237 research outputs found
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
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 - g cm 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, , 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
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