Methodology for the Assessment of Imprecise Multi-State System Availability

Most existing studies of a system’s availability in the presence of epistemic uncertainties assume that the system is binary. In this paper, a new methodology for the estimation of the availability of multi-state systems is developed, taking into consideration epistemic uncertainties. This paper formulates a combined approach, based on continuous Markov chains and interval contraction methods, to address the problem of computing the availability of multi-state systems with imprecise failure and repair rates. The interval constraint propagation method, which we refer to as the forward–backward propagation (FBP) contraction method, allows us to contract the probability intervals, keeping all the values that may be consistent with the set of constraints. This methodology is guaranteed, and several numerical examples of systems with complex architectures are studied.

On discrete weighted Hardy type inequalities and properties of weighted discrete Muckenhoupt classes

In this paper, first we prove some new refinements of discrete weighted inequalities with negative powers on finite intervals. Next, by employing these inequalities, we prove that the self-improving property (backward propagation property) of the weighted discrete Muckenhoupt classes holds. The main results give exact values of the limit exponents as well as the new constants of the new classes. As an application, we establish the self-improving property (forward propagation property) of the discrete Gehring class.

Single-Sensor EMI Source Localization Using Time Reversal: An Experimental Validation

The localization of electromagnetic interference (EMI) sources is of high importance in electromagnetic compatibility applications. Recently, a novel localization technique based on the time-reversal cavity (TRC) concept was proposed using only one sensor, and its application to localize EMI sources was validated numerically. In this paper, we present a validation of the proposed time-reversal process in which the forward step of the time-reversal process is performed experimentally and the backward step is carried out via numerical simulations, a realistic scenario which is applicable to practical source localization problems. To the best of the authors’ knowledge, this is the first implementation of a three-dimensional electromagnetic time-reversal process in which the forward signal is provided experimentally while the backward propagation step is carried out numerically. The considered experimental setup is formed by a partially open cavity and two monopole antennas to emulate the EMI source and the sensor (receiving antenna), respectively. Assuming that the location of the source is the feed point of the monopole antenna, the resulting three-dimensional location error in the experimental validation was only 1.49 cm, which is about one-third the length of the monopole antenna, corresponding to about λmin/2 (diffraction limit).

Memory-efficient source wavefield reconstruction and its application to 3D reverse time migration

Reverse time migration (RTM) generally uses the zero-lag crosscorrelation imaging condition, requiring the source and receiver wavefields to be known at the same time step. However, the receiver wavefield is calculated in time-reversed order, opposite to the order of the forward-propagated source wavefield. The inconvenience can be resolved by storing the source wavefield on a computer memory/disk or by reconstructing the source wavefield on the fly for multiplication with the receiver wavefield. The storage requirements for the former approach can be very large. Hence, we have followed the latter route and developed an efficient source wavefield reconstruction method. During forward propagation, the boundary wavefields at N layers of the spatial grid points and a linear combination of wavefields at M − N layers of the spatial grid points are stored. During backward propagation, it reconstructs the source wavefield using the saved wavefields based on a new finite-difference stencil ( M is the operator length parameter, and 0 ≤ N ≤ M). Unlike existing methods, our method allows a trade-off between accuracy and storage by adjusting N. A maximum-norm-based objective function is constructed to optimize the reconstruction coefficients based on the minimax approximation using the Remez exchange algorithm. Dispersion and stability analyses reveal that our method is more accurate and marginally less stable than the method that requires storage of a combination of boundary wavefields. Our method has been applied to 3D RTM on synthetic and field data. Numerical examples indicate that our method with N = 1 can produce images that are close to those obtained using a conventional method of storing M layers of boundary wavefields. The memory usage of our method is ( N + 1)/ M times that of the conventional method.

Study of Forward and Backward Modes in Double-Sided Dielectric-Filled Corrugated Waveguides

This work studies the propagation characteristics of a rectangular waveguide with aligned/ misaligned double-sided dielectric-filled metallic corrugations. Two modes are found to propagate in the proposed double-sided configuration below the hollow-waveguide cutoff frequency: a quasi-resonant mode and a backward mode. This is in contrast to the single-sided configuration, which only allows for backward propagation. Moreover, the double-sided configuration can be of interest for waveguide miniaturization on account of the broader band of its backward mode. The width of the stopband between the quasi-resonant and backward modes can be controlled by the misalignment of the top and bottom corrugations, being null for the glide-symmetric case. The previous study is complemented with numerical results showing the impact of the height of the corrugations, as well as the filling dielectric permittivity, on the bandwidth and location of the appearing negative-effective-permeability band. The multi-modal transmission-matrix method has also been employed to estimate the rejection level and material losses in the structure and to determine which port modes are associated with the quasi-resonant and backward modes. Finally, it is shown that glide symmetry can advantageously be used to reduce the dispersion and broadens the operating band of the modes.

Reciprocating propagation of laser pulse intensity in free space

Constant-speed straight-line propagation in free space is a basic characteristic of light, and spatiotemporal couplings recently were used to control light propagation. In the method of flying focus, where temporal chirp and longitudinal chromatism were combined, tunable-velocities and even backward-propagation were demonstrated. We studied the transverse and longitudinal effects of the flying focus in space-time and found in a specific physics interval existing an unusual reciprocating propagation that was quite different from the previous result. By increasing the Rayleigh length in space and the temporal chirp in time, the created flying focus can propagate along a longitudinal axis firstly forward, secondly backward, and lastly forward again, and the longitudinal spatial resolution improves with increasing the temporal chirp. When this light is applied in a radiation pressure simulation, a reciprocating radiation-force can be produced accordingly. This finding extends the control of light and might enable important potential applications.

Direct Optimal Control Approach to Laser-Driven Quantum Particle Dynamics

Optimal control theory is usually formulated as an indirect method requiring the solution of a two-point boundary value problem. Practically, the solution is obtained by iterative forward and backward propagation of quantum wavepackets. Here, we propose direct optimal control as a robust and flexible alternative. It is based on a discretization of the dynamical equations resulting in a nonlinear optimization problem. The method is illustrated for the case of laser-driven wavepacket dynamics in a bistable potential. The wavepacket is parameterized in terms of a single Gaussian function and field optimization is performed for a wide range of particle masses and lengths of the control interval. Using the optimized field in a full quantum propagation still yields reasonable control yields for most of the considered cases. Analysis of the deviations leads to conditions which have to be fulfilled to make the semiclassical single Gaussian approximation meaningful for field optimization.

A framework for modeling and assessing system resilience using a Bayesian network : a case study of an interdependent electrical infrastructure systems

This research utilizes Bayesian network to address a range of possible risks to the electrical power system and its interdependent networks (EIN) and offers possible options to mitigate the consequences of a disruption. The interdependent electrical infrastructure system in Washington, D.C. is used as a case study to quantify the resilience using the Bayesian network. Quantification of resilience is further analyzed based on different types of analysis such as forward propagation, backward propagation, sensitivity analysis, and information theory. The general insight drawn from these analyses indicate that reliability, backup power source, and resource restoration are the prime factors contributed towards enhancing the resilience of an interdependent electrical infrastructure system.

Nonreciprocal second harmonic generation in a magnetoelectric material

Mirror symmetries are of particular importance because they are connected to fundamental properties and conservation laws. Spatial inversion and time reversal are typically associated to charge and spin phenomena, respectively. When both are broken, magnetoelectric cross-coupling can arise. In the optical regime, a difference between forward and backward propagation of light may result. Usually, this nonreciprocal response is small. We show that a giant nonreciprocal optical response can occur when transferring from linear to nonlinear optics, specifically second harmonic generation (SHG). CuB2O4 exhibits SHG transmission changes by almost 100% upon reversal of a magnetic field of just ±10 mT. The observed nonreciprocity results from an interference between magnetic-dipole and electric-dipole SHG. Although the former is inherently weaker than the latter, a resonantly enhanced magnetic-dipole transition has a comparable amplitude as a nonresonant electric-dipole transition, thus maximizing the nonreciprocity. Multiferroics and magnetoelectrics are an obvious materials platform to exhibit nonreciprocal nonlinear optical functionalities.