Random Function Of Time Research Articles

Evidence for coherent quantum phase slips across a Josephson junction array

Superconducting order in a sufficiently narrow and infinitely long wire is destroyed at zero temperature by quantum fluctuations, which induce $2\ensuremath{\pi}$ slips of the phase of the order parameter. However, in a finite-length wire, coherent quantum phase slips would manifest themselves simply as shifts of energy levels in the excitation spectrum of an electrical circuit incorporating this wire. The higher the phase slips' probability amplitude, the larger are the shifts. Phase slips occurring at different locations along the wire interfere with each other. Due to the Aharonov-Casher effect, the resulting full amplitude of a phase slip depends on the offset charges surrounding the wire. Slow temporal fluctuations of the offset charges make the phase-slip amplitudes random functions of time, and therefore turn energy level shifts into linewidths. We experimentally observed this effect on a long Josephson junction array acting as a ``slippery'' wire. The slip-induced linewidths, despite being only of order $100\phantom{\rule{0.28em}{0ex}}\phantom{\rule{4pt}{0ex}}\mathrm{kHz}$, were resolved from the flux-dependent dephasing of the fluxonium qubit.

Random functions with nonlinear regression and their application

This paper presents a mathematical description of the dynamic properties of nonlinear random physical signals, i.e., signals modeled by random functions of time (processes and sequences) with a nonlinear the regression. It is shown that traditional methods of correlation and spectral analyses are poorly suitable or not at all for representing their dynamics. As an alternative, the paper gives a description and analysis of such signals using time (concorrelation functions) and frequency (conspectral density) concors. They exist for all random functions and the modulus of their values re invariant to any instantaneous one-to-one monotonic transformations of signals.

Ride Analysis of an Indian Railway Coach using Lagrangian Dynamics

This paper details a coupled vertical-lateral 37 degrees of freedom mathematical model of an Indian Railway general sleeper ICF coach is formulated using Lagrangian dynamics. In this analysis, the vertical and lateral irregularities of railway track are incorporated as a random function of time. The simulated results are compared with the experimental data obtained through actual rail vehicle testing. The ride comfort is evaluated incorporating ISO 2631-1 standard.

Specification methods are for electrical index systems of electric traction in transient state of its work. 1. The theoretical results

In the article three methods for determination of the wasteful losses of electric energy in a system of DC traction supply based upon the advanced mathematical techniques for analysis of electric values, which are random functions of time, are suggested.

Variations of the solution to a stochastic heat equation

We consider the solution to a stochastic heat equation. This solution is a random function of time and space. For a fixed point in space, the resulting random function of time, $F(t)$, has a nontrivial quartic variation. This process, therefore, has infinite quadratic variation and is not a semimartingale. It follows that the classical It\^{o} calculus does not apply. Motivated by heuristic ideas about a possible new calculus for this process, we are led to study modifications of the quadratic variation. Namely, we modify each term in the sum of the squares of the increments so that it has mean zero. We then show that these sums, as functions of $t$, converge weakly to Brownian motion.

Intermittency of passive-scalar decay: Strange eigenmodes in random shear flows

The decay of the concentration of a passive scalar released in a spatially periodic shear flow with random time dependence is examined. Periodic boundary conditions are assumed, placing the problem in the strange-eigenmode regime where the concentration decay is exponential in the long-time limit. The focus is on the limit of small diffusivity κ⪡1 (large Péclet number), which is studied using a combination of asymptotic methods and numerical simulations. Two specific flows are considered: both have a sinusoidal velocity profile, but the random function of time is either (i) the amplitude of the sinusoid or (ii) its phase. The behavior of the passive scalar in each flow is very different. The decay rate (or Lyapunov exponent) λ, in particular, which characterizes the long-time decay in almost all flow realizations, scales as κ2∕3 in (i) and κ3∕8 in (ii). The temporal intermittency of the scalar decay, associated with fluctuations in the speed of decay, is examined in detail. It is quantified by comparing the decay rate λ with the decay rates γp of the ensemble-averaged pth moment of the concentration. The two flows exhibit some intermittency, with γp≠pλ. It is, however, much weaker for flow (i), where the γp and λ satisfy κ2∕3 power laws, than for flow (ii), where the γp are proportional to κ1∕2 and are therefore asymptotically smaller than λ. The results for flow (ii) highlight the possible difficulty in relating the behavior of the passive scalar in single flow realizations to predictions made for ensemble-averaged quantities such as concentration moments.

Managing variability in the summary and comparison of gait data

Variability in quantitative gait data arises from many potential sources, including natural temporal dynamics of neuromotor control, pathologies of the neurological or musculoskeletal systems, the effects of aging, as well as variations in the external environment, assistive devices, instrumentation or data collection methodologies. In light of this variability, unidimensional, cycle-based gait variables such as stride period should be viewed as random variables and prototypical single-cycle kinematic or kinetic curves ought to be considered as random functions of time. Within this framework, we exemplify some practical solutions to a number of commonly encountered analytical challenges in dealing with gait variability. On the topic of univariate gait variables, robust estimation is proposed as a means of coping with contaminated gait data, and the summary of non-normally distributed gait data is demonstrated by way of empirical examples. On the summary of gait curves, we discuss methods to manage undesirable phase variation and non-robust spread estimates. To overcome the limitations of conventional comparisons among curve landmarks or parameters, we propose as a viable alternative, the combination of curve registration, robust estimation, and formal statistical testing of curves as coherent units. On the basis of these discussions, we provide heuristic guidelines for the summary of gait variables and the comparison of gait curves.

High Frequency Dynamics in Hemoglobin Measured by Magnetic Relaxation Dispersion

The magnetic relaxation dispersion profiles for formate, acetate, and water protons are reported for aqueous solutions of hemoglobin singly and doubly labeled with a nitroxide and mercury(II) ion at cysteines at β-93. Using two spin labels, one nuclear and one electron spin, a long intramolecular vector is defined between the two β-93 positions in the protein. The paramagnetic contributions to the observed 1H spin-lattice relaxation rate constant are isolated from the magnetic relaxation dispersion profiles obtained on a dual-magnet apparatus that provides spectral density functions characterizing fluctuations sensed by intermoment dipolar interactions in the time range from the tens of microseconds to ∼1 ps. Both formate and acetate ions are found to bind specifically within 5 Å of the β-93 spin-label position and the relaxation dispersion has inflection points corresponding to correlation times of 30 ps and 4 ns for both ions. The 4-ns motion is identified with exchange of the anions from the site, whereas the 30-ps correlation time is identified with relative motions of the spin label and the bound anion in the protein environment close to β-93. The magnetic field dependence of the paramagnetic contributions in both cases is well described by a simple Lorentzian spectral density function; no peaks in the spectral density function are observed. Therefore, the high frequency motions of the protein monitored by the intramolecular vector defined by the electron and nuclear spin are well characterized by a stationary random function of time. Attempts to examine long vector fluctuations by employing electron spin and nuclear spin double-labeling techniques did not yield unambiguous characterization of the high frequency motions of the vector between β-93 positions on different chains.

Monte Carlo simulation for the response analysis of long-span suspended cables under wind loads

This paper presents a time-domain approach for analyzing nonlinear random vibrations of long-span suspended cables under transversal wind. A consistent continuous model of the cable, fully accounting for geometrical nonlinearities inherent in cable behavior, is adopted. The effects of spatial correlation are properly included by modeling wind velocity fluctuation as a random function of time and of a single spatial variable ranging over cable span, namely as a one-variate bi-dimensional (1V-2D) random field. Within the context of a Galerkin`s discretization of the equations governing cable motion, a very efficient Monte Carlo-based technique for second-order analysis of the response is proposed. This procedure starts by generating sample functions of the generalized aerodynamic loads by using the spectral decomposition of the cross-power spectral density function of wind turbulence field. Relying on the physical meaning of both the spectral properties of wind velocity fluctuation and the mode shapes of the vibrating cable, the computational efficiency is greatly enhanced by applying a truncation procedure according to which just the first few significant loading and structural modal contributions are retained.

Bayesian Analysis and Prediction of Failures in Underground Trains

AbstractBased upon failure data (date and odometer reading) in the early operating time, a public transportation company is interested in checking the actual reliability of the door opening system of its subway trains before their warranty expires. We consider non‐homogeneous Poisson processes with a double scale because both time and kilometres are recorded for each failure. Different choices to model the relation between operated time and kilometres run are possible: in this paper the kilometres run are incorporated within the intensity function as a random function of time, modelled as a gamma process. Furthermore a periodic component is introduced to deal with the seasonality in the data. Bayesian inference is then carried out via Monte Carlo simulation, obtaining prediction intervals for the expected number of failures during periods of desired length, using only part of the data. The predictions are then compared with the observed data. Copyright © 2003 John Wiley & Sons, Ltd.

Noise Effects on the Transient Shear Flow of Tumbling Nematic Liquid Crystals

This paper describes a stochastic approach to nematodynamics in a specific case. We start from the director equation derived from the Leslie-Ericksen theory for a monodomain and we assume that the shear rate is a random function of time. This assumption is a simple way to account for the occurrence of noise in the velocity field produced by any thermal or mechanical fluctuations. We show that this approach provides a new framework allowing for the description of transient rheology upon flow inception in low molecular weight nematic liquid crystals. A bidimensional model in which the director stays in the shear plane is developed and compared to experimental data for the tumbling nematic formed by the dissolution of a side-chain polymer in 5CB.

Lifetimes and on–off distributions for single-molecule kinetics. Stochastic approach and extraction of information from experimental data

We introduce a stochastic approach for the computation of lifetime distributions of various chemical states in single-molecule kinetics, where the rate coefficients of the process are random functions of time. We consider a given realization for the rate coefficients and derive a partial differential equation for the instantaneous, fluctuating values of lifetime distributions and solve it by using the method of characteristics. The overall lifetime distributions are dynamic averages of the fluctuating lifetime distributions over all possible values of the rate coefficients. We develop methods of evaluating these dynamical averages for various types of stochastic processes, which describe the fluctuations of the rate coefficients. For a single molecule with two chemical states, of which one is fluorescent and the other not, the lifetime distributions are the same as the on and off time distributions, which are experimental observables. In this case we discuss in detail the relationships between intramolecular dynamics and the on and off time distributions. We develop methods for extracting quantitative and qualitative information about intramolecular fluctuations from measured values of on and of time distributions, for determining if the intramolecular fluctuations are long range or short range, and for the evaluation of the statistical properties of the fluctuating rate coefficients.

Memory effects and oscillations in single-molecule kinetics.

An exactly solvable model for single-molecule kinetics is suggested, based on the following assumptions: (i) A single molecule can exist in different chemical states and the random transitions from one chemical state to another can be described by a local master equation with time-dependent transition rates. (ii) Because of conformational and other intramolecular fluctuations the rate coefficients in the master equation are random functions of time; their stochastic properties are represented in terms of a set of control parameters. We assume that the fluctuating rate coefficients fulfill a separability condition, that is, they are made up of the multiplicative contributions of two factors: (a) a universal factor, which depends on the vector of control parameters and is the same for all chemical transformation processes and (b) process-dependent factors, which depend on the initial and final chemical states of the molecule but are independent of the control parameters. For systems with two chemical states the condition of separability is automatically fulfilled. We introduce an intrinsic time scale, which makes it possible to compute theoretically various experimental observables, such as the correlation functions of the fluorescent signal. We analyze the connections between the condition of separability and detailed balance, and discuss the possible cause of chemical oscillations in single molecule kinetics. We show that the intrinsic dynamics of the molecule, expressed by the fluctuations of the control parameters, may lead to damped oscillations of the correlation functions of the fluorescent signal. The influence of the random fluctuations on the control parameters may be described by a renormalized master equation with nonfluctuating apparent rate coefficients. The apparent rate coefficients do not have to obey a condition of detailed balance, even though the real rate coefficients do obey such a condition. It follows that the renormalized master equation may have damped oscillatory solutions.

The First Spectral Analysis of Solar Radio Spike Event

The first spectral analysis of a spike event has been performed. It was found that the peak frequency of spectrum of the spike event on Oct. 2, 1993 drifted from higher to lower frequency for the first group of spikes, but the frequency remained almost the same for the second group. Only if the mean energy of electron beam is a monotonic or random function of time and its pitch angle is a monotonically decreasing function of mean energy, then the different observed characteristics of evolution of the peak frequency with time may be interpreted by the location of resonant circle. The spike radio emissions with one and the same peak frequency probably originated from the same region of electron cyclotron maser instability.

Transport Properties of Markovian Anderson Model

We consider the Anderson model in l 2(ℤd), d≥ 1, with potentials whose values at any site of the lattice are Markovian independent random functions of time. The upper and lower bounds for the moments |X|p (t, ο) with probability 1 are obtained. We obtain also upper and lower bounds for the averaged diffusion constant and upper bounds for the correlation function. The results present diffusive behaviour in dimensions d=1,2 up to logarithmic factors.

Oscillating Tidal Barriers and Random Waves

The interaction between sea waves and the oscillating gates designed to close the three inlets of Venice lagoon and to protect the city from the phenomenon of high waters is studied. Previous studies of this topic, which considered monochromatic waves, are extended to consider random waves characterized by a narrow-band wave spectrum, such that the incoming wave strongly resembles a monochromatic wave, slowly modulated by a random function of time and space. A linear stability analysis of basic synchronous response of the barrier to the incident wave shows that the excitation of subharmonic oscillations of the gates is possible. When the width 𝒮* of the incoming wave spectrum tends to zero, the results of previous studies which considered an oscillatory forcing of constant amplitude tends to be recovered. Unexpectedly, as the width of the spectrum increases, the unstable regions in the parameter space widen. However, a weakly nonlinear stability analysis shows that the regime configuration, i.e., the configuration attained by gate oscillations for large time, is characterized by values of the amplitude of the subharmonic oscillations that decrease as the width of the spectrum increases. Present results suggest that for large band spectra the subharmonic oscillations cannot be detected. These findings result from linear and nonlinear amplitude equations characterized by time-dependent coefficients that introduce new interesting features in the time development of the amplitude of subharmonic perturbations of the gate oscillations.

Markovian Anderson Model: Bounds for the Rate of Propagation

We consider the Anderson model in \(\) with potentials whose values at any site of the lattice are Markovian independent random functions of time. For solutions \(\) to the time-dependent Schrodinger equation we show under some conditions that with probability 1 $$$$ $$$$ where \(\) for d=1,2 and \(\) for \(\).

Performance degradation of a Michelson interferometer when its misalignment angle is a rapidly varying, random time series

When subjected to random background vibrations, a standard, circular-aperture Michelson interferometer with a dynamic alignment servo system has a misalignment angle that is a random function of time. Here we derive formulas for the loss in performance when the misalignment angle is modeled as a stationary stochastic time series and show how these formulas are simplified when the power spectrum is band-limited white noise.

Markovian Anderson model

We consider the Anderson model in l 2( Z d ) with potentials whose values at any site of the lattice are independent random functions of time. For solutions ψ( t, n) to the time-dependent Schrödinger equation, we prove, under some conditions, that with probability 1 [Display omitted] [Display omitted] where α > 1/2, β < 1/2 for d = 1,2, and β < 1/ d for d ≤ 3.

Comment: Systematic errors in ground referenced geometric height monitoring

Manolakis and Lefas see (IEE Proc.-F, vol.140, no.2, p.138-44, 1993) mentioned that the errors in range measurements are due to inner mode delay differences, the effects of bottom and top antenna switching and other factors, such as varying range delay and bias correction quantisation factors, along with transponder time delay. This error is treated by the authors as fixed bias. In general, it is not uniform throughout. The end behaviour is influenced by many factors and therefore cannot be adequately modelled by deterministic variables, and hence this error is to be treated as a random time function.