Finite field-energy of a point charge in QED

We consider a simple nonlinear (quartic in the fields) gauge-invariant modification of classical electrodynamics, which possesses a regularizing ability sufficient to make the field energy of a point charge finite. The model is exactly solved in the class of static central-symmetric electric fields. Collation with quantum electrodynamics (QED) results in the total field energy about twice the electron mass. The proof of the finiteness of the field energy is extended to include any polynomial selfinteraction, thereby the one that stems from the truncated expansion of the Euler-Heisenberg local Lagrangian in QED in powers of the field strenth

Cortical free association dynamics: distinct phases of a latching network

A Potts associative memory network has been proposed as a simplified model of macroscopic cortical dynamics, in which each Potts unit stands for a patch of cortex, which can be activated in one of S local attractor states. The internal neuronal dynamics of the patch is not described by the model, rather it is subsumed into an effective description in terms of graded Potts units, with adaptation effects both specific to each attractor state and generic to the patch. If each unit, or patch, receives effective (tensor) connections from C other units, the network has been shown to be able to store a large number p of global patterns, or network attractors, each with a fraction a of the units active, where the critical load p_c scales roughly like p_c ~ (C S^2)/(a ln(1/a)) (if the patterns are randomly correlated). Interestingly, after retrieving an externally cued attractor, the network can continue jumping, or latching, from attractor to attractor, driven by adaptation effects. The occurrence and duration of latching dynamics is found through simulations to depend critically on the strength of local attractor states, expressed in the Potts model by a parameter w. Here we describe with simulations and then analytically the boundaries between distinct phases of no latching, of transient and sustained latching, deriving a phase diagram in the plane w-T, where T parametrizes thermal noise effects. Implications for real cortical dynamics are briefly reviewed in the conclusions

Effect of the heliospheric interface on the distribution of interstellar hydrogen atom inside the heliosphere

This paper deals with the modeling of the interstellar hydrogen atoms (H atoms) distribution in the heliosphere. We study influence of the heliospheric interface, that is the region of the interaction between solar wind and local interstellar medium, on the distribution of the hydrogen atoms in vicinity of the Sun. The distribution of H atoms obtained in the frame of the self-consistent kinetic-gasdynamic model of the heliospheric interface is compared with a simplified model which assumes Maxwellian distribution of H atoms at the termination shock and is called often as 'hot' model. This comparison shows that the distribution of H atoms is significantly affected by the heliospheric interface not only at large heliocentric distances, but also in vicinity of the Sun at 1-5 AU. Hence, for analysis of experimental data connected with direct or undirect measurements of the interstellar atoms one necessarily needs to take into account effects of the heliospheric interface. In this paper we propose a new model that is relatively simple but takes into account all major effects of the heliospheric interface. This model can be applied for analysis of backscattered Ly-alpha radiation data obtained on board of different spacecraft.Comment: published in Astronomy Letter

A 450-day light curve of the radio afterglow of GRB 970508: Fireball calorimetry

We report on the results of an extensive monitoring campaign of the radio afterglow of GRB 970508, lasting 450 days after the burst. The spectral and temporal radio behavior indicate that the fireball has undergone a transition to sub-relativistic expansion at t~100 days. This allows us to perform "calorimetry" of the explosion. The derived total energy, ~5\times 10^{50} erg, is well below the ~5\times 10^{51} erg inferred under the assumption of spherical symmetry from gamma-ray and early afterglow observations. A natural consequence of this result, which can also account for deviations at t<100 days from the spherical relativistic fireball model predictions, is that the fireball was initially a wide-angle jet of opening angle ~30 degrees. Our analysis also allows to determine the energy fractions carried by electrons and magnetic field, and the density of ambient medium surrounding the fireball. We find that during the sub-relativistic expansion electrons and magnetic field are close to equipartition, and that the density of the ambient medium is ~1/cm^3. The inferred density rules out the possibility that the fireball expands into a strongly non-uniform medium, as would be expected, e.g., in the case of a massive star progenitor.Comment: 33 pages, including 7 figures, submitted to Ap

Coupled quintessence and vacuum decay

We discuss observational consequences of a class of cosmological models characterized by the dilution of pressureless matter attenuated with respect to the usual $a^{-3}$ scaling due to the decay of vacuum energy. We carry out a joint statistical analysis of observational data from the new \emph{gold} sample of 182 SNe Ia, recent estimates of the CMB shift parameter, and BAO measurements from the SDSS to show that such models favor the decay of vacuum only into the dark matter sector, and that the separately conserved baryons cannot be neglected. In order to explore ways to more fundamentally motivated models, we also derive a coupled scalar field version for this general class of vacuum decay scenarios.Comment: 6 pages, 3 figures, LaTe

Phase transition in ultrathin magnetic films with long-range interactions: Monte Carlo simulation of the anisotropic Heisenberg model

Ultrathin magnetic films can be modeled as an anisotropic Heisenberg model with long-range dipolar interactions. It is believed that the phase diagram presents three phases: An ordered ferromagnetic phase I, a phase characterized by a change from out-of-plane to in-plane in the magnetization II, and a high-temperature paramagnetic phase III. It is claimed that the border lines from phase I to III and II to III are of second order and from I to II is first order. In the present work we have performed a very careful Monte Carlo simulation of the model. Our results strongly support that the line separating phases II and III is of the BKT type.Comment: 7 page