothelial production of NO is significantly enhanced by temporal variability of wall shear stress, we posit that stochastic shear stress stimulation of the endothelium yields the baseline continual production of NO by the endothelium. The proposed stochastic formulation captures the natural continuous and microscopic variability, whose amplitude is measurable and is of the scale of cellular dimensions. It provides a realistic model of NO generation and regulation.

    View details for DOI 10.3389/fncom.2015.00131

    View details for Web of Science ID 000364958600001

    View details for PubMedID 26578944

  • Design of nanoporous materials with optimal sorption capacity JOURNAL OF APPLIED PHYSICS Zhang, X., Urita, K., Moriguchi, I., Tartakovsky, D. M. 2015; 117 (24)

    View details for DOI 10.1063/1.4923057

    View details for Web of Science ID 000357613900029

  • A boundary-layer solution for flow at the soil-root interface JOURNAL OF MATHEMATICAL BIOLOGY Severino, G., Tartakovsky, D. M. 2015; 70 (7): 1645-1668

    Abstract

    Transpiration, a process by which plants extract water from soil and transmit it to the atmosphere, is a vital (yet least quantified) component of the hydrological cycle. We propose a root-scale model of water uptake, which is based on first principles, i.e. employs the generally accepted Richards equation to describe water flow in partially saturated porous media (both in a root and the ambient soil) and makes no assumptions about the kinematic structure of flow in a root-soil continuum. Using the Gardner (exponential) constitutive relation to represent the relative hydraulic conductivities in the Richards equations and treating the root as a cylinder, we use a matched asymptotic expansion technique to derive approximate solutions for transpiration rate and the size of a plant capture zone. These solutions are valid for roots whose size is larger than the macroscopic capillary length of a host soil. For given hydraulic properties, the perturbation parameter used in our analysis relates a root's size to the macroscopic capillary length of the ambient soil. This parameter determines the width of a boundary layer surrounding the soil-root interface, within which flow is strictly horizontal (perpendicular to the root). Our analysis provides a theoretical justification for the standard root-scale cylindrical flow model of plant transpiration that imposes a number of kinematic constraints on water flow in a root-soil continuum.

    View details for DOI 10.1007/s00285-014-0813-8

    View details for Web of Science ID 000354196800006

    View details for PubMedID 25008964

  • Linear functional minimization for inverse modeling WATER RESOURCES RESEARCH Barajas-Solano, D. A., WOHLBERG, B. E., Vesselinov, V. V., Tartakovsky, D. M. 2015; 51 (6): 4516-4531
  • Critical behavior and magnetocaloric effect of Pr1-xCaxMnO3 JOURNAL OF APPLIED PHYSICS Ho, T. A., Thanh, T. D., Yu, Y., Tartakovsky, D. M., Ho, T. O., Thang, P. D., Anh-Tuan Le, A. T., The-Long Phan, T. L., Yu, S. C. 2015; 117 (17)

    View details for DOI 10.1063/1.4914537

    View details for Web of Science ID 000354984100345

  • Hematocrit dispersion in asymmetrically bifurcating vascular networks AMERICAN JOURNAL OF PHYSIOLOGY-HEART AND CIRCULATORY PHYSIOLOGY Sriram, K., Intaglietta, M., Tartakovsky, D. M. 2014; 307 (11): H1576-H1586

    Abstract

    Quantitative modeling of physiological processes in vasculatures requires an accurate representation of network topology, including vessel branching. We propose a new approach for reconstruction of vascular network, which determines how vessel bifurcations distribute red blood cells (RBC) in the microcirculation. Our method follows the foundational premise of Murray's law in postulating the existence of functional optimality of such networks. It accounts for the non-Newtonian behavior of blood by allowing the apparent blood viscosity to vary with discharge hematocrit and vessel radius. The optimality criterion adopted in our approach is the physiological cost of supplying oxygen to the tissue surrounding a blood vessel. Bifurcation asymmetry is expressed in terms of the amount of oxygen consumption associated with the respective tissue volumes being supplied by each daughter vessel. The vascular networks constructed with our approach capture a number of physiological characteristics observed in in vivo studies. These include the nonuniformity of wall shear stress in the microcirculation, the significant increase in pressure gradients in the terminal sections of the network, the nonuniformity of both the hematocrit partitioning at vessel bifurcations and hematocrit across the capillary bed, and the linear relationship between the RBC flux fraction and the blood flow fraction at bifurcations.

    View details for DOI 10.1152/ajpheart.00283.2014

    View details for Web of Science ID 000346019900005

    View details for PubMedID 25217657

  • Identifying Transport Behavior of Single-Molecule Trajectories BIOPHYSICAL JOURNAL Regner, B. M., Tartakovsky, D. M., Sejnowski, T. J. 2014; 107 (10): 2345-2351

    Abstract

    Models of biological diffusion-reaction systems require accurate classification of the underlying diffusive dynamics (e.g., Fickian, subdiffusive, or superdiffusive). We use a renormalization group operator to identify the anomalous (non-Fickian) diffusion behavior from a short trajectory of a single molecule. The method provides quantitative information about the underlying stochastic process, including its anomalous scaling exponent. The classification algorithm is first validated on simulated trajectories of known scaling. Then it is applied to experimental trajectories of microspheres diffusing in cytoplasm, revealing heterogeneous diffusive dynamics. The simplicity and robustness of this classification algorithm makes it an effective tool for analysis of rare stochastic events that occur in complex biological systems.

    View details for DOI 10.1016/j.bpj.2014.10.005

    View details for Web of Science ID 000345195700006

    View details for PubMedID 25418303

  • Vegetation Pattern Formation Due to Interactions Between Water Availability and Toxicity in Plant-Soil Feedback BULLETIN OF MATHEMATICAL BIOLOGY Marasco, A., Iuorio, A., Carteni, F., Bonanomi, G., Tartakovsky, D. M., Mazzoleni, S., Giannino, F. 2014; 76 (11): 2866-2883

    Abstract

    Development of a comprehensive theory of the formation of vegetation patterns is still in progress. A prevailing view is to treat water availability as the main causal factor for the emergence of vegetation patterns. While successful in capturing the occurrence of multiple vegetation patterns in arid and semiarid regions, this hypothesis fails to explain the presence of vegetation patterns in humid environments. We explore the rich structure of a toxicity-mediated model of the vegetation pattern formation. This model consists of three PDEs accounting for a dynamic balance between biomass, water, and toxic compounds. Different (ecologically feasible) regions of the model's parameter space give rise to stable spatial vegetation patterns in Turing and non-Turing regimes. Strong negative feedback gives rise to dynamic spatial patterns that continuously move in space while retaining their stable topology.

    View details for DOI 10.1007/s11538-014-0036-6

    View details for Web of Science ID 000345138900007

    View details for PubMedID 25338554

  • Replacing the Transfusion of 1-2 Units of Blood with Plasma Expanders that Increase Oxygen Delivery Capacity: Evidence from Experimental Studies. Journal of functional biomaterials Tsai, A. G., Salazar Vázquez, B. Y., Cabrales, P., Kistler, E. B., Tartakovsky, D. M., Subramaniam, S., Acharya, S. A., Intaglietta, M. 2014; 5 (4): 232-245

    Abstract

    At least a third of the blood supply in the world is used to transfuse 1-2 units of packed red blood cells for each intervention and most clinical trials of blood substitutes have been carried out at this level of oxygen carrying capacity (OCC) restoration. However, the increase of oxygenation achieved is marginal or none at all for molecular hemoglobin (Hb) products, due to their lingering vasoactivity. This has provided the impetus for the development of "oxygen therapeutics" using Hb-based molecules that have high oxygen affinity and target delivery of oxygen to anoxic areas. However it is still unclear how these oxygen carriers counteract or mitigate the functional effects of anemia due to obstruction, vasoconstriction and under-perfusion. Indeed, they are administered as a low dosage/low volume therapeutic Hb (subsequently further diluted in the circulatory pool) and hence induce extremely small OCC changes. Hyperviscous plasma expanders provide an alternative to oxygen therapeutics by increasing the oxygen delivery capacity (ODC); in anemia they induce supra-perfusion and increase tissue perfusion (flow) by as much as 50%. Polyethylene glycol conjugate albumin (PEG-Alb) accomplishes this by enhancing the shear thinning behavior of diluted blood, which increases microvascular endothelial shear stress, causes vasodilation and lowering peripheral vascular resistance thus facilitating cardiac function. Induction of supra-perfusion takes advantage of the fact that ODC is the product of OCC and blood flow and hence can be maintained by increasing either or both. Animal studies suggest that this approach may save a considerable fraction of the blood supply. It has an additional benefit of enhancing tissue clearance of toxic metabolites.

    View details for DOI 10.3390/jfb5040232

    View details for PubMedID 25350267

  • Non-Newtonian Flow of Blood in Arterioles: Consequences for Wall Shear Stress Measurements MICROCIRCULATION Sriram, K., Intaglietta, M., Tartakovsky, D. M. 2014; 21 (7): 628-639

    Abstract

    Our primary goal is to investigate the effects of non-Newtonian blood properties on wall shear stress in microvessels. The secondary goal is to derive a correction factor for the Poiseuille-law-based indirect measurements of wall shear stress.The flow is assumed to exhibit two distinct, immiscible and homogeneous fluid layers: an inner region densely packed with RBCs, and an outer cell-free layer whose thickness depends on discharge hematocrit. The cell-free layer is assumed to be Newtonian, while rheology of the RBC-rich core is modeled using the Quemada constitutive law.Our model provides a realistic description of experimentally observed blood velocity profiles, tube hematocrit, core hematocrit, and apparent viscosity over a wide range of vessel radii and discharge hematocrits.Our analysis reveals the importance of incorporating this complex blood rheology into estimates of WSS in microvessels. The latter is accomplished by specifying a correction factor, which accounts for the deviation of blood flow from the Poiseuille law.

    View details for DOI 10.1111/micc.12141

    View details for Web of Science ID 000343818400007

    View details for PubMedID 24703006

  • Information theoretic approach to complex biological network reconstruction: application to cytokine release in RAW 264.7 macrophages BMC SYSTEMS BIOLOGY Farhangmehr, F., Maurya, M. R., Tartakovsky, D. M., Subramaniam, S. 2014; 8

    Abstract

    High-throughput methods for biological measurements generate vast amounts of quantitative data, which necessitate the development of advanced approaches to data analysis to help understand the underlying mechanisms and networks. Reconstruction of biological networks from measured data of different components is a significant challenge in systems biology.We use an information theoretic approach to reconstruct phosphoprotein-cytokine networks in RAW 264.7 macrophage cells. Cytokines are secreted upon activation of a wide range of regulatory signals transduced by the phosphoprotein network. Identifying these components can help identify regulatory modules responsible for the inflammatory phenotype. The information theoretic approach is based on estimation of mutual information of interactions by using kernel density estimators. Mutual information provides a measure of statistical dependencies between interacting components. Using the topology of the network derived, we develop a data-driven parsimonious input-output model of the phosphoprotein-cytokine network.We demonstrate the applicability of our information theoretic approach to reconstruction of biological networks. For the phosphoprotein-cytokine network, this approach not only captures most of the known signaling components involved in cytokine release but also predicts new signaling components involved in the release of cytokines. The results of this study are important for gaining a clear understanding of macrophage activation during the inflammation process.

    View details for DOI 10.1186/1752-0509-8-77

    View details for Web of Science ID 000338890900001

    View details for PubMedID 24964861

  • Cumulative distribution function solutions of advection-reaction equations with uncertain parameters PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES Boso, F., Broyda, S. V., Tartakovsky, D. M. 2014; 470 (2166)

    Abstract

    We derive deterministic cumulative distribution function (CDF) equations that govern the evolution of CDFs of state variables whose dynamics are described by the first-order hyperbolic conservation laws with uncertain coefficients that parametrize the advective flux and reactive terms. The CDF equations are subjected to uniquely specified boundary conditions in the phase space, thus obviating one of the major challenges encountered by more commonly used probability density function equations. The computational burden of solving CDF equations is insensitive to the magnitude of the correlation lengths of random input parameters. This is in contrast to both Monte Carlo simulations (MCSs) and direct numerical algorithms, whose computational cost increases as correlation lengths of the input parameters decrease. The CDF equations are, however, not exact because they require a closure approximation. To verify the accuracy and robustness of the large-eddy-diffusivity closure, we conduct a set of numerical experiments which compare the CDFs computed with the CDF equations with those obtained via MCSs. This comparison demonstrates that the CDF equations remain accurate over a wide range of statistical properties of the two input parameters, such as their correlation lengths and variance of the coefficient that parametrizes the advective flux.

    View details for DOI 10.1098/rspa.2014.0189

    View details for Web of Science ID 000335326400021

    View details for PubMedID 24910529

  • Noise propagation in hybrid models of nonlinear systems: The Ginzburg-Landau equation JOURNAL OF COMPUTATIONAL PHYSICS Taverniers, S., Alexander, F. J., Tartakovsky, D. M. 2014; 262: 313-324
  • Analytical models of heat conduction in fractured rocks JOURNAL OF GEOPHYSICAL RESEARCH-SOLID EARTH Martinez, A. R., Roubinet, D., Tartakovsky, D. M. 2014; 119 (1): 83-98
  • Hybrid modeling of heterogeneous geochemical reactions in fractured porous media WATER RESOURCES RESEARCH Roubinet, D., Tartakovsky, D. M. 2013; 49 (12): 7945-7956
  • Stochastic smoothed profile method for modeling random roughness in flow problems COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING Zayernouri, M., Park, S., Tartakovsky, D. M., Karniadakis, G. E. 2013; 263: 99-112
  • Exact PDF equations and closure approximations for advective-reactive transport JOURNAL OF COMPUTATIONAL PHYSICS Venturi, D., Tartakovsky, D. M., Tartakovsky, A. M., Karniadakis, G. E. 2013; 243: 323-343
  • Anomalous Diffusion of Single Particles in Cytoplasm BIOPHYSICAL JOURNAL Regner, B. M., Vucinic, D., Domnisoru, C., Bartol, T. M., Hetzer, M. W., Tartakovsky, D. M., Sejnowski, T. J. 2013; 104 (8): 1652-1660

    Abstract

    The crowded intracellular environment poses a formidable challenge to experimental and theoretical analyses of intracellular transport mechanisms. Our measurements of single-particle trajectories in cytoplasm and their random-walk interpretations elucidate two of these mechanisms: molecular diffusion in crowded environments and cytoskeletal transport along microtubules. We employed acousto-optic deflector microscopy to map out the three-dimensional trajectories of microspheres migrating in the cytosolic fraction of a cellular extract. Classical Brownian motion (BM), continuous time random walk, and fractional BM were alternatively used to represent these trajectories. The comparison of the experimental and numerical data demonstrates that cytoskeletal transport along microtubules and diffusion in the cytosolic fraction exhibit anomalous (nonFickian) behavior and posses statistically distinct signatures. Among the three random-walk models used, continuous time random walk provides the best representation of diffusion, whereas microtubular transport is accurately modeled with fractional BM.

    View details for DOI 10.1016/j.bpj.2013.01.049

    View details for Web of Science ID 000318262300006

    View details for PubMedID 23601312

  • Probability Density Function Method for Langevin Equations with Colored Noise PHYSICAL REVIEW LETTERS Wang, P., Tartakovsky, A. M., Tartakovsky, D. M. 2013; 110 (14)

    Abstract

    Understanding the mesoscopic behavior of dynamical systems described by Langevin equations with colored noise is a fundamental challenge in a variety of fields. We propose a new approach to derive closed-form equations for joint and marginal probability density functions of state variables. This approach is based on a so-called large-eddy-diffusivity closure and can be used to model a wide class of non-Markovian processes described by the noise with an arbitrary correlation function. We demonstrate the accuracy of the proposed probability density function method for several linear and nonlinear Langevin equations.

    View details for DOI 10.1103/PhysRevLett.110.140602

    View details for Web of Science ID 000316959200005

    View details for PubMedID 25166972

  • Assessment and management of risk in subsurface hydrology: A review and perspective ADVANCES IN WATER RESOURCES Tartakovsky, D. M. 2013; 51: 247-260
  • CDF SOLUTIONS OF BUCKLEY-LEVERETT EQUATION WITH UNCERTAIN PARAMETERS MULTISCALE MODELING & SIMULATION Wang, P., Tartakovsky, D. M., Jarman, K. D., Tartakovsky, A. M. 2013; 11 (1): 118-133

    View details for DOI 10.1137/120865574

    View details for Web of Science ID 000316861400005

  • COMPUTING GREEN'S FUNCTIONS FOR FLOW IN HETEROGENEOUS COMPOSITE MEDIA INTERNATIONAL JOURNAL FOR UNCERTAINTY QUANTIFICATION Barajas-Solano, D. A., Tartakovsky, D. M. 2013; 3 (1): 39-46
  • Particle-tracking simulations of anomalous transport in hierarchically fractured rocks COMPUTERS & GEOSCIENCES Roubinet, D., de Dreuzy, J., Tartakovsky, D. M. 2013; 50: 52-58
  • An Information-theoretic Algorithm to Data-driven Genetic Pathway Interaction Network Reconstruction of Dynamic Systems 2013 IEEE INTERNATIONAL CONFERENCE ON BIOINFORMATICS AND BIOMEDICINE (BIBM) Farhangmehr, F., Tartakovsky, D. M., Sadatmousavi, P., Maurya, M. R., Subramaniam, S. 2013
  • A NEW PHYSIOLOGICAL BOUNDARY CONDITION FOR HEMODYNAMICS SIAM JOURNAL ON APPLIED MATHEMATICS Cousins, W., Gremaud, P. A., Tartakovsky, D. M. 2013; 73 (3): 1203-1223

    View details for DOI 10.1137/120895470

    View details for Web of Science ID 000321040600006

  • Stochastic operator-splitting method for reaction-diffusion systems JOURNAL OF CHEMICAL PHYSICS Choi, T., Maurya, M. R., Tartakovsky, D. M., Subramaniam, S. 2012; 137 (18)

    Abstract

    Many biochemical processes at the sub-cellular level involve a small number of molecules. The local numbers of these molecules vary in space and time, and exhibit random fluctuations that can only be captured with stochastic simulations. We present a novel stochastic operator-splitting algorithm to model such reaction-diffusion phenomena. The reaction and diffusion steps employ stochastic simulation algorithms and Brownian dynamics, respectively. Through theoretical analysis, we have developed an algorithm to identify if the system is reaction-controlled, diffusion-controlled or is in an intermediate regime. The time-step size is chosen accordingly at each step of the simulation. We have used three examples to demonstrate the accuracy and robustness of the proposed algorithm. The first example deals with diffusion of two chemical species undergoing an irreversible bimolecular reaction. It is used to validate our algorithm by comparing its results with the solution obtained from a corresponding deterministic partial differential equation at low and high number of molecules. In this example, we also compare the results from our method to those obtained using a Gillespie multi-particle (GMP) method. The second example, which models simplified RNA synthesis, is used to study the performance of our algorithm in reaction- and diffusion-controlled regimes and to investigate the effects of local inhomogeneity. The third example models reaction-diffusion of CheY molecules through the cytoplasm of Escherichia coli during chemotaxis. It is used to compare the algorithm's performance against the GMP method. Our analysis demonstrates that the proposed algorithm enables accurate simulation of the kinetics of complex and spatially heterogeneous systems. It is also computationally more efficient than commonly used alternatives, such as the GMP method.

    View details for DOI 10.1063/1.4764108

    View details for Web of Science ID 000311317800003

    View details for PubMedID 23163359

  • Autoregulation and mechanotransduction control the arteriolar response to small changes in hematocrit AMERICAN JOURNAL OF PHYSIOLOGY-HEART AND CIRCULATORY PHYSIOLOGY Sriram, K., Vazquez, B. Y., Tsai, A. G., Cabrales, P., Intaglietta, M., Tartakovsky, D. M. 2012; 303 (9): H1096-H1106

    Abstract

    Here, we present an analytic model of arteriolar mechanics that accounts for key autoregulation mechanisms, including the myogenic response and the vasodilatory effects of nitric oxide (NO) in the vasculature. It couples the fluid mechanics of blood flow in arterioles with solid mechanics of the vessel wall and includes the effects of wall shear stress- and stretch-induced endothelial NO production. The model can be used to describe the regulation of blood flow and NO transport under small changes in hematocrit and to analyze the regulatory response of arterioles to small changes in hematocrit. Our analysis revealed that the experimentally observed paradoxical increase in cardiac output with small increases in hematocrit results from the combination of increased NO production and the effects of a strong myogenic response modulated by elevated levels of WSS. Our findings support the hypothesis that vascular resistance varies inversely with blood viscosity for small changes in hematocrit in a healthy circulation that responds to shear stress stimuli. They also suggest beneficial effects independent of changes in O(2) carrying capacity associated with the postsurgical transfusion of one or two units of blood.

    View details for DOI 10.1152/ajpheart.00438.2012

    View details for Web of Science ID 000310650300002

    View details for PubMedID 22923620

  • Uncertainty quantification in kinematic-wave models JOURNAL OF COMPUTATIONAL PHYSICS Wang, P., Tartakovsky, D. M. 2012; 231 (23): 7868-7880
  • Comparison of statistical and optimisation-based methods for data-driven network reconstruction of biochemical systems IET SYSTEMS BIOLOGY Asadi, B., Maurya, M. R., Tartakovsky, D. M., Subramaniam, S. 2012; 6 (5): 155-U53

    Abstract

    Data-driven reconstruction of biological networks is a crucial step towards making sense of large volumes of biological data. Although several methods have been developed recently to reconstruct biological networks, there are few systematic and comprehensive studies that compare different methods in terms of their ability to handle incomplete datasets, high data dimensions and noisy data. The authors use experimentally measured and synthetic datasets to compare three popular methods - principal component regression (PCR), linear matrix inequalities (LMI) and least absolute shrinkage and selection operator (LASSO) - in terms of root-mean-squared error (RMSE), average fractional error in the value of the coefficients, accuracy, sensitivity, specificity and the geometric mean of sensitivity and specificity. This comparison enables the authors to establish criteria for selection of an appropriate approach for network reconstruction based on a priori properties of experimental data. For instance, although PCR is the fastest method, LASSO and LMI perform better in terms of accuracy, sensitivity and specificity. Both PCR and LASSO are better than LMI in terms of fractional error in the values of the computed coefficients. Trade-offs such as these suggest that more than one aspect of each method needs to be taken into account when designing strategies for network reconstruction.

    View details for DOI 10.1049/iet-syb.2011.0052

    View details for Web of Science ID 000310434300001

    View details for PubMedID 23101870

  • PEG-albumin supraplasma expansion is due to increased vessel wall shear stress induced by blood viscosity shear thinning AMERICAN JOURNAL OF PHYSIOLOGY-HEART AND CIRCULATORY PHYSIOLOGY Sriram, K., Tsai, A. G., Cabrales, P., Meng, F., Acharya, S. A., Tartakovsky, D. M., Intaglietta, M. 2012; 302 (12): H2489-H2497

    Abstract

    We studied the extreme hemodilution to a hematocrit of 11% induced by three plasma expanders: polyethylene glycol (PEG)-conjugated albumin (PEG-Alb), 6% 70-kDa dextran, and 6% 500-kDa dextran. The experimental component of our study relied on microelectrodes and cardiac output to measure both the rheological properties of plasma-expander blood mixtures and nitric oxide (NO) bioavailability in vessel walls. The modeling component consisted of an analysis of the distribution of wall shear stress (WSS) in the microvessels. Our experiments demonstrated that plasma expansion with PEG-Alb caused a state of supraperfusion with cardiac output 40% above baseline, significantly increased NO vessel wall bioavailability, and lowered peripheral vascular resistance. We attributed this behavior to the shear thinning nature of blood and PEG-Alb mixtures. To substantiate this hypothesis, we developed a mathematical model of non-Newtonian blood flow in a vessel. Our model used the Quemada rheological constitutive relationship to express blood viscosity in terms of both hematocrit and shear rate. The model revealed that the net effect of the hemodilution induced by relatively low-viscosity shear thinning PEG-Alb plasma expanders is to reduce overall blood viscosity and to increase the WSS, thus intensifying endothelial NO production. These changes act synergistically, significantly increasing cardiac output and perfusion due to lowered overall peripheral vascular resistance.

    View details for DOI 10.1152/ajpheart.01090.2011

    View details for Web of Science ID 000305430100004

    View details for PubMedID 22505638

  • Impact of endothelium roughness on blood flow JOURNAL OF THEORETICAL BIOLOGY Park, S. W., Intaglietta, M., Tartakovsky, D. M. 2012; 300: 152-160

    Abstract

    Cell free layer (CFL), a plasma layer bounded by the red blood cell (RBC) core and the endothelium, plays an important physiological role. Its width affects the effective blood viscosity as well as the scavenging and production of nitric oxide (NO). Measurements of the CFL and its spatio-temporal variability are highly uncertain, exhibiting random fluctuations. Yet traditional models of blood flow and NO scavenging treat the CFL's bounding surfaces as deterministic and smooth. We investigate the effects of the endothelium roughness and uncertain (random) spatial variability on blood flow and the estimates of effective blood viscosity.

    View details for DOI 10.1016/j.jtbi.2012.01.017

    View details for Web of Science ID 000302113100016

    View details for PubMedID 22300799

  • Lagrangian models of reactive transport in heterogeneous porous media with uncertain properties PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES Severino, G., Tartakovsky, D. M., Srinivasan, G., Viswanathan, H. 2012; 468 (2140): 1154-1174
  • A Bayesian approach to integrate temporal data into probabilistic risk analysis of monitored NAPL remediation ADVANCES IN WATER RESOURCES Fernandez-Garcia, D., Bolster, D., Sanchez-Vila, X., Tartakovsky, D. M. 2012; 36: 108-120
  • Introduction to the special issue on uncertainty quantification and risk assessment ADVANCES IN WATER RESOURCES Tartakovsky, D. M., Nowak, W., Bolster, D. 2012; 36: 1-2
  • Probabilistic analysis of maintenance and operation of artificial recharge ponds ADVANCES IN WATER RESOURCES Pedretti, D., Barahona-Palomo, M., Bolster, D., Fernandez-Garcia, D., Sanchez-Vila, X., Tartakovsky, D. M. 2012; 36: 23-35
  • Semi-analytical solutions for solute transport and exchange in fractured porous media WATER RESOURCES RESEARCH Roubinet, D., de Dreuzy, J., Tartakovsky, D. M. 2012; 48
  • Probabilistic analysis of groundwater-related risks at subsurface excavation sites ENGINEERING GEOLOGY Jurado, A., De Gaspari, F., Vilarrasa, V., Bolster, D., Sanchez-Vila, X., Fernandez-Garcia, D., Tartakovsky, D. M. 2012; 125: 35-44
  • Hybrid models of reactive transport in porous and fractured media ADVANCES IN WATER RESOURCES Battiato, I., Tartakovsky, D. M., Tartakovsky, A. M., Scheibe, T. D. 2011; 34 (9): 1140-1150
  • Mean arterial pressure nonlinearity in an elastic circulatory system subjected to different hematocrits BIOMECHANICS AND MODELING IN MECHANOBIOLOGY Branigan, T., Bolster, D., Salazar Vazquez, B. Y., Intaglietta, M., Tartakovsky, D. M. 2011; 10 (4): 591-598

    Abstract

    The level of hematocrit (Hct) is known to affect mean arterial pressure (MAP) by influencing blood viscosity. In the healthy population, an increase in Hct (and corresponding increase in viscosity) tends to raise MAP. However, data from a clinical study of type 2 diabetic patients indicate that this relationship is not universal. Instead, individuals in the lower levels of Hct range display a decrease in MAP for a given rise in Hct. After reaching a minimum, this trend is reversed, so that further increases in Hct lead to increases in MAP. We hypothesize that this anomalous behavior occurs due to changes in the circulatory autoregulation mechanism. To substantiate this hypothesis, we develop a physically based mathematical model that incorporates autoregulation mechanisms. Our model replicates the anomalous U-shaped relationship between MAP and Hct found in diabetic patients in the same range of Hct variability.

    View details for DOI 10.1007/s10237-010-0258-y

    View details for Web of Science ID 000292040600014

    View details for PubMedID 20878440

  • Integration of cardiovascular regulation by the blood/endothelium cell-free layer WILEY INTERDISCIPLINARY REVIEWS-SYSTEMS BIOLOGY AND MEDICINE Hightower, C. M., Vazquez, B. Y., Park, S. W., Sriram, K., Martini, J., Yalcin, O., Tsai, A. G., Cabrales, P., Tartakovsky, D. M., Johnson, P. C., Intaglietta, M. 2011; 3 (4): 458-470

    Abstract

    The cell-free layer (CFL) width separating red blood cells in flowing blood from the endothelial cell membrane is shown to be a regulator of the balance between nitric oxide (NO) production by the endothelium and NO scavenging by blood hemoglobin. The CFL width is determined by hematocrit (Hct) and the vessel wall flow velocity gradient. These factors and blood and plasma viscosity determine vessel wall shear stress which regulates the production of NO in the vascular wall. Mathematical modeling and experimental findings show that vessel wall NO concentration is a strong nonlinear function of Hct and that small Hct variations have comparatively large effects on blood pressure regulation. Furthermore, NO concentration is a regulator of inflammation and oxygen metabolism. Therefore, small, sustained perturbations of Hct may have long-term effects that can promote pro-hypertensive and pro-inflammatory conditions. In this context, Hct and its variability are directly related to vascular tone, peripheral vascular resistance, oxygen transport and delivery, and inflammation. These effects are relevant to the analysis and understanding of blood pressure regulation, as NO bioavailability regulates the contractile state of blood vessels. Furthermore, regulation of the CFL is a direct function of blood composition therefore understanding of its physiology relates to the design and management of fluid resuscitation fluids. From a medical perspective, these studies propose that it should be of clinical interest to note small variations in patient's Hct levels given their importance in modulating the CFL width and therefore NO bioavailability. WIREs Syst Biol Med 2011 3 458-470 DOI: 10.1002/wsbm.150

    View details for DOI 10.1002/wsbm.150

    View details for Web of Science ID 000291821300006

    View details for PubMedID 21523919

  • PDF equations for advective-reactive transport in heterogeneous porous media with uncertain properties JOURNAL OF CONTAMINANT HYDROLOGY Tartakovsky, D. M., Broyda, S. 2011; 120-21: 129-140
  • Applicability regimes for macroscopic models of reactive transport in porous media JOURNAL OF CONTAMINANT HYDROLOGY BATTIATO, I., Tartakovsky, D. M. 2011; 120-21: 18-26
  • PDF equations for advective-reactive transport in heterogeneous porous media with uncertain properties. Journal of contaminant hydrology Tartakovsky, D. M., Broyda, S. 2011; 120-121: 129-140

    Abstract

    We consider advective-reactive solute transport in porous media whose hydraulic and transport properties are uncertain. These properties are treated as random fields, which renders nonlinear advection-reaction transport equations stochastic. We derive a deterministic equation for the probability density function (PDF) of the concentration of a solute that undergoes heterogeneous reactions, e.g., precipitation or dissolution. The derivation treats exactly (without linearization) a reactive term in the transport equation which accounts for uncertainty (randomness) in both flow velocity and kinetic rate constants but requires a closure, such as a Large-Eddy-Diffusivity (LED) approximation used in the present analysis. No closure is required when reaction rates are the only source of uncertainty. We use exact concentration PDFs obtained for this setting to analyze the accuracy of our general, LED-based PDF equations.

    View details for DOI 10.1016/j.jconhyd.2010.08.009

    View details for PubMedID 20926156

  • Applicability regimes for macroscopic models of reactive transport in porous media. Journal of contaminant hydrology BATTIATO, I., Tartakovsky, D. M. 2011; 120-121: 18-26

    Abstract

    We consider transport of a solute that undergoes a nonlinear heterogeneous reaction: after reaching a threshold concentration value, it precipitates on the solid matrix to form a crystalline solid. The relative importance of three key pore-scale transport mechanisms (advection, molecular diffusion, and reaction) is quantified by the Péclet (Pe) and Damköhler (Da) numbers. We use multiple-scale expansions to upscale a pore-scale advection-diffusion equation with reactions entering through a boundary condition on the fluid-solid interface, and to establish sufficient conditions under which macroscopic advection-dispersion-reaction equations provide an accurate description of the pore-scale processes. These conditions are summarized by a phase diagram in the (Pe, Da)-space, parameterized with a scale-separation parameter that is defined as the ratio of characteristic lengths associated with the pore- and macro-scales.

    View details for DOI 10.1016/j.jconhyd.2010.05.005

    View details for PubMedID 20598771

  • Reduced complexity models for probabilistic forecasting of infiltration rates ADVANCES IN WATER RESOURCES Wang, P., Tartakovsky, D. M. 2011; 34 (3): 375-382
  • The Effect of Small Changes in Hematocrit on Nitric Oxide Transport in Arterioles ANTIOXIDANTS & REDOX SIGNALING Sriram, K., Vazquez, B. Y., Yalcin, O., Johnson, P. C., Intaglietta, M., Tartakovsky, D. M. 2011; 14 (2): 175-185

    Abstract

    We report the development of a mathematical model that quantifies the effects of small changes in systemic hematocrit (Hct) on the transport of nitric oxide (NO) in the microcirculation. The model consists of coupled transport equations for NO and oxygen (O2) and accounts for both shear-induced NO production by the endothelium and the effect of changing systemic Hct on the rate of NO production and the rate of NO scavenging by red blood cells. To incorporate the dependence of the plasma layer width on changes in Hct, the model couples the hemodynamics of blood in arterioles with NO and O2 transport in the plasma layer. A sensitivity analysis was conducted to determine the effects of uncertain model parameters (the thicknesses of endothelial surface layers and diffusion coefficients of NO and O2 in muscle tissues and vascular walls) on the model's predictions. Our analysis reveals that small increases in Hct may raise NO availability in the vascular wall. This finding sheds new light on the experimental data that show that the blood circulation responds to systematic increases of Hct in a manner that is consistent with increasing NO production followed by a plateau.

    View details for DOI 10.1089/ars.2010.3266

    View details for Web of Science ID 000285390800001

    View details for PubMedID 20560785

  • PROBABILISTIC PREDICTIONS OF INFILTRATION INTO HETEROGENEOUS MEDIA WITH UNCERTAIN HYDRAULIC PARAMETERS INTERNATIONAL JOURNAL FOR UNCERTAINTY QUANTIFICATION Wang, P., Tartakovsky, D. M. 2011; 1 (1): 35-47
  • Probability density functions for passive scalars dispersed in random velocity fields GEOPHYSICAL RESEARCH LETTERS Dentz, M., Tartakovsky, D. M. 2010; 37
  • Stochastic hybrid modeling of intracellular calcium dynamics JOURNAL OF CHEMICAL PHYSICS Choi, T., Maurya, M. R., Tartakovsky, D. M., Subramaniam, S. 2010; 133 (16)

    Abstract

    Deterministic models of biochemical processes at the subcellular level might become inadequate when a cascade of chemical reactions is induced by a few molecules. Inherent randomness of such phenomena calls for the use of stochastic simulations. However, being computationally intensive, such simulations become infeasible for large and complex reaction networks. To improve their computational efficiency in handling these networks, we present a hybrid approach, in which slow reactions and fluxes are handled through exact stochastic simulation and their fast counterparts are treated partially deterministically through chemical Langevin equation. The classification of reactions as fast or slow is accompanied by the assumption that in the time-scale of fast reactions, slow reactions do not occur and hence do not affect the probability of the state. Our new approach also handles reactions with complex rate expressions such as Michaelis-Menten kinetics. Fluxes which cannot be modeled explicitly through reactions, such as flux of Ca(2+) from endoplasmic reticulum to the cytosol through inositol 1,4,5-trisphosphate receptor channels, are handled deterministically. The proposed hybrid algorithm is used to model the regulation of the dynamics of cytosolic calcium ions in mouse macrophage RAW 264.7 cells. At relatively large number of molecules, the response characteristics obtained with the stochastic and deterministic simulations coincide, which validates our approach in the limit of large numbers. At low doses, the response characteristics of some key chemical species, such as levels of cytosolic calcium, predicted with stochastic simulations, differ quantitatively from their deterministic counterparts. These observations are ubiquitous throughout dose response, sensitivity, and gene-knockdown response analyses. While the relative differences between the peak-heights of the cytosolic [Ca(2+)] time-courses obtained from stochastic (mean of 16 realizations) and deterministic simulations are merely 1%-4% for most perturbations, it is specially sensitive to levels of G(βγ) (relative difference as large as 90% at very low G(βγ)).

    View details for DOI 10.1063/1.3496996

    View details for Web of Science ID 000283753600055

    View details for PubMedID 21033822

  • Uncertainty quantification in modeling flow and transport in porous media STOCHASTIC ENVIRONMENTAL RESEARCH AND RISK ASSESSMENT Guadagnini, A., Tartakovsky, D. M. 2010; 24 (7): 953-954
  • Probability density functions for advective-reactive transport in radial flow STOCHASTIC ENVIRONMENTAL RESEARCH AND RISK ASSESSMENT Broyda, S., Dentz, M., Tartakovsky, D. M. 2010; 24 (7): 985-992
  • Elastic Response of Carbon Nanotube Forests to Aerodynamic Stresses PHYSICAL REVIEW LETTERS Battiato, I., Bandaru, P. R., Tartakovsky, D. M. 2010; 105 (14)

    Abstract

    The ability to determine static and (hydro)dynamic properties of carbon nanotubes (CNTs) is crucial for many applications. While their static properties (e.g., solubility and wettability) are fairly well understood, their mechanical responses (e.g., deflection under shear) to ambient fluid flow are to a large extent unknown. We analyze the elastic response of single-walled CNT forests, attached to the bottom wall of a channel, to the aerodynamic loading exerted by both laminar and turbulent flows. Our analysis yields analytical expressions for velocity distributions, the drag coefficient, and bending profiles of individual CNTs. This enables us to determine flexural rigidity of CNTs in wind-tunnel experiments. The model predictions agree with laboratory experiments for a large range of channel velocities.

    View details for DOI 10.1103/PhysRevLett.105.144504

    View details for Web of Science ID 000282362600004

    View details for PubMedID 21230836

  • Uncertainty quantification via random domain decomposition and probabilistic collocation on sparse grids JOURNAL OF COMPUTATIONAL PHYSICS Lin, G., Tartakovsky, A. M., Tartakovsky, D. M. 2010; 229 (19): 6995-7012
  • Random walk particle tracking simulations of non-Fickian transport in heterogeneous media JOURNAL OF COMPUTATIONAL PHYSICS Srinivasan, G., Tartakovsky, D. M., Dentz, M., Viswanathan, H., Berkowitz, B., Robinson, B. A. 2010; 229 (11): 4304-4314
  • On the use of analytical solutions to design pumping tests in leaky aquifers connected to a stream JOURNAL OF HYDROLOGY Christensen, S., Zlotnik, V. A., Tartakovsky, D. M. 2010; 381 (3-4): 341-351
  • Predicting Vertical Connectivity Within an Aquifer System BAYESIAN ANALYSIS Short, M., Higdon, D., Guadagnini, L., Guadagnini, A., Tartakovsky, D. M. 2010; 5 (3): 557-581

    View details for DOI 10.1214/10-BA522

    View details for Web of Science ID 000282051600009

  • Functional optical imaging at the microscopic level JOURNAL OF BIOMEDICAL OPTICS Salazar Vazquez, B. Y., Hightower, C. M., Sapuppo, F., Tartakovsky, D. M., Intaglietta, M. 2010; 15 (1)

    Abstract

    Functional microscopic imaging of in vivo tissues aims at characterizing parameters at the level of the unitary cellular components under normal conditions, in the presence of blood flow, to understand and monitor phenomena that lead to maintaining homeostatic balance. Of principal interest are the setting of shear stress on the endothelium; formation of the plasma layer, where the balance between nitric oxide production and scavenging is established; and formation of the oxygen gradients that determine the distribution of oxygen from blood into the tissue. Optical techniques that enable the analysis of functional microvascular processes are the measurement of blood vessel dimensions by image shearing, the photometric analysis of the extent of the plasma layer, the dual-slit methodology for measuring blood flow velocity, and the direct measurement of oxygen concentration in blood and tissue. Each of these technologies includes the development of paired, related mathematical approaches that enable characterizing the transport properties of the blood tissue system. While the technology has been successful in analyzing the living tissue in experimental conditions, deployment to clinical settings remains an elusive goal, due to the difficulty of obtaining optical access to the depth of the tissue.

    View details for DOI 10.1117/1.3280270

    View details for Web of Science ID 000276944200012

    View details for PubMedID 20210428

  • On breakdown of macroscopic models of mixing-controlled heterogeneous reactions in porous media ADVANCES IN WATER RESOURCES BATTIATO, I., Tartakovsky, D. M., Tartakovsky, A. M., Scheibe, T. 2009; 32 (11): 1664-1673
  • Optimal design of pumping tests in leaky aquifers for stream depletion analysis JOURNAL OF HYDROLOGY Christensen, S., Zlotnik, V. A., Tartakovsky, D. M. 2009; 375 (3-4): 554-565
  • Abrupt-Interface Solution for Carbon Dioxide Injection into Porous Media TRANSPORT IN POROUS MEDIA Dentz, M., Tartakovsky, D. M. 2009; 79 (1): 15-27
  • Closure to "Stream Depletion by Groundwater Pumping in Leaky Aquifers" by Vitaly A. Zlotnik and Daniel M. Tartakovsky JOURNAL OF HYDROLOGIC ENGINEERING Zlotnik, V. A., Tartakovsky, D. M. 2009; 14 (8): 889-891
  • Response to "Comments on Abrupt-Interface Solution for Carbon Dioxide Injection into Porous Media by Dentz and Tartakovsky (2008)" by Lu et al. TRANSPORT IN POROUS MEDIA Dentz, M., Tartakovsky, D. M. 2009; 79 (1): 39-41
  • Probability density functions for advective-reactive transport with uncertain reaction rates WATER RESOURCES RESEARCH Tartakovsky, D. M., Dentz, M., Lichtner, P. C. 2009; 45
  • Effects of spatio-temporal variability of precipitation on contaminant migration in the vadose zone GEOPHYSICAL RESEARCH LETTERS Wang, P., Quinlan, P., Tartakovsky, D. M. 2009; 36
  • Probabilistic risk analysis of groundwater remediation strategies WATER RESOURCES RESEARCH Bolster, D., Barahona, M., Dentz, M., Fernandez-Garcia, D., Sanchez-Vila, X., TRINCHERO, P., Valhondo, C., Tartakovsky, D. M. 2009; 45
  • Perspective on theories of non-Fickian transport in heterogeneous media ADVANCES IN WATER RESOURCES Neuman, S. P., Tartakovsky, D. M. 2009; 32 (5): 670-680
  • Delineation of geological facies from poorly differentiated data ADVANCES IN WATER RESOURCES Wohlberg, B., Tartakovsky, D. M. 2009; 32 (2): 225-230
  • Hydrogeophysical Approach for Identification of Layered Structures of the Vadose Zone from Electrical Resistivity Data VADOSE ZONE JOURNAL Tartakovsky, A. M., Bolster, D., Tartakovsky, D. M. 2008; 7 (4): 1207-1214
  • Probabilistic risk analysis of building contamination INDOOR AIR Bolster, D. T., Tartakovsky, D. M. 2008; 18 (5): 351-364

    Abstract

    We present a general framework for probabilistic risk assessment (PRA) of building contamination. PRA provides a powerful tool for the rigorous quantification of risk in contamination of building spaces. A typical PRA starts by identifying relevant components of a system (e.g. ventilation system components, potential sources of contaminants, remediation methods) and proceeds by using available information and statistical inference to estimate the probabilities of their failure. These probabilities are then combined by means of fault-tree analyses to yield probabilistic estimates of the risk of system failure (e.g. building contamination). A sensitivity study of PRAs can identify features and potential problems that need to be addressed with the most urgency. Often PRAs are amenable to approximations, which can significantly simplify the approach. All these features of PRA are presented in this paper via a simple illustrative example, which can be built upon in further studies.The tool presented here can be used to design and maintain adequate ventilation systems to minimize exposure of occupants to contaminants.

    View details for DOI 10.1111/j.1600-0668.2008.00536.x

    View details for Web of Science ID 000259236800002

    View details for PubMedID 18681912

  • Stochastic Langevin model for flow and transport in porous media PHYSICAL REVIEW LETTERS Tartakovsky, A. M., Tartakovsky, D. M., Meakin, P. 2008; 101 (4)

    Abstract

    We present a new model for fluid flow and solute transport in porous media, which employs smoothed particle hydrodynamics to solve a Langevin equation for flow and dispersion in porous media. This allows for effective separation of the advective and diffusive mixing mechanisms, which is absent in the classical dispersion theory that lumps both types of mixing into dispersion coefficient. The classical dispersion theory overestimates both mixing-induced effective reaction rates and the effective fractal dimension of the mixing fronts associated with miscible fluid Rayleigh-Taylor instabilities. We demonstrate that the stochastic (Langevin equation) model overcomes these deficiencies.

    View details for DOI 10.1103/PhysRevLett.101.044502

    View details for Web of Science ID 000258427100025

    View details for PubMedID 18764333

  • A reduced complexity model for probabilistic risk assessment of groundwater contamination WATER RESOURCES RESEARCH Winter, C. L., Tartakovsky, D. M. 2008; 44 (6)
  • Self-consistent four-point closure for transport in steady random flows PHYSICAL REVIEW E Dentz, M., Tartakovsky, D. M. 2008; 77 (6)

    Abstract

    Ensemble averaging of advection-dispersion equations describing transport of a passive scalar in incompressible random velocity fields requires a closure approximation. Commonly used approaches, such as the direct interaction approximation and large-eddy simulations as well as equivalent renormalization schemes, employ so-called two-point (or one-loop) closures. These approaches have proven to be adequate for transport in zero-mean (unbiased) time-dependent random velocity fields with increasing accuracy for decreasing temporal coherence. In the opposite limit of steady velocity fields with finite bias, however, these schemes fail to predict effective transport properties both quantitatively and qualitatively, leading to an obvious inconsistency for transverse dispersion in two spatial dimensions. For this case, two-point closures predict that macroscopic transverse dispersion increases as the square root of the disorder variance while it has been proven rigorously that there is no disorder-induced contribution to macroscopic transverse dispersion for purely advective transport. Furthermore, two-point closures significantly underestimate the disorder-induced contribution to longitudinal dispersion. We derive a four-point closure for stochastically averaged transport equations that goes beyond classical one-loop schemes and demonstrate that it is exact for transverse dispersion and correctly predicts an increase of the longitudinal disorder-induced dispersion coefficient with the square of the variance of the strong disorder. The predicted values of asymptotic longitudinal dispersion coefficients are consistent with those obtained via Monte Carlo random walk simulations.

    View details for DOI 10.1103/PhysRevE.77.066307

    View details for Web of Science ID 000257287600049

    View details for PubMedID 18643371

  • Nonlinear localization of light in disordered optical fiber arrays PHYSICAL REVIEW A Srinivasan, G., Aceves, A., Tartakovsky, D. M. 2008; 77 (6)
  • Stream depletion by groundwater pumping in leaky aquifers JOURNAL OF HYDROLOGIC ENGINEERING Zlotnik, V. A., Tartakovsky, D. M. 2008; 13 (2): 43-50
  • Uncertain future of hydrogeology Fall Annual Meeting of the American-Geophysical-Union Tartakovsky, D. M., Winter, C. L. ASCE-AMER SOC CIVIL ENGINEERS. 2008: 37–39
  • Machine learning methods for inverse modeling GEOENV VI - GEOSTATISTICS FOR ENVIRONMENTAL APPLICATIONS, PROCEEDINGS Tartakovsky, D. M., Guadagnini, A., Wohlberg, B. E. 2008; 15: 117-125
  • HYBRID SIMULATIONS OF REACTION-DIFFUSION SYSTEMS IN POROUS MEDIA SIAM JOURNAL ON SCIENTIFIC COMPUTING Tartakovsky, A. M., Tartakovsky, D. M., Scheibe, T. D., Meakin, P. 2008; 30 (6): 2799-2816

    View details for DOI 10.1137/070691097

    View details for Web of Science ID 000260850200006

  • Hybrid numerical methods for multiscale simulations of subsurface biogeochemical processes SCIDAC 2008: SCIENTIFIC DISCOVERY THROUGH ADVANCED COMPUTING Scheibe, T. D., Tartakovsky, A. M., Tartakovsky, D. M., Redden, G. D., Meakin, P., Palmer, B. J., Schuchardt, K. L. 2008; 125
  • Quantification of uncertainty in geochemical reactions WATER RESOURCES RESEARCH Srinivasan, G., Tartakovsky, D. M., Robinson, B. A., Aceves, A. B. 2007; 43 (12)
  • Type curve interpretation of late-time pumping test data in randomly heterogeneous aquifers WATER RESOURCES RESEARCH Neuman, S. P., Blattstein, A., Riva, M., Tartakovsky, D. M., Guadagnini, A., Ptak, T. 2007; 43 (10)
  • Analytical models of contaminant transport in coastal aquifers ADVANCES IN WATER RESOURCES Bolster, D. T., Tartakovsky, D. M., Dentz, M. 2007; 30 (9): 1962-1972
  • Nearest-neighbor classification for facies delineation WATER RESOURCES RESEARCH Tartakovsky, D. M., Wohlberg, B., Guadagnini, A. 2007; 43 (7)
  • Probabilistic risk analysis in subsurface hydrology GEOPHYSICAL RESEARCH LETTERS Tartakovsky, D. M. 2007; 34 (5)
  • Ergodicity of pumping tests WATER RESOURCES RESEARCH Sanchez-Vila, X., Tartakovsky, D. M. 2007; 43 (3)
  • Stochastic modeling of complex systems COMPUTING IN SCIENCE & ENGINEERING Tartakovsky, D. M., Xiu, D. 2007; 9 (2): 8-9
  • Particle methods for simulation of subsurface multiphase fluid flow and biogeochemical processes SCIDAC 2007: SCIENTIFIC DISCOVERY THROUGH ADVANCED COMPUTING Meakin, P., Tartakovsky, A., Scheibe, T., Tartakovsky, D., Redden, G., Long, P. E., Brooks, S. C., Xu, Z. 2007; 78
  • Hybrid numerical methods for multiscale simulations of subsurface biogeochemical processes SCIDAC 2007: SCIENTIFIC DISCOVERY THROUGH ADVANCED COMPUTING Scheibe, T. D., Tartakovsky, A. M., Tartakovsky, D. M., Redden, G. D., Meakin, P. 2007; 78
  • Stochastic analysis of transport in tubes with rough walls JOURNAL OF COMPUTATIONAL PHYSICS Tartakovsky, D. M., Xiu, D. 2006; 217 (1): 248-259
  • Multivariate sensitivity analysis of saturated flow through simulated highly heterogeneous groundwater aquifers JOURNAL OF COMPUTATIONAL PHYSICS Winter, C. L., Guadagnini, A., Nychka, D., Tartakovsky, D. M. 2006; 217 (1): 166-175
  • Delay mechanisms of non-Fickian transport in heterogeneous media GEOPHYSICAL RESEARCH LETTERS Dentz, M., Tartakovsky, D. M. 2006; 33 (16)
  • Variable-density flow in porous media JOURNAL OF FLUID MECHANICS Dentz, M., Tartakovsky, D. M., Abarca, E., Guadagnini, A., Sanchez-Vila, X., Carrera, J. 2006; 561: 209-235
  • Asymptotic analysis of cross-hole hydraulic tests in fractured granite GROUND WATER Illman, W. A., Tartakovsky, D. M. 2006; 44 (4): 555-563

    Abstract

    Illman and Tartakovsky (2005a, 2005b) developed a new approach for the interpretation of three-dimensional pneumatic well tests conducted in porous or fractured geologic media, which is based on a straight-line analysis of late-time data. We modify this approach to interpret three-dimensional well tests in the saturated zone and use it to analyze the cross-hole hydraulic test data collected in the Full-Scale Engineered Barrier Experiment gallery at the Grimsel Test Site in Switzerland. The equivalent hydraulic conductivity and specific storage obtained from our analysis increase with the radial distance between the centroids of the pumping and monitoring intervals. Since this scale effect is observed from a single test type (cross-hole tests), it is less ambiguous than scale effects typically inferred from laboratory and multiple types of hydraulic tests (e.g., slug, single- and cross-hole tests). The statistical analysis of the estimated hydraulic parameters shows a strong correlation between equivalent hydraulic conductivity and specific storage.

    View details for DOI 10.1111/j.1745-6584.2006.00201.x

    View details for Web of Science ID 000238655300013

    View details for PubMedID 16857033

  • Numerical methods for differential equations in random domains SIAM JOURNAL ON SCIENTIFIC COMPUTING Xiu, D., Tartakovsky, D. M. 2006; 28 (3): 1167-1185

    View details for DOI 10.1137/040613160

    View details for Web of Science ID 000239701100018

  • Subsurface characterization with support vector machines IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING Wohlberg, B., Tartakovsky, D. M., Guadagnini, A. 2006; 44 (1): 47-57
  • Asymptotic analysis of cross-hole pneumatic injection tests in unsaturated fractured tuff ADVANCES IN WATER RESOURCES Illman, W. A., Tartakovsky, D. M. 2005; 28 (11): 1217-1229
  • Algorithm refinement for stochastic partial differential equations: II. Correlated systems JOURNAL OF COMPUTATIONAL PHYSICS Alexander, F. J., Garcia, A. L., Tartakovsky, D. M. 2005; 207 (2): 769-787
  • Noise in algorithm refinement methods COMPUTING IN SCIENCE & ENGINEERING Alexander, F. J., Tartakovsky, D. M., Garcia, A. L. 2005; 7 (3): 32-38
  • Asymptotic analysis of three-dimensional pressure interference tests: A point source solution WATER RESOURCES RESEARCH Illman, W. A., Tartakovsky, D. M. 2005; 41 (1)
  • Delineation of geologic facies with statistical learning theory GEOPHYSICAL RESEARCH LETTERS Tartakovsky, D. M., Wohlberg, B. E. 2004; 31 (18)
  • Probabilistic reconstruction of geologic facies JOURNAL OF HYDROLOGY Guadagnini, L., Guadagnini, A., Tartakovsky, D. M. 2004; 294 (1-3): 57-67
  • Nonlocal and localized analyses of conditional mean transient flow in bounded, randomly heterogeneous porous media WATER RESOURCES RESEARCH Ye, M., Neuman, S. P., Guadagnini, A., Tartakovsky, D. M. 2004; 40 (5)
  • Transient flow in a heterogeneous vadose zone with uncertain parameters VADOSE ZONE JOURNAL Tartakovsky, A. M., Garcia-Naranjo, L., Tartakovsky, D. M. 2004; 3 (1): 154-163
  • Uncertainty quantification for flow in highly heterogeneous porous media COMPUTATIONAL METHODS IN WATER RESOURCES, VOLS 1 AND 2 Xiu, D., Tartakovsky, D. M. 2004; 55: 695-703
  • A geostatistical model for distribution of facies in highly heterogeneous aquifers GEOENV IV - GEOSTATISTICS FOR ENVIRONMENTAL APPLICATIONS: PROCEEDINGS Guadagnini, L., Guadagnini, A., Tartakovsky, D. M. 2004; 13: 211-222
  • Effective properties of random composites SIAM JOURNAL ON SCIENTIFIC COMPUTING Tartakovsky, D. M., Guadagnini, A. 2004; 26 (2): 625-635
  • A two-scale nonperturbative approach to uncertainty analysis of diffusion in random composites MULTISCALE MODELING & SIMULATION Xiu, D. B., Tartakovsky, D. M. 2004; 2 (4): 662-674

    View details for DOI 10.1137/03060268X

    View details for Web of Science ID 000224122300006

  • A perturbation solution to the transient Henry problem for seawater intrusion COMPUTATIONAL METHODS IN WATER RESOURCES, VOLS 1 AND 2 Tartakovsky, D. A., Guadagnini, A., Sanchez-Vila, X., Dentz, M., Carrera, J. 2004; 55: 1573-1581
  • Stochastic analysis of effective rate constant for heterogeneous reactions ModelCARE 2002 Conference Lichtner, P. C., Tartakovsky, D. M. SPRINGER. 2003: 419–29
  • Random domain decomposition for flow in heterogeneous stratified aquifers ModelCARE 2002 Conference Guadagnini, A., Guadagnini, L., Tartakovsky, D. M., Winter, C. L. SPRINGER. 2003: 394–407
  • Stochastic averaging of nonlinear flows in heterogeneous porous media JOURNAL OF FLUID MECHANICS Tartakovsky, D. M., Guadagnini, A., Riva, M. 2003; 492: 47-62
  • Unsaturated flow in heterogeneous soils with spatially distributed uncertain hydraulic parameters JOURNAL OF HYDROLOGY Tartakovsky, D. M., Lu, Z. M., Guadagnini, A., Tartakovsky, A. M. 2003; 275 (3-4): 182-193
  • Moment differential equations for flow in highly heterogeneous porous media SURVEYS IN GEOPHYSICS Winter, C. L., Tartakovsky, D. M., Guadagnini, A. 2003; 24 (1): 81-106
  • PDF methods for reactive transport in porous media Conference on Calibration and Reliability in Groundwater Modelling (ModelCARE 2002) Tartakovsky, D. M., Lichtner, P. C., Pawar, R. J. INT ASSOC HYDROLOGICAL SCIENCES. 2003: 162–67
  • Solution of moment equations of groundwater flow in random composite layered aquifers Conference on Calibration and Reliability in Groundwater Modelling (ModelCARE 2002) Guadagnini, A., Guadagnini, L., Tartakovsky, D. M., Winter, C. L. INT ASSOC HYDROLOGICAL SCIENCES. 2003: 108–14
  • Algorithm refinement for Stochastic partial differential equations RAREFIED GAS DYNAMICS Alexander, F. J., Garcia, A. L., Tartakovsky, D. M. 2003; 663: 915-922
  • Algorithm refinement for stochastic partial differential equations. I. Linear diffusion JOURNAL OF COMPUTATIONAL PHYSICS Alexander, F. J., Garcia, A. L., Tartakovsky, D. M. 2002; 182 (1): 47-66
  • Localization of mean flow and apparent transmissivity tensor for bounded randomly heterogeneous aquifers TRANSPORT IN POROUS MEDIA Tartakovsky, D. M., Guadagnini, A., Ballio, F., Tartakovsky, A. M. 2002; 49 (1): 41-58
  • Groundwater flow in heterogeneous composite aquifers WATER RESOURCES RESEARCH Winter, C. L., Tartakovsky, D. M. 2002; 38 (8)
  • Theoretical interpretation of a pronounced permeability scale effect in unsaturated fractured tuff WATER RESOURCES RESEARCH Hyun, Y., Neuman, S. P., Vesselinov, V. V., Illman, W. A., Tartakovsky, D. M., Di Federico, V. 2002; 38 (6)
  • Numerical solutions of moment equations for flow in heterogeneous composite aquifers WATER RESOURCES RESEARCH Winter, C. L., Tartakovsky, D. M., Guadagnini, A. 2002; 38 (5)
  • Conditional moment analysis of steady state unsaturated flow in bounded, randomly heterogeneous soils WATER RESOURCES RESEARCH Lu, Z. M., Neuman, S. P., Guadagnini, A., Tartakovsky, D. M. 2002; 38 (4)
  • Nonlocal and localized analyses of conditional mean transient flow in bounded, randomly nonuniform domains COMPUTATIONAL METHODS IN WATER RESOURCES, VOLS 1 AND 2, PROCEEDINGS Ye, M., Neuman, S. P., Guadagnini, A., Tartakovsky, D. M. 2002; 47: 1155-1162
  • Mean and variance of DNAPL finger development in a saturated, randomly heterogeneous porous medium COMPUTATIONAL METHODS IN WATER RESOURCES, VOLS 1 AND 2, PROCEEDINGS Tartakovsky, A. M., Neuman, S. P., Tartakovsky, D. M. 2002; 47: 1307-1314
  • Theoretical foundation for conductivity scaling GEOPHYSICAL RESEARCH LETTERS Winter, C. L., Tartakovsky, D. M. 2001; 28 (23): 4367-4369
  • Prior mapping for nonlinear flows in random environments PHYSICAL REVIEW E Tartakovsky, D. M., Guadagnini, A. 2001; 64 (3)

    Abstract

    We analyze nonlinear flows in randomly heterogeneous environments, which are characterized by state-dependent diffusion coefficients with spatially correlated structures. The prior Kirchhoff mapping is used to describe such systems by linear stochastic partial differential equations with multiplicative noise. These are solved through moment equations which are closed, alternatively, either by perturbation expansions, or by a posterior linear mapping closure. The latter relies on the assumption that the state variable is a spatially distributed Gaussian field. We demonstrate that the former approach is more robust.

    View details for Web of Science ID 000171136400010

    View details for PubMedID 11580383

  • Dynamics of free surfaces in random porous media SIAM JOURNAL ON APPLIED MATHEMATICS Tartakovsky, D. M., Winter, C. L. 2001; 61 (6): 1857-1876
  • Kinematic structure of minipermeameter flow WATER RESOURCES RESEARCH Tartakovsky, D. M., Moulton, J. D., Zlotnik, V. A. 2000; 36 (9): 2433-2442
  • Effective hydraulic conductivity and transmissivity for heterogeneous aquifers MATHEMATICAL GEOLOGY Tartakovsky, D. M., Guadagnini, A., Guadagnini, L. 2000; 32 (6): 751-759
  • Mean flow in composite porous media GEOPHYSICAL RESEARCH LETTERS Winter, C. L., Tartakovsky, D. M. 2000; 27 (12): 1759-1762
  • Effective hydraulic conductivity in multiscale random fields with truncated power variograms Symposium on Theory, Modeling, and Field Investigation in Hydrogeology in Honor of Shlomo P Neumans 60th Birthday Di Federico, V., Tartakovsky, D. M. GEOLOGICAL SOC AMER INC. 2000: 81–89
  • Stochastic analysis of groundwater pumping from bounded, randomly heterogeneous aquifers Symposium on Theory, Modeling, and Field Investigation in Hydrogeology in Honor of Shlomo P Neumans 60th Birthday Guadagnini, A., Tartakovsky, D. M. GEOLOGICAL SOC AMER INC. 2000: 73–79
  • Propagation of measurement errors in reservoir modeling XIIIth International Conference on Computational Methods in Water Resources Pawar, R. J., Tartakovsky, D. M. A A BALKEMA PUBLISHERS. 2000: 15–20
  • Direct solution of unsaturated flow in randomly heterogeneous soils XIIIth International Conference on Computational Methods in Water Resources Lu, Z. M., Neuman, S. P., Guadagnini, A., Tartakovsky, D. M. A A BALKEMA PUBLISHERS. 2000: 785–792
  • Three-dimensional steady state flow to a well in a randomly heterogeneous aquifer ModelCARE 1999 Conference Riva, M., Guadagnini, A., Neuman, S. P., Tartakovsky, D. M. INT ASSOC HYDROLOGICAL SCIENCES. 2000: 131–36
  • Anisotropy, lacunarity, and upscaled conductivity and its autocovariance in multiscale random fields with truncated power variograms WATER RESOURCES RESEARCH Di Federico, V., Neuman, S. P., Tartakovsky, D. M. 1999; 35 (10): 2891-2908
  • Extension of "Transient flow in bounded randomly heterogeneous domains, 1, Exact conditional moment equations and recursive approximations" WATER RESOURCES RESEARCH Tartakovsky, D. M., Neuman, S. P. 1999; 35 (6): 1921-1925
  • Conditional stochastic averaging of steady state unsaturated flow by means of Kirchhoff transformation WATER RESOURCES RESEARCH Tartakovsky, D. M., Neuman, S. P., Lu, Z. M. 1999; 35 (3): 731-745
  • Some aspects of head-variance evaluation COMPUTATIONAL GEOSCIENCES Tartakovsky, D. M., Mitkov, I. 1999; 3 (1): 89-92
  • Dynamics of wetting fronts in porous media PHYSICAL REVIEW E Mitkov, I., Tartakovsky, D. M., Winter, C. L. 1998; 58 (5): R5245-R5248
  • Transient flow in bounded randomly heterogeneous domains 2. Localization of conditional mean equations and temporal nonlocality effects WATER RESOURCES RESEARCH Tartakovsky, D. M., Neuman, S. P. 1998; 34 (1): 13-20
  • Transient effective hydraulic conductivities under slowly and rapidly varying mean gradients in bounded three-dimensional random media WATER RESOURCES RESEARCH Tartakovsky, D. M., Neuman, S. P. 1998; 34 (1): 21-32
  • Transient flow in bounded randomly heterogeneous domains 1. Exact conditional moment equations and recursive approximations WATER RESOURCES RESEARCH Tartakovsky, D. M., Neuman, S. P. 1998; 34 (1): 1-12
  • An analytical solution for contaminant transport in nonuniform flow TRANSPORT IN POROUS MEDIA Tartakovsky, D. M., Di Federico, V. 1997; 27 (1): 85-97
  • Effective hydraulic conductivity of bounded, strongly heterogeneous porous media WATER RESOURCES RESEARCH Paleologos, E. K., Neuman, S. P., Tartakovsky, D. 1996; 32 (5): 1333-1341