Large deviations in boundary-driven systems: Numerical evaluation and effective large-scale behavior

We study rare events in systems of diffusive fields driven out of equilibrium by the boundaries. We present a numerical technique and use it to calculate the probabilities of rare events in one and two dimensions. Using this technique, we show that the probability density of a slowly varying configuration can be captured with a small number of long wave-length modes. For a configuration which varies rapidly in space this description can be complemented by a local equilibrium assumption

Transport of Cosmic Rays in Chaotic Magnetic Fields

The transport of charged particles in disorganised magnetic fields is an important issue which concerns the propagation of cosmic rays of all energies in a variety of astrophysical environments, such as the interplanetary, interstellar and even extra-galactic media, as well as the efficiency of Fermi acceleration processes. We have performed detailed numerical experiments using Monte-Carlo simulations of particle propagation in stochastic magnetic fields in order to measure the parallel and transverse spatial diffusion coefficients and the pitch angle scattering time as a function of rigidity and strength of the turbulent magnetic component. We confirm the extrapolation to high turbulence levels of the scaling predicted by the quasi-linear approximation for the scattering frequency and parallel diffusion coefficient at low rigidity. We show that the widely used Bohm diffusion coefficient does not provide a satisfactory approximation to diffusion even in the extreme case where the mean field vanishes. We find that diffusion also takes place for particles with Larmor radii larger than the coherence length of the turbulence. We argue that transverse diffusion is much more effective than predicted by the quasi-linear approximation, and appears compatible with chaotic magnetic diffusion of the field lines. We provide numerical estimates of the Kolmogorov length and magnetic line diffusion coefficient as a function of the level of turbulence. Finally we comment on applications of our results to astrophysical turbulence and the acceleration of high energy cosmic rays in supernovae remnants, in super-bubbles, and in jets and hot spots of powerful radio-galaxies.Comment: To be published in Physical Review D, 20 pages 9 figure

Ensemble v-representable ab-initio density functional calculation of energy and spin in atoms: atest of exchange-correlation approximations

The total energies and the spin states for atoms and their first ions with Z = 1-86 are calculated within the the local spin-density approximation (LSDA) and the generalized-gradient approximation (GGA) to the exchange-correlation (xc) energy in density-functional theory. Atoms and ions for which the ground-state density is not pure-state v-representable, are treated as ensemble v- representable with fractional occupations of the Kohn-Sham system. A newly developed algorithm which searches over ensemble v-representable densities [E. Kraisler et al., Phys. Rev. A 80, 032115 (2009)] is employed in calculations. It is found that for many atoms the ionization energies obtained with the GGA are only modestly improved with respect to experimental data, as compared to the LSDA. However, even in those groups of atoms where the improvement is systematic, there remains a non-negligible difference with respect to the experiment. The ab-initio electronic configuration in the Kohn-Sham reference system does not always equal the configuration obtained from the spectroscopic term within the independent-electron approximation. It was shown that use of the latter configuration can prevent the energy-minimization process from converging to the global minimum, e.g. in lanthanides. The spin values calculated ab-initio fit the experiment for most atoms and are almost unaffected by the choice of the xc-functional. Among the systems with incorrectly obtained spin there exist some cases (e.g. V, Pt) for which the result is found to be stable with respect to small variations in the xc-approximation. These findings suggest a necessity for a significant modification of the exchange-correlation functional, probably of a non-local nature, to accurately describe such systems. PACS numbers: 31.15.

Transition temperature of a dilute homogeneous imperfect Bose gas

The leading-order effect of interactions on a homogeneous Bose gas is theoretically predicted to shift the critical temperature by an amount \Delta\Tc = # a_{scatt} n^{1/3} T_0 from the ideal gas result T_0, where a_{scatt} is the scattering length and n is the density. There have been several different theoretical estimates for the numerical coefficient #. We claim to settle the issue by measuring the numerical coefficient in a lattice simulation of O(2) phi^4 field theory in three dimensions---an effective theory which, as observed previously in the literature, can be systematically matched to the dilute Bose gas problem to reproduce non-universal quantities such as the critical temperature. We find # = 1.32 +- 0.02.Comment: 4 pages, submitted to Phys. Rev. Lett; minor changes due to improvement of analysis in the longer companion pape

Auxiliary master equation for nonequilibrium dual-fermion approach

We introduce auxiliary quantum master equation - dual fermion approach (QME-DF) and argue that it presents a convenient way to describe steady-states of correlated impurity systems. The combined scheme yields an expansion around a reference much closer to the true nonequilibrium state than in the original dual fermion formulation. In steady-state situations, the scheme is numerically cheaper and allows to avoid long time propagation of previous considerations. Anderson impurity is used as a test model. The QME-DF simulations are compared with numerically exact tdDMRG results.Comment: 8 pages, 4 figure

Sow body condition at weaning and reproduction performance in organic piglet production

The objective was to investigate the variation in backfat at weaning and its relations to reproduction results in organic sow herds in Denmark. The study included eight herds and 573 sows. The average backfat at weaning mean�13 mm; SD�4.2 mm) ranging from 10.5 to 17.3 mm among herds shows that it is possible to avoid poor body condition at weaning even with a lactation length of seven weeks or more. No main effect of backfat at weaning on reproduction performance was found, but the probability of a successful reproduction after weaning tended to decrease with decreasing backfat for first parity sows, whereas the opposite was the case for multiparous sows

The robustness of speech representations obtained from simulated auditory nerve fibers under different noise conditions

Different methods of extracting speech features from an auditory model were systematically investigated in terms of their robustness to different noises. The methods either computed the average firing rate within frequency channels (spectral features) or inter-spike-intervals (timing features) from the simulated auditory nerve response. When used as the front-end for an automatic speech recognizer, timing features outperformed spectral features in Gaussian noise. However, this advantage was lost in babble, because timing features extracted the spectro-temporal structure of babble noise, which is similar to the target speaker. This suggests that different feature extraction methods are optimal depending on the background noise

Graph Treewidth and Geometric Thickness Parameters

Consider a drawing of a graph $G$ in the plane such that crossing edges are coloured differently. The minimum number of colours, taken over all drawings of $G$, is the classical graph parameter "thickness". By restricting the edges to be straight, we obtain the "geometric thickness". By further restricting the vertices to be in convex position, we obtain the "book thickness". This paper studies the relationship between these parameters and treewidth. Our first main result states that for graphs of treewidth $k$, the maximum thickness and the maximum geometric thickness both equal $\lceil{k/2}\rceil$. This says that the lower bound for thickness can be matched by an upper bound, even in the more restrictive geometric setting. Our second main result states that for graphs of treewidth $k$, the maximum book thickness equals $k$ if $k \leq 2$ and equals $k+1$ if $k \geq 3$. This refutes a conjecture of Ganley and Heath [Discrete Appl. Math. 109(3):215-221, 2001]. Analogous results are proved for outerthickness, arboricity, and star-arboricity.Comment: A preliminary version of this paper appeared in the "Proceedings of the 13th International Symposium on Graph Drawing" (GD '05), Lecture Notes in Computer Science 3843:129-140, Springer, 2006. The full version was published in Discrete & Computational Geometry 37(4):641-670, 2007. That version contained a false conjecture, which is corrected on page 26 of this versio

Lagrange formalism of memory circuit elements: classical and quantum formulations

The general Lagrange-Euler formalism for the three memory circuit elements, namely, memristive, memcapacitive, and meminductive systems, is introduced. In addition, {\it mutual meminductance}, i.e. mutual inductance with a state depending on the past evolution of the system, is defined. The Lagrange-Euler formalism for a general circuit network, the related work-energy theorem, and the generalized Joule's first law are also obtained. Examples of this formalism applied to specific circuits are provided, and the corresponding Hamiltonian and its quantization for the case of non-dissipative elements are discussed. The notion of {\it memory quanta}, the quantum excitations of the memory degrees of freedom, is presented. Specific examples are used to show that the coupling between these quanta and the well-known charge quanta can lead to a splitting of degenerate levels and to other experimentally observable quantum effects

Two superluminous supernovae from the early universe discovered by the Supernova Legacy Survey

We present spectra and lightcurves of SNLS 06D4eu and SNLS 07D2bv, two hydrogen-free superluminous supernovae discovered by the Supernova Legacy Survey. At z = 1.588, SNLS 06D4eu is the highest redshift superluminous SN with a spectrum, at M_U = -22.7 is one of the most luminous SNe ever observed, and gives a rare glimpse into the restframe ultraviolet where these supernovae put out their peak energy. SNLS 07D2bv does not have a host galaxy redshift, but based on the supernova spectrum, we estimate it to be at z ~ 1.5. Both supernovae have similar observer-frame griz lightcurves, which map to restframe lightcurves in the U-band and UV, rising in ~ 20 restframe days or longer, and declining over a similar timescale. The lightcurves peak in the shortest wavelengths first, consistent with an expanding blackbody starting near 15,000 K and steadily declining in temperature. We compare the spectra to theoretical models, and identify lines of C II, C III, Fe III, and Mg II in the spectrum of SNLS 06D4eu and SCP 06F6, and find that they are consistent with an expanding explosion of only a few solar masses of carbon, oxygen, and other trace metals. Thus the progenitors appear to be related to those suspected for SNe Ic. A high kinetic energy, 10^52 ergs, is also favored. Normal mechanisms of powering core- collapse or thermonuclear supernovae do not seem to work for these supernovae. We consider models powered by 56Ni decay and interaction with circumstellar material, but find that the creation and spin-down of a magnetar with a period of 2ms, magnetic field of 2 x 10^14 Gauss, and a 3 solar mass progenitor provides the best fit to the data.Comment: ApJ, accepted, 43 pages, 15 figure