1,775 research outputs found
Wall influence on dynamics of a microbubble
The nonlinear dynamic behaviour of microscopic bubbles near a wall is
investigated. The Keller-Miksis-Parlitz equation is adopted, but modified to
account for the presence of the wall. This base model describes the time
evolution of the bubble surface, which is assumed to remain spherical, and
accounts for the effect of acoustic radiation losses owing to liquid
compressibility in the momentum conservation. Two situations are considered:
the base case of an isolated bubble in an unbounded medium; and a bubble near a
solid wall. In the latter case, the wall influence is modeled by including a
symmetrically oscillating image bubble. The bubble dynamics is traced using a
numerical solution of the model equation. Subsequently, Floquet theory is used
to accurately detect the bifurcation point where bubble oscillations stop
following the driving ultrasound frequency and undergo period-changing
bifurcations. Of particular interest is the detection of the subcritical period
tripling and quadrupling transition. The parametric bifurcation maps are
obtained as functions of non-dimensional parameters representing the bubble
radius, the frequency and pressure amplitude of the driving ultrasound field
and the distance from the wall. It is shown that the presence of the wall
generally stabilises the bubble dynamics, so that much larger values of the
pressure amplitude are needed to generate nonlinear responses.Comment: 25 pages, 14 figure
Birth and growth of cavitation bubbles within water under tension confined in a simple synthetic tree
Water under tension, as can be found in several systems including tree
vessels, is metastable. Cavitation can spontaneously occur, nucleating a
bubble. We investigate the dynamics of spon- taneous or triggered cavitation
inside water filled microcavities of a hydrogel. Results show that a stable
bubble is created in only a microsecond timescale, after transient
oscillations. Then, a diffusion driven expansion leads to filling of the
cavity. Analysis reveals that the nucleation of a bubble releases a tension of
several tens of MPa, and a simple model captures the different time scales of
the expansion process
Resonant Metalenses for Breaking the Diffraction Barrier
We introduce the resonant metalens, a cluster of coupled subwavelength
resonators. Dispersion allows the conversion of subwavelength wavefields into
temporal signatures while the Purcell effect permits an efficient radiation of
this information in the far-field. The study of an array of resonant wires
using microwaves provides a physical understanding of the underlying mechanism.
We experimentally demonstrate imaging and focusing from the far-field with
resolutions far below the diffraction limit. This concept is realizable at any
frequency where subwavelength resonators can be designed.Comment: 4 pages, 3 figure
Bottleneck Routing Games with Low Price of Anarchy
We study {\em bottleneck routing games} where the social cost is determined
by the worst congestion on any edge in the network. In the literature,
bottleneck games assume player utility costs determined by the worst congested
edge in their paths. However, the Nash equilibria of such games are inefficient
since the price of anarchy can be very high and proportional to the size of the
network. In order to obtain smaller price of anarchy we introduce {\em
exponential bottleneck games} where the utility costs of the players are
exponential functions of their congestions. We find that exponential bottleneck
games are very efficient and give a poly-log bound on the price of anarchy:
, where is the largest path length in the
players' strategy sets and is the set of edges in the graph. By adjusting
the exponential utility costs with a logarithm we obtain games whose player
costs are almost identical to those in regular bottleneck games, and at the
same time have the good price of anarchy of exponential games.Comment: 12 page
Modelling acoustic scattering, sound speed, and attenuation in gassy soft marine sediments
Vertex Sparsifiers: New Results from Old Techniques
Given a capacitated graph and a set of terminals ,
how should we produce a graph only on the terminals so that every
(multicommodity) flow between the terminals in could be supported in
with low congestion, and vice versa? (Such a graph is called a
flow-sparsifier for .) What if we want to be a "simple" graph? What if
we allow to be a convex combination of simple graphs?
Improving on results of Moitra [FOCS 2009] and Leighton and Moitra [STOC
2010], we give efficient algorithms for constructing: (a) a flow-sparsifier
that maintains congestion up to a factor of , where , (b) a convex combination of trees over the terminals that maintains
congestion up to a factor of , and (c) for a planar graph , a
convex combination of planar graphs that maintains congestion up to a constant
factor. This requires us to give a new algorithm for the 0-extension problem,
the first one in which the preimages of each terminal are connected in .
Moreover, this result extends to minor-closed families of graphs.
Our improved bounds immediately imply improved approximation guarantees for
several terminal-based cut and ordering problems.Comment: An extended abstract appears in the 13th International Workshop on
Approximation Algorithms for Combinatorial Optimization Problems (APPROX),
2010. Final version to appear in SIAM J. Computin
Resonance regimes of scattering by small bodies with impedance boundary conditions
The paper concerns scattering of plane waves by a bounded obstacle with
complex valued impedance boundary conditions. We study the spectrum of the
Neumann-to-Dirichlet operator for small wave numbers and long wave asymptotic
behavior of the solutions of the scattering problem. The study includes the
case when is an eigenvalue or a resonance. The transformation from the
impedance to the Dirichlet boundary condition as impedance grows is described.
A relation between poles and zeroes of the scattering matrix in the non-self
adjoint case is established. The results are applied to a problem of scattering
by an obstacle with a springy coating. The paper describes the dependence of
the impedance on the properties of the material, that is on forces due to the
deviation of the boundary of the obstacle from the equilibrium position
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