[BOOK][B] An introduction to partial differential equations

Y Pinchover, J Rubinstein - 2005 - books.google.com
A complete introduction to partial differential equations, this textbook provides a rigorous yet
accessible guide to students in mathematics, physics and engineering. The presentation is …

Fast reaction, slow diffusion, and curve shortening

J Rubinstein, P Sternberg, JB Keller - SIAM Journal on Applied Mathematics, 1989 - SIAM
The reaction-diffusion problem \[ u_1 = \varepsilon \Delta u - \varepsilon ^{ - 1} V_n ( u ),\quad
u( {x,0,\varepsilon } ) = g( x ),\quad\partial _n u = 0\text{ on }\partial \Omega \] for a vector $u…

Intensity control with a free-form lens

J Rubinstein, G Wolansky - JOSA A, 2007 - opg.optica.org
A family of free-form lenses for intensity control is designed. The lens can shape an incident
collimated beam with a given intensity distribution I_1 into a new collimated beam with …

Diffusion‐controlled reactions: Mathematical formulation, variational principles, and rigorous bounds

J Rubinstein, S Torquato - The Journal of chemical physics, 1988 - pubs.aip.org
This paper is concerned with the problem of predicting the effective rate constant k associated
with diffusion-controlled reactions in media composed of static and reactive traps (sinks) …

Adjustable-focus lenses based on the Alvarez principle

S Barbero, J Rubinstein - Journal of Optics, 2011 - iopscience.iop.org
We present a comprehensive approach for the design of adjustable-focus lenses based on
the Alvarez principle. The design methodology consists of dividing the lens into two parts: the …

Nonlocal reaction—diffusion equations and nucleation

J Rubinstein, P Sternberg - IMA Journal of Applied Mathematics, 1992 - academic.oup.com
A nonlocal reaction-diffusion equation is presented and analysed using matched asymptotic
expansions and multiple timescales. The problem models a binary mixture undergoing …

Flow in random porous media: mathematical formulation, variational principles, and rigorous bounds

J Rubinstein, S Torquato - Journal of fluid mechanics, 1989 - cambridge.org
The problem of the slow viscous flow of a fluid through a random porous medium is considered.
The macroscopic Darcy's law, which defines the fluid permeability k, is first derived in an …

Neutrophil-to-lymphocyte ratio predicts progression and recurrence of non–muscle-invasive bladder cancer

…, D Margel, T Bar-On, O Nativ, J Rubinstein… - … Oncology: Seminars and …, 2015 - Elsevier
Objective Neutrophil-to-lymphocyte ratio (NLR) predicts advanced stage disease and
decreased survival in patients undergoing radical cystectomy for urothelial carcinoma of the …

Variational Problems¶ on Multiply Connected Thin Strips I:¶ Basic Estimates and Convergence¶ of the Laplacian Spectrum

J Rubinstein, M Schatzman - Archive for Rational Mechanics and Analysis, 2001 - Springer
Let M be a planar embedded graph whose arcs meet transversally at the vertices. Let ?(ɛ)
be a strip-shaped domain around M, of width ɛ except in a neighborhood of the singular …

Minimizers and gradient flows for singularly perturbed bi-stable potentials with a Dirichlet condition

NC Owen, J Rubinstein… - Proceedings of the …, 1990 - royalsocietypublishing.org
Minimizers and gradient flows are studied for the functional ∫ Ω W(u) + ϵ 2 ∣∇u∣ 2 dx, Ω
⊆ R n , ϵ > 0, where u satisfies a Dirichlet condition u = h ϵ on ∂Ω. Here W is taken to be a …