Dynamics of thermal ignition of spray flames in mixing layers

Conditions are identified under which analyses of laminar mixing layers can shed light on aspects of turbulent spray combustion. With this in mind, laminar spray-combustion models are formulated for both non-premixed and partially premixed systems. The laminar mixing layer separating a hot-air stream from a monodisperse spray carried by either an inert gas or air is investigated numerically and analytically in an effort to increase understanding of the ignition process leading to stabilization of high-speed spray combustion. The problem is formulated in an Eulerian framework, with the conservation equations written in the boundary-layer approximation and with a one-step Arrhenius model adopted for the chemistry description. The numerical integrations unveil two different types of ignition behaviour depending on the fuel availability in the reaction kernel, which in turn depends on the rates of droplet vaporization and fuel-vapour diffusion. When sufficient fuel is available near the hot boundary, as occurs when the thermochemical properties of heptane are employed for the fuel in the integrations, combustion is established through a precipitous temperature increase at a well-defined thermal-runaway location, a phenomenon that is amenable to a theoretical analysis based on activation-energy asymptotics, presented here, following earlier ideas developed in describing unsteady gaseous ignition in mixing layers. By way of contrast, when the amount of fuel vapour reaching the hot boundary is small, as is observed in the computations employing the thermochemical properties of methanol, the incipient chemical reaction gives rise to a slowly developing lean deflagration that consumes the available fuel as it propagates across the mixing layer towards the spray. The flame structure that develops downstream from the ignition point depends on the fuel considered and also on the spray carrier gas, with fuel sprays carried by air displaying either a lean deflagration bounding a region of distributed reaction or a distinct double-flame structure with a rich premixed flame on the spray side and a diffusion flame on the air side. Results are calculated for the distributions of mixture fraction and scalar dissipation rate across the mixing layer that reveal complexities that serve to identify differences between spray-flamelet and gaseous-flamelet problems.

On a comparison method to reaction-diffusion systems and its applications to chemotaxis

In this paper we consider a general system of reaction-diffusion equations and introduce a comparison method to obtain qualitative properties of its solutions. The comparison method is applied to study the stability of homogeneous steady states and the asymptotic behavior of the solutions of different systems with a chemotactic term. The theoretical results obtained are slightly modified to be applied to the problems where the systems are coupled in the differentiated terms and / or contain nonlocal terms. We obtain results concerning the global stability of the steady states by comparison with solutions of Ordinary Differential Equations.

“Coarse” stability and bifurcation analysis using time-steppers: A reaction-diffusion example

Evolutionary, pattern forming partial differential equations (PDEs) are often derived as limiting descriptions of microscopic, kinetic theory-based models of molecular processes (e.g., reaction and diffusion). The PDE dynamic behavior can be probed through direct simulation (time integration) or, more systematically, through stability/bifurcation calculations; time-stepper-based approaches, like the Recursive Projection Method [Shroff, G. M. & Keller, H. B. (1993) SIAM J. Numer. Anal. 30, 1099–1120] provide an attractive framework for the latter. We demonstrate an adaptation of this approach that allows for a direct, effective (“coarse”) bifurcation analysis of microscopic, kinetic-based models; this is illustrated through a comparative study of the FitzHugh-Nagumo PDE and of a corresponding Lattice–Boltzmann model.

Configurational diffusion down a folding funnel describes the dynamics of DNA hairpins

Elucidating the mechanism of folding of polynucleotides depends on accurate estimates of free energy surfaces and a quantitative description of the kinetics of structure formation. Here, the kinetics of hairpin formation in single-stranded DNA are measured after a laser temperature jump. The kinetics are modeled as configurational diffusion on a free energy surface obtained from a statistical mechanical description of equilibrium melting profiles. The effective diffusion coefficient is found to be strongly temperature-dependent in the nucleation step as a result of formation of misfolded loops that do not lead to subsequent zipping. This simple system exhibits many of the features predicted from theoretical studies of protein folding, including a funnel-like energy surface with many folding pathways, trapping in misfolded conformations, and non-Arrhenius folding rates.

Optimized CUDA-Based PDE Solver for Reaction Diffusion Systems on Arbitrary Surfaces

Partial differential equation (PDE) solvers are commonly employed to study and characterize the parameter space for reaction-diffusion (RD) systems while investigating biological pattern formation. Increasingly, biologists wish to perform such studies with arbitrary surfaces representing ‘real’ 3D geometries for better insights. In this paper, we present a highly optimized CUDA-based solver for RD equations on triangulated meshes in 3D. We demonstrate our solver using a chemotactic model that can be used to study snakeskin pigmentation, for example. We employ a finite element based approach to perform explicit Euler time integrations. We compare our approach to a naive GPU implementation and provide an in-depth performance analysis, demonstrating the significant speedup afforded by our optimizations. The optimization strategies that we exploit could be generalized to other mesh based processing applications with PDE simulations.

Bifurcation Analysis of Reaction Diffusion Systems on Arbitrary Surfaces

In this article we present a computational framework for isolating spatial patterns arising in the steady states of reaction-diffusion systems. Such systems have been used to model many different phenomena in areas such as developmental and cancer biology, cell motility and material science. Often one is interested in identifying parameters which will lead to a particular pattern. To attempt to answer this, we compute eigenpairs of the Laplacian on a variety of domains and use linear stability analysis to determine parameter values for the system that will lead to spatially inhomogeneous steady states whose patterns correspond to particular eigenfunctions. This method has previously been used on domains and surfaces where the eigenvalues and eigenfunctions are found analytically in closed form. Our contribution to this methodology is that we numerically compute eigenpairs on arbitrary domains and surfaces. Here we present various examples and demonstrate that mode isolation is straightforward especially for low eigenvalues. Additionally we see that if two or more eigenvalues are in a permissible range then the inhomogeneous steady state can be a linear combination of the respective eigenfunctions. Finally we show an example which suggests that pattern formation is robust on similar surfaces in cases that the surface either has or does not have a boundary.

Ligand diffusion on protein surface observed in molecular dynamics simulation

The process of binding of small ligands to dihydrofolate reductase protein has been investigated using all-atom molecular dynamics simulations. The existence of a mechanism that facilitates the search of the binding site by the ligand is demonstrated. The mechanism consists of ligand diffusing on the protein’s surface. It has been discussed in the literature before, but has not been explicitly confirmed for realistic molecular systems. The strength of this nonspecific binding is roughly estimated and found to be essential for the binding kinetics.