Homogeneous rotating universe with flat space

The homogeneous, anisotropic cosmological model is considered. It satisfies three physically reasonable conditions: it is space homogeneous, possesses flat space like sections and is filled with expanding, rotating and shearing matter. The asymptotic solution is presented and general properties are discussed. The question how the rotation influences the behaviour of matter near the singularity is investigated.     

The history of star formation in the universe

Our primary means of studying how galaxies form and evolve over cosmic time is through measurements of the rate at which massive stars are born in galaxies per unit comoving volume of the universe. Only recently have the most distant, most massively star-forming galaxies in the universe even been discovered, and these discoveries are challenging the standard cosmological scenario in which galaxies form hierarchically, with low-mass objects collapsing first and then merging to form larger and larger systems over cosmic time. We now know that these incredibly luminous galaxies, which have all but vanished in the local universe, are cocooned in dust, hiding them from optical view. They can only be detected at long wavelengths where the dust reradiates the starlight that it has absorbed. In this review, I trace the spectacular progress that has been made over the last decade towards understanding the cosmic history of star formation, with a particular emphasis on the important role of dusty sources in that history.     

Statevector reduction in discrete time: A random walk in Hilbert space

A simple model is presented in which the statevector evolves every seconds in one of two ways, according to a particular probability rule. It is shown that this random walk in Hilbert space results in reduction of the statevector. It is also shown how the continuous spontaneous localization (CSL) theory of statevector reduction is achieved as a limiting case of this model, exactly as Brownian motion is a limiting case of ordinary random walk. Finally, a slightly different but completely equivalent form of the CSL equations suggested by the simple model given here is discussed.     

Phase space analysis for anisotropic universe with nonlinear bulk viscosity

In this paper, we discuss phase space analysis of locally rotationally symmetric Bianchi type I universe model by taking a noninteracting mixture of dust like and viscous radiation like fluid whose viscous pressure satisfies a nonlinear version of the Israel–Stewart transport equation. An autonomous system of equations is established by defining normalized dimensionless variables. In order to investigate stability of the system, we evaluate corresponding critical points for different values of the parameters. We also compute power-law scale factor whose behavior indicates different phases of the universe model. It is found that our analysis does not provide a complete immune from fine-tuning because the exponentially expanding solution occurs only for a particular range of parameters. We conclude that stable solutions exist in the presence of nonlinear model for bulk viscosity with different choices of the constant parameter m for anisotropic universe.     

A physical model for dimensional reduction and its effects on the observable parameters of the universe

We construct a physical model to study the effects of dimensional reduction that might have taken place during the inflationary phase of the universe. The model we propose is a (1 + D)-dimensional (D > 3), nonsingular, spatially homogeneous and isotropic Friedmann model. We consider dimensional reduction to take place in a stepwise manner and interpret each step as a phase transition. Independent of the details of the process of dimensional reduction, we impose suitable boundary conditions across the transitions and trace the effects of dimensional reduction to the currently observable parameters of the universe. In order to exhibit the cosmological features of the proposed model, we construct a (1 + 4)-dimensional toy model for both closed and open cases of Friedmann geometries. It is shown that in these models the universe makes transition into the lower dimension when the critical length parameter l _4,3, which signals dimensional reduction, reaches the Planck length in D = 3. The numerical models we present in this paper have the capability of making definite predictions about the cosmological parameters of the universe such as the Hubble parameter, age and density.     

Primordial black hole formation by stabilized embedded strings in the early universe

Primordial black hole formation by cosmic string collapses is reconsidered in the case where the winding number of the string is larger than unity. The line energy density of a multiple winding string becomes greater than that of a single winding string so that the probability of black hole formation by string collapse during loop oscillation would be strongly enhanced. Moreover, this probability could be affected by changes in gravity theory due to large extra dimensions based on the brane universe model. In addition, a wider class of strings which are stable compared to conventional cosmic strings can contribute to such a scenario. Although the production of the multiple winding defect is suppressed and its number density should be small, the enhancement of black hole formation by the increased energy density may provide a large number of evaporating black holes in the present universe which gives more stringent constraints on the string model compared to the ordinary string scenario.     

Magnetic field correlation tensor in a universe with a multiply connected space section

The concept of statistical homogeneity and isotropy for vector fields for cosmological models with multiply connected space sections is analyzed. Considering a flat 3D torus as an example, it is shown that the correlation tensor of a statistically homogeneous and isotropic (locally) solenoidal vector field in this case depends on a countable set of functions corresponding to various classes of geodesics connecting the points in which the tensor is calculated. In contrast, such a tensor in a simply connected Universe depends on just one function.     

The time response of structures with bounded parameters and interval initial conditions

Uncertainty plays an important role in the performance of structures. In this paper, we focus on the dynamic response of structures with bounded parameters and interval initial conditions, and present a new method to determine the supremum and infimum of the time response. The method is based on the vertex solution theorem for the first-order deviation of the dynamic response from its central value and avoids interval extension problems present in current methods, where the length of the interval increases significantly due to the intermediate calculations. The method is more accurate than existing perturbation methods and provides tighter bounds on the response. The approach neglects the second-order terms in the equation of motion, and care should be exercised when the parameter variations are large. The other advantage of this method is its ability to solve problems with uncertainties in the initial conditions.     

Towards localisation by Gaussian random potentials in multi-dimensional continuous space

A rigorous proof is outlined to exclude the absolutely continuous spectrum at sufficiently low energies for a quantum-mechanical particle moving in multi-dimensional Euclidean space under the influence of certain Gaussian random potentials, which are homogeneous with respect to Euclidean translations.     

Model building by coset space dimensional reduction in eight-dimensions

We investigate gauge-Higgs unification models in eight-dimensional spacetime where extra-dimensional space has the structure of a four-dimensional compact coset space. The combinations of the coset space and the gauge group in the eight-dimensional spacetime of such models are listed. After the dimensional reduction of the coset space, we identified SO(10)$\mathrm{SO}(10)$, SO(10)×U(1)$\mathrm{SO}(10)\times \mathrm{U}(1)$ and SO(10)×U(1)×U(1)$\mathrm{SO}(10)\times \mathrm{U}(1)\times \mathrm{U}(1)$ as the possible gauge groups in the four-dimensional theory that can accomodate the Standard Model and thus is phenomenologically promising. Representations for fermions and scalars for these gauge groups are tabulated.     

The formation of primary galactic nuclei during phase transitions in the early universe

A new mechanism describing the formation of protogalaxies is proposed, based on the second-order phase transition in the inflation stage and the domain wall formation upon the end of inflation. The presence of closed domain walls with the size markedly exceeding the cosmological horizon at the instant of their formation and the wall collapse in the postinflation epoch (when the wall size becomes comparable with the cosmological horizon) lead to the formation of massive black hole clusters that can serve as nuclei for the future galaxies. The black hole mass distributions obtained do not contradict the available experimental data. The number of black holes with M ～ 100 solar masses (M _⊙) and above is comparable with the number of galaxies in the visible Universe. Development of the proposed approach gives grounds for a principally new scenario of galaxy formation in the model of a hot Universe.     

Dynamics of the Manakov-typed bound vector solitons with random initial perturbations

Dynamics of the bound vector solitons with random initial perturbations is investigated for the Manakov model, which describes the propagation of the multimode soliton pulses in nonlinear fiber optics and two-component matter-wave solitons in the quasi-one-dimensional Bose–Einstein condensates (BECs) without confining potential. We review the analytic two-bound-vector-soliton solutions and give the three-bound-vector-soliton solutions. Breakup of the typical bound state is presented numerically when the symmetry and asymmetry random perturbations are added to the initial conditions. Relationship between the lifetime of the bound state and amplitude of the random perturbation is discussed. Meanwhile, existence of the symmetry-recovering is illustrated for the bound vector solitons with the asymmetry random perturbations. Discussions of this paper could be expected to be helpful in interpreting the dynamics of the Manakov-typed bound vector solitons when the random initial noises in nonlinear optical fibers or stochastic quantum fluctuations in the BECs are considered.     

非线性强度任意二聚的非线性链的透射性质

用离散的非线性薛定谔的递推关系研究了非线性强度任意二聚的非线性链的透射性质. 结果表明该链存在一个共振透射态,共振态的能量为非线性强度与入射波振幅模平方的乘积; 取出射波振幅为定值和取入射波振幅模为定值来计算透射系数,其结果在非共振态有明显的差别: 取出射波振幅为定值时电子的透射随能量为单值函数,而取入射波振幅模为定值时电子的透射呈现多稳态. 并指出只有取入射波振幅模为定值时才能真正反映非线性强度对电子透射性质的影响.     

Impact of initial lattice structures on networks generated by traces of random walks

We show that the platform stage of network evolution plays a principal role in the topology of resulting networks generated by short-cuts stimulated by the movements of a random walker, the mechanism of which tends to produce power-law degree distributions. To examine the numerical results, we have developed a statistical method which relates the power-law exponent γ to random properties of the subgraph developed in the platform stage. As a result, we find that an important exponent in the network evolution is α, which characterizes the size of the subgraph in the form V∼t^α, where V and t denote the number of vertices in the subgraph and the time variable, respectively. 2D lattices can impose specific limitations on the walker’s diffusion, which keeps the value of α within a moderate range and provides typical properties of complex networks. 1D and 3D cases correspond to different ends of the spectrum for α, with 2D cases in between. Especially for 2D square lattices, a discontinuous change of the network structure is observed, which varies according to whether γ is greater or less than 2. For 1D cases, we show that emergence of nearly complete subgraphs is guaranteed by α<1/2, although the transient power-law is permitted at low increase rates of edges. Additionally, the model exhibits a spontaneous emergence of highly clustered structures regardless of its initial structure.     

Brake squeal reduction of vehicle disc brake system with interval parameters by uncertain optimization

An uncertain optimization method for brake squeal reduction of vehicle disc brake system with interval parameters is presented in this paper. In the proposed method, the parameters of frictional coefficient, material properties and the thicknesses of wearing components are treated as uncertain parameters, which are described as interval variables. Attention is focused on the stability analysis of a brake system in squeal, and the stability of brake system is investigated via the complex eigenvalue analysis (CEA) method. The dominant unstable mode is extracted by performing CEA based on a linear finite element (FE) model, and the negative damping ratio corresponding to the dominant unstable mode is selected as the indicator of instability. The response surface method (RSM) is applied to approximate the implicit relationship between the unstable mode and the system parameters. A reliability-based optimization model for improving the stability of the vehicle disc brake system with interval parameters is constructed based on RSM, interval analysis and reliability analysis. The Genetic Algorithm is used to get the optimal values of design parameters from the optimization model. The stability analysis and optimization of a disc brake system are carried out, and the results show that brake squeal propensity can be reduced by using stiffer back plates. The proposed approach can be used to improve the stability of the vehicle disc brake system with uncertain parameters effectively.     

The quickest detection of jump-like variations in parameters of random processes

We have formulated the rules for determining optimal stop times for various functions of losses in the problem of the quickest detection of jump-like variation in signal parameters in continuous time. We have found expressions for the functions of a posteriori losses. It is shown that to solve the problem of the quickest detection of detuning one can use the algorithms for optimal r.m.s. estimation of the jump appearance time. N. I. Lobachevskii State University, Nizhny Novgorod, Russia. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 40, No. 10, pp. 1260–1276, October, 1997.