# Fine structure of a one-dimensional discrete point system

Fine structure of a one-dimensional discrete point system We consider a system of N points x 1 < ... < x N on a segment of the real line. An ideal system (crystal) is a system where all distances between neighbors are the same. Deviation from idealness is characterized by a system of finite differences ∇ i 1 = x x+1 − x i , ∇ i k+1 = ∇ i+1 k − ∇ i k , for all possible i and k. We find asymptotic estimates as N → ∞, k→∞, for a system of points minimizing the potential energy of a Coulomb system in an external field. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Problems of Information Transmission Springer Journals

# Fine structure of a one-dimensional discrete point system

, Volume 48 (3) – Oct 17, 2012
14 pages
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Publisher
SP MAIK Nauka/Interperiodica
Copyright
Copyright © 2012 by Pleiades Publishing, Ltd.
Subject
Engineering; Information Storage and Retrieval; Systems Theory, Control; Electrical Engineering; Communications Engineering, Networks
ISSN
0032-9460
eISSN
1608-3253
D.O.I.
10.1134/S0032946012030088
Publisher site
See Article on Publisher Site

### Abstract

We consider a system of N points x 1 < ... < x N on a segment of the real line. An ideal system (crystal) is a system where all distances between neighbors are the same. Deviation from idealness is characterized by a system of finite differences ∇ i 1 = x x+1 − x i , ∇ i k+1 = ∇ i+1 k − ∇ i k , for all possible i and k. We find asymptotic estimates as N → ∞, k→∞, for a system of points minimizing the potential energy of a Coulomb system in an external field.

### Journal

Problems of Information TransmissionSpringer Journals

Published: Oct 17, 2012

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