Short time scales in the Kramers problem: a stepwise growth of the escape flux

We prove rigorously and demonstrate in simulations that, for a potential system staying initially at the bottom of a well, the escape flux over the barrier grows on times of the order of a period of eigenoscillation in a stepwise manner, provided that friction is small or moderate. If the initial state is not at the bottom of the well, then, typically, some of the steps transform into oscillations. The stepwise/oscillatory evolution at short times appears to be a generic feature of a noise-induced flux.     

Activated tunneling decay of metastable state: Solution of the Kramers problem

At sufficiently low friction the Fokker-Planck equation for Brownian motion in a potential well is reduced to an integral equation for the energy variable. The basic small parameter of the problem is the ratio of the temperature T to the depth U₀ of the well. Quantum tunneling effects are naturally incorporated into the calculations. An explicit solution for Kramers' problem of the lifetime of the Brownian particle in the potential well is given.     

A Remark on the Kramers Problem

We present new point of view on the old problem, the Kramers problem. The passages from the Fokker–Planck equation to the Smoluchowski equation, including corrections to the Smoluchowski current, is treated through an asymptotic expansion of the solution of the stochastic dynamical equations. The case of an extremely weak force of friction is also discussed.     

Incursive fractals: a robust mechanism of basin erosion preceding the optimal escape from a potential well

Comparative cell-to-cell mappings of the basins of driven oscillators with cubic and quartic potential wells show remarkable qualitative and quantitative correlations. We conclude that the recently identified erosion by incursive fractals is a robust phenomenon facilitating the optimal escape from a well.     

On the intrinsic time scales involved in synchronization: a data-driven approach

We address the problem of detecting, from scalar observations, the time scales involved in synchronization of complex oscillators with several spectral components. Using a recent data-driven procedure for analyzing nonlinear and nonstationary signals [Huang, Proc. R. Soc. London A 454, 903 (1998)], we decompose a time series in distinct oscillation modes which may display a time varying spectrum. When applied to coupled oscillators with multiple time scales, we found that motions are captured in a finite number of phase-locked oscillations. Further, in the synchronized state distinct phenomena as phase slips, anti-phase or perfect phase locking can be simultaneously observed at specific time scales. This fully data-driven approach (without a priori choice of filters or basis functions) is tested on numerical examples and illustrated on electric intracranial signals recorded from an epileptic patient. Implications for the study of the build-up of synchronized states in nonstationary and noisy systems are pointed out.     

New developments in ESCA-instrumentation

The different components of an ESCA-system are analyzed theoretically and conditions of optimum performance are used as basis for the design of differe     

A scaling theory of bifurcations in the symmetric weak-noise escape problem

We consider two-dimensional overdamped double-well systems perturbed by white noise. In the weak-noise limit the most probable fluctuational path leading from either point attractor to the separatrix (the most probable escape path, or MPEP) must terminate on the saddle between the two wells. However, as the parameters of a symmetric double-well system are varied, a unique MPEP may bifurcate into two equally likely MPEPs. At the bifurcation point in parameter space, the activation kinetics of the system become non-Arrhenius. We quantify the non-Arrhenius behavior of a system at the bifurcation point, by using the Maslov-WKB method to construct an approximation to the quasistationary probability distribution of the system that is valid in a boundary layer near the separatrix. The approximation is a formal asymptotic solution of the Smoluchowski equation. Our construction relies on a new scaling theory, which yields critical exponents describing weak-noise behavior at the bifurcation point, near the saddle.     

Complex local dynamics in DNA on the picosecond and nanosecond time scales

Time-resolved Stokes shift measurements of the local structural relaxation of three DNA oligonucleotides are presented. Logarithmic relaxation is seen for over three decades in time (40 ps-40 ns), indicating a complex relaxation among a large number of conformational substates. The observed relaxation is the same in all the sequences. Sequence dependence of the localized dynamics of DNA does not appear within this time range. We infer that 30%-50% of the relaxation is faster than 40 ps, has a nonlogarithmic decay and has a sequence dependent amplitude.     

A note on the tunneling time problem

A remarkable feature of barrier penetration in quantum theory is that a particle tunneling through a barrier appears to do so in zero time. We analyze the conditions that would make possible an actual measurement of an anomalously short traversal time and conclude that such a measurement cannot be made.     

Anomalous transport in fluid fleld with random waiting time depending on the preceding jump length

Anomalous(or non-Fickian) transport behaviors of particles have been widely observed in complex porous media.To capture the energy-dependent characteristics of non-Fickian transport of a particle in flow fields,in the present paper a generalized continuous time random walk model whose waiting time probability distribution depends on the preceding jump length is introduced,and the corresponding master equation in Fourier-Laplace space for the distribution of particles is derived.As examples,two generalized advection-dispersion equations for Gaussian distribution and levy flight with the probability density function of waiting time being quadratic dependent on the preceding jump length are obtained by applying the derived master equation.     

Exploiting the diversity of time scales in the immune system: A B-cell antibody model

Using the continuous shape space formalism, we develop an immune system model involving both B lymphocytes and antibody molecules. The binding and cross-linking of receptors on B cells stimulates the cells to divide and, with a lag, to secrete antibody. Using the method of multiple scales, we show how to correctly formulate long-time-scale equations for the population dynamics of B cells, the total antibody concentration, and rate of antibody secretion. We compare our model with previous phenomenological formulations.     

Two energy scales and breakdown of renormalizability in the Kondo problem

It is shown that a second energy scale T ₀ ≫ T _k arises in the Kondo problem. Perturbation theory is valid only in the region T > T ₀. For this reason, the transition from weak to strong coupling occurs at temperatures much higher than the Kondo temperature T _k. Pis’ma Zh. éksp. Teor. Fiz. 70, No. 2, 106–111 (25 July 1999)     

Relaxation dynamics at different time scales in electrostatic complexes: time-salt superposition

In this Letter we show that in the rheology of electrostatically assembled soft materials, salt concentration plays a similar role as temperature for polymer melts, and as strain rate for soft solids. We rescale linear and nonlinear rheological data of a set of model electrostatic complexes at different salt concentrations to access a range of time scales that is otherwise inaccessible. This provides new insights into the relaxation mechanisms of electrostatic complexes, which we rationalize in terms of a microscopic mechanism underlying salt-enhanced activated processes.     

New results on global exponential stability of competitive neural networks with different time scales and time-varying delays

This paper studies the global exponential stability of competitive neural networks with different time scales and time-varying delays. By using the method of the proper Lyapunov functions and inequality technique, some sufficient conditions are presented for global exponential stability of delay competitive neural networks with different time scales. These conditions obtained have important leading significance in the designs and applications of global exponential stability for competitive neural networks. Finally, an example with its simulation is provided to demonstrate the usefulness of the proposed criteria.     

Dynamic importance sampling for the escape problem in nonequilibrium systems: observation of shifts in optimal paths

The activation problem is investigated in two-dimensional nonequilibrium systems. A numerical approach based on dynamic importance sampling (DIMS) is introduced. DIMS accelerates the simulations and allows the investigation to access noise intensities that were previously forbidden. The escape path is observed to be shifted compared to a heteroclinic trajectory calculated in the limit of zero-noise intensity. A theory to account for such shifts is presented and shown to agree with the simulations for a wide range of noise intensities.     

国际医学物理学的新发展

文章评述了国际医学物理学近印年的新发展，着重介绍了数字影像物理学和放射治疗物理学的新进展及其对临床应用高新医疗器械的重要作用，并谈及国际医学物理学的新发展对中国医学物理学发展的启示．     

New developments in the surface analysis of solids

In both fundamental and applied surface physics, it is essential to know as much as possible about the chemical composition of the outer atomic layers of solids. Rapid progress has recently been made in the development of analytical methods which could be used in surface analysis. All utilize some type of emission (photons, electrons, atoms, molecules, ions), caused by excitation of the surface states. Both the “excitation” and emission processes must meet certain basic requirements as regards information depth, form in which the information is obtained, sensitivity, changes in the surface layer during analysis, etc. The more important of the methods that qualify, namely Auger-Electron Spectroscopy (AES), photo-Electron Spectroscopy for Chemical Analysis (ESCA) and the static method of Secondary-Ion Mass Spectrometry (SIMS), are discussed and their potentialities and limitations illustrated by characteristic examples.