Multidimensional Z-Matrix with Control Parameters and Its Applications in Image Encryption

An n-dimensional Z-matrix with control parameters is presented, and its periodicity and chaos are testified. Experimental results show that the proposed Z-matrix has a long period and changeable periodicity with different dimensions. Some examples of image encryption with a Z-matrix of different dimensions are listed for demonstrating its applications.     

科赫分形基底上受限固-固模型动力学标度行为的数值研究

为分析基底结构对离散生长模型动力学性质的影响, 本文在随机游走指数十分接近而分形维数和谱维数均不相同的科赫格子和科赫曲线分形基底上对受限固-固(restricted solid-on-solid)模型的生长过程进行数值模拟研究. 通过分析表面宽度和饱和表面极值高度的统计行为发现: 随机游走的动力学指数能够对饱和粗化表面的动力学行为起主要贡献. 尽管分形基底具有不同的分形维数和谱维数, 但是在两种分形基底上得到了在误差范围内相同的粗造度指数. 两种分形基底上饱和表面相对生长高度极大(小)值分布分别可以很好的塌缩在一起, 且很好的满足Asym2Sig函数分布.     

Function projective lag synchronization of fractional-order chaotic systems

Function projective lag synchronization of different structural fractional-order chaotic systems is investigated. It is shown that the slave system can be synchronized with the past states of the driver up to a scaling function matrix. According to the stability theorem of linear fractional-order systems, a nonlinear fractional-order controller is designed for the synchronization of systems with the same and different dimensions. Especially, for two different dimensional systems, the synchronization is achieved in both reduced and increased dimensions. Three kinds of numerical examples are presented to illustrate the effectiveness of the scheme.     

The Atomic Hydrogen in Two Spatial Dimensions

We resolve the problem of atomic hydrogen in two spatial dimensions exactly. Its spectrum ia different from that in three dimensions, M the angular momentum is not quantised in integer or half of odd-integer. We a h calculate the ground state energies for different cases of the parameter α, which may be related to the statistics of the electron in the atom.     

The Effect of Space Dimensions on a Generalized Hydrogen-Atom Specific Heat in the Generalized Boltzmann-Gibbs Statistics

In this article, the effect of the space dimensions on the generalized hydrogen-atom specific heat in the generalized Boltzmann-Gibbs statistics is studied. The temperature dependence of the specific heat for a few different values of q and for different low space dimensions using Tsallis statistics is numerically calculated. The results indicate that for a fixed value of q, as the space dimension increases the temperature range where the specific heat has a nonzero value, decreases, while the general behavior of the specific heat does not show any change. Also, there exits a q-independent quantity related to two specific temperatures of the system which is almost linearly dependent on the space dimensions.     

不同维度ZnO能带结构和电子态密度的研究

本文采用基于密度泛函理论的第一性原理计算方法来研究不同维度ZnO的能带结构和电子态密度.参考实验上的ZnO晶格参数构建不同维度的ZnO模型并进行结构优化后再计算能带结构和电子态密度.研究结果表明二维和三维ZnO都属于直接带隙半导体且二维ZnO的禁带宽度大于三维ZnO;从三维变到二维,ZnO的电子局域化程度变高且Zn 3d轨道电子从能量较低的能级向能量较高的能级跃迁.本文的研究展示了二维和三维ZnO能带结构和电子态密度的异同,为二维ZnO基的器件研究提供了一定的理论参考价值.     

KAM theorems for the product of two involutions of different types

The properties of quasiperiodic motions in Hamiltonian, volume preserving, and reversible systems are summarized. KAM theorems concerning lower-dimensional invariant tori are announced for G-reversible mappings A such that the fixed point manifolds Fix(G) and Fix(AG) of the reversing involutions G and AG are of different dimensions. The case where the manifold Fix(G) itself consists of several connected components of different dimensions is also briefly discussed.     

Design new chaotic maps based on dimension expansion

Based on the high-dimensional(HD) chaotic maps and the sine function, a new methodology of designing new chaotic maps using dimension expansion is proposed. This method accepts N dimensions of any existing HD chaotic map as inputs to generate new dimensions based on the combined results of those inputs. The main principle of the proposed method is to combine the results of the input dimensions, and then performs a sine-transformation on them to generate new dimensions.The characteristics of the generated dimensions are totally different compared to the input dimensions. Thus, both of the generated dimensions and the input dimensions are used to create a new HD chaotic map. An example is illustrated using one of the existing HD chaotic maps. Results show that the generated dimensions have better chaotic performance and higher complexity compared to the input dimensions. Results also show that, in the most cases, the generated dimensions can obtain robust chaos which makes them attractive to usage in a different practical application.     

Gravitational anomalies

It is shown that in certain parity-violating theories in 4k+2 dimensions, general covariance is spoiled by anomalies at the one-loop level. This occurs when Weyl fermions of $\text{spin}\text{-}\text{1}\text{2}\text{or}\text{-3}\text{2}$ or self-dual antisymmetric tensor fields are coupled to gravity. (For Dirac fermions there is no trouble.) The conditions for anomaly cancellation between fields of different spin is investigated. In six dimensions this occurs in certain theories with a fairly elaborate field content. In ten dimensions there is a unique theory with anomaly cancellation between fields of different spin. It is the chiral n = 2 supergravity theory, which is the low-energy limit of one of the superstring theories. Beyond ten dimensions there is no way to cancel anomalies between fields of different spin.     

Corrections to the Hawking Tunneling Radiation from MDR

We investigate some aspects of black hole (BH) thermodynamics in the framework of a modified dispersion relation. We calculate a minimal length and a maximal momentum to find a relation between spacetime dimensions and the presence of logarithmic prefactor in the black hole entropy relation. We show that the logarithmic prefactor appears not only in an even number of dimensions but also in an odd number of dimensions. In addition, the sign of the logarithmic factor is different for positive values of α in all dimensions. Using the corrected entropy, the black hole radiation probability is calculated in the tunneling formalism, which is corrected up to the same order of the Planck length and shows a more probable quantum tunneling.     

Review of Recent Developments in the Random-Field Ising Model

A lot of progress has been made recently in our understanding of the random-field Ising model thanks to large-scale numerical simulations. In particular, it has been shown that, contrary to previous statements: the critical exponents for different probability distributions of the random fields and for diluted antiferromagnets in a field are the same. Therefore, critical universality, which is a perturbative renormalization-group prediction, holds beyond the validity regime of perturbation theory. Most notably, dimensional reduction is restored at five dimensions, i.e., the exponents of the random-field Ising model at five dimensions and those of the pure Ising ferromagnet at three dimensions are the same.     

On clusters and critical dimensions in spin glasses

We discuss the problem of critical dimensions in the Sherrington-Kirkpatrick model of a spin glass, using the presence of clusters above T_c. It is argued that these clusters are ramified. This fact accounts for the different (upper) critical dimensions of the spherical and Ising models. The special role of dimension four is pointed out.     

Dimensions and Waiting Times for Gibbs Measures

For shifts of finite type, we relate the waiting time between two different orbits, one chosen according to an ergodic measure, the other according to a Gibbs measure, to Billingsley dimensions of generic sets. This is achieved by computing Billingsley dimensions of saturated sets in terms of a relative entropy which satisfies a pointwise ergodic result. As a by-product, a similar result is obtained for match lengths that are dual quantities of waiting times.     

Interaction between lexical and grammatical language systems in the brain

This review concentrates on two different language dimensions: lexical/semantic and grammatical. This distinction between a lexical/semantic system and a grammatical system is well known in linguistics, but in cognitive neurosciences it has been obscured by the assumption that there are several forms of language disturbances associated with focal brain damage and hence language includes a diversity of functions (phoneme discrimination, lexical memory, grammar, repetition, language initiation ability, etc.), each one associated with the activity of a specific brain area. The clinical observation of patients with cerebral pathology shows that there are indeed only two different forms of language disturbances (disturbances in the lexical/semantic system and disturbances in the grammatical system); these two language dimensions are supported by different brain areas (temporal and frontal) in the left hemisphere. Furthermore, these two aspects of the language are developed at different ages during child's language acquisition, and they probably appeared at different historical moments during human evolution. Mechanisms of learning are different for both language systems: whereas the lexical/semantic knowledge is based in a declarative memory, grammatical knowledge corresponds to a procedural type of memory. Recognizing these two language dimensions can be crucial in understanding language evolution and human cognition.     

Photodetection of coherent radiation scattered by a moving diffusely-reflecting surface,by a finite-aperture receiver

The question of the effect of the dimensions and form of the receiver aperture on the spectral properties of the photocurrent in the case of photodetection of scattered coherent radiation is studied theoretically and experimentally. It is shown that this effect is essentially different in the near and far wave zones. Formulae are obtained for the photocurrent spectra for different dimensions of receiver apertures.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 7, pp. 52–58, July, 1971.In conclusion, the authors have the pleasant task of acknowledging the assistance of E. P. Kuznetsov in preparing the experiment and of thanking I. P. Mazan'ko for his interest in the work and useful discussions.     

Casimir Effect at Finite Temperature in the Presence of Compactified Universal Extra Dimensions

We analyse the Casimir effect for parallel plates at finite temperature in the presence of compactified universal extra dimensions and analytically show the thermal corrections to the effect in detail. The Casimir effect for different sizes of universal extra dimensions is investigated to test the five-dimensional Kaluza-Klein theory.     

A computational and experimental study of resonators in three dimensions

In a previous work by the present authors, a computational and experimental investigation of the acoustic properties of two-dimensional slit resonators was carried out. The present paper reports the results of a study extending the previous work to three dimensions. This investigation has two basic objectives. The first is to validate the computed results from direct numerical simulations of the flow and acoustic fields of slit resonators in three dimensions by comparing with experimental measurements in a normal incidence impedance tube. The second objective is to study the flow physics of resonant liners responsible for sound wave dissipation. Extensive comparisons are provided between computed and measured acoustic liner properties with both discrete frequency and broadband sound sources. Good agreements are found over a wide range of frequencies and sound pressure levels. Direct numerical simulation confirms the previous finding in two dimensions that vortex shedding is the dominant dissipation mechanism at high sound pressure intensity. However, it is observed that the behavior of the shed vortices in three dimensions is quite different from those of two dimensions. In three dimensions, the shed vortices tend to evolve into ring (circular in plan form) vortices, even though the slit resonator opening from which the vortices are shed has an aspect ratio of 2.5. Under the excitation of discrete frequency sound, the shed vortices align themselves into two regularly spaced vortex trains moving away from the resonator opening in opposite directions. This is different from the chaotic shedding of vortices found in two-dimensional simulations. The effect of slit aspect ratio at a fixed porosity is briefly studied. For the range of liners considered in this investigation, it is found that the absorption coefficient of a liner increases when the open area of the single slit is subdivided into multiple, smaller slits.     

Mixing of a passive scalar across a thin shearless layer: concentration of intermittency on the sides of the turbulent interface

The advection of a passive scalar through an initial flat interface separating two different isotropic decaying turbulent fields is investigated in two and three dimensions. Simulations have been performed for a range of Taylor’s microscale Reynolds numbers from 45 to 250 and for a Schmidt number equal to 1. Different to the case where the transport involves the momentum and kinetic energy only and one intermittency layer is formed in the low-turbulent energy side of the system, in the passive scalar concentration field two intermittent layers are observed to develop at the sides of the interface. The layers move normally to the interface in opposite directions. The dimensionality produces different time scaling of the passive scalar diffusion, which is much faster in the two-dimensional case. In two dimensions, the propagation of the intermittent layers exhibits a significant asymmetry with respect to the initial position of the interface and is deeper for the layer which moves towards the high kinetic energy side of the system. In three dimensions, the two intermittent layers propagate nearly symmetrically with respect the centre of the mixing region. During the temporal decay, inside the mixing, which is both inhomogeneous and anisotropic but devoid of a mean velocity shear, the passive scalar spectra are computed. In three dimensions, the exponent in the scaling range gets in time a value close to that of the kinetic energy spectrum of isotropic turbulence (?5/3). In two dimensions, instead the exponent settles down to a value that is about one-half of the corresponding isotropic case. By means of an analysis based on simple wavy perturbations of the interface we show that the formation of the double layer of intermittency is a dynamic general feature not specific to the turbulent transport. These results of our numerical study are discussed in the context of experimental results and numerical simulations.     

Dirac quasinormal modes of <Emphasis Type="Italic">D</Emphasis>-dimensional de Sitter spacetime

We find exact solutions to the Dirac equation in D-dimensional de Sitter spacetime. Using these solutions we analytically calculate the de Sitter quasinormal (QN) frequencies of the Dirac field. For the massive Dirac field this computation is similar to that previously published for massive fields of half-integer spin moving in four dimensions. However to calculate the QN frequencies of the massless Dirac field we must use distinct methods in odd and even dimensions, therefore the computation is different from that already known for other massless fields of integer spin.     

Charge and/or spin limits for black holes at a non-commutative scale

We study the cosmological dynamics for R ^p exp(λ R) gravity theory in the metric formalism, using dynamical systems approach. Considering higher-dimensional FRW geometries in case of an imperfect fluid which has two different scale factors in the normal and extra dimensions, we find the exact solutions, and study its behaviour and stability for both vacuum and matter cases. It is found that stable solutions corresponding to accelerated expansion at late times exist, which can describe the inflationary era of the Universe. We also study the evolution of scale factors both in the normal and extra dimensions for different values of anisotropy parameter and the number of extra dimensions for such a scenario.