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Jun 30, 2018
06/18

by
Chia-Yu Hsieh; YunKyong Hyon; Hijin Lee; Tai-Chia Lin; Chun Liu

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In order to describe the dynamics of crowded ions (charged particles), we use an energetic variation approach to derive a modified Poisson-Nernst-Planck (PNP) system which includes an extra dissipation due to the effective velocity differences between ion species. Such a system is more complicated than the original PNP system but with the same equilibrium states. Using Schauder's fixed-point theorem, we develop a local existence theorem of classical solutions for the modified PNP system....

Topics: Mathematics, Analysis of PDEs, Mathematical Physics

Source: http://arxiv.org/abs/1407.8245

4
4.0

Jun 30, 2018
06/18

by
Diogo A. Gomes; Hiroyoshi Mitake

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In this paper, we investigate the existence and uniqueness of solutions to a stationary mean field game model introduced by J.-M. Lasry and P.-L. Lions. This model features a quadratic Hamiltonian with possibly singular congestion effects. Thanks to a new class of a-priori bounds, combined with the continuation method, we prove the existence of smooth solutions in arbitrary dimensions.

Topics: Mathematics, Analysis of PDEs

Source: http://arxiv.org/abs/1407.8267

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4.0

Jun 30, 2018
06/18

by
Friedrich Knop; Bernhard Krötz; Eitan Sayag; Henrik Schlichtkrull

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We apply the local structure theorem and the polar decomposition to a real spherical space Z=G/H and control the volume growth on Z. We define the Harish-Chandra Schwartz space on Z. We give a geometric criterion to ensure $L^p$-integrability of matrix coefficients on Z.

Topics: Mathematics, Representation Theory

Source: http://arxiv.org/abs/1407.8006

4
4.0

Jun 30, 2018
06/18

by
Hoai-Minh Nguyen

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This paper is devoted to the study of cloaking via anomalous localized resonance (CALR) in the two and three dimensional quasistatic regimes. CALR associated with negative index materials was discovered by Milton and Nicorovicci in [21] and attracted a lot attention in the scientific community. Two key figures of this phenomenon are the localized resonance, i.e., the fields blow up in some regions and remain bounded in some others, and the connection between the localized resonance and the blow...

Topics: Mathematics, Analysis of PDEs

Source: http://arxiv.org/abs/1407.7977

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5.0

Jun 30, 2018
06/18

by
Meysam Alishahi; Hossein Hajiabolhassan

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For a graph $G$, the tree graph ${\cal T}_{G,t}$ has all tree subgraphs of $G$ with $t$ vertices as vertex set and two tree subgraphs are neighbors if they are edge-disjoint. Also, the $r^{th}$ cut number of $G$ is the minimum number of edges between parts of a partition of vertex set of $G$ into two parts such that each part has size at least $r$. We show that if $t=(1-o(1))n$ and $n$ is large enough, then for any dense graph $G$ with $n$ vertices, the chromatic number of the tree graph ${\cal...

Topics: Mathematics, Combinatorics

Source: http://arxiv.org/abs/1407.8035