Analysis of White Noise Limits for Stochastic Systems with Two Fast Relaxation Times

In this paper we present a rigorous asymptotic analysis for stochastic systems with two fast relaxation times. The mathematical model analyzed in this paper consists of a Langevin equation for the particle motion with time-dependent force constructed through an infinite dimensional Gaussian noise process. We study the limit as the particle relaxation time as well as the correlation time of the noise tend to zero and we obtain the limiting equations under appropriate assumptions on the Gaussian noise. We show that the limiting equation depends on the relative magnitude of the two fast time scales of the system. In particular, we prove that in the case where the two relaxation times converge to zero at the same rate there is a drift correction, in addition to the limiting It\^{o} integral, which is not of Stratonovich type. If, on the other hand, the colored noise is smooth on the scale of particle relaxation then the drift correction is the standard Stratonovich correction. If the noise is rough on this scale then there is no drift correction. Strong (i.e. pathwise) techniques are used for the proof of the convergence theorems.Comment: 35 pages, 0 figures, To appear in SIAM J. MM

Computer simulation of on-orbit manned maneuvering unit operations

Simulation of spacecraft on-orbit operations is discussed in reference to Martin Marietta's Space Operations Simulation laboratory's use of computer software models to drive a six-degree-of-freedom moving base carriage and two target gimbal systems. In particular, key simulation issues and related computer software models associated with providing real-time, man-in-the-loop simulations of the Manned Maneuvering Unit (MMU) are addressed with special attention given to how effectively these models and motion systems simulate the MMU's actual on-orbit operations. The weightless effects of the space environment require the development of entirely new devices for locomotion. Since the access to space is very limited, it is necessary to design, build, and test these new devices within the physical constraints of earth using simulators. The simulation method that is discussed here is the technique of using computer software models to drive a Moving Base Carriage (MBC) that is capable of providing simultaneous six-degree-of-freedom motions. This method, utilized at Martin Marietta's Space Operations Simulation (SOS) laboratory, provides the ability to simulate the operation of manned spacecraft, provides the pilot with proper three-dimensional visual cues, and allows training of on-orbit operations. The purpose here is to discuss significant MMU simulation issues, the related models that were developed in response to these issues and how effectively these models simulate the MMU's actual on-orbiter operations

Influence of zinc on distiller’s yeast:cellular accumulation of zinc and impact on spirit congeners

Accumulation of zinc by a whisky distilling yeast strain of Saccharomyces cerevisiae was studied during fermentation of malt wort and synthetic defined medium. Zinc uptake by yeast cells was very rapid in malt wort, as zinc (0.32 μg/mL) was completely removed from the fermentation medium within one hour. The type of fermentable carbohydrate had an impact on the kinetics of zinc accumulation, with maltose most effective at enhancing metal uptake at zinc concentrations above 3.2 μg/mL. Enriching yeast cells with zinc by “preconditioning” impacted on the production of flavour congeners in the distillates produced from fermented cultures. Such distillates were characterized by an altered flavour and aroma profile. In particular, the production of some higher alcohols increased when yeast cells were preconditioned with zinc. This phenomenon is yeast strain related. Industrial fermentation processes, including brewing and distilling, may benefit from optimization of zinc bioavailability in yeast cultures resulting in more efficient fermentations and improved product quality

MCMC methods for functions modifying old algorithms to make\ud them faster

Many problems arising in applications result in the need\ud to probe a probability distribution for functions. Examples include Bayesian nonparametric statistics and conditioned diffusion processes. Standard MCMC algorithms typically become arbitrarily slow under the mesh refinement dictated by nonparametric description of the unknown function. We describe an approach to modifying a whole range of MCMC methods which ensures that their speed of convergence is robust under mesh refinement. In the applications of interest the data is often sparse and the prior specification is an essential part of the overall modeling strategy. The algorithmic approach that we describe is applicable whenever the desired probability measure has density with respect to a Gaussian process or Gaussian random field prior, and to some useful non-Gaussian priors constructed through random truncation. Applications are shown in density estimation, data assimilation in fluid mechanics, subsurface geophysics and image registration. The key design principle is to formulate the MCMC method for functions. This leads to algorithms which can be implemented via minor modification of existing algorithms, yet which show enormous speed-up on a wide range of applied problems

Controlled Nanoparticle Formation by Diffusion Limited Coalescence

Polymeric nanoparticles (NPs) have a great application potential in science and technology. Their functionality strongly depends on their size. We present a theory for the size of NPs formed by precipitation of polymers into a bad solvent in the presence of a stabilizing surfactant. The analytical theory is based upon diffusion-limited coalescence kinetics of the polymers. Two relevant time scales, a mixing and a coalescence time, are identified and their ratio is shown to determine the final NP diameter. The size is found to scale in a universal manner and is predominantly sensitive to the mixing time and the polymer concentration if the surfactant concentration is sufficiently high. The model predictions are in good agreement with experimental data. Hence the theory provides a solid framework for tailoring nanoparticles with a priori determined size.Comment: 4 pages, 3 figure

Radiative Corrections to W and Quark Propagators in the Resonance Region

We discuss radiative corrections to W and quark propagators in the resonance region, |s-M^2| \lsim M*Gamma. We show that conventional mass renormalization, when applied to photonic or gluonic corrections, leads in next to leading order (NLO) to contributions proportional to [M*Gamma/(s-M^2)]^n, (n=1,2...), i.e. to a non-convergent series in the resonance region, a difficulty that affects all unstable particles coupled to massless quanta. A solution of this problem, based on the concepts of pole mass and width, is presented. It elucidates the issue of renormalization of amplitudes involving unstable particles and automatically circumvents the problem of apparent on-shell singularities. The roles of the Fried-Yennie gauge and the Pinch Technique prescription are discussed. Because of special properties of the photonic and gluonic contributions, and in contrast with the Z case, the gauge dependence of the conventional on-shell definition of mass is unbounded in NLO. The evaluations of the width in the conventional and pole formulations are compared and shown to agree in NLO but not beyond.Comment: 19 pages, 7 figures, LaTeX (uses epsfig). Slight rewording of the abstract and one of the sentences of the text. Minor misprints corrected. To appear in Phys. Rev.

Acoustic characterization of crack damage evolution in sandstone deformed under conventional and true triaxial loading

We thank the Associate Editor, Michelle Cooke, and the reviewers, Ze'ev Reches and Yves Guéguen, for useful comments which helped to improve the manuscript. We thank J.G. Van Munster for providing access to the true triaxial apparatus at KSEPL and for technical support during the experimental program. We thank R. Pricci for assistance with technical drawings of the apparatus. This work was partly funded by NERC award NE/N002938/1 and by a NERC Doctoral Studentship, which we gratefully acknowledge. Supporting data are included in a supporting information file; any additional data may be obtained from J.B. (e-mail: [email protected]).Peer reviewedPublisher PD

Nonlinear optics of fibre event horizons

The nonlinear interaction of light in an optical fibre can mimic the physics at an event horizon. This analogue arises when a weak probe wave is unable to pass through an intense soliton, despite propagating at a different velocity. To date, these dynamics have been described in the time domain in terms of a soliton-induced refractive index barrier that modifies the velocity of the probe. Here, we complete the physical description of fibre-optic event horizons by presenting a full frequency-domain description in terms of cascaded four-wave mixing between discrete single-frequency fields, and experimentally demonstrate signature frequency shifts using continuous wave lasers. Our description is confirmed by the remarkable agreement with experiments performed in the continuum limit, reached using ultrafast lasers. We anticipate that clarifying the description of fibre event horizons will significantly impact on the description of horizon dynamics and soliton interactions in photonics and other systems.Comment: 7 pages, 5 figure