# 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

Problems of Information Transmission, Volume 48 (3) – Oct 17, 2012
14 pages

/lp/springer_journal/fine-structure-of-a-one-dimensional-discrete-point-system-ixRFyGPlh4
Publisher
Springer Journals
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

## You’re reading a free preview. Subscribe to read the entire article.

### DeepDyve is your personal research library

It’s your single place to instantly
that matters to you.

over 18 million articles from more than
15,000 peer-reviewed journals.

All for just \$49/month

### Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

### Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

### Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

### Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

DeepDyve

DeepDyve

### Pro

Price

FREE

\$49/month
\$360/year

Save searches from
PubMed

Create lists to

Export lists, citations