Application of the continuum surface force model to the Rayleigh — Taylor instability problem

The surface tension effect is introduced according to the continuum model for the surface tension force. A smooth variation of the mollified function of the volume fraction (the color function) across the interface between immiscible fluids occurs due to the convolution of the original color function with the smooth kernel function. The polynomial eighth-degree kernel formulated for plane two-dimensional flows bounded by solid walls or symmetry planes is tested for the Rayleigh — Taylor instability problem.     

确定恒星表面有效温度的非参数估计方法

恒星表面有效温度是恒星的一个重要物理参量,是恒星光谱差异的重要因素。文章采用非参数估计算法对恒星表面温度进行估计。首先对历史光谱数据进行主成分分析(PCA)处理,再根据PCA特征数据与其表面温度的对应关系建立温度的估计模型,该模型是基于高斯核函数的。方法不依赖对光谱进行精确测量,就可以得到较高估计精度的温度值,对大样本光谱分析具有重要意义。     

On pseudo-continuities in the eigenvalue continuum of one-speed neutron transport theory

We report on a new closed-form approximant to the singular eigenfunction transient solution of the one-speed, one-dimensional neutron transport equation with an anisotropic scattering kernel. It is proved that the associated eigenvalue continuum must be pointwise perforated.     

Continuum limit of a hierarchical SU(2) lattice gauge theory in 4 dimensions

We study nonperturbative renormalizability of ad=4 hierarchical SU(2) gauge model that realizes Migdal's recursion relation as an exact renormalization group transformation. A continuum limit of effective actions is shown to exist as the scaling limit, both for initial Wilson and heat kernel actions. These limit effective actions exhibit ultraviolet asymptotic freedom and provide a strictly positive string tension.     

A generalized simple random walk in one dimension related to the Gaussian polynomials

A generalization of the relation between the simple random walk on a regular lattice and the diffusion equation in a continuous space is described. In one dimension we consider a random walk of a walker with exponentially decreasing mobility with respect to time. It has an exact solution of the conditional probability, that is expressed in terms of the Gaussian polynomials, a generalization of binomial coefficients. Taking a suitable continuum limit we obtain the corresponding transport equation from the recursion relation of the discrete random walk process. The kernel of this differential equation is also directly obtained from that conditional probability by the same continuum limit.     

YM2:Continuum expectations,lattice convergence,and lassos

The two dimensional Yang-Mills theory (YM₂) is analyzed in both the continuum and the lattice. In the complete axial gauge the continuum theory may be defined in terms of a Lie algebra valued white noise, and parallel translation may be defined by stochastic differential equations. This machinery is used to compute the expectations of gauge invariant functions of the parallel translation operators along a collection of curvesC. The expectation values are expressed as finite dimensional integrals with densities that are products of the heat kernel on the structure group. The time parameters of the heat kernels are determined by the areas enclosed by the collectionC, and the arguments are determined by the crossing topologies of the curves inC. The expectations for the Wilson lattice models have a similar structure, and from this it follows that in the limit of small lattice spacing the lattice expectations converge to the continuum expectations. It is also shown that the lasso variables advocated by L. Gross [36] exist and are sufficient to generate all the measurable functions on the YM₂-measure space.     

Integral formulation of the Ginzburg-Landau theory of the laser

The most probable laser mode amplitudes are calculated on the basis of the stationary momentum space solution of the Fokker-Planck equation for a continuum mode laser oscillator, which has been derived in a previous paper. Using Fourier transform techniques the expression is transformed from momentum space to configuration space, such that an integral equation results for the most probable field configuration. The kernel is calculated explicitly and the earlier presented Ginzburg-Landau equation for the laser field is recovered together with its boundary condition.     

Asymptotic Analysis of a Slightly Rarefied Gas with Nonlocal Boundary Conditions

In this paper nonlocal boundary conditions for the Navier–Stokes equations are derived, starting from the Boltzmann equation in the limit for the Knudsen number being vanishingly small. In the same spirit of (Lombardo et al. in J. Stat. Phys. 130:69–82, 2008) where a nonlocal Poisson scattering kernel was introduced, a gaussian scattering kernel which models nonlocal interactions between the gas molecules and the wall boundary is proposed. It is proved to satisfy the global mass conservation and a generalized reciprocity relation. The asymptotic expansion of the boundary-value problem for the Boltzmann equation, provides, in the continuum limit, the Navier–Stokes equations associated with a class of nonlocal boundary conditions of the type used in turbulence modeling.     

Channeled spectropolarimetry using a coherent white-light continuum

We carry out polarization measurements using a coherent white-light continuum as a light source for channeled spectropolarimetry. The white-light continuum, whose spectrum ranges from the UV to the IR region, is generated in Kr gas by a terawatt femtosecond laser system. The complete set of Stokes parameters from 450-700 nm are reconstructed from one spectral measurement. Also, the effectiveness of channeled spectropolarimetry using a coherent white-light continuum is experimentally demonstrated with a highly attenuating sample whose transmittance is as low as 10(-6).     

<Superscript>6</Superscript>He + <Superscript>6</Superscript>He Clustering of <Superscript>12</Superscript>Be in a Microscopic Algebraic Approach

The norm kernel of the A=12 system composed of two ⁶He clusters, and the L=0 basis functions (in the SU(3) and angular momentum-coupled schemes) are analytically obtained in the Fock-Bargmann space. The norm kernel has a diagonal form in the former basis, but the asymptotic conditions are naturally defined in the latter one. The system is a good illustration for the method of projection of the norm kernel to the basis functions in the presence of SU(3) degeneracy that was proposed by the authors. The coupled-channel problem is considered in the algebraic version of the resonating-group method, with the multiple decay thresholds being properly accounted for. The structure of the ground state of ¹²Be obtained in the approximation of zero-range nuclear force is compared with the shell-model predictions. In the continuum part of the spectrum, the S-matrix is constructed, the asymptotic normalization coefficients are deduced and their energy dependence is analyzed.     

Connected kernel methods in nuclear reactions: (III). Effective interactions

The recently derived connected kernel equation (CKE) for N-body scattering operators is applied to direct nuclear reactions. A spectral representation is derived for the kernel of the CKE in order to obtain manageable approximations. This allows the kernel to be split into orders corresponding to the propagation of different numbers of bound clusters. By formally solving one part of the kernel at a time, the CKE is written as a hierarchy of nested equations in increasingly many variables. The first equation of this hierarchy is a set of coupled channel Lippmann-Schwinger equations coupling together all two-cluster channels. These equations reduce to the usual coupled channel equations for inelastic scattering and to the coupled channel Born approximation for rearrangement reactions when weak coupling assumptions are made. The second equation of the hierarchy is a two-variable integral equation for the effective interactions appearing in the coupled channel equations. The driving terms and kernel of this integral equation are obtained from the third equation of the hierarchy which is a three-variable integral equation and so forth. The use of the spectral expansion results in a renormalized theory in the sense that the bound state and reaction problems are separated. This permits the inclusion of nuclear models in the theory in a straightforward manner. The hierarchy is applied to a particular example, that of nucleon-nucleus scattering. For this case the hierarchy is truncated at the level allowing no more than three clusters in the continuum. By suppressing exchange and keeping only one-particle transfer and single-nucléon knockout channels, a set of equations for the optical potentials and transfer operators is obtained. These equations provide a three-body treatment of the single scattering approximation to the optical potential. Iteration of the equations yields the usual single scattering approximation in first order including three-body off-shell effects. After suppression of Fermi motion and off-shell effects, the standard impulse approximation is recovered. Modifications of the method for other cases are discussed and other possible applications suggested.     

Algorithm for solving the Faddeev equations in the three-body continuum under avoidance of moving logarithmic singularities

A new method is presented for solving the Faddeev equations in the three-body continuum, which avoids the moving logarithmic singularities present in momentum space methods used up to now. The new algorithm leads to a simple structure of the Faddeev integral kernel, what simplifies significantly the numerical realization. Its application in nuclear physics is, however, still plagued by the presence of the virtual-state pole in the nucleon-nucleon¹S₀ channel. Omitting that channel in calculations with the Bonn-B potential we demonstrate excellent agreement between three-nucleon observables obtained with the new and a former method. Since the codes are quite different, this can be considered as a convincing test.     

First passage time problems for a class of master equations with separable kernels

We discuss first passage time problems for a class of one-dimensional master equations with separable kernels. For this class of master equations the integral equation for first passage time moments can be transformed exactly into ordinary differential equations. When the separable kernel has only a single term the equation for the mean first passage time obtained is exactly that for simple diffusion. The boundary conditions, however, differ from those appropriate to simple diffusion. The equations for higher moments differ slightly from those for simple diffusion. Analysis is presented, of a generalization of a model of a random walk with long-range jumps first investigated by Lindenberg and Shuler. Since the equations can be solved exactly one can study the behavior of boundary conditions in the continuum limit. The generalization to a larger number of terms in the separable kernel leads to higher order equations for the first passage time moments. In each case, boundary conditions can be found directly from the original master equation.     

Parity Projected QCD Sum Rule of the Nucleon with MEM

The nucleon and its negative-parity excited states are examined in a maximum entropy method analysis of QCD sum rules. We derive the parity projected nucleon sum rules with all known first order α _s corrections to the Wilson coefficients of the operator product expansion (OPE). As these corrections have turned out to be large, we suppress them by using a phase-rotated Gaussian kernel. This phase rotation strongly suppresses the continuum contribution and improves the convergence of the OPE. The resulting sum rule has the interesting feature that it is dominated by the term containing the chiral condensate of dimension 3. Analyzing this sum rule by the maximum entropy method, we are able to extract information of both the positive and negative parity states.     

Excitonic effects in solids described by time-dependent density-functional theory

Starting from the many-body Bethe-Salpeter equation we derive an exchange-correlation kernel f(xc) that reproduces excitonic effects in bulk materials within time-dependent density functional theory. The resulting f(xc) accounts for both self-energy corrections and the electron-hole interaction. It is static, nonlocal, and has a long-range Coulomb tail. Taking the example of bulk silicon, we show that the -alpha/q(2) divergency is crucial and can, in the case of continuum excitons, even be sufficient for reproducing the excitonic effects and yielding excellent agreement between the calculated and the experimental absorption spectrum.     

Energy-based coupling of smooth particle hydrodynamics and molecular dynamics with thermal fluctuations

We propose a thermodynamically consistent and energy conserving coupling scheme between the atomistic and the continuum domain. The coupling scheme links the two domains using the DPDE (Dissipative Particle Dynamics at constant Energy) thermostat and is designed to handle strong temperature gradients across the atomistic/continuum domain interface. The fundamentally different definitions of temperature in the continuum and atomistic domain – internal energy and heat capacity versus particle velocity – are accounted for in a straightforward and conceptually intuitive way by the DPDE thermostat. We verify the here proposed scheme using a fluid, which is simultaneously represented as a continuum using Smooth Particle Hydrodynamics, and as an atomistically resolved liquid using Molecular Dynamics. In the case of equilibrium contact between both domains, we show that the correct microscopic equilibrium properties of the atomistic fluid are obtained. As an example of a strong non-equilibrium situation, we consider the propagation of a steady shock-wave from the continuum domain into the atomistic domain, and show that the coupling scheme conserves both energy and shock-wave dynamics.     

核密度估计时-空域滤波红外背景抑制方法

提出一种基于核密度估计的时-空域滤波算法,用于红外搜索跟踪系统图像的背景抑制。算法分为空域滤波和时域滤波两部分。在空域滤波中,采用核密度估计算法对背景进行平滑;在时域滤波中,采用核密度估计算法对经过空域滤波后的图像灰度值进行概率计算,判别属于背景残差的灰度值,然后做进一步的滤除。核方法对背景有很好的光滑性且易于计算机实现,实验表明,这种非参方法设计的时-空域滤波算法对背景杂波有非常良好的抑制效果,信噪比也得到明显提高。     

Continuum approach to car-following models

A continuum version of the car-following Bando model is developed using a series expansion of the headway in terms of the density. This continuum model obeys the same stability criterion as its discrete counterpart. To compare both models we show that traveling wave solutions of the Bando model are very similar to those of the continuum model in the limit of small changes of headway. As the change of headway across the wave increases the solutions gradually diverge. Our transformation relating headway to density enables predictions of the global impact and characteristics of any car-following model using the analogous continuum model. In contrast, we show that the conventional continuum models which account for effects of pressure and dispersion predict behavior which is distinct from the global behavior of discrete models.     

Electronic interband transitions: Plasmons,Frenkel- and Wannier-excitons

From the equation of motion for electron-hole pairs, an eigenvalue equation for electronic interband transitions of a two-band model is derived. In addition to the continuum of free electron-hole pairs, its spectrum shows discrete excitonic and plasmonic lines. Applying complementary approximations to the integral kernel of the eigenvalue equation, one obtains alternatively the hydrogenic spectrum of the Wannier excitons or a transverse Frenkel exciton and a longitudinal plasmon. As regards the solution of the full eigenvalue equation, the possibility of coexistence between excitons and plasmons is established, and longitudinal-transverse splitting of the Wannier excitons is found.     

Optimisation of the Altarelli-Parisi equations

By using renormalisation group ideas the next-to-leading order Altarelli-Parisi kernel is reexpressed as a leading order kernel with a coupling which resums the next to leading logarithmic corrections exactly, including those due to the coefficient function. The regularisation of the kernel is also given. The results of evolvingxF ₃ using several alternative forms for the kernel are compared with the currently available data onxF ₃ ^νFe and a value of Λ≈500MeV is extracted.