# The minimum of potential energy of a System of point charges

@inproceedings{Yudin1993TheMO, title={The minimum of potential energy of a System of point charges}, author={Valery A. Yudin}, year={1993} }

A moving target indicator for illuminating only those objects in motion. The invention consists of a phosphorous excitation source such as a defocused electron beam or ultraviolet light synchronized with a focused CO2 or similar laser for producing a thermal raster. By modulating the laser with image information, only the time changing intensities (moving objects) produce a visible phosphorescent image since only changing thermal temperature image patterns produce visible images.

## 37 Citations

Order and disorder in energy minimization

- Mathematics
- 2010

How can we understand the origins of highly symmetrical objects? One way is to characterize them as the solutions of natural optimization problems from discrete geometry or physics. In this paper, we…

Distinctive Computational Approaches for Solution of Energy Optimization of Particles

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In this work QPSO is extremely effective and successful at delivering near- optimal results, as it compared the results with Genetic Algorithm and PSO.

Immersed boundary method with non-uniform distribution of Lagrangian markers for a non-uniform Eulerian mesh

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Trade-offs and design principles in the spatial organization of catalytic particles

- ChemistrybioRxiv
- 2020

It is shown that two fundamental trade-offs arise, the first between efficient inter-catalyst transport and depletion of substrate, and the second between steric confinement of intermediate products and accessibility of catalysts to substrate.

Discrete Logarithmic Energy on the Sphere

- Mathematics
- 2002

In this article we consider the problem posed by Whyte, about the distribution of N point charges on the unit sphere, whose mutual distances have maximal geometric mean. Some properties of the…

Universally optimal distribution of points on spheres

- Mathematics
- 2006

We study configurations of points on the unit sphere that minimize potential energy for a broad class of potential functions (viewed as functions of the squared Euclidean distance between points).…

Potential Theory and Geometry of the Farthest Distance Function

- Mathematics
- 2013

The farthest distance function of a compact set in the plane is expressed via the logarithmic potential of a unit measure. In the case of a polygon, we give a geometric formula for the representing…

On Korkin-Zolotarev’s construction

- Mathematics
- 1994

It is proved that the minimum of the potential energy of 24 unit charges placed on the sphere in R is equal to 637975/72. This minimum is attained on the minimal vectors of the lattice ES. Let χ =…

Estimates of the maximal value of angular code distance for 24 and 25 points on the unit sphere in ℝ4

- Mathematics
- 2000

The present paper is devoted to the well-known problem of determining the maximum number of elementsτm(s) of a sphericals-code (−1<-s<1) in Euclidean space ℝm of dimensionm>-2; to be exact, here we…

Moment methods in energy minimization: New bounds for Riesz minimal energy problems

- Mathematics, Computer ScienceTransactions of the American Mathematical Society
- 2019

The first time a four-point bound has been computed for a problem in discrete geometry is computed, suggesting that the second step of the hierarchy may be sharp throughout a phase transition and may be universally sharp for five particles on the unit sphere.

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