Langevin Equation for the Density of a System of Interacting Langevin Processes

We present a simple derivation of the stochastic equation obeyed by the density function for a system of Langevin processes interacting via a pairwise potential. The resulting equation is considerably different from the phenomenological equations usually used to describe the dynamics of non conserved (Model A) and conserved (Model B) particle systems. The major feature is that the spatial white noise for this system appears not additively but multiplicatively. This simply expresses the fact that the density cannot fluctuate in regions devoid of particles. The steady state for the density function may however still be recovered formally as a functional integral over the coursed grained free energy of the system as in Models A and B.Comment: 6 pages, latex, no figure

Gravitational Lensing by Power-Law Mass Distributions: A Fast and Exact Series Approach

We present an analytical formulation of gravitational lensing using familiar triaxial power-law mass distributions, where the 3-dimensional mass density is given by $\rho(X,Y,Z) = \rho_0 [1 + (\frac{X}{a})^2 + (\frac{Y}{b})^2 + (\frac{Z}{c})^2]^{-\nu/2}$. The deflection angle and magnification factor are obtained analytically as Fourier series. We give the exact expressions for the deflection angle and magnification factor. The formulae for the deflection angle and magnification factor given in this paper will be useful for numerical studies of observed lens systems. An application of our results to the Einstein Cross can be found in Chae, Turnshek, & Khersonsky (1998). Our series approach can be viewed as a user-friendly and efficient method to calculate lensing properties that is better than the more conventional approaches, e.g., numerical integrations, multipole expansions.Comment: 24 pages, 3 Postscript figures, ApJ in press (October 10th

The statistics of critical points of Gaussian fields on large-dimensional spaces

We calculate the average number of critical points of a Gaussian field on a high-dimensional space as a function of their energy and their index. Our results give a complete picture of the organization of critical points and are of relevance to glassy and disordered systems, and to landscape scenarios coming from the anthropic approach to string theory.Comment: 5 page

The Performance of Hillside Fills During the Northridge Earthquake

Many hillside fills located in the Santa Monica, Santa Susana, and San Gabriel Mountains were damaged during the 1994 Northridge Earthquake. While no deaths have been attributed to fill movement, on the order of tens of millions of dollars in property damage was caused by fill movements which typically involved less than about 7.5cm (3 inches) of localized displacement. Some of the damage was induced by permanent deformations of underlying native materials, but most appears to have resulted from ground failure or ground shaking phenomena associated directly with the fill materials. These phenomena include cyclic compaction, lurching, and amplification of shaking within the fills. This paper presents a preliminary summary of the typical distress to fills caused by the Northridge Earthquake, and discusses the probable mechanisms of failure

Extremal driving as a mechanism for generating long-term memory

It is argued that systems whose elements are renewed according to an extremal criterion can generally be expected to exhibit long-term memory. This is verified for the minimal extremally driven model, which is first defined and then solved for all system sizes N\geq2 and times t\geq0, yielding exact expressions for the persistence R(t)=[1+t/(N-1)]^{-1} and the two-time correlation function C(t_{\rm w}+t,t_{\rm w})=(1-1/N)(N+t_{\rm w})/(N+t_{\rm w}+t-1). The existence of long-term memory is inferred from the scaling of C(t_{\rm w}+t,t_{\rm w})\sim f(t/t_{\rm w}), denoting {\em aging}. Finally, we suggest ways of investigating the robustness of this mechanism when competing processes are present.Comment: 5 pages, no figures; requires IOP style files. To appear as a J. Phys. A. lette

Ultrasonic Detection of a Plastic Hinge in Bolted Timber Connections

Connections between structural members are critical elements that typically govern the performance of structural systems; hence, techniques for monitoring the condition of connections are needed to provide early warning of structural damage. Plastic hinge formation in fasteners frequently occurs in timber connections when the yield capacity is exceeded. An innovative pulse echo testing technique was developed for detecting the formation of a plastic hinge in bolted timber connections and estimating the associated magnitude of connection displacement. A shift in overall signal centroid proved to be the best flTedictor of plastic hinge formation, with a coefficient of determination (R2) of 0.9. As the plastic hinge angle increased, the signal centroid shifted to the right since a higher proportion of pulse energy was forced to undergo multiple transverse wave reflections caused by the deformed geometry of the bolt. Because the determination of a shift in signal centroid requires the availability of prior test information for the initially undeformed fastener, an alternate linear relationship between echo amplitude ratios and plastic hinge formation was also proposed with an adjusted R2 of 0.87. This three parameter regression equation had the advantages of requiring no prior testing information and eliminating ambiguity in signal analysis associated with selection of echo start and end points. Plastic hinge formation was correlated with connection ductility, magnitude of connection overload and energy based measures of connection damage to assess residual connection capacity

Slow Logarithmic Decay of Magnetization in the Zero Temperature Dynamics of an Ising Spin Chain: Analogy to Granular Compaction

We study the zero temperature coarsening dynamics in an Ising chain in presence of a dynamically induced field that favors locally the `-' phase compared to the `+' phase. At late times, while the `+' domains still coarsen as $t^{1/2}$, the `-' domains coarsen slightly faster as $t^{1/2}\log (t)$. As a result, at late times, the magnetization decays slowly as, $m(t)=-1 +{\rm const.}/{\log (t)}$. We establish this behavior both analytically within an independent interval approximation (IIA) and numerically. In the zero volume fraction limit of the `+' phase, we argue that the IIA becomes asymptotically exact. Our model can be alternately viewed as a simple Ising model for granular compaction. At late times in our model, the system decays into a fully compact state (where all spins are `-') in a slow logarithmic manner $\sim 1/{\log (t)}$, a fact that has been observed in recent experiments on granular systems.Comment: 4 pages Revtex, 3 eps figures, supersedes cond-mat/000221

Glassy trapping of manifolds in nonpotential random flows

We study the dynamics of polymers and elastic manifolds in non potential static random flows. We find that barriers are generated from combined effects of elasticity, disorder and thermal fluctuations. This leads to glassy trapping even in pure barrier-free divergenceless flows $v {f \to 0}{\sim} f^\phi$ ($\phi > 1$). The physics is described by a new RG fixed point at finite temperature. We compute the anomalous roughness $R \sim L^\zeta$ and dynamical $t\sim L^z$ exponents for directed and isotropic manifolds.Comment: 5 pages, 3 figures, RevTe