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Abstract A discrete time quantum walker is considered in one dimension, where at each step, the translation can be more than one unit length chosen randomly. In the simplest case, the probability that the distance travelled is ℓ is taken as P (ℓ) = α δ (ℓ − 1) + (1 − α) δ (ℓ − 2 n) with n > 1. Even the n = 1 case shows a drastic change in the scaling behaviour for any α ≠ 0 , 1. Specifically, 〈 x 2 〉 ∝ t 3 ∕ 2 for 0 < α < 1 implying the walk is slower compared to the usual quantum walk. This scaling behaviour, which is neither conventional quantum nor classical, can be justified using a simple form for the probability density. The decoherence effect is characterised by two parameters which vanish in a power law manner close to α = 0 and 1 with an exponent ≈ 0. 5. It is also shown that randomness is the essential ingredient for the decoherence effect. Highlights • A quantum walk with random step length on a line is considered. • The results show the behaviour 〈 x 2 〉 ∝ t 3 ∕ 2. • Two quantities characterising the decoherence are identified and studied. • Conventional scaling behaviour is noted for periodically varying step lengths. [ABSTRACT FROM AUTHOR]

Abstract This paper considers a class of nonlinear filtering algorithms based on variational Bayesian (VB) theory to settle the unknown measurement noise problem in target tracking system. When the unknown measurement noise is conditionally independent of states, based on the variational idea, estimate of probability density function of state is converted into approximation two probability density functions for both unknown noise and nonlinear states. Then, an iterative algorithm is established to jointly estimate the state and the unknown measurement noise using variational Bayesian inference. Thus, the unknown measurement noise could be estimated as hidden state. The convergence result of the proposed nonlinear probability density function approximation algorithm is also given. The simulation results of typical examples show that the proposed VB based methods have superior performance to these classic algorithms in target tracking problems. [ABSTRACT FROM AUTHOR]

Abstract A cantilever with an open surface crack excited by the pedestal movement with the form of the Gaussian white noise was modeled in this paper. The open crack was simplified as an elastic hinge and the modal functions of the cracked cantilever were obtained. The dynamical equation governing the transverse motion was gained with the Kane's method after sufficient consideration of the geometrical nonlinearity and the axial inertia. Both quasi-conservative stochastic averaging method and the improved energy envelop stochastic averaging method which is effective on strong nonlinearity were applied to analyze the responses of the cantilever model theoretically. The stationary probability density function (PDF) of the amplitude, as well as the joint stationary PDF of the displacement and velocity, was investigated. For the purpose of exploring the reliability of the cantilever, the reliability function was established to avoid the potential fatigue or damage. Numerical simulations were carried out to vindicate the theoretical analysis. The advantage of the improved energy envelop stochastic averaging method was explicated by the digital results of both the stationary PDF of the amplitude and the joint PDF of displacement and velocity. Furthermore, the accuracy of the prediction on the reliability given by the theoretical analysis was also vindicated by the numerical simulation (Monte Carlo method) of the reliability. [ABSTRACT FROM AUTHOR]

Abstract We investigate the nonlocal dynamics of a single particle placed in an infinite well with moving walls. It is shown that in this situation, the Schrödinger equation (SE) violates local causality by causing instantaneous changes in the probability current everywhere inside the well. This violation is formalized by designing a gedanken faster-than-light communication device which uses an ensemble of long narrow cavities and weak measurements to resolve the weak value of the momentum far away from the movable wall. Our system is free from the usual features causing nonphysical violations of local causality when using the (nonrelativistic) SE, such as instantaneous changes in potentials or states involving arbitrarily high energies or velocities. We explore in detail several possible artifacts that could account for the failure of the SE to respect local causality for systems involving time-dependent boundary conditions. Highlights • We study a quantum particle placed in an infinite well with a moving wall. • We show that the current density is modified instantaneously when the wall moves. • We indicate how this could be experimentally recorded with weak measurements. • By circumventing the measurement noise this effect could give rise to signaling. • We examine the possible artefacts that could account for this unphysical behavior. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to present a network realization theory for a class of mixed quantum–classical linear stochastic systems. Two forms, the standard form and the general form, of this class of linear mixed quantum–classical systems are proposed. Necessary and sufficient conditions for their physical realizability are derived. Based on these physical realizability conditions, a network synthesis theory for this class of linear mixed quantum–classical systems is developed, which clearly exhibits the quantum component, the classical component, and their interface. An example is used to illustrate the theory presented in this paper. [ABSTRACT FROM AUTHOR]

Flow regime map is often used in choosing constitutive correlations for the two-phase flow model. The related research mainly concentrates on the vertical upward and horizontal flow, while it is not sufficient in the vertical downward flow. Downward flow is very important as it is frequently encountered in the industrial applications. To enrich the downward flow research, an experiment is performed on a piping system with an inner diameter of 0.1524 m. Four different flow patterns (bubbly flow, cap bubbly flow, churn turbulent flow, and annular flow) are classified with the artificial neural network method. The probability density function (PDF) profile of each flow pattern is discussed. The proposed flow regime map is compared with the other experiments and the effect of the pipe size is discussed. The existing downward flow regime boundary criteria are assessed with the experiment results. It is found that these criteria cannot fit the experiment results well. A set of general boundary criteria are still needed. In this paper, the criteria for the boundary of the bubbly flow, the boundary between the cap bubbly flow and the slug flow, and the boundary of the falling film regime are proposed. They are verified with the experiments on different size pipes. A significant inlet effect on the flow regime boundary is found. The falling film boundary criterion proposed cannot be applied when a sparger is used to inject gas into the downward test section. [ABSTRACT FROM AUTHOR]

Over the years, combinations of different methods that use multi-satellites and multi-sensors have been developed for estimating global precipitation. Recently, studies that have evaluated Integrated Multi-satellite Retrievals for GPM (IMERG) Final-Run (FR) version V-03D and other precipitation products have indicated better performance for IMERG-FR compared to other similar products in different climate regimes. This study comprehensively evaluates the two GPM-IMERG products, specifically IMERG-FR and IMERG-Real-Time (RT) late-run, against a dense station network (62 stations) in northeast Austria from mid-March 2015 to the end of January 2016 using different time-scales. Both products are examined against station data in capturing the occurrence and statistical characteristics of precipitation intensity. With regard to probability density functions (PDFs), the satellite precipitation estimate (SPE) products have detected more heavy and extreme precipitation events than the ground measurements. Both precipitation products at all time-scales, except for IMERG-RT 12-hourly and daily precipitation, capture less occurrence of precipitation than the station dataset for light precipitation. This partially explains the under-detection of precipitation events. For all time-scales, both IMERG products' CDFs (Cumulative Distribution Function) are well above that of the stations' precipitation. For lower precipitation levels, IMERG-RT is slightly below the IMERG-FR whereas IMERG-RT is above IMERG-FR at higher precipitation levels. Furthermore, for entire spectrum precipitation rates (P ≥ 0.1 mm), 1, 3, 6-hourly, IMERG-FR did not show a clear improvement of the Bias over IMERG-RT, while for 12-hourly and daily precipitation estimates, the bias in IMERG-FR has improved compared to IMERG-RT. In addition, IMERG-FR shows a considerable improvement in RMSE as compared to IMERG-RT. IMERG-FR, however, systematically underestimates moderate to extreme precipitation and overestimates light precipitation for all time scales against rain-gauges in northeast Austria. When comparing the bias, RMSE, and correlation coefficients, IMERG-FR has outperformed IMERG-RT particularly for 6-hourly, 12-hourly, and daily precipitation. Despite the general low probability of detection (POD) and threat score (TS) and the high false alarm ratio (FAR) within specified precipitation thresholds, the contingency table shows relatively acceptable values of the POD, TS and FAR for precipitation without classification. [ABSTRACT FROM AUTHOR]

We discuss several features of the classical quantum potential appearing in Covariant Quantum Mechanics. In particular, we compare the “observed potential” A [ K , G , o ] of the joined spacetime connection K with the potential A ↑ of the cosymplectic phase 2-form Ω [ K , G ] and with the potential A ↑ of the upper quantum connection Ч ↑ . Moreover, we discuss the distinguished observer o [ Ψ ] and the distinguished timelike potential A [ Ψ ] associated with a non-vanishing quantum section Ψ. We show that the above objects play a natural role in the context of the kinetic quantum momentum Q [ Ψ ] , of the quantum probability current J [ Ψ ] , of the Schrödinger operator S [ Ψ ] and of the classical fluid associated with a non-vanishing quantum section Ψ. [ABSTRACT FROM AUTHOR]

Based on the random theory of the probability density evolution method (PDEM), a refined random wheel/rail contact model for train-track-bridge systems is proposed. The trace line method with the law of equal slopes is developed to determine the wheel/rail contact locations, which are described by probability density functions on the wheel/rail surface. The number theoretic method (NTM) and stochastic harmonic functions (SHFs) are employed to generate the representative random track irregularities. Considering the excitation of random track irregularities and the wheel/rail contact geometry, the wheel/rail normal contact force and the tangential creep force are accurately calculated and analyzed using the proposed wheel/rail contact model. A high-speed railway case study is presented to reveal the random dynamic characteristics of a train-track-bridge system and the wheel/rail interaction. The results show that the time-varying probability density evolution functions of the wheel/rail contact points can effectively indicate both the phenomenon of wear on the rail surface and its distribution characteristics. Additionally, some significant conclusions are obtained. [ABSTRACT FROM AUTHOR]

Motivated by that the quartic potential can confined Lévy flights, we investigate the escape rate of an inertial Lévy particle from a truncated quartic potential well via Langevin simulation. The escape rate still depends on the noise intensity in a power-law form in low noise intensity, but the exponent and the inverse coefficient vary significantly for different Lévy indexes compared with previous works. Trimodal structure of the probability density function was found in simulations. The probability density function in a quasi-stable state exhibits transition among unimodal, bimodal, and trimodal structures. A metastable state by stable state approach is developed to calculate the escape rate analytically, which may be applied to extensive escape problems. The theoretical approach is confirmed by Langevin simulation for the Cauchy case of Lévy flight in the applied potential. [ABSTRACT FROM AUTHOR]

There are relatively few publications that assess capacity decline in enough commercial cells to quantify cell-to-cell variation, but those that do show a surprisingly wide variability. Capacity curves cross each other often, a challenge for efforts to measure the state of health and predict the remaining useful life (RUL) of individual cells. We analyze capacity fade statistics for 24 commercial pouch cells, providing an estimate for the time to 5% failure. Our data indicate that RUL predictions based on remaining capacity or internal resistance are accurate only once the cells have already sorted themselves into “better” and “worse” ones. Analysis of our failure data, using maximum likelihood techniques, provide uniformly good fits for a variety of definitions of failure with normal and with 2- and 3-parameter Weibull probability density functions, but we argue against using a 3-parameter Weibull function for our data. pdf fitting parameters appear to converge after about 15 failures, although business objectives should ultimately determine whether data from a given number of batteries provides sufficient confidence to end lifecycle testing. Increased efforts to make batteries with more consistent lifetimes should lead to improvements in battery cost and safety. [ABSTRACT FROM AUTHOR]

Results related to the filtered non-premixed turbulent flame statistics are presented. Considering non-premixed turbulent combustion modeling in the framework of large eddy simulations (LES), a turbulent flamelet equation is derived based on the filtered governing equations. Using a direct numerical simulation (DNS) data set, the statistical properties of two important parameters, the scalar dissipation and chemical source term, are analyzed in details. Numerical results show that for the scalar dissipation term, the probability density function (PDF) of the magnitude of the mixture fraction gradient changes is strongly dependent on the filter scale, whereas the PDF of the turbulent diffusivity is almost invariant. Theoretically from the scalar structure function a scaling law can be expected for the conditional mean of the difference between the filtered and nonfiltered scalars with respect to the filter scale, which is important for estimating the chemical source in the subgrid scale models. [ABSTRACT FROM AUTHOR]

In this paper we present a framework to model the effect of multiple sources of degradation on deteriorating systems, and to find easy-to-evaluate expressions for important reliability quantities. By considering the system deterioration as a general increasing Lévy process (i.e., a subordinator), which is a process with independent, stationary and non-negative increments, the proposed methodology allows the modeling of shock-based degradation (in the form of compound Poisson processes) with different distributions of shock sizes, progressive degradation as deterministic linear drift plus a Gamma process, and multiple sources of degradation by the superposition of any of these models into the same mathematical formalism. In addition, we obtain expressions for the reliability quantities (reliability function, and probability density and moments of the lifetime L ), and the mean and central moments of the deterioration process X t . Moreover, we present efficient and accurate numerical methods to compute the reliability quantities and to simulate sample paths. Several deterioration models are compared in terms of their reliability quantities, the simulated sample paths and the feasible moments of the deterioration X t . Furthermore, we propose a method to mix different Lévy models that extend the available moments with possible applications to data fitting. The results demonstrate the generality, versatility, efficiency and accuracy of the proposed Lévy degradation framework, which can open a new productive research field in the area of probabilistic degradation models. [ABSTRACT FROM AUTHOR]

The mobilized shear strength ( τ f m ) of a soil is the most important design parameter governing ultimate limit states. The authors have proposed some models and equations to characterize several useful aspects of the mean, variance, and probability density function of τ f m for a two dimensional (2D) spatially variable clay specimen. This paper demonstrates that the models and equations developed for 2D can be extended to three-dimensional (3D) cases. An important class of 3D cases are examined in detail: two horizontal scales of fluctuation (SOF) are equal, and both are larger than the vertical SOF. A key observation for 3D cases is that the averaging effect over the potential slip planes is significantly stronger than that for 2D cases. The upshot is that the phenomenon of the critical SOF (e.g., SOF producing the lowest mean value of τ f m ) is less clear for 3D cases. [ABSTRACT FROM AUTHOR]

The analysis of reliability of complex engineering systems remains a challenge in the field of reliability. It will be even more difficult if correlated random vectors are involved, which is generally the case as practical engineering systems invariably contain parameters that are mutually correlated. A new method for transforming correlated distributions, involving the Nataf transformation, is proposed that avoids the solution of integral equations; the method is based on the Taylor series expansion of the probability density function (PDF) of a bivariate normal distribution resulting in an explicit polynomial equation of the equivalent correlation coefficient. The required numerical results can be obtained efficiently and accurately. The proposed method for transformation of correlated random vectors is useful for developing a method for system reliability including complex systems with correlated random vectors. Based on the complete system failure process (originally defined as the development process of nonlinearity) and the fourth-moment method, the analysis of system reliability for elastic-plastic material avoids the identification of the potential failure modes of the system and their mutual correlations which are required in the traditional methods. Finally, four examples are presented – two examples to illustrate the potential of the new method for transformation of correlated random vectors, and two examples to illustrate the application of the proposed more effective method for system reliability. [ABSTRACT FROM AUTHOR]

Entropic measures provide analytic tools to help us understand the stability of quantum systems. The spreading of the quantum-mechanical probability cloud for solitonic profile mass Schrödinger equation with a potential V ( ax ) = − V 0 csch 2 ( ax ) is studied in position and momentum space by means of global (Shannon’s information entropy) information-theoretic measures. The position information entropy is considered only for x > 0 due to the singular point at x = 0 . The entropy densities ρ s ( x ) and ρ s ( p ) are demonstrated and the BBM inequality is saturated. [ABSTRACT FROM AUTHOR]

Bell appealed to the theory of relativity in formulating his principle of local causality. But he maintained that quantum field theories do not conform to that principle, even when their field equations are relativistically covariant and their observable algebras satisfy a relativistically motivated microcausality condition. A pragmatist view of quantum theory and an interventionist approach to causation prompt the reevaluation of local causality and microcausality. Local causality cannot be understood as a reasonable requirement on relativistic quantum field theories: it is unmotivated even if applicable to them. But microcausality emerges as a sufficient condition for the consistent application of a relativistic quantum field theory. [ABSTRACT FROM AUTHOR]

A popular view in contemporary Boltzmannian statistical mechanics is to interpret the measures as typicality measures. In measure-theoretic dynamical systems theory measures can similarly be inter- preted as typicality measures. However, a justification why these measures are a good choice of typicality measures is missing, and the paper attempts to fill this gap. The paper first argues that Pitowsky's (2012) justification of typicality measures does not fit the bill. Then a first proposal of how to justify typicality measures is presented. The main premises are that typicality measures are invariant and are related to the initial probability distribution of interest (which are translation-continuous or translation-close). The conclusions are two theorems which show that the standard measures of statistical mechanics and dynamical systems are typicality measures. There may be other typicality measures, but they agree about judgements of typicality. Finally, it is proven that if systems are ergodic or epsilon-ergodic, there are uniqueness results about typicality measures. [ABSTRACT FROM AUTHOR]

Abstract: For a sequence of strictly stationary random fields that are uniformly and satisfy a Lindeberg condition, a central limit theorem is obtained for sequences of “rectangular” sums from the given random fields. The “Lindeberg CLT” is then used to prove a CLT for some kernel estimators of probability density for some strictly stationary random fields satisfying , and whose probability density and joint densities are absolutely continuous. [Copyright &y& Elsevier]