Reasoning about transfinite sequences

We introduce a family of temporal logics to specify the behavior of systems with Zeno behaviors. We extend linear-time temporal logic LTL to authorize models admitting Zeno sequences of actions and quantitative temporal operators indexed by ordinals replace the standard next-time and until future-time operators. Our aim is to control such systems by designing controllers that safely work on $\omega$-sequences but interact synchronously with the system in order to restrict their behaviors. We show that the satisfiability problem for the logics working on $\omega^k$-sequences is EXPSPACE-complete when the integers are represented in binary, and PSPACE-complete with a unary representation. To do so, we substantially extend standard results about LTL by introducing a new class of succinct ordinal automata that can encode the interaction between the different quantitative temporal operators.Comment: 38 page

Interplay of Anisotropy and Disorder in the Doping-Dependent Melting and Glass Transitions of Vortices in Bi2_2Sr2_2CaCu2_2O8+δ_{8+\delta}

We study the oxygen doping dependence of the equilibrium first-order melting and second-order glass transitions of vortices in Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$. Doping affects both anisotropy and disorder. Anisotropy scaling is shown to collapse the melting lines only where thermal fluctuations are dominant. Yet, in the region where disorder breaks that scaling, the glass lines are still collapsed. A quantitative fit to melting and replica symmetry breaking lines of a 2D Ginzburg-Landau model further reveals that disorder amplitude weakens with doping, but to a lesser degree than thermal fluctuations, enhancing the relative role of disorder.Comment: 4 pages, 4 figure

Equilibrium First-Order Melting and Second-Order Glass Transitions of the Vortex Matter in Bi2_2Sr2_2CaCu2_2O8_8

The thermodynamic $H-T$ phase diagram of Bi$_2$Sr$_2$CaCu$_2$O$_8$ was mapped by measuring local \emph{equilibrium} magnetization $M(H,T)$ in presence of vortex `shaking'. Two equally sharp first-order magnetization steps are revealed in a single temperature sweep, manifesting a liquid-solid-liquid sequence. In addition, a second-order glass transition line is revealed by a sharp break in the equilibrium $M(T)$ slope. The first- and second-order lines intersect at intermediate temperatures, suggesting the existence of four phases: Bragg glass and vortex crystal at low fields, glass and liquid at higher fields.Comment: 5 pages, 4 figures. To be published in Phys. Rev. Let

The Dynamical Behaviors in (2+1)-Dimensional Gross-Neveu Model with a Thirring Interaction

We analyze (2+1)-dimensional Gross-Neveu model with a Thirring interaction, where a vector-vector type four-fermi interaction is on equal terms with a scalar-scalar type one. The Dyson-Schwinger equation for fermion self-energy function is constructed up to next-to-leading order in 1/N expansion. We determine the critical surface which is the boundary between a broken phase and an unbroken one in ($\alpha_c,~ \beta_c,~ N_c$) space. It is observed that the critical behavior is mainly controlled by Gross-Neveu coupling $\alpha_c$ and the region of the broken phase is separated into two parts by the line $\alpha_c=\alpha_c^*(=\frac{8}{\pi^2})$. The mass function is strongly dependent upon the flavor number N for $\alpha > \alpha_c^*$, while weakly for $\alpha \alpha_c^*$, the critical flavor number $N_c$ increases as Thirring coupling $\beta$ decreases. By driving the CJT effective potential, we show that the broken phase is energetically preferred to the symmetric one. We discuss the gauge dependence of the mass function and the ultra-violet property of the composite operators.Comment: 19 pages, LaTex, 6 ps figure files(uuencoded in seperate file

Community and Clinical Epidemiology of Borderline Personality Disorder

Several studies of the prevalence of Borderline Personality Disorder (BPD) in community and clinical settings have been carried out to date. Although results vary according to sampling method and assessment method, median point prevalence of BPD is roughly 1%, with higher or lower rates in certain community subpopulations. In clinical settings, BPD prevalence is around 10-12% in outpatient psychiatric clinics and 20-22% among inpatient clinics. Further research is needed to identify the prevalence and correlates of BPD in other clinical settings (e.g., primary care) and to investigate the impact of demographic variables on BPD prevalence

Dimensional Reduction and Quantum-to-Classical Reduction at High Temperatures

We discuss the relation between dimensional reduction in quantum field theories at finite temperature and a familiar quantum mechanical phenomenon that quantum effects become negligible at high temperatures. Fermi and Bose fields are compared in this respect. We show that decoupling of fermions from the dimensionally reduced theory can be related to the non-existence of classical statistics for a Fermi field.Comment: 11 pages, REVTeX, revised v. to be published in Phys. Rev. D: some points made more explici

Nature of 45 degree vortex lattice reorientation in tetragonal superconductors

The transformation of the vortex lattice in a tetragonal superconductor which consists of its 45 degree reorientation relative to the crystal axes is studied using the nonlocal London model. It is shown that the reorientation occurs as two successive second order (continuous) phase transitions. The transition magnetic fields are calculated for a range of parameters relevant for borocarbide superconductors in which the reorientation has been observed

Can Sigma Models Describe Finite Temperature Chiral Transitions?

Large-N expansions and computer simulations indicate that the universality class of the finite temperature chiral symmetry restoration transition in the 3D Gross-Neveu model is mean field theory. This is a counterexample to the standard 'sigma model' scenario which predicts the 2D Ising model universality class. We trace the breakdown of the standard scenario (dimensional reduction and universality) to the absence of canonical scalar fields in the model. We point out that our results could be generic for theories with dynamical symmetry breaking, such as Quantum Chromodynamics.Comment: 9 pages, 2 ps figure