On the diffusive anomalies in a long-range Hamiltonian system

We scrutinize the anomalies in diffusion observed in an extended long-range system of classical rotors, the HMF model. Under suitable preparation, the system falls into long-lived quasi-stationary states presenting super-diffusion of rotor phases. We investigate the diffusive motion of phases by monitoring the evolution of their probability density function for large system sizes. These densities are shown to be of the $q$-Gaussian form, $P(x)\propto (1+(q-1)[x/\beta]^2)^{1/(1-q)}$, with parameter $q$ increasing with time before reaching a steady value $q\simeq 3/2$. From this perspective, we also discuss the relaxation to equilibrium and show that diffusive motion in quasi-stationary trajectories strongly depends on system size.Comment: 5 pages, 5 figures. References added and correcte

Effect of air-fuel ratio on detonation in gasoline engines

The study of the effect of mixture strength on detonation may be divided into two parts, namely: a) the measurement of the effect in engines; and b) the explanation of the effect

Γ-limit for the extended Fisher-Kolmogorov equation

We consider the Lyapunov functional, of the rescaled Extended Fisher-Kolmogorov equation This is a fourth order generalization of the Fisher-Kolmogorov or Allen-Cahn equation. We prove that if ε → 0, then tends to the area functional in the sense of Γ-limits, where the transition energy is given by the one-dimensional kink of the Extended Fisher-Kolmogorov equatio

One-dimensional symmetry and Liouville type results for the fourth order Allen-Cahn equation in RN^N

In this paper, we prove an analogue of Gibbons' conjecture for the extended fourth order Allen-Cahn equation in R N , as well as Liouville type results for some solutions converging to the same value at infinity in a given direction. We also prove a priori bounds and further one-dimensional symmetry and rigidity results for semilinear fourth order elliptic equations with more general nonlinearities

Large Deviations in Stochastic Heat-Conduction Processes Provide a Gradient-Flow Structure for Heat Conduction

We consider three one-dimensional continuous-time Markov processes on a lattice, each of which models the conduction of heat: the family of Brownian Energy Processes with parameter $m$, a Generalized Brownian Energy Process, and the Kipnis-Marchioro-Presutti process. The hydrodynamic limit of each of these three processes is a parabolic equation, the linear heat equation in the case of the BEP$(m)$ and the KMP, and a nonlinear heat equation for the GBEP($a$). We prove the hydrodynamic limit rigorously for the BEP$(m)$, and give a formal derivation for the GBEP($a$). We then formally derive the pathwise large-deviation rate functional for the empirical measure of the three processes. These rate functionals imply gradient-flow structures for the limiting linear and nonlinear heat equations. We contrast these gradient-flow structures with those for processes describing the diffusion of mass, most importantly the class of Wasserstein gradient-flow systems. The linear and nonlinear heat-equation gradient-flow structures are each driven by entropy terms of the form $-\log \rho$; they involve dissipation or mobility terms of order $\rho^2$ for the linear heat equation, and a nonlinear function of $\rho$ for the nonlinear heat equation.Comment: 29 page

Early Type Galaxies in the Mid Infrared: a new flavor to their stellar populations

The mid infrared emission of early type galaxies traces the presence of intermediate age stellar populations as well as even tiny amounts of ongoing star formation. Here we discuss high S/N Spitzer IRS spectra of a sample of Virgo early type galaxies, with particular reference to NGC 4435. We show that, by combining mid infrared spectroscopic observations with existing broad band fluxes, it is possible to obtain a very clean picture of the nuclear activity in this galaxy.Comment: 4 pages; proceedings of IAU Symposium No. 241, "Stellar Populations as Building Blocks of Galaxies", editors A. Vazdekis and R. Peletie

Dynamics and stability of vortex-antivortex fronts in type II superconductors

The dynamics of vortices in type II superconductors exhibit a variety of patterns whose origin is poorly understood. This is partly due to the nonlinearity of the vortex mobility which gives rise to singular behavior in the vortex densities. Such singular behavior complicates the application of standard linear stability analysis. In this paper, as a first step towards dealing with these dynamical phenomena, we analyze the dynamical stability of a front between vortices and antivortices. In particular we focus on the question of whether an instability of the vortex front can occur in the absence of a coupling to the temperature. Borrowing ideas developed for singular bacterial growth fronts, we perform an explicit linear stability analysis which shows that, for sufficiently large front velocities and in the absence of coupling to the temperature, such vortex fronts are stable even in the presence of in-plane anisotropy. This result differs from previous conclusions drawn on the basis of approximate calculations for stationary fronts. As our method extends to more complicated models, which could include coupling to the temperature or to other fields, it provides the basis for a more systematic stability analysis of nonlinear vortex front dynamics.Comment: 13 pages, 8 figure

Nuclear Components in the Bulges of Disk Galaxies

By combining surface brightness profiles from images taken in the HST/NICMOS F160W and ground-based (GB) $K$ bands, we have obtained NIR profiles for a well studied sample of inclined disk galaxies, spanning radial ranges from 20 pc to a few kpc. We fit PSF-convolved Sersic-plus-exponential laws to the profiles, and compare the results with the fits to the ground-based data alone. HST profiles show light excesses over the best-fit Sersic law in the inner ~1 arcsec. This is often as a result of inner power-law cusps similar to the inner profiles of intermediate-luminosity elliptical galaxies.Comment: 4 pages, 5 figures. Poster paper to "The Central kpc of Starbursts and AGN: the La Palma connection'', Eds. J.H. Knapen, J.E. Beckman, I. Shlosman and T.J. Mahoney, ASP conf. series, in press (2001

Internal kinematics of spiral galaxies in distant clusters III. Velocity fields from FORS2/MXU spectroscopy

(Abridged) We study the impact of cluster environment on the evolution of spiral galaxies by examining their structure and kinematics. Rather than two-dimensional rotation curves, we observe complete velocity fields by placing three adjacent and parallel FORS2 MXU slits on each object, yielding several emission and absorption lines. The gas velocity fields are reconstructed and decomposed into circular rotation and irregular motions using kinemetry. To quantify irregularities in the gas kinematics, we define three parameters: sigma_{PA} (standard deviation of the kinematic position angle), Delta phi (the average misalignment between kinematic and photometric position angles) and k_{3,5} (squared sum of the higher order Fourier terms). Using local, undistorted galaxies from SINGS, these can be used to establish the regularity of the gas velocity fields. Here we present the analysis of 22 distant galaxies in the MS0451.6-0305 field with 11 members at z=0.54. In this sample we find both field (4 out of 8) and cluster (3 out of 4) galaxies with velocity fields that are both irregular and asymmetric. We show that these fractions are underestimates of the actual number of galaxies with irregular velocity fields. The values of the (ir)regularity parameters for cluster galaxies are not very different from those of the field galaxies, implying that there are isolated field galaxies that are as distorted as the cluster members. None of the deviations in our small sample correlate with photometric/structural properties like luminosity or disk scale length in a significant way. Our 3D-spectroscopic method successfully maps the velocity field of distant galaxies, enabling the importance and efficiency of cluster specific interactions to be assessed quantitatively.Comment: accepted for publication in A&A, high resolution version available at http://www.astro.rug.nl/~kutdemir/papers