Noisy Classical Field Theories with Two Coupled Fields: Dependence of Escape Rates on Relative Field Stiffnesses

Exit times for stochastic Ginzburg-Landau classical field theories with two or more coupled classical fields depend on the interval length on which the fields are defined, the potential in which the fields deterministically evolve, and the relative stiffness of the fields themselves. The latter is of particular importance in that physical applications will generally require different relative stiffnesses, but the effect of varying field stiffnesses has not heretofore been studied. In this paper, we explore the complete phase diagram of escape times as they depend on the various problem parameters. In addition to finding a transition in escape rates as the relative stiffness varies, we also observe a critical slowing down of the string method algorithm as criticality is approached.Comment: 16 pages, 10 figure

The Order of Phase Transitions in Barrier Crossing

A spatially extended classical system with metastable states subject to weak spatiotemporal noise can exhibit a transition in its activation behavior when one or more external parameters are varied. Depending on the potential, the transition can be first or second-order, but there exists no systematic theory of the relation between the order of the transition and the shape of the potential barrier. In this paper, we address that question in detail for a general class of systems whose order parameter is describable by a classical field that can vary both in space and time, and whose zero-noise dynamics are governed by a smooth polynomial potential. We show that a quartic potential barrier can only have second-order transitions, confirming an earlier conjecture [1]. We then derive, through a combination of analytical and numerical arguments, both necessary conditions and sufficient conditions to have a first-order vs. a second-order transition in noise-induced activation behavior, for a large class of systems with smooth polynomial potentials of arbitrary order. We find in particular that the order of the transition is especially sensitive to the potential behavior near the top of the barrier.Comment: 8 pages, 6 figures with extended introduction and discussion; version accepted for publication by Phys. Rev.

New Limits on Local Lorentz Invariance in Mercury and Cesium

We report new bounds on Local Lorentz Invariance (LLI) violation in Cs and Hg. The limits are obtained through the observation of the the spin- precession frequencies of 199Hg and 133Cs atoms in their ground states as a function of the orientation of an applied magnetic field with respect to the fixed stars. We measure the amplitudes of the dipole couplings to a preferred direction in the equatorial plane to be 19(11) nHz for Hg and 9(5) microHz for Cs. The upper bounds established here improve upon previous bounds by about a factor of four. The improvement is primarily due to mounting the apparatus on a rotating table. New bounds are established on several terms in the standard model extension including the first bounds on the spin-couplings of the neutron and proton to the z direction, <7e-30 GeV and <7e-29 GeV, respectively.Comment: 17 pages, 6 figure

Estimating changes in temperature extremes from millennial scale climate simulations using generalized extreme value (GEV) distributions

Changes in extreme weather may produce some of the largest societal impacts of anthropogenic climate change. However, it is intrinsically difficult to estimate changes in extreme events from the short observational record. In this work we use millennial runs from the CCSM3 in equilibrated pre-industrial and possible future conditions to examine both how extremes change in this model and how well these changes can be estimated as a function of run length. We estimate changes to distributions of future temperature extremes (annual minima and annual maxima) in the contiguous United States by fitting generalized extreme value (GEV) distributions. Using 1000-year pre-industrial and future time series, we show that the magnitude of warm extremes largely shifts in accordance with mean shifts in summertime temperatures. In contrast, cold extremes warm more than mean shifts in wintertime temperatures, but changes in GEV location parameters are largely explainable by mean shifts combined with reduced wintertime temperature variability. In addition, changes in the spread and shape of the GEV distributions of cold extremes at inland locations can lead to discernible changes in tail behavior. We then examine uncertainties that result from using shorter model runs. In principle, the GEV distribution provides theoretical justification to predict infrequent events using time series shorter than the recurrence frequency of those events. To investigate how well this approach works in practice, we estimate 20-, 50-, and 100-year extreme events using segments of varying lengths. We find that even using GEV distributions, time series that are of comparable or shorter length than the return period of interest can lead to very poor estimates. These results suggest caution when attempting to use short observational time series or model runs to infer infrequent extremes.Comment: 33 pages, 22 figures, 1 tabl

Practical Bayesian Modeling and Inference for Massive Spatial Datasets On Modest Computing Environments

With continued advances in Geographic Information Systems and related computational technologies, statisticians are often required to analyze very large spatial datasets. This has generated substantial interest over the last decade, already too vast to be summarized here, in scalable methodologies for analyzing large spatial datasets. Scalable spatial process models have been found especially attractive due to their richness and flexibility and, particularly so in the Bayesian paradigm, due to their presence in hierarchical model settings. However, the vast majority of research articles present in this domain have been geared toward innovative theory or more complex model development. Very limited attention has been accorded to approaches for easily implementable scalable hierarchical models for the practicing scientist or spatial analyst. This article is submitted to the Practice section of the journal with the aim of developing massively scalable Bayesian approaches that can rapidly deliver Bayesian inference on spatial process that are practically indistinguishable from inference obtained using more expensive alternatives. A key emphasis is on implementation within very standard (modest) computing environments (e.g., a standard desktop or laptop) using easily available statistical software packages without requiring message-parsing interfaces or parallel programming paradigms. Key insights are offered regarding assumptions and approximations concerning practical efficiency.Comment: 20 pages, 4 figures, 2 table

Analytical Rebridging Monte Carlo: Application to cis/trans Isomerization in Proline-Containing, Cyclic Peptides

We present a new method, the analytical rebridging scheme, for Monte Carlo simulation of proline-containing, cyclic peptides. The cis/trans isomerization is accommodated by allowing for two states of the amide bond. We apply our method to five peptides that have been previously characterized by NMR methods. Our simulations achieve effective equilibration and agree well with experimental data in all cases. We discuss the importance of effective equilibration and the role of bond flexibility and solvent effects on the predicted equilibrium properties.Comment: 29 pages, 8 PostScript figures, LaTeX source. to appear in J. Chem. Phys., 199

Photonic band mixing in linear chains of optically coupled micro-spheres

The paper deals with optical excitations arising in a one-dimensional chain of identical spheres due optical coupling of whispering gallery modes (WGM). The band structure of these excitations depends significantly on the inter-mixing between WGMs characterized by different values of angular quantum number, $l$. We develop a general theory of the photonic band structure of these excitations taking these effects into account and applied it to several cases of recent experimental interest. In the case of bands originating from WQMs with the angular quantum number of the same parity, the calculated dispersion laws are in good qualitative agreement with recent experiment results. Bands resulting from hybridization of excitations resulting from whispering gallery modes with different parity of $l$ exhibits anomalous dispersion properties characterized by a gap in the allowed values of \emph{wave numbers} and divergence of group velocity.Comment: RevTex, 28 pages, 7 Figure

Spin Susceptibility of a 2D Electron System in GaAs towards the Weak Interaction Region

We determine the spin susceptibility $\chi$ in the weak interaction regime of a tunable, high quality, two-dimensional electron system in a GaAs/AlGaAs heterostructure. The band structure effects, modifying mass and g-factor, are carefully taken into accounts since they become appreciable for the large electron densities of the weak interaction regime. When properly normalized, $\chi$ decreases monotonically from 3 to 1.1 with increasing density over our experimental range from 0.1 to $4\times10^{11} cm^{-2}$. In the high density limit, $\chi$ tends correctly towards $\chi\to 1$ and compare well with recent theory.Comment: Submitted to Physical Review

Magnetic Reversal in Nanoscopic Ferromagnetic Rings

We present a theory of magnetization reversal due to thermal fluctuations in thin submicron-scale rings composed of soft magnetic materials. The magnetization in such geometries is more stable against reversal than that in thin needles and other geometries, where sharp ends or edges can initiate nucleation of a reversed state. The 2D ring geometry also allows us to evaluate the effects of nonlocal magnetostatic forces. We find a `phase transition', which should be experimentally observable, between an Arrhenius and a non-Arrhenius activation regime as magnetic field is varied in a ring of fixed size.Comment: RevTeX, 23 pages, 7 figures, to appear in Phys. Rev.

Approach to equilibrium in adiabatically evolving potentials

For a potential function (in one dimension) which evolves from a specified initial form $V_{i}(x)$ to a different $V_{f}(x)$ asymptotically, we study the evolution, in an overdamped dynamics, of an initial probability density to its final equilibeium.There can be unexpected effects that can arise from the time dependence. We choose a time variation of the form $V(x,t)=V_{f}(x)+(V_{i}-V_{f})e^{-\lambda t}$. For a $V_{f}(x)$, which is double welled and a $V_{i}(x)$ which is simple harmonic, we show that, in particular, if the evolution is adiabatic, the results in a decrease in the Kramers time characteristics of $V_{f}(x)$. Thus the time dependence makes diffusion over a barrier more efficient. There can also be interesting resonance effects when $V_{i}(x)$ and $V_{f}(x)$ are two harmonic potentials displaced with respect to each other that arise from the coincidence of the intrinsic time scale characterising the potential variation and the Kramers time.Comment: This paper contains 5 page