An exact analytical solution is obtained for the problem of three-dimensional transient heat conduction in the multilayered sphere. The sphere has multiple layers in the radial direction and, in each layer, time-dependent and spatially nonuniform volumetric internal heat sources are considered. To obtain the temperature distribution, the eigenfunction expansion method is used. An arbitrary comb...

The well-known radial graph layout technique has plenty of advantages for graph visualization and graph exploration, but is quite limited in the size of graphs it can display effectively because the layout is inherently global and allows far away or out of view nodes to distort the focus region. The primary contribution of this project is to introduce sub tree clustering to allow the layout alg...

The peculiarity of this BVP is its rotation symmetry: with u = u (r, 0) a solution of (1.1), for any (p the function R~ u : = u (r, 0 + ~o) is also a solution. Calling two functions u 1 and u 2 geometrically distinct (as in [4]) ifR~ ul + u2 for all ~o, we will derive multiplicity results for geometrically distinct solutions of (1.1). In particular, we shall distinguish between non-radial and r...

Analytical series solution is proposed for the transient boundary-value problem ofmultilayer heat conduction in r–h spherical coordinates. Spatially non-uniform, but time-independent, volumetric heat sources may exist in the concentric layers. Proposed solution is valid for any combination of homogenous boundary conditions of the first or second kind in the h -direction. However, inhomogeneous ...

This paper is concerned with the two new boundary-type radial basis function collocation schemes, boundary knot method (BKM) and boundary particle method (BPM). The BKM is developed based on the dual reciprocity theorem, while the BKM employs the multiple reciprocity technique. Unlike the method of fundamental solution, the two methods use the non-singular general solution instead of singular f...

Based on the radial basis functions (RBF) and T-Trefftz solution, this paper presents a new meshless method for numerically solving various partial differential equation systems. First, the analog equation method (AEM) is used to convert the original patial differential equation to an equivalent Poisson’s equation. Then, the radial basis functions (RBF) are employed to approxiamate the inhomoge...

An exact solution of the Einstein field equations is found under the assumption of spherically symmetry and the existence of one-parameter group of homothetic motions. This solution has a singularity at r = 0, and has non-vanishing expansion, acceleration and shear. Tidal forces in radial direction will not stretch an observer falling in this fluid. If the material is represented by perfect flu...

Many radial basis function (RBF) methods contain a free shape parameter that plays an important role for the accuracy of the method. In most papers the authors end up choosing this shape parameter by trial and error or some other ad hoc means. In this paper, we propose applying the genetic algorithm to determine a good shape parameter of radial basis functions for the solution of partial differ...

This work introduces the weighted radial basis collocation method for boundary value problems. We first show that the employment of least-squares functional with quadrature rules constitutes an approximation of the direct collocation method. Standard radial basis collocation method, however, yields a larger solution error near boundaries. The residuals in the least-squares functional associated...

The electric potential of the contractile vacuole (CV) of Paramecium multimicronucleatum was measured in situ using microelectrodes, one placed in the CV and the other (reference electrode) in the cytosol of a living cell. The CV potential in a mechanically compressed cell increased in a stepwise manner to a maximal value (approximately 80 mV) early in the fluid-filling phase. This stepwise cha...