72 research outputs found
Transformation elastodynamics and active exterior acoustic cloaking
This chapter consists of three parts. In the first part we recall the
elastodynamic equations under coordinate transformations. The idea is to use
coordinate transformations to manipulate waves propagating in an elastic
material. Then we study the effect of transformations on a mass-spring network
model. The transformed networks can be realized with "torque springs", which
are introduced here and are springs with a force proportional to the
displacement in a direction other than the direction of the spring terminals.
Possible homogenizations of the transformed networks are presented, with
potential applications to cloaking. In the second and third parts we present
cloaking methods that are based on cancelling an incident field using active
devices which are exterior to the cloaked region and that do not generate
significant fields far away from the devices. In the second part, the exterior
cloaking problem for the Laplace equation is reformulated as the problem of
polynomial approximation of analytic functions. An explicit solution is given
that allows to cloak larger objects at a fixed distance from the cloaking
device, compared to previous explicit solutions. In the third part we consider
the active exterior cloaking problem for the Helmholtz equation in 3D. Our
method uses the Green's formula and an addition theorem for spherical outgoing
waves to design devices that mimic the effect of the single and double layer
potentials in Green's formula.Comment: Submitted as a chapter for the volume "Acoustic metamaterials:
Negative refraction, imaging, lensing and cloaking", Craster and Guenneau
ed., Springe
miR-22 represses cancer progression by inducing cellular senescence
The microRNA miR-22 targets CDK6, SIRT1, and Sp1—genes involved in regulation of the senescence program—to suppress cell growth and proliferation
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