956 research outputs found
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
On A New Formulation of Micro-phenomena: Basic Principles, Stationary Fields And Beyond
In a series of essays, beginning with this article, we are going to develop a
new formulation of micro-phenomena based on the principles of reality and
causality. The new theory provides with us a new depiction of micro-phenomena
assuming an unified concept of information, matter and energy. So, we suppose
that in a definite micro-physical context (including other interacting
particles), each particle is enfolded by a probability field whose existence is
contingent upon the existence of the particle, but it can locally affect the
physical status of the particle in a context-dependent manner. The dynamics of
the whole particle-field system obeys deterministic equations in a manner that
when the particle is subjected to a conservative force, the field also
experiences a conservative complex force which its form is determined by the
dynamics of particle. So, the field is endowed with a given amount of energy,
but its value is contingent upon the physical conditions the particle is
subjected to. Based on the energy balance of the particle and its associated
field, we argue why the field has a probabilistic objective nature. In such a
way, the basic elements of this new formulation, its application for some
stationary states and its nonlinear generalization for conservative systems are
discussed here.Comment: 35 pages, 5 figures, 3 appendice
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 (), and decreases gradually
after further increasing the disorder percentage.Comment: accepted by PRB, brief report, discussion on Poisson ratio adde
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