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Stress relaxation models with polyconvex entropy in Lagrangean and Eulerian coordinates
Get PDFThe embedding of the equations of polyconvex elastodynamics to an augmented
symmetric hyperbolic system provides in conjunction with the relative entropy method
a robust stability framework for approximate solutions \cite{LT06}.
We devise here a model of stress relaxation motivated by the
format of the enlargement process which formally approximates
the equations of polyconvex elastodynamics. The model is endowed with
an entropy function which is not convex but rather of polyconvex type.
Using the relative entropy we prove a stability estimate and convergence
of the stress relaxation model to polyconvex elastodynamics in the
smooth regime. As an application, we show that models of pressure relaxation for
real gases in Eulerian coordinates fit into the proposed framework
Magnetic soliton dynamics driven by spin-transfer torque in perpendicular magnetic anisotropy devices
Get PDFThis paper demonstrates how to excite a complex soliton mode in nanomagnets with perpendicular to plane magnetic anisotropy by means of the non-uniform injection of a spin-polarized current via a nano-aperture. We present two different numerical frameworks. In the first one, the polarizer has perpendicular anisotropy, the excited mode exhibits oscillation frequency in the GHz range with a spatial distribution localized near the nano-aperture. The study of the topological density indicates that the persistent magnetization dynamics is characterized by a rotation of two bubble/antibubble pairs.
The second scenario corresponds to the experimental framework by [S. M. Mohseni, et al, Science, 339, 1295, (2013).], where the polarizer has an in-plane anisotropy polarizer whose magnetization is tilted under the action of a large external field. Our study identifies the topological density of the dissipative droplet formed in that geometry as a bubble/antibubble pair.
The methodological study introduced here for the spintronic oscillators and based on the time domain evolution of the topological density should be very useful in the fundamental understanding of the soliton dynamics
A small remark on the derivation of the Plateau angle conditions for the vector-valued Allen-Cahn equation
Get PDFStress relaxation models with polyconvex entropy in Lagrangean and Eulerian coordinates
Get PDFThe embedding of the equations of polyconvex elastodynamics to an augmented
symmetric hyperbolic system provides in conjunction with the relative entropy method
a robust stability framework for approximate solutions \cite{LT06}.
We devise here a model of stress relaxation motivated by the
format of the enlargement process which formally approximates
the equations of polyconvex elastodynamics. The model is endowed with
an entropy function which is not convex but rather of polyconvex type.
Using the relative entropy we prove a stability estimate and convergence
of the stress relaxation model to polyconvex elastodynamics in the
smooth regime. As an application, we show that models of pressure relaxation for
real gases in Eulerian coordinates fit into the proposed framework
Effect of Solvent on the Self-Assembly of Dialanine and Diphenylalanine Peptides
Get PDFDiphenylalanine (FF) is a very common peptide with many potential applications, both biological and technological, due to a large number of different nanostructures which it attains. The current work concerns a detailed study of the self assembled structures of FF in two different solvents, an aqueous (H2O) and an organic (CH3OH) through simulations and experiments. Detailed atomistic Molecular Dynamics (MD) simulations of FF in both solvents have been performed, using an explicit solvent model. The self assembling propensity of FF in water is obvious while in methanol a very weak self assembling propensity is observed. We studied and compared structural properties of FF in the two different solvents and a comparison with a system of dialanine (AA) in the corresponding solvents was also performed. In addition, temperature dependence studies were carried out. Finally, the simulation predictions were compared to new experimental data, which were produced in the framework of the present work. A very good qualitative agreement between simulation and experimental observations was found
A software framework for computing Newton polytopes of resultants and (reduced) discriminants
Get PDFWe present a new software for computing Newton polytopes
of resultant and discriminant polynomials. We illustrate its use with a number of examples
Selective imaging of extended reflectors in a two-dimensional waveguide
Get PDFWe consider the problem of selective imaging extended reflectors in waveguides using the response matrix of the scattered field obtained with an active array. Selective imaging amounts to being able to focus at the edges of a reflector which typically give raise to weaker echoes than those coming from its main body. To this end, we propose a selective imaging method that uses projections on low rank
subspaces of a weighted modal projection of the array response matrix, . We analyze
theoretically our imaging method for a simplified model problem where the scatterer is a vertical one-dimensional perfect reflector. In this case, we show that the
rank of equals the size of the reflector devided by the cross-range array resolution which is for an array spanning the whole depth of the waveguide. We also derive analytic expressions for the singular vectors of which allows us to show how selective imaging can be achieved. Our numerical simulations are in very good
agreement with the theory and illustrate the robustness of our imaging functional for reflectors of various shapes
Inversions of Statistical Parameters of an Acoustic Signal in Range-dependent Environments with Applications in Ocean Acoustic Tomography
Get PDFThe paper presents an application of a method for the characterization of underwater acoustic signals based on the statistics of their wavelet transform sub-band coefficients in range-dependent environments. As it was illustrated in previous works, this statistical characterization scheme is a very efficient tool for obtaining observables to be exploited in problems of ocean acoustic tomography and geoacoustic inversion, when range-independent environments are considered. Now the scheme is applied in range-dependent environments for the estimation of range-dependent features in shallow water.
A simple denoising strategy, also presented in the paper, is shown to enhance the quality of the inversion results, as it helps to keep the signal characterization to the energy significant part of it. The results presented for typical test cases are encouraging and indicative of the potential of the method for the treatment of inverse problems in acoustical oceanography
On the construction and properties of weak solutions describing dynamic cavitation
Get PDFWe consider the problem of dynamic cavity formation in isotropic compressible nonlinear elastic media. For the equations
of radial elasticity we construct self-similar weak solutions that describe a cavity emanating from a state of uniform deformation.
For dimensions d =2, 3 we show that cavity formation is necessarily associated with a unique precursor shock.
We also study the bifurcation diagram and do a detailed analysis of the singular asymptotics associated to cavity initiation
as a function of the cavity speed of the self-similar profiles. We show that
for stress free cavities the critical stretching associated with dynamically cavitating solutions coincides with the critical stretching in the bifurcation diagram of equilibrium elasticity. Our analysis treats both stress-free cavities and cavities with contents