scholarly journals ENUMERATION OF DIMER CONFIGURATIONS ON A FRACTAL LATTICE

2018 ◽  
Vol 9 (2) ◽  
Author(s):  
Dušanka Marčetić ◽  
Sunčica Elezović Hadžić ◽  
Ivan Živić
Keyword(s):  
Thermodynamic Limit ◽  
Statistical Physics ◽  
Asymptotic Form ◽  
Diatomic Molecules ◽  
Canonical Model ◽  
Two Dimensional ◽  
Self Similarity ◽  
Dimer Model ◽  
Fractal Lattice ◽  
Physical Phenomena

In this paper, we present a solution to the close-packed dimer problem on a fractal lattice. The dimer model is canonical model in statistical physics related with many physical phenomena. Originally, it was introduced as a model for adsorption of diatomic molecules on surfaces. Here we assume that the two dimensional substrate on which the adsorption occurs is nonhomogeneous and we represent it by the modified rectangular (MR) fractal lattice. Self-similarity of the fractal lattice enables exact recursive enumeration of all close-packed dimer configurations at every stage of fractal construction. Asymptotic form for the overall number of dimer coverings is determined and entropy per dimer in the thermodynamic limit is obtained.

CALCULATION OF THE DEPENDENCE OF THE DISTANCE TO THE LOCATED OBJECT FROM THE CORNER POSITION OF THE VEHICLE LINE

2018 ◽  
pp. 14-18
Author(s):  
V. V. Artyushenko ◽  
A. V. Nikulin
Keyword(s):  
Real Time ◽  
Statistical Physics ◽  
Angular Position ◽  
Three Dimensional ◽  
Line Of Sight ◽  
Two Dimensional ◽  
Radar Station ◽  
Flight Mode ◽  
Vector Algebra ◽  
Analytical Expressions

To simulate echoes from the earth’s surface in the low flight mode, it is necessary to reproduce reliably the delayed reflected sounding signal of the radar in real time. For this, it is necessary to be able to calculate accurately and quickly the dependence of the distance to the object being measured from the angular position of the line of sight of the radar station. Obviously, the simplest expressions for calculating the range can be obtained for a segment or a plane. In the text of the article, analytical expressions for the calculation of range for two-dimensional and three-dimensional cases are obtained. Methods of statistical physics, vector algebra, and the theory of the radar of extended objects were used. Since the calculation of the dependence of the range of the object to the target from the angular position of the line of sight is carried out on the analytical expressions found in the paper, the result obtained is accurate, and due to the relative simplicity of the expressions obtained, the calculation does not require much time.

WEAK SELF-SIMILAR SETS IN SEPARABLE COMPLETE METRIC SPACES

Fractals ◽  
2017 ◽  
Vol 25 (02) ◽  
pp. 1750021
Author(s):  
R. K. ASWATHY ◽  
SUNIL MATHEW
Keyword(s):  
Metric Spaces ◽  
Complete Metric Space ◽  
Sufficient Conditions ◽  
Finite Union ◽  
Self Similarity ◽  
Complete Metric Spaces ◽  
Self Similar ◽  
Necessary And Sufficient ◽  
Physical Phenomena

Self-similarity is a common tendency in nature and physics. It is wide spread in geo-physical phenomena like diffusion and iteration. Physically, an object is self-similar if it is invariant under a set of scaling transformation. This paper gives a brief outline of the analytical and set theoretical properties of different types of weak self-similar sets. It is proved that weak sub self-similar sets are closed under finite union. Weak sub self-similar property of the topological boundary of a weak self-similar set is also discussed. The denseness of non-weak super self-similar sets in the set of all non-empty compact subsets of a separable complete metric space is established. It is proved that the power of weak self-similar sets are weak super self-similar in the product metric and weak self-similarity is preserved under isometry. A characterization of weak super self-similar sets using weak sub contractions is also presented. Exact weak sub and super self-similar sets are introduced in this paper and some necessary and sufficient conditions in terms of weak condensation IFS are presented. A condition for a set to be both exact weak super and sub self-similar is obtained and the denseness of exact weak super self similar sets in the set of all weak self-similar sets is discussed.

Self-Replicating Patterns in 2D Linear Cellular Automata

2014 ◽  
Vol 24 (01) ◽  
pp. 1430002 ◽  
Author(s):  
Selman Uguz ◽  
Uḡur Sahin ◽  
Hasan Akin ◽  
Irfan Siap
Keyword(s):  
Cellular Automata ◽  
Self Assembly ◽  
Statistical Physics ◽  
Spatial Scales ◽  
Real Life ◽  
Continuous System ◽  
Random Number Generation ◽  
Two Dimensional ◽  
Textile Design ◽  
Genetics Research

This paper studies the theoretical aspects of two-dimensional cellular automata (CAs), it classifies this family into subfamilies with respect to their visual behavior and presents an application to pseudo random number generation by hybridization of these subfamilies. Even though the basic construction of a cellular automaton is a discrete model, its macroscopic behavior at large evolution times and on large spatial scales can be a close approximation to a continuous system. Beyond some statistical properties, we consider geometrical and visual aspects of patterns generated by CA evolution. The present work focuses on the theory of two-dimensional CA with respect to uniform periodic, adiabatic and reflexive boundary CA (2D PB, AB and RB) conditions. In total, there are 512 linear rules over the binary field ℤ2for each boundary condition and the effects of these CA are studied on applications of image processing for self-replicating patterns. After establishing the representation matrices of 2D CA, these linear CA rules are classified into groups of nine and eight types according to their boundary conditions and the number of neighboring cells influencing the cells under consideration. All linear rules have been found to be rendering multiple self-replicating copies of a given image depending on these types. Multiple copies of any arbitrary image corresponding to CA find innumerable applications in real life situation, e.g. textile design, DNA genetics research, statistical physics, molecular self-assembly and artificial life, etc. We conclude by presenting a successful application for generating pseudo numbers to be used in cryptography by hybridization of these 2D CA subfamilies.

Two-Dimensional Numerical Model for Studies of Collective Beam-Plasma Interaction

2010 ◽  
Vol 5 (2) ◽  
pp. 85-97
Author(s):  
Andrey V. Terekhov ◽  
Igor V. Timofeev ◽  
Konstantin V. Lotov
Keyword(s):  
Numerical Model ◽  
Electron Beams ◽  
Modulational Instability ◽  
Two Dimensional ◽  
Particle In Cell ◽  
Plasma Energy ◽  
Proposed Model ◽  
The Laplace Operator ◽  
Physical Phenomena ◽  
Powerful Electron

A two-dimensional particle-in-cell numerical model is developed to simulate collective relaxation of powerful electron beams in plasmas. To increase the efficiency of parallel particle-in-cell simulations on supercomputers, the Dichotomy Algorithm is used for inversion of the Laplace operator. The proposed model is tested with several well-known physical phenomena and is shown to adequately simulate basic effects of the beam driven turbulence. Also, the modulational instability is studied in the regime when the energy of pumping wave significantly exceeds the thermal plasma energy

scholarly journals Double Hopf Bifurcation in Microbubble Oscillators with Delay Coupling

2020 ◽  
Vol 2020 ◽  
pp. 1-9
Author(s):  
Jinbin Wang ◽  
Rui Zhang ◽  
Lifenq Ma
Keyword(s):  
Hopf Bifurcation ◽  
Center Manifold ◽  
Two Dimensional ◽  
Main Attention ◽  
Dimensional Parameter ◽  
Center Manifold Reduction ◽  
Double Hopf Bifurcation ◽  
Physical Phenomena ◽  
Manifold Reduction ◽  
Theoretical Results

Using center manifold reduction methodswe investigate the double Hopf bifurcation in the dynamics of microbubble with delay couplingwith main attention focused on nonresonant double Hopf bifurcation. We obtain the normal form of the system in the vicinity of the double Hopf point and classify the bifurcations in a two-dimensional parameter space near the critical point. Some numerical simulations support the applicability of the theoretical results. In particularwe give the explanation for some physical phenomena of the system using the obtained mathematical results.

scholarly journals Dichotomy between frustrated local spins and conjugated electrons in a two-dimensional metal–organic framework

Nanoscale ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 955-961 ◽  
Author(s):  
Wei Jiang ◽  
Zheng Liu ◽  
Jia-Wei Mei ◽  
Bin Cui ◽  
Feng Liu
Keyword(s):  
Metal Organic Framework ◽  
Electronic States ◽  
Two Dimensional ◽  
Metal Organic ◽  
Physical Phenomena ◽  
Organic Framework

Dichotomy between local spins and conjugated electrons spawns various exotic physical phenomena. We discover a 2D MOF dichotomy system and propose to characterize the exotic electronic states using STM.

The transient behaviour of the simple random walk in the plane

1988 ◽  
Vol 25 (01) ◽  
pp. 58-69 ◽  
Author(s):  
D. Y. Downham ◽  
S. B. Fotopoulos
Keyword(s):  
Random Walk ◽  
Transient Process ◽  
Asymptotic Form ◽  
Simple Random Walk ◽  
Rectangular Lattice ◽  
Two Dimensional ◽  
Transient Behaviour ◽  
Practical Implications ◽  
Asymptotic Forms

For the simple two-dimensional random walk on the vertices of a rectangular lattice, the asymptotic forms of several properties are well known, but their forms can be insufficiently accurate to describe the transient process. Inequalities with the correct asymptotic form are derived for six such properties. The rates of approach to the asymptotic form are derived. The accuracy of the bounds and some practical implications of the results are discussed.

Sign in / Sign up

Export Citation Format

Share Document