Anomalous roughness with system size dependent local roughness exponent

We note that in a system far from equilibrium the interface roughening may depend on the system size which plays the role of control parameter. To detect the size effect on the interface roughness, we study the scaling properties of rough interfaces formed in paper combustion experiments. Using paper sheets of different width \lambda L, we found that the turbulent flame fronts display anomalous multi-scaling characterized by non universal global roughness exponent \alpha and the system size dependent spectrum of local roughness exponents,\xi_q, whereas the burning fronts possess conventional multi-affine scaling. The structure factor of turbulent flame fronts also exhibit unconventional scaling dependence on \lambda These results are expected to apply to a broad range of far from equilibrium systems, when the kinetic energy fluctuations exceed a certain critical value.Comment: 33 pages, 16 figure

Asymptotics for turbulent flame speeds of the viscous G-equation enhanced by cellular and shear flows

G-equations are well-known front propagation models in turbulent combustion and describe the front motion law in the form of local normal velocity equal to a constant (laminar speed) plus the normal projection of fluid velocity. In level set formulation, G-equations are Hamilton-Jacobi equations with convex ($L^1$ type) but non-coercive Hamiltonians. Viscous G-equations arise from either numerical approximations or regularizations by small diffusion. The nonlinear eigenvalue $\bar H$ from the cell problem of the viscous G-equation can be viewed as an approximation of the inviscid turbulent flame speed $s_T$. An important problem in turbulent combustion theory is to study properties of $s_T$, in particular how $s_T$ depends on the flow amplitude $A$. In this paper, we will study the behavior of $\bar H=\bar H(A,d)$ as $A\to +\infty$ at any fixed diffusion constant $d > 0$. For the cellular flow, we show that $$\bar H(A,d)\leq O(\sqrt {\mathrm {log}A}) \quad \text{for all $d>0$}.$$ Compared with the inviscid G-equation ($d=0$), the diffusion dramatically slows down the front propagation. For the shear flow, the limit \nit $\lim_{A\to +\infty}{\bar H(A,d)\over A} = \lambda (d) >0$ where $\lambda (d)$ is strictly decreasing in $d$, and has zero derivative at $d=0$. The linear growth law is also valid for $s_T$ of the curvature dependent G-equation in shear flows.Comment: 27 pages. We improve the upper bound from no power growth to square root of log growt

Hydrodynamic Stability Analysis of Burning Bubbles in Electroweak Theory and in QCD

Assuming that the electroweak and QCD phase transitions are first order, upon supercooling, bubbles of the new phase appear. These bubbles grow to macroscopic sizes compared to the natural scales associated with the Compton wavelengths of particle excitations. They propagate by burning the old phase into the new phase at the surface of the bubble. We study the hydrodynamic stability of the burning and find that for the velocities of interest for cosmology in the electroweak phase transition, the shape of the bubble wall is stable under hydrodynamic perturbations. Bubbles formed in the cosmological QCD phase transition are found to be a borderline case between stability and instability.Comment: preprint # SLAC-PUB-5943, SCIPP 92/56 38 pages, 10 figures (submitted via `uufiles'), phyzzx format minor snafus repaire

The Thermonuclear Explosion Of Chandrasekhar Mass White Dwarfs

The flame born in the deep interior of a white dwarf that becomes a Type Ia supernova is subject to several instabilities. We briefly review these instabilities and the corresponding flame acceleration. We discuss the conditions necessary for each of the currently proposed explosion mechanisms and the attendant uncertainties. A grid of critical masses for detonation in the range $10^7$ - $2 \times 10^9$ g cm$^{-3}$ is calculated and its sensitivity to composition explored. Prompt detonations are physically improbable and appear unlikely on observational grounds. Simple deflagrations require some means of boosting the flame speed beyond what currently exists in the literature. ``Active turbulent combustion'' and multi-point ignition are presented as two plausible ways of doing this. A deflagration that moves at the ``Sharp-Wheeler'' speed, $0.1 g_{\rm eff} t$, is calculated in one dimension and shows that a healthy explosion is possible in a simple deflagration if the front moves with the speed of the fastest floating bubbles. The relevance of the transition to the ``distributed burning regime'' is discussed for delayed detonations. No model emerges without difficulties, but detonation in the distributed regime is plausible, will produce intermediate mass elements, and warrants further study.Comment: 28 pages, 4 figures included, uses aaspp4.sty. Submitted to Ap

Finite size effects near the onset of the oscillatory instability

A system of two complex Ginzburg - Landau equations is considered that applies at the onset of the oscillatory instability in spatial domains whose size is large (but finite) in one direction; the dependent variables are the slowly modulated complex amplitudes of two counterpropagating wavetrains. In order to obtain a well posed problem, four boundary conditions must be imposed at the boundaries. Two of them were already known, and the other two are first derived in this paper. In the generic case when the group velocity is of order unity, the resulting problem has terms that are not of the same order of magnitude. This fact allows us to consider two distinguished limits and to derive two associated (simpler) sub-models, that are briefly discussed. Our results predict quite a rich variety of complex dynamics that is due to both the modulational instability and finite size effects

Geometry-controlled kinetics

It has long been appreciated that transport properties can control reaction kinetics. This effect can be characterized by the time it takes a diffusing molecule to reach a target -- the first-passage time (FPT). Although essential to quantify the kinetics of reactions on all time scales, determining the FPT distribution was deemed so far intractable. Here, we calculate analytically this FPT distribution and show that transport processes as various as regular diffusion, anomalous diffusion, diffusion in disordered media and in fractals fall into the same universality classes. Beyond this theoretical aspect, this result changes the views on standard reaction kinetics. More precisely, we argue that geometry can become a key parameter so far ignored in this context, and introduce the concept of "geometry-controlled kinetics". These findings could help understand the crucial role of spatial organization of genes in transcription kinetics, and more generally the impact of geometry on diffusion-limited reactions.Comment: Submitted versio

c-REDUCE: Incorporating sequence conservation to detect motifs that correlate with expression

<p>Abstract</p> <p>Background</p> <p>Computational methods for characterizing novel transcription factor binding sites search for sequence patterns or "motifs" that appear repeatedly in genomic regions of interest. Correlation-based motif finding strategies are used to identify motifs that correlate with expression data and do not rely on promoter sequences from a pre-determined set of genes.</p> <p>Results</p> <p>In this work, we describe a method for predicting motifs that combines the correlation-based strategy with phylogenetic footprinting, where motifs are identified by evaluating orthologous sequence regions from multiple species. Our method, c-REDUCE, can account for variability at a motif position inferred from evolutionary information. c-REDUCE has been tested on ChIP-chip data for yeast transcription factors and on gene expression data in <it>Drosophila</it>.</p> <p>Conclusion</p> <p>Our results indicate that utilizing sequence conservation information in addition to correlation-based methods improves the identification of known motifs.</p

Resolvent methods for steady premixed flame shapes governed by the Zhdanov-Trubnikov equation

Using pole decompositions as starting points, the one parameter (-1 =< c < 1) nonlocal and nonlinear Zhdanov-Trubnikov (ZT) equation for the steady shapes of premixed gaseous flames is studied in the large-wrinkle limit. The singular integral equations for pole densities are closely related to those satisfied by the spectral density in the O(n) matrix model, with n = -2(1 + c)/(1 - c). They can be solved via the introduction of complex resolvents and the use of complex analysis. We retrieve results obtained recently for -1 =< c =< 0, and we explain and cure their pathologies when they are continued naively to 0 < c < 1. Moreover, for any -1 =< c < 1, we derive closed-form expressions for the shapes of steady isolated flame crests, and then bicoalesced periodic fronts. These theoretical results fully agree with numerical resolutions. Open problems are evoked.Comment: v2: 29 pages, 6 figures, some typos correcte

A Gateway MultiSite Recombination Cloning Toolkit

The generation of DNA constructs is often a rate-limiting step in conducting biological experiments. Recombination cloning of single DNA fragments using the Gateway system provided an advance over traditional restriction enzyme cloning due to increases in efficiency and reliability. Here we introduce a series of entry clones and a destination vector for use in two, three, and four fragment Gateway MultiSite recombination cloning whose advantages include increased flexibility and versatility. In contrast to Gateway single-fragment cloning approaches where variations are typically incorporated into model system-specific destination vectors, our Gateway MultiSite cloning strategy incorporates variations in easily generated entry clones that are model system-independent. In particular, we present entry clones containing insertions of GAL4, QF, UAS, QUAS, eGFP, and mCherry, among others, and demonstrate their in vivo functionality in Drosophila by using them to generate expression clones including GAL4 and QF drivers for various trp ion channel family members, UAS and QUAS excitatory and inhibitory light-gated ion channels, and QUAS red and green fluorescent synaptic vesicle markers. We thus establish a starter toolkit of modular Gateway MultiSite entry clones potentially adaptable to any model system. An inventory of entry clones and destination vectors for Gateway MultiSite cloning has also been established (www.gatewaymultisite.org)

Erroneous attribution of relevant transcription factor binding sites despite successful prediction of cis-regulatory modules

<p>Abstract</p> <p>Background</p> <p><it>Cis</it>-regulatory modules are bound by transcription factors to regulate gene expression. Characterizing these DNA sequences is central to understanding gene regulatory networks and gaining insight into mechanisms of transcriptional regulation, but genome-scale regulatory module discovery remains a challenge. One popular approach is to scan the genome for clusters of transcription factor binding sites, especially those conserved in related species. When such approaches are successful, it is typically assumed that the activity of the modules is mediated by the identified binding sites and their cognate transcription factors. However, the validity of this assumption is often not assessed.</p> <p>Results</p> <p>We successfully predicted five new <it>cis</it>-regulatory modules by combining binding site identification with sequence conservation and compared these to unsuccessful predictions from a related approach not utilizing sequence conservation. Despite greatly improved predictive success, the positive set had similar degrees of sequence and binding site conservation as the negative set. We explored the reasons for this by mutagenizing putative binding sites in three <it>cis</it>-regulatory modules. A large proportion of the tested sites had little or no demonstrable role in mediating regulatory element activity. Examination of loss-of-function mutants also showed that some transcription factors supposedly binding to the modules are not required for their function.</p> <p>Conclusions</p> <p>Our results raise important questions about interpreting regulatory module predictions obtained by finding clusters of conserved binding sites. Attribution of function to these sites and their cognate transcription factors may be incorrect even when modules are successfully identified. Our study underscores the importance of empirical validation of computational results even when these results are in line with expectation.</p