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Observation of self-accelerating Bessel-like optical beams along arbitrary trajectories
Get PDFWe experimentally demonstrate self-accelerating Bessel-like optical beams propagating along arbitrary trajectories in free space. With computer generated holography, such beams are designed to follow different controllable trajectories while their main lobe transverse profiles remain nearly invariant and symmetric. Examples include parabolic, snake-like, hyperbolic, hyperbolic secant, and even three-dimensional spiraling trajectories. The self-healing property of such beams is also demonstrated. This new class of optical beams can be considered as a hybrid between accelerating and non-accelerating nondiffracting beams that may find a variety of applications
BPX-Preconditioning for isogeometric analysis
Get PDFWe consider elliptic PDEs (partial differential equations) in the framework of isogeometric analysis, i.e., we treat the physical domain by means of a B-spline or Nurbs mapping which we assume to be regular. The numerical solution of the PDE is computed by means of tensor product B-splines mapped onto the physical domain. We construct additive multilevel preconditioners and show that they are asymptotically optimal, i.e., the spectral condition number of the resulting preconditioned stiffness matrix is independent of . Together with a nested iteration scheme, this enables an iterative solution scheme of optimal linear complexity. The theoretical results are substantiated by numerical examples in two and three space dimensions
A quantitative study of source imaging in random waveguides
Get PDFWe present a quantitative study of coherent array imaging of remote
sources in randomly perturbed waveguides with bounded cross-section.\ud
We study how long range cumulative scattering by perturbations of
the boundary and the medium impedes the imaging process. We show
that boundary scattering effects can be mitigated with filters that
enhance the coherent part of the data. The filters are obtained by
optimizing a measure of quality of the image. The point is that
there is an optimal trade-off between the robustness and resolution
of images in such waveguides, which can be found adaptively, as the
data are processed to form the image. Long range scattering by
perturbations of the medium is harder to mitigate than scattering by randomly
perturbed boundaries. Coherent imaging
methods do not work and more complex incoherent methods, based on
transport models of energy, should be used instead. Such methods are
nor useful, nor needed in waveguides with perturbed boundaries. We
explain all these facts using rigorous asymptotic stochastic
analysis of the wave field in randomly perturbed waveguides. We
also analyze the adaptive coherent imaging method and obtain a
quantitative agreement with the results of numerical simulations
New formulas for Maslov's canonical operator in a neighborhood of focal points and caustics in 2D semiclassical asymptotics
Get PDFWe suggest a new representation of Maslov’s canonical operator in a neighborhood of caustics using a
special class of coordinate systems (eikonal coordinates) on Lagrangian manifolds. We present the results
in the two-dimensional case and illustrate them with examples
Dynamic Heterogeneity in Fully Miscible Blends of Polystyrene with Oligostyrene
Get PDFBinary blends of polystyrene with oligostyrene are perfectly miscible (χ=0) yet dynamically heterogeneous. This is evidenced by independent probing of the dipole relaxation perpendicular to the backbone by dielectric spectroscopy and molecular dynamics. The self-concentration model with a single intra-molecular length scale qualitatively describes the slower segmental dynamics. A quantitative comparison based on MD however, requires a composition-dependent length scale. The pertinent dynamic length scale that best describes the slow segmental dynamics in miscible blends relates to both intra- and inter-molecular contributions
On the Generalization of the Hébraud-Lequeux Model to Multidimensional Flows
Get PDFIn this article we build a model for multidimensional flows based on the idea of Hébraud and Lequeux for soft glassy materials. Care is taken to build a frame indifferent multi-dimensional model.
The main goal of this article is to prove that the methodology we have developed to study the well-posedness and the glass transition for the original Hébraud-Lequeux model can be successfully generalized. Thus this work may be used as a starting point for more sophisticated studies in the modeling of general flows of glassy materials
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
Singular limiting induced from continuum solutions and the problem of dynamic cavitation
Get PDFIn the works of
K.A. Pericak-Spector and S. Spector [Pericak-Spector, Spector 1988, 1997] a class of self-similar
solutions are constructed for the equations of radial isotropic elastodynamics
that describe cavitating solutions. Cavitating solutions decrease the total
mechanical energy and provide a striking example of non-uniqueness of entropy weak solutions
(for polyconvex energies) due to point-singularities at the cavity. To resolve
this paradox, we introduce the concept of singular limiting induced from continuum solution (or slic-solution),
according to which a discontinuous motion is a slic-solution if its averages
form a family of smooth approximate solutions to the problem. It turns out that there is an energetic cost for
creating the cavity, which is captured by the notion of slic-solution but neglected by the
usual entropic weak solutions. Once this cost is accounted for, the total mechanical energy of the
cavitating solution is in fact larger than that of the homogeneously deformed state.
We also apply the notion of slic-solutions to a one-dimensional example describing the onset of fracture,
and to gas dynamics in Langrangean coordinates with Riemann data inducing vacuum in the wave fan
Simulated acoustic emissions from coupled strings
Get PDFWe consider traveling transverse waves on two identical uniform taut strings that are elastically coupled through springs that gradually decrease their stiffness over a region of finite length. The wave system can be decomposed into two modes: an in-phase mode ( + ) that is transparent to the coupling springs, and an out-of-phase mode ( − ) that engages the coupling springs and can resonate at a particular location depending on the excitation frequency. The system exhibits linear mode conversion whereby an incoming ( + ) wave is reflected back from the resonance location both as a propagating ( + ) wave and an evanescent ( − ) wave, while both types emerge as propagating forward through the resonance location. We match a local transition layer expansion to the WKB expansion to obtain estimates of the reflection and transmission coefficients. The reflected waves may be an analog for stimulated emissions from the ear
Inversion of acoustical data from the SW06 experiment, using a statistical method for signal characterization
Get PDFhis paper presents an application of an acoustic signal characterization scheme for ocean acoustic tomography and geoacoustic inversions proposed by Taroudakis et al., using real data. The work is the first attempt to validate the proposed scheme with data taken from sea experiments. The data have been collected during the SW06 experiment held in the New Jersey Continental Shelf and the inversion results (sea-bed geoacoustic parameters and source range) are compared with those reported by Bonnel and Chapman. The comparison and the signal reconstruction using estimated values of the model parameters is satisfactory being an indication that the new signal characterization method can be used in practical applications of acoustical oceanography