1,441 research outputs found
Superlensing effect of an anisotropic metamaterial slab with near-zero dynamic mass
A metamaterial slab of anisotropic mass with one diagonal component being
infinity and the other being zero is demonstrated to behave as a superlens for
acoustic imaging beyond the diffraction limit. The underlying mechanism for
extraordinary transmission of evanescent waves is attributed to the zero mass
effect. Microstructure design for such anisotropic lens is also presented. In
contrast to the anisotropic superlens based on Fabry-P\'erot resonant
mechanism, the proposed lens operates without the limitation on lens thickness,
thus more flexible in practical applications. Numerical modeling is performed
to validate the proposed ideas.Comment: 4 figure
Optimal output consensus for linear systems: A topology free approach
In this paper, for any homogeneous system of agents with linear continuous
time dynamics, we formulate an optimal control problem. In this problem a
convex cost functional of the control signals of the agents shall be minimized,
while the outputs of the agents shall coincide at some given finite time. This
is an instance of the rendezvous or finite time consensus problem. We solve
this problem without any constraints on the communication topology and provide
a solution as an explicit feedback control law for the case when the dynamics
of the agents is output controllable. It turns out that the communication graph
topology induced by the solution is complete. Based on this solution for the
finite time consensus problem, we provide a solution to the case of infinite
time horizon. Furthermore, we investigate under what circumstances it is
possible to express the controller as a feedback control law of the output
instead of the states.Comment: 8 page
Malliavin calculus for backward stochastic differential equations and application to numerical solutions
In this paper we study backward stochastic differential equations with
general terminal value and general random generator. In particular, we do not
require the terminal value be given by a forward diffusion equation. The
randomness of the generator does not need to be from a forward equation,
either. Motivated from applications to numerical simulations, first we obtain
the -H\"{o}lder continuity of the solution. Then we construct several
numerical approximation schemes for backward stochastic differential equations
and obtain the rate of convergence of the schemes based on the obtained
-H\"{o}lder continuity results. The main tool is the Malliavin calculus.Comment: Published in at http://dx.doi.org/10.1214/11-AAP762 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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