Escape Rates in a Stochastic Environment with Multiple Scales

We consider a stochastic environment with two time scales and outline a general theory that compares two methods to reduce the dimension of the original system. The first method involves the computation of the underlying deterministic center manifold followed by a naive replacement of the stochastic term. The second method allows one to more accurately describe the stochastic effects and involves the derivation of a normal form coordinate transform that is used to find the stochastic center manifold. The results of both methods are used along with the path integral formalism of large fluctuation theory to predict the escape rate from one basin of attraction to another. The general theory is applied to the example of a surface flow described by a generic, singularly perturbed, damped, nonlinear oscillator with additive, Gaussian noise. We show how both nonlinear reduction methods compare in escape rate scaling. Additionally, the center manifolds are shown to predict high pre-history probability regions of escape. The theoretical results are confirmed using numerical computation of the mean escape time and escape prehistory, and we briefly discuss the extension of the theory to stochastic control.Comment: 32 pages, 8 figures, Final revision to appear in SIAM Journal on Applied Dynamical System

Atom chips on direct bonded copper substrates

We present the use of direct bonded copper (DBC) for the straightforward fabrication of high power atom chips. Atom chips using DBC have several benefits: excellent copper/substrate adhesion, high purity, thick (> 100 microns) copper layers, high substrate thermal conductivity, high aspect ratio wires, the potential for rapid (< 8 hr) fabrication, and three dimensional atom chip structures. Two mask options for DBC atom chip fabrication are presented, as well as two methods for etching wire patterns into the copper layer. The wire aspect ratio that optimizes the magnetic field gradient as a function of power dissipation is determined to be 0.84:1 (height:width). The optimal wire thickness as a function of magnetic trapping height is also determined. A test chip, able to support 100 A of current for 2 s without failing, is used to determine the thermal impedance of the DBC. An assembly using two DBC atom chips to provide magnetic confinement is also shown.Comment: 8 pages, 5 figure

Metastability and small eigenvalues in Markov chains

In this letter we announce rigorous results that elucidate the relation between metastable states and low-lying eigenvalues in Markov chains in a much more general setting and with considerable greater precision as was so far available. This includes a sharp uncertainty principle relating all low-lying eigenvalues to mean times of metastable transitions, a relation between the support of eigenfunctions and the attractor of a metastable state, and sharp estimates on the convergence of probability distribution of the metastable transition times to the exponential distribution.Comment: 5pp, AMSTe

Cavitation induced by explosion in a model of ideal fluid

We discuss the problem of an explosion in the cubic-quintic superfluid model, in relation to some experimental observations. We show numerically that an explosion in such a model might induce a cavitation bubble for large enough energy. This gives a consistent view for rebound bubbles in superfluid and we indentify the loss of energy between the successive rebounds as radiated waves. We compute self-similar solution of the explosion for the early stage, when no bubbles have been nucleated. The solution also gives the wave number of the excitations emitted through the shock wave.Comment: 21 pages,13 figures, other comment

A better automatic body-wave picker with broad applicability

For robust earthquake analysis, we need efficient and reliable automatic body-wave recognition methods. To do this, we combine the advantages of standard methods in an innovative and generalized approach. Using the component energy correlation method, we demonstrate the mathematical and practical advantages of the correlation operator and apply this operator to the S¯T/L¯T and R¯P/L¯P methods. We also implement multi-scale versions of these methods to reduce the dependence on user-defined time-scale parameters. We compare our results systematically to different methods, propose an optimal approach and demonstrate its reliability

Nucleation and condensational growth to CCN sizes during a sustained pristine biogenic SOA event in a forested mountain valley

The Whistler Aerosol and Cloud Study (WACS 2010), included intensive measurements of trace gases and particles at two sites on Whistler Mountain. Between 6–11 July 2010 there was a sustained high-pressure system over the region with cloud-free conditions and the highest temperatures of the study. During this period, the organic aerosol concentrations rose from &lt;1 μg m&lt;sup&gt;−3&lt;/sup&gt; to &amp;sim;6 μg m&lt;sup&gt;−3&lt;/sup&gt;. Precursor gas and aerosol composition measurements show that these organics were almost entirely of secondary biogenic nature. Throughout 6–11 July, the anthropogenic influence was minimal with sulfate concentrations &lt;0.2 μg m&lt;sup&gt;−3&lt;/sup&gt; and SO&lt;sub&gt;2&lt;/sub&gt; mixing ratios &amp;approx; 0.05–0.1 ppbv. Thus, this case provides excellent conditions to probe the role of biogenic secondary organic aerosol in aerosol microphysics. Although SO&lt;sub&gt;2&lt;/sub&gt; mixing ratios were relatively low, box-model simulations show that nucleation and growth may be modeled accurately if &lt;i&gt;J&lt;/i&gt;&lt;sub&gt;nuc&lt;/sub&gt; = 3 × 10&lt;sup&gt;&amp;minus;7&lt;/sup&gt;[H&lt;sub&gt;2&lt;/sub&gt;SO&lt;sub&gt;4&lt;/sub&gt;] and the organics are treated as effectively non-volatile. Due to the low condensation sink and the fast condensation rate of organics, the nucleated particles grew rapidly (2–5 nm h&lt;sup&gt;&amp;minus;1&lt;/sup&gt;) with a 10–25% probability of growing to CCN sizes (100 nm) in the first two days as opposed to being scavenged by coagulation with larger particles. The nucleated particles were observed to grow to &amp;sim;200 nm after three days. Comparisons of size-distribution with CCN data show that particle hygroscopicity (&amp;kappa;) was &amp;sim;0.1 for particles larger 150 nm, but for smaller particles near 100 nm the κ value decreased near midway through the period from 0.17 to less than 0.06. In this environment of little anthropogenic influence and low SO&lt;sub&gt;2&lt;/sub&gt;, the rapid growth rates of the regionally nucleated particles – due to condensation of biogenic SOA – results in an unusually high efficiency of conversion of the nucleated particles to CCN. Consequently, despite the low SO&lt;sub&gt;2&lt;/sub&gt;, nucleation/growth appear to be the dominant source of particle number

Multivariate curve resolution of time course microarray data

BACKGROUND: Modeling of gene expression data from time course experiments often involves the use of linear models such as those obtained from principal component analysis (PCA), independent component analysis (ICA), or other methods. Such methods do not generally yield factors with a clear biological interpretation. Moreover, implicit assumptions about the measurement errors often limit the application of these methods to log-transformed data, destroying linear structure in the untransformed expression data. RESULTS: In this work, a method for the linear decomposition of gene expression data by multivariate curve resolution (MCR) is introduced. The MCR method is based on an alternating least-squares (ALS) algorithm implemented with a weighted least squares approach. The new method, MCR-WALS, extracts a small number of basis functions from untransformed microarray data using only non-negativity constraints. Measurement error information can be incorporated into the modeling process and missing data can be imputed. The utility of the method is demonstrated through its application to yeast cell cycle data. CONCLUSION: Profiles extracted by MCR-WALS exhibit a strong correlation with cell cycle-associated genes, but also suggest new insights into the regulation of those genes. The unique features of the MCR-WALS algorithm are its freedom from assumptions about the underlying linear model other than the non-negativity of gene expression, its ability to analyze non-log-transformed data, and its use of measurement error information to obtain a weighted model and accommodate missing measurements

Genetic Networks Controlling Structural Outcome of Glucosinolate Activation across Development

Most phenotypic variation present in natural populations is under polygenic control, largely determined by genetic variation at quantitative trait loci (QTLs). These genetic loci frequently interact with the environment, development, and each other, yet the importance of these interactions on the underlying genetic architecture of quantitative traits is not well characterized. To better study how epistasis and development may influence quantitative traits, we studied genetic variation in Arabidopsis glucosinolate activation using the moderately sized Bayreuth×Shahdara recombinant inbred population, in terms of number of lines. We identified QTLs for glucosinolate activation at three different developmental stages. Numerous QTLs showed developmental dependency, as well as a large epistatic network, centered on the previously cloned large-effect glucosinolate activation QTL, ESP. Analysis of Heterogeneous Inbred Families validated seven loci and all of the QTL×DPG (days post-germination) interactions tested, but was complicated by the extensive epistasis. A comparison of transcript accumulation data within 211 of these RILs showed an extensive overlap of gene expression QTLs for structural specifiers and their homologs with the identified glucosinolate activation loci. Finally, we were able to show that two of the QTLs are the result of whole-genome duplications of a glucosinolate activation gene cluster. These data reveal complex age-dependent regulation of structural outcomes and suggest that transcriptional regulation is associated with a significant portion of the underlying ontogenic variation and epistatic interactions in glucosinolate activation