Robert Finn
Professor of Mathematics, Emeritus
Academic Appointments
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Emeritus Faculty, Acad Council, Mathematics
All Publications
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Capillary Graph-Interfaces "in-the-Large"
VIETNAM JOURNAL OF MATHEMATICS
2019; 47 (1): 113–32
View details for DOI 10.1007/s10013-018-0307-x
View details for Web of Science ID 000458887500007
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Experimental Confirmation of Predicted Rise Heights in a Surface Tension Configuration Introduced by Laplace
JOURNAL OF MATHEMATICAL FLUID MECHANICS
2018; 20 (4): 1701–5
View details for DOI 10.1007/s00021-018-0385-2
View details for Web of Science ID 000451973300014
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The Laplace Parallel Plates Problem in Capillarity Theory
JOURNAL OF MATHEMATICAL FLUID MECHANICS
2018; 20 (4): 1681–99
View details for DOI 10.1007/s00021-018-0384-3
View details for Web of Science ID 000451973300013
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The Force Singularity for Partially Immersed Parallel Plates
JOURNAL OF MATHEMATICAL FLUID MECHANICS
2016; 18 (4): 739-755
View details for DOI 10.1007/s00021-016-0260-y
View details for Web of Science ID 000386341100007
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On the Capillarity Equation in Two Dimensions
JOURNAL OF MATHEMATICAL FLUID MECHANICS
2016; 18 (4): 731-738
View details for DOI 10.1007/s00021-016-0257-6
View details for Web of Science ID 000386341100006
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Attractions and repulsions of parallel plates partially immersed in a liquid bath: III
BOUNDARY VALUE PROBLEMS
2013
View details for DOI 10.1186/1687-2770-2013-277
View details for Web of Science ID 000209345400005
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Mutual Attractions of Partially Immersed Parallel Plates
JOURNAL OF MATHEMATICAL FLUID MECHANICS
2013; 15 (2): 273-301
View details for DOI 10.1007/s00021-012-0105-2
View details for Web of Science ID 000319777800003
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Capillary Forces on Partially Immersed Plates
International Conference on Differential and Difference Equations and Applications
SPRINGER. 2013: 13–25
View details for DOI 10.1007/978-1-4614-7333-6_2
View details for Web of Science ID 000347149500002
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Thomas Young's Surface Tension Diagram: Its History, Legacy, and Irreconcilabilities
JOURNAL OF MATHEMATICAL FLUID MECHANICS
2012; 14 (3): 445-453
View details for DOI 10.1007/s00021-011-0079-5
View details for Web of Science ID 000308064800003
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Occlusion criteria in tubes under transverse body forces
JOURNAL OF FLUID MECHANICS
2011; 682: 397-414
View details for DOI 10.1017/jfm.2011.230
View details for Web of Science ID 000294775800017
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Criteria for Floating I
JOURNAL OF MATHEMATICAL FLUID MECHANICS
2011; 13 (1): 103-115
View details for DOI 10.1007/s00021-009-0009-y
View details for Web of Science ID 000288808000007
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Maximum Principle and Gradient Estimates for Stationary Solutions of the Navier-Stokes Equations: A Partly Numerical Investigation
International Conference on Mathematical Fluid Mechanics
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
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On Young's Paradox, and the attractions of immersed parallel plates
PHYSICS OF FLUIDS
2010; 22 (1)
View details for DOI 10.1063/1.3276213
View details for Web of Science ID 000274180800038
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Floating Bodies in Neutral Equilibrium
JOURNAL OF MATHEMATICAL FLUID MECHANICS
2009; 11 (3): 459-463
View details for DOI 10.1007/s00021-008-0269-y
View details for Web of Science ID 000270982200008
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Floating Bodies Subject to Capillary Attractions
JOURNAL OF MATHEMATICAL FLUID MECHANICS
2009; 11 (3): 443-458
View details for DOI 10.1007/s00021-008-0268-z
View details for Web of Science ID 000270982200007
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The Floating Ball "Paradox"
JOURNAL OF MATHEMATICAL FLUID MECHANICS
2008; 10 (4): 583-587
View details for DOI 10.1007/s00021-007-0243-0
View details for Web of Science ID 000262838600007
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Capillary surfaces in wedge domains
PACIFIC JOURNAL OF MATHEMATICS
2008; 236 (2): 283-305
View details for Web of Science ID 000256850000004
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On the capillary problem for compressible fluids
JOURNAL OF MATHEMATICAL FLUID MECHANICS
2007; 9 (1): 87-103
View details for DOI 10.1007/s00021-005-0203-5
View details for Web of Science ID 000244753500005
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Compressible fluids in a capillary tube
PACIFIC JOURNAL OF MATHEMATICS
2006; 224 (2): 201-229
View details for Web of Science ID 000240148300002
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Equilibrium configurations of an infinite cylinder in an unbounded fluid
PHYSICS OF FLUIDS
2006; 18 (4)
View details for DOI 10.1063/1.2185661
View details for Web of Science ID 000237136900047
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The contact angle in capillarity
PHYSICS OF FLUIDS
2006; 18 (4)
View details for DOI 10.1063/1.2185655
View details for Web of Science ID 000237136900046
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On a singular behavior of capillary surfaces
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
2004; 19 (1): 95-105
View details for DOI 10.1007/s00526-003-0202-4
View details for Web of Science ID 000187132400004
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A new example of singular height transition for capillary surfaces
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
2004; 19 (1): 107-115
View details for DOI 10.1007/s00526-003-0203-3
View details for Web of Science ID 000187132400005
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On a theorem of Lancaster and Siegel
PACIFIC JOURNAL OF MATHEMATICS
2004; 213 (1): 111-119
View details for Web of Science ID 000187721500007
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Computational investigation of unusual behavior in certain capillary tubes
MICROGRAVITY SCIENCE AND TECHNOLOGY
2004; 15 (4): 31-38
View details for Web of Science ID 000226063000004
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Capillary rise in nesting cylinders
PHYSICS OF FLUIDS
2003; 15 (6): 1545-1551
View details for DOI 10.1063/1.1566449
View details for Web of Science ID 000182795300018
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Some unusual comparison properties of capillary surfaces
PACIFIC JOURNAL OF MATHEMATICS
2002; 205 (1): 119-137
View details for Web of Science ID 000176650000006
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Eight remarkable properties of capillary surfaces
MATHEMATICAL INTELLIGENCER
2002; 24 (3): 21-33
View details for Web of Science ID 000176632700008
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Liquid bridges, edge blobs, and Scherk-type capillary surfaces
INDIANA UNIVERSITY MATHEMATICS JOURNAL
2001; 50 (1): 411-441
View details for Web of Science ID 000171494500006
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Measurement of critical contact angle in a microgravity space experiment
EXPERIMENTS IN FLUIDS
2000; 28 (3): 197-205
View details for Web of Science ID 000086477200001
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Vertex theorems for capillary drops on support planes
MATHEMATISCHE NACHRICHTEN
2000; 209: 115-135
View details for Web of Science ID 000085094700005
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Capillary surfaces in an exotic container: results from Space experiments
JOURNAL OF FLUID MECHANICS
1999; 394: 119-135
View details for Web of Science ID 000082689600006
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C-singular solutions of the capillary problem
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK
1999; 512: 1-25
View details for Web of Science ID 000081977400001
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Discontinuous behavior of liquids between parallel and tilted plates
PHYSICS OF FLUIDS
1998; 10 (1): 39-43
View details for Web of Science ID 000071095800006
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Regularity properties of H-graphs
COMMENTARII MATHEMATICI HELVETICI
1998; 73 (3): 379-399
View details for Web of Science ID 000075469000003
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Comments on a paper of Keller, King and Merchant
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS
1996; 27 (7): 857-861
View details for Web of Science ID A1996VC63000012
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Local and global existence criteria for capillary surfaces in wedges.
CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS
1996; 4 (4): 305-322
View details for Web of Science ID A1996UR18200001
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On cylindrical container sections for a capillary free-surface experiment
MICROGRAVITY SCIENCE AND TECHNOLOGY
1996; 9 (3): 169-174
View details for Web of Science ID A1996XG06100008
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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
SPRINGER-VERLAG BERLIN. 1996: 261–270
View details for Web of Science ID A1996BF89D00017
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Capillary wedges revisited
SIAM JOURNAL ON MATHEMATICAL ANALYSIS
1996; 27 (1): 56-69
View details for Web of Science ID A1996TV10900004
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CAPILLARY SURFACES IN A WEDGE - DIFFERING CONTACT ANGLES
MICROGRAVITY SCIENCE AND TECHNOLOGY
1994; 7 (2): 152-155
View details for Web of Science ID A1994PB21800015
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GRADIENT AND GAUSS CURVATURE BOUNDS FOR H-GRAPHS
Symposium on Comparison Methods and Stability Theory
MARCEL DEKKER. 1994: 137–150
View details for Web of Science ID A1994BB12C00011
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On the contact angle in capillarity
3rd International Colloquium on Differential Equations
VSP BV. 1993: 55–62
View details for Web of Science ID A1993BF25K00006
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DROP-TOWER EXPERIMENTS FOR CAPILLARY SURFACES IN AN EXOTIC CONTAINER
AIAA JOURNAL
1992; 30 (1): 134-137
View details for Web of Science ID A1992GZ91500018
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EXOTIC CONTAINERS FOR CAPILLARY SURFACES
JOURNAL OF FLUID MECHANICS
1991; 224: 383-394
View details for Web of Science ID A1991FG99100019
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INSTABILITY OF CERTAIN CAPILLARY SURFACES
MANUSCRIPTA MATHEMATICA
1989; 63 (2): 209-213
View details for Web of Science ID A1989T295700005
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MOON SURFACES, AND BOUNDARY-BEHAVIOR OF CAPILLARY SURFACES FOR PERFECT WETTING AND NON-WETTING
PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY
1988; 57: 542-576
View details for Web of Science ID A1988R096000005
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THE CAPILLARY CONTACT-ANGLE .2. THE INCLINED PLANE
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
1988; 10 (2): 165-196
View details for Web of Science ID A1988N256300005
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THE INCLINATION OF AN H-GRAPH
LECTURE NOTES IN MATHEMATICS
1988; 1340: 40-60
View details for Web of Science ID A1988Q818600005
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THE CAPILLARY CONTACT-ANGLE .1. THE HORIZONTAL PLANE AND STICK-SLIP MOTION
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
1987; 123 (1): 1-17
View details for Web of Science ID A1987G770800001
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ON THE EXTREMALS OF A SUBSIDIARY CAPILLARY PROBLEM
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK
1984; 353: 215-220
View details for Web of Science ID A1984TX62500010
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A SUBSIDIARY VARIATIONAL PROBLEM AND EXISTENCE CRITERIA FOR CAPILLARY SURFACES
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK
1984; 353: 196-214
View details for Web of Science ID A1984TX62500009
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THE INFLUENCE OF BOUNDARY GEOMETRY ON CAPILLARY SURFACES WITHOUT GRAVITY
ASTERISQUE
1984: 157-165
View details for Web of Science ID A1984TP91400011
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SOME PROPERTIES OF CAPILLARY FREE SURFACES
ANNALS OF MATHEMATICS STUDIES
1983: 323-338
View details for Web of Science ID A1983SB53200020
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EXISTENCE CRITERIA FOR CAPILLARY FREE SURFACES WITHOUT GRAVITY
INDIANA UNIVERSITY MATHEMATICS JOURNAL
1983; 32 (3): 439-460
View details for Web of Science ID A1983QV10300008
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GLOBAL SIZE AND SHAPE ESTIMATES FOR SYMMETRIC SESSILE DROPS
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK
1982; 335: 9-36
View details for Web of Science ID A1982PJ62200002
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ON THE LAPLACE FORMULA AND THE MENISCUS HEIGHT FOR A CAPILLARY SURFACE
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK
1981; 61 (3): 165-173
View details for Web of Science ID A1981LS78500004
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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
1981; 61 (3): 175-177
View details for Web of Science ID A1981LS78500005
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THE SESSILE LIQUID-DROP .1. SYMMETRIC CASE
PACIFIC JOURNAL OF MATHEMATICS
1980; 88 (2): 541-587
View details for Web of Science ID A1980LK34300013
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SHAPE OF A PENDENT LIQUID-DROP
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES
1979; 292 (1391): 307-340
View details for Web of Science ID A1979HK42400001
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EXISTENCE AND NON EXISTENCE OF CAPILLARY SURFACES
MANUSCRIPTA MATHEMATICA
1979; 28 (1-3): 1-11
View details for Web of Science ID A1979HA99100001
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NON EXISTENCE AND EXISTENCE OF CAPILLARY SURFACES
MANUSCRIPTA MATHEMATICA
1979; 28 (1-3): 13-20
View details for Web of Science ID A1979HA99100002
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HEIGHT OF A CAPILLARY SURFACE
MATHEMATISCHE ZEITSCHRIFT
1976; 147 (1): 93-95
View details for Web of Science ID A1976BH54600010
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BEHAVIOR OF A CAPILLARY SURFACE AT A SINGULAR POINT
JOURNAL D ANALYSE MATHEMATIQUE
1976; 30: 156-163
View details for Web of Science ID A1976CK99900009
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SINGULAR SOLUTION OF CAPILLARY EQUATION .1. EXISTENCE
INVENTIONES MATHEMATICAE
1975; 29 (2): 143-148
View details for Web of Science ID A1975AL83300004
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SINGULAR SOLUTION OF CAPILLARY EQUATION .2. UNIQUENESS
INVENTIONES MATHEMATICAE
1975; 29 (2): 149-159
View details for Web of Science ID A1975AL83300005
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CAPILLARY FREE SURFACES IN ABSENCE OF GRAVITY
ACTA MATHEMATICA
1974; 132 (3-4): 177-198
View details for Web of Science ID A1974T560900003
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CAPILLARY FREE SURFACES IN A GRAVITATIONAL-FIELD
ACTA MATHEMATICA
1974; 132 (3-4): 207-223
View details for Web of Science ID A1974T560900005
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NOTE ON CAPILLARY PROBLEM
ACTA MATHEMATICA
1974; 132 (3-4): 199-205
View details for Web of Science ID A1974T560900004
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UNIFORMIZATION OF PLANE DIRECTION FIELDS, AND OF SECOND-ORDER PARTIAL DIFFERENTIAL OPERATORS
PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY
1973; 73 (JAN): 87-109
View details for Web of Science ID A1973O488000013
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ON A CLASS OF CAPILLARY SURFACES
JOURNAL D ANALYSE MATHEMATIQUE
1970; 23: 65-?
View details for Web of Science ID A1970H133300005
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ON BEHAVIOR OF A CAPILLARY SURFACE IN A WEDGE
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
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