Probability Density, Diagrammatic Technique, and Epsilon Expansion in the Theory of Wave Turbulence

We apply the methods of Field Theory to study the turbulent regimes of statistical systems. First we show how one can find their probability densities. For the case of the theory of wave turbulence with four-wave interaction we calculate them explicitly and study their properties. Using those densities we show how one can in principle calculate any correlation function in this theory by means of direct perturbative expansion in powers of the interaction. Then we give the general form of the corrections to the kinetic equation and develop an appropriate diagrammatic technique. This technique, while resembling that of $\varphi^4$ theory, has many new distinctive features. The role of the $\epsilon=d-4$ parameter is played here by the parameter $\kappa=\beta + d - \alpha - \gamma$ where $\beta$ is the dimension of the interaction, $d$ is the space dimension, $\alpha$ is the dimension of the energy spectrum and $\gamma$ is the ``classical'' wave density dimension. If $\kappa > 0$ then the Kolmogorov index is exact, and if $\kappa < 0$ then we expect it to be modified by the interaction. For $\kappa$ a small negative number, $\alpha<1$ and a special form of the interaction we compute this modification explicitly with the additional assumption of the irrelevance of the IR divergencies which still needs to be verified.Comment: 26 pages, PUPT-146

Evaluation of the state of the art of psychological variables among exercisers at different levels

There is growing interest in the field of sport psychology to measure psychological variables among exercisers at different levels and between exercisers and non-exercisers, in order to identify beneficial activities in non-clinical and clinical groups (such as patients with metabolic diseases or osteoarticular disorders) and to implement psychological drivers for the promotion of greater athletic achievement and healthier lifestyles. [Clemente et al. 2019; Bernstein et al 2019; Zur et al. 2019]. The populations involved in these studies are highly heterogeneous and vary from professional athletes to laypeople, including fragile populations, such as the elderly, and people with chronic diseases, such as diabetes or obesity, who can benefit from physical activity [Kosteli et al. 2018; Ku et al. 2017; Matson et al. 2019]. Variables such as self-efficacy and self-regulation, depression, emotion, stress, and affect have been analysed and compared among athletes of various levels. Furthermore, a correlation of these variables with physical activity has been demonstrated [Zur et al. 2019; Myers et al 2017; Looyestyn et al. 2018]. Among different sport populations (e.g. athletes, semi-professional sport performers, and amateurs), psychological variables are assessed through validated scales and questionnaires and can be correlated with sport performance using objectively measured physical parameters (e.g. resting muscle tension, skin conductance, and respiration rate) through biofeedback technology [Myers et al 2017]. Novel technologies, including the use of computerised tests or online surveys, the involvement of participants using social media, the use of micro-electromechanical systems (MEMS) including wearables devices and sensor systems (such as global positioning systems - GPS, accelerometers, and heart rate monitoring sensors) appear promising for collection of relevant physical parameters [Lutz et al. 2019] and can be used both in regular exercise performers and laypeople [Looyestyn et al. 2018; Lin et al. 2018; Myers et al 2017]

Galilean invariance and homogeneous anisotropic randomly stirred flows

The Ward-Takahashi (WT) identities for incompressible flow implied by Galilean invariance are derived for the randomly forced Navier-Stokes equation (NSE), in which both the mean and fluctuating velocity components are explicitly present. The consequences of Galilean invariance for the vertex renormalization are drawn from this identity.Comment: REVTeX 4, 4 pages, no figures. To appear as a Brief Report in the Physical Review

Local Spin Glass Order in 1D

We study the behavior of one dimensional Kac spin glasses as function of the interaction range. We verify by Montecarlo numerical simulations the crossover from local mean field behavior to global paramagnetism. We investigate the behavior of correlations and find that in the low temperature phase correlations grow at a faster rate then the interaction range. We completely characterize the growth of correlations in the vicinity of the mean-field critical region

Imagining virtual community: online media fandom and the construction of virtual collectivity

This thesis uses ethnographic research into online media fandom, focusing on self-reflexive analytical documents that fans call meta, to investigate longstanding questions about the nature of virtual community. It argues that virtual documents should be seen as complete and complex interactions in their original form and as social contexts in their own right, and presents a new approach to ethnographic methodology and ethics suited to working in this context. Fans have incorporated various technologies into the infrastructure that constitutes their community, and these have had various effects on the structure and substance of fannish documents and interactions – and on the character of the community as a whole. The stability and visibility of the digital archive is an important feature of virtual community – one that makes fandom more visible, accessible, and historically grounded for both old and new members. This research also deals with conflict, not as a necessarily divisive force but as a natural and important part of how communities evolve and how members negotiate and articulate what their community should be. It discusses fanfiction as a controversial and sometimes problematic genre, and considers trigger warnings as the solution fans have developed to protect vulnerable members of their community from potentially harmful content (such as rape). It also examines conflict with outside authorities, like creators and the administrators who control the virtual spaces that fans inhabit. These conflicts illuminate creativity and feminism as fannish values, presenting fandom as a community that embraces sex-positive female sexuality. More importantly, they suggest that the creation and maintenance of a ‘safe space’ where all members feel respected and comfortable is a key feature of online community. In addition, fannish storytelling (particularly the creation of what fans call fanon) is part of the production of local knowledge, of boundary mechanisms that mark and separate members of the community from outsiders. These stories as part of the process by which fans position themselves within the broader community – and in so doing, locate themselves within smaller cohorts of fans who affirm and support aspects of their personal experiences and marginalised identities (e.g. as women, members of the LGBTQIA+ community, or people of colour) through the reorientation and appropriation of story

Gauge fixing, BRS invariance and Ward identities for randomly stirred flows

The Galilean invariance of the Navier-Stokes equation is shown to be akin to a global gauge symmetry familiar from quantum field theory. This symmetry leads to a multiple counting of infinitely many inertial reference frames in the path integral approach to randomly stirred fluids. This problem is solved by fixing the gauge, i.e., singling out one reference frame. The gauge fixed theory has an underlying Becchi-Rouet-Stora (BRS) symmetry which leads to the Ward identity relating the exact inverse response and vertex functions. This identification of Galilean invariance as a gauge symmetry is explored in detail, for different gauge choices and by performing a rigorous examination of a discretized version of the theory. The Navier-Stokes equation is also invariant under arbitrary rectilinear frame accelerations, known as extended Galilean invariance (EGI). We gauge fix this extended symmetry and derive the generalized Ward identity that follows from the BRS invariance of the gauge-fixed theory. This new Ward identity reduces to the standard one in the limit of zero acceleration. This gauge-fixing approach unambiguously shows that Galilean invariance and EGI constrain only the zero mode of the vertex but none of the higher wavenumber modes.Comment: 36 pages REVTeX; to appear in Nuclear Physics

The Exact N-point Generating Function in Polyakov-Burgers Turbulence

We find the exact N-point generating function in Polyakov's approach to Burgers turbulence.Comment: 7 pages,Latex,no figure

Logarithmic Corrections in Dynamic Isotropic Percolation

Based on the field theoretic formulation of the general epidemic process we study logarithmic corrections to scaling in dynamic isotropic percolation at the upper critical dimension d=6. Employing renormalization group methods we determine these corrections for some of the most interesting time dependent observables in dynamic percolation at the critical point up to and including the next to leading correction. For clusters emanating from a local seed at the origin we calculate the number of active sites, the survival probability as well as the radius of gyration.Comment: 9 pages, 3 figures, version to appear in Phys. Rev.

On Critical Exponents and the Renormalization of the Coupling Constant in Growth Models with Surface Diffusion

It is shown by the method of renormalized field theory that in contrast to a statement based on a mathematically ill-defined invariance transformation and found in most of the recent publications on growth models with surface diffusion, the coupling constant of these models renormalizes nontrivially. This implies that the widely accepted supposedly exact scaling exponents are to be corrected. A two-loop calculation shows that the corrections are small and these exponents seem to be very good approximations.Comment: 4 pages, revtex, 2 postscript figures, to appear in Phys.Rev.Let

Response Functions in Phase Ordering Kinetics

We discuss the behavior of response functions in phase ordering kinetics within the perturbation theory approach developed earlier. At zeroth order the results agree with previous gaussian theory calculations. At second order the nonequilibrium exponents \lambda and \lambda_{R} are changed but remain equal.Comment: 29 page