Equilibrium states of a test particle coupled to finite size heat baths

We report on numerical simulations of the dynamics of a test particle coupled to competing Boltzmann heat baths of finite size. After discussing some features of the single bath case, we show that the presence of two heat baths further constraints the conditions necessary for the test particle to thermalize with the heat baths. We find that thermalization is a spectral property in which the oscillators of the bath with frequencies in the range of the test particle characteristic frequency determine its degree of thermalization. We also find an unexpected frequency shift of the test particle response with respect to the spectra of the two heat baths. Finally, we discuss implications of our results for the study of high-frequency nanomechanical resonators through cold damping cooling techniques, and for engineering reservoirs capable of mitigating the back-action on a mechanical system.Comment: Strongly related to arXiV:0810.3251 (appeared in European Physical Journal B 61, 271 (2008

The Bloch-Okounkov correlation functions, a classical half-integral case

Bloch and Okounkov's correlation function on the infinite wedge space has connections to Gromov-Witten theory, Hilbert schemes, symmetric groups, and certain character functions of \hgl_\infty-modules of level one. Recent works have calculated these character functions for higher levels for \hgl_\infty and its Lie subalgebras of classical type. Here we obtain these functions for the subalgebra of type $D$ of half-integral levels and as a byproduct, obtain $q$-dimension formulas for integral modules of type $D$ at half-integral level.Comment: v2: minor changes to the introduction; accepted for publication in Letters in Mathematical Physic

Quantification of Maceration Changes using Post Mortem MRI in Fetuses

BACKGROUND: Post mortem imaging is playing an increasingly important role in perinatal autopsy, and correct interpretation of imaging changes is paramount. This is particularly important following intra-uterine fetal death, where there may be fetal maceration. The aim of this study was to investigate whether any changes seen on a whole body fetal post mortem magnetic resonance imaging (PMMR) correspond to maceration at conventional autopsy. METHODS: We performed pre-autopsy PMMR in 75 fetuses using a 1.5 Tesla Siemens Avanto MR scanner (Erlangen, Germany). PMMR images were reported blinded to the clinical history and autopsy data using a numerical severity scale (0 = no maceration changes to 2 = severe maceration changes) for 6 different visceral organs (total 12). The degree of maceration at autopsy was categorized according to severity on a numerical scale (1 = no maceration to 4 = severe maceration). We also generated quantitative maps to measure the liver and lung T2. RESULTS: The mean PMMR maceration score correlated well with the autopsy maceration score (R(2) = 0.93). A PMMR score of ≥4.5 had a sensitivity of 91%, specificity of 64%, for detecting moderate or severe maceration at autopsy. Liver and lung T2 were increased in fetuses with maceration scores of 3-4 in comparison to those with 1-2 (liver p = 0.03, lung p = 0.02). CONCLUSIONS: There was a good correlation between PMMR maceration score and the extent of maceration seen at conventional autopsy. This score may be useful in interpretation of fetal PMMR

Three-State Feshbach Resonances Mediated By Second-Order Couplings

We present an analytical study of three-state Feshbach resonances induced by second-order couplings. Such resonances arise when the scattering amplitude is modified by the interaction with a bound state that is not directly coupled to the scattering state containing incoming flux. Coupling occurs indirectly through an intermediate state. We consider two problems: (i) the intermediate state is a scattering state in a distinct open channel; (ii) the intermediate state is an off-resonant bound state in a distinct closed channel. The first problem is a model of electric-field-induced resonances in ultracold collisions of alkali metal atoms [Phys. Rev. A 75, 032709 (2007)] and the second problem is relevant for ultracold collisions of complex polyatomic molecules, chemical reaction dynamics, photoassociation of ultracold atoms, and electron - molecule scattering. Our analysis yields general expressions for the energy dependence of the T-matrix elements modified by three-state resonances and the dependence of the resonance positions and widths on coupling amplitudes for the weak-coupling limit. We show that the second problem can be generalized to describe resonances induced by indirect coupling through an arbitrary number of sequentially coupled off-resonant bound states and analyze the dependence of the resonance width on the number of the intermediate states.Comment: 27 pages, 4 figures; added a reference; journal reference/DOI refer to final published version, which is a shortened and modified version of this preprin

An Explicit Conditioning Method for Image Reconstruction in Electrical Capacitance Tomography

A new electrical capacitance tomography (ECT) image reconstruction method, termed Sensitivity Factor Regularization (SFR), is developed. The SFR method provides an explicit formulation for solving the image reconstruction problem that performs better than other explicit methods, such as linear back-projection and Tikhonov regularization, while providing the same computational efficiency. The computational ease of the SFR method renders it an attractive option for ECT where real-time imaging is required and theoretical statistical evaluation of proposed electrode configurations may readily be performed. A statistical study is conducted using SFR image reconstructions for investigating the impact of electrode density on image quality for a symmetric ECT system characterizing a square cross-section. A larger number of smaller electrodes allows more data to be gathered for use in image reconstruction, but degrades signal-to-noise ratio in the measurements. The statistical study using SFR clearly identifies a theoretical optimum electrode density that minimizes reconstructed image error for a given level of measurement noise