A Linearization Approach for Rational Nonlinear Models in Mathematical Physics

In this paper,a novel method for linearization of rational second order nonlinear models is discussed.In particular,we discuss an application of the δ expansion method(created to deal with problems in Quantum Field Theory) which will enable both the linearization and perturbation expansion of such equations.Such a method allows for one to quickly obtain the order zero perturbation theory in terms of certain special functions which are governed by linear equations.Higher order perturbation theories can then be obtained in terms of such special functions.One benefit to such a method is that it may be applied even to models without small physical parameters,as the perturbation is given in terms of the degree of nonlinearity,rather than any physical parameter.As an application,we discuss a method of linearizing the six Painleve equations by an application of the method.In addition to highlighting the benefits of the method,we discuss certain shortcomings of the method.     

Travelling Waves for a Density Dependent Diffusion Nagumo Equation over the Real Line

We consider the density dependent diffusion Nagumo equation, where the diffusion coefficient is a simple power function. This equation is used in modelling electrical pulse propagation in nerve axons and in population genetics (amongst other areas). In the present paper, the δ-expansion method is applied to a travelling wave reduction of the problem, so that we may obtain globally valid perturbation solutions (in the sense that the perturbation solutions are valid over the entire infinite domain, not just locally; hence the results are a generalization of the local solutions considered recently in the literature). The resulting boundary value problem is solved on the real line subject to conditions at z → ±∞. Whenever a perturbative method is applied, it is important to discuss the accuracy and convergence properties of the resulting perturbation expansions. We compare our results with those of two different numerical methods (designed for initial and boundary value problems, respectively) and deduce that the perturbation expansions agree with the numerical results after a reasonable number of iterations. Finally, we are able to discuss the influence of the wave speed c and the asymptotic concentration value α on the obtained solutions. Upon recasting the density dependent diffusion Nagumo equation as a two-dimensional dynamical system, we are also able to discuss the influence of the nonlinear density dependence (which is governed by a power-law parameter m) on oscillations of the travelling wave solutions.     

pH‐induced reorientation of microperoxidase‐11 in mesoporous molecular sieves

The resonance Raman spectra of microperoxidase‐11 loaded into the siliceous materials MCM‐41 and SBA‐15 demonstrate a pH dependence indicative of a protonation event on the substrate. An unusual change in relative Raman intensities without a shift in wavenumbers is observed upon lowering the system pH. Protonation of the silica surface is suggested to induce a reorientation of the MP‐11 fragments within the silica framework. Copyright © 2006 John Wiley & Sons, Ltd.     

Inverse problems related to ion channels

Ion channels are proteins with a hole down theirmiddle that allow ions to move across otherwise impermeable cellmembranes, thereby controlling many important physiological functions. The transport process of the ions can be described using the Poisson-Nernst-Plank equations, a system of coupled nonlinear partial differential equations. Based on this model we derive a simplified surrogate model that captures the main features of the associated current-voltage curves of the ion channel. This surrogate model is then used to identify individual channel parameters based on current data. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Aircraft wake vortices – prediction and mitigation

The current abstract presents selected topics investigated within the wake-vortex research program of DLR. Two approaches are addressed that both aim at increasing airport capacity without compromising safety. One approach is to directly alleviate wake vortex strength and stability by constructive measures at the aircraft wings. The other approach utilizes the dominant influence of meteorological parameters like turbulence, wind shear, and temperature stratification on wake vortex fate. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Knotted linear force-free magnetic fields-topological aspects

The problem of computing linear force-free magnetic fields on a knotted multiply-connected domain is considered. The domain is the support of the current distribution, and the linear force-free fieldproblem reduces to finding an eigenfield of a self-adjoint curl operator. In this context, the GKN Theorem is reformulated in terms of symplectic geometry in order to characterize the self-adjoint extensions of the curl operator restricted to solenoidal vector fields. When further restricted to the isotopy invariant boundary conditions, the self-adjoint extensions are parametrized by the Lagrangian subspaces of the symplectic form on the first homology group of the boundary. This paper discusses some of the topological aspects and gives some pointers for the associated finite element discretization. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Stress relaxation of PBI based membrane electrode assemblies

Stress relaxation in the membrane electrode assemblies (MEA) in PEM fuel cells subjected to compressive loads is analyzed. This behavior is important because nonzero contact stress is required to maintain low electric resistivity in the fuel cell stack. Experimental results are used to guide the choice of the viscoelastic properties of the constituents of the MEA, the membrane and the gas diffusion layer (GDL), needed for the model. These properties are incorporated into the model that treats the membrane as a porous-viscoelastic solid, and the gas diffusion layer as a nonlinear elastic solid. Using numerical simulations (finite element method), the stress relaxation curves for the MEA are obtained for different fluid flow boundary conditions, variations in the material properties of the membrane and the GDL. The results are compared to experimental stress relaxation curves. Most of the experimental data were obtained at a temperature of 180 °C, corresponding to operating conditions, so in the model the temperature was considered fixed and equal to this value.     

Molecular dynamics simulations of the thermal conductivity of methane hydrate

Nonequilibrium molecular dynamics simulations with the nonpolarizable SPC/E (Berendsen et al., J. Phys. Chem. 1987, 91, 6269) and the polarizable COS/G2 (Yu and van Gunsteren, J. Chem. Phys. 2004, 121, 9549) force fields have been employed to calculate the thermal conductivity and other associated properties of methane hydrate over a temperature range from 30 to 260 K. The calculated results are compared to experimental data over this same range. The values of the thermal conductivity calculated with the COS/G2 model are closer to the experimental values than are those calculated with the nonpolarizable SPC/E model. The calculations match the temperature trend in the experimental data at temperatures below 50 K; however, they exhibit a slight decrease in thermal conductivity at higher temperatures in comparison to an opposite trend in the experimental data. The calculated thermal conductivity values are found to be relatively insensitive to the occupancy of the cages except at low (T相似文献