By considering the potential parameter Γ as a function of another potential parameter λ[47], We successfully extend the analysis of two-dimensional autonomous dynamical system of quintessence scalar field model to three-dimension, which makes us be able to exactly research the critical points of a large number of potentials beyond the exponential potential. We find that there are ten critical p...

Symmetry breaking surface fields give rise to nontrivial and long-ranged order parameter profiles for critical systems such as fluids, alloys or magnets confined to wedges. We discuss the properties of the corresponding universal scaling functions of the order parameter profile and the two-point correlation function and determine the critical exponents η and η ⊥ for the so-called normal transit...

In this paper, we consider comparison-based adaptive stochastic algorithms for solving numerical optimisation problems. We consider a specific subclass of algorithms that we call comparison-based step-size adaptive randomized search (CB-SARS), where the state variables at a given iteration are a vector of the search space and a positive parameter, the step-size, typically controlling the overal...

We study the long-time, large scale transport in a three-parameter family of isotropic, incompressible velocity fields with power-law spectra. Scaling law for transport is characterized by the scaling exponent q and the Hurst exponent H , as functions of the parameters. The parameter space is divided into regimes of scaling laws of different functional forms of the scaling exponent and the Hurs...

We study the stochastic fractional diffusive limit of a kinetic equation involving a small parameter and perturbed by a smooth random term. Generalizing the method of perturbed test functions, under an appropriate scaling for the small parameter, and with the moment method used in the deterministic case, we show the convergence in law to a stochastic fluid limit involving a fractional Laplacian.

Corresponding Author: Muhammad Asif Khan Department of Electrical and Electronics Engineering, Universiti Teknologi PETRONAS, Darul Ridzuan, 31750 Perak, Malaysia Email: [email protected] Abstract: Robust chaotic maps with wide robust region are favored in cryptography as it extends the key length. Chaotic tent map has robust chaos for control parameter μ = 2. Perturbation of control parameter v...

Recent work indicates that the interaction between body-size-dependent demographic processes can generate macroecological patterns such as the scaling of population density with body size. In this study, we evaluate this possibility for grazing protists and also test whether demographic parameters in these models are correlated after controlling for body size. We compiled data on the body-size ...

We introduce a new disorder regime for directed polymers in dimension 1 + 1 that sits between the weak and strong disorder regimes. We call it the intermediate disorder regime. It is accessed by scaling the inverse temperature parameter β to zero as the polymer length n tends to infinity. The natural choice of scaling is βn := βn−1/4. We show that the polymer measure under this scaling has prev...

In this two-part paper, information-theoretic capacity scaling laws are analyzed in an underwater acoustic network with n regularly located nodes on a square, in which both bandwidth and received signal power can be limited significantly. Parts I and II deal with an extended network of unit node density and a dense network of unit area, respectively. A narrow-band model is assumed where the car...

Numerical and experimental investigations of intermittency in chaotic systems often lead to claims of universal classes based on the scaling of the average length of the laminar phase with parameter variation. We demonstrate that the scaling in general depends on the choice of the threshold used to define a proper laminar region in the phase space. For sufficiently large values of the threshold...