Heat transfer and Fourier's law in off-equilibrium systems

We study the most suitable procedure to measure the effective temperature in off-equilibrium systems. We analyze the stationary current established between an off-equilibrium system and a thermometer and the necessary conditions for that current to vanish. We find that the thermometer must have a short characteristic time-scale compared to the typical decorrelation time of the glassy system to correctly measure the effective temperature. This general conclusion is confirmed analyzing an ensemble of harmonic oscillators with Monte Carlo dynamics as an illustrative example of a solvable model of a glass. We also find that the current defined allows to extend Fourier's law to the off-equilibrium regime by consistently defining effective transport coefficients. Our results for the oscillator model explain why thermal conductivities between thermalized and frozen degrees of freedom in structural glasses are extremely small.Comment: 7 pages, REVTeX, 4 eps figure

Why charges go to the surface: a generalized Thomson problem

We study a generalization of a Thomson problem of n particles confined to a sphere and interacting by a 1/r^g potential. It is found that for g \le 1 the electrostatic repulsion expels all the charges to the surface of the sphere. However for g>1 and n>n_c(g) occupation of the bulk becomes energetically favorable. It is curious to note that the Coulomb law lies exactly on the interface between these two regimes

Ground state of a large number of particles on a frozen topography

Problems consisting in finding the ground state of particles interacting with a given potential constrained to move on a particular geometry are surprisingly difficult. Explicit solutions have been found for small numbers of particles by the use of numerical methods in some particular cases such as particles on a sphere and to a much lesser extent on a torus. In this paper we propose a general solution to the problem in the opposite limit of a very large number of particles M by expressing the energy as an expansion in M whose coefficients can be minimized by a geometrical ansatz. The solution is remarkably universal with respect to the geometry and the interaction potential. Explicit solutions for the sphere and the torus are provided. The paper concludes with several predictions that could be verified by further theoretical or numerical work.Comment: 9 pages, 9 figures, LaTeX fil

Crystalline Order on a Sphere and the Generalized Thomson Problem

We attack generalized Thomson problems with a continuum formalism which exploits a universal long range interaction between defects depending on the Young modulus of the underlying lattice. Our predictions for the ground state energy agree with simulations of long range power law interactions of the form 1/r^{gamma} (0 < gamma < 2) to four significant digits. The regime of grain boundaries is studied in the context of tilted crystalline order and the generality of our approach is illustrated with new results for square tilings on the sphere.Comment: 4 pages, 5 eps figures Fig. 2 revised, improved Fig. 3, reference typo fixe

Relativistic integro-differential form of the Lorentz-Dirac equation in 3D without runaways

It is well known that the third-order Lorentz-Dirac equation admits runaway solutions wherein the energy of the particle grows without limit, even when there is no external force. These solutions can be denied simply on physical grounds, and on the basis of careful analysis of the correspondence between classical and quantum theory. Nonetheless, one would prefer an equation that did not admit unphysical behavior at the outset. Such an equation - an integro-differential version of the Lorentz-Dirac equation - is currently available either in 1 dimension only, or in 3 dimensions only in the non-relativistic limit. It is shown herein how the Lorentz-Dirac equation may be integrated without approximation, and is thereby converted to a second-order integro-differential equation in 3D satisfying the above requirement. I.E., as a result, no additional constraints on the solutions are required because runaway solutions are intrinsically absent. The derivation is placed within the historical context established by standard works on classical electrodynamics by Rohrlich, and by Jackson.Comment: (updated journal reference & email address

Limits on models of the ultrahigh energy cosmic rays based on topological defects

An erratum exists for this article. Please see the description link below for details.Using the propagation of ultrahigh energy nucleons, photons, and electrons in the universal radiation backgrounds, we obtain limits on the luminosity of topological defect scenarios for the origin of the highest energy cosmic rays. The limits are set as a function of the mass of the X particles emitted by the cosmic strings or other defects, the cosmological evolution of the topological defects, and the strength of the extragalactic magnetic fields. The existing data on the cosmic ray spectrum and on the isotropic 100 MeV gamma-ray background limit significantly the parameter space in which topological defects can generate the flux of the highest energy cosmic rays, and rule out models with the standard X-particle mass of 10¹⁶GeV and higher.R. J. Protheroe and Todor Stane

The nature of the highest energy cosmic rays

Ultra high energy gamma rays produce electron--positron pairs in interactions on the geomagnetic field. The pair electrons suffer magnetic bremsstrahlung and the energy of the primary gamma ray is shared by a bunch of lower energy secondaries. These processes reflect the structure of the geomagnetic field and cause experimentally observable effects. The study of these effects with future giant air shower arrays can identify the nature of the highest energy cosmic rays as either gamma-rays or nuclei.Comment: 15 pages of RevTeX plus 6 postscript figures, tarred, gzipped and uuencoded. Subm. to Physical Review