Noise-Activated Escape from a Sloshing Potential Well

We treat the noise-activated escape from a one-dimensional potential well of an overdamped particle, to which a periodic force of fixed frequency is applied. We determine the boundary layer behavior, and the physically relevant length scales, near the oscillating well top. We show how stochastic behavior near the well top generalizes the behavior first determined by Kramers, in the case without forcing. Both the case when the forcing dies away in the weak noise limit, and the case when it does not, are examined. We also discuss the relevance of various scaling regimes to recent optical trap experiments.Comment: 9 pages, no figures, REVTeX, expanded versio

The Escape Problem for Irreversible Systems

The problem of noise-induced escape from a metastable state arises in physics, chemistry, biology, systems engineering, and other areas. The problem is well understood when the underlying dynamics of the system obey detailed balance. When this assumption fails many of the results of classical transition-rate theory no longer apply, and no general method exists for computing the weak-noise asymptotics of fundamental quantities such as the mean escape time. In this paper we present a general technique for analysing the weak-noise limit of a wide range of stochastically perturbed continuous-time nonlinear dynamical systems. We simplify the original problem, which involves solving a partial differential equation, into one in which only ordinary differential equations need be solved. This allows us to resolve some old issues for the case when detailed balance holds. When it does not hold, we show how the formula for the mean escape time asymptotics depends on the dynamics of the system along the most probable escape path. We also present new results on short-time behavior and discuss the possibility of focusing along the escape path.Comment: 24 pages, APS revtex macros (version 2.1) now available from PBB via `get oldrevtex.sty

Second harmonic generation from strongly coupled localized and propagating phonon-polariton modes

We experimentally investigate second harmonic generation from strongly coupled localized and propagative phonon polariton modes in arrays of silicon carbide nanopillars. Our results clearly demonstrate the hybrid nature of the system's eigenmodes and distinct manifestation of strong coupling in the linear and nonlinear response. While in linear reflectivity the intensity of the two strongly-coupled branches is essentially symmetric and well explained by their respective localized or propagative components, the second harmonic signal presents a strong asymmetry. Analyzing it in detail, we reveal the importance of interference effects between the nonlinear polarization terms originating in the bulk and in the phonon polariton modes, respectively.Comment: 7 pages, 4 figure

Review of Microfluidic Devices and Imaging Techniques for Fluid Flow Study in Porous Geomaterials

Understanding transport phenomena and governing mechanisms of different physical and chemical processes in porous media has been a critical research area for decades. Correlating fluid flow behaviour at the micro-scale with macro-scale parameters, such as relative permeability and capillary pressure, is key to understanding the processes governing subsurface systems, and this in turn allows us to improve the accuracy of modelling and simulations of transport phenomena at a large scale. Over the last two decades, there have been significant developments in our understanding of pore-scale processes and modelling of complex underground systems. Microfluidic devices (micromodels) and imaging techniques, as facilitators to link experimental observations to simulation, have greatly contributed to these achievements. Although several reviews exist covering separately advances in one of these two areas, we present here a detailed review integrating recent advances and applications in both micromodels and imaging techniques. This includes a comprehensive analysis of critical aspects of fabrication techniques of micromodels, and the most recent advances such as embedding fibre optic sensors in micromodels for research applications. To complete the analysis of visualization techniques, we have thoroughly reviewed the most applicable imaging techniques in the area of geoscience and geo-energy. Moreover, the integration of microfluidic devices and imaging techniques was highlighted as appropriate. In this review, we focus particularly on four prominent yet very wide application areas, namely “fluid flow in porous media”, “flow in heterogeneous rocks and fractures”, “reactive transport, solute and colloid transport”, and finally “porous media characterization”. In summary, this review provides an in-depth analysis of micromodels and imaging techniques that can help to guide future research in the in-situ visualization of fluid flow in porous media

A Scaling Theory of Bifurcations in the Symmetric Weak-Noise Escape Problem

We consider the overdamped limit of two-dimensional double well systems perturbed by weak 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 MPEP's. At the bifurcation point in parameter space, the activation kinetics of the system become non-Arrhenius. In this paper 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 analysis relies on the development of a new scaling theory, which yields `critical exponents' describing weak-noise behavior near the saddle, at the bifurcation point.Comment: LaTeX, 60 pages, 24 Postscript figures. Uses epsf macros to include the figures. A file in `uufiles' format containing the figures is separately available at ftp://platinum.math.arizona.edu/pub/papers-rsm/paperF/figures.uu and a Postscript version of the whole paper (figures included) is available at ftp://platinum.math.arizona.edu/pub/papers-rsm/paperF/paperF.p

The human gastric pathogen Helicobacter pylori has a potential acetone carboxylase that enhances its ability to colonize mice

<p>Abstract</p> <p>Background</p> <p><it>Helicobacter pylori </it>colonizes the human stomach and is the etiological agent of peptic ulcer disease. All three <it>H. pylori </it>strains that have been sequenced to date contain a potential operon whose products share homology with the subunits of acetone carboxylase (encoded by <it>acxABC</it>) from <it>Xanthobacter autotrophicus </it>strain Py2 and <it>Rhodobacter capsulatus </it>strain B10. Acetone carboxylase catalyzes the conversion of acetone to acetoacetate. Genes upstream of the putative <it>acxABC </it>operon encode enzymes that convert acetoacetate to acetoacetyl-CoA, which is metabolized further to generate two molecules of acetyl-CoA.</p> <p>Results</p> <p>To determine if the <it>H. pylori acxABC </it>operon has a role in host colonization the <it>acxB </it>homolog in the mouse-adapted <it>H. pylori </it>SS1 strain was inactivated with a chloramphenicol-resistance (<it>cat</it>) cassette. In mouse colonization studies the numbers of <it>H. pylori </it>recovered from mice inoculated with the <it>acxB:cat </it>mutant were generally one to two orders of magnitude lower than those recovered from mice inoculated with the parental strain. A statistical analysis of the data using a Wilcoxin Rank test indicated the differences in the numbers of <it>H. pylori </it>isolated from mice inoculated with the two strains were significant at the 99% confidence level. Levels of acetone associated with gastric tissue removed from uninfected mice were measured and found to range from 10–110 μmols per gram wet weight tissue.</p> <p>Conclusion</p> <p>The colonization defect of the <it>acxB:cat </it>mutant suggests a role for the <it>acxABC </it>operon in survival of the bacterium in the stomach. Products of the <it>H. pylori acxABC </it>operon may function primarily in acetone utilization or may catalyze a related reaction that is important for survival or growth in the host. <it>H. pylori </it>encounters significant levels of acetone in the stomach which it could use as a potential electron donor for microaerobic respiration.</p