Eric Darve
Associate Professor of Mechanical Engineering
Bio
Professor Darve's research is focused on the development of numerical methods for large scale scientific computing with applications in biomolecular simulations, acoustics, electromagnetics, and microfluidics. In these applications, the computational expense of simulating large and complex systems is very significant and in many instances beyond current computer capabilities. He is developing innovative numerical techniques to reduce this computational expense and enable the simulation of complex systems over realistic time scales. Professor Darve also uses processors with novel architectures, such as GPUs and the Cell processor, for scientific computing. Applications range from particle simulation to fluid dynamics and solving partial differential equations.
Honors & Awards

Kenneth and Barbara Oshman Faculty Scholar Award, Stanford University (2011)

H. Julian Allen Award, NASA (2010)

Habilitation Diriger des Recherches, France (2007)

Leslie Fox Prize in Numerical Analysis, IMA (2001)

James H. Clark Faculty Scholar, Stanford University (2001)
Professional Education

PhD, Paris VI University, Paris, Applied Mathematics (1999)

MS, Paris IX University, Paris, Applied Mathematics (1994)

BS, Paris VI University, Paris, Mathematics and Physics (1993)
201617 Courses
 Introduction to parallel computing using MPI, openMP, and CUDA
CME 213, ME 339 (Spr)  Numerical Linear Algebra
CME 302 (Aut)  Ordinary Differential Equations for Engineers
CME 102, ENGR 155A (Win) 
Independent Studies (11)
 Advanced Reading and Research
SCCM 499 (Win, Sum)  Engineering Problems
ME 391 (Aut, Win, Spr, Sum)  Engineering Problems and Experimental Investigation
ME 191 (Aut, Win, Spr, Sum)  Experimental Investigation of Engineering Problems
ME 392 (Aut, Win, Spr, Sum)  Honors Research
ME 191H (Aut, Win, Spr, Sum)  Master's Research
CME 291 (Aut, Win, Spr, Sum)  Ph.D. Research
CME 400 (Aut, Win, Spr, Sum)  Ph.D. Teaching Experience
ME 491 (Aut, Win, Spr, Sum)  Practical Training
ME 299A (Aut, Win, Spr, Sum)  Practical Training
ME 299B (Aut, Win, Spr, Sum)  Special Research Topics in Computational and Mathematical Engineering
CME 399 (Spr, Sum)
 Advanced Reading and Research

Prior Year Courses
201516 Courses
 Introduction to parallel computing using MPI, openMP, and CUDA
CME 213, ME 339 (Spr)  Numerical Linear Algebra
CME 302 (Aut)
201415 Courses
 Introduction to parallel computing using MPI, openMP, and CUDA
CME 213, ME 339 (Spr)  Numerical Linear Algebra
CME 302 (Aut)  Parallel Computing Projects
CME 213B (Win)
201314 Courses
 Introduction to parallel computing using MPI, openMP, and CUDA
CME 213, ME 339 (Spr)  Numerical Linear Algebra
CME 302 (Aut)
 Introduction to parallel computing using MPI, openMP, and CUDA
Stanford Advisees

Postdoctoral Faculty Sponsor
Kai Yang 
Doctoral (Program)
Victor Minden 
Doctoral Dissertation Reader (AC)
Victor Minden, Yanming Wang 
Doctoral Dissertation Advisor (AC)
Chao Chen, Ruoxi Wang
All Publications
 SOLVING THE SCALAR WAVE EQUATION VIA A DIRECTIONAL FAST MULTIPOLE METHOD
 Dynamic simulations of the instability of sedimenting fibers
 A KALMAN FILTER POWERED BY HMATRICES FOR QUASICONTINUOUS DATA ASSIMILATION PROBLEMS
 CFD for Blood Transfusions on the Battlefield and Inhalation of Toxic Agents in the Lung
 Concentration fluctuations in the dilute sedimentation of anisotropic particles 15th US National Congress

A fast block lowrank dense solver with applications to finiteelement matrices
JOURNAL OF COMPUTATIONAL PHYSICS
2016; 304: 170188
View details for DOI 10.1016/j.jcp.2015.10.012
View details for Web of Science ID 000365041900008

Realtime data assimilation for largescale systems: The spectral Kalman filter
ADVANCES IN WATER RESOURCES
2015; 86: 260272
View details for DOI 10.1016/j.advwatres.2015.07.017
View details for Web of Science ID 000365623500002

A new sparse matrix vector multiplication graphics processing unit algorithm designed for finite element problems
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
2015; 102 (12): 17841814
View details for DOI 10.1002/nme.4865
View details for Web of Science ID 000354625300002

A comparison of weighted ensemble and Markov state model methodologies
JOURNAL OF CHEMICAL PHYSICS
2015; 142 (21)
Abstract
Computation of reaction rates and elucidation of reaction mechanisms are two of the main goals of molecular dynamics (MD) and related simulation methods. Since it is time consuming to study reaction mechanisms over long time scales using brute force MD simulations, two ensemble methods, Markov State Models (MSMs) and Weighted Ensemble (WE), have been proposed to accelerate the procedure. Both approaches require clustering of microscopic configurations into networks of "macrostates" for different purposes. MSMs model a discretization of the original dynamics on the macrostates. Accuracy of the model significantly relies on the boundaries of macrostates. On the other hand, WE uses macrostates to formulate a resampling procedure that kills and splits MD simulations for achieving better efficiency of sampling. Comparing to MSMs, accuracy of WE rate predictions is less sensitive to the definition of macrostates. Rigorous numerical experiments using alanine dipeptide and pentaalanine support our analyses. It is shown that MSMs introduce significant biases in the computation of reaction rates, which depend on the boundaries of macrostates, and Accelerated Weighted Ensemble (AWE), a formulation of weighted ensemble that uses the notion of colors to compute fluxes, has reliable flux estimation on varying definitions of macrostates. Our results suggest that whereas MSMs provide a good idea of the metastable sets and visualization of overall dynamics, AWE provides reliable rate estimations requiring less efforts on defining macrostates on the high dimensional conformational space.
View details for DOI 10.1063/1.4921890
View details for Web of Science ID 000355931800069
View details for PubMedID 26049485

OPTIMIZING THE ADAPTIVE FAST MULTIPOLE METHOD FOR FRACTAL SETS
SIAM JOURNAL ON SCIENTIFIC COMPUTING
2015; 37 (2): A1040A1066
View details for DOI 10.1137/140962681
View details for Web of Science ID 000353838400020

AWEWQ: FastForwarding Molecular Dynamics Using the Accelerated Weighted Ensemble
JOURNAL OF CHEMICAL INFORMATION AND MODELING
2014; 54 (10): 30333043
Abstract
A limitation of traditional molecular dynamics (MD) is that reaction rates are difficult to compute. This is due to the rarity of observing transitions between metastable states since high energy barriers trap the system in these states. Recently the weighted ensemble (WE) family of methods have emerged which can flexibly and efficiently sample conformational space without being trapped and allow calculation of unbiased rates. However, while WE can sample correctly and efficiently, a scalable implementation applicable to interesting biomolecular systems is not available. We provide here a GPLv2 implementation called AWEWQ of a WE algorithm using the master/worker distributed computing WorkQueue (WQ) framework. AWEWQ is scalable to thousands of nodes and supports dynamic allocation of computer resources, heterogeneous resource usage (such as central processing units (CPU) and graphical processing units (GPUs) concurrently), seamless heterogeneous cluster usage (i.e., campus grids and cloud providers), and support for arbitrary MD codes such as GROMACS, while ensuring that all statistics are unbiased. We applied AWEWQ to a 34 residue protein which simulated 1.5 ms over 8 months with peak aggregate performance of 1000 ns/h. Comparison was done with a 200 μs simulation collected on a GPU over a similar timespan. The folding and unfolded rates were of comparable accuracy.
View details for DOI 10.1021/ci500321g
View details for Web of Science ID 000343849600036
View details for PubMedID 25207854

A Kalman filter powered by H2matrices for quasicontinuous data assimilation problems
WATER RESOURCES RESEARCH
2014; 50 (5): 37343749
View details for DOI 10.1002/2013WR014607
View details for Web of Science ID 000337672900008

Method and advantages of genetic algorithms in parameterization of interatomic potentials: Metal oxides
COMPUTATIONAL MATERIALS SCIENCE
2014; 81: 453465
View details for DOI 10.1016/j.commatsci.2013.08.054
View details for Web of Science ID 000326940300064

CAUCHY FAST MULTIPOLE METHOD FOR GENERAL ANALYTIC KERNELS
SIAM JOURNAL ON SCIENTIFIC COMPUTING
2014; 36 (2): A396A426
View details for DOI 10.1137/120891617
View details for Web of Science ID 000335817600005

TASKBASED FMM FOR MULTICORE ARCHITECTURES
SIAM JOURNAL ON SCIENTIFIC COMPUTING
2014; 36 (1): C66C93
View details for DOI 10.1137/130915662
View details for Web of Science ID 000333415500024

An Fast Direct Solver for Partial Hierarchically SemiSeparable Matrices
JOURNAL OF SCIENTIFIC COMPUTING
2013; 57 (3): 477501
View details for DOI 10.1007/s109150139714z
View details for Web of Science ID 000326401200003

Largescale stochastic linear inversion using hierarchical matrices
COMPUTATIONAL GEOSCIENCES
2013; 17 (6): 913927
View details for DOI 10.1007/s1059601393640
View details for Web of Science ID 000328319900004

ANALYSIS OF THE ACCELERATED WEIGHTED ENSEMBLE METHODOLOGY
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS
2013: 171181
View details for Web of Science ID 000328571500019

The accuracy of the CHARMM22/CMAP and AMBER ff99SB force fields for modelling the antimicrobial peptide cecropin P1
MOLECULAR SIMULATION
2013; 39 (11): 922936
View details for DOI 10.1080/08927022.2013.781599
View details for Web of Science ID 000323634200009

A fast algorithm for sparse matrix computations related to inversion
JOURNAL OF COMPUTATIONAL PHYSICS
2013; 242: 915945
View details for DOI 10.1016/j.jcp.2013.01.036
View details for Web of Science ID 000319049800046

FOURIERBASED FAST MULTIPOLE METHOD FOR THE HELMHOLTZ EQUATION
SIAM JOURNAL ON SCIENTIFIC COMPUTING
2013; 35 (1): A79A103
View details for DOI 10.1137/11085774X
View details for Web of Science ID 000315575000004

Accuracy in Oneway and Twoway Algorithms for Computing Desired Entries in the Inverse of Sparse Matrices
11TH INTERNATIONAL CONFERENCE OF NUMERICAL ANALYSIS AND APPLIED MATHEMATICS 2013, PTS 1 AND 2 (ICNAAM 2013)
2013; 1558: 15011504
View details for DOI 10.1063/1.4825806
View details for Web of Science ID 000331472800355
 Taskbased FMM for multicore architectures 2013

An\ mathcal O (N\ log N) Fast Direct Solver for Partial Hierarchically SemiSeparable Matrices
Journal of Scientific Computing
2013; 57 (3): 477501
View details for DOI 10.1007/s109150139714z

Fast Algorithms for Bayesian Inversion
Computational Challenges in the Geosciences
2013; 156: 101142
View details for DOI 10.1007/9781461474340_5
 Taskbased Parallelization of the Fast Multipole Method on NVIDIA GPUs and Multicore Processors 2013
 Optimizing the Blackbox FMM for Smooth and Oscillatory Kernels 2013
 Composition and reuse with compiled domainspecific languages 2013

Application of Hierarchical Matrices to Linear Inverse Problems in Geostatistics
OIL & GAS SCIENCE AND TECHNOLOGYREVUE D IFP ENERGIES NOUVELLES
2012; 67 (5): 857875
View details for DOI 10.2516/ogst/2012064
View details for Web of Science ID 000314141700010

Fast directional multilevel summation for oscillatory kernels based on Chebyshev interpolation
JOURNAL OF COMPUTATIONAL PHYSICS
2012; 231 (4): 11751196
View details for DOI 10.1016/j.jcp.2011.09.027
View details for Web of Science ID 000300462100005

Extension and optimization of the FIND algorithm: Computing Green's and lessthan Green's functions
JOURNAL OF COMPUTATIONAL PHYSICS
2012; 231 (4): 11211139
View details for DOI 10.1016/j.jcp.2011.05.027
View details for Web of Science ID 000300462100003

Optimizing the multipoletolocal operator in the fast multipole method for graphical processing units
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
2012; 89 (1): 105133
View details for DOI 10.1002/nme.3240
View details for Web of Science ID 000298589300005

Time integrators based on approximate discontinuous Hamiltonians
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
2012; 89 (1): 71104
View details for DOI 10.1002/nme.3236
View details for Web of Science ID 000298589300004

Folding Proteins at 500 ns/hour with Work Queue
2012 IEEE 8TH INTERNATIONAL CONFERENCE ON ESCIENCE (ESCIENCE)
2012
View details for Web of Science ID 000315360600019

Optimization of the parallel blackbox fast multipole method on CUDA
Innovative Parallel Computing (InPar)
2012: 1  14
View details for DOI 10.1109/InPar.2012.6339607
 Poster: Matrices over Runtime Systems at Exascale 2012

Folding Proteins at 500 ns/hour with Work Queue
2012
View details for DOI 10.1109/eScience.2012.6404429
 EFFICIENT DATA ASSIMILATION TOOL IN CONJUNCTION WITH TOUGH2 FOR CO2 MONITORING 2012
 Matrices Over Runtime Systems at Exascale 2012

Matrices Over Runtime Systems @ Exascale
2012 SC COMPANION: HIGH PERFORMANCE COMPUTING, NETWORKING, STORAGE AND ANALYSIS (SCC)
2012: 13301331
View details for Web of Science ID 000320824300158

Fast Multipole Method Using the Cauchy Integral Formula
NUMERICAL ANALYSIS OF MULTISCALE COMPUTATIONS
2012; 82: 127144
View details for DOI 10.1007/9783642219436_6
View details for Web of Science ID 000310180800006

Assembly of finite element methods on graphics processors
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING
2011; 85 (5): 640669
View details for DOI 10.1002/nme.2989
View details for Web of Science ID 000286775000007

The fast multipole method on parallel clusters, multicore processors, and graphics processing units
COMPTES RENDUS MECANIQUE
2011; 339 (23): 185193
View details for DOI 10.1016/j.crme.2010.12.005
View details for Web of Science ID 000287768400012

Liszt: a domain specific language for building portable meshbased PDE solvers
2011
View details for DOI 10.1145/2063384.2063396

Generalized Fast Multipole Method
9TH WORLD CONGRESS ON COMPUTATIONAL MECHANICS AND 4TH ASIAN PACIFIC CONGRESS ON COMPUTATIONAL MECHANICS
2010; 10
View details for DOI 10.1088/1757899X/10/1/012230
View details for Web of Science ID 000290445000231
 The CUDA codes to perform M2L operation in FMM 2010

Generalized fast multipole method
2010
View details for DOI 10.1088/1757899X/10/1/012230
 An implementation of lowfrequency fast multipole BIEM for Helmholtz'equation on GPU 2010
 Application of assembly of finite element methods on graphics processors for realtime elastodynamics GPU Computing Gems edited by Hwu, Wenmei, W. Elsevier. 2010: 1

Introduction to Assembly of Finite Element Methods on Graphics Processors
9TH WORLD CONGRESS ON COMPUTATIONAL MECHANICS AND 4TH ASIAN PACIFIC CONGRESS ON COMPUTATIONAL MECHANICS
2010; 10
View details for DOI 10.1088/1757899X/10/1/012009
View details for Web of Science ID 000290445000010

The blackbox fast multipole method
JOURNAL OF COMPUTATIONAL PHYSICS
2009; 228 (23): 87128725
View details for DOI 10.1016/j.jcp.2009.08.031
View details for Web of Science ID 000271671100011

A hybrid method for the parallel computation of Green's functions
JOURNAL OF COMPUTATIONAL PHYSICS
2009; 228 (14): 50205039
View details for DOI 10.1016/j.jcp.2009.03.035
View details for Web of Science ID 000267846500005

Computing generalized Langevin equations and generalized FokkerPlanck equations
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
2009; 106 (27): 1088410889
Abstract
The MoriZwanzig formalism is an effective tool to derive differential equations describing the evolution of a small number of resolved variables. In this paper we present its application to the derivation of generalized Langevin equations and generalized nonMarkovian FokkerPlanck equations. We show how long time scales rates and metastable basins can be extracted from these equations. Numerical algorithms are proposed to discretize these equations. An important aspect is the numerical solution of the orthogonal dynamics equation which is a partial differential equation in a high dimensional space. We propose efficient numerical methods to solve this orthogonal dynamics equation. In addition, we present a projection formalism of the MoriZwanzig type that is applicable to discrete maps. Numerical applications are presented from the field of Hamiltonian systems.
View details for DOI 10.1073/pnas.0902633106
View details for Web of Science ID 000267796100005
View details for PubMedID 19549838

Highionicstrength electroosmotic flows in uncharged hydrophobic nanochannels
JOURNAL OF COLLOID AND INTERFACE SCIENCE
2009; 330 (1): 194200
Abstract
We report molecular dynamics simulation results of highionicstrength electroosmotic flows inside uncharged nanochannels. The possibility of this unusual electrokinetic phenomenon has been discussed by Dukhin et al. [A. Dukhin, S. Dukhin, P. Goetz, Langmuir 21 (2005) 9990]. Our computed velocity profiles clearly indicate the presence of a net flow with a maximum velocity around 2 m/s. We found the apparent zeta potential to be 29.7+/6.8 mV, using the HelmholtzSmoluchowski relation and the measured mean velocity. This value is comparable to experimentally measured values in Dukhin et al. and references therein. We also investigate the orientations of water molecules in response to an electric field by computing polarization density. Water molecules in the bulk region are oriented along the direction of the external electric field, while their nearwall orientation shows oscillations. The computation of threedimensional density distributions of sodium and chloride ions around each individual water molecule show that chloride ions tend to concentrate near a water molecule, whereas sodium ions are diffusely distributed.
View details for DOI 10.1016/j.jcis.2008.10.029
View details for Web of Science ID 000262229700028
View details for PubMedID 19007939

Optimization of the FIND Algorithm to Compute the Inverse of a Sparse Matrix
IWCE13: 2009 13TH INTERNATIONAL WORKSHOP ON COMPUTATIONAL ELECTRONICS
2009: 285288
View details for Web of Science ID 000272988200074
 Concentration distributions of arbitrary shaped particles in microfluidic channel flows Bulletin of the American Physical Society 2009; 54 (19)

Optimization of the FIND algorithm to compute the inverse of a sparse matrix
2009
View details for DOI 10.1109/IWCE.2009.5091136

Computing generalized Langevin equations and generalized Fokker–Planck equations
edited by Chorin, Alexandre, J.
2009
View details for DOI 10.1073/pnas.0902633106

Large calculation of the flow over a hypersonic vehicle using a GPU
JOURNAL OF COMPUTATIONAL PHYSICS
2008; 227 (24): 1014810161
View details for DOI 10.1016/j.jcp.2008.08.023
View details for Web of Science ID 000261207600009

Computing entries of the inverse of a sparse matrix using the FIND algorithm
JOURNAL OF COMPUTATIONAL PHYSICS
2008; 227 (22): 94089427
View details for DOI 10.1016/j.jcp.2008.06.033
View details for Web of Science ID 000260645700006

Fast electrostatic force calculation on parallel computer clusters
JOURNAL OF COMPUTATIONAL PHYSICS
2008; 227 (19): 85518567
View details for DOI 10.1016/j.jcp.2008.06.016
View details for Web of Science ID 000259753700005

Stability of asynchronous variational integrators
JOURNAL OF COMPUTATIONAL PHYSICS
2008; 227 (18): 83678394
View details for DOI 10.1016/j.jcp.2008.05.017
View details for Web of Science ID 000258972000007

Adaptive biasing force method for scalar and vector free energy calculations
JOURNAL OF CHEMICAL PHYSICS
2008; 128 (14)
Abstract
In free energy calculations based on thermodynamic integration, it is necessary to compute the derivatives of the free energy as a function of one (scalar case) or several (vector case) order parameters. We derive in a compact way a general formulation for evaluating these derivatives as the average of a mean force acting on the order parameters, which involves first derivatives with respect to both Cartesian coordinates and time. This is in contrast with the previously derived formulas, which require first and second derivatives of the order parameter with respect to Cartesian coordinates. As illustrated in a concrete example, the main advantage of this new formulation is the simplicity of its use, especially for complicated order parameters. It is also straightforward to implement in a molecular dynamics code, as can be seen from the pseudocode given at the end. We further discuss how the approach based on time derivatives can be combined with the adaptive biasing force method, an enhanced sampling technique that rapidly yields uniform sampling of the order parameters, and by doing so greatly improves the efficiency of free energy calculations. Using the backbone dihedral angles Phi and Psi in NacetylalanylN'methylamide as a numerical example, we present a technique to reconstruct the free energy from its derivatives, a calculation that presents some difficulties in the vector case because of the statistical errors affecting the derivatives.
View details for DOI 10.1063/1.2829861
View details for Web of Science ID 000255470300020
View details for PubMedID 18412436
 A blackbox Fast Multipole Method 2008
 BIRS 08w5074: Mathematical and numerical methods for free energy calculations in molecular systems 2008

Fast inverse using nested dissection for NEGF
JOURNAL OF COMPUTATIONAL ELECTRONICS
2007; 6 (13): 187190
View details for DOI 10.1007/s1082500601128
View details for Web of Science ID 000208473600045
 Thermodynamic integration using constrained and unconstrained dynamics Free Energy Calculations 2007; 86: 119170

Stability of asynchronous variational integrators
21ST INTERNATIONAL WORKSHOP ON PRINCIPLES OF ADVANCED AND DISTRIBUTED SIMULATION, PROCEEDINGS
2007: 3844
View details for Web of Science ID 000248079800006

Stabilization of a suspension of sedimenting rods by inducedcharge electrophoresis
PHYSICS OF FLUIDS
2006; 18 (12)
View details for DOI 10.1063/1.2404948
View details for Web of Science ID 000243158200013

The effect of stratification on the wave number selection in the instability of sedimenting spheroids
PHYSICS OF FLUIDS
2006; 18 (12)
View details for DOI 10.1063/1.2396913
View details for Web of Science ID 000243158200003

Hydrodynamic interactions in the inducedcharge electrophoresis of colloidal rod dispersions
JOURNAL OF FLUID MECHANICS
2006; 563: 223259
View details for DOI 10.1017/S0022112006001376
View details for Web of Science ID 000241085500011

Effect of flexibility on the shearinduced migration of shortchain polymers in parabolic channel flow
JOURNAL OF FLUID MECHANICS
2006; 557: 297306
View details for DOI 10.1017/S0022112006000243
View details for Web of Science ID 000238820700013

Molecular dynamics simulation of electroosmotic flows in rough wall nanochannels
PHYSICAL REVIEW E
2006; 73 (5)
Abstract
We performed equilibrium and nonequilibrium molecular dynamics simulation to study electroosmotic flows inside charged nanochannels with different types of surface roughness. We modeled surface roughness as a sequence of twodimensional subnanoscale grooves and ridges (step functiontype roughness) along the flow direction. The amplitude, spatial period, and symmetry of surface roughness were varied. The amplitude of surface roughness was on the order of the Debye length. The walls have uniform negative charges at the interface with fluids. We included only positive ions (counterions) for simplicity of computation. For the smooth wall, we compared our molecular dynamics simulation results to the wellknown PoissonBoltzmann theory. The density profiles of water molecules showed "layering" near the wall. For the rough walls, the density profiles measured from the wall are similar to those for the smooth wall except near where the steps are located. Because of the layering of water molecules and the finite size effect of ions and the walls, the ionic distribution departs from the Boltzmann distribution. To further understand the structure of water molecules and ions, we computed the polarization density. Near the wall, its z component dominates the other components, indicating the preferred orientation ("ordering") of water molecules. Especially, inside the groove for the rough walls, its maximum is 10% higher (stronger ordering) than for the smooth wall. The dielectric constant, computed with a ClausiusMosottitype equation, confirmed the ordering near the wall and the enhanced ordering inside the groove. The residence time and the diffusion coefficient, computed using the velocity autocorrelation function, showed that the diffusion of water and ions along the direction normal to the wall is significantly reduced near the wall and further decreases inside the groove. Along the flow direction, the diffusion of water and ions inside the groove is significantly lowered while it is similar to the bulk value elsewhere. We performed nonequilibrium molecular dynamics simulation to compute electroosmotic velocities and flow rates. The velocity profiles correspond to those for overlapped electric double layers. For the rough walls, velocity inside the groove is close to zero, meaning that the channel height is effectively reduced. The flow rate was found to decrease as the period of surface roughness decreases or the amplitude of surface roughness increases. We defined the zeta potential as the electrostatic potential at the location of a slip plane. We computed the electrostatic potential with the ionic distribution and the dielectric constant both from our molecular dynamics simulation. We estimated the slip plane from the velocity profile. The zeta potential showed the same trend as the flow rate: it decreases with an increasing amplitude and a decreasing period of surface roughness.
View details for DOI 10.1103/PhysRevE.73.051203
View details for Web of Science ID 000237951300019
View details for PubMedID 16802924

The growth of concentration fluctuations in dilute dispersions of orientable and deformable particles under sedimentation
JOURNAL OF FLUID MECHANICS
2006; 553: 347388
View details for DOI 10.1017/S0022112006009025
View details for Web of Science ID 000237366800015

Numerical Methods for Calculating the Potential of Mean Force
New Algorithms for Macromolecular Simulation
2006; 49: 213249
View details for DOI 10.1007/3540316183_13

A Bayesian approach to calculating free energies in chemical and biological systems
BAYESIAN INFERENCE AND MAXIMUM ENTROPY METHODS IN SCIENCE AND ENGINEERING
2006; 872: 2330
View details for Web of Science ID 000244484400003
 Stratification and wavenumber selection in the instability of sedimenting spheroids 2006
 The Dynamics of Rodlike Particles under Sedimentation and InducedCharge Electrophoresis 2006
 Adaptive Biasing Force Method for Vector Free Energy Calculations 2006
 Electric Double Layer Structures near Rough Surfaces: Molecular Dynamics Simulation Bulletin of the American Physical Society 2006
 Fast Inverse using Nested Dissection for the Non Equilibrium Green's Function 11th International Workshop on Computational Electronics 2006
 Effect of flexibility on the shearinduced migration of short polymers in parabolic channel flow 2006

A smooth particlemesh Ewald algorithm for Stokes suspension simulations: The sedimentation of fibers
PHYSICS OF FLUIDS
2005; 17 (3)
View details for DOI 10.1063/1.1862262
View details for Web of Science ID 000227372600031

Interactions of wall roughness and electroosmotic flows inside nanochannels
ICMM 2005: 3RD INTERNATIONAL CONFERENCE ON MICROCHANNELS AND MINICHANNELS, PT B
2005: 641645
View details for Web of Science ID 000243025800091
 Concentration fluctuations in dilute suspensions of orientable and deformable particles under sedimentation 2005
 Hydrodynamic interactions in colloidal dispersions of conducting rods under inducedcharge electrophoresis 2005

Inducedcharge electrophoresis in suspensions of rodlike particles: Theory and simulations
PROCEEDINGS OF THE ASME FLUIDS ENGINEERING DIVISION
2005; 261: 251256
View details for Web of Science ID 000243038600033

Microstructure in the sedimentation of anisotropic and deformable particles
PROCEEDINGS OF THE ASME FLUIDS ENGINEERING DIVISION
2005; 261: 797803
View details for Web of Science ID 000243038600101

Efficient fast multipole method for lowfrequency scattering
JOURNAL OF COMPUTATIONAL PHYSICS
2004; 197 (1): 341363
View details for DOI 10.1016/j.jcp.2003.12.002
View details for Web of Science ID 000221833000016

A fast multipole method for Maxwell equations stable at all frequencies
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY AMATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
2004; 362 (1816): 603628
Abstract
The solution of Helmholtz and Maxwell equations by integral formulations (kernel in exp(i kr)/r) leads to large dense linear systems. Using direct solvers requires large computational costs in O(N(3)). Using iterative solvers, the computational cost is reduced to large matrixvector products. The fast multipole method provides a fast numerical way to compute convolution integrals. Its application to Maxwell and Helmholtz equations was initiated by Rokhlin, based on a multipole expansion of the interaction kernel. A second version, proposed by Chew, is based on a planewave expansion of the kernel. We propose a third approach, the stableplanewave expansion, which has a lower computational expense than the multipole expansion and does not have the accuracy and stability problems of the planewave expansion. The computational complexity is Nlog N as with the other methods.
View details for DOI 10.1098/rsta.2003.1337
View details for Web of Science ID 000220407200010
View details for PubMedID 15306510

Assessing the efficiency of free energy calculation methods
JOURNAL OF CHEMICAL PHYSICS
2004; 120 (8): 35633578
Abstract
The efficiencies of two recently developed methods for calculating free energy changes along a generalized coordinate in a system are discussed in the context of other, related approaches. One method is based on Jarzynski's identity [Phys. Rev. Lett. 78, 2690 (1997)]. The second method relies on thermodynamic integration of the average force and is called the adaptive biasing force method [Darve and Pohorille, J. Chem. Phys. 115, 9169 (2001)]. Both methods are designed such that the system evolves along the chosen coordinate(s) without experiencing free energy barriers and they require calculating the instantaneous, unconstrained force acting on this coordinate using the formula derived by Darve and Pohorille. Efficiencies are analyzed by comparing analytical estimates of statistical errors and by considering two numerical examplesinternal rotation of hydrated 1,2dichloroethane and transfer of fluoromethane across a waterhexane interface. The efficiencies of both methods are approximately equal in the first but not in the second case. During transfer of fluoromethane the system is easily driven away from equilibrium and, therefore, the performance of the method based on Jarzynski's identity is poor.
View details for DOI 10.1063/1.1642607
View details for Web of Science ID 000189139700006
View details for PubMedID 15268518
 Computing flow rate of electroosmotic flows in nanochannels with different wall roughness The Smithsonian/NASA Astrophysics Data System 2004

Calculating transport properties of nanodevices
2004
View details for DOI 10.1117/12.571494
 Dynamic Simulations of Sedimenting Fibers with Fast Fourier Transform Acceleration Abstracts of the Papers 2004
 Pattern formation in sedimenting suspensions of spheroids 2004

Analysis and performance results of a molecular modeling application on Merrimac
2004
View details for DOI 10.1109/SC.2004.69

Calculating transport properties of nanodevices
NANOSENSING: MATERIALS AND DEVICES
2004; 5593: 452463
View details for DOI 10.1117/12.571494
View details for Web of Science ID 000226789700046

Fast multipole method for lowfrequency electromagnetic scattering
COMPUTATIONAL FLUID AND SOLID MECHANICS 2003, VOLS 1 AND 2, PROCEEDINGS
2003: 12991302
View details for Web of Science ID 000184938200317
 Unfolding of proteins: Thermal and mechanical unfolding 2003
 Surface tension evaluation in lennardjones fluid system with untruncated potentials 2003

Calculating free energies using a scaledforce molecular dynamics algorithm
MOLECULAR SIMULATION
2002; 28 (12): 113144
View details for DOI 10.1080/08927020290004412
View details for Web of Science ID 000176122400009

Calculating free energies using average force
JOURNAL OF CHEMICAL PHYSICS
2001; 115 (20): 91699183
View details for Web of Science ID 000172129300010

The fast multipole method I: error analysis and asymptotic complexity
SIAM JOURNAL ON NUMERICAL ANALYSIS
2000; 38 (1): 98128
View details for Web of Science ID 000088263500006

The fast multipole method: Numerical implementation
JOURNAL OF COMPUTATIONAL PHYSICS
2000; 160 (1): 195240
View details for Web of Science ID 000086782500010
 Méthodes multipôles rapides: Résolution des équations de Maxwell par formulations intégrales 1999; 133 ( 99 PA06 6598): 228

Advanced structuredunstructured solver for electromagnetic scattering from multimaterial objects
1997
View details for DOI 10.2514/6.1997863
 THE MULTISTEP FAST MULTIPOLE METHOD: ALGORITHM AND ERROR ESTIMATION 1997

Fastmultipole method: a mathematical study
Comptes Rendus de l'Académie des SciencesSeries IMathematics
1997; 325 (9): 1037–1042
View details for DOI http://dx.doi.org/10.1016/S07644442(97)89101X