Global Stabilization of the Navier-Stokes-Voight and the damped nonlinear wave equations by finite number of feedback controllers

In this paper we introduce a finite-parameters feedback control algorithm for stabilizing solutions of the Navier-Stokes-Voigt equations, the strongly damped nonlinear wave equations and the nonlinear wave equation with nonlinear damping term, the Benjamin-Bona-Mahony-Burgers equation and the KdV-Burgers equation. This algorithm capitalizes on the fact that such infinite-dimensional dissipative dynamical systems posses finite-dimensional long-time behavior which is represented by, for instance, the finitely many determining parameters of their long-time dynamics, such as determining Fourier modes, determining volume elements, determining nodes , etc..The algorithm utilizes these finite parameters in the form of feedback control to stabilize the relevant solutions. For the sake of clarity, and in order to fix ideas, we focus in this work on the case of low Fourier modes feedback controller, however, our results and tools are equally valid for using other feedback controllers employing other spatial coarse mesh interpolants

3D Raman mapping of the collagen fibril orientation in human osteonal lamellae

AbstractChemical composition and fibrillar organization are the major determinants of osteonal bone mechanics. However, prominent methodologies commonly applied to investigate mechanical properties of bone on the micro scale are usually not able to concurrently describe both factors. In this study, we used polarized Raman spectroscopy (PRS) to simultaneously analyze structural and chemical information of collagen fibrils in human osteonal bone in a single experiment. Specifically, the three-dimensional arrangement of collagen fibrils in osteonal lamellae was assessed. By analyzing the anisotropic intensity of the amide I Raman band of collagen as a function of the orientation of the incident laser polarization, different parameters related to the orientation of the collagen fibrils and the degree of alignment of the fibrils were derived. Based on the analysis of several osteons, two major fibrillar organization patterns were identified, one with a monotonic and another with a periodically changing twist direction. These results confirm earlier reported twisted and oscillating plywood arrangements, respectively. Furthermore, indicators of the degree of alignment suggested the presence of disordered collagen within the lamellar organization of the osteon. The results show the versatility of the analytical PRS approach and demonstrate its capability in providing not only compositional, but also 3D structural information in a complex hierarchically structured biological material. The concurrent assessment of chemical and structural features may contribute to a comprehensive characterization of the microstructure of bone and other collagen-based tissues

On Renyi entropies characterizing the shape and the extension of the phase space representation of quantum wave functions in disordered systems

We discuss some properties of the generalized entropies, called Renyi entropies and their application to the case of continuous distributions. In particular it is shown that these measures of complexity can be divergent, however, their differences are free from these divergences thus enabling them to be good candidates for the description of the extension and the shape of continuous distributions. We apply this formalism to the projection of wave functions onto the coherent state basis, i.e. to the Husimi representation. We also show how the localization properties of the Husimi distribution on average can be reconstructed from its marginal distributions that are calculated in position and momentum space in the case when the phase space has no structure, i.e. no classical limit can be defined. Numerical simulations on a one dimensional disordered system corroborate our expectations.Comment: 8 pages with 2 embedded eps figures, RevTex4, AmsMath included, submitted to PR

Shell model on a random gaussian basis

Pauli-projected random gaussians are used as a representation to solve the shell model equations. The elements of the representation are chosen by a variational procedure. This scheme is particularly suited to describe cluster formation and cluster decay in nuclei. It overcomes the basis-size problem of the ordinary shell model and the technical difficulties of the cluster-configuration shell model. The model reproduces the $\alpha$-decay width of $^{212}$Po satisfactorily.Comment: Latex, Submitted to Phys. Lett. B, 7 pages, 2 figures available upon request, ATOMKI-1994-

Positron scattering and annihilation from the hydrogen molecule at zero energy

The confined variational method is used to generate a basis of correlated gaussians to describe the interaction region wave function for positron scattering from the H$_2$ molecule. The scattering length was $\approx -2.7$ $a_0$ while the zero energy $Z_{\rm eff}$ of 15.7 is compatible with experimental values. The variation of the scattering length and $Z_{\rm eff}$ with inter-nuclear distance was surprisingly rapid due to virtual state formation at $R \approx 3.4$ $a_0$

Interaction-assisted propagation of Coulomb-correlated electron-hole pairs in disordered semiconductors

A two-band model of a disordered semiconductor is used to analyze dynamical interaction induced weakening of localization in a system that is accessible to experimental verification. The results show a dependence on the sign of the two-particle interaction and on the optical excitation energy of the Coulomb-correlated electron-hole pair.Comment: 4 pages and 3 ps figure