An inequality connecting entropy distance,Fisher Information and large deviations

In this paper we introduce a new generalisation of the relative Fisher Information for Markov jump processes on a finite or countable state space, and prove an inequality which connects this object with the relative entropy and a large deviation rate functional. In addition to possessing various favourable properties, we show that this generalised Fisher Information converges to the classical Fisher Information in an appropriate limit. We then use this generalised Fisher Information and the aforementioned inequality to qualitatively study coarse-graining problems for jump processes on discrete spaces.     

超强频率梳激光场驱动下多光子共振谐波辐射的相位突变研究

本文从理论上研究了在双色频率梳激光场驱动下多光子谐波辐射光谱中的相位突变现象。我们利用Floquet理论非微扰地模拟了频率梳激光场与原子分子等量子系统的相互作用过程。谐波辐射信号是多光子偶极跃迁相干叠加的结果,通过调节频率梳激光场间的相对相位,可以相干地控制谐波辐射信号的强度。通过对谐波信号进行傅里叶变换,可以提取不同跃迁路径的相对相位信息。我们通过改变频率梳组激光场的强度和频率组分实现多光子跃迁频率,让其跨越共振跃迁频率时,谐波相位会发生突变。从而可以观测超强激光场驱动下量子系统共振跃迁频率的斯塔克能移。     

Transition probabilities of Lévy‐type processes: Parametrix construction

We present an existence result for Lévy‐type processes which requires only weak regularity assumptions on the symbol with respect to the space variable x. Applications range from existence and uniqueness results for Lévy‐driven SDEs with Hölder continuous coefficients to existence results for stable‐like processes and Lévy‐type processes with symbols of variable order. Moreover, we obtain heat kernel estimates for a class of Lévy and Lévy‐type processes. The paper includes an extensive list of Lévy(‐type) processes satisfying the assumptions of our results.     

Physics-based plasticity model incorporating microstructure changes for severe plastic deformation

During machining processes, materials undergo severe deformations that lead to different behavior than in the case of slow deformation. The microstructure changes, as a consequence, affect the materials properties and therefore influence the functionality of the component. Developing material models capable of capturing such changes is therefore critical to better understand the interaction process–materials. In this paper, we introduce a new physics model associating Mechanical Threshold Stress (MTS) with Dislocation Density (DD) models. The modeling and the experimental results of a series of large strain experiments on polycrystalline copper (OFHC) involving sequences of shear deformation and strain rate (varying from quasi-static to dynamic) are very similar to those observed in processes such as machining. The Kocks–Mecking model, using the mechanical threshold stress as an internal state variable, correlates well with experimental results and strain rate jump experiments. This model was compared to the well-known Johnson–Cook model that showed some shortcomings in capturing the stain jump. The results show a high effect of rate sensitivity of strain hardening at large strains. Coupling the mechanical threshold stress dislocation density (MTS–DD), material models were implemented in the Abaqus/Explicit FE code. The model shows potentialities in predicting an increase in dislocation density and a reduction in cell size. It could ideally be used in the modeling of machining processes.     

Existence and uniqueness of perturbed reflected jump diffusion processes

In this article, we establish the existence of the solution to the càdlàg perturbed Skorohod problem. As an application, we obtain the existence and uniqueness of the solution to the perturbed reflected jump diffusion processes.     

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In this paper, we extend the previous Markov-modulated reflected Brownian motion model discussed in [1] to a Markov-modulated reflected jump diffusion process, where the jump component is described as a Markov-modulated compound Poisson process. We compute the joint stationary distribution of the bivariate Markov jump process. An abstract example with two states is given to illustrate how the stationary equation described as a system of ordinary integro-differential equations is solved by choosing appropriate boundary conditions. As a special case, we also give the sationary distribution for this Markov jump process but without Markovian regime-switching.     

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In this paper, the asymptotic behavior of the weak solution (u_t)_{t\ge0} to the non-local Cauchy problems as stated in (1) is considered. Only using lower bounds of jumping kernel J(x,y) for large |x-y|, it is obtained that \|u_t\|_p\le c(t)\|u_0\|_q with any 1\le q相似文献   

Resilient dissipative dynamic output feedback control for uncertain Markov jump Lur’e systems with time-varying delays

The resilient dissipative dynamic output feedback control problem for a class of uncertain Markov jump Lur’e systems with piecewise homogeneous transition probabilities and time-varying delays in the discrete-time domain are examined in this study. The designed controller can tolerate additive uncertainties in the controller gain matrix, which result from controller implementations. The time-varying delays are also supposed to be mode-dependent with lower and upper bounds known a priori. By constructing a Lyapunov–Krasovskii functional candidate, the sufficient conditions regarding the existence of desired resilient dissipative controllers are obtained in terms of linear matrix inequalities, thereby ensuring that the resulting closed-loop system is stochastically stable and strictly dissipative. Two numerical examples were established to illustrate the effectiveness of the proposed theoretical results.