Academic Appointments


  • Emeritus Faculty, Acad Council, Mathematics

All Publications


  • Capillary Graph-Interfaces "in-the-Large" VIETNAM JOURNAL OF MATHEMATICS Finn, R. 2019; 47 (1): 113–32
  • Experimental Confirmation of Predicted Rise Heights in a Surface Tension Configuration Introduced by Laplace JOURNAL OF MATHEMATICAL FLUID MECHANICS Bhatnagar, R., Li, W., Cho, S., Finn, R. 2018; 20 (4): 1701–5
  • The Laplace Parallel Plates Problem in Capillarity Theory JOURNAL OF MATHEMATICAL FLUID MECHANICS Bhatnagar, R., Finn, R. 2018; 20 (4): 1681–99
  • The Force Singularity for Partially Immersed Parallel Plates JOURNAL OF MATHEMATICAL FLUID MECHANICS Bhatnagar, R., Finn, R. 2016; 18 (4): 739-755
  • On the Capillarity Equation in Two Dimensions JOURNAL OF MATHEMATICAL FLUID MECHANICS Bhatnagar, R., Finn, R. 2016; 18 (4): 731-738
  • Attractions and repulsions of parallel plates partially immersed in a liquid bath: III BOUNDARY VALUE PROBLEMS Bhatnagar, R., Finn, R. 2013
  • Mutual Attractions of Partially Immersed Parallel Plates JOURNAL OF MATHEMATICAL FLUID MECHANICS Finn, R., Lu, D. 2013; 15 (2): 273-301
  • Capillary Forces on Partially Immersed Plates International Conference on Differential and Difference Equations and Applications Finn, R. SPRINGER. 2013: 13–25
  • Thomas Young's Surface Tension Diagram: Its History, Legacy, and Irreconcilabilities JOURNAL OF MATHEMATICAL FLUID MECHANICS Finn, R., McCuan, J., Wente, H. C. 2012; 14 (3): 445-453
  • Occlusion criteria in tubes under transverse body forces JOURNAL OF FLUID MECHANICS Manning, R., Collicott, S., Finn, R. 2011; 682: 397-414
  • Criteria for Floating I JOURNAL OF MATHEMATICAL FLUID MECHANICS Finn, R. 2011; 13 (1): 103-115
  • Maximum Principle and Gradient Estimates for Stationary Solutions of the Navier-Stokes Equations: A Partly Numerical Investigation International Conference on Mathematical Fluid Mechanics Finn, R., Ouazzi, A., Turek, S. SPRINGER-VERLAG BERLIN. 2010: 253–269
  • On Young's Paradox, and the attractions of immersed parallel plates PHYSICS OF FLUIDS Finn, R. 2010; 22 (1)

    View details for DOI 10.1063/1.3276213

    View details for Web of Science ID 000274180800038

  • Floating Bodies in Neutral Equilibrium JOURNAL OF MATHEMATICAL FLUID MECHANICS Finn, R., Sloss, M. 2009; 11 (3): 459-463
  • Floating Bodies Subject to Capillary Attractions JOURNAL OF MATHEMATICAL FLUID MECHANICS Finn, R. 2009; 11 (3): 443-458
  • The Floating Ball "Paradox" JOURNAL OF MATHEMATICAL FLUID MECHANICS Finn, R. 2008; 10 (4): 583-587
  • Capillary surfaces in wedge domains PACIFIC JOURNAL OF MATHEMATICS Chen, J. T., Finn, R., Miersemann, E. 2008; 236 (2): 283-305
  • On the capillary problem for compressible fluids JOURNAL OF MATHEMATICAL FLUID MECHANICS Finn, R., Luli, G. K. 2007; 9 (1): 87-103
  • Compressible fluids in a capillary tube PACIFIC JOURNAL OF MATHEMATICS Athanassenas, M., Finn, R. 2006; 224 (2): 201-229
  • Equilibrium configurations of an infinite cylinder in an unbounded fluid PHYSICS OF FLUIDS Bhatnagar, R., Finn, R. 2006; 18 (4)

    View details for DOI 10.1063/1.2185661

    View details for Web of Science ID 000237136900047

  • The contact angle in capillarity PHYSICS OF FLUIDS Finn, R. 2006; 18 (4)

    View details for DOI 10.1063/1.2185655

    View details for Web of Science ID 000237136900046

  • On a theorem of Lancaster and Siegel PACIFIC JOURNAL OF MATHEMATICS Shi, D. Z., Finn, R. 2004; 213 (1): 111-119
  • A new example of singular height transition for capillary surfaces CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS Finn, R. 2004; 19 (1): 107-115
  • Computational investigation of unusual behavior in certain capillary tubes MICROGRAVITY SCIENCE AND TECHNOLOGY Brady, V., Concus, P., Finn, R. 2004; 15 (4): 31-38
  • On a singular behavior of capillary surfaces CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS Finn, R., Lee, D. 2004; 19 (1): 95-105
  • Capillary rise in nesting cylinders PHYSICS OF FLUIDS Brady, V., Concus, P., Finn, R. 2003; 15 (6): 1545-1551

    View details for DOI 10.1063/1.1566449

    View details for Web of Science ID 000182795300018

  • Some unusual comparison properties of capillary surfaces PACIFIC JOURNAL OF MATHEMATICS Finn, R., Kosmodem'ynaskii, A. A. 2002; 205 (1): 119-137
  • Eight remarkable properties of capillary surfaces MATHEMATICAL INTELLIGENCER Finn, R. 2002; 24 (3): 21-33
  • Liquid bridges, edge blobs, and Scherk-type capillary surfaces INDIANA UNIVERSITY MATHEMATICS JOURNAL Concus, P., Finn, R., McCuan, J. 2001; 50 (1): 411-441
  • Measurement of critical contact angle in a microgravity space experiment EXPERIMENTS IN FLUIDS Concus, P., Finn, R., Weislogel, M. 2000; 28 (3): 197-205
  • Vertex theorems for capillary drops on support planes MATHEMATISCHE NACHRICHTEN Finn, R., McCuan, J. 2000; 209: 115-135
  • Capillary surfaces in an exotic container: results from Space experiments JOURNAL OF FLUID MECHANICS Concus, P., Finn, R., Weislogel, M. 1999; 394: 119-135
  • C-singular solutions of the capillary problem JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK Finn, R., Neel, R. W. 1999; 512: 1-25
  • Regularity properties of H-graphs COMMENTARII MATHEMATICI HELVETICI Finn, R., Lu, J. N. 1998; 73 (3): 379-399
  • Discontinuous behavior of liquids between parallel and tilted plates PHYSICS OF FLUIDS Concus, P., Finn, R. 1998; 10 (1): 39-43
  • Comments on a paper of Keller, King and Merchant NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS Concus, P., Finn, R. 1996; 27 (7): 857-861
  • Local and global existence criteria for capillary surfaces in wedges. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS Finn, R. 1996; 4 (4): 305-322
  • On cylindrical container sections for a capillary free-surface experiment MICROGRAVITY SCIENCE AND TECHNOLOGY Chen, A., Concus, P., Finn, R., Weislogel, M. 1996; 9 (3): 169-174
  • Proboscis container shapes for the USML-2 Interface Configuration Experiment IXth European Symposium on Gravity-Dependent Phenomena in Physical Sciences - Materials and Fluids Under Low Gravity Concus, P., Finn, R., Weislogel, M. SPRINGER-VERLAG BERLIN. 1996: 261–270
  • Capillary wedges revisited SIAM JOURNAL ON MATHEMATICAL ANALYSIS Concus, P., Finn, R. 1996; 27 (1): 56-69
  • CAPILLARY SURFACES IN A WEDGE - DIFFERING CONTACT ANGLES MICROGRAVITY SCIENCE AND TECHNOLOGY Concus, P., Finn, R. 1994; 7 (2): 152-155
  • GRADIENT AND GAUSS CURVATURE BOUNDS FOR H-GRAPHS Symposium on Comparison Methods and Stability Theory Finn, R. MARCEL DEKKER. 1994: 137–150
  • On the contact angle in capillarity 3rd International Colloquium on Differential Equations Finn, R. VSP BV. 1993: 55–62
  • DROP-TOWER EXPERIMENTS FOR CAPILLARY SURFACES IN AN EXOTIC CONTAINER AIAA JOURNAL Concus, P., Finn, R., Weislogel, M. 1992; 30 (1): 134-137
  • EXOTIC CONTAINERS FOR CAPILLARY SURFACES JOURNAL OF FLUID MECHANICS Concus, P., Finn, R. 1991; 224: 383-394
  • INSTABILITY OF CERTAIN CAPILLARY SURFACES MANUSCRIPTA MATHEMATICA Concus, P., Finn, R. 1989; 63 (2): 209-213
  • MOON SURFACES, AND BOUNDARY-BEHAVIOR OF CAPILLARY SURFACES FOR PERFECT WETTING AND NON-WETTING PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY Finn, R. 1988; 57: 542-576
  • THE CAPILLARY CONTACT-ANGLE .2. THE INCLINED PLANE MATHEMATICAL METHODS IN THE APPLIED SCIENCES Finn, R., SHINBROT, M. 1988; 10 (2): 165-196
  • THE INCLINATION OF AN H-GRAPH LECTURE NOTES IN MATHEMATICS Finn, R. 1988; 1340: 40-60
  • THE CAPILLARY CONTACT-ANGLE .1. THE HORIZONTAL PLANE AND STICK-SLIP MOTION JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS Finn, R., SHINBROT, M. 1987; 123 (1): 1-17
  • THE INFLUENCE OF BOUNDARY GEOMETRY ON CAPILLARY SURFACES WITHOUT GRAVITY ASTERISQUE Finn, R. 1984: 157-165
  • ON THE EXTREMALS OF A SUBSIDIARY CAPILLARY PROBLEM JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK Concus, P., Finn, R. 1984; 353: 215-220
  • A SUBSIDIARY VARIATIONAL PROBLEM AND EXISTENCE CRITERIA FOR CAPILLARY SURFACES JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK Finn, R. 1984; 353: 196-214
  • SOME PROPERTIES OF CAPILLARY FREE SURFACES ANNALS OF MATHEMATICS STUDIES Finn, R. 1983: 323-338
  • EXISTENCE CRITERIA FOR CAPILLARY FREE SURFACES WITHOUT GRAVITY INDIANA UNIVERSITY MATHEMATICS JOURNAL Finn, R. 1983; 32 (3): 439-460
  • GLOBAL SIZE AND SHAPE ESTIMATES FOR SYMMETRIC SESSILE DROPS JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK Finn, R. 1982; 335: 9-36
  • ON THE LAPLACE FORMULA AND THE MENISCUS HEIGHT FOR A CAPILLARY SURFACE ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK Finn, R. 1981; 61 (3): 165-173
  • ADDENDA TO MY PAPER, ON THE LAPLACE FORMULA AND THE MENISCUS HEIGHT FOR A CAPILLARY SURFACE PRECEDING IN THIS ISSUE ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK Finn, R. 1981; 61 (3): 175-177
  • THE SESSILE LIQUID-DROP .1. SYMMETRIC CASE PACIFIC JOURNAL OF MATHEMATICS Finn, R. 1980; 88 (2): 541-587
  • NON EXISTENCE AND EXISTENCE OF CAPILLARY SURFACES MANUSCRIPTA MATHEMATICA Finn, R., Giusti, E. 1979; 28 (1-3): 13-20
  • EXISTENCE AND NON EXISTENCE OF CAPILLARY SURFACES MANUSCRIPTA MATHEMATICA Finn, R. 1979; 28 (1-3): 1-11
  • SHAPE OF A PENDENT LIQUID-DROP PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES Concus, P., Finn, R. 1979; 292 (1391): 307-340
  • HEIGHT OF A CAPILLARY SURFACE MATHEMATISCHE ZEITSCHRIFT Concus, P., Finn, R. 1976; 147 (1): 93-95
  • BEHAVIOR OF A CAPILLARY SURFACE AT A SINGULAR POINT JOURNAL D ANALYSE MATHEMATIQUE Finn, R. 1976; 30: 156-163
  • SINGULAR SOLUTION OF CAPILLARY EQUATION .1. EXISTENCE INVENTIONES MATHEMATICAE Concus, P., Finn, R. 1975; 29 (2): 143-148
  • SINGULAR SOLUTION OF CAPILLARY EQUATION .2. UNIQUENESS INVENTIONES MATHEMATICAE Concus, P., Finn, R. 1975; 29 (2): 149-159
  • CAPILLARY FREE SURFACES IN ABSENCE OF GRAVITY ACTA MATHEMATICA Concus, P., Finn, R. 1974; 132 (3-4): 177-198
  • CAPILLARY FREE SURFACES IN A GRAVITATIONAL-FIELD ACTA MATHEMATICA Concus, P., Finn, R. 1974; 132 (3-4): 207-223
  • NOTE ON CAPILLARY PROBLEM ACTA MATHEMATICA Finn, R. 1974; 132 (3-4): 199-205
  • UNIFORMIZATION OF PLANE DIRECTION FIELDS, AND OF SECOND-ORDER PARTIAL DIFFERENTIAL OPERATORS PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY Finn, R. 1973; 73 (JAN): 87-109
  • ON A CLASS OF CAPILLARY SURFACES JOURNAL D ANALYSE MATHEMATIQUE Concus, P., Finn, R. 1970; 23: 65-?
  • ON BEHAVIOR OF A CAPILLARY SURFACE IN A WEDGE PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA Concus, P., Finn, R. 1969; 63 (2): 292-?

    Abstract

    Estimates above and below are obtained for the height of the equilibrium-free surface of a liquid when the liquid partially fills a cylindrical container whose cross section contains a corner with interior angle 2alpha. The surface is characterized by the condition that its mean curvature be proportional to its height above a reference plane (or, in the case of zero gravity, that the mean curvature be constant), and by the requirement that it meet the container wall with prescribed contact angle gamma. It turns out that the qualitative behavior of such a surface near the vertex changes markedly, according as alpha + gamma < (1/2)pi, or alpha + gamma >/= (1/2)pi. In the former case, the surface is either unbounded or fails to exist, while in the latter case every such surface is bounded. Some experimental comparisons are indicated, and an application to the problem of describing the mechanism of water rise in trees is discussed.The above results describe a limiting case among corresponding properties that hold for surfaces defined over domains with smooth boundaries. This extension is indicated, as well as a formal extension to n-dimensional surfaces; here the interest centers on the fact that it is the mean curvature of an (n-1)-dimensional boundary element that controls the local behavior of the n-dimensional solution surface.

    View details for Web of Science ID A1969D965700013

    View details for PubMedID 16591761