Theses

M.Sc. "Absorptive Multistability in a System of Three-Level Active Centers",
Ural Technical University, Sverdlovsk, Russia, 1982.

Main results of this thesis were published in

V.V.Zverev and B.Y.Rubinstein, Izv. Vuzov, Fizika, Dep. 522-84 (in Russian). English version.

Ph.D. "Chaotic Dynamics and Statistical Characteristics of Radiation in a Ring Cavity with a Nonlinear Element",
Irkutsk StateUniversity, Irkutsk, Russia, 1989.

Papers

1. V.V.Zverev and B.Y.Rubinstein
"Coherent States of the Hydrogen Atom'',
Soviet Physics-Lebedev Institute Reports, 11, 1, 1982  (in Russian). English version.

2. V.V.Zverev and B.Y.Rubinstein.
"Multistability Resulting from Random Rearrangements in a Ring  Resonator with a Nonlinear Element'',
Optics and Spectroscopy,  62, 519, 1987.

3. V.V.Zverev and B.Y.Rubinstein
"Random Self-modulation of Radiation in a Ring Cavity. Case of Strong Mixing'',
Optics and Spectroscopy,  65, 571, 1988.

4. V.V.Zverev and B.Y.Rubinstein
"Autostochastisity and Conversion of Lasing Fluctuations in the Ring Cavity with a Nonlinear Element'',
Optics and Spectroscopy, 70, 763, 1991.

5.  V.V.Zverev and B.Y.Rubinstein
"Chaotic Oscillations and Noise Transformations in the Simple Dissipative System with Delayed Feedback'',
 Journ. of Stat.Phys.,  63, 229, 1991.

6. A.B.Borisov, V.V.Zverev, B.Y.Rubinstein, and B.N.Fillipov
"On the Magnetization Chaotic Dynamics in the Ferromagnetic Resonance Region'',
 JMMM,  110, 202, 1992.

7. L.M.Pismen and B.Y.Rubinstein
 "Motion of Interacting Point Defects in Nematics'',
 Phys.Rev.Lett.  69, 96, 1992.

8. B.Y.Rubinstein and L.M.Pismen
  "Vortex Motion in the Spatially Inhomogeneous Conservative Ginzburg-Landau Model'',
  Physica D78, 1, 1994.

9.  L.M.Pismen, B.Y.Rubinstein and M.G.Velarde
"On Automated Derivation of Amplitude Equations in Nonlinear Bifurcation Problems'',
Int.J.Bif.Chaos  6, 1, 1996.

10. L.M.Pismen and B.Y.Rubinstein
"Tools for Nonlinear Analysis: I. Unfolding of Dynamical Systems",
deposited at http://www.arXiv.org: chao-dyn/9601017

11.  B.Y.Rubinstein and L.M.Pismen
"Resonant Two-Dimensional Patterns in Optical Cavities with a Rotated Beam'',
Phys.Rev.  A56, 4264, 1997.

12.   B.Y.Rubinstein and L.M.Pismen
 "Resonant Patterns in a Two-Component Optical System with 2-D Feedback'',
 Opt.Commun.  145, 159, 1998.

13.   L.M.Pismen, R.Imbihl, B.Y.Rubinstein and M.I.Monin
"Two-Tier Symmetry-Breaking Model of Patterns on a Catalytic Surface'',
Phys.Rev.  E58, 2065, 1998.

14.  L.M.Pismen and B.Y.Rubinstein
"Ripening of Surface Phases Coupled with Oscillatory Dynamics and
Self-Induced Spatial Chaos through Surface Roughening'',
 Chaos  9, 55, 1999.

15.  L.M.Pismen and B.Y.Rubinstein
"Quasicrystalline and Dynamic Planforms in Nonlinear Optics'',
 Chaos, Solitons and Fractals, 10, 761, 1999.

16.  L.M.Pismen and B.Y.Rubinstein
"Computer Tools for Bifurcation Analysis: General Approach with
 Applications to Dynamical and Distributed Systems'',
 Int. J. Bif. Chaos, 9, 983, 1999.

17.  L.M.Pismen, B.Y.Rubinstein and I.Bazhlekov
"Spreading of a Wetting Film Under the Action of Van der Waals Forces'',
Phys. Fluids, 12, 480, 2000.

18.  B.Y.Rubinstein and A.M.Leshansky
"Dynamics of Thin Liquid Films with Non-Soluble Surfactants: Weakly Nonlinear Analysis'',
 Langmuir, 16, 2049, 2000.

19.  O.A.Nekhamkina, A.A.Nepomnyashchy, B.Y.Rubinstein and M.Sheintuch
"Nonlinear Analysis of Turing Patterns in Convection-Reaction-Diffusion Systems'',
 PRE,  61, 2436, 2000.

20.  O.A.Nekhamkina, B.Y.Rubinstein and M.Sheintuch
 "Spatiotemporal Patterns in Thermokinetic Model of Cross-Flow Reactors'',
AIChE Journal, 46, 1632, 2000.

21.   O.A.Nekhamkina, B.Y.Rubinstein and M.Sheintuch
 "Spatiotemporal Patterns in Models of Cross-Flow Reactors. Regular and Oscillatory Kinetics'' ,
Chemical Engineering Science, 56, 771, 2001.

22.  L.M.Pismen and B.Y.Rubinstein
"Kinetic Slip Condition, van der Waals Forces, and Dynamic Contact Angle'',
Langmuir, 17, 5265, 2001.

23. L.G.Fel and B.Y.Rubinstein
"Sylvester Waves in the Coxeter Groups",
Ramanujan Journal, 6, 307, 2002.

24.  B.Y.Rubinstein and S.G.Bankoff
"Dynamics of  Thin Liquid Films on a Coated Solid Surface
with Insoluble Surfactants: Weakly Nonlinear Analysis'',
Langmuir, 17, 1306, 2001.

25.  A.A. Golovin, B.Y.Rubinstein and L.M.Pismen
"Effect of Van der Waals Interactions on Fingering Instability
of Thermally Driven Thin Wetting Films",
Langmuir, 17, 3930, 2001.

26.  M.I.Monine, A.Schaak, B.Y.Rubinstein, R.Imbihl and L.M.Pismen
"Dynamics of Subsurface Oxygen Formation in Catalytic Water Formation
on Rh(111) surface - experiment and simulation",
Catalysis Today, 70, 321, 2001.

27.  B.Y.Rubinstein
"On Explicit Formula for Restricted Partition Function",
deposited at http://www.arXiv.org: NT/0105218

28.  B.Y.Rubinstein, S.G.Bankoff and S.H.Davis
"Instability of Subcooled Boiling Film on a Vertical Wall",
Int. Journ. Heat Mass Transfer, 45(25), 4937, 2002.

29.  I.L.Kliakhandler and B.Y.Rubinstein
"Spectral Filtering Formalism and its Application for Multi-Phase Deep-Water Wavetrains",
Studies in Applied Mathematics, 110, 205, 2003.

30.  S.J.Watson, F.Otto, B.Y.Rubinstein and S.H.Davis
"Coarsening Dynamics of the Convective Cahn-Hilliard Equation",
Physica D, 178, 127, 2003.

31.  B.Y.Rubinstein and L.F.Fel
"Restricted Partition Function as Bernoulli and Eulerian Polynomials of Higher Order",
Ramanujan Journal, 11, 331, 2006.

32.  V.V.Zverev and B.Y.Rubinstein
"Dynamical Symmetries and Well-Localized Hydrogenic Wave Packets",
Proceedings of Institute of Mathematics of NAS of Ukraine,
Editors A.G. Nikitin, V.M. Boyko, R.O. Popovych and I.A.Yehorchenko, Kyiv,
Institute of Mathematics, 50, Part 2, 1018, 2004.
Deposited at http://www.arXiv.org:quant-ph/0310103

33. B.Y.Rubinstein and L.M.Braverman
"The chasing method for linear boundary value problems",
in  New Ideas in Symbolic Computation: Proceedings of the 6th
    International Mathematica Symposium,
Positive Corporation, Hampshire, England, 2004.

34. A.A.Podolny, M.A.Zaks, B.Y.Rubinstein, A.A.Golovin and A.A.Nepomnyashchy
"Dynamics of Domain Walls Governed by the Convective Cahn-Hilliar Equation",
Physica D, 201, 291, 2005.

35. A.M.Leshansky and B.Y.Rubinstein
"Nonlinear rupture of thin liquid films on solid surfaces",
PRE, 71, 040601(R), 2005.

36. B.Y.Rubinstein
"An Explicit Formula for Restricted Partition Function through Bernoulli Polynomials",
Ramanujan Journal, accepted, 2006.
This paper contains an explicit solution of the long standing number theory problem -
counting a number of partitions of a given positive integer N into a positive integers from a
given list {n1, n2, ..., np}. This problem was attacked by many famous mathematicians including
Euler, Catalan and Sylvester.

37. B.Y.Rubinstein, K. Jacobson and A. Mogilner
"Multiscale Two-Dimensional Modeling of a Motile Simple-Shaped Cell",
SIAM Journal of Multiscale Modeling and Simulations, 3, 413, 2005.

38. B.Y. Rubinstein and A. Mogilner
"The Physics of Filopodial Protrusion",
Biophys. J., 89, 782, 2005.

39. L.G.Fel and B.Y.Rubinstein
"Power Sums Related to Semigroups S(d1,d2,d3)",
Semigroups Forum, accepted, 2006.
Deposited at http://www.arXiv.org/abs/math.NT/0411444

40. B.Y. Rubinstein, A.A. Nepomnyashchy, and A.A. Golovin
"Stability of localized solutions in a subcritically unstable
  pattern-forming system under a global delayed control",
PRE, 74, 046213, 2007.

41. B.Y.Rubinstein
"Extension of the Bernoulli and Eulerian Polynomials of Higher
Order and Vector Partition Function".
Ramanujan Journal, submitted.
Deposited at http://www.arxiv.org/abs/math.CO/0612076

42. L.F.Fel and B.Y.Rubinstein
"Are Almost All Numerical Semigroups S(d1,d2,d3) Nonsymmetric?"
in preparation.

Books
L.Braverman, D.Nevelev, B.Rubinstein, and L.Pismen
 Partial Differential Equations Pack, 190 pp.
 Haifa, 1995.