1,852 research outputs found
Numerical estimation of derivatives with an application to radiative transfer in spherical shells
Numerical estimation of derivatives with application to radiative transfer in spherical shell
Decision-making in a fuzzy environment
Decision making where goals or constraints are not sharply defined boundaries and fuzzy using dynamic programmin
Invariant imbedding and perturbation techniques applied to diffuse reflection from spherical shells
Invariant imbedding and perturbation techniques applied to diffuse reflection from spherical shell
Estimation of internal source distributions using external field measurements in radiative transfer
Intensity of emergent radiation for finite homogeneous slab which absorbs radiation and scatters it isotropicall
The invariant imbedding equation for the dissipation function of a homogeneous finite slab
Differential-integral equation for dissipation function and derivation of conservation relationship connecting reflection, transmission and dissipation functions of finite sla
Analytic calculation of energies and wave functions of the quartic and pure quartic oscillators
Ground state energies and wave functions of quartic and pure quartic
oscillators are calculated by first casting the Schr\"{o}dinger equation into a
nonlinear Riccati form and then solving that nonlinear equation analytically in
the first iteration of the quasilinearization method (QLM). In the QLM the
nonlinear differential equation is solved by approximating the nonlinear terms
by a sequence of linear expressions. The QLM is iterative but not perturbative
and gives stable solutions to nonlinear problems without depending on the
existence of a smallness parameter. Our explicit analytic results are then
compared with exact numerical and also with WKB solutions and it is found that
our ground state wave functions, using a range of small to large coupling
constants, yield a precision of between 0.1 and 1 percent and are more accurate
than WKB solutions by two to three orders of magnitude. In addition, our QLM
wave functions are devoid of unphysical turning point singularities and thus
allow one to make analytical estimates of how variation of the oscillator
parameters affects physical systems that can be described by the quartic and
pure quartic oscillators.Comment: 8 pages, 12 figures, 1 tabl
Negativity as a distance from a separable state
The computable measure of the mixed-state entanglement, the negativity, is
shown to admit a clear geometrical interpretation, when applied to
Schmidt-correlated (SC) states: the negativity of a SC state equals a distance
of the state from a pertinent separable state. As a consequence, a SC state is
separable if and only if its negativity vanishes. Another remarkable
consequence is that the negativity of a SC can be estimated "at a glance" on
the density matrix. These results are generalized to mixtures of SC states,
which emerge in certain quantum-dynamical settings.Comment: 9 pages, 1 figur
Stabilizing unstable periodic orbits in the Lorenz equations using time-delayed feedback control
For many years it was believed that an unstable periodic orbit with an odd
number of real Floquet multipliers greater than unity cannot be stabilized by
the time-delayed feedback control mechanism of Pyragus. A recent paper by
Fiedler et al uses the normal form of a subcritical Hopf bifurcation to give a
counterexample to this theorem. Using the Lorenz equations as an example, we
demonstrate that the stabilization mechanism identified by Fiedler et al for
the Hopf normal form can also apply to unstable periodic orbits created by
subcritical Hopf bifurcations in higher-dimensional dynamical systems. Our
analysis focuses on a particular codimension-two bifurcation that captures the
stabilization mechanism in the Hopf normal form example, and we show that the
same codimension-two bifurcation is present in the Lorenz equations with
appropriately chosen Pyragus-type time-delayed feedback. This example suggests
a possible strategy for choosing the feedback gain matrix in Pyragus control of
unstable periodic orbits that arise from a subcritical Hopf bifurcation of a
stable equilibrium. In particular, our choice of feedback gain matrix is
informed by the Fiedler et al example, and it works over a broad range of
parameters, despite the fact that a center-manifold reduction of the
higher-dimensional problem does not lead to their model problem.Comment: 21 pages, 8 figures, to appear in PR
Answer Set Programming for Non-Stationary Markov Decision Processes
Non-stationary domains, where unforeseen changes happen, present a challenge
for agents to find an optimal policy for a sequential decision making problem.
This work investigates a solution to this problem that combines Markov Decision
Processes (MDP) and Reinforcement Learning (RL) with Answer Set Programming
(ASP) in a method we call ASP(RL). In this method, Answer Set Programming is
used to find the possible trajectories of an MDP, from where Reinforcement
Learning is applied to learn the optimal policy of the problem. Results show
that ASP(RL) is capable of efficiently finding the optimal solution of an MDP
representing non-stationary domains
Gigantic transmission band edge resonance in periodic stacks of anisotropic layers
We consider Fabry-Perot cavity resonance in periodic stacks of anisotropic
layers with misaligned in-plane anisotropy at the frequency close to a photonic
band edge. We show that in-plane dielectric anisotropy can result in a dramatic
increase in field intensity and group delay associated with the transmission
resonance. The field enhancement appears to be proportional to forth degree of
the number N of layers in the stack. By contrast, in common periodic stacks of
isotropic layers, those effects are much weaker and proportional to N^2. Thus,
the anisotropy allows to drastically reduce the size of the resonance cavity
with similar performance. The key characteristic of the periodic arrays with
the gigantic transmission resonance is that the dispersion curve omega(k)at the
photonic band edge has the degenerate form Delta(omega) ~ Delta(k)^4, rather
than the regular form Delta(omega) ~ Delta(k)^2. This can be realized in
specially arranged stacks of misaligned anisotropic layers. The degenerate band
edge cavity resonance with similar outstanding properties can also be realized
in a waveguide environment, as well as in a linear array of coupled multimode
resonators, provided that certain symmetry conditions are in place.Comment: To be submitted to Phys. Re
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