391 research outputs found
Some exact solutions to the Lighthill Whitham Richards Payne traffic flow equations II: moderate congestion
We find a further class of exact solutions to the Lighthill Whitham Richards
Payne (LWRP) traffic flow equations. As before, using two consecutive
Lagrangian transformations, a linearization is achieved. Next, depending on the
initial density, we either obtain exact formulae for the dependence of the car
density and velocity on x, t, or else, failing that, the same result in a
parametric representation. The calculation always involves two possible
factorizations of a consistency condition. Both must be considered. In physical
terms, the lineup usually separates into two offshoots at different velocities.
Each velocity soon becomes uniform. This outcome in many ways resembles not
only Rowlands, Infeld and Skorupski J. Phys. A: Math. Theor. 46 (2013) 365202
(part I) but also the two soliton solution to the Korteweg-de Vries equation.
This paper can be read independently of part I. This explains unavoidable
repetitions. Possible uses of both papers in checking numerical codes are
indicated at the end. Since LWRP, numerous more elaborate models, including
multiple lanes, traffic jams, tollgates etc. abound in the literature. However,
we present an exact solution. These are few and far between, other then found
by inverse scattering. The literature for various models, including ours, is
given. The methods used here and in part I may be useful in solving other
problems, such as shallow water flow.Comment: 15 pages, 7 figure
Theoretical confirmation of Feynman's hypothesis on the creation of circular vortices in Bose-Einstein condensates: III
In two preceding papers (Infeld and Senatorski 2003 J. Phys.: Condens. Matter
15 5865, and Senatorski and Infeld 2004 J. Phys.: Condens. Matter 16 6589) the
authors confirmed Feynman's hypothesis on how circular vortices can be created
from oppositely polarized pairs of linear vortices (first paper), and then gave
examples of the creation of several different circular vortices from one linear
pair (second paper). Here in part III, we give two classes of examples of how
the vortices can interact. The first confirms the intuition that the
reconnection processes which join two interacting vortex lines into one,
practically do not occur. The second shows that new circular vortices can also
be created from pairs of oppositely polarized coaxial circular vortices. This
seems to contradict the results for such pairs given in Koplik and Levine 1996
Phys. Rev. Lett. 76 4745.Comment: 10 pages, 7 figure
Fully three dimensional breather solitons can be created using Feshbach resonance
We investigate the stability properties of breather solitons in a
three-dimensional Bose-Einstein Condensate with Feshbach Resonance Management
of the scattering length and con ned only by a one dimensional optical lattice.
We compare regions of stability in parameter space obtained from a fully 3D
analysis with those from a quasi two-dimensional treatment. For moderate con
nement we discover a new island of stability in the 3D case, not present in the
quasi 2D treatment. Stable solutions from this region have nontrivial dynamics
in the lattice direction, hence they describe fully 3D breather solitons. We
demonstrate these solutions in direct numerical simulations and outline a
possible way of creating robust 3D solitons in experiments in a Bose Einstein
Condensate in a one-dimensional lattice. We point other possible applications.Comment: 4 pages, 4 figures; accepted to Physical Review Letter
Nonlinear Electron Oscillations in a Viscous and Resistive Plasma
New non-linear, spatially periodic, long wavelength electrostatic modes of an
electron fluid oscillating against a motionless ion fluid (Langmuir waves) are
given, with viscous and resistive effects included. The cold plasma
approximation is adopted, which requires the wavelength to be sufficiently
large. The pertinent requirement valid for large amplitude waves is determined.
The general non-linear solution of the continuity and momentum transfer
equations for the electron fluid along with Poisson's equation is obtained in
simple parametric form. It is shown that in all typical hydrogen plasmas, the
influence of plasma resistivity on the modes in question is negligible. Within
the limitations of the solution found, the non-linear time evolution of any
(periodic) initial electron number density profile n_e(x, t=0) can be
determined (examples). For the modes in question, an idealized model of a
strictly cold and collisionless plasma is shown to be applicable to any real
plasma, provided that the wavelength lambda >> lambda_{min}(n_0,T_e), where n_0
= const and T_e are the equilibrium values of the electron number density and
electron temperature. Within this idealized model, the minimum of the initial
electron density n_e(x_{min}, t=0) must be larger than half its equilibrium
value, n_0/2. Otherwise, the corresponding maximum n_e(x_{max},t=tau_p/2),
obtained after half a period of the plasma oscillation blows up. Relaxation of
this restriction on n_e(x, t=0) as one decreases lambda, due to the increase of
the electron viscosity effects, is examined in detail. Strong plasma viscosity
is shown to change considerably the density profile during the time evolution,
e.g., by splitting the largest maximum in two.Comment: 16 one column pages, 11 figures, Abstract and Sec. I, extended, Sec.
VIII modified, Phys. Rev. E in pres
Stability analysis of three-dimensional breather solitons in a Bose-Einstein Condensate
We investigate the stability properties of breather soliton trains in a
three-dimensional Bose-Einstein Condensate with Feshbach Resonance Management
of the scattering length. This is done so as to generate both attractive and
repulsive interaction. The condensate is con ned only by a one dimensional
optical lattice and we consider both strong, moderate, and weak con nement. By
strong con nement we mean a situation in which a quasi two dimensional soliton
is created. Moderate con nement admits a fully three dimensional soliton. Weak
con nement allows individual solitons to interact. Stability properties are
investigated by several theoretical methods such as a variational analysis,
treatment of motion in e ective potential wells, and collapse dynamics. Armed
with all the information forthcoming from these methods, we then undertake a
numerical calculation. Our theoretical predictions are fully con rmed, perhaps
to a higher degree than expected. We compare regions of stability in parameter
space obtained from a fully 3D analysis with those from a quasi two-dimensional
treatment, when the dynamics in one direction are frozen. We nd that in the 3D
case the stability region splits into two parts. However, as we tighten the con
nement, one of the islands of stability moves toward higher frequencies and the
lower frequency region becomes more and more like that for quasi 2D. We
demonstrate these solutions in direct numerical simulations and, importantly,
suggest a way of creating robust 3D solitons in experiments in a Bose Einstein
Condensate in a one-dimensional lattice.Comment: 14 pages, 6 figures; accepted to Proc. Roy. Soc. London
Coherent Orthogonal Polynomials
We discuss as a fundamental characteristic of orthogonal polynomials like the
existence of a Lie algebra behind them, can be added to their other relevant
aspects. At the basis of the complete framework for orthogonal polynomials we
put thus --in addition to differential equations, recurrence relations, Hilbert
spaces and square integrable functions-- Lie algebra theory.
We start here from the square integrable functions on the open connected
subset of the real line whose bases are related to orthogonal polynomials. All
these one-dimensional continuous spaces allow, besides the standard uncountable
basis , for an alternative countable basis . The matrix elements
that relate these two bases are essentially the orthogonal polynomials: Hermite
polynomials for the line and Laguerre and Legendre polynomials for the
half-line and the line interval, respectively.
Differential recurrence relations of orthogonal polynomials allow us to
realize that they determine a unitary representation of a non-compact Lie
algebra, whose second order Casimir gives rise to the second order
differential equation that defines the corresponding family of orthogonal
polynomials. Thus, the Weyl-Heisenberg algebra with for
Hermite polynomials and with for Laguerre and
Legendre polynomials are obtained.
Starting from the orthogonal polynomials the Lie algebra is extended both to
the whole space of the functions and to the corresponding
Universal Enveloping Algebra and transformation group. Generalized coherent
states from each vector in the space and, in particular,
generalized coherent polynomials are thus obtained.Comment: 11 page
Spatially incoherent modulational instability in a non local medium
We investigate one-dimensional transverse modulational instability in a non
local medium excited with a spatially incoherent source. Employing undoped
nematic liquid crystals in a planar pre-tilted configuration, we investigate
the role of the spectral broadening induced by incoherence in conjunction with
the spatially non local molecular reorientation. The phenomenon is modeled
using the Wigner transform.Comment: 13 pages with 4 figures included. To be published in Laser Physics
Letter
Spontaneous symmetry breaking of gap solitons in double-well traps
We introduce a two dimensional model for the Bose-Einstein condensate with
both attractive and repulsive nonlinearities. We assume a combination of a
double well potential in one direction, and an optical lattice along the
perpendicular coordinate. We look for dual core solitons in this model,
focusing on their symmetry-breaking bifurcations. The analysis employs a
variational approximation, which is verified by numerical results. The
bifurcation which transforms antisymmetric gap solitons into asymmetric ones is
of supercritical type in the case of repulsion; in the attraction model,
increase of the optical latttice strength leads to a gradual transition from
subcritical bifurcation (for symmetric solitons) to a supercritical one.Comment: 6 pages, 5 figure
A Generalization of the Kepler Problem
We construct and analyze a generalization of the Kepler problem. These
generalized Kepler problems are parameterized by a triple
where the dimension is an integer, the curvature is a real
number, the magnetic charge is a half integer if is odd and is 0 or
1/2 if is even. The key to construct these generalized Kepler problems is
the observation that the Young powers of the fundamental spinors on a punctured
space with cylindrical metric are the right analogues of the Dirac monopoles.Comment: The final version. To appear in J. Yadernaya fizik
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