Página 1 dos resultados de 963 itens digitais encontrados em 1.017 segundos

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

BARROS, Saulo R. M.; PEIXOTO, Pedro S.
Fonte: PERGAMON-ELSEVIER SCIENCE LTD Publicador: PERGAMON-ELSEVIER SCIENCE LTD
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
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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

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

Loya, José Antonio; Villa, E. I.; Fernández-Sáez, José
Tipo: info:eu-repo/semantics/acceptedVersion Formato: application/pdf
Relevância na Pesquisa
57.746826%
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.

## ‣ Front propagation sustained by additive noise

Tirapegui Zurbano, Enrique Lincoyán; Falcón, Claudio; Clerc Gavilán, Marcel Gabriel
Fonte: AMERICAN PHYSICAL SOC Publicador: AMERICAN PHYSICAL SOC
Tipo: Artículo de revista
Português
Relevância na Pesquisa
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.

## ‣ Additive Noise Induces Front Propagation

Falcon, C.; Tirapegui, Enrique; Clerc, M. G.
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.

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

Kupervasser, Oleg
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
47.78441%
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

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

Kumar, Niraj; Tripathy, Goutam
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
47.689824%
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

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

Froemberg, Daniela; Schmidt-Martens, Hauke; Sokolov, Igor M.; Sagues, Francesc
Tipo: Artigo de Revista Científica
Relevância na Pesquisa
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.

Cencini, M.; Torcini, A.; Vergni, D.; Vulpiani, A.
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

## ‣ Multiple Front Propagation Into Unstable States

Montagne, R.; Amengual, A.; Hernandez-Garcia, E.; Miguel, M. San
Tipo: Artigo de Revista Científica
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

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

Rasmussen, Anders R.; Sørensen, Mads P.; Gaididei, Yuri B.; Christiansen, Peter L.
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...

## ‣ Multiple Front Propagation into Unstable States

Montagne, R.; Amengual, A.; Hernandez-Garcia, E.; Miguel, M. San
Tipo: Artigo de Revista Científica
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

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

van Saarloos, Wim; van Hecke, Martin; Holyst, Robert
Tipo: Artigo de Revista Científica
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.

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

Robinson, Martin; Flegg, Mark; Erban, Radek
Tipo: Artigo de Revista Científica
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...

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

Torcini, Alessandro; Vulpiani, Angelo; Rocco, Andrea
Tipo: Artigo de Revista Científica
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...

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

Cesaroni, A.; Muratov, C. B.; Novaga, M.
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
47.78441%
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.

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

Mahoney, John; Bargteil, Dylan; Kingsbury, Mark; Mitchell, Kevin; Solomon, Tom
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

## ‣ Front propagation in laminar flows

Abel, M.; Celani, A.; Vergni, D.; Vulpiani, A.
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

## ‣ Front propagation into unstable states

van Saarloos, Wim
Tipo: Artigo de Revista Científica
Português
Relevância na Pesquisa
48.007393%
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)...

## ‣ Thin front propagation in random shear flows

Chinappi, M.; Cencini, M.; Vulpiani, A.
Tipo: Artigo de Revista Científica
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