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Fourier integrals and a new representation of Maslov's canonical operator near caustics
Get PDFWe suggest a new representation of Maslov's canonical operator
in a neighborhood of the caustics using a special class of coordinate systems
(\eikonal coordinates") on Lagrangian manifolds
Structure and Dynamics of Poly(methyl-methacrylate)/Graphene systems through Atomistic Molecular Dynamics Simulations
Get PDFThe main goal of the present work is to examine the effect of graphene layers on the sructural and dynamical properties of polymer systems. We study hybrid poly(methyl
methacrylate) (PMMA)/graphene interfacial systems, through detailed atomistic molecular dynamics (MD) simulations. In order to characterize the interface, various properties related to density, structure and dynamics of polymer chains are calculated, as a function of the distance from the substrate. A series of different hybrid systems, with
width ranging between [2.60 – 13.35] nm, are being modeled. In addition, we compare the properties of the macromolecular chains to the properties of the orresponding bulk system at the same temperature. We observe a strong effect of graphene layers on both
structure and dynamics of the PMMA chains. Furthermore the PMMA/graphene interface is characterized by different length scales, depending on the actual property we probe:
Density of PMMA polymer chains is larger than the bulk value, for polymer chains close to graphene layers up to distances of about [1.0-1.5]nm. Chain conformations are
perturbed for distances up to about 2-3 radius of gyration from graphene. Segmental dynamics of PMMA is much slower close to the solid layers up to about [2-3]nm. Finally
terminal-chain dynamics is slower, compared to the bulk one, up to distances of about 5-7 radius of gyration
Accelerating and abruptly-autofocusing beam waves in the Fresnel zone of antenna arrays
Get PDFWe introduce the concept of spatially accelerating (curved) beam waves in the Fresnel region of properly designed antenna arrays. These are transversely localized EM waves that propagate in free space in a diffraction-resisting manner, while at the same time laterally shifting their amplitude pattern along a curved trajectory. The proposed
beams are the radiowave analogue of Airy and related accelerating optical waves, which, in contrast to their optical counterparts, are produced by the interference of discrete radiating elements rather than by the evolution of a continuous wavefront. Two dyadic array configurations are proposed comprising 2D line antennas: linear phased arrays
with a power-law phase variation and curved power-law arrays with in-phase radiating elements. Through analysis and numerical simulations, the formation of broadside accelerating beams with power-law trajectories is studied versus the array parameters. Furthermore, the abrupt autofocusing effect, that occurs when beams of this kind interfere with opposite acceleration, is investigated. The concept and the related antenna setups can be of use in radar and wireless communications applications
The problem of dynamic cavitation in nonlinear elasticity
Get PDFThe notion of singular limiting induced from continuum solutions (slic-solutions) is applied to
the problem of cavitation in nonlinear elasticity, in order to re-assess an example of non-uniqueness of
entropic weak solutions (with polyconvex energy) due to a forming cavity
A Molecular Dynamics Study of Polymer/Graphene Nanocomposites
Get PDFGraphene based polymer nanocomposites are hybrid materials with
a very broad range of technological applications. In this work, we study three
hybrid polymer/graphene interfacial systems (polystyrene/graphene,
poly(methyl methacrylate)/graphene and polyethylene/graphene) through
detailed atomistic molecular dynamics (MD) simulations. Density profiles,
structural characteristics and mobility aspects are being examined at the
molecular level for all model systems. In addition, we compare the properties
of the hybrid systems to the properties of the corresponding bulk ones, as well
as to theoretical predictions
Molecular Dynamics of Polyisoprene/Polystyrene Oligomer Blends: The role of self-concentration and fluctuations on blend dynamics
Get PDFThe effect of self-concentration and intermolecular packing on the dynamics of polyisoprene (PI)/polystyrene (PS) blends is examined by extensive atomistic simulations.
Direct information on local structure of the blend system allows a quantitative calculation of self- and effective composition terms at various length scales that
are introduced to proposed models of blend dynamics. Through a detailed statistical analysis, the full distribution of relaxation times associated with reorienation of carbon-hydrogen bonds was extracted and compared to literature experimental data. A direct relation between relaxation times and local effective composition is
found. Following an implementation of a model involving local composition as well as concentration fluctuations the relevant length scales characterizing the segmental
dynamics of both components were critically examined. For PI the distribution of times becomes narrower for the system with the lowest PS content and then broadens
as more PS is added. This is in contrast to the slow component (PS), where an extreme breadth is found for relaxation times in the 25/75 system prior to narrowing
as we increase PI concentration. The chain dynamics was directly quantified by diffusion coefficients as well as the terminal (maximum) relaxation time of each component
in the mixed state. Strong coupling between the friction coefficients of the two components was predicted that leads to very similar chain dynamics for PI and PS, particularly for high concentrations of PI. We anticipate this finding to the rather short oligomers (below the Rouse regime) studied here as well as to the rather similar size of PI and PS chains. The ratio of the terminal to the segmental relaxation time, τterm/τseg,c, presents a clear qualitative difference for the constituents: for PS the above ratio is almost independent of blend composition and very similar to the pure state. In contrast, for PI this ratio depends strongly on the composition of the blend; i.e. the terminal relaxation time of PI increases more than its segmental relaxation time, as the concentration of PS increases, resulting into a larger terminal/segmental
ratio. We explain this disparity, based on the different length scales characterizing dynamics. The relevant length for the segmental dynamics of PI is about 0.4-0.6 nm,
smaller than chain dimensions which are expected to characterize terminal dynamics, whereas for PS associated length scales are similar (about 0.7-1.0 nm) rendering a
uniform change with mixing
Spectral theory of some non-selfadjoint linear differential operators
Get PDFWe give a characterisation of the spectral properties of linear differential operators with constant coefficients, acting on functions defined on a bounded interval, and determined by general linear boundary conditions. The boundary conditions may be such that the resulting operator is not selfadjoint.
We associate the spectral properties of such an operator with the properties of the solution of a corresponding boundary value problem for the partial differential equation . Namely, we are able to establish an explicit correspondence between the properties of the family of eigenfunctions of the operator, and in particular whether this family is a basis, and the existence and properties of the unique solution of the associated boundary value problem. When such a unique solution exists, we consider its representation as a complex contour integral that is obtained using a transform method recently proposed by Fokas and one of the authors. The analyticity properties of the integrand in this representation are crucial for studying the spectral theory of the associated operator
Extinction time for a random walk in a random environment
Get PDFWe consider a random walk with death in moving in a time dependent
environment. The environment is a system of particles which
describes
a current flux from to . Its evolution
is influenced by the presence of the random walk and in turns it affects
the jump rates of the random walk in a neighborhood of the endpoints,
determining also the rate for the random
walk to die. We prove an upper bound (uniform in )
for the probability of extinction by time
which goes as , and positive constants