A Path Integral Generalization of Bell Local Hidden Variable Models for Unstable Particles

Kinetic analysis in criticality accident is necessary for the estimation of the integral power and the dose. The analysis must be performed even for the geometry of several regions which are weakly coupled, i.e. each region is apart from other regions or/and moderating material exists between the regions. A kinetic analysis method for weakly coupled systems has been developed to analyze the first pulse in super prompt criticality accidents. In the method, time dependent fission probability density functions after a fission in each region are calculated by Monte Carlo method from the time between the collisions. By using the fission probability density functions, kinetic behavior of each region can be calculated. The difference of the functions between the different systems is discussed based on the difference of compositions and geometry of the systems.

For transportation system analysis in a new space dimension with respect to individual trips’ remaining distances, vehicle trips demand has two main components: the departure time and the trip distance. In particular, the trip distance distribution (TDD) is a direct input to the bathtub model in the new space dimension, and is a very important variable to consider in many applications, such as the development of distance-based congestion pricing strategies or mileage tax. For a good understanding of the demand pattern, both the distribution of trip initiation and trip distance should be calibrated from real data. In this paper, it is assumed that the demand pattern can be described by the joint distribution of trip distance and departure time. In other words, TDD is assumed to be time-dependent, and a calibration and validation methodology of the joint probability is proposed, based on log-likelihood maximization and the Kolmogorov–Smirnov test. The calibration method is applied to empirical for-hire vehicle trips in Chicago, and it is concluded that TDD varies more within a day than across weekdays. The hypothesis that TDD follows a negative exponential, log-normal, or Gamma distribution is rejected. However, the best fit is systematically observed for the time-dependent log-normal probability density function. In the future, other trip distributions should be considered and also non-parametric probability density estimation should be explored for a better understanding of the demand pattern.

Moment Closure for Local Control Models of Calcium-Induced Calcium Release in Cardiac Myocytes

Time-dependent probability distribution for number of infection in a stochastic SIS model: case study COVID-19.

We have examined the time dependence and spatial distribution of the deposition rate of YBa2Cu3O7 (YBCO) thin films in 90° off-axis radio frequency planar magnetron sputtering throughout the life of a target. We have found that although the amount of YBCO sputtered from the target is constant, the amount of YBCO deposited on the substrate decreases linearly over time. Furthermore, the time dependence of the deposition rate changes at different positions on the substrate. The changes in the deposition rate at any point along the substrate as a function of time can be explained by the change in the angular distribution of the sputtered particles that is caused by changes in the target erosion groove geometry, and the decrease in the kinetic energy of sputtered particles that is indicated by the decrease in the self-bias voltage over time.

<p><span lang="EN-US">Present study focuses on some foundational problems of quantum theory specifically deals with the concept of probability density and relating introductory problems. In this sense, the work initially investigates the origins of the general probability theory and re-examines the concepts of spatial and temporal probability densities based on genuine epistemological and ontological arguments. In order to tackle the foundational problems, standard theory is primarily memorised and criticized scientifically and philosophically in terms of foundationally disappearing term of time dependent potential energy within the time and space dependent Schrödinger wave equation. Based on those arguments, the problematic inconsistency between the spatial and temporal probability density functions is underlined. Given the problem, an original approach previously suggested, is concisely described and extended to resolve the existing problem. The novel approach, based on a novel time dependent Schrödinger wave equation, resolves the discrepancy with the classical wave equation and also leads to time dependent temporal probability densities even for the time free potential energies. Novel temporal probability density function is also normalized and has a fluctuation period of around 10<sup>-16 </sup>s which is very short compared to the atomic time scales.</span></p>

Displaced and squeezed number states

An analytical method based on stochastic differential equations is presented for the stochastic damage and reliability analysis of hysteretic structures to earthquake excitations. The differential forms of hysteretic constitutive laws and of measures of structural damages are described. The time-dependent joint probability density function of seismic responses including the measures of damages as well as their statistics are evaluated. The seismic reliability functions are directly evaluated from the probability density functions of structural damages.

A procedure is described that can be used to reconstruct the quantum state of a molecular ensemble from time-dependent internuclear probability density functions determined by time-resolved electron diffraction. The procedure makes use of established techniques for evaluating the density matrix and the phase-space joint probability density, that is, the Wigner function. A novel expression for describing electron diffraction intensities in terms of the Wigner function is presented. An approximate variant of the method, neglecting the off-diagonal elements of the density matrix, was tested by analyzing gas electron diffraction data for N2 in a Boltzmann distribution and TRED data obtained from the 193 nm photodissociation of CS2 to carbon monosulfide, CS, at 20, 40, and 120 ns after irradiation. The coherent changes in the nuclear subsystem by time-resolved electron diffraction method determine the fundamental transition from the standard kinetics to the dynamics of the phase trajectory of the molecule and the tomography of molecular quantum state.

We use molecular simulations to examine how the dynamics of a coarse-grained polymer melt are altered by additives of variable size and interaction strength with the polymer matrix. The effect of diluent size σ on polymer dynamics changes significantly when its size is comparable to the polymer segment size. For each σ, we show that the localization model (LM) quantitatively describes the dependence of the segmental relaxation time τ on temperature T in terms of dynamic free volume, quantified by the Debye-Waller factor ⟨u^{2}⟩. Within this model, we show that the additive size alone controls the functional form of the T dependence. The LM parameters reach asymptotic values when the diluent size exceeds the monomer size, converging to a limit applicable to macroscopic interfaces.

A non-conforming computational methodology for modeling coupled problems

The [formula omitted]-Adic Schrödinger equation and the two-slit experiment in quantum mechanics

In many ambits of the chemical sciences it happens to deal with complex systems udergoing thermal fluctuations in the overdamped regime of the motion (i.e., multidimensional diffusive processes). Although such stochastic dynamics are well specified in terms of the Fokker–Planck–Smoluchowski equation for the time-dependent probability density, the solution becomes rapidly unfeasible as the number of degrees of freedom increases beyond a few units. Here we present a strategy, based on inequalities for “completely monotone decreasing” functions viewed as convex functions of time, to by-pass such a difficulty and aimed to achieve only bounds (but with low computational effort) on some quantities that pertain the system’s dynamics. Namely, we derive (i) a lower bound for the maximum value of the probability density that develops from a given initial condition, and (ii) a lower bound on the correlation time for a generic self-correlation function. The former bound is quantified by means of simple operations on the initial condition, while the latter is gained by the knowledge of an initial “piece” of correlation function to be supplied, for instance, by molecular or Brownian dynamics simulations. Some practical applications are discussed.

Arrival processes to queues often exhibit time dependence, but time-dependent queues are notoriously difficult to analyze. Usually one adopts some kind of steady-state approximation for time-dependent performance. We consider a range of queueing models that see wide use in practice, particularly in the modeling of service industry applications, and develop approximations for the error involved in using a steady-state approximation for time-dependent quantities. We focus on the distribution of the waiting time before reaching service, although the approach we use could be extended to many other performance measures. The results reinforce and extend what is known about such errors. For example, customer abandonment leads to dramatic reductions in the error in steady-state approximations as compared to a system without customer abandonment.

An analytic solution of the time-dependent Boltzmann kinetic equation is found for the first time. The plasma-wall transition (PWT) layer is analyzed using time-dependent velocity distribution functions for electrons and ions. The process of wall charging by electrons is described and estimated. For states close to the time-independent (stationary) state, for which the time dependence of the PWT parameters is weak, (i) the potential shapes in the pre-sheath (PS) and the Debye sheath (DS) are analyzed and (ii) the intermediate region, which bridges the PS and DS sublayers, is defined and its characteristic length is determined. The ion kinetics are dominated by charge exchange with cold neutrals and electron-impact ionization collisions of neutrals. The charge-exchange mean free path λcx is assumed to be constant and much larger than the electron Debye length λDe. The detailed time dependence of the PS sublayer's approach of the stationary state is found. It is proved that the stationary state can be realized only if the floating-potential condition is fulfilled.