Banach空间二阶非线性微分方程的弱Carathéodory解

本文定义了二阶微分方程的弱 Carathéodory解 ,在不涉及紧型条件的情形下 ,直接用迭代法证明了 Banach空间二阶非线性常微分方程两点边值问题存在唯一解 ,并给出逼近解迭代序列的误差估计 ,对周期边值问题得到类似的结果     

一类广义Liénard系统解的有界性

研究了一类广义 Liénard系统dxdt=p(y) -F(x) ,　 dydt=-g(x) (E)解的有界性 .首先获得了系统 (E)存在无界解的两个新的充分条件 ,然后获得系统 (E)所有解正向有界的若干充分条件和充要条件 ,所获结果改进和扩展了文 [1 -2 ]中的相应结果 .     

一类具时滞的Liénard型方程的周期解

考虑一类具时滞的 Liénard型方程x+f[x(t) ]x(t) +g[t,x(t-τ(t) ) ]=p(t) =p(t+T) ,利用重合度理论 ,获得了此方程至少存在一个 T周期解的充分条件     

The Discrete Approximation of Continuous-state Nonlinear Branching Processes in Lévy Random Environments北大核心CSCD

In this paper, we establish the discrete approximation of continuous-state nonlinear branching processes in Lévy random environments by using tightness and convergence sequence in infinite dimensional product space via stochastic differential equations. Taking α-stable branching as an example, the conditions which are given to discretize continuous-state nonlinear branching processes in Lévy random environments are verified. © 2022 Chinese Academy of Sciences. All rights reserved.     

Effects of Cone Angles on Nonlinear Vibration Responses of Functionally Graded Shells北大核心CSCD

The nonlinear vibration responses of functionally graded materials (FGMs) shells with different cone angles under external loads were studied. Firstly, the Voigt model was employed to describe the physical properties along the thickness direction of FGMs conical shells. Then, the motion equations were derived based on the 1st-order shear deformation theory, the von Kármán geometric nonlinearity and Hamilton’s principle. Next, the Galerkin method was applied to discretize the motion equations and the governing equations were simplified into a 1DOF nonlinear vibration differential equation under Volmir’s assumption. Finally, the nonlinear motion equations were solved with the harmonic balance method and the Runge-Kutta method, and the amplitude frequency response characteristic curves of the FGMs conical shells were obtained. The effects of different material distribution functions and different ceramic volume fraction exponents on the amplitude frequency response curves of conical shells were discussed. The bifurcation diagrams of conical shells with different cone angles, as well as time process diagrams and phase diagrams for different excitation amplitudes, were described. The motion characteristics were characterized by Poincaré maps. The results show that, the FGMs conical shells present the nonlinear characteristics of hardening springs. The chaotic motions of the FGMs conical shells are restrained and not prone to motion instability with the increase of the cone angle. The FGMs conical shell present a process from the periodic motion to the multi-periodic motion and then to chaos with the increase of the excitation amplitude. © 2022 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

MORPHOLOGICAL STUDIES ON THERMOTROPIC LIQUID CRYSTALLINE POLYESTER——MORPHOLOGY OF SHEAR ORIENTED FILMS

The morphology of shear-oriented films of a thermotropic liquid crystalline polyester containing a triad ester mesogenic unit and a flexible spacer has been investigated in details. The formation conditions and process, the fine structures and the relaxation process of mat structure in the oriented films have been observed and discussed.     

L~p空间中的Fejér和Hermite-Hadamard型不等式

给出了二阶导数属于Lp空间时Fejér和Hermite-Hadamard型不等式的推广,得到两个新结果.     

Quantum simulation of zero-temperature quantum phases and incompressible states of light via non-Markovian reservoir engineering techniques

We review recent theoretical developments on the stabilization of strongly correlated quantum fluids of light in driven-dissipative photonic devices through novel non-Markovian reservoir engineering techniques. This approach allows one to compensate losses and refill selectively the photonic population so as to sustain a desired steady state. It relies in particular on the use of a frequency-dependent incoherent pump, which can be implemented, e.g., via embedded two-level systems maintained at a strong inversion of population. As specific applications of these methods, we discuss the generation of Mott Insulator (MI) and Fractional Quantum Hall (FQH) states of light. As a first step, we present the case of a narrowband emission spectrum and show how this allows for the stabilization of MI and FQH states under the condition that the photonic states are relatively flat in energy. As soon as the photonic bandbwidth becomes comparable to the emission linewidth, important non-equilibrium signatures and entropy generation appear, and a novel dissipative phase transition from a Mott Insulating state toward a superfluid (SF) phase is unveiled. As a second step, we review a more advanced configuration based on reservoirs with a broadband frequency distribution, and we highlight the potential of this configuration for the quantum simulation of equilibrium quantum phases at zero temperature with tunable chemical potential. As a proof of principle, we establish the applicability of our scheme to the Bose–Hubbard model by confirming the presence of a perfect agreement with the ground-state predictions both in the Mott insulating and superfluid regions, and more generally in all parts of the parameter space. Future prospects towards the quantum simulation of more complex configurations are finally outlined, along with a discussion of our scheme as a concrete realization of quantum annealing.     

Particle-size segregation in dense granular avalanches

Particles of differing sizes are notoriously prone to segregate, which is a chronic problem in the manufacture of a wide variety of products that are used by billions of people worldwide every day. Segregation is the single most important factor in product non-uniformity, which can lead to significant handling problems as well as complete batches being discarded at huge financial loss. It is generally regarded that the most important mechanism for segregation is the combination of kinetic sieving and squeeze expulsion in shallow granular avalanches. These free-surface flows are more common than one might expect, often forming part of more complicated flows in drums, heaps and silos, where there is mass exchange with underlying regions of static or slowly moving grains. The combination of segregation and solid–fluid granular phase transitions creates incredibly complicated and beautiful patterns in the resulting deposits, but a full understanding of such effects lies beyond our capabilities at present. This paper reviews recent advances in our ability to model the basic segregation processes in a single avalanche (without mass exchange) and the subtle feedback effects that they can have on the bulk flow. This is particularly important for geophysical applications, where segregation can spontaneously self-channelize and lubricate the flow, significantly enhancing the run-out of debris-flows, pyroclastic flows, rock-falls and snow-slab avalanches.     

Computational Aspect for Function-Valued Padé-Type Approximation

The computational problems of two special determinants are investigated. Those tion for computing Fredholm integral equation of the second kind. The main tool to be used in this paper is the well-known Schur complement theorem.