Effective one-dimensional description of confined diffusion biased by a transverse gravitational force

Diffusion of point-like non interacting particles in a two-dimensional (2D) channel of varying cross section is considered. The particles are biased by a constant force in the transverse direction. We apply our recurrence mapping procedure, which enables us to derive an effective one-dimensional (1D) evolution equation, governing the 1D density of the particles in the channel. In the limit of stationary flow, we arrive at an extended Fick-Jacobs equation, corrected by an effective diffusion coefficient D(x), depending on the longitudinal coordinate x. Our result is an approximate formula for D(x), involving also influence of the transverse force. Our calculations are verified on the stationary diffusion in a linear cone, which is exactly solvable.Comment: 10 pages, 7 figures, submitted in Phys. Rev.

Stochastic Analysis of a Churn-Tolerant Structured Peer-to-Peer Scheme

We present and analyze a simple and general scheme to build a churn (fault)-tolerant structured Peer-to-Peer (P2P) network. Our scheme shows how to "convert" a static network into a dynamic distributed hash table(DHT)-based P2P network such that all the good properties of the static network are guaranteed with high probability (w.h.p). Applying our scheme to a cube-connected cycles network, for example, yields a $O(\log N)$ degree connected network, in which every search succeeds in $O(\log N)$ hops w.h.p., using $O(\log N)$ messages, where $N$ is the expected stable network size. Our scheme has an constant storage overhead (the number of nodes responsible for servicing a data item) and an $O(\log N)$ overhead (messages and time) per insertion and essentially no overhead for deletions. All these bounds are essentially optimal. While DHT schemes with similar guarantees are already known in the literature, this work is new in the following aspects: (1) It presents a rigorous mathematical analysis of the scheme under a general stochastic model of churn and shows the above guarantees; (2) The theoretical analysis is complemented by a simulation-based analysis that validates the asymptotic bounds even in moderately sized networks and also studies performance under changing stable network size; (3) The presented scheme seems especially suitable for maintaining dynamic structures under churn efficiently. In particular, we show that a spanning tree of low diameter can be efficiently maintained in constant time and logarithmic number of messages per insertion or deletion w.h.p. Keywords: P2P Network, DHT Scheme, Churn, Dynamic Spanning Tree, Stochastic Analysis

Conditions for the Quantum to Classical Transition: Trajectories vs. Phase Space Distributions

We contrast two sets of conditions that govern the transition in which classical dynamics emerges from the evolution of a quantum system. The first was derived by considering the trajectories seen by an observer (dubbed the ``strong'' transition) [Bhattacharya, et al., Phys. Rev. Lett. 85: 4852 (2000)], and the second by considering phase-space densities (the ``weak'' transition) [Greenbaum, et al., Chaos 15, 033302 (2005)]. On the face of it these conditions appear rather different. We show, however, that in the semiclassical regime, in which the action of the system is large compared to $\hbar$, and the measurement noise is small, they both offer an essentially equivalent local picture. Within this regime, the weak conditions dominate while in the opposite regime where the action is not much larger than Planck's constant, the strong conditions dominate.Comment: 8 pages, 2 eps figure

Associations of body composition measures and C2, a marker for small artery elasticity: The MESA.

ObjectiveLower C2, a continuous blood pressure waveform characteristic asserted to represent small artery elasticity, predicts future cardiovascular disease events. It is hypothesized that the paradoxical positive association between body mass index (BMI) and C2 may reflect muscle instead of excess fat.MethodsIn a multi-ethnic, community-living cohort of 1,960 participants, computed tomography scans of the abdomen were used to measure visceral adipose tissue (VAT) and total abdominal muscle tissue (TAMT), and applanation tonometry of the radial arteries was used to assess C2. The period cross-sectional associations between BMI, TAMT, and VAT with C2 were ascertained.ResultsThe mean age was 62 ± 9 years and 51% were male. After adjustments for age, gender, ethnicity, pack years smoking cigarettes, diabetes, hypertension, and total and HDL cholesterol, higher BMI (standardized beta = 0.09, P-value < 0.01) and more TAMT (standardized beta = 0.12, P-value < 0.01) were significantly associated with higher C2. In contrast, more VAT (standardized beta = -0.09, P-value < 0.01) was associated with lower C2.ConclusionsIn multivariable analysis, VAT, in contrast to TAMT and BMI, was associated with less compliant small arteries. Visceral fat may be a better marker for detrimental excess body fat than BMI

It's Hard to Learn How Gravity and Electromagnetism Couple

We construct the most general effective Lagrangian coupling gravity and electromagnetism up to mass dimension 6 by enumerating all possible non-minimal coupling terms respecting both diffeomorphism and gauge invariance. In all, there are only two unique terms after field re-definitions; one is known to arise from loop effects in QED while the other is a parity violating term which may be generated by weak interactions within the standard model of particle physics. We show that neither the cosmological propagation of light nor, contrary to earlier claims, solar system tests of General Relativity are useful probes of these terms. These non-minimal couplings of gravity and electromagnetism may remain a mystery for the foreseeable future.Comment: 9 pages. Minor corrections made. To appear in Phys. Rev.

Element specific characterization of heterogeneous magnetism in (Ga,Fe)N films

We employ x-ray spectroscopy to characterize the distribution and magnetism of particular alloy constituents in (Ga,Fe)N films grown by metal organic vapor phase epitaxy. Furthermore, photoelectron microscopy gives direct evidence for the aggregation of Fe ions, leading to the formation of Fe-rich nanoregions adjacent to the samples surface. A sizable x-ray magnetic circular dichroism (XMCD) signal at the Fe L-edges in remanence and at moderate magnetic fields at 300 K links the high temperature ferromagnetism with the Fe(3d) states. The XMCD response at the N K-edge highlights that the N(2p) states carry considerable spin polarization. We conclude that FeN{\delta} nanocrystals, with \delta > 0.25, stabilize the ferromagnetic response of the films.Comment: 4 pages, 3 figures, 1 tabl

One-loop corrections to the instanton transition in the two-dimensional Abelian Higgs model

We present an evaluation of the fluctuation determinant which appears as a prefactor in the instanton transition rate for the two-dimensional Abelian Higgs model. The corrections are found to change the rate at most by a factor of 2 for 0.4 < M_W/M_H < 2.0.Comment: DO-TH-94/17, 20 pages, 4 figures appended as uucompressed .eps files, LaTeX, needs epsfig.st