An Analytical and a Numerical Method for Nonlinear Convection-Radiation Problems in Porous FinsRead the full article
Advances in Mathematical Physics publishes papers that seek to understand mathematical basis of physical phenomena, and solve problems in physics via mathematical approaches.
Chief Editor, Prof Di Matteo (Department of Mathematics, King’s College London), engages in world-leading multidisciplinary and data-driven research focussed on the analysis of complex data from the perspective of a statistical physicist.
Latest ArticlesMore articles
Numerical Treating of Mixed Integral Equation Two-Dimensional in Surface Cracks in Finite Layers of Materials
The goal of this paper is study the mixed integral equation with singular kernel in two-dimensional adding to the time in the Volterra integral term numerically. We established the problem from the plane strain problem for the bounded layer medium composed of different materials that contains a crack on one of the interface. Also, the existence of a unique solution of the equation proved. Therefore, a numerical method is used to translate our problem to a system of two-dimensional Fredholm integral equations (STDFIEs). Then, Toeplitz matrix (TMM) and the Nystrom product methods (NPM) are used to solve the STDFIEs with Cauchy kernel. Numerical examples are presented, and their results are compared with the analytical solution to demonstrate the validity and applicability of the methods. The codes were written in Maple.
Regularity for a Nonlinear Discontinuous Subelliptic System with Drift on the Heisenberg Group
In this paper, we prove the partial Hölder regularity of weak solutions and the partial Morrey regularity to horizontal gradients of weak solutions to a nonlinear discontinuous subelliptic system with drift on the Heisenberg group by the -harmonic approximation, where the coefficients in the nonlinear subelliptic system are discontinuous and satisfy the VMO condition for , ellipticity and growth condition with the growth index for the Heisenberg gradient variable, and the nonhomogeneous terms satisfy the controllable growth condition and the natural growth condition, respectively.
New Results on the Equivalence of -Functionals and Modulus of Continuity of Functions Defined on the Sobolev Space Constructed by the Generalized Jacobi-Dunkl Operator
In this paper, we establish some new generalized results on the equivalence of -functionals and modulus of continuity of functions defined on the Sobolev space , by using the harmonic analysis related to the Jacobi-Dunkl operator , where and .
An Improved Version of Residual Power Series Method for Space-Time Fractional Problems
The task of present research is to establish an enhanced version of residual power series (RPS) technique for the approximate solutions of linear and nonlinear space-time fractional problems with Dirichlet boundary conditions by introducing new parameter . The parameter allows us to establish the best numerical solutions for space-time fractional differential equations (STFDE). Since each problem has different Dirichlet boundary conditions, the best choice of the parameter depends on the problem. This is the major contribution of this research. The illustrated examples also show that the best approximate solutions of various problems are constructed for distinct values of parameter . Moreover, the efficiency and reliability of this technique are verified by the numerical examples.
Single Reflect-Mirror Laser Communication Tracking-Pointing System Load Technology for Micronanosatellite
In order to realize low-orbit microsatellite laser communication, L- and U-frame structures are designed, respectively, for the payload of single-lens reflex (SLR) laser communication tracking and pointing system. According to the characteristics of each load structure, the detailed system design is carried out, and the modal analysis is carried out on the key structural parts of the L- and U-frames to ensure the reliability of each load structure. The pointing accuracy of the two load structures is also calculated and analyzed. Finally, the conclusion is that both of the two load structures can meet the technical and accuracy requirements of low-orbit communication, but obviously, the U-frame structure has higher accuracy, greater pitching angle, and better reliability; eventually, the U-frame structure is adopted in this design. Then, we have completed the manufacture and assembly of the principle prototype and carried out a vibration test experiment on the principle prototype. The results show that the U-type loading structure SLR laser communication tracking and pointing system achieves the expected design purpose and can meet the technical requirements of the low-orbit microsatellite laser communication.
Human Position Detection Based on Depth Camera Image Information in Mechanical Safety
The devices used for human position detection in mechanical safety mainly include safety light curtain, safety laser scanner, safety pad, and vision system. However, these devices may be bypassed when used, and human or equipment cannot be distinguished. To solve this problem, a depth camera is proposed as a human position detection device in mechanical safety. The process of human position detection based on depth camera image information is given; it mainly includes image information acquisition, human presence detection, and distance measurement. Meanwhile, a human position detection method based on Intel RealSense depth camera and MobileNet-SSD algorithm is proposed and applied to robot safety protection. The result shows that the image information collected by the depth camera can detect the human position in real time, which can replace the existing mechanical safety human position detection device. At the same time, the depth camera can detect only human but not mobile devices and realize the separation and early warning of people and mobile devices.