THE REMARKABLE NATURE OF RADIALLY SYMMETRIC DEFORMATION OF ANISOTROPIC PIEZOELECTRIC INCLUSION

The present paper deals with spherically symmetric deformation of an inclusion- matrix problem, which consists of an infinite isotropic matrix and a spherically uniform anisotropic piezoelectric inclusion. The interface between the two phases is supposed to be perfect and the system is subjected to uniform loadings at infinity. Exact solutions are obtained for solid spherical piezoelectric inclusion and isotropic matrix. When the system is subjected to a remote traction, analytical results show that remarkable nature exists in the spherical inclusion. It is demonstrated that an infinite stress appears at the center of the inclusion. Furthermore, a cavitation may occur at the center of the inclusion when the system is subjected to uniform tension, while a black hole may be formed at the center of the inclusion when the applied traction is uniform pressure. The appearance of different remarkable nature depends only on one non-dimensional material parameter and the type of the remote traction, while is independent of the magnitude of the traction.

Modeling vibration behavior of delaminated composite laminates using meshfree method in Hamilton system

Free vibration analysis of composite laminates with delaminations is performed based on a three-dimensional semi-analytical model established by introducing the local radial point interpolation method（LRPIM） into a Hamilton system. The governing equation is derived with a transfer matrix technique and a spring layer model based on a local weak-form equivalent to the modified Hellinger-Reissner variational principle. Main superiority of the present model is that the scale of the governing equation involves only the so-called state variables at the top and bottom surfaces, and is insensitive to the thickness and the layer number of the composite laminates. Several numerical examples for analyzing the vibration frequencies and mode shapes of delaminated composite beams and plates are given to validate the model. The results are in good agreement with the pre-existing results.

Radially Symmetrical Problems for Compressible Fluids with a High-Resolution Boundary Condition

Imposing appropriate numerical boundary conditions at the symmetrical center r=0 is vital when computing compressible fluids with radial symmetry.Extrapolation and other traditional techniques are often employed,but spurious numerical oscillations or wall-heating phenomena can occur.In this paper,we emphasize that because of the conservation property,the updating formula of the boundary cell average can coincide with the one for interior cell averages.To achieve second-order accuracy both in time and space,we associate obtaining the inner boundary value at r=0 with the resolution of the corresponding one-sided generalized Riemann problem(GRP).Acoustic approximation is applied in this process.It creates conditions to avoid the singularity of type 1/r and aids in obtaining the value of the singular quantity using L’Hospital’s rule.Several challenging scenarios are tested to demonstrate the effectiveness and robustness of our approach.

Global Existence of the Radially Symmetric Strong Solution to Navier-Stokes-Poisson Equations for Isentropic Compressible Fluids

We prove the two existence results of the radially symmetric strong solutions to the Navier- Stokes-Poisson equations for isentropic compressible fluids. The important point in this paper is that the initial density is vacuum. It is different from weak solutions. Now we need some compatibility condition.

Computational solution of an acid-mediated tumor-growth radial model under logistic growth regimes for normal and cancer cells

Tumor invasion follows a complex mechanism which involves cell migration and proliferation.To study the processes in which primary and secondary metastases invade and damage the normal cells,mathematical models are often extremely useful.In this paper,we present a mathematical model of acid-mediated tumor growth consisting of radially symmetric reaction-diffusion equations.The assumption on the radial symmetry of the solutions is imposed here in view that tumors present spherical symmetry at the microscopic level.Moreover,we consider various empirical mechanisms which describe the propagation of tumors by considering cancer cells,normal cells,and the concentration of H+ions.Among other assumptions,we suppose that these components follow logistictype growth rates.Evidently,this is an important difference with respect to various other mathematical models for tumor growth available in the literature.Moreover,we also add competition terms of normal and tumor cells growth.We carry out a balancing study of the equations of the model,and a numerical model is proposed to produce simulations.Various practical remarks derived from our assumptions are provided in the discussion of our simulations.

Deformation Argument under PSP Condition and Applications

In this paper we introduce a new deformation argument,in which C^(0)-group action and a new ty pe of Palais Smale condition PSP play important roles.This type of deformation results are studied in[17,21]and has many different applications[10,11,17,21]et al.Typically it can be applied to nonlinear scalar field equations.We give a survey in an abstract functional setting.We also present another application to nonlinear elliptic problems in strip-like domains.Under conditions related to[5,6],we show the existence of infinitely many solutions.This ex tends the results in[8].