Wavespeed analysis: Approximating Arrhenius kinetics with step-function kinetics

The accuracy of using step-function approximations to the Arrhenius exponential in computing the wavespeed in combustion wave propagation is investigated. Gaseous and gasless combustion, and first- and second-order reactions are included in the study. The theoretical analysis is based on Melnikov theory from dynamical systems. The error is shown to be small in most instances. The analytical results are supported with numerical simulations.     

Existence of solutions for some non‐Fredholm integro‐differential equations with the bi‐Laplacian

We prove the existence of solutions for some semilinear elliptic equations in the appropriate H⁴ spaces using the fixed‐point technique where the elliptic equation contains fourth‐order differential operators with and without Fredholm property, generalizing the previous results.     

Reaction–Diffusion Equations in Immunology

Computational Mathematics and Mathematical Physics - The paper is devoted to the recent works on reaction–diffusion models of virus infection dynamics in human and animal organisms. Various...     

Mathematical modeling of interfacial gel polymerization for weak and strong gel effects

Frontal polymerization (FP) is a process in which a spatially localized reaction zone propagates into a monomer converting it into a polymer. Two types of FP processes have been observed experimentally. One is exothermic FP, which occurs due to diffusion of heat released in the polymerization reactions and which we have previously studied. The other is an isothermal FP process, also referred to as interfacial gel polymerization, which is due to mass diffusion of the species coupled with the gel effect. In a previous work we proposed and studied analytically a model of interfacial gel polymerization. That work discussed the case of an excessive amount of initiator in the initial mixture. In addition, it was assumed that the parameters of the problem were such that the steady‐state assumption (SSA) concerning the total concentration of radicals holds not only in the bulk region, which is typically the case, but also in the gel region, which may limit the applicability of the results. In this work we seek to resolve the limitations associated with these two main assumptions. We relax the SSA in the gel region, analyze the various situations of initiator consumption for a weak gel effect, and study the case of a strong gel effect. We obtain analytical results, including the time‐dependent propagation velocity of the reaction zone and the distance traveled by the front before it breaks down due to reactions ahead of the front, which are in good agreement with our numerical simulations.     

High‐Density Lipoprotein Nanoparticles Deliver RNAi to Endothelial Cells to Inhibit Angiogenesis

Systemic delivery of therapeutic nucleic acids to target cells and tissues outside of the liver remains a major challenge. A biomimetic high‐density lipoprotein nanoparticle (HDL NP) is synthesized for delivery of a cholesteryl‐modified therapeutic nucleic acid to vascular endothelial cells (ECs), a cell type naturally targeted by HDL. HDL NPs adsorb cholesteryl‐modified oligonucleotides and protect them from nuclease degradation. As proof of principle, we deliver RNAi targeting vascular endothelial growth factor receptor 2 (VEGFR2) to ECs to effectively silence target mRNA and protein expression in vitro. In addition, data show that treatment strongly attenuates in vivo neovascularization measured using a standard angiogenesis assay and in hypervascular tumor allografts where a striking reduction in tumor growth is observed. For effective delivery, HDL NPs require the expression of the cell surface protein scavenger receptor type‐B1 (SR‐B1). No toxicity of HDL NPs is measured in vitro or after in vivo administration. Thus, by using a biomimetic approach to nucleic acid delivery, data demonstrate that systemically administered RNAi–HDL NPs target SR‐B1 expressing ECs to deliver functional anti‐angiogenic RNAi as a potential treatment of cancer and other neovascular diseases.     

Asymptotic numerical analysis of the diffusion‐discrete absorption equation

The diffusion‐discrete absorption (DDA) equation is considered. This equation contains the standard diffusion term and the discrete sorption expressed by a sum of large number of δ‐functions with the support at a non‐uniform mesh multiplied by the unknown function (concentration). The main result of the paper is the homogenization (continualization) of this equation when the small parameter is the characteristic step h of the mesh. The error estimates are proved for the difference of the exact solution of the DDA equation and the solution of the homogenized differential equation. Copyright © 2012 John Wiley & Sons, Ltd.     

Frontal polymerization with encapsulated monomer

Thermal frontal polymerization (TFP) is the process that converts monomers into polymers by means of a spatially localized self-propagating thermal reaction wave. Free radical frontal polymerization systems can suffer from a limited pot life, i.e. the systems will spontaneously polymerize while remaining at ambient pressure and temperature before they can be used. One way to avoid this undesirable spontaneous polymerization is by microencapsulating the monomer. The release of monomer from its shell can be modeled as a temperature dependent or temperature independent reaction; we consider both cases. Conditions are established which reduce the current model to the standard FP model and extinction limits are determined by employing an asymptotic analysis of the reaction zone in the limit as the reaction zone shrinks to an interface.