Front Propagation and Diffusion in the A <--> A + A Hard-core Reaction on a Chain

We study front propagation and diffusion in the reaction-diffusion system A $\leftrightharpoons$ A + A on a lattice. On each lattice site at most one A particle is allowed at any time. In this paper, we analyze the problem in the full range of parameter space, keeping the discrete nature of the lattice and the particles intact. Our analysis of the stochastic dynamics of the foremost occupied lattice site yields simple expressions for the front speed and the front diffusion coefficient which are in excellent agreement with simulation results.Comment: 5 pages, 5 figures, to appear in Phys. Rev.

Fronts in randomly advected and heterogeneous media and nonuniversality of Burgers turbulence: Theory and numerics

A recently established mathematical equivalence--between weakly perturbed Huygens fronts (e.g., flames in weak turbulence or geometrical-optics wave fronts in slightly nonuniform media) and the inviscid limit of white-noise-driven Burgers turbulence--motivates theoretical and numerical estimates of Burgers-turbulence properties for specific types of white-in-time forcing. Existing mathematical relations between Burgers turbulence and the statistical mechanics of directed polymers, allowing use of the replica method, are exploited to obtain systematic upper bounds on the Burgers energy density, corresponding to the ground-state binding energy of the directed polymer and the speedup of the Huygens front. The results are complementary to previous studies of both Burgers turbulence and directed polymers, which have focused on universal scaling properties instead of forcing-dependent parameters. The upper-bound formula can be heuristically understood in terms of renormalization of a different kind from that previously used in combustion models, and also shows that the burning velocity of an idealized turbulent flame does not diverge with increasing Reynolds number at fixed turbulence intensity, a conclusion that applies even to strong turbulence. Numerical simulations of the one-dimensional inviscid Burgers equation using a Lagrangian finite-element method confirm that the theoretical upper bounds are sharp within about 15% for various forcing spectra (corresponding to various two-dimensional random media). These computations provide a new quantitative test of the replica method. The inferred nonuniversality (spectrum dependence) of the front speedup is of direct importance for combustion modeling.Comment: 20 pages, 2 figures, REVTeX 4. Moved some details to appendices, added figure on numerical metho

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

Emergence of pulled fronts in fermionic microscopic particle models

We study the emergence and dynamics of pulled fronts described by the Fisher-Kolmogorov-Petrovsky-Piscounov (FKPP) equation in the microscopic reaction-diffusion process A + A A$ on the lattice when only a particle is allowed per site. To this end we identify the parameter that controls the strength of internal fluctuations in this model, namely, the number of particles per correlated volume. When internal fluctuations are suppressed, we explictly see the matching between the deterministic FKPP description and the microscopic particle model.Comment: 4 pages, 4 figures. Accepted for publication in Phys. Rev. E as a Rapid Communicatio

Shift in the velocity of a front due to a cut-off

We consider the effect of a small cut-off epsilon on the velocity of a traveling wave in one dimension. Simulations done over more than ten orders of magnitude as well as a simple theoretical argument indicate that the effect of the cut-off epsilon is to select a single velocity which converges when epsilon tends to 0 to the one predicted by the marginal stability argument. For small epsilon, the shift in velocity has the form K(log epsilon)^(-2) and our prediction for the constant K agrees very well with the results of our simulations. A very similar logarithmic shift appears in more complicated situations, in particular in finite size effects of some microscopic stochastic systems. Our theoretical approach can also be extended to give a simple way of deriving the shift in position due to initial conditions in the Fisher-Kolmogorov or similar equations.Comment: 12 pages, 3 figure

On the small-scale stability of thermonuclear flames in Type Ia supernovae

We present a numerical model which allows us to investigate thermonuclear flames in Type Ia supernova explosions. The model is based on a finite-volume explicit hydrodynamics solver employing PPM. Using the level-set technique combined with in-cell reconstruction and flux-splitting schemes we are able to describe the flame in the discontinuity approximation. We apply our implementation to flame propagation in Chandrasekhar-mass Type Ia supernova models. In particular we concentrate on intermediate scales between the flame width and the Gibson-scale, where the burning front is subject to the Landau-Darrieus instability. We are able to reproduce the theoretical prediction on the growth rates of perturbations in the linear regime and observe the stabilization of the flame in a cellular shape. The increase of the mean burning velocity due to the enlarged flame surface is measured. Results of our simulation are in agreement with semianalytical studies.Comment: 9 pages, 7 figures, Uses AASTEX, emulateapj5.sty, onecolfloat.sty. Replaced with accepted version (ApJ), Figures 1 and 3 are ne

The role of cell-cell adhesion in wound healing

We present a stochastic model which describes fronts of cells invading a wound. In the model cells can move, proliferate, and experience cell-cell adhesion. We find several qualitatively different regimes of front motion and analyze the transitions between them. Above a critical value of adhesion and for small proliferation large isolated clusters are formed ahead of the front. This is mapped onto the well-known ferromagnetic phase transition in the Ising model. For large adhesion, and larger proliferation the clusters become connected (at some fixed time). For adhesion below the critical value the results are similar to our previous work which neglected adhesion. The results are compared with experiments, and possible directions of future work are proposed.Comment: to appear in Journal of Statistical Physic

Values of the Federal Public Lands

v, 158 p. ; 28 cmhttps://scholar.law.colorado.edu/books_reports_studies/1038/thumbnail.jp

Acute pressure overload of the right ventricle. Comparison of two models of right-left shunt. Pulmonary artery to left atrium and right atrium to left atrium: experimental study

<p>Abtract</p> <p>Background</p> <p>In right ventricular failure (RVF), an interatrial shunt can relieve symptoms of severe pulmonary hypertension by reducing right ventricular preload and increasing systemic flow. Using a pig model to determine if a pulmonary artery - left atrium shunt (PA-LA) is better than a right atrial - left atrial shunt (RA-LA), we compared the hemodynamic effects and blood gases between the two shunts.</p> <p>Methods</p> <p>Thirty, male Large White pigs weighting in average 21.3 kg ± 0.7 (SEM) were divided into two groups (15 pigs per group): In group 1, banding of the pulmonary artery and a pulmonary artery to left atrium shunt with an 8 mm graft (PA-LA) was performed and in group 2 banding of the pulmonary artery and right atrial to left atrial shunt (RA-LA) with a similar graft was performed. Hemodynamic parameters and blood gases were measured from all cardiac chambers in 10 and 20 minutes, half and one hour interval from the baseline (30 min from the banding). Cardiac output and flow of at the left anterior descending artery was also monitored.</p> <p>Results</p> <p>In both groups, a stable RVF was generated. The PA-LA shunt compared to the RA-LA shunt has better hemodynamic performance concerning the decreased right ventricle afterload, the 4 fold higher mean pressure of the shunt, the better flow in left anterior descending artery and the decreased systemic vascular resistance. Favorable to the PA-LA shunt is also the tendency - although not statistically significant - in relation to central venous pressure, left atrial filling and cardiac output.</p> <p>Conclusion</p> <p>The PA-LA shunt can effectively reverse the catastrophic effects of acute RVF offering better hemodynamic characteristics than an interatrial shunt.</p

How Common is Common Human Reason?:The Plurality of Moral Perspectives and Kant’s Ethics

In his practical philosophy, Kant aims to systematize and ground a conception of morality that every human being already in some form is supposedly committed to in virtue of her common human reason. While Kantians especially in the last few years have explicitly acknowledged the central role of common human reason for a correct understanding of Kant’s ethics, there has been very little detailed critical discussion of the very notion of a common human reason as Kant envisages it. Sticker critically discusses in what ways Kant is committed to the notion that there are certain rational insights and rational capacities that all humans share, and thus investigates critically how Kant thinks moral normativity appears to the common human being, the rational agent who did not enjoy special education or philosophical training