Moderate deviations for martingale differences and applications to φ -mixing sequences

For a R d -valued sequence of martingale differences { m k } k S 1 , we obtain a moderate deviation principle for the sequence of partial sums { Z n ( t ) 1 ~ k =1 [ nt ] m k / b n , t ] [0,1]}, in the space of càdlàg functions equipped with the Skorohod topology, under the following conditions: a Chen-Ledoux type condition, an exponential convergence in probability of the associated quadratic variation process of the martingale, and a condition of "Lindeberg" type. For the small jumps of Z n (·), we apply the general result of Puhalskii [Puhalskii, A. (1994). "Large deviations of semimartingales via convergence of the predictable characteristics". Stoch. Stoch. Rep. , 49 , pp. 27-85]. Following the method of Ledoux [Ledoux, M. (1992). "Sur les déviations modérées des sommes de variables aléatoires vectorielles indépendantes de même loi". Ann. Inst. H. Poincaré , 28 , pp. 267-280] and Arcones [Arcones, A. (1999). "The large deviation principle for stochastic processes", Submitted for publication], we prove that the large jumps part of Z n (·) is negligible in the sense of the moderate deviations. One can regard our result as an extension to martingale differences, of the beautiful characterization of moderate deviations for i.i.d.r.v. case due to Chen [Chen, X. (1991). "The moderate deviations of independent vectors in Banach space". Chin. J. Appl. Probab. Stat. , 7 , pp. 124-32] and Ledoux [Ledoux, M. (1992). "Sur les déviations modérées des sommes de variables aléatoires vectorielles indépendantes de même loi". Ann. Inst. H. Poincaré , 28 , pp. 267-280]. Using the Gordin [Gordin, M.I. (1969). "The central limit theorem for stationary processes". Soviet Math. Dokl. , 10 , pp. 1174-1176] decomposition, the martingale result is applied to prove the moderate deviation principle for a wide class of stationary { -mixing sequences of random variables.     

Random doubly stochastic tridiagonal matrices

Let \begin{align*}{\mathcal T}\end{align*}n be the compact convex set of tridiagonal doubly stochastic matrices. These arise naturally in probability problems as birth and death chains with a uniform stationary distribution. We study ‘typical’ matrices T∈ \begin{align*}{\mathcal T}\end{align*}n chosen uniformly at random in the set \begin{align*}{\mathcal T}\end{align*}n. A simple algorithm is presented to allow direct sampling from the uniform distribution on \begin{align*}{\mathcal T}\end{align*}n. Using this algorithm, the elements above the diagonal in T are shown to form a Markov chain. For large n, the limiting Markov chain is reversible and explicitly diagonalizable with transformed Jacobi polynomials as eigenfunctions. These results are used to study the limiting behavior of such typical birth and death chains, including their eigenvalues and mixing times. The results on a uniform random tridiagonal doubly stochastic matrices are related to the distribution of alternating permutations chosen uniformly at random.© 2012 Wiley Periodicals, Inc. Random Struct. Alg., 42, 403–437, 2013     

Lüders deformation and superplastic flow of metals extruded by KOBO method

The work brings the results of the study on mechanical properties of some metallic materials subjected to very large plastic deformation by KOBO extrusion. The unexpected features of the KOBO products like Lüders deformation in pure metals and superplastic flow in coarse grain materials are discussed in terms of micro- and nano-scale elements of their structure. The choice to the experiment materials having different crystallographic and phase structure (commercial purity aluminium, multiphase aluminium 7075 alloy, pure zinc and multiphase magnesium AZ91 alloy) and different history (extrusion, casting) allowed to identify the common nano-size elements of the structure generated during the KOBO deformation which seems to be responsible for the mechanical behaviour of these materials. In particular, clusters of point defects (self-interstitials) formed under the KOBO extrusion conditions (cyclic change in the deformation path, high hydrostatic pressure) were found in these materials regardless of grain size and material early history. They correlate with appearance of unstable Lüders-like or even Portevin–LeChatelier deformation at ambient and superplastic flow at elevated temperatures.     

Critical dynamics associated with dynamic disordering near the depinning transition in different vortex phases

We study a depinning transition based on transient dynamics of vortices driven by a suddenly applied dc current, focusing on whether a difference in the equilibrium vortex phase that can lead to a different vortex flow will change the critical behavior. After preparing an ordered initial vortex configuration, we measure the time evolution of voltage associated with dynamic disordering in three magnetic fields, corresponding to the ordered phase (OP), disordered phase (DP), and coexistence phase. The critical behavior of the depinning transition is commonly observed in these phases, pointing to the universality of the transition. However, the critical behavior is most marked in the coexistence phase, while the suppression of the critical region and that of dynamic disordering are observed in OP and DP, respectively, whose origin is attributed to the different flow states among these phases.     

Soft mode dispersion and ‘waterfall’ phenomenon in relaxors revisited

Results of recent inelastic neutron scattering studies of lead-based relaxor ferroelectrics by Gvasaliya et al. [J. Phys.: Condens. Matter 17, 4343 (2005); J. Phys.: Condens. Matter 19, 016219 (2007)] have put in question the existence of the “waterfall” anomaly–an apparent vertical dispersion segment joining the TA and TO branches–observed earlier in low-energy [ξ00] phonon dispersion curves of these materials. In the present article, we review the results of earlier experiments and model calculations together with the outcome of our recent measurements on PMN using the same instrumental set-up as Gvasaliya et al. to conclude that the “waterfall” feature is not an experimental artefact. We also give some hints on a possible explanation of the results of Gvasaliya et al., by exploring the fact that the reported dispersion of the underdamped transverse optic branch follows the longitudinal acoustic (LA) branch dispersion surprisingly closely.     

Routes to bursting in a periodically driven oscillator

The dynamical behaviors of a periodic excited oscillator with multiple time scales in the form that order gap exists between the frequency of the excitation and the natural frequency, are investigated in this Letter. By regarding the whole excitation term as a parameter, bifurcation sets are derived, which divide the generalized parameter space into several regions corresponding to different kinds of dynamics. Different types of bursting phenomena, such as fold/Hopf bursting, fold/Hopf/homoclinic bursting and Hopf/homoclinic bursting, are presented, the mechanism of which is obtained based on the bifurcations of the generalized autonomous system as well as the introduction of the so-called transformed phase portraits. Furthermore, the evolution of the bursting is discussed in details, in which one may find that when the two limit cycles caused by the Hopf bifurcations of the two related equilibrium points interact with each other, homoclinic bifurcation may occur, leading to the merge of the two cycles to form a large amplitude cycle. The homoclinic bifurcation may cause the two asymmetric bursters to merge into a symmetric enlarged burster, in which the large amplitude of the spiking state agrees well with the amplitude of the cycle caused by the homoclinic bifurcation.     

Dissociation of deuteron, <Superscript>6</Superscript>He and <Superscript>11</Superscript>Be from Coulomb dissociation reaction cross-section

The fragmentation of deuteron, ⁶He and ¹¹Be have been studied during interaction with the ²⁰⁸Pb nucleus at various projectile energies. The Coulomb dissociation cross-sections and the momentum distribution of the break-up fragments have been analysed within the framework of the direct fragmentation model. The post-acceleration effect of deuteron during break-up and the halo structures of both the ⁶He and ¹¹Be have been investigated.      

System Size Resonance Associated with Canard Phenomenon in a Biological Cell System

通过研究发现,内噪声对细胞内钙振荡是有影响的,当体系处于由确定性方程所确定的稳定区域时,如果考虑内噪声的作用,就会有随机的钙振荡发生. 并且这种振荡的行为随着体系尺度的变化出现两个最大值,表明了尺度共振现象的发生. 这种行为是与体系的Canard现象密切相关的. 最佳的体系尺度与真实的细胞体积是相吻合的,并且这种吻合基本不随控制参数的改变而改变.