Energies and spacings of point charges on a sphere

Glasser, Leslie; Every, A. G.

doi:10.1088/0305-4470/25/9/020

Cited by 69 publications

(58 citation statements)

References 12 publications

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“…′ is the dimension of M. It is expected that the same kind of results hold [243,244,116,197,40,33,41], although it has not been proved yet, except in the case of the sphere in dimension d = 2 with V (x) = − log |x| [44].…”

Section: 7mentioning

confidence: 93%

The crystallization conjecture: a review

Blanc¹,

Lewin²

2015

EMS Surv. Math. Sci.

134

191

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In this article we describe the crystallization conjecture. It states that, in appropriate physical conditions, interacting particles always place themselves into periodic configurations, breaking thereby the natural translation-invariance of the system. This famous problem is still largely open. Mathematically, it amounts to studying the minima of a real-valued function defined on R 3N where N is the number of particles, which tends to infinity. We review the existing literature and mention several related open problems, of which many have not been thoroughly studied.

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Section: 7mentioning

confidence: 93%

The crystallization conjecture: a review

Blanc¹,

Lewin²

2015

EMS Surv. Math. Sci.

134

191

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“…, y N } of nanotraps that minimizes H, and consequently maximizes C 0 , will be (roughly) uniformly distributed over the surface of the target sphere. This discrete optimization problem for points on the sphere is a generalization of the classical Fekete point problems of [20,5,39,27,44,7]. In addition, as a result of the different Green's functions involved, this problem is different from the discrete optimization problem derived in [12] to minimize the average MFPT for the narrow escape problem.…”

Section: R→∞ ∂ωRmentioning

confidence: 99%

First Passage Statistics for the Capture of a Brownian Particle by a Structured Spherical Target with Multiple Surface Traps

Lindsay¹,

Bernoff²,

Ward³

2017

Multiscale Model. Simul.

106

153

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Abstract. We study the first passage time problem for a diffusing molecule in an enclosed region to hit a small spherical target whose surface contains many small absorbing traps. This study is motivated by two examples of cellular transport. The first is the intracellular process through which proteins transit from the cytosol to the interior of the nucleus through nuclear pore complexes that are distributed on the nuclear surface. The second is the problem of chemoreception, in which cells sense their surroundings through diffusive contact with receptors distributed on the cell exterior. Using a matched asymptotic analysis in terms of small absorbing pore radius, we derive and numerically verify a high order expansion for the capacitance of the structured target which incorporates surface effects and gives explicit information on interpore interaction through a Coulomb-type discrete energy with additional logarithmic dependencies. In the large N dilute surface trap fraction limit, a single homogenized Robin boundary condition ∂nv + κv = 0 is derived in which κ depends on the total absorbing fraction, the characteristic pore scale, and parameters relating to interpore interactions.

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“…In [1] the author obtains that the vertices of the regular icosahedron solve the Whyte's problem (α = 0), and claims that the methods he uses can be applied to solve the Thompson problem for N = 12. For other values of N , the problem has been constantly attacked with numerical methods (see [5], [9], [15], [16], [17]), with better configurations appearing in the literature occasionally.…”

mentioning

confidence: 99%