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

What works in intelligence

This report analyses police intelligence practice in Britain through the lens of the ‘what works?’ concept. It is based on a survey of a self-selected group of intelligence staff together with interviews with a random sample of their number. Participants reflected on: their skills and abilities; their training; their successes and their failures; and the utility of the structures and processes within which they operated. We found that respondents broadly agreed on what contributed to effective practice. For example, analysts, intelligence officers and managers ranked a skilled workforce as of greatest import. Human intelligence (HUMINT); operational teams, capable of responding quickly to intelligence; information technology; and plentiful sources of intelligence in their communities, were consistently ranked the top four significant factors in their successes. At the same time, we conclude that while the ‘what works?’ approach has some value when applied to policing, there are clear limits to its explanatory power. We conclude that the ‘what works?’ approach also raises important, albeit largely ignored, questions about institutional memory and identity and that institutional and cultural factors represent significant barriers to the adoption of evidence-based practice in policing

Size of supernumerary teats in sheep correlates with complexity of the anatomy and microenvironment.

Supernumerary nipples or teats (polythelia) are congenital accessory structures that may develop at any location along the milk line and have been implicated in the pathogenesis of mastitis. We describe the anatomy and histology of 27 spontaneously occurring supernumerary teats from 16 sheep, delineating two groups of teats - simple and anatomically complex - according to the complexity of the anatomy and microenvironment. Anatomically complex supernumerary teats exhibited significantly increased length and barrel diameter compared with simple supernumerary teats. A teat canal and/or teat cistern was present in anatomically complex teats, with smooth muscle fibres forming a variably well-organised encircling teat sphincter. Complex supernumerary teats also exhibited immune cell infiltrates similar to those of normal teats, including lymphoid follicle-like structures at the folds of the teat cistern-teat canal junction, and macrophages that infiltrated the peri-cisternal glandular tissue. One complex supernumerary teat exhibited teat end hyperkeratosis. These anatomical and histological features allow inference that supernumerary teats may be susceptible to bacterial ingress through the teat canal and we hypothesise that this may be more likely in those teats with less well-organised encircling smooth muscle. The teat cistern of anatomically complex teats may also constitute a focus of milk accumulation and thus a possible nidus for bacterial infection, potentially predisposing to mastitis. We suggest that size of the supernumerary teat, and relationship to the main teats, particularly in the case of 'cluster teats', should be considerations if surgical removal is contemplated.British Veterinary Association Animal Welfare Foundation (BVA AWF) Norman Hayward Fun

The road not taken: understanding barriers to the development of police intelligence practice

To better understand police intelligence practice, we examined practitioners’ views of their work and their relations with the wider law enforcement community. We surveyed intelligence staff (n = 110) and interviewed a random sample of respondents (n = 12). Our analysis suggested that traditionalism and the dominant action-oriented culture limit the organization’s understanding of intelligence practice. Largely, the focus in that context has been on street cops’ propensity to reject reflection in favor of action, but intelligence practitioners need also look to themselves. Too often, the philosophy of “need to know” is prioritized over its antithesis, “dare to share.” Though perceived by practitioners as low-risk and consistent with organizational norms, we argue that inappropriately applied “need to know” is the enemy of efficiency and real accountability, offering low levels of reward and discouraging the kinds of partnership, reciprocity, and multi-directional knowledge transfer that policing needs to be successful in the information age. We reconceptualized an interactivity/isolationism continuum, used in the natural sciences, to help interpret that phenomenon. We argue that isolationism is but one factor in a complex organizational dynamic, but it is a significant one because it can subtly limit the influence and reach of the intelligence milieu in previously unacknowledged ways

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.

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

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.

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