Numerical Simulation Solution of the BCS Pairing Problem

We propose a new simulation computational method to solve the reduced BCS Hamiltonian based on spin analogy and submatrix diagonalization. Then we further apply this method to solve superconducting energy gap and the results are well consistent with those obtained by Bogoliubov transformation method. The exponential problem of 2N-dimensional matrix is reduced to the polynomial problem of N-dimensional matrix. It is essential to validate this method on a real quantum computer and is helpful to understanding the many-body quantum theory.     

Numerical Simulation Solution of the BCS Pairing Problem

We propose a new simulation computational method to solve the reduced BCS Hamiltonian based on spin analogy and submatrix diagonalization. Then we further apply this method to solve superconducting energy gap and the results are well consistent with those obtained by Bogoliubov transformation method. The exponential problem of 2^N-dimensional matrix is reduced to the polynomial problem of N-dimensional matrix. It is essential to validate this method on a real quantum computer and is helpful to understanding the many-body quantum theory.     

Exact and Numerical Solution of the Fractional Sturm–Liouville Problem with Neumann Boundary Conditions

In this paper, we study the fractional Sturm–Liouville problem with homogeneous Neumann boundary conditions. We transform the differential problem to an equivalent integral one on a suitable function space. Next, we discretize the integral fractional Sturm–Liouville problem and discuss the orthogonality of eigenvectors. Finally, we present the numerical results for the considered problem obtained by utilizing the midpoint rectangular rule.     

Matching-Updating Mechanism: A Solution for the Stable Marriage Problem with Dynamic Preferences

We studied the stable marriage problem with dynamic preferences. The dynamic preference model allows the agent to change its preferences at any time, which may cause instability in a matching. However, preference changing in SMP instances does not necessarily break all pairs of an existing match. Sometimes, only a few couples want to change their partners, while others choose to stay with their current partners; this motivates us to find stable matching on a new instance by updating an existing match rather than restarting the matching process from scratch. By using the update mechanism, we try to minimize the revision cost when rematching occurs. The challenge when updating a matching is that a cyclic process may exist, and stable matching is never achieved. Our proposed mechanism can update a match and avoid the cyclic process.     

Numerical Approximation of a Nonlinear 3D Heat Radiation Problem

In this paper, we are concerned with the numerical approximation of a steady-state heat radiation problem with a nonlinear Stefan-Boltzmann boundary condition in$\mathbb{R}^3$. We first derive an equivalent minimization problem and then present a finite element analysis to the solution of such a minimization problem. Moreover, we apply the Newton iterative method for solving the nonlinear equation resulting from the minimization problem. A numerical example is given to illustrate theoretical results.     

A New Quasi-Exactly Solvable Problem and Its Connection with an Anharmonic Oscillator

The two-dimensional hydrogen with a linear potential in a magnetic field is solved by two different methods. Furthermore the connection between the model and an anharmonic oscillator is investigated by methods of KS transformation.     

反应堆高阶κ本征方程数值计算方法的改进

针对反应堆高阶κ-本征方程数值计算问题，提出了提高计算效率和计算精度的改进方法，并以一维问题为例，对该方法进行了验证。The solution methods for the higher order oped yet in the nuclear reactor engineering. Based on harmonics and higher order eigenvalues are not well develthe analysis of the convergence process of power iteration, a new approach for setting the starting values of higher order harmonic flux has been proposed. The results of numerical tests demonstrate that the proposed method could effectively improve the efficiency of calculations of higher order harmonics. In addition, a new type of criterion that judges the convergence of higher order harmonics dynamically has been proposed, it has been verified that the new convergence criterion could effectively prevent the buildup of numerical errors introduced in the solution of lower order harmonics in the solution of higher order harmonics.     

A New Quasi-Exactly Solvable Problem and Its Connection with an AnharmonicOscillator

The two-dimensional hydrogen with a linear potential in a magnetic field is solved by two different methods. Furthermore the connection between the model and an anharmonic oscillator is investigated by methods of KS transformation.     

Generalized Solution of Inverse Problem for Ising Connection Matrix on d-Dimensional Hypercubic Lattice

We analyze a connection matrix of a d-dimensional Ising system and solve the inverse problem, restoring the constants of interaction between spins, based on the known spectrum of its eigenvalues. When the boundary conditions are periodic, we can account for interactions between spins that are arbitrarily far. In the case of the free boundary conditions, we have to restrict ourselves with interactions between the given spin and the spins of the first d coordination spheres.     

Determination of Temperature Dependence of Thermophysical Parameters in Solids: Numerical Solution of the Problem

Technical Physics - Two approaches one presented to determine the thermophysical properties of materials. Necessary experimental data on thermal curves have been extracted by simulation modeling of...     

Application of a Factorial Design Method to Determine the Accuracy of a Solution to an Inverse Heat Conduction Problem

A numerical/experimental inverse procedure was employed to estimate the temperature-dependent thermal conductivity of a solid body in which 1D heat conduction in a top heated cylindrical sample is assumed. The emphasis is focused on the issue of sensitivity of results to selected assumptions made in inverse calculations. It has been found that the accuracy of heat capacity evaluation brings the largest contribution to final errors (up to 74%). Density accounts for one-fourth to one-third of the total error of determination. The failure to ensure unidirectional heat conduction in a sample during an experiment is important only at elevated temperatures.     

Rigorous Solution of the Gardner Problem

 We prove rigorously the well-known result of Gardner about the typical fractional volume of interactions between N spins which solve the problem of storing a given set of p random patterns. The Gardner formula for this volume in the limit N, p→∞, p/N→α is proven for all values of α. Besides, we prove a useful criterion for the factorisation of all correlation functions for a class of models of classical statistical mechanics. Received: 2 December 2001 / Accepted: 12 June 2002 Published online: 31 January 2003 Communicated by A. Kupiainen     

Solution of a Generalized Inverse Spectral Problem for Weakly Resolved Spectra Using a Coefficient of Correlation

We consider in a new statement the inverse problem of the theory of vibrational spectra of molecules, in which a theoretical spectral curve directly gets closer to the experimental one. A coefficient of correlation between the curves is used as a criterion of the closeness of the curves and as a functional of the inverse problem. The procedure developed for solving the inverse problem makes it possible to dispense with the preliminary referencing of frequencies in an experimental spectrum and with its expansion into elementary absorption bands.     

An Efficient Numerical Solution Method for Elliptic Problems in Divergence Form

In this paper the problem $-{\rm div}(a(x,y)\nabla u)=f$ with Dirichlet boundary conditions on a square is solved iteratively with high accuracy for $u$ and $\nabla u$ using a new scheme called "hermitian box-scheme". The design of the scheme is based on a "hermitian box", combining the approximation of the gradient by the fourth order hermitian derivative, with a conservative discrete formulation on boxes of length 2$h$. The iterative technique is based on the repeated solution by a fast direct method of a discrete Poisson equation on a uniform rectangular mesh. The problem is suitably scaled before iteration. The numerical results obtained show the efficiency of the numerical scheme. This work is the extension to strongly elliptic problems of the hermitian box-scheme presented by Abbas and Croisille (J. Sci. Comput., 49 (2011), pp. 239--267).     

Solutions of the Multivariate Inverse Frobenius–Perron Problem

We address the inverse Frobenius–Perron problem: given a prescribed target distribution ρ, find a deterministic map M such that iterations of M tend to ρ in distribution. We show that all solutions may be written in terms of a factorization that combines the forward and inverse Rosenblatt transformations with a uniform map; that is, a map under which the uniform distribution on the d-dimensional hypercube is invariant. Indeed, every solution is equivalent to the choice of a uniform map. We motivate this factorization via one-dimensional examples, and then use the factorization to present solutions in one and two dimensions induced by a range of uniform maps.     

Numerical Solution of the Three-Dimensional Helmholtz Equation

We apply the homotopy analysis method to solve the nonhomogeneous multidimensional partial differential equation model problem. The analytic solutions are calculated in terms of convergent series with easily computable components. The nonhomogeneous problem is quickly solved by observing the self-canceling ＂noise＂ terms whose sum vanishes in the limit. Numerical results clearly reveal the complete reliability and efficiency of the proposed algorithm.