Existence of homoclinic solutions for nonlinear second-order coupled systems

This work presents sufficient conditions for the existence of homoclinic solutions for second order coupled discontinuous systems of differential equations on the real line without the usual growth condition in the literature.The arguments apply the fixed point theory, Green's functions technique, $L^1$-Carathéodory functions, lower and upper solutions and Schauder's fixed point theorem.     

Analysis of an elasto-piezoelectric system of hemivariational inequalities with thermal effects

In this paper we prove the existence and uniqueness of a weak solution for a dynamic electo-viscoelastic problem that describes a contact between a body and a foundation. We assume the body is made from thermoviscoelastic material and consider nonmonotone boundary conditions for the contact. We use recent results from the theory of hemivariational inequalities and the fixed point theory.     

Inhomogeneous ‘longitudinal’ plane waves in a deformed elastic material

By definition, a homogeneous isotropic compressible Hadamard material has the property that an infinitesimal longitudinal homogeneous plane wave may propagate in every direction when the material is maintained in a state of arbitrary finite static homogeneous deformation. Here, as regards the wave, 74404208261q/xxlarge8216.gif" alt="lsquo" align="BASELINE" BORDER="0">homogeneous74404208261q/xxlarge8217.gif" alt="rsquo" align="BASELINE" BORDER="0"> means that the direction of propagation of the wave is parallel to the direction of eventual attenuation; and 74404208261q/xxlarge8216.gif" alt="lsquo" align="BASELINE" BORDER="0">longitudinal74404208261q/xxlarge8217.gif" alt="rsquo" align="BASELINE" BORDER="0"> means that the wave is linearly polarized in a direction parallel to the direction of propagation. In other words, the displacement is of the form u = ncos k(n · x – ct), where n is a real vector. It is seen that the Hadamard material is the most general one for which a 74404208261q/xxlarge8216.gif" alt="lsquo" align="BASELINE" BORDER="0">longitudinal74404208261q/xxlarge8217.gif" alt="rsquo" align="BASELINE" BORDER="0"> inhomogeneous plane wave may also propagate in any direction of a predeformed body. Here, 74404208261q/xxlarge8216.gif" alt="lsquo" align="BASELINE" BORDER="0">inhomogeneous74404208261q/xxlarge8217.gif" alt="rsquo" align="BASELINE" BORDER="0"> means that the wave is attenuated, in a direction distinct from the direction of propagation; and 74404208261q/xxlarge8216.gif" alt="lsquo" align="BASELINE" BORDER="0">longitudinal74404208261q/xxlarge8217.gif" alt="rsquo" align="BASELINE" BORDER="0"> means that the wave is elliptically polarized in the plane containing these two directions, and that the ellipse of polarization is similar and similarly situated to the ellipse for which the real and imaginary parts of the complex wave vector are conjugate semi-diameters. In other words, the displacement is of the form u = 74404208261q/xxlarge8476.gif" alt="real" align="BASELINE" BORDER="0">{S exp i74404208261q/xxlarge969.gif" alt="ohgr" align="BASELINE" BORDER="0">(S · x – ct)}, where S is a complex vector (or bivector). Then a Generalized Hadamard material is introduced. It is the most general homogeneous isotropic compressible material which allows the propagation of infinitesimal 74404208261q/xxlarge8216.gif" alt="lsquo" align="BASELINE" BORDER="0">longitudinal74404208261q/xxlarge8217.gif" alt="rsquo" align="BASELINE" BORDER="0"> inhomogeneous plane circularly polarized waves for all choices of the isotropic directional bivector. Finally, the most general forms of response functions are found for homogeneously deformed isotropic elastic materials in which 74404208261q/xxlarge8216.gif" alt="lsquo" align="BASELINE" BORDER="0">longitudinal74404208261q/xxlarge8217.gif" alt="rsquo" align="BASELINE" BORDER="0"> inhomogeneous plane waves may propagate with a circular polarization in each of the two planes of central circular section of the 74404208261q/10659_2005_Article_4399_TeX2GIFIE1.gif" alt=" $$\mathbb{B}$$ " align="middle" border="0"> ⁿ -ellipsoid, where 74404208261q/10659_2005_Article_4399_TeX2GIFIE2.gif" alt=" $$\mathbb{B}$$ " align="middle" border="0"> is the left Cauchy-Green strain tensor corresponding to the primary pure homogeneous deformation.     

Epitaxy of Binary Compounds and Alloys

The present work aims at constructing a theoretical framework within which to address the issues of morphological instabilities (one-dimensional step bunching and two-dimensional step meandering), alloying, and phase segregation in binary systems in the context of (physical or chemical) vapor deposition. The length scale of interest, although nanoscopic, is sufficiently large that the steps on a vicinal surface can be viewed as smooth curves and, correspondingly, the theory is a continuum one. In a departure from theories inaugurated by Burton, Cabrera, and Frank [The growth of crystals and the equilibrium structure of their surfaces. Phil. Trans. Roy. Soc. A 243 (1951) 299–358] the steps are endowed with a thermodynamic structure whose main ingredients are a step free-energy density and edge species chemical potentials. Moreover, crystal anisotropy, with its altering of the dynamics of steps and the associated morphological instabilities, is accounted for – in a manner consistent with the second law – both in the thermodynamic and kinetic properties of terraces and, more importantly, of steps. Additionally, in contrast with most of the literature on the subject (cf. [J. Krug, Introduction to step dynamics and step instabilities. In: A. Voigt (ed.) Multiscale Modeling in Epitaxial Growth. Birkhäusser, Berlin (2005)]), adsorption–desorption along the steps, bulk atomic diffusion, and chemical reactions (both on the terraces and along the step edges) are incorporated and coupled to the other mechanisms, e.g., terrace adatom diffusion and step attachment–detachment kinetics, whose interplay governs the evolution of steps on vicinal surfaces. Importantly, aided by the concept of configurational forces for which a separate balance law is postulated Configurational Forces as Basic Concepts of Continuum Physics. Springer, Berlin Heidelberg New York (2000)]), the proposed theory allows the steps to evolve away from local equilibrium thus contributing to a general treatment of the dynamics of steps. Finally, a specialization to the epitaxy of binary compounds and alloys is afforded, yielding a generalization of the classical Gibbs–Thomson relation in the former and novel evolution equations for an individual step in the latter.     

A Generalized Fourier Approximation in Anti-plane Cosserat Elasticity

In the present paper we use the modification of Kupradze’s method of generalized Fourier series for the treatment of interior and exterior Dirichlet and Neumann boundary-value problems arising in a linear theory of anti-plane elasticity which includes the effects of material microstructure.     

A novel harmonic balance analysis for the Van Der Pol oscillator

This study focuses on a novel harmonic balance formulation, the high-dimensional harmonic balance method. To investigate a non-linearity in the damping term, the system chosen for study is the Van der Pol's oscillator. Both unforced and forced oscillators are analyzed. The results from the analysis are compared with those obtained from the classical harmonic balance and the time marching (Runge-Kutta) methods.     

Competition Between Radial Expansion and Thickening in the Enlargement of an Intracranial Saccular Aneurysm

Rupture of intracranial saccular aneurysms is the leading cause of spontaneous subarachnoid hemorrhage, which results in significant morbidity and mortality. Although many have suggested that saccular aneurysms enlarge and rupture due to mechanical instabilities, our recent nonlinear analyses suggest that at least certain classes of aneurysms do not exhibit a quasi-static limit point instability or dynamic instabilities in response to periodic loading. Based on an increased understanding of the ubiquitous role of growth and remodeling within the vasculature and recent histopathological data on saccular aneurysms, it is hypothesized that a stress-mediated regulation of collagen turnover causes their enlargement. There is a need, however, for a theoretical framework to explore this and competing hypotheses. In this paper, we present a 2-D constrained mixture model for growth and remodeling of an ellipsoidally shaped saccular aneurysm and numerically simulate enlargement and changes in material symmetry in the aneurysmal wall. Results suggest that ellipsoidal aneurysms tend toward spherical shapes, and a competition between radial expansion and wall thickening plays a critical role in determining the stability of an enlarging lesion.     

Mixed Formulations of Bending Problems for Homogeneous Elastic Plates and Beams

Mixed formulations of bending problems for homogeneous plates (beams) are proposed, whose essence is that the deformation of a plate (beam) near its fixed boundary is described by the three74qmm240056/xxlarge8208.gif" alt="dash" align="MIDDLE" BORDER="0">dimensional elasticity equations, and the remaining part by the conventional equations of plate (beam) bending. At the interface between these regions, the solutions of these equations are joined. The mixed formulation allows one to describe the three74qmm240056/xxlarge8208.gif" alt="dash" align="MIDDLE" BORDER="0">dimensional stress state in the neighborhood of the fixed boundaries of plates (beams) and take into account the complex nature of the fixing conditions. Finite74qmm240056/xxlarge8208.gif" alt="dash" align="MIDDLE" BORDER="0">element implementation is more efficient for the mixed formulations of plate (beam) bending problems than for the well74qmm240056/xxlarge8208.gif" alt="dash" align="MIDDLE" BORDER="0">known three74qmm240056/xxlarge8208.gif" alt="dash" align="MIDDLE" BORDER="0">dimensional formulations.     

Uniform stability of semilinear wave equations with arbitrary local memory effects versus frictional dampings

This paper is concerned with the mixed initial–boundary value problem for semilinear wave equations with complementary frictional dampings and memory effects. We successfully establish uniform exponential and polynomial decay rates for the solutions to this initial–boundary value problem under much weak conditions concerning memory effects. More specifically, we obtain the exponential and polynomial decay rates after removing the fundamental condition that the memory-effect region includes a part of the system boundary, while the condition is a necessity in the previous literature; moreover, for the polynomial decay rates we only assume minimal conditions on the memory kernel function g, without the usual assumption of $g^{\prime }$ controlled by g.     

Controlled Synthesis of Large Single Crystals of Metal-Organic Framework CPO-27-Ni Prepared by a Modulation Approach: In situ Single-Crystal X-ray Diffraction Studies

The size of single crystals of the metal-organic framework CPO-27-Ni was incrementally increased through a series of modulated syntheses. A novel linker modulated synthesis using 2,5-dihydroxyterephthalic acid and the isomeric ligand 4,6-dihydroxyisophthalic acid yielded large single crystals of CPO-27-Ni (∼70 μm). All materials were shown to have high crystallinity and phase purity through powder X-ray diffraction, electron microscopy methods, thermogravimetry, and compositional analysis. For the first time single-crystal structure analyses were carried out on CPO-27-Ni. High BET surface areas and nitric oxide (NO) release efficiencies were recorded for all materials. Large single crystals of CPO-27-Ni showed a prolonged NO release and proved suitable for in situ single-crystal diffraction experiments to follow the NO adsorption. An efficient activation protocol was developed, leading to a dehydrated structure after just 4 h, which subsequently was NO-loaded, leading to a first NO loaded single-crystal structural model of CPO-27-Ni.