Nonlinear relaxation time and the detection of weak signals

Laser systems can be used to detect very weak optical signals. The physical mechanism is the dynamical process of the relaxation of a laser from an unstable state to a steady stable state. We present an analysis of this process based on the study of the nonlinear relaxation time. Our analytical results are compared with numerical integration of the stochastic differential equations that model this process.

Classical cross sections for relativistic spinning particles

We propose a definition of classical differential cross sections for particles with essentially nonplanar orbits, such as spinning ones. We give also a method for its computation. The calculations are carried out explicitly for electromagnetic, gravitational, and short-range scalar interactions up to the linear terms in the slow-motion approximation. The contribution of the spin-spin terms is found to be at best 10-6 times the post-Newtonian ones for the gravitational interaction.

When telegrapher's equation furnishes a better approximation to transport equation than the difussion approximation

It has been suggested that a solution to the transport equation which includes anisotropic scattering can be approximated by the solution to a telegrapher's equation [A.J. Ishimaru, Appl. Opt. 28, 2210 (1989)]. We show that in one dimension the telegrapher's equation furnishes an exact solution to the transport equation. In two dimensions, we show that, since the solution can become negative, the telegrapher's equation will not furnish a usable approximation. A comparison between simulated data in three dimensions indicates that the solution to the telegrapher's equation is a good approximation to that of the full transport equation at the times at which the diffusion equation furnishes an equally good approximation.

Stable alpha-synuclein oligomers strongly inhibit chaperone activity of the Hsp70 system by weak interactions with J-domain co-chaperones.

α-Synuclein aggregation and accumulation in Lewy bodies are implicated in progressive loss of dopaminergic neurons in Parkinson disease and related disorders. In neurons, the Hsp70s and their Hsp40-like J-domain co-chaperones are the only known components of chaperone network that can use ATP to convert cytotoxic protein aggregates into harmless natively refolded polypeptides. Here we developed a protocol for preparing a homogeneous population of highly stable β-sheet enriched toroid-shaped α-Syn oligomers with a diameter typical of toxic pore-forming oligomers. These oligomers were partially resistant to in vitro unfolding by the bacterial Hsp70 chaperone system (DnaK, DnaJ, GrpE). Moreover, both bacterial and human Hsp70/Hsp40 unfolding/refolding activities of model chaperone substrates were strongly inhibited by the oligomers but, remarkably, not by unstructured α-Syn monomers even in large excess. The oligomers acted as a specific competitive inhibitor of the J-domain co-chaperones, indicating that J-domain co-chaperones may preferably bind to exposed bulky misfolded structures in misfolded proteins and, thus, complement Hsp70s that bind to extended segments. Together, our findings suggest that inhibition of the Hsp70/Hsp40 chaperone system by α-Syn oligomers may contribute to the disruption of protein homeostasis in dopaminergic neurons, leading to apoptosis and tissue loss in Parkinson disease and related neurodegenerative diseases.

Mean first-passage time of continuous non-Markovian processes driven by colored noise

An equation for mean first-passage times of non-Markovian processes driven by colored noise is derived through an appropriate backward integro-differential equation. The equation is solved in a Bourret-like approximation. In a weak-noise bistable situation, non-Markovian effects are taken into account by an effective diffusion coefficient. In this situation, our results compare satisfactorily with other approaches and experimental data.

Approximation and support theorem for a wave equation in two space dimensions

We prove a characterization of the support of the law of the solution for a stochastic wave equation with two-dimensional space variable, driven by a noise white in time and correlated in space. The result is a consequence of an approximation theorem, in the convergence of probability, for equations obtained by smoothing the random noise. For some particular classes of coefficients, approximation in the Lp-norm for p¿1 is also proved.

Reinforced Earth and Stone Columns for Weak Subsoil Conditions, HR-510, 1980

Reinforced Earth is a French development that has been used in the United States for approximately ten years. Virbro-Replacement, more commonly referred to as stone columns, is an outgrowth of deep densification of cohesionless soils originally developed in Germany. Reinforced Earth has applicability when wall height is greater than about twelve feet and deep seated foundation failure is not a concern. Stone columns are applicable when soft, cohesive subsoil conditions are encountered and bearing capacity and shearing resistance must be increased. The conditions in Sioux City on Wesley Way can be summarized as: (1) restricted right of way, (2) fill height in excess of 25 feet creating unstable conditions, (3) adjacent structures that could not be removed. After analyzing alternatives, it was decided that Reinforced Earth walls constructed on top of stone columns were the most practical approach.