Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userQuantum ergodic restriction for Cauchy data: Interior QUE and restricted QUE
134
0
0.0
(
0
)
Ask ChatGPT about the research
No Arabic abstract
We prove a quantum ergodic restriction theorem for the Cauchy data of a sequence of quantum ergodic eigenfunctions on a hypersurface $H$ of a Riemannian manifold $(M, g)$. The technique of proof is to use a Rellich type identity to relate quantum ergodicity of Cauchy data on $H$ to quantum ergodicity of eigenfunctions on the global manifold $M$. This has the interesting consequence that if the eigenfunctions are quantum unique ergodic on the global manifold $M$, then the Cauchy data is automatically quantum unique ergodic on $H$ with respect to operators whose symbols vanish to order one on the glancing set of unit tangential directions to $H$.
rate research
Read More
Visible Light Communications (VLC) is a new paradigm in wireless communications. The characteristics of this technology, which uses light-emitting diode-based lighting devices as transmitting elements, make it possible to be considered a complement to current wireless radio communication systems. ----- Les comunicacions per llum visible o Visible Light Communications (VLC) son un nou paradigma en comunicacions sense fils. Les caracteristiques que presenta aquesta tecnologia, que utilitza els dispositius dil{lgem{}}luminacio basats en diodes emissors de llum com elements transmissors, fa que es pugui considerar un complement dels actuals sistemes de comunicacio inal`ambrics.
We consider an evolution equation with the Caputo-Dzhrbashyan fractional derivative of order $alpha in (1,2)$ with respect to the time variable, and the second order uniformly elliptic operator with variable coefficients acting in spatial variables. This equation describes the propagation of stress pulses in a viscoelastic medium. Its properties are intermediate between those of parabolic and hyperbolic equations. In this paper, we construct and investigate a fundamental solution of the Cauchy problem, prove existence and uniqueness theorems for such equations.
We analyze the analytic Landau damping problem for the Vlasov-HMF equation, by fixing the asymptotic behavior of the solution. We use a new method for this scattering problem, closer to the one used for the Cauchy problem. In this way we are able to compare the two results, emphasizing the different influence of the plasma echoes in the two approaches. In particular, we prove a non-perturbative result for the scattering problem.
The contents of the paper is now covered in two separate papers arXiv:0904.2188 and arXiv:0904.2602. Please refer to those. Note that you can still access the original version arXiv:0711.4082v1.
We introduce a fundamental restriction on the strain energy function and stress tensor for initially stressed elastic solids. The restriction applies to strain energy functions $W$ that are explicit functions of the elastic deformation gradient $mathbf{F}$ and initial stress $boldsymbol tau$, i.e. $W:= W(mathbf F, boldsymbol tau)$. The restriction is a consequence of energy conservation and ensures that the predicted stress and strain energy do not depend upon an arbitrary choice of reference configuration. We call this restriction: initial stress reference independence (ISRI). It transpires that almost all strain energy functions found in the literature do not satisfy ISRI, and may therefore lead to unphysical behaviour, which we illustrate via a simple example. To remedy this shortcoming we derive three strain energy functions that do satisfy the restriction. We also show that using initial strain (often from a virtual configuration) to model initial stress leads to strain energy functions that automatically satisfy ISRI. Finally, we reach the following important result: ISRI reduces the number of unknowns of the linear stress tensor of initially stressed solids. This new way of reducing the linear stress may open new pathways for the non-destructive determination of initial stresses via ultrasonic experiments, among others.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
