Front propagation in certain one-dimensional exclusion models

1988 ◽  
Vol 51 (5-6) ◽  
pp. 863-869 ◽  
Author(s):  
Maury Bramson
Keyword(s):  
Front Propagation ◽  
One Dimensional

Front propagation in the one-dimensional autocatalyticA+B→2Areaction with decay

1999 ◽  
Vol 59 (3) ◽  
pp. 2561-2565 ◽  
Author(s):  
V. N. Kuzovkov ◽  
J. Mai ◽  
I. M. Sokolov ◽  
A. Blumen
Keyword(s):  
Front Propagation ◽  
One Dimensional ◽  
The One

BDNF and NT-3 Increase Velocity of Activity Front Propagation in Unidimensional Hippocampal Cultures

2010 ◽  
Vol 104 (6) ◽  
pp. 2932-2939 ◽  
Author(s):  
Shimshon Jacobi ◽  
Jordi Soriano ◽  
Elisha Moses
Keyword(s):  
Chronic Treatment ◽  
Synaptic Connection ◽  
Front Propagation ◽  
Excitatory Input ◽  
Synaptic Delay ◽  
One Dimensional ◽  
Propagation Front ◽  
Connection Probability ◽  
Neurotrophin 3 ◽  
Hippocampal Cultures

Neurotrophins are known to promote synapse development as well as to regulate the efficacy of mature synapses. We have previously reported that in two-dimensional rat hippocampal cultures, brain-derived neurotrophic factor (BDNF) and neurotrophin-3 significantly increase the number of excitatory input connections. Here we measure the effect of these neurotrophic agents on propagating fronts that arise spontaneously in quasi-one-dimensional rat hippocampal cultures. We observe that chronic treatment with BDNF increased the velocity of the propagation front by about 30%. This change is attributed to an increase in the excitatory input connectivity. We analyze the experiment using the Feinerman–Golomb/Ermentrout–Jacobi/Moses–Osan model for the propagation of fronts in a one-dimensional neuronal network with synaptic delay and introduce the synaptic connection probability between adjacent neurons as a new parameter of the model. We conclude that BDNF increases the number of excitatory connections by favoring the probability to form connections between neurons, but without significantly modifying the range of the connections (connectivity footprint).

scholarly journals Propagation of combustion waves in the shell–core energetic materials with external heat losses

2017 ◽  
Vol 473 (2199) ◽  
pp. 20160937
Author(s):  
V. V. Gubernov ◽  
V. N. Kudryumov ◽  
A. V. Kolobov ◽  
A. A. Polezhaev
Keyword(s):  
Solid Fuel ◽  
Energetic Materials ◽  
Energetic Material ◽  
Front Propagation ◽  
Heat Losses ◽  
Combustion Waves ◽  
One Dimensional ◽  
The One ◽  
Composite Solid ◽  
Linear Stability Problem

In this paper, the properties and stability of combustion waves propagating in the composite solid energetic material of the shell–core type are numerically investigated within the one-dimensional diffusive-thermal model with heat losses to the surroundings. The flame speed is calculated as a function of the parameters of the model. The boundaries of stability are determined in the space of parameters by solving the linear stability problem and direct integration of the governing non-stationary equations. The results are compared with the characteristics of the combustion waves in pure solid fuel. It is demonstrated that a stable travelling combustion wave solution can exist for the parameters of the model for which the flame front propagation is unstable in pure solid fuel and it can propagate several times faster even in the presence of significant heat losses.

Nonlinear Behaviour of Mass Transfer Mechanisms in Solvent Oil Recovery

2017 ◽  
Vol 379 ◽  
pp. 181-188 ◽  
Author(s):  
Shelley Lorimer ◽  
Caine Smithaniuk
Keyword(s):  
Mass Transfer ◽  
Front Propagation ◽  
Nonlinear Effects ◽  
Simulation Software ◽  
Solvent Recovery ◽  
One Dimensional ◽  
Solvent Front ◽  
Recovery Processes ◽  
And Diffusion ◽  
Transfer Mechanisms

Literature has indicated that, experimentally, solvent fronts in hybrid thermal solvent recovery processes progress more rapidly than what can be predicted using current approximations and more rapidly than thermal processes alone [1]. The equations that govern thermal multiphase flow through porous media are extremely complex and it is very difficult to decouple the contribution of the mass transfer mechanisms from the thermal effects. This paper explores the behavior of the mass transfer mechanisms in these processes through an examination of the nonlinear one-dimensional advection diffusion/dispersion (ADD) equation using finite difference methods. Earlier work [2] indicated that the linear ADD equation, using physically estimated parameters for diffusion and dispersion coefficients obtained from the literature, could not account for the solvent front progression rate predicted by Edmunds [3]. The results in this preliminary study indicate that the nonlinear effects are important in predicting the progression of a solvent front using the one dimensional ADD equation. The shapes and rate of propagation of the concentration profiles are influenced by both velocity and diffusion functionality. These results are more consistent with the solvent front propagation rate predicted by Edmunds [3]. These results also suggest that including nonlinear effects in traditional reservoir simulation software may be necessary in the modeling of solvent processes. Further work is needed to explore and understand the influence of the velocity and diffusion functionality necessary to mimic the behaviour observed in thermal solvent recovery processes and to further increase the understanding of their impact on solvent front propagation.

FLAME PROPAGATION IN ONE-DIMENSIONAL STATIONARY ERGODIC MEDIA

2007 ◽  
Vol 17 (01) ◽  
pp. 155-169 ◽  
Author(s):  
L. A. CAFFARELLI ◽  
K.-A. LEE ◽  
A. MELLET
Keyword(s):  
Free Boundary ◽  
Boundary Problem ◽  
Combustion Rate ◽  
Traveling Waves ◽  
Random Media ◽  
Front Propagation ◽  
Periodic Case ◽  
One Dimensional ◽  
A Free Boundary Problem ◽  
Effective Speed

This paper investigates front propagation in random media for a free boundary problem arising in combustion theory. We show the existence of asymptotic traveling waves solutions with effective speed depending only on the essential infimum of the combustion rate. This result generalizes a previous result of the same authors in the periodic case.

scholarly journals Extended stable equilibrium invaded by an unstable state

2019 ◽  
Vol 9 (1) ◽  
Author(s):  
Camila Castillo-Pinto ◽  
Marcel G. Clerc ◽  
Gregorio González-Cortés
Keyword(s):  
Domain Walls ◽  
Stable Equilibrium ◽  
Energy State ◽  
Front Propagation ◽  
Unstable State ◽  
Dimensional Model ◽  
One Dimensional ◽  
First Order ◽  
Contagious Diseases ◽  
Pattern Forming

Abstract Coexistence of states is an indispensable feature in the observation of domain walls, interfaces, shock waves or fronts in macroscopic systems. The propagation of these nonlinear waves depends on the relative stability of the connected equilibria. In particular, one expects a stable equilibrium to invade an unstable one, such as occur in combustion, in the spread of permanent contagious diseases, or in the freezing of supercooled water. Here, we show that an unstable state generically can invade a locally stable one in the context of the pattern forming systems. The origin of this phenomenon is related to the lower energy unstable state invading the locally stable but higher energy state. Based on a one-dimensional model we reveal the necessary features to observe this phenomenon. This scenario is fulfilled in the case of a first order spatial instability. A photo-isomerization experiment of a dye-dopant nematic liquid crystal, allow us to observe the front propagation from an unstable state.

Continuous description of lattice discreteness effects in front propagation

2011 ◽  
Vol 369 (1935) ◽  
pp. 412-424 ◽  
Author(s):  
Marcel G. Clerc ◽  
Ricardo G. Elías ◽  
René G. Rojas
Keyword(s):  
Bifurcation Diagram ◽  
Front Propagation ◽  
Discrete Equation ◽  
Periodic Lattice ◽  
Particle Type ◽  
One Dimensional ◽  
Continuous Description ◽  
Spatially Periodic ◽  
Fundamental Physical ◽  
Good Agreement

Models describing microscopic or mesoscopic phenomena in physics are inherently discrete, where the lattice spacing between fundamental components, such as in the case of atomic sites, is a fundamental physical parameter. The effect of spatial discreteness over front propagation phenomenon in an overdamped one-dimensional periodic lattice is studied. We show here that the study of front propagation leads in a discrete description to different conclusions that in the case of its, respectively, continuous description, and also that the results of the discrete model, can be inferred by effective continuous equations with a supplementary spatially periodic term that we have denominated Peierls–Nabarro drift , which describes the bifurcation diagram of the front speed, the appearance of particle-type solutions and their snaking bifurcation diagram. Numerical simulations of the discrete equation show quite good agreement with the phenomenological description.

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