The following coupled Schrodinger system with a small perturbationis considered, where β and ε are small parameters. The whole system has a periodic solution with the aid of a Fourier series expansion technique, and...
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The following coupled Schrodinger system with a small perturbation
is considered, where β and ε are small parameters. The whole system has a periodic solution with the aid of a Fourier series expansion technique, and its dominant system has a heteroclinic solution. Then adjusting some appropriate constants and applying the fixed point theorem and the perturbation method yield that this heteroclinic solution deforms to a heteroclinic solution exponentially approaching the obtained periodic solution （called the generalized heteroclinic solution thereafter）.
By molecular dynamics simulations employing an embedded atom method potential, we have investigated structural transformations in single crystal A1 caused by uniaxial strain loading along the [001], [011] and [111] di...
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By molecular dynamics simulations employing an embedded atom method potential, we have investigated structural transformations in single crystal A1 caused by uniaxial strain loading along the [001], [011] and [111] directions. We find that the structural transition is strongly dependent on the crystal orientations. The entire structure phase transition only occurs when loading along the [001] direction, and the increased amplitude of temperature for [001] loading is evidently lower than that for other orientations. The morphology evolutions of the structural transition for [011] and [111] loadings are analysed in detail. The results indicate that only 20% of atoms transit to the hcp phase for [011] and [111] loadings, and the appearance of the hcp phase is due to the partial dislocation moving forward on {lll}fcc family. For [011] loading, the hcp phase grows to form laminar morphology in four planes, which belong to the {111}fcc family; while for [111] loading, the hcp phase grows into a laminar structure in three planes, which belong to the {111}fcc family except for the （111） plane. In addition, the phase transition is evaluated by using the radial distribution functions.
Thresholding is an important form of image segmentation and is a first step in the processing of images for many applications. The selection of suitable thresholds is ideally an automatic process, requiring the use of...
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Thresholding is an important form of image segmentation and is a first step in the processing of images for many applications. The selection of suitable thresholds is ideally an automatic process, requiring the use of some criterion on which to base the selection. One such criterion is the maximization of the information theoretic entropy of the resulting background and object probability distributions. Most processes using this concept have made use of the one-dimensional (1D) grey-level histogram of the image. In an effort to use more of the information available in the image, the present approach evaluates two-dimensional (2D) entropies based on the 2D (grey-level/local average grey-level) "histogram" or scatterplot. The 2D threshold vector that maximizes both background and object class entropies is selected.
Chatwin and Sullivan (1990) proposed simple results for the relationships between moments of scalar fluctuations in self-similar turbulent shear flows. They showed these relationships to be well satisfied by observati...
Chatwin and Sullivan (1990) proposed simple results for the relationships between moments of scalar fluctuations in self-similar turbulent shear flows. They showed these relationships to be well satisfied by observations from a range of experiments. Here their theory is extended to the skewness, kurtosis and higher order equivalents. It is shown that the relationships between these normalised moments are parameter-free, and are identical to those for zero molecular diffusion. Experimental observations are presented which show a remarkable degree of collapse when these normalised moments are plotted against each other. The agreement with the theoretical results is reasonably good, and better than for some other standard statistical distributions which are commonly applied to such observations. This is true not only for the concentration, but also for generalised doses. It is concluded that the simple theory provides a satisfactory basis for a model of both the concentration and of dose. Furthermore, the results suggest that the concentration and the dose can be modelled through a perturbation to a two-state model.
We propose a five-parameter dumbbell model to describe the fusion and fission processes of massive nuclei, where the collective variables are： distance ρ between center-of-mass of two fusing nuclei, neck parameter ...
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We propose a five-parameter dumbbell model to describe the fusion and fission processes of massive nuclei, where the collective variables are： distance ρ between center-of-mass of two fusing nuclei, neck parameter ν, asymmetry D, two deformation variables β1 and β2. The present model has macroscopic qualitative expression of polarization and nuclear collision of head to head, sphere to sphere, waist to waist and so on. The conception of ＂projectile eating target＂ based on open mouth and swallow is proposed to describe nuclear fusion process, and then our understanding of the probability of fusion and quasi-fission is in agreement with some previous work. The calculated fission barriers of a lot of compound nuclei are compared with the experimental data.
In some applications, the accuracy of the numerical solution of an elliptic problem needs to be increased only in certain parts of the domain. In this paper, local refinement is introduced for an overlapping additive ...
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In some applications, the accuracy of the numerical solution of an elliptic problem needs to be increased only in certain parts of the domain. In this paper, local refinement is introduced for an overlapping additive Schwarz algorithm for the p-version finite element method. Both uniform and variable degree refinements are considered. The resulting algorithm is highly parallel and scalable. In two and three dimensions, we prove an optimal bound for the condition number of the iteration operator under certain hypotheses on the refinement region. This bound is independent of the degree p, the number of subdomains N(r) and the mesh size H. In the general two dimensional case, we prove an almost optimal bound with polylogarithmic growth in p.
We prove that the gradient descent training of a two-layer neural network on empirical or population risk may not decrease population risk at an order faster than t−4/(d−2) under mean field scaling. The loss functiona...
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A solution to the linear Boltzmann equation satisfies an energy bound,which reflects a natural fact:The energy of particles in a finite volume is bounded in time by the energy of particles initially occupying the volu...
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A solution to the linear Boltzmann equation satisfies an energy bound,which reflects a natural fact:The energy of particles in a finite volume is bounded in time by the energy of particles initially occupying the volume augmented by the energy transported into the volume by particles entering the volume over *** this paper,we present boundary conditions(BCs)for the spherical harmonic(P_(N))approximation,which ensure that this fundamental energy bound is satisfied by the P_(N) *** BCs are compatible with the characteristic waves of P_(N) equations and determine the incoming waves ***,energy bound and compatibility,are shown on abstract formulations of P_(N) equations and BCs to isolate the necessary structures and *** BCs are derived from a Marshak type formulation of BC and base on a non-classical even/odd-classification of spherical harmonic functions and a stabilization step,which is similar to the truncation of the series expansion in the P_(N) *** show that summation by parts(SBP)finite differences on staggered grids in space and the method of simultaneous approximation terms(SAT)allows to maintain the energy bound also on the semi-discrete level.
We consider a simple two strategy game in which each pure strategy is an evolutionarily stable strategy (ESS). Under the usual dynamical equations, the large-time behaviour of the system will depend upon the initial c...
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We consider a simple two strategy game in which each pure strategy is an evolutionarily stable strategy (ESS). Under the usual dynamical equations, the large-time behaviour of the system will depend upon the initial conditions and the pay-off matrix. If spatial effects are included to give a reaction-diffusion system, we prove that travelling wavefronts can occur which in effect replace one ESS by another. The 'strength' or 'dominance' of each ESS which decides the 'winner' in a precisely defined sense is determined by its pay-off and by its diffusion rate. Good strategies have large pay-offs and small diffusion rates.
This paper is devoted to considering the three-dimensional viscous primitive equations of the large-scale atmosphere. First, we prove the global well-posedness for the primitive equations with weaker initial data than...
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This paper is devoted to considering the three-dimensional viscous primitive equations of the large-scale atmosphere. First, we prove the global well-posedness for the primitive equations with weaker initial data than that in [11]. Second, we obtain the existence of smooth solutions to the equations. Moreover, we obtain the compact global attractor in V for the dynamical system generated by the primitive equations of large-scale atmosphere, which improves the result of [11].
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