The equivalence between the TE,TM model and the Darwin models

In this paper,we study the TE,TM model by using the decompositions of the vector fields in 2-D bounded multiply connected domains and 2-D unbounded domains,respectively.We find that the TE,TM model and the Darwin models are equivalent if we assume some regularity of the initial data.     

Equivalent formulations of ＂the equation of life＂

Motivated by progress in theoretical biology a recent proposal on a general and quantitative dynamical framework for nonequilibrium processes and dynamics of complex systems is briefly reviewed. It is nothing but the evolutionary process discovered by Charles Darwin and Alfred Wallace. Such general and structured dynamics may be tentatively named "the equation of life". Three equivalent formulations are discussed, and it is also pointed out that such a quantitative dynamical framework leads naturally to the powerful Boltzmann–Gibbs distribution and the second law in physics. In this way, the equation of life provides a logically consistent foundation for thermodynamics. This view clarifies a particular outstanding problem and further suggests a unifying principle for physics and biology.     

Theory of high temperature superconductivity in YBa2Cu3O7_δ

A theory of high temperature superconductivity in YBa₂Cu₃O₇__δ compound has been developed on the basis of the momentum pairing of electrons through the relativistic Darwin interaction. The transport behaviour of electrons is explained in terms of a mechanism of correlated electron transfer arising from the electron-phonon coupling. A model Hamiltonian has been developed to describe the superconducting properties of the system. This gives an energy gap which is higher than the BCS value. Attempts have been made to explain the absence of isotope effect, the linear dependence of specific heat, the presence of larger temperature-independent paramagnetism in the normal phase and the softening of some of the optic phonon modes observed in this system.     

任意温度密度下的原子结构计算

本文用含有电子自作用修正的TF势求解了任意温度物质密度下的Schrodinger波动方程。为了能够处理相对论效应,波动方程中又引入了质速修正项和Darwin项以及自旋-轨道耦合修正项。本文着重计算了Fe、Rb在几种温度密度下的情况,并在表中给出了计算结果与更准确结果的比较。用现行方法获得的数据与HFS方法的结果也是可以媲美的。     

Fine structure in the hydrogen atom boxed in a spherical impenetrable cavity

The spectrum of the hydrogen atom confined in a spherical impenetrable box of radius R_c has been investigated by many authors up to date, but not at the level of relativistic corrections. It is well known that, as R_c diminishes, all energy levels and the pressure increase very rapidly, whereas the polarizability goes to zero. In this report, we have computed the relativistic corrections that underlie the fine structure of the confined hydrogen atom, as a function of R_c. Such corrections correspond to relativistic kinetic energy, spin‐orbit coupling and the Darwin term, which are calculated in the frame of time‐independent perturbation theory, for which, use was made of the exact confined hydrogen atom wave functions. We show that for a confinement radius of 0.5 au the relativistic corrections increase up to three orders of magnitude with respect to those corresponding to the free atom. As R_c decreases, the kinetic energy correction and the spin‐orbit coupling for become negative whereas their absolute value and the Darwin term, which is positive, increase very rapidly.     

Single-electron transport through an individual InAs SAQD embedded in a graded-dope semiconductor nano-pillar

By using the semiconductor nano-pillar with a graded-dope configuration, we implemented the measurement for a single-electron transport through an individual InAs self-assembled quantum dot (SAQD). An atomic-force microscope observation showed that the SAQD had a disk-like shape with a diameter of 30 nm. We succeeded in observing a significant diamagnetic shift of the Coulomb oscillation peak under the magnetic field applied perpendicular to the disk plane. The measurement gave us a lateral confinement energy of 14 meV and an electron effective mass of 0.039, which provided us with quantitative evidence that the constituent material of the observed quantum dot originates from the InAs SAQD.     

Darwin and Molecular Biology

Darwin's “idea of thehe century”, the principle of selection, is as important in the age of molecular biology as it was a hundred years ago. As a natural law it is open to rigorous physical proof, if certain prerequisites are met, and to quantitative experimental test—in vitro and in vivo—under defined laboratory conditions.     

An Evolution Based on Various Energy Strategies

The simplest model of the evolution of agents with different energy strategies is considered. The model is based on the most general thermodynamic ideas and includes the procedures for selection, inheritance, and variability. The problem of finding a universal strategy (principle) as a selection of possible competing strategies is solved. It is shown that when there is non-equilibrium between the medium and agents, a direction in the evolution of agents arises, but at the same time, depending on the conditions of the evolution, different strategies can be successful. However, for this case, the simulation results reveal that in the presence of significant competition of agents, the strategy that has the maximum total energy dissipation of agents arising as a result of evolution turns out to be successful. Thus, it is not the specific strategy that is universal, but the maximization of dissipation. This result discovers an interesting connection between the basic principles of Darwin–Wallace evolution and the maximum entropy production principle.     

Exterior problem of magnetic field in Darwin model and its numerical solution

In this paper, we consider the solutions of magnetic field in the Darwin model to the Maxwell's equations in 2D unbounded domain. We first deduce the variational formulation and prove the well‐posedness of the weak solution, and then prove the existence and uniqueness of the infinite element solution. Error estimate and the numerical examples are provided. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2008     

Post-Newtonian Approximation of the Vlasov–Nordström System

ABSTRACT

We study the Nordström–Vlasov system, which describes the dynamics of a self-gravitating ensemble of collisionless particles in the framework of the Nordström scalar theory of gravitation. If the speed of light c is considered as a parameter, it is known that in the Newtonian limit c → ∞ the Vlasov–Poisson system is obtained. In this paper we determine a higher approximation and establish a pointwise error estimate of order 𝒪(c ^?4). Such an approximation is usually called a 1.5 post-Newtonian approximation.