986 research outputs found

### Hoffmann-Infeld Black Hole Solutions in Lovelock Gravity

Five-dimensional black holes are studied in Lovelock gravity coupled to
Hoffmann-Infeld non-linear electrodynamics. It is shown that some of these
solutions present a double peak behavior of the temperature as a function of
the horizon radius. This feature implies that the evaporation process, though
drastic for a period, leads to an eternal black hole remnant. Moreover, the
form of the caloric curve corresponds to the existence of a plateau in the
evaporation rate, which implies that black holes of intermediate scales turn
out to be unstable. The geometrical aspects, such as the absence of conical
singularity, the structure of horizons, etc. are also discussed. In particular,
solutions that are asymptotically AdS arise for special choices of the
parameters, corresponding to charged solutions of five-dimensional Chern-Simons
gravity.Comment: 6 pages, 5 figures, Revtex4. References added and comments clarified;
version accepted for publicatio

### The Total Acquisition Number of Random Geometric Graphs

Let $G$ be a graph in which each vertex initially has weight 1. In each step,
the weight from a vertex $u$ to a neighbouring vertex $v$ can be moved,
provided that the weight on $v$ is at least as large as the weight on $u$. The
total acquisition number of $G$, denoted by $a_t(G)$, is the minimum
cardinality of the set of vertices with positive weight at the end of the
process. In this paper, we investigate random geometric graphs $G(n,r)$ with
$n$ vertices distributed u.a.r. in $[0,\sqrt{n}]^2$ and two vertices being
adjacent if and only if their distance is at most $r$. We show that
asymptotically almost surely $a_t(G(n,r)) = \Theta( n / (r \lg r)^2)$ for the
whole range of $r=r_n \ge 1$ such that $r \lg r \le \sqrt{n}$. By monotonicity,
asymptotically almost surely $a_t(G(n,r)) = \Theta(n)$ if $r < 1$, and
$a_t(G(n,r)) = \Theta(1)$ if $r \lg r > \sqrt{n}$

### 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

### Electromagnetic Oscillations in a Spherical Conducting Cavity with Dielectric Layers. Application to Linear Accelerators

We present an analysis of electromagnetic oscillations in a spherical
conducting cavity filled concentrically with either dielectric or vacuum
layers. The fields are given analytically, and the resonant frequency is
determined numerically. An important special case of a spherical conducting
cavity with a smaller dielectric sphere at its center is treated in more
detail. By numerically integrating the equations of motion we demonstrate that
the transverse electric oscillations in such cavity can be used to accelerate
strongly relativistic electrons. The electron's trajectory is assumed to be
nearly tangential to the dielectric sphere. We demonstrate that the interaction
of such electrons with the oscillating magnetic field deflects their trajectory
from a straight line only slightly. The Q factor of such a resonator only
depends on losses in the dielectric. For existing ultra low loss dielectrics, Q
can be three orders of magnitude better than obtained in existing cylindrical
cavities.Comment: Extended version with one new section, modified title and new
abstract, 10 pages, 13 figure

### Transverse Instability of Solitons Propagating on Current-Carrying Metal Thin Films

Small amplitude, long waves travelling over the surface of a current-carrying
metal thin film are studied. The equation of motion for the metal surface is
determined in the limit of high applied currents, when surface electromigration
is the predominant cause of adatom motion. If the surface height h is
independent of the transverse coordinate y, the equation of motion reduces to
the Korteweg-de Vries equation. One-dimensional solitons (i.e., those with h
independent of y) are shown to be unstable against perturbations to their shape
with small transverse wavevector.Comment: 25 pages with 2 figures. To appear in Physica

### 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

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