Instanton filtering for the stochastic Burgers equation

We address the question whether one can identify instantons in direct numerical simulations of the stochastically driven Burgers equation. For this purpose, we first solve the instanton equations using the Chernykh-Stepanov method [Phys. Rev. E 64, 026306 (2001)]. These results are then compared to direct numerical simulations by introducing a filtering technique to extract prescribed rare events from massive data sets of realizations. Using this approach we can extract the entire time history of the instanton evolution which allows us to identify the different phases predicted by the direct method of Chernykh and Stepanov with remarkable agreement

Exploring the currency of violence in Serious Organised Crime (SOC)

Book Chapte

Unstable decay and state selection II

The decay of unstable states when several metastable states are available for occupation is investigated using path-integral techniques. Specifically, a method is described which allows the probabilities with which the metastable states are occupied to be calculated by finding optimal paths, and fluctuations about them, in the weak noise limit. The method is illustrated on a system described by two coupled Langevin equations, which are found in the study of instabilities in fluid dynamics and superconductivity. The problem involves a subtle interplay between non-linearities and noise, and a naive approximation scheme which does not take this into account is shown to be unsatisfactory. The use of optimal paths is briefly reviewed and then applied to finding the conditional probability of ending up in one of the metastable states, having begun in the unstable state. There are several aspects of the calculation which distinguish it from most others involving optimal paths: (i) the paths do not begin and end on an attractor, and moreover, the final point is to a large extent arbitrary, (ii) the interplay between the fluctuations and the leading order contribution are at the heart of the method, and (iii) the final result involves quantities which are not exponentially small in the noise strength. This final result, which gives the probability of a particular state being selected in terms of the parameters of the dynamics, is remarkably simple and agrees well with the results of numerical simulations. The method should be applicable to similar problems in a number of other areas such as state selection in lasers, activationless chemical reactions and population dynamics in fluctuating environments.Comment: 28 pages, 6 figures. Accepted for publication in Phys. Rev.

Mode-coupling theory and the fluctuation-dissipation theorem for nonlinear Langevin equations with multiplicative noise

In this letter, we develop a mode-coupling theory for a class of nonlinear Langevin equations with multiplicative noise using a field theoretic formalism. These equations are simplified models of realistic colloidal suspensions. We prove that the derived equations are consistent with the fluctuation-dissipation theorem. We also discuss the generalization of the result given here to real fluids, and the possible description of supercooled fluids in the aging regime. We demonstrate that the standard idealized mode-coupling theory is not consistent with the FDT in a strict field theoretic sense.Comment: 14 pages, to appear in J. Phys.

Symmetries of the stochastic Burgers equation

All Lie symmetries of the Burgers equation driven by an external random force are found. Besides the generalized Galilean transformations, this equation is also invariant under the time reparametrizations. It is shown that the Gaussian distribution of a pumping force is not invariant under the symmetries and breaks them down leading to the nontrivial vacuum (instanton). Integration over the volume of the symmetry groups provides the description of fluctuations around the instanton and leads to an exactly solvable quantum mechanical problem.Comment: 4 pages, REVTeX, replaced with published versio

Continuum Derrida Approach to Drift and Diffusivity in Random Media

By means of rather general arguments, based on an approach due to Derrida that makes use of samples of finite size, we analyse the effective diffusivity and drift tensors in certain types of random medium in which the motion of the particles is controlled by molecular diffusion and a local flow field with known statistical properties. The power of the Derrida method is that it uses the equilibrium probability distribution, that exists for each {\em finite} sample, to compute asymptotic behaviour at large times in the {\em infinite} medium. In certain cases, where this equilibrium situation is associated with a vanishing microcurrent, our results demonstrate the equality of the renormalization processes for the effective drift and diffusivity tensors. This establishes, for those cases, a Ward identity previously verified only to two-loop order in perturbation theory in certain models. The technique can be applied also to media in which the diffusivity exhibits spatial fluctuations. We derive a simple relationship between the effective diffusivity in this case and that for an associated gradient drift problem that provides an interesting constraint on previously conjectured results.Comment: 18 pages, Latex, DAMTP-96-8

In search of community history

This editorial response to the preceding article by Dennis Mills addresses the meaning of community history. Rejecting an over-tight definition, we argue for a methodologically distinct community history, combining a micro-historical approach with a sensitivity to the discursive construction of the term 'community'. Furthermore the role of family and community historians should be to adapt a critical stance towards contemporary meanings of both past 'communities' and past 'families'. The article concludes that Withington and Shephard's schema for approaching the history of 'community' offers a practical way forward for the family and community historian

Type I interferon is required for T helper (Th) 2 induction by dendritic cells

Type 2 inflammation is a defining feature of infection with parasitic worms (helminths), as well as being responsible for widespread suffering in allergies. However, the precise mechanisms involved in T helper (Th) 2 polarization by dendritic cells (DCs) are currently unclear. We have identified a previously unrecognized role for type I IFN (IFN-I) in enabling this process. An IFN-I signature was evident in DCs responding to the helminth Schistosoma mansoni or the allergen house dust mite (HDM). Further, IFN-I signaling was required for optimal DC phenotypic activation in response to helminth antigen (Ag), and efficient migration to, and localization with, T cells in the draining lymph node (dLN). Importantly, DCs generated from Ifnar1-/- mice were incapable of initiating Th2 responses in vivo. These data demonstrate for the first time that the influence of IFN-I is not limited to antiviral or bacterial settings but also has a central role to play in DC initiation of Th2 responses

Fostering relations: first sex and marital timings for children raised by kin and non-kin carers

Kinship fostering is generally preferred to non-kin fostering by policy makers in the U.S. and elsewhere. Researchers and policy makers alike tend to provide several proximate reasons for why this may be, generally neglecting an ultimate evolutionary framework. However, kin selection theory predicts that in the absence of genetically related parents, care from kin will result in the most similar life history outcomes. In low-fertility settings, parents typically favour increased investment in embodied capital and thus delayed reproductive life history strategy. Using archival data from the original Kinsey survey, collected in the U.S. from 1938 to 1963, we used survival analyses to compare the effects of living with kin and non-kin fosterers in childhood on timings of first sex and marriage. Our results support a kin selection hypothesis showing that while fostered children have accelerated life histories compared to children from "intact families", kin fosterers buffer children from early sexual and reproductive behaviors, compared to children cared for by non-kin. © 2014 The Authors

Gilbert Damping in Conducting Ferromagnets II: Model Tests of the Torque-Correlation Formula

We report on a study of Gilbert damping due to particle-hole pair excitations in conducting ferromagnets. We focus on a toy two-band model and on a four-band spherical model which provides an approximate description of ferromagnetic (Ga,Mn)As. These models are sufficiently simple that disorder-ladder-sum vertex corrections to the long-wavelength spin-spin response function can be summed to all orders. An important objective of this study is to assess the reliability of practical approximate expressions which can be combined with electronic structure calculations to estimate Gilbert damping in more complex systems.Comment: 10 pages, 10 figures. Submitted to Phys. Rev.