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

Longwall shearer tracking system

A tracking system for measuring and recording the movements of a longwall shearer vehicle includes an optical tracking assembly carried at one end of a desired vehicle path and a retroreflector assembly carried by the vehicle. Continuous horizontal and vertical light beams are alternately transmitted by means of a rotating Dove prism to the reflector assembly. A vertically reciprocating reflector interrupts the continuous light beams and converts these to discrete horizontal and vertical light beam images transmitted at spaced intervals along the path. A second rotating Dove prism rotates the vertical images to convert them to a second series of horizontal images while the first mentioned horizontal images are left unrotated and horizontal. The images are recorded on a film

On a fourth order nonlinear Helmholtz equation

In this paper, we study the mixed dispersion fourth order nonlinear Helmholtz equation $\Delta^2 u -\beta \Delta u + \alpha u= \Gamma|u|^{p-2} u$ in $\mathbb R^N$ for positive, bounded and $\mathbb Z^N$-periodic functions $\Gamma$. Using the dual method of Evequoz and Weth, we find solutions to this equation and establish some of their qualitative properties

Estimates of higher-dimensional vacuum condensates from the instanton vacuum

We calculate the values of non-factorizable dimension-7 vacuum condensates in the instanton vacuum. We comment on a method, recently proposed by Oganesian, to estimate the dimension-7 condensates by factorization of dimension-10 condensates in various inequivalent ways. The instanton estimates could be used to analyze the stability of QCD sum rules with increasing dimensions.Comment: 8 pages, Late

Adjointness Relations as a Criterion for Choosing an Inner Product

This is a contribution to the forthcoming book "Canonical Gravity: {}From Classical to Quantum" edited by J. Ehlers and H. Friedrich. Ashtekar's criterion for choosing an inner product in the quantisation of constrained systems is discussed. An erroneous claim in a previous paper is corrected and a cautionary example is presented.Comment: 6 pages, MPA-AR-94-

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

The Order of Phase Transitions in Barrier Crossing

A spatially extended classical system with metastable states subject to weak spatiotemporal noise can exhibit a transition in its activation behavior when one or more external parameters are varied. Depending on the potential, the transition can be first or second-order, but there exists no systematic theory of the relation between the order of the transition and the shape of the potential barrier. In this paper, we address that question in detail for a general class of systems whose order parameter is describable by a classical field that can vary both in space and time, and whose zero-noise dynamics are governed by a smooth polynomial potential. We show that a quartic potential barrier can only have second-order transitions, confirming an earlier conjecture [1]. We then derive, through a combination of analytical and numerical arguments, both necessary conditions and sufficient conditions to have a first-order vs. a second-order transition in noise-induced activation behavior, for a large class of systems with smooth polynomial potentials of arbitrary order. We find in particular that the order of the transition is especially sensitive to the potential behavior near the top of the barrier.Comment: 8 pages, 6 figures with extended introduction and discussion; version accepted for publication by Phys. Rev.

A phase transition in a system driven by coloured noise

For a system driven by coloured noise, we investigate the activation energy of escape, and the dynamics during the escape. We have performed analogue experiments to measure the change in activation energy as the power spectrum of the noise varies. An adiabatic approach based on path integral theory allows us to calculate analytically the critical value at which a phase transition in the activation energy occurs

Large fluctuations and irreversibility in nonequilibrium systems.

Large rare fluctuations in a nonequilibrium system are investigated theoretically and by analogue electronic experiment. It is emphasized that the optimal paths calculated via the eikonal approximation of the Fokker-Planck equation can be identified with the locus of the ridges of the prehistory probability distributions which can be calculated and measured experimentally for paths terminating at a given final point in configuration sspace. The pattern of optimal paths and its singularities, such as caustics, cusps and switching lines has been calculated and measured experimentally for a periodically driven overdamped oscillator, yielding results that are shown to be in good agreement with each other