Narrow-escape times for diffusion in microdomains with a particle-surface affinity: Mean-field results

We analyze the mean time t_{app} that a randomly moving particle spends in a bounded domain (sphere) before it escapes through a small window in the domain's boundary. A particle is assumed to diffuse freely in the bulk until it approaches the surface of the domain where it becomes weakly adsorbed, and then wanders diffusively along the boundary for a random time until it desorbs back to the bulk, and etc. Using a mean-field approximation, we define t_{app} analytically as a function of the bulk and surface diffusion coefficients, the mean time it spends in the bulk between two consecutive arrivals to the surface and the mean time it wanders on the surface within a single round of the surface diffusion.Comment: 8 pages, 1 figure, submitted to JC

Ensemble dependence of Critical Casimir Forces in Films with Dirichlet Boundary Conditions

In a recent study [Phys. Rev. E \textbf{94}, 022103 (2016)] it has been shown that, for a fluid film subject to critical adsorption, the resulting critical Casimir force (CCF) may significantly depend on the thermodynamic ensemble. Here, we extend that study by considering fluid films within the so-called ordinary surface universality class. We focus on mean-field theory, within which the OP profile satisfies Dirichlet boundary conditions and produces a nontrivial CCF in the presence of external bulk fields or, respectively, a nonzero total order parameter within the film. Our analytical results are supported by Monte Carlo simulations of the three-dimensional Ising model. We show that, in the canonical ensemble, i.e., when fixing the so-called total mass within the film, the CCF is typically repulsive instead of attractive as in the grand canonical ensemble. Based on the Landau-Ginzburg free energy, we furthermore obtain analytic expressions for the order parameter profiles and analyze the relation between the total mass in the film and the external bulk field.Comment: 22 pages, 15 figures. Version 2: minor corrections; added Journal referenc

Spectroscopic properties of a two-dimensional time-dependent Cepheid model II. Determination of stellar parameters and abundances

Standard spectroscopic analyses of variable stars are based on hydrostatic one-dimensional model atmospheres. This quasi-static approach has theoretically not been validated. We aim at investigating the validity of the quasi-static approximation for Cepheid variables. We focus on the spectroscopic determination of the effective temperature $T_\mathrm{eff}$, surface gravity $\log \,g$, microturbulent velocity $\xi_\mathrm{t}$, and a generic metal abundance $\log\,A$ -- here taken as iron. We calculate a grid of 1D hydrostatic plane-parallel models covering the ranges in effective temperature and gravity encountered during the evolution of a two-dimensional time-dependent envelope model of a Cepheid computed with the radiation-hydrodynamics code CO5BOLD. We perform 1D spectral syntheses for artificial iron lines in local thermodynamic equilibrium varying the microturbulent velocity and abundance. We fit the resulting equivalent widths to corresponding values obtained from our dynamical model. For the four-parametric case, the stellar parameters are typically underestimated exhibiting a bias in the iron abundance of \approx-0.2\,\mbox{dex}. To avoid biases of this kind it is favourable to restrict the spectroscopic analysis to photometric phases $\phi_\mathrm{ph}\approx0.3\ldots 0.65$ using additional information to fix effective temperature and surface gravity. Hydrostatic 1D model atmospheres can provide unbiased estimates of stellar parameters and abundances of Cepheid variables for particular phases of their pulsations. We identified convective inhomogeneities as the main driver behind potential biases. For obtaining a complete view on the effects when determining stellar parameters with 1D models, multi-dimensional Cepheid atmosphere models are necessary for variables of longer period than investigated here.Comment: accepted for publication in Astronomy & Astrophysic

Spectroscopic properties of a two-dimensional time-dependent Cepheid model I. Description and validation of the model

Standard spectroscopic analyses of Cepheid variables are based on hydrostatic one-dimensional model atmospheres, with convection treated using various formulations of mixing-length theory. This paper aims to carry out an investigation of the validity of the quasi-static approximation in the context of pulsating stars. We check the adequacy of a two-dimensional time-dependent model of a Cepheid-like variable with focus on its spectroscopic properties. With the radiation-hydrodynamics code CO5BOLD, we construct a two-dimensional time-dependent envelope model of a Cepheid with $T_\mathrm{eff}= 5600$ K, $\log g=2.0$, solar metallicity, and a 2.8-day pulsation period. Subsequently, we perform extensive spectral syntheses of a set of artificial iron lines in local thermodynamic equilibrium. The set of lines allows us to systematically study effects of line strength, ionization stage, and excitation potential. We evaluate the microturbulent velocity, line asymmetry, projection factor, and Doppler shifts. The mean Doppler shift is non-zero and negative, -1 km/s, after averaging over several full periods and lines. This residual line-of-sight velocity (related to the "K-term") is primarily caused by horizontal inhomogeneities, and consequently we interpret it as the familiar convective blueshift ubiquitously present in non-pulsating late-type stars. Limited statistics prevent firm conclusions on the line asymmetries. Our two-dimensional model provides a reasonably accurate representation of the spectroscopic properties of a short-period Cepheid-like variable star. Some properties are primarily controlled by convective inhomogeneities rather than by the Cepheid-defining pulsations

Group Theoretical Quantum Tomography

The paper is devoted to the mathematical foundation of the quantum tomography using the theory of square-integrable representations of unimodular Lie groups.Comment: 13 pages, no figure, Latex2e. Submitted to J.Math.Phy