72 research outputs found
Ultrasonic tracking of a sinking ball in a vibrated dense granular suspension
Observing and understanding the movement of an intruder through opaque dense
suspensions such as quicksand remains a practical and conceptual challenge.
Here we use an ultrasonic probe to investigate the dynamics of a steel ball
sinking in a 3D dense glass bead packing saturated by water. We show that the
frictional model developed for dry granular media can be used to describe the
ball motion induced by horizontal vibration. From this rheology we infer the
static friction coefficient and effective viscosity that decrease when
increasing the vibration intensity. Our main finding is that the
vibration-induced reduction of the yield stress and increase of the sinking
depth are presumably due to induced slipping at the grain contacts but without
visible plastic rearrangements of grains, in contrast to dry granular packings.
To explain these results, we propose a mechanism of acoustic lubrication that
reduces the inter-particle friction and leads to a decrease of the yield
stress. This scenario is different from the mechanism of liquefaction usually
invoked in loosely packed quicksands where the vibration-induced compaction
increases the pore pressure and decreases the confining pressure on the solid
skeleton, thus reducing the granular resistance to external load.Comment: 9 pages and 5 figures, plus the supplemental information (1 page, 2
movies, 1 figure
Controlling Light Through Optical Disordered Media : Transmission Matrix Approach
We experimentally measure the monochromatic transmission matrix (TM) of an
optical multiple scattering medium using a spatial light modulator together
with a phase-shifting interferometry measurement method. The TM contains all
information needed to shape the scattered output field at will or to detect an
image through the medium. We confront theory and experiment for these
applications and we study the effect of noise on the reconstruction method. We
also extracted from the TM informations about the statistical properties of the
medium and the light transport whitin it. In particular, we are able to isolate
the contributions of the Memory Effect (ME) and measure its attenuation length
Coherent Backscattering of Light by Cold Atoms
Light propagating in an optically thick sample experiences multiple
scattering. It is now known that interferences alter this propagation, leading
to an enhanced backscattering, a manifestation of weak localization of light in
such diffuse samples. This phenomenon has been extensively studied with
classical scatterers. In this letter we report the first experimental evidence
for coherent backscattering of light in a laser-cooled gas of Rubidium atoms.Comment: 4 pages REVTEX, 1 page color image GIF, accepted for publication in
Phys. Rev. Let
Quasi Two-dimensional Transfer of Elastic Waves
A theory for multiple scattering of elastic waves is presented in a random
medium bounded by two ideal free surfaces, whose horizontal size is infinite
and whose transverse size is smaller than the mean free path of the waves. This
geometry is relevant for seismic wave propagation in the Earth crust. We derive
a time-dependent, quasi-2D radiative transfer equation, that describes the
coupling of the eigenmodes of the layer (surface Rayleigh waves, SH waves, and
Lamb waves). Expressions are found that relate the small-scale fluctuations to
the life time of the modes and to their coupling rates. We discuss a diffusion
approximation that simplifies the mathematics of this model significantly, and
which should apply at large lapse times. Finally, coherent backscattering is
studied within the quasi-2D radiative transfer equation for different source
and detection configurations.Comment: REVTeX, 36 pages with 10 figures. Submitted to Phys. Rev.
Localization of electromagnetic waves in a two dimensional random medium
Motivated by previous investigations on the radiative effects of the electric
dipoles embedded in structured cavities, localization of electromagnetic waves
in two dimensions is studied {\it ab initio} for a system consisting of many
randomly distributed two dimensional dipoles. A set of self-consistent
equations, incorporating all orders of multiple scattering of the
electromagnetic waves, is derived from first principles and then solved
numerically for the total electromagnetic field. The results show that
spatially localized electromagnetic waves are possible in such a simple but
realistic disordered system. When localization occurs, a coherent behavior
appears and is revealed as a unique property differentiating localization from
either the residual absorption or the attenuation effects
Diffusive and localization behavior of electromagnetic waves in a two-dimensional random medium
In this paper, we discuss the transport phenomena of electromagnetic waves in
a two-dimensional random system which is composed of arrays of electrical
dipoles, following the model presented earlier by Erdogan, et al. (J. Opt. Soc.
Am. B {\bf 10}, 391 (1993)). A set of self-consistent equations is presented,
accounting for the multiple scattering in the system, and is then solved
numerically. A strong localization regime is discovered in the frequency
domain. The transport properties within, near the edge of and nearly outside
the localization regime are investigated for different parameters such as
filling factor and system size. The results show that within the localization
regime, waves are trapped near the transmitting source. Meanwhile, the
diffusive waves follow an intuitive but expected picture. That is, they
increase with travelling path as more and more random scattering incurs,
followed by a saturation, then start to decay exponentially when the travelling
path is large enough, signifying the localization effect. For the cases that
the frequencies are near the boundary of or outside the localization regime,
the results of diffusive waves are compared with the diffusion approximation,
showing less encouraging agreement as in other systems (Asatryan, et al., Phys.
Rev. E {\bf 67}, 036605 (2003).)Comment: 8 pages 9 figure
Nonlinear Parabolic Equations arising in Mathematical Finance
This survey paper is focused on qualitative and numerical analyses of fully
nonlinear partial differential equations of parabolic type arising in financial
mathematics. The main purpose is to review various non-linear extensions of the
classical Black-Scholes theory for pricing financial instruments, as well as
models of stochastic dynamic portfolio optimization leading to the
Hamilton-Jacobi-Bellman (HJB) equation. After suitable transformations, both
problems can be represented by solutions to nonlinear parabolic equations.
Qualitative analysis will be focused on issues concerning the existence and
uniqueness of solutions. In the numerical part we discuss a stable
finite-volume and finite difference schemes for solving fully nonlinear
parabolic equations.Comment: arXiv admin note: substantial text overlap with arXiv:1603.0387
- …