Description of inverse energy cascade in homogeneous isotropic turbulence using an eigenvalue method

A description of inverse energy cascade(from small scale to large scale)in homogeneous isotropic turbulence is introduced by using an eigenvalue method.We show a special isotropic turbulence,in which the initial condition is constructed by reversing the velocity field in space,i.e.,the time-reversed turbulence.It is shown that the product of eigenvalues of the rate-of-strain tensor can quantitatively describe the backward energy transfer process.This description is consistent to the velocity derivative skewness Sk.However,compared with Sk,it is easier to be obtained,and it is expected to be extended to anisotropic turbulence.Furthermore,this description also works for the resolved velocity field,which means that it can be used in engineering turbulent flows.The description presented here is desired to inspire future investigation for the modeling of the backward energy transfer process and lay the foundation for the accurate prediction of complex flows.

Thermodynamic stability of interacting fermions system with matrix eigenvalue method

A matrix eigenvalue method is applied to analyse the thermodynamic stability of two-component interacting fermions. The non-relativistic and ultra-relativistic d = 1, 2, 3 dimensions have been discussed in detail, respectively. The corresponding stability region has been given according to the two-body interaction strength and the particle number density ratio.

The Multiplicity of Zeros of Algebraic System in Eigenvalue Method

This article deals with the structure relations between solutions toalgebraic system and matrices in eigenvalue method for solving the algebraic system-The authors first discuss the condition on the ideal generated by the given systemunder which the eigenspace of matrix has dimension 1 since in this case the zerocan be easily found. Then they study the relations between the multiplicity of zerosof the given system and orders of Jordan blocks of matrices formed in eigenvaluemethod.

An entropy-based multi-criterion group decision analysis method of selecting the optimum weak-subgrade treatment

Proper treatment of weak subgrade soil is very important to building a highway of good quality. We proposed an entropy-based multi-criterion group decision analysis method for a group of experts to evaluate alternatives of weak subgrade treatment, with an aim to select the optimum technique which is technically, economically and socially viable. We used fuzzy theory to analyze multiple experts＇ evaluation on various factors of each alterative treatment. Different experts＇ evaluations are integrated by the group eigenvalue method. An entropy weight is introduced to minimize the negative influences of subjective human factors of experts. The optimum alternative is identified with ideal point diseriminant analysis to calculate the distance of each alternative to the ideal point and prioritize all alternatives according to their distances. A case study on a section of the Shiman Expressway verified that the proposed method can give a rational decision on the optimum method of weak subgrade treatment.

Preconditioned Iterative Methods for Algebraic Systems from Multiplicative Half-Quadratic Regularization Image Restorations

Image restoration is often solved by minimizing an energy function consisting of a data-fidelity term and a regularization term.A regularized convex term can usually preserve the image edges well in the restored image.In this paper,we consider a class of convex and edge-preserving regularization functions,i.e.,multiplicative half-quadratic regularizations,and we use the Newton method to solve the correspondingly reduced systems of nonlinear equations.At each Newton iterate,the preconditioned conjugate gradient method,incorporated with a constraint preconditioner,is employed to solve the structured Newton equation that has a symmetric positive definite coefficient matrix. The eigenvalue bounds of the preconditioned matrix are deliberately derived,which can be used to estimate the convergence speed of the preconditioned conjugate gradient method.We use experimental results to demonstrate that this new approach is efficient, and the effect of image restoration is reasonably well.

Relative Efficiency Evaluation on Water Resource Utilization

Water resource allocation was defined as an input-output question in this paper, and a preliminary input-output index system was set up. Then GEM （group eigenvalue method）-MAUE （multi-attribute utility theory） model was applied to evaluate relative efficiency of water resource allocation plans. This model determined weights of indicators by GEM, and assessed the allocation schemes by MAUE. Compared with DEA （Data Envelopment Analysis） or ANN （Artificial Neural Networks）, the mode was more applicable in some cases where decision-makers had preference for certain indicators

ROBUST ACOUSTIC SOURCE LOCALIZATION FOR DIGITAL HEARING AIDS IN NOISE AND REVERBERANT ENVIRONMENT

A new method in digital hearing aids to adaptively localize the speech source in noise and reverberant environment is proposed. Based on the room reverberant model and the multichannel adaptive eigenvalue decomposition （MCAED） algorithm, the proposed method can iteratively estimate impulse response coefficients between the speech source and microphones by the adaptive subgradient projection method. Then, it acquires the time delays of microphone pairs, and calculates the source position by the geometric method. Compared with the traditional normal least mean square （NLMS） algorithm, the adaptive subgradient projection method achieves faster and more accurate convergence in a low signal-to-noise ratio （SNR） environment. Simulations for glasses digital hearing aids with four-component square array demonstrate the robust performance of the proposed method.

A SMALLEST SINGULAR VALUE METHOD FOR SOLVING INVERSE EIGENVALUE PROBLEMS

Utilizing the properties of the smallest singular value of a matrix, we propose a new, efficient and reliable algorithm for solving nonsymmetric matrix inverse eigenvalue problems, and compare it with a known method. We also present numerical experiments which illustrate our results.

TWO－DIMENSIONAL DEFORMATION OF ANANISOTROPIC ELASTIC BODY WITH A PARABOLIC BOUNDARY

In .the present paper, two-dimenstional deformation problems of an anisotropicboby. with a parabolic boundary. are sysiematically analysed by using Lekhnitskii'sformalism and the mapping functions method .then a special .structure─the half-infinitecrack problem is studied through the obtained results. the sinular fields and the sressiniensity. .factors near the crack tip are also obiained.

A 3D multi-field element for simulating the electromechanical coupling behavior of dielectric elastomers

We propose a multi-field implicit finite element method for analyzing the electromechanical behavior of dielectric elastomers. This method is based on a four-field variational principle, which includes displacement and electric potential for the electromechanical coupling analysis, and additional independent fields to address the incompressible constraint of the hyperelastic material. Linearization of the variational form and finite element discretization are adopted for the numerical implementation. A general FEM program framework is devel- oped using C＋＋ based on the open-source finite element library deal.II to implement this proposed algorithm. Numerical examples demonstrate the accuracy, convergence properties, mesh-independence properties, and scalability of this method. We also use the method for eigenvalue analysis of a dielectric elastomer actuator subject to electromechanical loadings. Our finite element implementation is available as an online supplementary material.

h-P Finite Element Approximation for Full-Potential Electronic Structure Calculations

The(continuous) finite element approximations of different orders for the computation of the solution to electronic structures were proposed in some papers and the performance of these approaches is becoming appreciable and is now well understood.In this publication,the author proposes to extend this discretization for full-potential electronic structure calculations by combining the refinement of the finite element mesh,where the solution is most singular with the increase of the degree of the polynomial approximations in the regions where the solution is mostly regular.This combination of increase of approximation properties,done in an a priori or a posteriori manner,is well-known to generally produce an optimal exponential type convergence rate with respect to the number of degrees of freedom even when the solution is singular.The analysis performed here sustains this property in the case of Hartree-Fock and Kohn-Sham problems.

Duffin-Kemmer-Petiau equation under Hartmann ring-shaped potential

We solve the DufRn-Kemmer-Petiau（DKP） equation in the presence of Hartmann ring-shaped potential in（3＋l）-dimensional space-time.We obtain the energy eigenvalues and eigenfunctions by the Nikiforov-Uvarov（NU）method.