On entire nonnegative solutions of quasilinear inequalities of elliptic type that vanish on a set of positive measure

In the article, it is proved that any nonnegative solution of an elliptic quasilinear inequality that vanishes on a subset of positive measure is trivial. __________ Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 25, pp. 112–118, 2005.     

A mixed‐FEM formulation for nonlinear incompressible elasticity in the plane

This article deals with an expanded mixed finite element formulation, based on the Hu‐Washizu principle, for a nonlinear incompressible material in the plane. We follow our related previous works and introduce both the stress and the strain tensors as further unknowns, which yields a two‐fold saddle point operator equation as the corresponding variational formulation. A slight generalization of the classical Babu?ka‐Brezzi's theory is applied to prove unique solvability of the continuous and discrete formulations, and to derive the corresponding a priori error analysis. An extension of the well‐known PEERS space is used to define an stable associated Galerkin scheme. Finally, we provide an a posteriori error analysis based on the classical Bank‐Weiser approach. © 2002 John Wiley & Sons, Inc. Numer Methods Partial Differential Eq 18: 105–128, 2002     

Discontinuous travelling wave solutions for certain hyperbolic systems

In an earlier paper on a malignant cell invasion model (Marchantet al., SIAM J. Appl. Math, 60, 2000) we introduced a novelform of discontinuous travelling wave solution. These solutionscould be studied easily by combining behaviour within a phaseplane with the Rankine–Hugoniot shock conditions, whichdescribe properties (such as the ratio of the jump discontinuitiesto the speed of propagation) that solutions may possess. Theseresults were new for several reasons. The shock conditions relateto hyperbolic equations (which the model is) but were appliedin a travelling wave ordinary differential equation phase planeusing techniques that usually apply to parabolic reaction–diffusionsystems. In addition the solutions possess singular behaviournear several points in the phase plane but in spite of thisthere exists a robust and stable family of physically interestingsolutions. In this paper we discuss two previously studied models, oneof detonation theory and one of angiogenesis. We show that eachof these models also possesses a family of discontinuous travellingwave solutions which was not previously discovered. Of particularinterest is the solution which has a blunt interface at thefront of the invading profile. In all three models it is thissolution that is seen to stably evolve from physically relevantinitial data, and for physically relevant parameter values. This work confirms the robustness of these novel travellingwave solutions and their applicability to a wider range of mathematicalmodelling situations.     

CIDEP spin probing of the nanopores in cotton

Time-resolved electron paramagnetic resonance (TREPR) experiments are reported on an α-hydroxy acetophenone in waterg-glycerol and ethanol-ethanediol mixtures over a viscosity range of 1–32 cP. The magnitude and viscosity dependence of the radical pair mechanism polarization is in good agreement with theory. The triplet mechanism polarization is found to increase with decreasing solvent polarity and this is ascribed to an increase in the α-cleavage rate constant. The liquid spectra are used to interpret TREPR spectra of the acetophenone in dry and wet cotton. In dry cotton anti-phase structure is seen and is due to some of the radical pairs being trapped in cages. The triplet and radical pair mechanism polarization shows that the acetophenone adsorbs to the apolar crystallite surface and releases radicals into the polar amorphous regions where they experience a microviscosity of approximately 30 cP. In wet cotton there are no cages and the viscosity is greater than in ethanol alone.     

Threshold electrical switching in As45Te55-xInx and As50Te50-xInx glasses

The electrical switching behaviour of As₄₅Te_55-xIn_x (5≤x≤15) and As₅₀Te_50-xIn_x (2.5≤x≤11.5) has been studied over a wide range of compositions. These glasses are found to exhibit threshold switching. The composition dependence of switching voltage (V_t) has been found to exhibit a change in slope and a local minimum at compositions x=10 and 12.5 for As₄₅Te_55-xIn_x and x=7.5 and 10.8 for As₅₀Te_50-xIn_x, respectively. The slope change in V_t verses x and the local minimum have been identified using two network topological effects, namely the rigidity percolation threshold and the chemical threshold. Received: 23 August 2001 / Accepted: 27 August 2001 / Published online: 11 February 2002     

Performance and simulation of an on-board guided-wave optical processor for airborne SAR applications

This paper describes the performance and simulation of a compact integrated optical processor for the real-time reconstruction of two-dimensional images in airborne stripmap synthetic aperture radar applications. The functional behavior of the processor is explained in some detail. The design criteria are briefly given. The simulation step allowed the main processor characteristics and properties to be identified. A number of comparisons were obtained in airborne SAR mission scenarios between the predictions of the optical device and those achieved by the modern electronic digital approach, based on the wavefront reconstruction method by matched filtering.     

Single chain force spectroscopy - Reading the sequence of HP protein models

We study the elastic properties of single A/B random copolymer chains, with a specific sequence and use them as theoretical model for so called HP proteins. HP proteins carry hydrophilic (P) and hydrophobic (H) monomers. We predict a rich structure in the force-extension relations which can be attributed to the information in the sequence. The variational method is used to probe local minima on the path of stretching and releasing for the chain molecules. At a given force, we find multiple configurations which are separated by energy barriers. A collapsed globular configuration consists of several domains which unravel cooperatively. Upon stretching, the unfolding path shows a stepwise pattern corresponding to the unfolding of each domain. While releasing, several cores can be created simultaneously in the middle of the chain, resulting in a different path of collapse. The long-range interactions and stiffness of the chain simplify the potential landscape given by the disorder in sequence. Received 5 March 2002 / Received in final form 16 May 2002 Published online 13 August 2002     

Wave propagation through a high-velocity elastic layer

We consider theoretical seismographs of a wave field passing through an elastic layer with high propagation velocity. We note the presence of a low-frequency part of the seismogram for longitudinal waves. It is shown that the propagation time of low-frequency vibrations is equal to that of longitudinal disturbances screened by the layer.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova, AN SSSR, Vol. 173, pp. 134–141, 1988.     

Transformation of the excitation energy in excimers and exciplexes of aromatic hydrocarbons

Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 54, No. 1, pp. 26–32, January, 1991.