503 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
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
Exact Solvability of the two-photon Rabi Hamiltonian
Exact spectrum of the two-photon Rabi Hamiltonian is found, proceeding in
full analogy with the solution of standard (one-photon) Rabi Hamiltonian,
published by Braak in Phys. Rev. Lett. 107, 100401 (2011). The Hamiltonian is
rewritten as a set of two differential equations. Symmetries that get hidden
after further treatment are found. One can plainly see, how the Hilbert space
splits into four disjunct subspaces, categorized by four values of the symmetry
parameter . There were only two values for the standard
Rabi model. Four analytic functions are introduced by a recurrence scheme for
the coefficients of their series expansion. All their roots yield the complete
spectrum of the Hamiltonian. Eigenstates in Bargmann space are also at
disposal
Effective photon mass and exact translating quantum relativistic structures
Using a variation of the celebrated Volkov solution, the Klein-Gordon
equation for a charged particle is reduced to a set of ordinary differential
equations, exactly solvable in specific cases. The new quantum relativistic
structures can reveal a localization in the radial direction perpendicular to
the wave packet propagation, thanks to a non-vanishing scalar potential. The
external electromagnetic field, the particle current density and the charge
density are determined. The stability analysis of the solutions is performed by
means of numerical simulations. The results are useful for the description of a
charged quantum test particle in the relativistic regime, provided spin effects
are not decisive
Ion-acoustic solitary waves and shocks in a collisional dusty negative ion plasma
We study the effects of ion-dust collisions and ion kinematic viscosities on
the linear ion-acoustic instability as well as the nonlinear propagation of
small amplitude solitary waves and shocks (SWS) in a negative ion plasma with
immobile charged dusts. {The existence of two linear ion modes, namely the
`fast' and `slow' waves is shown, and their properties are analyzed in the
collisional negative ion plasma.} {Using the standard reductive perturbation
technique, we derive a modified Korteweg-de Vries-Burger (KdVB) equation which
describes the evolution of small amplitude SWS.} {The profiles of the latter
are numerically examined with parameters relevant for laboratory and space
plasmas where charged dusts may be positively or negatively charged.} It is
found that negative ion plasmas containing positively charged dusts support the
propagation of SWS with negative potential. However, the perturbations with
both positive and negative potentials may exist when dusts are negatively
charged. The results may be useful for the excitation of SWS in laboratory
negative ion plasmas as well as for observation in space plasmas where charged
dusts may be positively or negatively charged.Comment: 13 pages, 9 figures; To appear in Physical Review
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
-sphere (), is a polynomial in the
interelectronic distance for a countably infinite set of values of the
radius . 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 model bears the greatest similarity to normal
physical systems.Comment: 4 pages, 0 figur
Scaling of energy spreading in strongly nonlinear disordered lattices
To characterize a destruction of Anderson localization by nonlinearity, we
study the spreading behavior of initially localized states in disordered,
strongly nonlinear lattices. Due to chaotic nonlinear interaction of localized
linear or nonlinear modes, energy spreads nearly subdiffusively. Based on a
phenomenological description by virtue of a nonlinear diffusion equation we
establish a one-parameter scaling relation between the velocity of spreading
and the density, which is confirmed numerically. From this scaling it follows
that for very low densities the spreading slows down compared to the pure power
law.Comment: 4 pages, 4 figure
- …