8,686 research outputs found
Reconstruction of annular bi-layered media in cylindrical waveguide section
A radial transverse resonance model for two cylindrical concentric layers
with different complex dielectric constants is presented. An inverse problem
with four unknowns - 3 physical material parameters and one dimensional
dielectric layer thickness parameter- is solved by employing TE110 and TE210
modes with different radial field distribution. First a Newton-Raphson
algorithm is used to solve a least square problem with a Lorentzian function
(as resonance model and "measured" data generator). Then found resonance
frequencies and quality factors are used in a second inverse Newton-Raphson
algorithm that solves four transverse resonance equations in order to get four
unknown parameters. The use of TE110 and TE210 models offers one dimensional
radial tomographic capability. An open ended coax quarter-wave resonator is
added to the sensor topology, and the effect on the convergence is
investigated
Limit Your Consumption! Finding Bounds in Average-energy Games
Energy games are infinite two-player games played in weighted arenas with
quantitative objectives that restrict the consumption of a resource modeled by
the weights, e.g., a battery that is charged and drained. Typically, upper
and/or lower bounds on the battery capacity are part of the problem
description. Here, we consider the problem of determining upper bounds on the
average accumulated energy or on the capacity while satisfying a given lower
bound, i.e., we do not determine whether a given bound is sufficient to meet
the specification, but if there exists a sufficient bound to meet it.
In the classical setting with positive and negative weights, we show that the
problem of determining the existence of a sufficient bound on the long-run
average accumulated energy can be solved in doubly-exponential time. Then, we
consider recharge games: here, all weights are negative, but there are recharge
edges that recharge the energy to some fixed capacity. We show that bounding
the long-run average energy in such games is complete for exponential time.
Then, we consider the existential version of the problem, which turns out to be
solvable in polynomial time: here, we ask whether there is a recharge capacity
that allows the system player to win the game.
We conclude by studying tradeoffs between the memory needed to implement
strategies and the bounds they realize. We give an example showing that memory
can be traded for bounds and vice versa. Also, we show that increasing the
capacity allows to lower the average accumulated energy.Comment: In Proceedings QAPL'16, arXiv:1610.0769
The Non-Classical Boltzmann Equation, and Diffusion-Based Approximations to the Boltzmann Equation
We show that several diffusion-based approximations (classical diffusion or
SP1, SP2, SP3) to the linear Boltzmann equation can (for an infinite,
homogeneous medium) be represented exactly by a non-classical transport
equation. As a consequence, we indicate a method to solve diffusion-based
approximations to the Boltzmann equation via Monte Carlo, with only statistical
errors - no truncation errors.Comment: 16 pages, 3 figure
Limiting absorption principle and radiation conditions for Schr\"odinger operators with long-range potentials
We show Rellich's theorem, the limiting absorption principle, and a
Sommerfeld uniqueness result for a wide class of one-body Schr\"odinger
operators with long-range potentials, extending and refining previously known
results. Our general method is based on elementary commutator estimates,
largely following the scheme developed recently by Ito and Skibsted
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