Use of post-processing to increase the order of accuracy of the trapezoidal rule at time integration of linear elastodynamics problems

In this paper, we suggest a very simple and effective post-processing procedure to increase the order of accuracy in time for numerical results obtained by the trapezoidal rule. We first derive a new exact, closed-form, a-priori error estimator for time integration of linear elastodynamics equations by the trapezoidal rule with non-uniform time increments. Based on this error estimator, we suggest a new post-processing procedure (containing additional time integration of elastodynamics equations by the trapezoidal rule with few time increments) that systematically improves the order of accuracy of numerical results, with the increase in the number of additional time increments used for post-processing. For example, the use of just one additional time increment for post-processing after time integration with any number of uniform time increments, renders the order of accuracy of numerical results equal to 10/3. Numerical examples of the application of the new techniques to a system with a single degree of freedom and to a multi-degree system confirm the corresponding increase in the order of convergence of numerical results after post-processing. Because the same trapezoidal rule is used for basic computations and post-processing, the new technique retains all of the properties of the trapezoidal rule, requires no writing of a new computer program for its implementation, and can be easily used with any existing commercial and research codes for elastodynamics.     

Computation of the far-field time domain solution of the scattering problem.

This paper presents a new technique for calculating the time domain (transient) far-field scattered pressure. The scattering problem is divided in two steps; the first step evaluates the field distribution inside the scatterer, and the second step generates the far-field scattered pressure by 3-D Radon transform of these data for each time step and summing over time. The algorithm results in considerable saving in CPU time and memory by simplifying the calculation along the path from scatterer to receiver. This technique can also be used in two dimensions.     

小孔流速实验中的排水时间和流量系数的研究

本文以水作为理想流体,考虑到水头损失和孔口缩流效应,对小孔流速实验涉及的容器排水问题进行了系统的理论和实验研究.从理论上推导得出了圆柱形容器排水时间的解析解,分析了排水时间和自由液面速度、流量系数之间的规律,提出了排水时间的等效性.实验上,加工了底部开有不同小孔的大型圆柱形容器,测量了容器排水时间随液面高度的变化关系,借助实验结果计算了流量系数值,验证了容器排水时间的等效性关系,实验结果与理论计算符合较好.     

On the concept of time and the origin of the cosmological temperature

Time arises in the theory of gravity through the semiclassical approximation of the gravitational part of the solution of the Wheeler-De Witt equation in the manner shown by Banks (SCAG). We generalize Banks' procedure by grafting a Born-Oppenheimer type approximation onto SCAG. This allows for the feedback of matter onto gravity, wherein the latter is driven by the (quantum) mean energy-momentum tensor of matter. The wave function is nonvanishing in classically forbidden configurations of gravity. In SCAG this is described by the evolution of matter in imaginary time. This is interpreted as an inverse temperature, and the norm of the matter wave function, no longer conserved for these gravitational configurations, is a partition function. A simple cosmological model is worked out to illustrate these ideas. In this model it is shown that the temperature of the matter which emerges into the classically permitted region is the inverse bounce time of the bounce executed by the system in the forbidden region (behind the horizon).Time present and time past are both perhaps present in time future. And time future contained in time past. If all time is eternally present All time is unredeemable.—T. S. Eliot, Burnt Norton,Four Quartets, 1943.In honor of Ilya Prigogine on the occasion of his 70th birthday.     

Generalization of the Fresnel law to the case of a pressure-wave-induced displacement of the interface between acoustic media

The problem of interaction between a nonsteady-state pressure wave and a moving interface between acoustic media is analyzed and solved for the first time with allowance for a finite displacement of the interface induced by the wave. An analytic solution is obtained using a nonlinear time transformation method. Expressions are obtained for the law of motion of the interface, and for the reflected and transmitted waves as a function of the time profile of the incident wave and the acoustic characteristics of the media. Zh. Tekh. Fiz. 69, 114–115 (April 1999)     

On the Asymptotic Convergence of the Transient and Steady-State Fluctuation Theorems

Nonequilibrium molecular dynamics simulations are used to demonstrate the asymptotic convergence of the transient and steady-state forms of the fluctuation theorem. In the case of planar Poiseuille flow, we find that the transient form, valid for all times, converges to the steady-state predictions on microscopic time scales. Further, we find that the time of convergence for the two theorems coincides with the time required for satisfaction of the asymptotic steady-state fluctuation theorem.     

On the influence of viscosity on the characteristic time of the instability of a charged drop

A nonlinear integral equation describing the evolution of spheroidal deformation of a drop that is unstable with respect to its intrinsic charge is derived and solved for arbitrary values of viscosity. It was shown that, due to an essentially nonlinear character of the phenomenon, the characteristic time of instability develop-ment equals the time of tenfold increase in the amplitude of an initial, physically infinitesimal spheroidal deformation of an unstable drop. The dependence of the instability characteristic time on the drop viscosity is described by an increasing linear function.     

On the possibility of observation of the future for movement in the field of black holes of different types

It is shown for a spherically symmetric black hole of general type that it is impossible to observe the infinite future of the Universe external to the hole during the finite proper time interval of the free fall. Quantitative evaluations of the effect of time dilatation for circular orbits around the Kerr black hole are obtained and it is shown that the effect is essential for ultrarelativistic energies of the rotating particle.     

On the time dependence of the dielectric dispersion for triglycine sulfate in the vicinity of the curie point

The evolution of the dielectric spectrum of triglycine sulfate with time is investigated in the frequency range from 20 MHz to 1 Hz at a temperature of 48.8°C for 420 min. It is revealed that the evolution of the dielectric spectrum exhibits a non-steady-state behavior due to the broadening of the relaxation-time spectrum. The process clearly manifests itself in a transformation of the Cole-Cole diagram with time. The transformation to a quasi-stationary state is completed in approximately 1 h. The phenomenon is explained by the retarded motion of domain walls. The inference is made that, for ferroelectrics, the time evolution of all parameters associated with the domain-wall state should be a universal property.     

Unstable combustion induced by oblique shock waves at the non-attaching condition of the oblique detonation wave

The instability of oblique shock wave (OSW) induced combustion is examined for a wedge with a flow turning angle greater than the maximum attach angle of the oblique detonation wave (ODW), where archival results rarely exist for this case in previous literatures. Numerical simulations were carried out for wedges of different length scales to account for the ratio of the chemical and fluid dynamic time scales. The results reveal three different regimes of combustion. (1) No ignition or decoupled combustion was observed if a fluid dynamic time is shorter than a chemical time behind an OSW. (2) Oscillatory combustion was observed behind an OSW if a fluid dynamic time is longer than a chemical time behind an OSW and the fluid dynamic time is shorter than the chemical time behind a normal shock wave (NSW) at the same Mach number. (3) Detached bow shock-induced combustion (or detached overdriven detonation wave) was observed if a fluid dynamic time is longer than a chemical time behind a NSW. Since no ignition or decoupled combustion occurs as a very slow reaction and the detached wave occurs as an infinitely fast reaction, the finite rate chemistry is considered to be the key for the oscillating combustion induced by an OSW over a wedge of a finite length with a flow turning angle greater than the maximum attach angle for an ODW. Since this case has not been previously reported, grid independency was tested intensively to account for the interaction between the shock and reaction waves and to determine the critical time scale where the oscillating combustion can be observed.     

微生物培养法推断纸张的相对生产时间

利用微生物培养法检测两种制浆方式的纸张,观察随着生产时间的不同,纸张上细菌和霉菌数量上的变化,根据其纸张上细菌和霉菌的变化规律,推断纸张的相对生产时间。该方法利用现代生物技术,对文件制成时间的检验提供一种新的思路和方法。     

Deriving currents on the one-dimensional lattice in the regime of dynamic localization

In this paper one deals with a transparent derivation of dynamic localization conditions for the electron on the 1D lattice proceeding irrespective of the concrete form of the periodic modulation of the time dependent electric field. This amounts to account for periodic zero minima generated in the time dependence of the mean square displacement (MSD). Related DL conditions have also been established by looking for the extremal points of the MSD. Interestingly enough, the conditions established in this manner are similar to the ones written down before for pure ac fields but exhibiting a rather unusual modulation. Related time dependent currents can be readily established, now by resorting to discrete derivatives. Our typical example is the dc-ac electric field. We found that in the regime of dynamic localization the MSD and the current get characterized by the same period, i.e by the period of the time dependent modulation. Moreover, the current crosses the time axis just in the maxima-locations of the MSD.     

The determination of the specific heat of a liquid in an electric calorimeter from the time dependence of the temperature

The paper describes two methods for determining the specific heat of a liquid in an electric calorimeter where the determination of the temperature change of the measured liquid before and after the experiment, which is necessary for determining the correction for thermal losses, is eliminated. It gives formulas for calculating the coefficients for the parabolic interpolation of the calorimeter temperature versus time on the assumption that the time measurements are equidistant.     

Time and temperature dependence of the specific heat of non-crystalline solids within the tunneling model

We propose a new way to introduce the measuring time in the Tunneling Model of non-crystalline solids. We have obtained a time dependent relation for the specific heat which can be used without limits in time or temperature. We prove that under the usual assumptions of the standard Tunneling Model and without free parameters one can understand quantitatively the experimentally observed time and temperature dependence of the specific heat and heat release experiments on vitreous silica over ten orders of magnitude in time. We also discuss the influence of conductions electrons on the time dependent specific heat. Time dependent experiments could provide useful information on the interaction of Tunneling Systems with conduction electrons.     

Origin of the usefulness of the natural-time representation of complex time series

The concept of natural time turned out to be useful in revealing dynamical features behind complex time series including electrocardiograms, ionic current fluctuations of membrane channels, seismic electric signals, and seismic event correlation. However, the origin of this empirical usefulness is yet to be clarified. Here, it is shown that this time domain is in fact optimal for enhancing the signals in time-frequency space by employing the Wigner function and measuring its localization property.     

Physics of the fastest communication

A communication system involves the transmission of information from source to destination and after receiving all the information or a complete signal an acknowledgement is then sent to the source by the destination itself to let the source know that it (destination) has received the signal. In this paper we examine about how to reduce the time of acknowledgement to make the communication faster. In this paper we present a method of sending an acknowledgement signal, in which the last quantum (sample) of the signal is used to compute the time of acknowledgement. The formula for calculating the time of acknowledgement in the case of a continuous time signal and a discrete time signal is also derived in the paper. This technique is applicable for analog communication, digital communication and space communication.     

Determination of the scintillator decay time by the autocorrelation method

An autocorrelation method is developed for determining the composition and decay time of scintillators. This method also allows studying the spatial distribution of nuclear radiation and controlling the amount of the dopants introduced in the scintillator. The decay time is measured from a few nanoseconds to microseconds. It is found out that the decay time increases in plastic scintillators with a wavelength shifter and a Gd doped.     

The Quantum-Classical Comparison of the Arrival-Time Distribution Through the Probability Current

We consider the arrival time distribution defined through the quantum probability current for a Gaussian wave packet representing free particles in quantum mechanics in order to explore the issue of the classical limit of arrival time. We formulate the classical analogue of the arrival time distribution for an ensemble of free particles represented by a phase space distribution function evolving under the classical Liouville's equation. The classical probability current so constructed matches with the quantum probability current in the limit of minimum uncertainty. Further, it is possible to show in general that smooth transitions from the quantum mechanical probability current and the mean arrival time to their respective classical values are obtained in the limit of large mass of the particles.     

Correlations in the adiabatic response of chaotic systems

Adiabatic variation of the parameters of a chaotic system results in a fluctuating reaction force. The quantum analog of a classical dissipative force, proportional to the time integral of the force-force correlation function, vanishes. We study this quantum-classical crossover for random matrix models. For the Gaussian unitary ensemble the crossover is found to take place on the Heisenberg time scale and the finite time integral practically vanishes for longer times. For the Gaussian orthogonal case, there is no such time scale and the integral falls off inversely proportional to time.     

Optimal estimation of the amplitude of signal with known frequency in the presence of thermal noise

In the torsion pendulum experiments, the thermal noise sets the most fundamental limit to the accurate estimation of the amplitude of the signal with known frequency. The variance of the conventional method can meet the limit only when the measurement time is much longer than the relaxation time of the pendulum. By using the maximum likelihood estimation and the equation-of-motion filter operator, we propose an optimal(minimum variance, unbiased) amplitude estimation method without limitation of the measurement time, where thermal fluctuation is the leading noise. While processing the experimental data tests of the Newtonian gravitational inverse square law, the variance of our method has been improved than before and the measurement time of determining the amplitude with this method has been reduced about half than before for the same uncertainty. These results are significant for the torsion experiment when the measurement time is limited.