The criminal prosecution of inter-male sex 1850-1970: a Lancashire case study.

The thesis addresses two related issues. Firstly, the lack of an accurate longitudinal reading of the incidence of indictable prosecutions predicated on the criminalisation of sexualised behaviours between males for the period 1850-1970; that is, consensual conducts (including ‘victimless’ behaviour discriminately criminalised) together with coercive behaviours. The results of the enumerative part of this investigation demonstrate significant variations in the frequency of prosecutions during what was a seminal period of criminalisation of such conduct. The rarity of cases of the later nineteenth century, followed by a slow, and sometimes erratic, increase during the inter-war years (1919-1939) preceded a more energetic period of prosecutions in the two decades about the publication of the government commissioned ‘Wolfenden’ Report (1957). The primary sources used to produce this accurate longitudinal count of the criminal prosecutions and, in particular, the Calendars also provided the evidential basis for the second task of this investigation. To date, there has been no in-depth longitudinal reading of the treatment of such cases by the four main constituent ‘players’ within the Criminal Justice System that were charged with the practical realisation of Parliament’s abstract criminalisation. This thesis provides both a quantitative and qualitative reading of the sometime consistent and divergent attitudinal relationship between these four ‘players’ in the prosecution of sexualised conduct between males: the prosecution, defence, adjudication and presiding judiciary. The practical criminalisation of inter-male sex 1850-1970: A Lancashire case study. These two complimentary readings are contextualised within a number of contingent realities of the period that suggest the criminalisation of sexualised behaviours was not a major policing priority for much of the period. Further, that when such cases did come to trial the success rate and, therein further prosecutions, was heavily reliant on the role of the defendant cooperating with their own conviction. Finally, the choice of these investigatory goals was in large part addressed by a reading of the specialised historiography within this relatively new field of study and thereby in part an attempt to light-up previously unexplored territory

Spectral Degeneracies in the Totally Asymmetric Exclusion Process

We study the spectrum of the Markov matrix of the totally asymmetric exclusion process (TASEP) on a one-dimensional periodic lattice at ARBITRARY filling. Although the system does not possess obvious symmetries except translation invariance, the spectrum presents many multiplets with degeneracies of high order. This behaviour is explained by a hidden symmetry property of the Bethe Ansatz. Combinatorial formulae for the orders of degeneracy and the corresponding number of multiplets are derived and compared with numerical results obtained from exact diagonalisation of small size systems. This unexpected structure of the TASEP spectrum suggests the existence of an underlying large invariance group. Keywords: ASEP, Markov matrix, Bethe Ansatz, Symmetries.Comment: 19 pages, 1 figur

Stationary and Transient Work-Fluctuation Theorems for a Dragged Brownian Particle

Recently Wang et al. carried out a laboratory experiment, where a Brownian particle was dragged through a fluid by a harmonic force with constant velocity of its center. This experiment confirmed a theoretically predicted work related integrated (I) Transient Fluctuation Theorem (ITFT), which gives an expression for the ratio for the probability to find positive or negative values for the fluctuations of the total work done on the system in a given time in a transient state. The corresponding integrated stationary state fluctuation theorem (ISSFT) was not observed. Using an overdamped Langevin equation and an arbitrary motion for the center of the harmonic force, all quantities of interest for these theorems and the corresponding non-integrated ones (TFT and SSFT, resp.) are theoretically explicitly obtained in this paper. While the (I)TFT is satisfied for all times, the (I)SSFT only holds asymptotically in time. Suggestions for further experiments with arbitrary velocity of the harmonic force and in which also the ISSFT could be observed, are given. In addition, a non-trivial long-time relation between the ITFT and the ISSFT was discovered, which could be observed experimentally, especially in the case of a resonant circular motion of the center of the harmonic force.Comment: 20 pages, 3 figure

The Steady State Fluctuation Relation for the Dissipation Function

We give a proof of transient fluctuation relations for the entropy production (dissipation function) in nonequilibrium systems, which is valid for most time reversible dynamics. We then consider the conditions under which a transient fluctuation relation yields a steady state fluctuation relation for driven nonequilibrium systems whose transients relax, producing a unique nonequilibrium steady state. Although the necessary and sufficient conditions for the production of a unique nonequilibrium steady state are unknown, if such a steady state exists, the generation of the steady state fluctuation relation from the transient relation is shown to be very general. It is essentially a consequence of time reversibility and of a form of decay of correlations in the dissipation, which is needed also for, e.g., the existence of transport coefficients. Because of this generality the resulting steady state fluctuation relation has the same degree of robustness as do equilibrium thermodynamic equalities. The steady state fluctuation relation for the dissipation stands in contrast with the one for the phase space compression factor, whose convergence is problematic, for systems close to equilibrium. We examine some model dynamics that have been considered previously, and show how they are described in the context of this work.Comment: 30 pages, 1 figur

Zero-range process with open boundaries

We calculate the exact stationary distribution of the one-dimensional zero-range process with open boundaries for arbitrary bulk and boundary hopping rates. When such a distribution exists, the steady state has no correlations between sites and is uniquely characterized by a space-dependent fugacity which is a function of the boundary rates and the hopping asymmetry. For strong boundary drive the system has no stationary distribution. In systems which on a ring geometry allow for a condensation transition, a condensate develops at one or both boundary sites. On all other sites the particle distribution approaches a product measure with the finite critical density \rho_c. In systems which do not support condensation on a ring, strong boundary drive leads to a condensate at the boundary. However, in this case the local particle density in the interior exhibits a complex algebraic growth in time. We calculate the bulk and boundary growth exponents as a function of the system parameters

On the Fluctuation Relation for Nose-Hoover Boundary Thermostated Systems

We discuss the transient and steady state fluctuation relation for a mechanical system in contact with two deterministic thermostats at different temperatures. The system is a modified Lorentz gas in which the fixed scatterers exchange energy with the gas of particles, and the thermostats are modelled by two Nos\'e-Hoover thermostats applied at the boundaries of the system. The transient fluctuation relation, which holds only for a precise choice of the initial ensemble, is verified at all times, as expected. Times longer than the mesoscopic scale, needed for local equilibrium to be settled, are required if a different initial ensemble is considered. This shows how the transient fluctuation relation asymptotically leads to the steady state relation when, as explicitly checked in our systems, the condition found in [D.J. Searles, {\em et al.}, J. Stat. Phys. 128, 1337 (2007)], for the validity of the steady state fluctuation relation, is verified. For the steady state fluctuations of the phase space contraction rate \zL and of the dissipation function \zW, a similar relaxation regime at shorter averaging times is found. The quantity \zW satisfies with good accuracy the fluctuation relation for times larger than the mesoscopic time scale; the quantity \zL appears to begin a monotonic convergence after such times. This is consistent with the fact that \zW and \zL differ by a total time derivative, and that the tails of the probability distribution function of \zL are Gaussian.Comment: Major revision. Fig.10 was added. Version to appear in Journal of Statistical Physic

Generalized empty-interval method applied to a class of one-dimensional stochastic models

In this work we study, on a finite and periodic lattice, a class of one-dimensional (bimolecular and single-species) reaction-diffusion models which cannot be mapped onto free-fermion models. We extend the conventional empty-interval method, also called {\it interparticle distribution function} (IPDF) method, by introducing a string function, which is simply related to relevant physical quantities. As an illustration, we specifically consider a model which cannot be solved directly by the conventional IPDF method and which can be viewed as a generalization of the {\it voter} model and/or as an {\it epidemic} model. We also consider the {\it reversible} diffusion-coagulation model with input of particles and determine other reaction-diffusion models which can be mapped onto the latter via suitable {\it similarity transformations}. Finally we study the problem of the propagation of a wave-front from an inhomogeneous initial configuration and note that the mean-field scenario predicted by Fisher's equation is not valid for the one-dimensional (microscopic) models under consideration.Comment: 19 pages, no figure. To appear in Physical Review E (November 2001

Phase fluctuations in the ABC model

We analyze the fluctuations of the steady state profiles in the modulated phase of the ABC model. For a system of $L$ sites, the steady state profiles move on a microscopic time scale of order $L^3$. The variance of their displacement is computed in terms of the macroscopic steady state profiles by using fluctuating hydrodynamics and large deviations. Our analytical prediction for this variance is confirmed by the results of numerical simulations

Determinant representation for some transition probabilities in the TASEP with second class particles

We study the transition probabilities for the totally asymmetric simple exclusion process (TASEP) on the infinite integer lattice with a finite, but arbitrary number of first and second class particles. Using the Bethe ansatz we present an explicit expression of these quantities in terms of the Bethe wave function. In a next step it is proved rigorously that this expression can be written in a compact determinantal form for the case where the order of the first and second class particles does not change in time. An independent geometrical approach provides insight into these results and enables us to generalize the determinantal solution to the multi-class TASEP.Comment: Minor revision; journal reference adde

An Exactly Solvable Two-Way Traffic Model With Ordered Sequential Update

Within the formalism of matrix product ansatz, we study a two-species asymmetric exclusion process with backward and forward site-ordered sequential update. This model, which was originally introduced with the random sequential update, describes a two-way traffic flow with a dynamic impurity and shows a phase transition between the free flow and traffic jam. We investigate the characteristics of this jamming and examine similarities and differences between our results and those with random sequential update.Comment: 25 pages, Revtex, 7 ps file