Generating Static Fluid Spheres by Conformal Transformations

We generate an explicit four-fold infinity of physically acceptable exact perfect fluid solutions of Einstein's equations by way of conformal transformations of physically unacceptable solutions (one way to view the use of isotropic coordinates). Special cases include the Schwarzschild interior solution and the Einstein static universe. The process we consider involves solving two equations of the Riccati type coupled by a single generating function rather than a specification of one of the two metric functions.Comment: 4 pages revtex4, two figures, Final form to appear in Phys. Rev.

New classes of exact solutions of three-dimensional Navier-Stokes equations

New classes of exact solutions of the three-dimensional unsteady Navier-Stokes equations containing arbitrary functions and parameters are described. Various periodic and other solutions, which are expressed through elementary functions are obtained. The general physical interpretation and classification of solutions is given.Comment: 11 page

Network growth model with intrinsic vertex fitness

© 2013 American Physical SocietyWe study a class of network growth models with attachment rules governed by intrinsic node fitness. Both the individual node degree distribution and the degree correlation properties of the network are obtained as functions of the network growth rules. We also find analytical solutions to the inverse, design, problems of matching the growth rules to the required (e.g., power-law) node degree distribution and more generally to the required degree correlation function. We find that the design problems do not always have solutions. Among the specific conditions on the existence of solutions to the design problems is the requirement that the node degree distribution has to be broader than a certain threshold and the fact that factorizability of the correlation functions requires singular distributions of the node fitnesses. More generally, the restrictions on the input distributions and correlations that ensure solvability of the design problems are expressed in terms of the analytical properties of their generating functions

A numerical method for computing radially symmetric solutions of a dissipative nonlinear modified Klein-Gordon equation

In this paper we develop a finite-difference scheme to approximate radially symmetric solutions of the initial-value problem with smooth initial conditions in an open sphere around the origin, where the internal and external damping coefficients are constant, and the nonlinear term follows a power law. We prove that our scheme is consistent of second order when the nonlinearity is identically equal to zero, and provide a necessary condition for it to be stable order n. Part of our study will be devoted to compare the physical effects of the damping coefficients

Young's modulus of Graphene: a molecular dynamics study

The Young's modulus of graphene is investigated through the intrinsic thermal vibration in graphene which is `observed' by molecular dynamics, and the results agree quite well with the recent experiment [Science \textbf{321}, 385 (2008)]. This method is further applied to show that the Young's modulus of graphene: 1. increases with increasing size and saturation is reached after a threshold value of the size; 2. increases from 0.95 TPa to 1.1 TPa as temperature increases in the region [100, 500]K; 3. is insensitive to the isotopic disorder in the low disorder region ($< 5$), and decreases gradually after further increasing the disorder percentage.Comment: accepted by PRB, brief report, discussion on Poisson ratio adde

Two electrons on a hypersphere: a quasi-exactly solvable model

We show that the exact wave function for two electrons, interacting through a Coulomb potential but constrained to remain on the surface of a $\mathcal{D}$-sphere ($\mathcal{D} \ge 1$), is a polynomial in the interelectronic distance $u$ for a countably infinite set of values of the radius $R$. A selection of these radii, and the associated energies, are reported for ground and excited states on the singlet and triplet manifolds. We conclude that the $\mathcal{D}=3$ model bears the greatest similarity to normal physical systems.Comment: 4 pages, 0 figur