Adolf Reinach: An Intellectual Biography

The essay provides an account of the development of Reinach’s philosophy of “Sachverhalte” (states of affairs) and on problems in the philosophy of law, leading up to his discovery of the theory of speech acts in 1913. Reinach’s relations to Edmund Husserl and to the Munich phenomenologists are also dealt with

The Effects of Weak Spatiotemporal Noise on a Bistable One-Dimensional System

We treat analytically a model that captures several features of the phenomenon of spatially inhomogeneous reversal of an order parameter. The model is a classical Ginzburg-Landau field theory restricted to a bounded one-dimensional spatial domain, perturbed by weak spatiotemporal noise having a flat power spectrum in time and space. Our analysis extends the Kramers theory of noise-induced transitions to the case when the system acted on by the noise has nonzero spatial extent, and the noise itself is spatially dependent. By extending the Langer-Coleman theory of the noise-induced decay of a metastable state, we determine the dependence of the activation barrier and the Kramers reversal rate prefactor on the size of the spatial domain. As this is increased from zero and passes through a certain critical value, a transition between activation regimes occurs, at which the rate prefactor diverges. Beyond the transition, reversal preferentially takes place in a spatially inhomogeneous rather than in a homogeneous way. Transitions of this sort were not discovered by Langer or Coleman, since they treated only the infinite-volume limit. Our analysis uses higher transcendental functions to handle the case of finite volume. Similar transitions between activation regimes should occur in other models of metastable systems with nonzero spatial extent, perturbed by weak noise, as the size of the spatial domain is varied.Comment: 16 page

Magnetic correlations of the quasi-one-dimensional half-integer spin-chain antiferromagnets SrM2M_2V2_2O8_8 (MM = Co, Mn)

Magnetic correlations of two iso-structural quasi-one-dimensional (1D) antiferromagnetic spin-chain compounds Sr$M_2$V$_2$O$_8$ ($M$ = Co, Mn) have been investigated by magnetization and powder neutron diffraction. Two different collinear antiferromagnetic (AFM) structures, characterized by the propagation vectors, $k$ = (0 0 1) and $k$ = (0 0 0), have been found below $\sim$ 5.2 K and $\sim$ 42.2 K for the Co- and Mn-compounds, respectively. For the Mn-compound, AFM chains (along the $c$ axis) order ferromagnetically within the $ab$ plane, whereas, for the Co-compound, AFM chains order ferro-/antiferromagnetically along the $a/b$ direction. The critical exponent study confirms that the Co- and Mn-compounds belong to the Ising and Heisenberg universality classes, respectively. For both compounds, short-range spin-spin correlations are present over a wide temperature range above $T_N$. The reduced ordered moments at base temperature (1.5 K) indicate the presence of quantum fluctuations in both compounds due to the quasi-1D magnetic interactions.Comment: 14 pages, 10 figures, 9 table

Noisy Classical Field Theories with Two Coupled Fields: Dependence of Escape Rates on Relative Field Stiffnesses

Exit times for stochastic Ginzburg-Landau classical field theories with two or more coupled classical fields depend on the interval length on which the fields are defined, the potential in which the fields deterministically evolve, and the relative stiffness of the fields themselves. The latter is of particular importance in that physical applications will generally require different relative stiffnesses, but the effect of varying field stiffnesses has not heretofore been studied. In this paper, we explore the complete phase diagram of escape times as they depend on the various problem parameters. In addition to finding a transition in escape rates as the relative stiffness varies, we also observe a critical slowing down of the string method algorithm as criticality is approached.Comment: 16 pages, 10 figure

Realistic Magnetohydrodynamical Simulation of Solar Local Supergranulation

Three-dimensional numerical simulations of solar surface magnetoconvection using realistic model physics are conducted. The thermal structure of convective motions into the upper radiative layers of the photosphere, the main scales of convective cells and the penetration depths of convection are investigated. We take part of the solar photosphere with size of 60x60 Mm in horizontal direction and by depth 20 Mm from level of the visible solar surface. We use a realistic initial model of the Sun and apply equation of state and opacities of stellar matter. The equations of fully compressible radiation magnetohydrodynamics with dynamical viscosity and gravity are solved. We apply: 1) conservative TVD difference scheme for the magnetohydrodynamics, 2) the diffusion approximation for the radiative transfer, 3) dynamical viscosity from subgrid scale modeling. In simulation we take uniform two-dimesional grid in gorizontal plane and nonuniform grid in vertical direction with number of cells 600x600x204. We use 512 processors with distributed memory multiprocessors on supercomputer MVS-100k in the Joint Computational Centre of the Russian Academy of Sciences.Comment: 6 pages, 5 figures, submitted to the proceedings of the GONG 2008 / SOHO XXI conferenc

A New Limit on Signals of Lorentz Violation in Electrodynamics

We describe the results of an experiment to test for spacetime anisotropy terms that might exist from Lorentz violations. The apparatus consists of a pair of cylindrical superconducting cavity-stabilized oscillators operating in the TM_{010} mode with one axis east-west and the other vertical. Spatial anisotropy is detected by monitoring the beat frequency at the sidereal rate and its first harmonic. We see no anisotropy to a part in 10^{13}. This puts a comparable bound on four linear combinations of parameters in the general Standard Model extension, and a weaker bound of <4 x 10^{-9} on three others.Comment: 4 pages, 3 figures, 2 table

A Weighted Estimate for the Square Function on the Unit Ball in \C^n

We show that the Lusin area integral or the square function on the unit ball of \C^n, regarded as an operator in weighted space $L^2(w)$ has a linear bound in terms of the invariant $A_2$ characteristic of the weight. We show a dimension-free estimate for the ``area-integral'' associated to the weighted $L^2(w)$ norm of the square function. We prove the equivalence of the classical and the invariant $A_2$ classes.Comment: 11 pages, to appear in Arkiv for Matemati

The role of surface generated radicals in catalytic combustion

Experiments were conducted to better understand the role of catalytic surface reactions in determining the ignition characteristics of practical catalytic combustors. Hydrocarbon concentrations, carbon monoxide and carbon dioxide concentrations, hydroxyl radical concentrations, and gas temperature were measured at the exit of a platinum coated, stacked plate, catalytic combustor during the ignition of lean propane-air mixtures. The substrate temperature profile was also measured during the ignition transient. Ignition was initiated by suddenly turning on the fuel and the time to reach steady state was of the order of 10 minutes. The gas phase reaction, showed no pronounced effect due to the catalytic surface reactions, except the absence of a hydroxyl radical overshoot. It is found that the transient ignition measurements are valuable in understanding the steady state performance characteristics

Efficient formalism for large scale ab initio molecular dynamics based on time-dependent density functional theory

A new "on the fly" method to perform Born-Oppenheimer ab initio molecular dynamics (AIMD) is presented. Inspired by Ehrenfest dynamics in time-dependent density functional theory, the electronic orbitals are evolved by a Schroedinger-like equation, where the orbital time derivative is multiplied by a parameter. This parameter controls the time scale of the fictitious electronic motion and speeds up the calculations with respect to standard Ehrenfest dynamics. In contrast to other methods, wave function orthogonality needs not be imposed as it is automatically preserved, which is of paramount relevance for large scale AIMD simulations.Comment: 5 pages, 3 color figures, revtex4 packag