A Dynamical Systems Approach to Geodesics in Bianchi Cosmologies

To understand the observational properties of cosmological models, in particular, the temperature of the cosmic microwave background radiation, it is necessary to study their null geodesics. Dynamical systems theory, in conjunction with the orthonormal frame approach, has proved to be an invaluable tool for analyzing spatially homogeneous cosmologies. It is thus natural to use such techniques to study the geodesics of these models. We therefore augment the Einstein field equations with the geodesic equations, all written in dimensionless form, obtaining an extended system of first-order ordinary differential equations that simultaneously describes the evolution of the gravitational field and the behavior of the associated geodesics. It is shown that the extended system is a powerful tool for investigating the effect of spacetime anisotropies on the temperature of the cosmic microwave background radiation, and that it can also be used for studying geodesic chaos.     

Minimally Coupled FRW Cosmologies as Dynamical Systems

The dynamical evolution of FRW cosmologies, minimally coupled to a finite set of scalar fields with an arbitrary potential, is studied. The general properties of the scale factor and the scalar fields, which are independent of the potential, are determined. It is shown that for k = 0, −1 the evolution of the Hubble function is growing, independently of thepotential, which allows expansive and contractive evolutions of the scale factor. Moreover, if the potential can take negative values, cyclic universes are possible. In the spherical geometry case, k = 1, the existence of expansive, contractive, or cyclic, universes is possible, independently of the condition stated above, namely that the potential would necessarily take negative values. Moreover, the existence of chaotic solutions can be obtained via a fine-tuning.     

Assisted Inflation in Bianchi VI0 Cosmologies

Exact models for Bianchi VI₀ spacetimes with multiple scalar fields with exponential potentials have been derived and analysed. It has been shown that these solutions, when they exist, attract neighbouring solutions in the two cases corresponding to interacting and non-interacting fields. Unlike the results obtained in a previous work dealing with the late-time inflationary behaviour of Bianchi VI₀ cosmologies, the knowledge of exact solutions has made possible to study in detail the occurrence of inflation before the asymptotic regime. As happened in preceding works, here as well inflation is more likely to happen with a higher number of non-interacting fields or a lower number of interacting scalar fields.     

Geodesics in a Quash-Spherical Spacetime: A Case of Gravitational Repulsion

No Heading Geodecis are studied in one of the Weyl metrics, referred to as the M-Q solution. First, arguments are provided, supporting our belief that this space-time is the more suitable (among the known solutions of the Weyl family) for discussing the properties of strong quasi-spherical gravitational fields. Then, the behaviour of geodesics is compared with the spherically symmetric situation, bringing out the sensitivity of the trajectories to deviations from spherical symmetry. Particular attention deserves the change of sign in proper radial acceleration of test particles moving radially along symmetry axis, close to the r = 2M surface, and related to the quadrupole moment of the source.     

Bianchi A Cosmological Models as the Simplest Dynamical Systems in R4

The behaviour of the vacuum non-tilted Bianchimodels of class A is studied in terms of dynamicalsystems theory. We introduce phase variables in whichthe Hamiltonian constraint is solved algebraically. It is shown that in these variables BianchiVIII and Bianchi IX models assume the form of afour-dimensional autonomous system with a polynomialvector field defined on the phase space, whereas Bianchi I and Bianchi II world models can be presentedas a one- and two-dimensional system, respectively. TheBianchi VI₀ and Bianchi VII₀ worldmodels are represented as a three-dimensional dynamicalsystem.     

Stochastic Perturbations to Dynamical Systems: A Response Theory Approach

Using the formalism of the Ruelle response theory, we study how the invariant measure of an Axiom A dynamical system changes as a result of adding noise, and describe how the stochastic perturbation can be used to explore the properties of the underlying deterministic dynamics. We first find the expression for the change in the expectation value of a general observable when a white noise forcing is introduced in the system, both in the additive and in the multiplicative case. We also show that the difference between the expectation value of the power spectrum of an observable in the stochastically perturbed case and of the same observable in the unperturbed case is equal to the variance of the noise times the square of the modulus of the linear susceptibility describing the frequency-dependent response of the system to perturbations with the same spatial patterns as the considered stochastic forcing. This provides a conceptual bridge between the change in the fluctuation properties of the system due to the presence of noise and the response of the unperturbed system to deterministic forcings. Using Kramers-Kronig theory, it is then possible to derive the real and imaginary part of the susceptibility and thus deduce the Green function of the system for any desired observable. We then extend our results to rather general patterns of random forcing, from the case of several white noise forcings, to noise terms with memory, up to the case of a space-time random field. Explicit formulas are provided for each relevant case analysed. As a general result, we find, using an argument of positive-definiteness, that the power spectrum of the stochastically perturbed system is larger at all frequencies than the power spectrum of the unperturbed system. We provide an example of application of our results by considering the spatially extended chaotic Lorenz 96 model. These results clarify the property of stochastic stability of SRB measures in Axiom A flows, provide tools for analysing stochastic parameterisations and related closure ansatz to be implemented in modelling studies, and introduce new ways to study the response of a system to external perturbations. Taking into account the chaotic hypothesis, we expect that our results have practical relevance for a more general class of system than those belonging to Axiom A.     

The Apparent Fractal Conjecture: Scaling Features in Standard Cosmologies

This paper presents an analysis of the smoothness problem in cosmology by focussing on the ambiguities originated in the simplifying hypotheses aimed at observationally verifying if the large-scale distribution of galaxies is homogeneous, and conjecturing that this distribution should follow a fractal pattern, in the sense of having a power-law type average density profile, in perturbed standard cosmologies. This is due to a geometrical effect, appearing when certain types of average densities are calculated along the past light cone. The paper starts by reviewing the argument concerning the possibility that the galaxy distribution follows such a scale invariant pattern, and the premises behind the assumption that the spatial homogeneity of standard cosmology can be observable. Next, it is argued that in order to discuss observable homogeneity one needs to make a clear distinction between local and average relativistic densities, and showing how the different distance definitions strongly affect them, leading the various average densities to display asymptotically opposite behaviours. Then the paper revisits Ribeiro's (1995) results, showing that in a fully relativistic treatment some observational average densities of the flat Friedmann model are not well defined at z 0.1, implying that at this range average densities behave in a fundamentally different manner as compared to the linearity of the Hubble law, well valid for z < 1. This conclusion brings into question the widespread assumption that relativistic corrections can always be neglected at low z. It is also shown how some key features of fractal cosmologies can be found in the Friedmann models. In view of those findings, it is suggested that the so-called contradiction between the cosmological principle, and the galaxy distribution forming an unlimited fractal structure, may not exist.     

Variable Separation Approach to Solve Nonlinear Systems

The variable separation approach method is very useful to solving (2 1 )-dimensional integrable systems. But the (1 1)-dimensional and (3 1 )-dimensional nonlinear systems are considered very little. In this letter, we extend this method to (1 1) dimensions by taking the Redekopp system as a simple example and (3 1)-dimensional Burgers system. The exact solutions are much general because they include some arbitrary functions and the form of the (3 1 )-dimensional universal formula obtained from many (2 1 )-dimensional systems is extended.     

Variable Separation Approach to Solve Nonlinear Systems

The variable separation approach method is very useful to solving (2 1)-dimensional integrable systems.But the (1 1)-dimensional and (3 1)-dimensional nonlinear systems are considered very little. In this letter, we extend this method to (1 1) dimensions by taking the Redekopp system as a simp!e example and (3 1)-dimensional Burgers system. The exact solutions are much general because they include some arbitrary functions and the form of the (3 1)-dimensional universal formula obtained from many (2 1)-dimensional systems is extended.     

The Self-Induced Approach to Decoherence in Cosmology

In this paper we will present the self-induced approach to decoherence, which does not require the interaction between the system and the environment: decoherence in closed quantum systems is possible. This fact has relevant consequences in cosmology, where the aim is to explain the emergence of classicality in the universe conceived as a closed (noninteracting) quantum system. In particular, we will show that the self-induced approach may be used for describing the evolution of a closed quantum universe, whose classical behavior arises as a result of decoherence.     

A Non-Euler-Lagrangean Approach to Variational Guided-Wave Optics

The variationality of a weak-form relation for solving guided-mode problems in linear graded-index media is shown to be provable in an intuitive fashion. A connection with variational crimes is discussed.     

Glafka 2004: The Decoherent Histories Approach to the Quantization of Cosmological Models

The decoherent histories approach is a particularly useful approach to quantum theory especially when time enters in a non-trivial way, or indeed, when there is no physical time coordinate at all, as is the case in quantum cosmology. Here, attempts to apply the decoherent histories approach to quantum cosmology are described.     

A Lattice-Based Approach to Percolation in Penetrable Sphere Systems

An heuristic mapping is presented that enables analysis of continuum percolation by penetrable spheres in terms of an analogous lattice model. The resulting framework is based upon the well-known Bethe lattice, which is modified by the inclusion of an adjustable proportion of fully connected subgraphs that provide a particularly simple, albeit operational, vehicle for modeling the effect of inter-particle clustering. The volume fraction at the percolation threshold is calculated as a function of (i) the degree of interpenetrability amongst the spheres, and: (ii) the extent of particle clustering, and the results are compared with findings from Monte Carlo (MC) simulations of this problem. It is found that a suitably chosen ansatz that reflects a monotonic increase in the degree of clustering with increasing inter-sphere penetrability leads to close agreement between percolation thresholds calculated using the present approach and the results of MC simulations.     

New Approach to Cluster Synchronization in Complex Dynamical Networks

In this paper, a distributed control strategy is proposed to make a complex dynamical network achieve cluster synchronization, which means that nodes in the same group achieve the same synchronization state, while nodes in different groups achieve different synchronization states. The local and global stability of the cluster synchronization state are analyzed. Moreover, simulation results verify the effectiveness of the new approach.     

A Closed-System Approach to Quantum Retrodiction in Open Systems

Ban (Int. J. Theor. Phys. 46:184, 2007) has shown how retrodictive open systems evolution may be treated as unitary using non-equilibrium thermo field dynamics. Here we describe the application of another technique with the same purpose, Fano diagonalisation.     

A New Asymptotic Approach to Solve Nonlinear Evolution Equations

A conformal-invariant asymptotic expansion approach to solve any nonlinear integrable and nonintegrable models with any dimensions is proposed. Taking the compound KdV-Burgers (cKdVB) equation and the KdV-Burgers (KdVB) equation as concrete examples,we obtain many new conformal-invariant models with Painleve' property and the approximate solutions of the cKdVB and KdVB equations. In some special cases, the approximate solutions become exact.     

f(R) theories of gravity in the Palatini approach matched with observations

We investigate the viability of f(R) theories in the framework of the Palatini approach as solutions to the problem of the observed accelerated expansion of the universe. Two physically motivated popular choices for f(R) are considered,: power law, f(R) = β R ⁿ , and logarithmic, f(R) = α ln R. Under the Palatini approach, both Lagrangians give rise to cosmological models comprising only standard matter and undergoing a present phase of accelerated expansion. We use the Hubble diagram of type Ia Supernovae and the data on the gas mass fraction in relaxed galaxy clusters to see whether these models are able to reproduce what is observed and to constrain their parameters. It turns out that they are indeed able to fit the data with values of the Hubble constant and of the matter density parameter in agreement with some model independent estimates, but the today deceleration parameter is higher than what is measured in the concordance ΛCDM model.     

一种提高轨道精度的改进姿态控制技术

针对我国长征系列火箭普遍存在的残骸落点普遍较理论落点靠前的现象,开展多次飞行数据的比较,结果发现一级上升段内火箭的飞行速度、位置与设计预示值之间的偏差存在极性稳定、幅值增加增大的特点,尤其是Y向速度偏差甚至超过5%,远大于预期值;本文针对该现象开展机理分析,最终确认现在长征系列火箭普遍采用的“姿态角偏差+角速度”控制方案对程序角持续变化的工况存在幅值及极性较为稳定的静差,该角偏差持续作用下,将导致X向和Y向速度及位置偏差;针对该机理,探索、比较潜在的解决措施,最终确定采用实现简便、控制效果好的“姿态角偏差+角速度偏差”双偏差姿态控制方案;仿真结果表明,双偏差姿态控制方案能显著提高助残骸落点精度及段轨道精度、降低气动载荷,有利于火箭飞行品质的提升。     

基于级联方程的量子耗散半经典方法

We present a semiclassical (SC) approach for quantum dissipative dynamics, constructed on basis of the hierarchical-equation-of-motion (HEOM) formalism. The dynamical components considered in the developed SC-HEOM are wavepackets'' phase-space moments of not only the primary reduced system density operator but also the auxiliary density operators (ADOs) of HEOM. It is a highly numerically efficient method, meanwhile taking into account the high-order effects of system-bath couplings. The SC-HEOM methodology is exemplified in this work on the hierarchical quantum master equation[J. Chem. Phys. 131, 214111 (2009)] and numerically demonstrated on linear spectra of anharmonic oscillators.     

Dynamical Running Mass of Quark in the Dyson-Schwinger Equation Approach

Based on the Dyson-Schwinger equations of QCD in the "rainbow" approximation, the fully dressed quarkpropagator Sf(p) is investigated, and then an algebraic parametrization form of the propagator is obtained as a solutionof the equations. The dressed quark amplitudes Af and Bf built up the fully dressed quark propagator and the dynamicalrunning masses Mf defined by Af and Bf for light quarks u, d and s are calculated, respectively. Using the predictedrunning masses Mf, quark condensates <0|q(0)q(0)|0> = -(0.255 GeV)a for u, d quarks, and <0|s s|0> = 0.8<0|q(0)q(0)]0)for s quark, and experimental pion decay constant fπ = 0.093 GeV, the masses of Goldstone bosons K, π, and η are alsoevaluated. The numerical results show that the masses of quarks are dependent on their momentum p2. The fully dressedquark amplitudes Af and Bf have correct behaviors which can be used for many purposes in our future researches onnonperturbative QCD.