Spectra of Harmonium in a magnetic field using an initial value representation of the semiclassical propagator

For two Coulombically interacting electrons in a quantum dot with harmonic confinement and a constant magnetic field, we show that time-dependent semiclassical calculations using the Herman-Kluk initial value representation of the propagator lead to eigenvalues of the same accuracy as WKB calculations with Langer correction. The latter are restricted to integrable systems, however, whereas the time-dependent initial value approach allows for applications to high-dimensional, possibly chaotic dynamics and is extendable to arbitrary shapes of the potential.Comment: 11 pages, 1 figur

Interaction of Human Chorionic Gonadotropin (hCG) and Asialo-hCG with Recombinant Human Thyrotropin Receptor.

hCG is a putative thyroid stimulator. The present studies were undertaken to examine its interaction and that of its desialylated variant asialo-hCG with recombinant human TSH (hTSH) receptor (hTSHr). To this end, we transfected a human thyroid carcinoma cell line (HTC) lacking endogenous TSHr with the full-length cDNA of the hTSHr. Unlike the wild type, the transfected cells, termed HTC-TSHr cells, were able to bind bovine TSH (bTSH) with high affinity and increase cAMP production in response to bTSH stimulation. Of the hCG forms, intact hCG displayed a weak activity to inhibit [125I] bTSH binding to HTC-TSHr cells, with 100 mg/L (2.6 x 10(-6) mol/L) producing maximally a 20% inhibition, whereas asialo-hCG achieved half-maximum binding inhibition at a concentration of 8 mg/L (2.3 x 10(-7) mol/L). The inhibitory constant (Ki) of asialo-hCG for recombinant hTSHr was calculated from saturation experiments in the presence of variable doses of bTSH and a fixed concentration of asialo-hCG to be approximately 8 x 10(-8) mol/L. The interaction of asialo-hCG with TSHr was further assessed by studies of the direct binding of the radioactively labeled hormone to both HTC and HTC-TSHr cells. [125I]Asialo-hCG binding to HTC-TSHr cells was 4.7%, compared to 1.5% in the wild-type cells lacking TSHr and was displaceable by bTSH (0.1-100 IU/L), indicating specific binding of the tracer to TSHr. Functionally, hCG (up to 100 mg/L; 2.6 x 10(-6) mol/L) proved unable to evoke any significant cAMP response over basal values in HTC-TSHr cells, as did asialo-hCG. Asialo-hCG, but not hCG, inhibited bTSH-stimulated adenylate cyclase activity in the cells in a dose-dependent manner. In conclusion, the present data show that intact hCG binds only weakly to HTC-TSHr cells and produces no significant cAMP stimulation, which is at variance with data obtained in FRTL-5 and Chinese hamster ovary-TSHr cells, but in good accord with previous findings in human thyroid membranes. Asialo-hCG, on the other hand, strongly binds to recombinant TSHr and inhibits the cAMP response to bTSH in HTC-TSHr cells, indicating that the desialylated hCG variant directly interacts with the receptor and truly is an antagonist of the hTSHr

Analytic expression for Taylor-Couette stability boundary

We analyze the mechanism that determines the boundary of stability in Taylor-Couette flow. By simple physical argument we derive an analytic expression to approximate the stability line for all radius ratios and all speed ratios, for co- and counterrotating cylinders. The expression includes viscosity and so generalizes Rayleigh's criterion. We achieve agreement with linear stability theory and with experiments in the whole parameter space. Explicit formulae are given for limiting cases.Comment: 6 pages (LaTeX with REVTEX) including 4 figures (Postscript) Revised, discussion of two additional references. See also http://staff-www.uni-marburg.de/~esse

Extended phase diagram of the Lorenz model

The parameter dependence of the various attractive solutions of the three variable nonlinear Lorenz model equations for thermal convection in Rayleigh-B\'enard flow is studied. Its bifurcation structure has commonly been investigated as a function of r, the normalized Rayleigh number, at fixed Prandtl number \sigma. The present work extends the analysis to the entire (r,\sigma) parameter plane. An onion like periodic pattern is found which is due to the alternating stability of symmetric and non-symmetric periodic orbits. This periodic pattern is explained by considering non-trivial limits of large r and \sigma. In addition to the limit which was previously analyzed by Sparrow, we identify two more distinct asymptotic regimes in which either \sigma/r or \sigma^2/r is constant. In both limits the dynamics is approximately described by Airy functions whence the periodicity in parameter space can be calculated analytically. Furthermore, some observations about sequences of bifurcations and coexistence of attractors, periodic as well as chaotic, are reported.Comment: 36 pages, 20 figure

Semiclassical Coherent States propagator

In this work, we derived a semiclassical approximation for the matrix elements of a quantum propagator in coherent states (CS) basis that avoids complex trajectories, it only involves real ones. For that propose, we used the, symplectically invariant, semiclassical Weyl propagator obtained by performing a stationary phase approximation (SPA) for the path integral in the Weyl representation. After what, for the transformation to CS representation SPA is avoided, instead a quadratic expansion of the complex exponent is used. This procedure also allows to express the semiclassical CS propagator uniquely in terms of the classical evolution of the initial point, without the need of any root search typical of Van Vleck Gutzwiller based propagators. For the case of chaotic Hamiltonian systems, the explicit time dependence of the CS propagator has been obtained. The comparison with a \textquotedbl{}realistic\textquotedbl{} chaotic system that derives from a quadratic Hamiltonian, the cat map, reveals that the expression here derived is exact up to quadratic Hamiltonian systems.Comment: 13 pages, 2 figure. Accepted for publication in PR

Lee-Yang zeros and phase transitions in nonequilibrium steady states

We consider how the Lee-Yang description of phase transitions in terms of partition function zeros applies to nonequilibrium systems. Here one does not have a partition function, instead we consider the zeros of a steady-state normalization factor in the complex plane of the transition rates. We obtain the exact distribution of zeros in the thermodynamic limit for a specific model, the boundary-driven asymmetric simple exclusion process. We show that the distributions of zeros at the first and second order nonequilibrium phase transitions of this model follow the patterns known in the Lee-Yang equilibrium theory.Comment: 4 pages RevTeX4 with 4 figures; revised version to appear in Phys. Rev. Let

Semi-autonomous Intersection Collision Avoidance through Job-shop Scheduling

In this paper, we design a supervisor to prevent vehicle collisions at intersections. An intersection is modeled as an area containing multiple conflict points where vehicle paths cross in the future. At every time step, the supervisor determines whether there will be more than one vehicle in the vicinity of a conflict point at the same time. If there is, then an impending collision is detected, and the supervisor overrides the drivers to avoid collision. A major challenge in the design of a supervisor as opposed to an autonomous vehicle controller is to verify whether future collisions will occur based on the current drivers choices. This verification problem is particularly hard due to the large number of vehicles often involved in intersection collision, to the multitude of conflict points, and to the vehicles dynamics. In order to solve the verification problem, we translate the problem to a job-shop scheduling problem that yields equivalent answers. The job-shop scheduling problem can, in turn, be transformed into a mixed-integer linear program when the vehicle dynamics are first-order dynamics, and can thus be solved by using a commercial solver.Comment: Submitted to Hybrid Systems: Computation and Control (HSCC) 201

Convective intensification of magnetic fields in the quiet Sun

Kilogauss-strength magnetic fields are often observed in intergranular lanes at the photosphere in the quiet Sun. Such fields are stronger than the equipartition field B_e, corresponding to a magnetic energy density that matches the kinetic energy density of photospheric convection, and comparable with the field B_p that exerts a magnetic pressure equal to the ambient gas pressure. We present an idealised numerical model of three-dimensional compressible magnetoconvection at the photosphere, for a range of values of the magnetic Reynolds number. In the absence of a magnetic field, the convection is highly supercritical and is characterised by a pattern of vigorous, time-dependent, “granular” motions. When a weak magnetic field is imposed upon the convection, magnetic flux is swept into the convective downflows where it forms localised concentrations. Unless this process is significantly inhibited by magnetic diffusion, the resulting fields are often much greater than B_e, and the high magnetic pressure in these flux elements leads to their being partially evacuated. Some of these flux elements contain ultra-intense magnetic fields that are significantly greater than B_p. Such fields are contained by a combination of the thermal pressure of the gas and the dynamic pressure of the convective motion, and they are constantly evolving. These ultra-intense fields develop owing to nonlinear interactions between magnetic fields and convection; they cannot be explained in terms of “convective collapse” within a thin flux tube that remains in overall pressure equilibrium with its surroundings