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Nonparaxial accelerating Bessel-like beams
Get PDFA new class of nonparaxial accelerating optical waves is introduced. These are beams with a Bessel-like profile that are capable of shifting laterally along fairly arbitrary trajectories as the wave propagates in free space. The concept expands on our previous proposal of paraxial accelerating Bessel-like beams to include beams with subwavelength lobes and/or large trajectory angles. Such waves are produced when the phase at the input plane is engineered so that the interfering ray cones are made to focus along the prespecified path. When the angle of these cones is fixed, the beams possess a diffraction-free Bessel profile on planes that stay normal to their trajectory, which can be considered as a generalized definition of diffractionless propagation in the nonparaxial regime. The analytical procedure leading to these results is based on a ray optics interpretation of Rayleigh-Sommerfeld diffraction and is presented in detail. The evolution of the proposed waves is demonstrated through a series of numerical examples and a variety of trajectories
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
Hierarchical multiscale modeling of polymer-solid interfaces: atomistic to coarse-grained description, and structural and conformational properties of polystyrene-gold systems
Get PDFA hierarchical simulation approach was developed in order to study polystyrene films sandwiched between two parallel Au(111) surfaces. The coarse-grained potentials describing the interaction of polystyrene with the gold surface were developed systematically using constrained
all-atom molecular simulations of a styrene trimer on the Au(111) surface. The model was validated by studying a 5 nm film of short (10mer) polystyrene chains using all-atom and
coarse-grained molecular dynamics simulations. The density, structure and conformational properties of coarse-grained films were found to be in excellent agreement with all-atom ones. The coarse-grained model was then used to study the structural and conformational properties of roughly 10 nm and 20 nm thick films with 10, 50, 100 and 200mer chains. The width of the interphase region of the polymer films is property specific. The density profiles reached the
bulk value around 1.5 nm from the interface, for all chain lengths. An estimate of the width of the interphase region based on the conformation tensor profile indicates that the interphase width is proportional to the square root of the chain length (number of monomers) and for 200mer chains the interphase width is approximately 6-9 nm
A relative entropy rate method for path space sensitivity analysis of stationary complex stochastic dynamics
Get PDFA compressible mixture model with phase transition
Get PDFWe introduce a new thermodynamically consistent diffuse interface model of Allen--Cahn/Navier--Stokes type for multi-component flows with phase transitions and chemical reactions.
For the introduced diffuse interface model, we investigate physically admissible sharp interface limits by matched asymptotic techniques.
We consider two scaling regimes, i.e.~a non-dissipative and a dissipative regime, where we recover in the sharp interface limit a generalized
Allen-Cahn/Euler system for mixtures with chemical
reactions in the bulk phases equipped with admissible interfacial conditions. The interfacial conditions satify, for instance, a Young--Laplace and a Stefan type law
Monitoring the sea environment using acoustics the role of the acoustical observatories
Get PDFThe presentation deals with theoretical factors and technical specifications pertinent to the design of an acoustical observatory for the monitoring of the marine environment. Two types of observatories are mentioned, namely active and passive. Among the various cases of active observatories, the ones related to ocean acoustic tomography are presented in some detail and the inverse problem of retrieving information from measured acoustic data is explained. Some basic issues related to the type of measurements that should be made for optimal use of the acoustic field are also given with related references. Finally, the basic features of passive observatories are underlined without going into details
Implicitization of curves and (hyper)surfaces using predicted support
Get PDFWe reduce implicitization of rational planar parametric curves and (hyper)surfaces to linear algebra, by interpolating the coefficients of the implicit equation.
For predicting the implicit support, we focus on methods that exploit input and output structure in the sense of sparse (or toric) elimination theory, namely by computing the Newton polytope of the implicit polynomial, via sparse resultant theory.
Our algorithm works even in the presence of base points but, in this case, the implicit equation shall be obtained as a factor of the produced polynomial.
We implement our methods on Maple, and some on Matlab as well, and study their numerical stability and efficiency on several classes of curves and surfaces.
We apply our approach to approximate implicitization,
and quantify the accuracy of the approximate output,
which turns out to be satisfactory on all tested examples; we also relate our measures to Hausdorff distance.
In building a square or rectangular matrix, an important issue is (over)sampling the given curve or surface: we conclude that unitary complexes offer the best tradeoff between speed and accuracy when numerical methods are employed, namely SVD, whereas for exact kernel computation random integers is the method of choice.
We compare our prototype to existing software and find that it is rather competitive
A note on perfect revivals in finite waveguide arrays
Get PDFWe propose a simple and algorithmic method for designing finite waveguide arrays capable of diffractionless transmission of arbitrary discrete beams by virtue of perfect revivals. Our approach utilizes an inverse matrix eignevalue theorem published by Hochstadt in 1974, which states that the Jacobi matrix, describing the system’s discrete evolution equations, is uniquely determined by its eigenvalues and the eigenvalues of its largest leading principal submatrix, as long as the two sets of eigenvalues interlace. It is further shown that, by arranging the two sets of eigenvalues symmetrically with respect to zero, the resulting Jacobi matrix has zero diagonal elements. Therefore, arrays with arbitrary revival lengths can be obtained by engineering only the inter-waveguide couplings
Relative entropy in diffusive relaxation
Get PDFWe establish convergence in the diffusive limit from entropy weak solutions of
the equations of compressible gas dynamics with friction to the porous media equation away from vacuum.
The result is based on a Lyapunov type of functional provided by a calculation of the relative entropy.
The relative entropy method is also employed to establish convergence from entropic weak solutions
of viscoelasticity with memory to the system of viscoelasticity of the rate-type