Academic Appointments

  • Emeritus Faculty, Acad Council, Mathematics

Contact

  • Academic
    rfinn@stanford.edu
    University - Emeritus faculty Department: Mathematics Position: Emeritus Faculty, Acad Council
    • 382-E
    • Stanford,  California  94305 
    (650) 725-4066 (fax)

Additional Info

  • Mail Code: 2125

2021-22 Courses

All Publications

  • Capillary Graph-Interfaces "in-the-Large" VIETNAM JOURNAL OF MATHEMATICS Finn, R. 2019; 47 (1): 113–32

    View details for DOI 10.1007/s10013-018-0307-x

    View details for Web of Science ID 000458887500007

  • 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

    View details for DOI 10.1007/s00021-018-0385-2

    View details for Web of Science ID 000451973300014

  • The Laplace Parallel Plates Problem in Capillarity Theory JOURNAL OF MATHEMATICAL FLUID MECHANICS Bhatnagar, R., Finn, R. 2018; 20 (4): 1681–99

    View details for DOI 10.1007/s00021-018-0384-3

    View details for Web of Science ID 000451973300013

  • The Force Singularity for Partially Immersed Parallel Plates JOURNAL OF MATHEMATICAL FLUID MECHANICS Bhatnagar, R., Finn, R. 2016; 18 (4): 739-755

    View details for DOI 10.1007/s00021-016-0260-y

    View details for Web of Science ID 000386341100007

  • On the Capillarity Equation in Two Dimensions JOURNAL OF MATHEMATICAL FLUID MECHANICS Bhatnagar, R., Finn, R. 2016; 18 (4): 731-738

    View details for DOI 10.1007/s00021-016-0257-6

    View details for Web of Science ID 000386341100006

  • Attractions and repulsions of parallel plates partially immersed in a liquid bath: III BOUNDARY VALUE PROBLEMS Bhatnagar, R., Finn, R. 2013

    View details for DOI 10.1186/1687-2770-2013-277

    View details for Web of Science ID 000209345400005

  • Mutual Attractions of Partially Immersed Parallel Plates JOURNAL OF MATHEMATICAL FLUID MECHANICS Finn, R., Lu, D. 2013; 15 (2): 273-301

    View details for DOI 10.1007/s00021-012-0105-2

    View details for Web of Science ID 000319777800003

  • Capillary Forces on Partially Immersed Plates International Conference on Differential and Difference Equations and Applications Finn, R. SPRINGER. 2013: 13–25

    View details for DOI 10.1007/978-1-4614-7333-6_2

    View details for Web of Science ID 000347149500002

  • 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

    View details for DOI 10.1007/s00021-011-0079-5

    View details for Web of Science ID 000308064800003

  • Occlusion criteria in tubes under transverse body forces JOURNAL OF FLUID MECHANICS Manning, R., Collicott, S., Finn, R. 2011; 682: 397-414

    View details for DOI 10.1017/jfm.2011.230

    View details for Web of Science ID 000294775800017

  • Criteria for Floating I JOURNAL OF MATHEMATICAL FLUID MECHANICS Finn, R. 2011; 13 (1): 103-115

    View details for DOI 10.1007/s00021-009-0009-y

    View details for Web of Science ID 000288808000007

  • 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

    View details for DOI 10.1007/978-3-642-04068-9_15

    View details for Web of Science ID 000289445900015

  • 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

    View details for DOI 10.1007/s00021-008-0269-y

    View details for Web of Science ID 000270982200008

  • Floating Bodies Subject to Capillary Attractions JOURNAL OF MATHEMATICAL FLUID MECHANICS Finn, R. 2009; 11 (3): 443-458

    View details for DOI 10.1007/s00021-008-0268-z

    View details for Web of Science ID 000270982200007

  • The Floating Ball "Paradox" JOURNAL OF MATHEMATICAL FLUID MECHANICS Finn, R. 2008; 10 (4): 583-587

    View details for DOI 10.1007/s00021-007-0243-0

    View details for Web of Science ID 000262838600007

  • Capillary surfaces in wedge domains PACIFIC JOURNAL OF MATHEMATICS Chen, J. T., Finn, R., Miersemann, E. 2008; 236 (2): 283-305

    View details for Web of Science ID 000256850000004

  • On the capillary problem for compressible fluids JOURNAL OF MATHEMATICAL FLUID MECHANICS Finn, R., Luli, G. K. 2007; 9 (1): 87-103

    View details for DOI 10.1007/s00021-005-0203-5

    View details for Web of Science ID 000244753500005

  • Compressible fluids in a capillary tube PACIFIC JOURNAL OF MATHEMATICS Athanassenas, M., Finn, R. 2006; 224 (2): 201-229

    View details for Web of Science ID 000240148300002

  • 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 singular behavior of capillary surfaces CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS Finn, R., Lee, D. 2004; 19 (1): 95-105

    View details for DOI 10.1007/s00526-003-0202-4

    View details for Web of Science ID 000187132400004

  • A new example of singular height transition for capillary surfaces CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS Finn, R. 2004; 19 (1): 107-115

    View details for DOI 10.1007/s00526-003-0203-3

    View details for Web of Science ID 000187132400005

  • On a theorem of Lancaster and Siegel PACIFIC JOURNAL OF MATHEMATICS Shi, D. Z., Finn, R. 2004; 213 (1): 111-119

    View details for Web of Science ID 000187721500007

  • Computational investigation of unusual behavior in certain capillary tubes MICROGRAVITY SCIENCE AND TECHNOLOGY Brady, V., Concus, P., Finn, R. 2004; 15 (4): 31-38

    View details for Web of Science ID 000226063000004

  • 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

    View details for Web of Science ID 000176650000006

  • Eight remarkable properties of capillary surfaces MATHEMATICAL INTELLIGENCER Finn, R. 2002; 24 (3): 21-33

    View details for Web of Science ID 000176632700008

  • Liquid bridges, edge blobs, and Scherk-type capillary surfaces INDIANA UNIVERSITY MATHEMATICS JOURNAL Concus, P., Finn, R., McCuan, J. 2001; 50 (1): 411-441

    View details for Web of Science ID 000171494500006

  • Measurement of critical contact angle in a microgravity space experiment EXPERIMENTS IN FLUIDS Concus, P., Finn, R., Weislogel, M. 2000; 28 (3): 197-205

    View details for Web of Science ID 000086477200001

  • Vertex theorems for capillary drops on support planes MATHEMATISCHE NACHRICHTEN Finn, R., McCuan, J. 2000; 209: 115-135

    View details for Web of Science ID 000085094700005

  • Capillary surfaces in an exotic container: results from Space experiments JOURNAL OF FLUID MECHANICS Concus, P., Finn, R., Weislogel, M. 1999; 394: 119-135

    View details for Web of Science ID 000082689600006

  • C-singular solutions of the capillary problem JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK Finn, R., Neel, R. W. 1999; 512: 1-25

    View details for Web of Science ID 000081977400001

  • Discontinuous behavior of liquids between parallel and tilted plates PHYSICS OF FLUIDS Concus, P., Finn, R. 1998; 10 (1): 39-43

    View details for Web of Science ID 000071095800006

  • Regularity properties of H-graphs COMMENTARII MATHEMATICI HELVETICI Finn, R., Lu, J. N. 1998; 73 (3): 379-399

    View details for Web of Science ID 000075469000003

  • Comments on a paper of Keller, King and Merchant NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS Concus, P., Finn, R. 1996; 27 (7): 857-861

    View details for Web of Science ID A1996VC63000012

  • Local and global existence criteria for capillary surfaces in wedges. CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS Finn, R. 1996; 4 (4): 305-322

    View details for Web of Science ID A1996UR18200001

  • 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

    View details for Web of Science ID A1996XG06100008

  • 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

    View details for Web of Science ID A1996BF89D00017

  • Capillary wedges revisited SIAM JOURNAL ON MATHEMATICAL ANALYSIS Concus, P., Finn, R. 1996; 27 (1): 56-69

    View details for Web of Science ID A1996TV10900004

  • CAPILLARY SURFACES IN A WEDGE - DIFFERING CONTACT ANGLES MICROGRAVITY SCIENCE AND TECHNOLOGY Concus, P., Finn, R. 1994; 7 (2): 152-155

    View details for Web of Science ID A1994PB21800015

  • GRADIENT AND GAUSS CURVATURE BOUNDS FOR H-GRAPHS Symposium on Comparison Methods and Stability Theory Finn, R. MARCEL DEKKER. 1994: 137–150

    View details for Web of Science ID A1994BB12C00011

  • On the contact angle in capillarity 3rd International Colloquium on Differential Equations Finn, R. VSP BV. 1993: 55–62

    View details for Web of Science ID A1993BF25K00006

  • DROP-TOWER EXPERIMENTS FOR CAPILLARY SURFACES IN AN EXOTIC CONTAINER AIAA JOURNAL Concus, P., Finn, R., Weislogel, M. 1992; 30 (1): 134-137

    View details for Web of Science ID A1992GZ91500018

  • EXOTIC CONTAINERS FOR CAPILLARY SURFACES JOURNAL OF FLUID MECHANICS Concus, P., Finn, R. 1991; 224: 383-394

    View details for Web of Science ID A1991FG99100019

  • INSTABILITY OF CERTAIN CAPILLARY SURFACES MANUSCRIPTA MATHEMATICA Concus, P., Finn, R. 1989; 63 (2): 209-213

    View details for Web of Science ID A1989T295700005

  • 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

    View details for Web of Science ID A1988R096000005

  • THE CAPILLARY CONTACT-ANGLE .2. THE INCLINED PLANE MATHEMATICAL METHODS IN THE APPLIED SCIENCES Finn, R., SHINBROT, M. 1988; 10 (2): 165-196

    View details for Web of Science ID A1988N256300005

  • THE INCLINATION OF AN H-GRAPH LECTURE NOTES IN MATHEMATICS Finn, R. 1988; 1340: 40-60

    View details for Web of Science ID A1988Q818600005

  • 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

    View details for Web of Science ID A1987G770800001

  • ON THE EXTREMALS OF A SUBSIDIARY CAPILLARY PROBLEM JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK Concus, P., Finn, R. 1984; 353: 215-220

    View details for Web of Science ID A1984TX62500010

  • A SUBSIDIARY VARIATIONAL PROBLEM AND EXISTENCE CRITERIA FOR CAPILLARY SURFACES JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK Finn, R. 1984; 353: 196-214

    View details for Web of Science ID A1984TX62500009

  • THE INFLUENCE OF BOUNDARY GEOMETRY ON CAPILLARY SURFACES WITHOUT GRAVITY ASTERISQUE Finn, R. 1984: 157-165

    View details for Web of Science ID A1984TP91400011

  • SOME PROPERTIES OF CAPILLARY FREE SURFACES ANNALS OF MATHEMATICS STUDIES Finn, R. 1983: 323-338

    View details for Web of Science ID A1983SB53200020

  • EXISTENCE CRITERIA FOR CAPILLARY FREE SURFACES WITHOUT GRAVITY INDIANA UNIVERSITY MATHEMATICS JOURNAL Finn, R. 1983; 32 (3): 439-460

    View details for Web of Science ID A1983QV10300008

  • GLOBAL SIZE AND SHAPE ESTIMATES FOR SYMMETRIC SESSILE DROPS JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK Finn, R. 1982; 335: 9-36

    View details for Web of Science ID A1982PJ62200002

  • 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

    View details for Web of Science ID A1981LS78500004

  • 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

    View details for Web of Science ID A1981LS78500005

  • THE SESSILE LIQUID-DROP .1. SYMMETRIC CASE PACIFIC JOURNAL OF MATHEMATICS Finn, R. 1980; 88 (2): 541-587

    View details for Web of Science ID A1980LK34300013

  • 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

    View details for Web of Science ID A1979HK42400001

  • EXISTENCE AND NON EXISTENCE OF CAPILLARY SURFACES MANUSCRIPTA MATHEMATICA Finn, R. 1979; 28 (1-3): 1-11

    View details for Web of Science ID A1979HA99100001

  • NON EXISTENCE AND EXISTENCE OF CAPILLARY SURFACES MANUSCRIPTA MATHEMATICA Finn, R., Giusti, E. 1979; 28 (1-3): 13-20

    View details for Web of Science ID A1979HA99100002

  • HEIGHT OF A CAPILLARY SURFACE MATHEMATISCHE ZEITSCHRIFT Concus, P., Finn, R. 1976; 147 (1): 93-95

    View details for Web of Science ID A1976BH54600010

  • BEHAVIOR OF A CAPILLARY SURFACE AT A SINGULAR POINT JOURNAL D ANALYSE MATHEMATIQUE Finn, R. 1976; 30: 156-163

    View details for Web of Science ID A1976CK99900009

  • SINGULAR SOLUTION OF CAPILLARY EQUATION .1. EXISTENCE INVENTIONES MATHEMATICAE Concus, P., Finn, R. 1975; 29 (2): 143-148

    View details for Web of Science ID A1975AL83300004

  • SINGULAR SOLUTION OF CAPILLARY EQUATION .2. UNIQUENESS INVENTIONES MATHEMATICAE Concus, P., Finn, R. 1975; 29 (2): 149-159

    View details for Web of Science ID A1975AL83300005

  • CAPILLARY FREE SURFACES IN ABSENCE OF GRAVITY ACTA MATHEMATICA Concus, P., Finn, R. 1974; 132 (3-4): 177-198

    View details for Web of Science ID A1974T560900003

  • CAPILLARY FREE SURFACES IN A GRAVITATIONAL-FIELD ACTA MATHEMATICA Concus, P., Finn, R. 1974; 132 (3-4): 207-223

    View details for Web of Science ID A1974T560900005

  • NOTE ON CAPILLARY PROBLEM ACTA MATHEMATICA Finn, R. 1974; 132 (3-4): 199-205

    View details for Web of Science ID A1974T560900004

  • 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

    View details for Web of Science ID A1973O488000013

  • ON A CLASS OF CAPILLARY SURFACES JOURNAL D ANALYSE MATHEMATIQUE Concus, P., Finn, R. 1970; 23: 65-?

    View details for Web of Science ID A1970H133300005

  • 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