Efficient inverse radiation analysis in a cylindrical geometry using a combined method of hybrid genetic algorithm and finite-difference Newton method

An inverse radiation problem was considered to estimate boundary conditions such as temperature distribution and emissivity in axisymmetric absorbing, emitting, and scattering medium, given the measured incident radiative heat fluxes. The finite-volume method was employed to solve a direct radiative transfer equation for a two-dimensional axisymmetric geometry. Various parameter estimators, such as conjugate-gradient method, hybrid genetic algorithm, and finite-difference Newton method, were employed to solve the inverse problems, while discussing their performances in terms of estimation accuracy and computational efficiency. Based on this, we proposed, as a best inverse analysis tool, a new combined method that adopted the hybrid genetic algorithm as an initial value selector and used the finite-difference Newton method as a parameter estimator.     

体积约束的非局部扩散问题的加罚有限元方法

针对非齐次和齐次体积约束的非局部扩散问题设计了新的有限元方法——加罚有限元方法,并给出该方法的误差分析.数值算例验证了加罚有限元方法的稳定性和有效性.     

Analysis of the escape in systems with four exit channels

In this paper, we have performed a numerical investigation of the escape of a particle from two different dynamical systems with the same number of exit channels. We have chosen specific values of the parameters of the systems so that the openings of the potential well in both systems are approximately of the same size. We have found that, in the galactic system, the distribution of the times of escape follows a sequential pattern that has never been detected before. Moreover, we have proved that this pattern is directly related to the geometry of the stable manifolds to the Lyapunov orbits located at the openings of the potential. Finally, we have shown that the different nature of the two systems affects the way the escape occurs, due to the difference in the geometry of the manifolds to the Lyapunov orbits in both systems.     

An Extremal Problem Arising in the Dynamics of Two-Phase Materials That Directly Reveals Information about the Internal Geometry

In two-phase materials, each phase having a non-local response in time, it has been found that for some driving fields the response somehow untangles at specific times, and allows one to directly infer useful information about the geometry of the material, such as the volume fractions of the phases. Motivated by this, and to obtain an algorithm for designing appropriate driving fields, we find approximate, measure independent, linear relations between the values that Markov functions take at a given set of possibly complex points, not belonging to the interval [-1,1] where the measure is supported. The problem is reduced to simply one of polynomial approximation of a given function on the interval [-1,1] and, to simplify the analysis, Chebyshev approximation is used. This allows one to obtain explicit estimates of the error of the approximation, in terms of the number of points and the minimum distance of the points to the interval [-1,1]. Assuming this minimum distance is bounded below by a number greater than 1/2, the error converges exponentially to zero as the number of points is increased. Approximate linear relations are also obtained that incorporate a set of moments of the measure. In the context of the motivating problem, the analysis also yields bounds on the response at any particular time for any driving field, and allows one to estimate the response at a given frequency using an appropriately designed driving field that effectively is turned on only for a fixed interval of time. The approximation extends directly to Markov-type functions with a positive semidefinite operator valued measure, and this has applications to determining the shape of an inclusion in a body from boundary flux measurements at a specific time, when the time-dependent boundary potentials are suitably tailored. © 2022 Wiley Periodicals, Inc.     

Jacobi矩阵特征值反问题

研究如下一类Jacobi矩阵特征值反问题:问题IEP:给定两个互异实数λ,μ(λ<μ)和两个n维非零实向量x,y,求n阶Jacobi矩阵J,使得(λ,x),(μ,y)分别恰是J的第i,j(i≠j)个特征对。还分析了Jacobi矩阵的特征性质,给出了一个特征对恰是Jacobi矩阵J的第i个特征对的充分必要条件,由此导出了问题IEP有解的充分必要条件。     

On diffuse reflection at the boundary for the Boltzmann equation and related equations

The paper considers diffuse reflection at the boundary with nonconstant boundary temperature and unbounded velocities. The solutions obtained are proved to conserve mass at the boundary. After a preliminary study of the collisionless case, the main results obtained are existence for the Boltzmann equation in a DiPerna-Lions framework with the above boundary conditions in a bounded measure sense, and existence together with uniqueness for the BGK equation with Maxwellian diffusion on the boundary in anL framework.Deceased.     

对称性对四体系统结构和内部运动的影响

文中用谐振子乘积基展开法求解了四体系统的Schrdinger方程.通过分析波函数及形状密度函数在多维坐标空间的分布,比较了四体全对称0⁺态,四体金对称0^－态和四体全反对称0⁺态,四体全反对称0^－态的结构和内部运动的差异;讨论了对称性的影响.     

Energy-level statistics of model quantum systems: Universality and scaling in a lattice-point problem

We investigate the statistics of the numberN(R, S) of lattice pointsnZ ², in an annular domain (R, w)=(R+w)A\RA, whereR, w>0. HereA is a fixed convex set with smooth boundary andw is chosen so that the area of (R, w) isS. The statistics comes fromR being taken as random (with a smooth density) in some interval [c ₁ T,c ₂,T],c ₂>c ₁>0. We find that in the limitT the variance and distribution of N=N(R; S)–S depend strongly on howS grows withT. There is a saturation regimeS/T, asT, in which the fluctuations in N coming from the two boundaries of are independent. Then there is a scaling regime,S/Tz, 0<z<, in which the distribution depends onz in an almost periodic way going to a Gaussian asz0. The variance in this limit approachesz for genericA, but can be larger for degenerate cases. The former behavior is what one would expect from the Poisson limit of a distribution for annuli of finite area.     

Calculation of geometrical coupling coefficients for the hyperspherical harmonics approach

An elegant and fast method for the calculation of geometrical structure coefficients needed for an expansion of a few-body wavefunction and interaction in hyperspherical harmonics has been proposed. A sum rule for the GSC has also been derived, which is useful for an independent check of the coefficients. The proposed method of computation is many orders of magnitude faster than conventional methods.