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## ‣ Computational aspects of harmonic wavelet Galerkin methods and an application to a precipitation front propagation model

Fonte: PERGAMON-ELSEVIER SCIENCE LTD
Publicador: PERGAMON-ELSEVIER SCIENCE LTD

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

57.585522%

#Harmonic wavelets#Connection coefficients#Pseudo-spectral#Burgers equation#Computational complexity#Front propagation#Precipitation fronts#Wavelet Galerkin method#BURGERS-EQUATION#SCHEME#Computer Science, Interdisciplinary Applications

This article is dedicated to harmonic wavelet Galerkin methods for the solution of partial differential equations. Several variants of the method are proposed and analyzed, using the Burgers equation as a test model. The computational complexity can be reduced when the localization properties of the wavelets and restricted interactions between different scales are exploited. The resulting variants of the method have computational complexities ranging from O(N(3)) to O(N) (N being the space dimension) per time step. A pseudo-spectral wavelet scheme is also described and compared to the methods based on connection coefficients. The harmonic wavelet Galerkin scheme is applied to a nonlinear model for the propagation of precipitation fronts, with the front locations being exposed in the sizes of the localized wavelet coefficients. (C) 2011 Elsevier Ltd. All rights reserved.; Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq); CNPq

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## ‣ Crack-front propagation during three-point-bending tests of polymethyl-methacrylate beams

Fonte: Elsevier
Publicador: Elsevier

Tipo: info:eu-repo/semantics/acceptedVersion
Formato: application/pdf

Publicado em /02/2010
Português

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#Crack-font propagation#PMMA#Three-point-bending#High-speed camera#Ingeniería Mecánica#Ingeniería Industrial

Crack front evolution in polymethyl methacrylate (PMMA) beams was measured during quasi static three point bending tests performed on a universal testing machine. A high speed camera was used to record the crack front propagation process through the specimen thickness and to determine the instantaneous crack length during the test, considering the effect of different initial notch lengths and loading point displacement rates. The average steady crack propagation speed was also calculated and correlated with the stored elastic energy, and these results have been compared with those reported by other authors for different test conditions. This experimental technique appears to be suitable to determine the influence of the test conditions on the crack propagation speed of PMMA specimens.; This research was carried out with the financial support of the Universidad Carlos III de Madrid and of the Comunidad Autónoma de Madrid under Project CCG08 UC3M/MAT 4464.

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## ‣ Front propagation sustained by additive noise

Fonte: AMERICAN PHYSICAL SOC
Publicador: AMERICAN PHYSICAL SOC

Tipo: Artículo de revista

Português

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47.84609%

The effect of noise in a motionless front between a periodic spatial state and an homogeneous one is studied. Numerical simulations show that noise induces front propagation. From the subcritical Swift-Hohenberg equation with noise, we deduce an adequate equation for the envelope and the core of the front. The equation of the core of the front is characterized by an asymmetrical periodic potential plus additive noise. The conversion of random fluctuations into direct motion of the core of the front is responsible of the propagation. We obtain an analytical expression for the velocity of the front, which is in good agreement with numerical simulations.

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## ‣ Additive Noise Induces Front Propagation

Fonte: Universidade do Chile
Publicador: Universidade do Chile

Tipo: Artículo de revista

Português

Relevância na Pesquisa

47.688247%

The effect of additive noise on a static front that connects a stable homogeneous state with an also stable
but spatially periodic state is studied. Numerical simulations show that noise induces front propagation.
The conversion of random fluctuations into direct motion of the front’s core is responsible of the
propagation; noise prefers to create or remove a bump, because the necessary perturbations to nucleate
or destroy a bump are different. From a prototype model with noise, we deduce an adequate equation for
the front’s core. An analytical expression for the front velocity is deduced, which is in good agreement
with numerical simulations.

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## ‣ Flame Front Propagation and Finger Competition and Formation of a Single Saffman-Taylor Finger without Surface Tension - PhD Thesis

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

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#Nonlinear Sciences - Pattern Formation and Solitons#Nonlinear Sciences - Exactly Solvable and Integrable Systems#37C99

Problems of interface growth have received much attention recently Such are,
for example, the duffusion limited aggregation (DLA), random sequential
adsorption (RSA), Laplacian growth or flame front propagation. We will mainly
pay attention in this Thesis to the numerical and analytical investigation of
the last two problems. In addition to the fact that flame front propagation is
an interesting physical problem we feel that we can also explain experimental
results on the basis of theoretical investigations. There exists possibility to
use methods found for the flame front propagation, in different fields where
similar problems appear such as the important model of Laplacian growth .; Comment: PhD thesis, 155 pages 34 figures made in Weizmann Institute of
Science in English and in Russian

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## ‣ Front propagation in A$\to$2A, A$\to$3A process in 1d: velocity, diffusion and velocity correlations

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 26/08/2006
Português

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We study front propagation in the reaction diffusion process
$\{A\stackrel{\epsilon}\to2A, A\stackrel {\epsilon_t}\to3A\}$ on a one
dimensional (1d) lattice with hard core interaction between the particles.
Using the leading particle picture, velocity of the front in the system is
computed using different approximate methods, which is in good agreement with
the simulation results. It is observed that in certain ranges of parameters,
the front velocity varies as a power law of $\epsilon_t$, which is well
captured by our approximate schemes. We also observe that the front dynamics
exhibits temporal velocity correlations and these must be taken care of in
order to find the exact estimates for the front diffusion coefficient. This
correlation changes sign depending upon the sign of $\epsilon_t-D$, where $D$
is the bare diffusion coefficient of $A$ particles. For $\epsilon_t=D$, the
leading particle and thus the front moves like an uncorrelated random walker,
which is explained through an exact analysis.; Comment: 8 figures

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## ‣ Front propagation in A+B -> 2A reaction under subdiffusion

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 15/04/2008
Português

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47.681685%

We consider an irreversible autocatalytic conversion reaction A+B -> 2A under
subdiffusion described by continuous time random walks. The reactants'
transformations take place independently on their motion and are described by
constant rates. The analog of this reaction in the case of normal diffusion is
described by the Fisher-Kolmogorov-Petrovskii-Piskunov (FKPP) equation leading
to the existence of a nonzero minimal front propagation velocity which is
really attained by the front in its stable motion. We show that for
subdiffusion this minimal propagation velocity is zero, which suggests
propagation failure.

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## ‣ Thin front propagation in steady and unsteady cellular flows

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

47.74347%

Front propagation in two dimensional steady and unsteady cellular flows is
investigated in the limit of very fast reaction and sharp front, i.e., in the
geometrical optics limit. In the steady case, by means of a simplified model,
we provide an analytical approximation for the front speed,
$v_{{\scriptsize{f}}}$, as a function of the stirring intensity, $U$, in good
agreement with the numerical results and, for large $U$, the behavior
$v_{{\scriptsize{f}}}\sim U/\log(U)$ is predicted. The large scale of the
velocity field mainly rules the front speed behavior even in the presence of
smaller scales. In the unsteady (time-periodic) case, the front speed displays
a phase-locking on the flow frequency and, albeit the Lagrangian dynamics is
chaotic, chaos in front dynamics only survives for a transient. Asymptotically
the front evolves periodically and chaos manifests only in the spatially
wrinkled structure of the front.; Comment: 12 pages, 13 figures

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## ‣ Multiple Front Propagation Into Unstable States

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 13/12/1993
Português

Relevância na Pesquisa

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The dynamics of transient patterns formed by front propagation in extended
nonequilibrium systems is considered. Under certain circumstances, the state
left behind a front propagating into an unstable homogeneous state can be an
unstable periodic pattern. It is found by a numerical solution of a model of
the Fr\'eedericksz transition in nematic liquid crystals that the mechanism of
decay of such periodic unstable states is the propagation of a second front
which replaces the unstable pattern by a another unstable periodic state with
larger wavelength. The speed of this second front and the periodicity of the
new state are analytically calculated with a generalization of the marginal
stability formalism suited to the study of front propagation into periodic
unstable states. PACS: 47.20.Ky, 03.40.Kf, 47.54.+r; Comment: 12 pages

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## ‣ Analytical and numerical modeling of front propagation and interaction of fronts in nonlinear thermoviscous fluids including dissipation

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

47.651826%

A wave equation, that governs finite amplitude acoustic disturbances in a
thermoviscous Newtonian fluid, and includes nonlinear terms up to second order,
is proposed. In contrast to the model known as the Kuznetsov equation, the
proposed nonlinear wave equation preserves the Hamiltonian structure of the
fundamental fluid dynamical equations in the non-dissipative limit. An exact
traveling front solution is obtained from a generalized traveling wave
assumption. This solution is, in an overall sense, equivalent to the Taylor
shock solution of the Burgers equation. However, in contrast to the Burgers
equation, the model equation considered here is capable to describe waves
propagating in opposite directions. Owing to the Hamiltonian structure of the
proposed model equation, the front solution is in agreement with the classical
Rankine-Hugoniot relations. The exact front solution propagates at supersonic
speed with respect to the fluid ahead of it, and subsonic speed with respect to
the fluid behind it, similarly to the fluid dynamical shock. Linear stability
analysis reveals that the front is stable when the acoustic pressure belongs to
a critical interval, and is otherwise unstable. These results are verified
numerically. Studies of head-on colliding fronts demonstrate that the front
propagation speed changes upon collision.; Comment: 11 pages...

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## ‣ Multiple Front Propagation into Unstable States

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 10/12/1993
Português

Relevância na Pesquisa

47.904253%

The dynamics of transient patterns formed by front propagation in extended
nonequilibrium systems is considered. Under certain circumstances, the state
left behind a front propagating into an unstable homogeneous state can be an
unstable periodic pattern. It is found by a numerical solution of a model of
the Fr\'eedericksz transition in nematic liquid crystals that the mechanism of
decay of such periodic unstable states is the propagation of a second front
which replaces the unstable pattern by a another unstable periodic state with
larger wavelength. The speed of this second front and the periodicity of the
new state are analytically calculated with a generalization of the marginal
stability formalism suited to the study of front propagation into periodic
unstable states. PACS: 47.20.Ky, 03.40.Kf, 47.54.+r; Comment: 12 pages, uuencoded, compressed, postscript file, RevTeX 3.0

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## ‣ Front propagation into unstable and metastable states in Smectic C* liquid crystals: linear and nonlinear marginal stability analysis

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 16/11/1994
Português

Relevância na Pesquisa

47.75783%

We discuss the front propagation in ferroelectric chiral smectics (SmC*)
subjected to electric and magnetic fields applied parallel to smectic layers.
The reversal of the electric field induces the motion of domain walls or fronts
that propagate into either an unstable or a metastable state. In both regimes,
the front velocity is calculated exactly. Depending on the field, the speed of
a front propagating into the unstable state is given either by the so-called
linear marginal stability velocity or by the nonlinear marginal stability
expression. The cross-over between these two regimes can be tuned by a magnetic
field. The influence of initial conditions on the velocity selection problem
can also be studied in such experiments. SmC$^*$ therefore offers a unique
opportunity to study different aspects of front propagation in an experimental
system.

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## ‣ Adaptive two-regime method: application to front propagation

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 21/12/2013
Português

Relevância na Pesquisa

47.78441%

The Adaptive Two-Regime Method (ATRM) is developed for hybrid (multiscale)
stochastic simulation of reaction-diffusion problems. It efficiently couples
detailed Brownian dynamics simulations with coarser lattice-based models. The
ATRM is a generalization of the previously developed Two-Regime Method [Flegg
et al, Journal of the Royal Society Interface, 2012] to multiscale problems
which require a dynamic selection of regions where detailed Brownian dynamics
simulation is used. Typical applications include a front propagation or
spatio-temporal oscillations. In this paper, the ATRM is used for an in-depth
study of front propagation in a stochastic reaction-diffusion system which has
its mean-field model given in terms of the Fisher equation [Fisher, Annals of
Eugenics, 1937]. It exhibits a travelling reaction front which is sensitive to
stochastic fluctuations at the leading edge of the wavefront. Previous studies
into stochastic effects on the Fisher wave propagation speed have focused on
lattice-based models, but there has been limited progress using off-lattice
(Brownian dynamics) models, which suffer due to their high computational cost,
particularly at the high molecular numbers that are necessary to approach the
Fisher mean-field model. By modelling only the wavefront itself with the
off-lattice model...

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## ‣ Front Propagation in Chaotic and Noisy Reaction-Diffusion Systems: a Discrete-Time Map Approach

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 06/07/2001
Português

Relevância na Pesquisa

47.87583%

We study the front propagation in Reaction-Diffusion systems whose reaction
dynamics exhibits an unstable fixed point and chaotic or noisy behaviour. We
have examined the influence of chaos and noise on the front propagation speed
and on the wandering of the front around its average position. Assuming that
the reaction term acts periodically in an impulsive way, the dynamical
evolution of the system can be written as the convolution between a spatial
propagator and a discrete-time map acting locally. This approach allows us to
perform accurate numerical analysis. They reveal that in the pulled regime the
front speed is basically determined by the shape of the map around the unstable
fixed point, while its chaotic or noisy features play a marginal role. In
contrast, in the pushed regime the presence of chaos or noise is more relevant.
In particular the front speed decreases when the degree of chaoticity is
increased, but it is not straightforward to derive a direct connection between
the chaotic properties (e.g. the Lyapunov exponent) and the behaviour of the
front. As for the fluctuations of the front position, we observe for the noisy
maps that the associated mean square displacement grows in time as $t^{1/2}$ in
the pushed case and as $t^{1/4}$ in the pulled one...

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## ‣ Front propagation in geometric and phase field models of stratified media

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

47.78441%

#Mathematics - Analysis of PDEs#Mathematical Physics#Nonlinear Sciences - Pattern Formation and Solitons

We study front propagation problems for forced mean curvature flows and their
phase field variants that take place in stratified media, i.e., heterogeneous
media whose characteristics do not vary in one direction. We consider phase
change fronts in infinite cylinders whose axis coincides with the symmetry axis
of the medium. Using the recently developed variational approaches, we provide
a convergence result relating asymptotic in time front propagation in the
diffuse interface case to that in the sharp interface case, for suitably
balanced nonlinearities of Allen-Cahn type. The result is established by using
arguments in the spirit of $\Gamma$-convergence, to obtain a correspondence
between the minimizers of an exponentially weighted Ginzburg-Landau type
functional and the minimizers of an exponentially weighted area type
functional. These minimizers yield the fastest traveling waves invading a given
stable equilibrium in the respective models and determine the asymptotic
propagation speeds for front-like initial data. We further show that
generically these fronts are the exponentially stable global attractors for
this kind of initial data and give sufficient conditions under which complete
phase change occurs via the formation of the considered fronts.

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## ‣ Invariant barriers to reactive front propagation in fluid flows

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

47.853994%

We present theory and experiments on the dynamics of reaction fronts in
two-dimensional, vortex-dominated flows, for both time-independent and
periodically driven cases. We find that the front propagation process is
controlled by one-sided barriers that are either fixed in the laboratory frame
(time-independent flows) or oscillate periodically (periodically driven flows).
We call these barriers \emph{burning invariant manifolds} (BIMs), since their
role in front propagation is analogous to that of invariant manifolds in the
transport and mixing of passive impurities under advection. Theoretically, the
BIMs emerge from a dynamical systems approach when the
advection-reaction-diffusion dynamics is recast as an ODE for front element
dynamics. Experimentally, we measure the location of BIMs for several
laboratory flows and confirm their role as barriers to front propagation.; Comment: 6 pages, 8 figures Comments: Added 1 figure, and discussion. Results
unchanged

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## ‣ Front propagation in laminar flows

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

47.688247%

The problem of front propagation in flowing media is addressed for laminar
velocity fields in two dimensions. Three representative cases are discussed:
stationary cellular flow, stationary shear flow, and percolating flow.
Production terms of Fisher-Kolmogorov-Petrovskii-Piskunov type and of Arrhenius
type are considered under the assumption of no feedback of the concentration on
the velocity. Numerical simulations of advection-reaction-diffusion equations
have been performed by an algorithm based on discrete-time maps. The results
show a generic enhancement of the speed of front propagation by the underlying
flow. For small molecular diffusivity, the front speed $V_f$ depends on the
typical flow velocity $U$ as a power law with an exponent depending on the
topological properties of the flow, and on the ratio of reactive and advective
time-scales. For open-streamline flows we find always $V_f \sim U$, whereas for
cellular flows we observe $V_f \sim U^{1/4}$ for fast advection, and $V_f \sim
U^{3/4}$ for slow advection.; Comment: Enlarged, revised version, 37 pages, 14 figures

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## ‣ Front propagation into unstable states

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

48.007393%

#Condensed Matter - Soft Condensed Matter#Nonlinear Sciences - Pattern Formation and Solitons#Physics - Fluid Dynamics

This paper is an introductory review of the problem of front propagation into
unstable states. Our presentation is centered around the concept of the
asymptotic linear spreading velocity v*, the asymptotic rate with which
initially localized perturbations spread into an unstable state according to
the linear dynamical equations obtained by linearizing the fully nonlinear
equations about the unstable state. This allows us to give a precise definition
of pulled fronts, nonlinear fronts whose asymptotic propagation speed equals
v*, and pushed fronts, nonlinear fronts whose asymptotic speed v^dagger is
larger than v*. In addition, this approach allows us to clarify many aspects of
the front selection problem, the question whether for a given dynamical
equation the front is pulled or pushed. It also is the basis for the universal
expressions for the power law rate of approach of the transient velocity v(t)
of a pulled front as it converges toward its asymptotic value v*. Almost half
of the paper is devoted to reviewing many experimental and theoretical examples
of front propagation into unstable states from this unified perspective. The
paper also includes short sections on the derivation of the universal power law
relaxation behavior of v(t)...

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## ‣ Thin front propagation in random shear flows

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 25/07/2005
Português

Relevância na Pesquisa

47.78441%

Front propagation in time dependent laminar flows is investigated in the
limit of very fast reaction and very thin fronts, i.e. the so-called
geometrical optics limit. In particular, we consider fronts evolving in time
correlated random shear flows, modeled in terms of Ornstein-Uhlembeck
processes. We show that the ratio between the time correlation of the flow and
an intrinsic time scale of the reaction dynamics (the wrinkling time $t_w$) is
crucial in determining both the front propagation speed and the front spatial
patterns. The relevance of time correlation in realistic flows is briefly
discussed in the light of the bending phenomenon, i.e. the decrease of
propagation speed observed at high flow intensities.; Comment: 5 Revtex4 pages, 4 figures included

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## ‣ Evidence for Slow Velocity Relaxation in Front Propagation in Rayleigh-B\'enard Convection

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 02/11/2001
Português

Relevância na Pesquisa

47.651826%

Recent theoretical work has shown that so-called pulled fronts propagating
into an unstable state always converge very slowly to their asymptotic speed
and shape. In the the light of these predictions, we reanalyze earlier
experiments by Fineberg and Steinberg on front propagation in a
Rayleigh-B\'enard cell. In contrast to the original interpretation, we argue
that in the experiments the observed front velocities were some 15% below the
asymptotic front speed and that this is in rough agreement with the predicted
slow relaxation of the front speed for the time scales probed in the
experiments. We also discuss the possible origin of the unusually large
variation of the wavelength of the pattern generated by the front as a function
of the dimensionless control parameter.; Comment: 6 pages, submitted to Physica D for its issue on the ,,Complex
Ginzburg-Landau Equations and its Applications''

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