Complementarity relation for irreversible process derived from stochastic energetics

When the process of a system in contact with a heat bath is described by classical Langevin equation, the method of stochastic energetics [K. Sekimoto, J. Phys. Soc. Jpn. vol. 66 (1997) p.1234] enables to derive the form of Helmholtz free energy and the dissipation function of the system. We prove that the irreversible heat Q_irr and the time lapse $Delta t} of an isothermal process obey the complementarity relation, Q_irr {Delta t} >= k_B T S_min, where S_min depends on the initial and the final values of the control parameters, but it does not depend on the pathway between these values.Comment: 3 pages. LaTeX with 6 style macro

Bosonization, vicinal surfaces, and hydrodynamic fluctuation theory

Through a Euclidean path integral we establish that the density fluctuations of a Fermi fluid in one dimension are related to vicinal surfaces and to the stochastic dynamics of particles interacting through long range forces with inverse distance decay. In the surface picture one easily obtains the Haldane relation and identifies the scaling exponents governing the low energy, Luttinger liquid behavior. For the stochastic particle model we develop a hydrodynamic fluctuation theory, through which in some cases the large distance Gaussian fluctuations are proved nonperturbatively

The Douglas County Drug Court: Characteristics Of Participants, Case Outcomes And Recidivism

The purpose of this report is to describe the characteristics of all offenders (N = 255) who were bound over to Douglas County District Court in 2001 and who were subsequently diverted to the Douglas County Drug Court. We present descriptive data on the characteristics of the drug court participants, focusing on their background characteristics and prior criminal record and on their case characteristics. We also present descriptive data on recidivism for drug court participants and for traditionally adjudicated offenders and compare the recidivism rates of these two groups of offenders, controlling for other predictors of the likelihood of recidivism

Cost/Benefit Analysis of the Douglas County Drug Court

The primary purpose of this cost-benefit evaluation of the Douglas County Drug Court (DCDC) is to provide administrators and policy-makers with critical information for future policy and funding decisions. This study expands and refines previous DCDC cost-benefit analyses through an investigation of drug court program investment, outcome and societal-impact costs and savings. This study employs a Transaction Cost model that examines complex, multi-agency events and costs for participants in drug court and non-drug court comparison groups. A “cost-to-taxpayer” approach is used that includes any criminal justice related costs (or avoided costs) generated by drug court or non-drug court comparison group participants, that directly impacts citizens either through tax-related expenditures or personal victimization costs/losses due to crimes committed by drug offenders

Felony Offenses In Douglas County District Court, 2001

The purpose of this report is describe the offender and case characteristics and the outcomes of all felony cases (N = 2,663) bound over for trial in Douglas County (Nebraska) District Court in 2001.1 We present descriptive data on these cases, focusing on defendants’ background characteristics and prior criminal record, the nature and seriousness of the charges for which the defendant was bound over to District Court, the disposition of the case, and case processing time. We also examine case dispositions and sentences for 15 different types of felony offenses and present descriptive data and case outcome data for defendants who were held in custody prior to trial and for non-violent defendants who were charged with property crimes (burglary, theft, fraud, and forgery). In the final section of the report we provide information on case characteristics and case outcomes for white and black defendants and for male and female defendants

On the spin--boson model with a sub--Ohmic bath

We study the spin--boson model with a sub--Ohmic bath using infinitesimal unitary transformations. Contrary to some results reported in the literature we find a zero temperature transition from an untrapped state for small coupling to a trapped state for strong coupling. We obtain an explicit expression for the renormalized level spacing as a function of the bare papameters of the system. Furthermore we show that typical dynamical equilibrium correlation functions exhibit an algebaric decay at zero temperature.Comment: 9 pages, 2 Postscript figure

Replica Bethe ansatz derivation of the Tracy-Widom distribution of the free energy fluctuations in one-dimensional directed polymers

The distribution function of the free energy fluctuations in one-dimensional directed polymers with $\delta$-correlated random potential is studied by mapping the replicated problem to the $N$-particle quantum boson system with attractive interactions. We find the full set of eigenfunctions and eigenvalues of this many-body system and perform the summation over the entire spectrum of excited states. It is shown that in the thermodynamic limit the problem is reduced to the Fredholm determinant with the Airy kernel yielding the universal Tracy-Widom distribution, which is known to describe the statistical properties of the Gaussian unitary ensemble as well as many other statistical systems.Comment: 23 page

Cluster-based reduced-order modelling of a mixing layer

We propose a novel cluster-based reduced-order modelling (CROM) strategy of unsteady flows. CROM combines the cluster analysis pioneered in Gunzburger's group (Burkardt et al. 2006) and and transition matrix models introduced in fluid dynamics in Eckhardt's group (Schneider et al. 2007). CROM constitutes a potential alternative to POD models and generalises the Ulam-Galerkin method classically used in dynamical systems to determine a finite-rank approximation of the Perron-Frobenius operator. The proposed strategy processes a time-resolved sequence of flow snapshots in two steps. First, the snapshot data are clustered into a small number of representative states, called centroids, in the state space. These centroids partition the state space in complementary non-overlapping regions (centroidal Voronoi cells). Departing from the standard algorithm, the probabilities of the clusters are determined, and the states are sorted by analysis of the transition matrix. Secondly, the transitions between the states are dynamically modelled using a Markov process. Physical mechanisms are then distilled by a refined analysis of the Markov process, e.g. using finite-time Lyapunov exponent and entropic methods. This CROM framework is applied to the Lorenz attractor (as illustrative example), to velocity fields of the spatially evolving incompressible mixing layer and the three-dimensional turbulent wake of a bluff body. For these examples, CROM is shown to identify non-trivial quasi-attractors and transition processes in an unsupervised manner. CROM has numerous potential applications for the systematic identification of physical mechanisms of complex dynamics, for comparison of flow evolution models, for the identification of precursors to desirable and undesirable events, and for flow control applications exploiting nonlinear actuation dynamics.Comment: 48 pages, 30 figures. Revised version with additional material. Accepted for publication in Journal of Fluid Mechanic

Mean-Field- and Classical Limit of Many-Body Schr\"odinger Dynamics for Bosons

We present a new proof of the convergence of the N-particle Schroedinger dynamics for bosons towards the dynamics generated by the Hartree equation in the mean-field limit. For a restricted class of two-body interactions, we obtain convergence estimates uniform in the Planck constant , up to an exponentially small remainder. For h=0, the classical dynamics in the mean-field limit is given by the Vlasov equation.Comment: Latex 2e, 18 page