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 $r \lg r > \sqrt{n}$

Superposition solutions to the extended KdV equation for water surface waves

The KdV equation can be derived in the shallow water limit of the Euler equations. Over the last few decades, this equation has been extended to include higher order effects. Although this equation has only one conservation law, exact periodic and solitonic solutions exist. Khare and Saxena \cite{KhSa,KhSa14,KhSa15} demonstrated the possibility of generating new exact solutions by combining known ones for several fundamental equations (e.g., Korteweg - de Vries, Nonlinear Schr\"{o}dinger). Here we find that this construction can be repeated for higher order, non-integrable extensions of these equations. Contrary to many statements in the literature, there seems to be no correlation between integrability and the number of nonlinear one variable wave solutions.Comment: 8 pages, 10 figure

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

Stability of ion acoustic nonlinear waves and solitons in magnetized plasmas

Early results concerning the shape and stability of ion acoustic waves are generalized to propagation at an angle to the magnetic field lines. Each wave has a critical angle for stability. Known soliton results are recovered as special cases. A historical overview of the problem concludes the paper.Comment: 7 pages, 3 figures. Version 2 introduces major changes: (1) addition of a co-author, (2) change of the title for a more adequate to the present contents (previous title: 'Self-focusing of nonlinear ion acoustic waves and solitons in magnetized plasmas IV'), (3) revision of some results, (4) illustration with examples supplied with 3 figures, (5) addition of a historical overvie

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