Narrow Results

The present paper studies continuity of generalized entropy functions and relative entropies defined using the notion of a deformed logarithmic function. In particular, two distinct definitions of relative entropy are discussed. As an application, all considered entropies are shown to satisfy Lesche's stability condition. The entropies of Tsallis' non-extensive thermostatistics are taken as examples.

The effective mass m_eff of the Pauli–Fierz Hamiltonian with ultraviolet cutoff Λ and the bare mass m in non-relativistic quantum electrodynamics (QED) with spin ½ is investigated. Analytic properties of m_eff in coupling constant e are shown. Let us set . The explicit form of constant a₂(Λ/m) depending on Λ/m is given. It is shown that the spin interaction enhances the effective mass and that there exist strictly positive constants c₁ and c₂ such that

In this work the notion of divergence of elementary cellular automata is introduced and it is analyzed from a cryptographic point of view. Specifically, the balancedness and propagation characteristics are analyzed.

CNN templates for image processing and pattern formation are derived from neural field equations, advection equations and reaction–diffusion equations by discretizing spatial integrals and derivatives. Many useful CNN templates are derived by this approach. Furthermore, self-organization is investigated from the viewpoint of divergence of vector fields.

The emergence of complexity is investigated from the viewpoint of the energy balance property and the divergence property of reaction–diffusion cellular neural networks.

This paper presents the nonlinear analysis of functionally graded curved panels under high temperature supersonic gas flows. The aerothermoelastic governing equations are determined via Hamilton's variational principle. The von Karman nonlinear strain–displacement relations are used to account for large deflections. The material properties are assumed to be temperature-dependent and varying through the thickness direction according to a power law distribution in terms of the volume fractions of the constituent components. The panel is assumed to be infinitely long and simply supported. The Galerkin method is applied to convert the partial differential governing equation into a set of ordinary differential equations and the resulting system of nonlinear equations is solved through a numerical integration scheme. The effects of volume fraction index, curved panel height-rise, and aerodynamic pressure, in conjunction with the applied thermal loading, on the dynamical behavior of the panel are investigated. Regular and chaotic motions regime are determined through bifurcation analysis using Poincaré maps of maximum panel deflection, panel time history, phase-space and frequency spectra as qualitative tools, while Lyapunov's exponents and dimension are used as quantitative tools.

In this note, we define four main categories of conservative flows: (a) those in which the dissipation is identically zero, (b) those in which the dissipation depends on the state of the system and is zero on average as a consequence of the orbits being bounded, (c) those in which the dissipation depends on the state of the system and is zero on average, but for which the orbit need not be bounded and a different proof is required, and (d) those in which the dissipation depends on the initial conditions and cannot be determined from the equations alone. We introduce a new 3D conservative jerk flow to serve as an example of the first two categories and show what might be the simplest examples for each category. Also, we categorize some of the existing known systems according to these definitions.

Taking into account the generalized uncertainty principle (GUP), we calculate the entropy of a scalar field in a Kerr spacetime. Different to previous work, we have used an new equation of the density of quantum states, which arises from the modified commutation relation . The divergence in the brick wall model is removed, without the cutoff.

In this paper, flutter and divergence instabilities of functionally graded porous plate strip reinforced with graphene nanoplatelets in supersonic flow and subjected to an axial loading are studied. The graphene nanoplatelets are distributed in the matrix either uniformly or non-uniformly along the thickness direction. Four graphene nanoplatelets distribution patterns namely, Patterns A through D are considered. Based on the modified Halpin–Tsai micromechanics model and the rule of mixture, the effective material properties of functionally graded plate strip reinforced with graphene nanoplatelets are obtained. The aerodynamic pressure is considered in accordance with the quasi-steady supersonic piston theory. To transform the governing equations of motion to a general eigenvalue problem, the Galerkin method is employed. The flutter aerodynamic pressure and stability boundaries are determined by solving standard complex eigenvalue problem. The effects of graphene nanoplatelets distributions, graphene nanoplatelets weight fraction, geometry of graphene nanoplatelets, porosity coefficient and porosity distributions on the flutter and divergence instabilities of the system are studied. The results show that the plate strip with symmetric distribution pattern (stiffness in the surface areas) and GPLs pattern A predict the highest stable area. The flutter and divergence regions decrease as the porosity coefficient increases. Besides, the critical aerodynamic loads increase by adding a small amount of GPL to the matrix.