Inverse design of layered periodic wave barriers based on deep learning

This study presents an approach based on deep learning to design layered periodic wave barriers with consideration of typical range of soil parameters. Three cases are considered where P wave and S wave exist separately or simultaneously. The deep learning model is composed of an autoencoder with a pretrained decoder which has three branches to output frequency attenuation domains for three different cases. A periodic activation function is used to improve the design accuracy, and condition variables are applied in the code layer of the autoencoder to meet the requirements of practical multi working conditions. Forty thousand sets of data are generated to train, validate, and test the model, and the designed results are highly consistent with the targets. The presented approach has great generality, feasibility, rapidity, and accuracy on designing layered periodic wave barriers which exhibit good performance in wave suppression in targeted frequency range.

Collision rate ansatz for quantum integrable systems

For quantum integrable systems the currents averaged with respect to a generalized Gibbs ensemble are revisited. An exact formula is known, which we call ``collision rate ansatz". While there is considerable work to confirm this ansatz in various models, our approach uses the symmetry of the current-charge susceptibility matrix, which holds in great generality. Besides some technical assumptions, the main input is the availability of a self-conserved current, i.e. some current which is itself conserved. The collision rate ansatz is then derived. The argument is carried out in detail for the Lieb-Liniger model and the Heisenberg XXZ chain. It is also explained how from the existence of a boost operator a self-conserved current can be deduced.

Associate Submersions and Qualitative Properties of Nonlinear Circuits with Implicit Characteristics

We introduce in this paper an equivalence notion for submersions [Formula: see text], [Formula: see text] open in [Formula: see text], which makes it possible to identify a smooth planar curve with a unique class of submersions. This idea, which extends to the nonlinear setting the construction of a dual projective space, provides a systematic way to handle global implicit descriptions of smooth planar curves. We then apply this framework to model nonlinear electrical devices as classes of equivalent functions. In this setting, linearization naturally accommodates incremental resistances (and other analogous notions) in homogeneous terms. This approach, combined with a projectively-weighted version of the matrix-tree theorem, makes it possible to formulate and address in great generality several problems in nonlinear circuit theory. In particular, we tackle unique solvability problems in resistive circuits, and discuss a general expression for the characteristic polynomial of dynamic circuits at equilibria. Previously known results, which were derived in the literature under unnecessarily restrictive working assumptions, are simply obtained here by using dehomogenization. Our results are shown to apply also to circuits with memristors. We finally present a detailed, graph-theoretic study of certain stationary bifurcations in nonlinear circuits using the formalism here introduced.

Interpolation by sums of series of exponentials and global Cauchy problem for convolution operators

The study is made of the problem of multiple interpolation on an infinite nodes set by the sums of absolutely convergent series of exponentials whose exponents are from a given set. For entire function conditions on nodes and exponents are obtained that give solubility of the problem. A new approach is demonstrated that enable us, for the case of holomorphic function in a domain, to obtain criteria of solubility of the problem for some class of exponents set and for a special class of nodes set. Moreover the necessity of the conditions is proved in great generality namely for arbitrary nodes sets and in the setting of interpolation by functions that are represented as the Laplace transforms of the Radon measures over the exponents set. Solubility is obtained of the global Cauchy problem for convolution operator with data on the nodes set in domain, in the form of the series of exponentials whose exponents belong to a sparse subset of zero set of characteristic function of the operator. The results substantially strengthen the known results on the theme.

Features of constrained entropic functional variational problems

We describe in great generality features concerning constrained entropic, functional variational problems that allow for a broad range of applications. Our discussion encompasses not only entropies but, potentially, any functional of the probability distribution, like Fisher-information or relative entropies, etc. In particular, in dealing with generalized statistics in straightforward fashion one may sometimes find that the celebrated relation between entropic small changes and mean energy ones, [Formula: see text], does not seems respected. We show here that, on the contrary, it is indeed obeyed by any system subject to a Legendre extremization process, i.e. in all constrained entropic variational problems.

On Finsler Geometry and Applications in Mechanics: Review and New Perspectives

In Finsler geometry, each point of a base manifold can be endowed with coordinates describing its position as well as a set of one or more vectors describing directions, for example. The associated metric tensor may generally depend on direction as well as position, and a number of connections emerge associated with various covariant derivatives involving affine and nonlinear coefficients. Finsler geometry encompasses Riemannian, Euclidean, and Minkowskian geometries as special cases, and thus it affords great generality for describing a number of phenomena in physics. Here, descriptions of finite deformation of continuous media are of primary focus. After a review of necessary mathematical definitions and derivations, prior work involving application of Finsler geometry in continuum mechanics of solids is reviewed. A new theoretical description of continua with microstructure is then outlined, merging concepts from Finsler geometry and phase field theories of materials science.

Fault Detection System Overall Design for Artillery Control Device

We designed the fault detection equipment for artillery cotrol device, and the performances and faults of the three subsystems can be detected, according to their signal characteristics. In this fault detcetion system, the MCU is used as the master controller, and the A/D conversion chip MAX197 is applied to acquisit and convers data. The data will be processed by the MCU, then be transfered to LCD intelligent terminal through serial port, and finally be displayed and preserved in the terminal. This detection system can complete data acquisition and real-time fault detection, locating the faults to the specific parts. It can also provide expert maintenance proposal in the three subsystems of artillery control device. Besides, this system has great generality and practicability, and it is convenient for upgrating and reforming.

Efficient Simulation for the Maximum of Infinite Horizon Discrete-Time Gaussian Processes

We consider the problem of estimating the probability that the maximum of a Gaussian process with negative mean and indexed by positive integers reaches a high level, sayb. In great generality such a probability converges to 0 exponentially fast in a power ofb. Under mild assumptions on the marginal distributions of the process and no assumption on the correlation structure, we develop an importance sampling procedure, called the target bridge sampler (TBS), which takes a polynomial (inb) number of function evaluations to achieve a small relative error. The procedure also yields samples of the underlying process conditioned on hittingbin finite time. In addition, we apply our method to the problem of estimating the tail of the maximum of a superposition of a large number,n, of independent Gaussian sources. In this situation TBS achieves a prescribed relative error with a bounded number of function evaluations asn↗ ∞. A remarkable feature of TBS is that it isnotbased on exponential changes of measure. Our numerical experiments validate the performance indicated by our theoretical findings.

Efficient Simulation for the Maximum of Infinite Horizon Discrete-Time Gaussian Processes

We consider the problem of estimating the probability that the maximum of a Gaussian process with negative mean and indexed by positive integers reaches a high level, sayb. In great generality such a probability converges to 0 exponentially fast in a power ofb. Under mild assumptions on the marginal distributions of the process and no assumption on the correlation structure, we develop an importance sampling procedure, called the target bridge sampler (TBS), which takes a polynomial (inb) number of function evaluations to achieve a small relative error. The procedure also yields samples of the underlying process conditioned on hittingbin finite time. In addition, we apply our method to the problem of estimating the tail of the maximum of a superposition of a large number,n, of independent Gaussian sources. In this situation TBS achieves a prescribed relative error with a bounded number of function evaluations asn↗ ∞. A remarkable feature of TBS is that it isnotbased on exponential changes of measure. Our numerical experiments validate the performance indicated by our theoretical findings.

FORECAST ERRORS IN SERVICE SYSTEMS

We investigate the presence and impact of forecast errors in the arrival rate of customers to a service system. Analysis of a large dataset shows that forecast errors can be large relative to the fluctuations naturally expected in a Poisson process. We show that ignoring forecast errors typically leads to overestimates of performance and that forecast errors of the magnitude seen in our dataset can have a practically significant impact on predictions of long-run performance. We also define short-run performance as the random percentage of calls received in a particular period that are answered in a timely fashion. We prove a central limit theorem that yields a normal-mixture approximation for its distribution for Markovian queues and we sketch an argument that shows that a normal-mixture approximation should be valid in great generality. Our results provide motivation for studying staffing strategies that are more flexible than the fixed-level staffing rules traditionally studied in the literature.