Sharif Digital Repository

The turbulent limit of three dimensional Burger equation was studied. An adjusting parameter emerged through the calculations, based on mean field analysis, that was the scaling exponent of conditional density-density correlations. Two kinds of solutions were also shown for velocity-increment probability density function (PDF)  

A unidirectional two-lane road is approximated by a set of two parallel closed one-dimensional chains. Two types of cars, i.e., slow and fast ones are considered in the system. Based on the Nagel-Schreckenberg model of traffic flow [K. Nagel and M. Schreckenberg, J. Phys. 2, 2221 (1992)], a set of reaction-diffusion processes is introduced to simulate the behavior of the cars. Fast cars can pass the slow ones using the passing lane. We write and solve the mean-field rate equations for the density of slow and fast cars, respectively. We also investigate the properties of the model through computer simulations and obtain the fundamental diagrams. A comparison between our results and the... 

An analytical solution is presented that reconstructs residual stress field from limited and incomplete data. The inverse problem of reconstructing residual stresses is solved using an appropriate form of the airy stress function. This function is chosen to satisfy the stress equilibrium equations together with the boundary conditions for a domain within a convex polygon. The analytical solution is demonstrated by developing a reference solution from which selected "measurement" points are used. An artificial error is then randomly added to "measurement" points for studying the stability of the reconstruction method utilizing Tikhonov- Morozov regularization technique. It is found that there... 

In this paper, the metric theory of Diophantine approximation associated with mixed type small linear forms is investigated. We prove Khintchine–Groshev type theorems for both the real and complex number systems. The motivation for these metrical results comes from their applications in signal processing. One such application is discussed explicitly. © Springer Nature Switzerland AG 2020  

In this paper, we present a novel structure of a snake-like robot. This structure enables passive locomotion in snake-like robots. Dynamic equations are obtained for motion in a horizontal plane, using Gibbs-Appell method. Kinematic model of the robot include numerous nonholonomic constraints, which can be omitted at the beginning by choosing proper coordinates to describe the model in Gibbs-Appell framework. In such a case, dynamic equations will be significantly simplified, resulting in considerable reduction of simulation time. Simulation results show that, by proper selection of initial conditions, joint angles operate in a limit cycle and robot can locomote steadily on a passive... 

The effects of using frequency-domain approximation in numerical simulation of fractional-order systems are analytically studied. The main aim in the study is to determine the number, location and stability property of the equilibriums in a fractional-order system and its frequency-based approximating counterpart. The comparison shows that the original fractional-order system and its frequency-based approximation may differ from each other in some or all issues considered in the study. Unfortunately, these differences can lead to wrong consequences in some special cases such as detecting chaos in the fractional-order systems. It is shown that using the frequency-domain approximation methods... 

The spin structure in a magnetic dot is studied as a function of the exchange coupling strength and dot size within the semiclassical approximation on a discrete lattice. As the exchange coupling is decreased or the size is increased, the ground state undergoes a phase change from a homogeneous single-domain ferromagnet (HSDF) to a spin vortex. The line separating these two phases has been calculated numerically for small system sizes. The dipolar interaction has been fully included in our calculations. Magnon frequencies in such a dot have also been calculated in both phases by the linearized equation of motion method. These results have also been reproduced from the Fourier transform of... 

Here we are concerned with the best approximation by polynomials to rational functions in the uniform norm. We give some new theorems about the best approximation of 1/(1+x) and 1/(x-a) where a>1. Finally we extend this problem to that of computing the best approximation of the Chebyshev expansion in uniform norm and give some results and conjectures about this. © 2005 IMACS. Published by Elsevier B.V. All rights reserved  

In this paper we study biased random K-satisfiability (K-SAT) problems in which each logical variable is negated with probability p. This generalization provides us a crossover from easy to hard problems and would help us in a better understanding of the typical complexity of random K-SAT problems. The exact solution of 1-SAT case is given. The critical point of K-SAT problems and results of replica method are derived in the replica symmetry framework. It is found that in this approximation αcp-(K-1) for p→0. Solving numerically the survey propagation equations for K=3 we find that for p