149,804 research outputs found
General stationary charged black holes as charged particle accelerators
We study the possibility of getting infinite energy in the center of mass
frame of colliding charged particles in a general stationary charged black
hole. For black holes with two-fold degenerate horizon, it is found that
arbitrary high center-of-mass energy can be attained, provided that one of the
particle has critical angular momentum or critical charge, and the remained
parameters of particles and black holes satisfy certain restriction. For black
holes with multiple-fold degenerate event horizons, the restriction is
released. For non-degenerate black holes, the ultra-high center-of-mass is
possible to be reached by invoking the multiple scattering mechanism. We obtain
a condition for the existence of innermost stable circular orbit with critical
angular momentum or charge on any-fold degenerate horizons, which is essential
to get ultra-high center-of-mass energy without fine-tuning problem. We also
discuss the proper time spending by the particle to reach the horizon and the
duality between frame dragging effect and electromagnetic interaction. Some of
these general results are applied to braneworld small black holes.Comment: 23 pages, no figures, revised version accepted for publication in
Phys. Rev.
Number and Amplitude of Limit Cycles emerging from {\it Topologically Equivalent} Perturbed Centers
We consider three examples of weekly perturbed centers which do not have {\it
geometrical equivalence}: a linear center, a degenerate center and a
non-hamiltonian center. In each case the number and amplitude of the limit
cycles emerging from the period annulus are calculated following the same
strategy: we reduce of all of them to locally equivalent perturbed integrable
systems of the form: , with
. This reduction allows us to find the Melnikov
function, , associated to each particular problem. We
obtain the information on the bifurcation curves of the limit cycles by solving
explicitly the equation in each case.Comment: 17 pages, 0 figure
Recommended from our members
Introduction to bifurcation-theory
The theory of bifurcation from equilibria based on center-manifold reductio, and Poincare-Birkhoff normal forms is reviewed at an introductory level. Both differential equations and maps are discussed, and recent results explaining the symmetry of the normal form are derived. The emphasis is on the simplest generic bifurcations in one-parameter systems. Two applications are developed in detail: a Hopf bifurcation occurring in a model of three-wave mode coupling and steady-state bifurcations occurring in the real Landau-Ginzburg equation. The former provides an example of the importance of degenerate bifurcations in problems with more than one parameter and the latter illustrates new effects introduced into a bifurcation problem by a continuous symmetry.Physic
Numerical model for the determination of the soil retention curve from global characteristics obtained via a centrifuge
A novel centrifuge set-up for the study of unsaturated flow characteri\-stics in porous media is examined. In this set-up, simple boundary conditions can be used, but a free moving boundary between unsaturated-saturated flow arises.
A precise and numerically efficient approximation is presented for the mathematical model based on Richards' nonlinear and degenerate equation expressed in terms of effective saturation using the Van Genuchten-Mualem approach for the soil parameters in the unsaturated zone. Sensitivity of the measurable quantities (rotational moment, center of gravity and time period to achieve quasi steady state) on the soil parameters is investigated in several numerical experiments. They show that the set-up is suitable for the determination of the soil parameters via the solution of an inverse problem in an iterative way
Dark matter concentration in the galactic center
It is shown that the matter concentration observed through stellar motion at
the galactic center (Eckart & Genzel, 1997, MNRAS, 284, 576 and Genzel et al.,
1996, ApJ, 472, 153) is consistent with a supermassive object of solar masses composed of self-gravitating, degenerate heavy neutrinos, as
an alternative to the black hole interpretation. According to the observational
data, the lower bounds on possible neutrino masses are
keV for or keV for , where is the
spin degeneracy factor. The advantage of this scenario is that it could
naturally explain the low X-ray and gamma ray activity of Sgr A, i.e. the
so called "blackness problem" of the galactic center.Comment: ApJ, 500, 591 (1998), AASTEX, aasms4.sty, v2 reference adde
The self-consistent general relativistic solution for a system of degenerate neutrons, protons and electrons in beta-equilibrium
We present the self-consistent treatment of the simplest, nontrivial,
self-gravitating system of degenerate neutrons, protons and electrons in
-equilibrium within relativistic quantum statistics and the
Einstein-Maxwell equations. The impossibility of imposing the condition of
local charge neutrality on such systems is proved, consequently overcoming the
traditional Tolman-Oppenheimer-Volkoff treatment. We emphasize the crucial role
of imposing the constancy of the generalized Fermi energies. A new approach
based on the coupled system of the general relativistic
Thomas-Fermi-Einstein-Maxwell equations is presented and solved. We obtain an
explicit solution fulfilling global and not local charge neutrality by solving
a sophisticated eigenvalue problem of the general relativistic Thomas-Fermi
equation. The value of the Coulomb potential at the center of the configuration
is and the system is intrinsically stable against
Coulomb repulsion in the proton component. This approach is necessary, but not
sufficient, when strong interactions are introduced.Comment: Letter in press, Physics Letters B (2011
Mapping Class Group Actions on Quantum Doubles
We study representations of the mapping class group of the punctured torus on
the double of a finite dimensional possibly non-semisimple Hopf algebra that
arise in the construction of universal, extended topological field theories. We
discuss how for doubles the degeneracy problem of TQFT's is circumvented. We
find compact formulae for the -matrices using the canonical,
non degenerate forms of Hopf algebras and the bicrossed structure of doubles
rather than monodromy matrices. A rigorous proof of the modular relations and
the computation of the projective phases is supplied using Radford's relations
between the canonical forms and the moduli of integrals. We analyze the
projective -action on the center of for an
-st root of unity. It appears that the -dimensional
representation decomposes into an -dimensional finite representation and a
-dimensional, irreducible representation. The latter is the tensor product
of the two dimensional, standard representation of and the finite,
-dimensional representation, obtained from the truncated TQFT of the
semisimplified representation category of .Comment: 45 page
A Subdivision Method for Computing Nearest Gcd with Certification
International audienceA new subdivision method for computing the nearest univariate gcd is described and analyzed. It is based on an exclusion test and an inclusion test. The xclusion test in a cell exploits Taylor expansion of the polynomial at the center of the cell. The inclusion test uses Smale's alpha-theorems to certify the existence and unicity of a solution in a cell. Under the condition of simple roots for the distance minimization problem, we analyze the complexity of the algorithm in terms of a condition number, which is the inverse of the distance to the set of degenerate systems. We report on some experimentation on representative examples to illustrate the behavior of the algorithm
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