Magneto-thermoelasticity with thermoelectric properties and fractional derivative heat transfer

In this work, a new model of the magneto-thermoelasticity theory has been constructed in the context of a new consideration of heat conduction with fractional derivative. A one-dimensional application for a conducting half-space of thermoelectric elastic material, which is thermally shocked in the presence of a magnetic field, has been solved using Laplace transform and state-space techniques (Ezzat, 2008 [1]). According to the numerical results and its graphs, a conclusion about the new theory of magneto-thermoelasticity has been constructed. The theories of coupled magneto-thermoelasticity and of generalized magneto-thermoelasticity with one relaxation time follow as limited cases. The result provides a motivation to investigate conducting thermoelectric materials as a new class of applicable materials.     

一维受迫谐振子量子运动的经典特性

对经典一维受迫谐振子量子化,求解量子化后体系的时间演化算符.应用相空间准概率分布函数,研究了体系的量子特性.研究结果表明,初始为真空态,经过时间演化,系统波函数是一个二维高斯波包;波包中心的振幅和相位受到作用力的调制,成为调幅、调相波,波包中心的运动与经典受迫谐振子的运动形式相同.     

基于径向基神经网络预测的混沌时间序列嵌入维数估计方法

根据Takens定理,研究了混沌时间序列相空间重构嵌入维数的选取问题.提出了基于径向基函数神经网络预测模型性能的嵌入维数估计方法,即根据嵌入维数与混沌时间序列预测模型性能的变化关系来确定嵌入维数.通过对几种典型混沌动力学系统的数值验证,结果表明该方法能够确定出合适的相空间重构嵌入维数. 关键词： 混沌 相空间重构 嵌入维数 预测     

Simulation of ion beam extraction and focusing system

The characteristics of ion beam extraction and focused to a volume as small as possible were investigated with the aid of computer code SIMION 3D version 7. This has been used to evaluate the extraction characteristics (accel-decel system) to generate an ion beam with low beam emittance and high brightness. The simulation process can provide a good study for optimizing the extraction and focusing system of the ion beam without any losses and transported to the required target. Also, a study of a simulation model for the extraction system of the ion source was used to describe the possible plasma boundary curvatures during the ion extraction that may be affected by the change in an extraction potential with a constant plasma density meniscus.     

Effective potential in curved space and cut-off regularizations

We consider derivation of the effective potential for a scalar field in curved space-time within the physical regularization scheme, using two sorts of covariant cut-off regularizations. The first one is based on the local momentum representation and Riemann normal coordinates and the second is operatorial regularization, based on the Fock-Schwinger-DeWitt proper-time representation. We show, on the example of a self-interacting scalar field, that these two methods produce equal results for divergences, but the first one gives more detailed information about the finite part. Furthermore, we calculate the contribution from a massive fermion loop and discuss renormalization group equations and their interpretation for the multi-mass theories.     

Semiclassics around a phase space caustic: An illustration using the Nelson Hamiltonian

The semiclassical formula for the coherent-state propagator is written in terms of complex classical trajectories of an equivalent classical system. Depending on the parameters involved, more than one trajectory may contribute to the calculation. Eventually, however, two contributing trajectories coalesce, characterizing what is called phase space caustic. In this case, the usual semiclassical formula for the propagator diverges, so that a uniform approximation is required to avoid this singularity. In this Letter, we present a non-trivial numerical application illustrating this scenario, showing the accuracy of the uniform formula that we have previously derived.     

光速在相对论中的核心地位

介绍了关于真空中光速的假定的重要作用,它不仅是相对论理论的基础,而且使人们能够定义同时性并测量空间距离.     

Fixed point theorems in piecewise continuous function spaces and applications to some nonlinear problems

The piecewise continuous function space is an important state space in various nonlinear problems. In this paper, we establish some new fixed point theorems for the perturbed contraction operators in piecewise continuous function spaces. Our results can be applied to various integral operators. Some previous results are improved in this literature. As applications, the existence and uniqueness of solutions of impulsive anti‐periodic boundary value problems and the Lasota–Wazewska models with delays are exhibited at last two sections. Copyright © 2013 John Wiley & Sons, Ltd.     

Nonlinear fractional differential equations of Sobolev type

Sobolev type nonlinear equations with time fractional derivatives are considered. Using the test function method, limiting exponents for nonexistence of solutions are found. Copyright © 2013 John Wiley & Sons, Ltd.