Multiplicative Noise: Applications in Cosmology and Field Theory

Physical situations involving multiplicative noise arise generically in cosmology and field theory. In this paper, the focus is first on exact nonlinear Langevin equations, appropriate in a cosmologica setting, for a system with one degree of freedom. The Langevin equations are derived using an appropriate time-dependent generalization of a model due to Zwanzig. These models are then extended to field theories and the generation of multiplicative noise in such a context is discussed. Important issues in both the cosmological and field theoretic cases are the fluctuation-dissipation relations and the relaxation time scale. Of some importance in cosmology is the fact that multiplicative noise can substantially reduce the relaxation time. In the field theoretic context such a noise can lead to a significant enhancement in the nucleation rate of topological defects.Comment: 21 pages, LaTex, LA-UR-93-210

Bone health in patients with multiple sclerosis relapses

OBJECTIVES: To evaluate the bone health and vitamin D levels of a cohort of patients with relapses of multiple sclerosis (MS) and to propose an algorithm for the management of bone health in this patient group. METHODS: We prospectively studied 56 consecutive patients from our acute relapse clinic. 3 patients were excluded from analysis as they were not deemed to have experienced an acute MS relapse. Bone health was assessed with vitamin D levels and Dual Energy X-ray Absorptiometry (DEXA) scanning (10 patients failed to attend for DEXA). Statistical analyses were used to compare groups and identify predictive variables. A review of the literature led to a proposed management protocol. RESULTS: Pre-relapse the baseline EDSS was ≤6.5 in all subjects, and <4.0 in the majority (66%). Most received corticosteroids. 51% had low bone mineral density (BMD) as defined by a T-score less than −1.0 on DEXA scanning. Three were osteoporotic (T-score less than −2.5). Thirty one of fifty (62%) subjects were Vitamin D deficient (25(OH)D less than 50 nmol/L). A range of variables, including previous corticosteroid usage, were not significantly predictive of reduced BMD. CONCLUSIONS: There was a high frequency of both low BMD and Vitamin D deficiency in this cohort of relatively young and largely ambulatory patients experiencing MS relapses. Current tools, such as the WHO FRAX algorithm, are inadequate in assessing bone status and fracture risk in this patient group, predominantly as they are focused on older age groups. We propose a simple clinical management algorithm

The isolated perfused mouse uterus as a model for the study of implantation in vitro. Methodology and morphology

In order to facilitate investigations of mammalian blastocyst implantation in the endometrium, an in-vitro organ perfusion technique was developed. This technique was designed to avoid the drawbacks of inVivo and cell culture investigations, while retaining physiological resolution of the endo- and paracrinology and specifically a normal epithelium to stroma relationship. The ovary, oviduct and uterine horn from 21 mice were perfused in-vitro for 10 hours. The surgical techniques for isolation of the organs as well as the perfusion procedure are described. The resultant morphology of the perfused tissue, including implantations is described and illustrated by light and transmission electron microscopy. The model seems to be useful for studying the mammalian implantation as implantation takes place and decidua is formed during perfusion

Intermittent random walks for an optimal search strategy: One-dimensional case

We study the search kinetics of an immobile target by a concentration of randomly moving searchers. The object of the study is to optimize the probability of detection within the constraints of our model. The target is hidden on a one-dimensional lattice in the sense that searchers have no a priori information about where it is, and may detect it only upon encounter. The searchers perform random walks in discrete time n=0,1,2, ..., N, where N is the maximal time the search process is allowed to run. With probability \alpha the searchers step on a nearest-neighbour, and with probability (1-\alpha) they leave the lattice and stay off until they land back on the lattice at a fixed distance L away from the departure point. The random walk is thus intermittent. We calculate the probability P_N that the target remains undetected up to the maximal search time N, and seek to minimize this probability. We find that P_N is a non-monotonic function of \alpha, and show that there is an optimal choice \alpha_{opt}(N) of \alpha well within the intermittent regime, 0 < \alpha_{opt}(N) < 1, whereby P_N can be orders of magnitude smaller compared to the "pure" random walk cases \alpha =0 and \alpha = 1.Comment: 19 pages, 5 figures; submitted to Journal of Physics: Condensed Matter; special issue on Chemical Kinetics Beyond the Textbook: Fluctuations, Many-Particle Effects and Anomalous Dynamics, eds. K.Lindenberg, G.Oshanin and M.Tachiy

Survival probability of a particle in a sea of mobile traps: A tale of tails

We study the long-time tails of the survival probability $P(t)$ of an $A$ particle diffusing in $d$-dimensional media in the presence of a concentration $\rho$ of traps $B$ that move sub-diffusively, such that the mean square displacement of each trap grows as $t^{\gamma}$ with $0\leq \gamma \leq 1$. Starting from a continuous time random walk (CTRW) description of the motion of the particle and of the traps, we derive lower and upper bounds for $P(t)$ and show that for $\gamma \leq 2/(d+2)$ these bounds coincide asymptotically, thus determining asymptotically exact results. The asymptotic decay law in this regime is exactly that obtained for immobile traps. This means that for sufficiently subdiffusive traps, the moving $A$ particle sees the traps as essentially immobile, and Lifshitz or trapping tails remain unchanged. For $\gamma > 2/(d+2)$ and $d\leq 2$ the upper and lower bounds again coincide, leading to a decay law equal to that of a stationary particle. Thus, in this regime the moving traps see the particle as essentially immobile. For $d>2$, however, the upper and lower bounds in this $\gamma$ regime no longer coincide and the decay law for the survival probability of the $A$ particle remains ambiguous

Comprehensive study of phase transitions in relaxational systems with field-dependent coefficients

We present a comprehensive study of phase transitions in single-field systems that relax to a non-equilibrium global steady state. The mechanism we focus on is not the so-called Stratonovich drift combined with collective effects, but is instead similar to the one associated with noise-induced transitions a la Horsthemke-Lefever in zero-dimensional systems. As a consequence, the noise interpretation (e.g., Ito vs Stratonvich) merely shifts the phase boundaries. With the help of a mean-field approximation, we present a broad qualitative picture of the various phase diagrams that can be found in these systems. To complement the theoretical analysis we present numerical simulations that confirm the findings of the mean-field theory

The Influence of E - Stim on Posture and Respiratory Function to Improve Aerobic Capacity: A Pilot

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Photoinduced suppression of the ferroelectric instability in PbTe

The interactions between electrons and phonons drive a large array of technologically relevant material properties including ferroelectricity, thermoelectricity, and phase-change behaviour. In the case of many group IV-VI, V, and related materials, these interactions are strong and the materials exist near electronic and structural phase transitions. Their close proximity to phase instability produces a fragile balance among the various properties. The prototypical example is PbTe whose incipient ferroelectric behaviour has been associated with large phonon anharmonicity and thermoelectricity. Experimental measurements on PbTe reveal anomalous lattice dynamics, especially in the soft transverse optical phonon branch. This has been interpreted in terms of both giant anharmonicity and local symmetry breaking due to off-centering of the Pb ions. The observed anomalies have prompted renewed theoretical and computational interest, which has in turn revived focus on the extent that electron-phonon interactions drive lattice instabilities in PbTe and related materials. Here, we use Fourier-transform inelastic x-ray scattering (FT-IXS) to show that photo-injection of free carriers stabilizes the paraelectric state. With support from constrained density functional theory (CDFT) calculations, we find that photoexcitation weakens the long-range forces along the cubic direction tied to resonant bonding and incipient ferroelectricity. This demonstrates the importance of electronic states near the band edges in determining the equilibrium structure.Comment: 9 page, 3 figure

Noise-Driven Mechanism for Pattern Formation

We extend the mechanism for noise-induced phase transitions proposed by Ibanes et al. [Phys. Rev. Lett. 87, 020601-1 (2001)] to pattern formation phenomena. In contrast with known mechanisms for pure noise-induced pattern formation, this mechanism is not driven by a short-time instability amplified by collective effects. The phenomenon is analyzed by means of a modulated mean field approximation and numerical simulations