output
19952020
most citedQuantitative Phase Field Model of Alloy Solidification

816 citations

researchers with a paper here

Counting papers with at most 25 authors, so collaboration author lists do not stand in for the people here.

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Showing math-phShow all

10 papers · 1 filter

math-ph2020★ 15 cited

Resonance scattering in a waveguide with identical thick barriers

A. Delitsyn, D. S. Grebenkov

We consider wave propagation across an infinite waveguide of an arbitrary bounded cross-section, whose interior is blocked by two identical thick barriers with holes. When the hole…

math-ph2019★ 15 cited

A physicist's guide to explicit summation formulas involving zeros of Bessel functions and related spectral sums

Denis S. Grebenkov

We summarize the mathematical basis and practical hints for the explicit analytical computation of spectral sums that involve the eigenvalues of the Laplace operator in simple doma…

math-ph2017★ 7 cited

Mode matching methods for spectral and scattering problems

A. Delitsyn, D. S. Grebenkov

We present several applications of mode matching methods in spectral and scattering problems. First, we consider the eigenvalue problem for the Dirichlet Laplacian in a finite cyli…

math-ph2017★ 19 cited

Spectral semi-classical analysis of a complex Schrödinger operator in exterior domains

Yaniv Almog, Denis Grebenkov, Bernard Helffer

Generalizing previous results obtained for the spectrum of the Dirichlet and Neumann realizations in a bounded domain of a Schrödinger operator with a purely imaginary potential $h…

math-ph2014★ 67 cited

First Exit Times of Harmonically Trapped Particles: A Didactic Review

D. S. Grebenkov

We revise the classical problem of characterizing first exit times of a harmonically trapped particle whose motion is described by one- or multi-dimensional Ornstein-Uhlenbeck proc…

math-ph2014★ 2 cited

Overlap of two Brownian trajectories: exact results for scaling functions

Mikhail V. Tamm, Vladimir I. Stadnichuk, Alena M. Ilyina +1

We consider two random walkers starting at the same time from different points in space separated by a given distance . We compute the average volume of the space visited…

math-ph2013

On the exponential decay of Laplacian eigenfunctions in planar domains with branches

Binh T. Nguyen, Andrey L. Delytsin, Denis S. Grebenkov

We consider the eigenvalue problem for the Laplace operator in a planar domain which can be decomposed into a bounded domain of arbitrary shape and elongated \branches" of variable…

math-ph2012★ 24 cited

Localization of Laplacian eigenfunctions in circular, spherical and elliptical domains

Binh-Thanh Nguyen, Denis Grebenkov

We consider Laplacian eigenfunctions in circular, spherical and elliptical domains in order to discuss three kinds of high-frequency localization: whispering gallery modes, bouncin…

math-ph2011★ 14 cited

Trapped modes in finite quantum waveguides

Andrey L. Delitsyn, Binh-Thanh Nguyen, Denis S. Grebenkov

The Laplace operator in infinite quantum waveguides (e.g., a bent strip or a twisted tube) often has a point-like eigenvalue below the essential spectrum that corresponds to a trap…

math-ph2011★ 13 cited

Exponential decay of Laplacian eigenfunctions in domains with branches

Andrey Delitsyn, Binh-Thanh Nguyen, Denis S. Grebenkov

The behavior of Laplacian eigenfunctions in domains with branches is investigated. If an eigenvalue is below a threshold which is determined by the shape of the branch, the associa…