The speed of biased random walk on percolation clusters

 We consider biased random walk on supercritical percolation clusters in ℤ². We show that the random walk is transient and that there are two speed regimes: If the bias is large enough, the random walk has speed zero, while if the bias is small enough, the speed of the random walk is positive. Received: 20 November 2002 / Revised version: 17 January 2003 Published online: 15 April 2003 Research supported by Microsoft Research graduate fellowship. Research partially supported by the DFG under grant SPP 1033. Research partially supported by NSF grant #DMS-0104073 and by a Miller Professorship at UC Berkeley. Mathematics Subject Classification (2000): 60K37; 60K35; 60G50 Key words or phrases: Percolation – Random walk     

The Calogero–Bogoyavlenskii–Schiff Equation in 2+1 Dimensions

We use the classical and nonclassical methods to obtain symmetry reductions and exact solutions of the (2+1)-dimensional integrable Calogero–Bogoyavlenskii–Schiff equation. Although this (2+1)-dimensional equation arises in a nonlocal form, it can be written as a system of differential equations and, in potential form, as a fourth-order partial differential equation. The classical and nonclassical methods yield some exact solutions of the (2+1)-dimensional equation that involve several arbitrary functions and hence exhibit a rich variety of qualitative behavior.     

Study of solar features causing GMSs with 250γ<<Emphasis Type="Italic">H</Emphasis><400γ

The effect of solar features on geospheric conditions leading to geomagnetic storms (GMSs) with planetary index,A ^P ≥ 20 and the range of horizontal component of the Earth’s magnetic fieldH such that 250γ <H < 400γ has been investigated using interplanetary magnetic field (IMF), solar wind plasma (SWP) and solar geophysical data (SGD) during the period 1978–99. Statistically, it is observed that maximum number of GMSs have occurred during the maximum solar activity years of 21st and 22nd solar cycles. A peculiar result has been observed during the years 1982, 1994 when sunspot numbers (SSNs) decrease very rapidly while numbers of GMSs increase. No distinct association between yearly occurrence of disturbed days and SSNs is observed. Maximum number of disturbed days have occurred during spring and rainy seasons showing a seasonal variation of disturbed days. No significant correlation between magnitude (intensity) of GMSs and importance ofH _α , X-ray solar flares has been observed. Maximum number of GMSs is associated with solar flares of lower importance, i.e., SF during the period 1978-93.H _α , X-ray solar flares occurred within lower helio-latitudes, i.e., (0–30)°N to (0–30)°S are associated with GMSs. NoH _α , X-ray solar flares have occurred beyond 40°N or 40°S in association with GMSs. In helio-latitude range (10–40)°N to (10–40)°S, the 89.5% concentration of active prominences and disappearing filaments (APDFs) are associated with GMSs. Maximum number of GMSs are associated with solar flares. Coronal mass ejections (CMEs) are related with eruptive prominences, solar flares, type IV radio burst and they occur at low helio-latitude. It is observed that CMEs related GMS events are not always associated with high speed solar wind streams (HSSWSs). In many individual events, the travel time between the explosion on the Sun and maximum activity lies between 58 and 118 h causing GMSs at the Earth.     

Demonstration of the stability or instability of multibreathers at low coupling

Whereas there exists a mathematical proof for one-site breathers stability, and an unpublished one for two-site breathers, the methods for determining the stability properties of multibreathers rely on numerical computation of the Floquet multipliers or on the weak nonlinearity approximation leading to discrete nonlinear Schrödinger equations. Here we present a set of multibreather stability theorems (MST) that provides a simple method to determine multibreathers stability in Klein–Gordon systems. These theorems are based in the application of degenerate perturbation theory to Aubry’s band theory. We illustrate them with several examples.     

Book Review:Brownian Agents and Active Particles. F. Schweitzer,Springer, Berlin, 2003

Journal of Statistical Physics -     

Failure of the Quasiparticle Picture of X-ray Absorption?

The Golden rule expression for x-ray absorption spectra (XAS) is typically calculated within a one-particle (quasiparticle) approximation and generally leads to good agreement between theory and experiment. The fact that a quasiparticle approximation works fairly well is surprising, since it neglects satellite excitations and intrinsic losses due to a suddenly created core-hole. The resolution of this paradox requires physics beyond the independent particle approximation. This is discussed here using an effective Green's function formulation based on a quasi-boson model that takes interference between inelastic losses into account. This approach shows that inelastic excitations such as multi-electron excitations tend to be suppressed, and that the XAS is given by a broadened quasiparticle particle approximation, together with weak satellite structure and edge singularity effects.     

Algorithms for Finite and Semi-Infinite Min–Max–Min Problems Using Adaptive Smoothing Techniques

We develop two implementable algorithms, the first for the solution of finite and the second for the solution of semi-infinite min-max-min problems. A smoothing technique (together with discretization for the semi-infinite case) is used to construct a sequence of approximating finite min-max problems, which are solved with increasing precision. The smoothing and discretization approximations are initially coarse, but are made progressively finer as the number of iterations is increased. This reduces the potential ill-conditioning due to high smoothing precision parameter values and computational cost due to high levels of discretization. The behavior of the algorithms is illustrated with three semi-infinite numerical examples.     

Self-organized amorphous material in silicon (0 0 1) by focused ion beam (FIB) system

A method using a focused ion beam (FIB) to prepare a silicon amorphous material is presented. The method involves the redeposition of sputtered material generated during the interaction of the Ga⁺ ion beam with a silicon substrate material. The shape and dimensions of this amorphous material are self-organized and reproducible. The stability of this amorphous material under electron irradiation was investigated in the transmission electron microscopy (TEM). Electron irradiation can induce recrystallization of the amorphous material, resulting in the lateral and vertical growth, starting at an amorphous-crystalline interface, of polysilicon containing defects.     

Planting in his Neighbor's Garden: David Hilbert and Early Göttingen Quantum Physics

David Hilbert (1862-1943) played an important role in establishing quantum physics in Göttingen. I analyze the ways in which his influence was decisive by comparison with Woldemar Voigt (1850-1919). Voigt was the leading Göttingen theoretical physicist before the arrival of Peter Debye (1884-1966), who was appointed to a new professorship in 1914 at Hilbert's instigation. I portray the Göttingen mathematicians, above all Hermann Minkowski (1864-1909) and David Hilbert, as planting the seeds for the blossoming of quantum physics under their student Max Born (1882-1970) in the 1920s.     

Multi-Wavelength Optical Packet Routing Technologies Based on Superstructured Fiber Bragg Gratings

A WDM compatible Edge-to-Edge Self-Routed optical packet switched network that simplifies the optical processing is proposed. The system employs all-optical packet label generation and recognition using coded superstructured Fiber Bragg gratings.