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May 28, 2013
Cellular Automata and Lattice Gases

Sequences of preimages in elementary cellular automata

We search for regularities in the sequences of numbers of preimages for elementary cellular automata. For 46 out of 88 "minimal" rules, we find recog…
Nov 24, 2015
Superconductivity

Symmetry and topology of two-dimensional noncentrosymmetric superco…

We present a detailed study of the gap symmetry and the quasiparticle wave function topology in two-dimensional superconductors without inversion cen…
Aug 27, 2010
Statistical Mechanics
Superconductivity

The absence of phase transition for the classical XY-model on Sierpin…

For the spin models with continuous symmetry on regular lattices and finite range of interactions the lower critical dimension is d=2. In two dimensi…
Nov 04, 2017
Exactly Solvable and Integrable Systems
Analysis of PDEs
Classical Analysis and ODEs
Mathematical Physics

The dynamics of conservative peakons in the NLS hierarchy

Using the tri-hamiltonian splitting method, the authors of [Anco and Mobasheramini, Physica D, 355:1--23, 2017] derived two $U(1)$-invariant nonlinea…
Jun 09, 2011
History and Overview

Observationes Cyclometricae by Adam Adamandy Kochański - Latin text …

Annotated parallel text in Latin and English of the classic paper of Adam Adamandy Kocha\'nski "Observationes Cyclometricae", published in Acta Erudi…
Jun 22, 2015
Cellular Automata and Lattice Gases

Solving two-dimensional density classification problem with two pro…

The density classification problem is one of the simplest yet non-trivial computing tasks which seem to be ideally suitable for cellular automata (CA…
Jun 11, 2010
Statistical Mechanics
Superconductivity

Monte Carlo study of the XY-model on Sierpinski gasket

We have performed a Monte Carlo study of the classical XY-model on two-dimensional Sierpinski gaskets of several cluster sizes. From the dependence o…
Nov 26, 2016
Superconductivity

Noncentrosymmetric superconductors in one dimension

We study the fermionic boundary modes (Andreev bound states) in a time-reversal invariant one-dimensional superconductor. In the presence of a substr…
Nov 09, 2007
Cellular Automata and Lattice Gases

Catalan numbers and power laws in cellular automaton rule 14

We discuss example of an elementary cellular automaton for which the density of ones decays toward its limiting value as a power of the number of ite…
May 26, 2011
Analysis of PDEs
Mathematical Physics

In general the method of group foliation reduction using a separation ansatz as illustrated in this paper is able to yield exact solutions to nonlinear 2nd order PDEs with power nonlinearities.

Exact Solutions of Nonlinear Partial Differential Equations by the …

A novel symmetry method for finding exact solutions to nonlinear PDEs is illustrated by applying it to a semilinear reaction-diffusion equation in mu…
Oct 29, 2012
Discrete Mathematics
Combinatorics

Square-Root Finding Problem In Graphs, A Complete Dichotomy Theorem

Graph G is the square of graph H if two vertices x,y have an edge in G if and only if x,y are of distance at most two in H. Given H it is easy to com…
Oct 18, 2012
Probability

In this section, we discuss the extent to which the conclusions of Theorem 2.1 extend beyond πd being an i.i.d. product density upon the d-dimensional hypercube and Xd0∼πd. First we present two extensions of Theorem 2.1. The second extension, Theore…

Optimal scaling of random walk Metropolis algorithms with discontinuo…

We consider the optimal scaling problem for high-dimensional random walk Metropolis (RWM) algorithms where the target distribution has a discontinuou…
Nov 08, 2011
History and Overview

"Solutio theorematum" by Adam Adamandy Kochański -- Latin text with …

Annotated parallel text in Latin and English of the paper of Adam Adamandy Kocha\'nski "Solutio Theorematum Ab illustri Viro in Actis hujus Anni Mens…
Feb 25, 2010
Superconductivity

Effects of impurities in noncentrosymmetric superconductors

Effects of disorder on superconducting properties of noncentrosymmetric compounds are discussed. Elastic impurity scattering, even for scalar impurit…
Jul 17, 2015
Mathematical Physics

Travelling waves and conservation laws for highly nonlinear wave eq…

A highly nonlinear, fourth-order wave equation that models the continuum theory of long wavelength pulses in weakly compressed, discrete, homogeneous…
Oct 30, 2014
Economics
Statistical Finance

When does the stock market listen to economic news? New evidence from…

We study association between macroeconomic news and stock market returns using the statistical theory of copulas, and a new comprehensive measure of …
Jun 05, 2013
Cellular Automata and Lattice Gases

Exponential convergence to equilibrium in cellular automata asympto…

We consider the problem of finding the density of 1's in a configuration obtained by $n$ iterations of a given cellular automaton (CA) rule, starting…
Oct 15, 2013
Statistical Mechanics
Superconductivity
Computational Physics

Absence of phase transition in the XY-model on Menger sponge

We have performed a Monte Carlo study of the classical XY-model on a Menger sponge with the Wolff cluster algorithm (U. Wolff, 1989). The Menger spon…
Aug 09, 2011
Cellular Automata and Lattice Gases

Response curves for cellular automata in one and two dimensions - an …

We consider the problem of computing a response curve for binary cellular automata -- that is, the curve describing the dependence of the density of …
Nov 21, 2010
Analysis of PDEs
Mathematical Physics

Symmetry analysis and exact solutions of semilinear heat flow in mu…

A symmetry group method is used to obtain exact solutions for a semilinear radial heat equation in $n>1$ dimensions with a general power nonlinearity…
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