相关论文: Non-linear model equation for three-dimensional Bu…
This study makes the first attempt to use the 2/3-order fractional Laplacian modeling of enhanced diffusing movements of random turbulent particle resulting from nonlinear inertial interactions. A combined effect of the inertial…
This study presents methane-air counterflow simulations, in computationally efficient similar form, allowing combustible mixtures to flow from one or both directions in order to learn more about multi-branched propagating flame structures…
We study in a strip of $\mathbb R^2$ a combustion model of flame propagation with stepwise temperature kinetics and zero-order reaction, characterized by two free interfaces, respectively the ignition and the trailing fronts. The latter…
We numerically solve the transport equations for a quark gas described by the the Nambu-Jona-Lasinio model. The mean field equations of motion, which consist of the Vlasov equation for the density and the gap equation for the mean field,…
The scaling of turbulent premixed flames is typically described by correlations derived for unity-Lewis-number fuels. However, their validity for hydrogen (H$_{2}$) remains uncertain due to the thermodiffusive effects associated with its…
Understanding the dynamics of flames at small scales opens up opportunities to enhance the performance of small-scale power generation devices, micro-reactors, fire safety devices, and numerous other systems that confine combustion to…
In recent years, a number of finite element methods have been formulated for the solution of partial differential equations on complex geometries based on non-matching or overlapping meshes. Examples of such methods include the fictitious…
Many systems of partial differential equations have been proposed as simplified representations of complex collective behaviours in large networks of neurons. In this survey, we briefly discuss their derivations and then review the…
We investigate mathematically a nonlinear approximation type approach recently introduced in [A. Ammar et al., J. Non-Newtonian Fluid Mech., 2006] to solve high dimensional partial differential equations. We show the link between the…
We describe the mathematical theory of diffusion and heat transport with a view to including some of the main directions of recent research. The linear heat equation is the basic mathematical model that has been thoroughly studied in the…
So far, flamelet theory has treated curvature as an independent parameter requiring specific means for closure. In this work, it is shown how the adoption of a two-dimensional orthogonal composition space allows obtaining formal…
The gap equation for fermions in a version of thermal QED in three dimensions is studied numerically in the Schwinger-Dyson formalism. The interest in this theory has been recently revived since it has been proposed as a model of…
An unsteady problem is considered for a space-fractional diffusion equation in a bounded domain. A first-order evolutionary equation containing a fractional power of an elliptic operator of second order is studied for general boundary…
We consider combustion problems in the presence of complex chemistry and nonlinear diffusion laws leading to fully nonlinear multispecies reaction-diffusion equations. We establish results of existence of solution and maximum principle,…
We investigate the Cahn-Hilliard equation with nonlinear diffusion and non-degenerate mobility modeling phase separation phenomena in complex systems (e.g., crystals and polymers). Previous results in the literature on this model relied on…
We consider a nonlinear third order dispersive equation which models the motion of a vortex filament immersed in an incompressible and inviscid fluid occupying the three dimensional half space. We prove the unique solvability of…
A method for solving model nonlinear equations describing plasma oscillations in the presence of viscosity and resistivity is given. By first going to the Lagrangian variables and then transforming the space variable conveniently, the…
Understanding the dynamics of wildfire is crucial for developing management and intervention strategies. Mathematical and computational models can be used to improve our understanding of wildfire processes and dynamics. This paper presents…
We investigate quantitative properties of nonnegative solutions $u(t,x)\ge 0$ to the nonlinear fractional diffusion equation, $\partial_t u + \mathcal{L}F(u)=0$ posed in a bounded domain, $x\in\Omega\subset \mathbb{R}^N$, with appropriate…
The statistics of wrinkling flame front is invetigated by the quantum filed theory methods. We dwell on the WKB approximation in the functional integral which is analogous to the Wyld functional integral in turbulence. The main contribution…