Memory effect in time fractional Schrödinger equation

A significant obstacle impeding the advancement of the time fractional Schrodinger equation lies in the challenge of determining its precise mathematical formulation.In order to address this,we undertake an exploration of the time fractional Schrodinger equation within the context of a non-Markovian environment.By leveraging a two-level atom as an illustrative case,we find that the choice to raise i to the order of the time derivative is inappropriate.In contrast to the conventional approach used to depict the dynamic evolution of quantum states in a non-Markovian environment,the time fractional Schrodinger equation,when devoid of fractional-order operations on the imaginary unit i,emerges as a more intuitively comprehensible framework in physics and offers greater simplicity in computational aspects.Meanwhile,we also prove that it is meaningless to study the memory of time fractional Schrodinger equation with time derivative 1<α≤2.It should be noted that we have not yet constructed an open system that can be fully described by the time fractional Schrodinger equation.This will be the focus of future research.Our study might provide a new perspective on the role of time fractional Schrodinger equation.

Effect of slake durability on time dependent swelling behavior of red-bed siltstone in Sichuan Basin

The swelling behavior of red-bed rocks is a significant factor in the abnormal uplift of subgrades for high-speed railways constructed on the red stratum in the Sichuan Basin,China.The prime objective of this paper is to investigate the impact of mineralogical composition,moisture content,and overburden load on the time-dependent unconfined and oedometric swelling behavior of red-bed siltstone in the context of differences in the slake durability.Twenty samples were prepared for the swelling test,with eleven used for the unconfined swelling and slake index tests and nine for the oedometric swelling test.The temporal dependency of swelling is characterized by the viscosity coefficient of water absorption in a proposed swelling model.Results indicate that the swelling deformation of red-bed rocks is due to a combination of hydration swelling within the rock matrix and crack expansion caused by air breakage.In the unconfined swelling test,the final axial swelling strain of red-bed rocks decreases linearly with increasing slake index,while the viscosity coefficient increases exponentially with the slake index.In the oedometric swelling test,red-bed rocks with lower slake durability show greater sensitivity to lateral constraint and overburden load compared to those with higher slake durability.

Effect and mechanism of on-chip electrostatic discharge protection circuit under fast rising time electromagnetic pulse

The electrostatic discharge(ESD)protection circuit widely exists in the input and output ports of CMOS digital circuits,and fast rising time electromagnetic pulse(FREMP)coupled into the device not only interacts with the CMOS circuit,but also acts on the protection circuit.This paper establishes a model of on-chip CMOS electrostatic discharge protection circuit and selects square pulse as the FREMP signals.Based on multiple physical parameter models,it depicts the distribution of the lattice temperature,current density,and electric field intensity inside the device.At the same time,this paper explores the changes of the internal devices in the circuit under the injection of fast rising time electromagnetic pulse and describes the relationship between the damage amplitude threshold and the pulse width.The results show that the ESD protection circuit has potential damage risk,and the injection of FREMP leads to irreversible heat loss inside the circuit.In addition,pulse signals with different attributes will change the damage threshold of the circuit.These results provide an important reference for further evaluation of the influence of electromagnetic environment on the chip,which is helpful to carry out the reliability enhancement research of ESD protection circuit.

Propagation Dynamics of Forced Pulsating Waves for a Time Periodic Lotka-Volterra Cooperative System with Nonlocal Effects in Shifting Habitats

In this paper, we will concern the existence, asymptotic behaviors and stability of forced pulsating waves for a Lotka-Volterra cooperative system with nonlocal effects under shifting habitats. By using the alternatively-coupling upper-lower solution method, we establish the existence of forced pulsating waves, as long as the shifting speed falls in a finite interval where the endpoints are obtained from KPP-Fisher speeds. The asymptotic behaviors of the forced pulsating waves are derived. Finally, with proper initial, the stability of the forced pulsating waves is studied by the squeezing technique based on the comparison principle.

Introducing an effective coherence function to generate non-uniform ground motion on topographic site using time-domain boundary element method

In this study,a comprehensive parametric analysis was performed on non-uniform excitation of V-shaped topography using the boundary element method in time domain.For this purpose,wave scattering analysis was carried out on a topography subjected to the SV-wave for different predominant frequencies and shape ratios.Based on the numerical results,new coherence and time delay functions are proposed to generate non-uniform ground motion for topographic irregularities.The efficiency and accuracy of the proposed functions for real engineering problems are indicated by comparison with observations reported in previous literature.

Design and operation strategies of the system for destroying time-sensitive target based on system effectiveness

To improve the effect of destroying time-sensitive target （TST）, a method of operational effectiveness evaluation is presented and some influential factors are analyzed based on the combat flow of system for destroying TST. Considering the possible operation modes of the system, a waved operation mode and a continuous operation mode are put forward at first. At the same time, some relative formulas are modified. In examples, the influential factors and operation modes are analyzed based on the system effectiveness. From simulation results, some design and operation strategies of the system for destroying time sensitive targets are concluded, which benefit to the improvement of the system effectiveness.

Interval of effective time-step size for the numerical computation of nonlinear ordinary differential equations

The computational uncertainty principle states that the numerical computation of nonlinear ordinary differential equations（ODEs） should use appropriately sized time steps to obtain reliable solutions.However,the interval of effective step size（IES） has not been thoroughly explored theoretically.In this paper,by using a general estimation for the total error of the numerical solutions of ODEs,a method is proposed for determining an approximate IES by translating the functions for truncation and rounding errors.It also illustrates this process with an example.Moreover,the relationship between the IES and its approximation is found,and the relative error of the approximation with respect to the IES is given.In addition,variation in the IES with increasing integration time is studied,which can provide an explanation for the observed numerical results.The findings contribute to computational step-size choice for reliable numerical solutions.

Frequency-time Domain Shielding Effectiveness of Materials and Their Strong Electromagnetic Field Test

To describe the shielding ability of materials accurately and comprehensively,the frequency-domain and time-domain shielding effectiveness(SE) of material is investigated.The relevance between them was analyzed based on the minimum phase method,and the time-domain SE can be derived from frequency-domain SE.The SE of an energy selective surface(ESS) made of a novel material is investigated,and the relationship between SE and radiation field intensity are analyzed.The results show that not only material,but also the intensity of radiation electric field shows influence on SE in its frequency; for some materials,the dependence of SE on radiation electric field intensity needs to be considered.Therefore,it is necessary to research on the SE of shielding material in high-intensity electromagnetic environment.

Earthquake-Affected Time-Space Domain, Recurrence Interval and Effective Preparation Time of Earthquakes

The study shows that earthquake-affected time-space domain (ETSD), i.e. a time-space range in which strong earthquakes are unable to occur owing to the influence of a prior earthquake occurring, shows a hyperbolic margin curve in the t(time)-r(distance) coordinate plane, which has a maximum affected radius r 0 at t=0 and a maximum influence time t 0 (i.e. the in-situ recurrence interval of earthquakes) at r=0. Based on the time-distance distributions of posterior earthquakes relative to prior ones in the regions of North China, Northwest China, Qinghai-Xizang (Tibet) plateau and Southwest China, the optimized and 90%-confidence margin curves are estimated using optimization and statistical analysis methods. This indicates that the concept and method of ETSD with 3-dimension (time-distance-magnitudes) instead of those of “recurrence interval" with 1-dimension (time) or 2-dimension (time-magnitude) provides a new approach to understanding the fluctuation of seismic activities, estimating the effective earthquake-preparation time of potential hypocenters, and therefore improving the medium- and long-term prediction of strong earthquakes.

Non-Equilibrium Grain-Boundary Segregation of Phosphorus And the Effective Time in Step Cooling Process

The non-equilibrium grain-boundary segregation of phosphorus in step cooling process in an industrial steel, 12CrlMoV, is studied based on the effective-time-method and compared with that in isothermal holding process. The non-equilibrium grain-boundary segregation concentration of phosphorus was measured with Auger Electron Spectroscopy (AES) and calculated based on the kinetic equations of non-equilibrium grain-boundary segregation. Results show that the calculated result is in good accordance with the experimental observation.

EXPERIMENTAL STUDY ON TIME EFFECT OF WET DRILLING PILE

Time effect of wet drilling pile is investigated through the static load experiment on pile No. 22 of Guanhe Bridge. Post-grouting under pile tip is adopted in the project. To study the bearing performance of the pile, the self-balanced method is used and two load cells are assembled in the pile body. The experiments are carried out before and after post-grouting. The upper part of the pile is not influenced by post-grouting under the pile tip. Experimental results of the upper part of the pile show that the bearing capacity and the rigidity of wet drilling pile increase with time passing on. Analysis results show the time effect of wet drilling pile is influenced by many factors, such as alteration of stress field around pile, characteristics of soil around pile, variety of mud cake, and property of residue under pile tip.

EFFECT OF TIME AND ENVIRONMENT ON THE DIMENSION PRECISION AND MASS OF LOM PROTOTYPES

The effect of time and environment on the dimension precision and mass of LOM prototypes was experimentally investigated.It is to identify the stability of the dimension of LOM prototypes after forming.The results show that the dimension and the mass tendency to grow,which is mainly caused by elastic recovery and moisture absorption and is characterized principally by the growth of Z dimension.Self restraint can be a significant factor to influence Z growth of LOM prototypes.

Time-sensitivity of the Kaiser effect of acoustic emission in limestone and its application to measurements of in-situ stress

Measuring in-situ stress by using the Kaiser effect in rocks has such advantages as timeefficiency, low cost and little limitation, but the precision of the method is dependent on rock properties and delay time of the measurement. In this paper, experiments on the Kaiser effect in limestones were performed, and it was found that the limestones had good ability to retain a memory of their recent stress history and high time-sensitivity. The longer the experiment was delayed from the extraction of the stone, the larger the Felicity ratio was. As the Felicity ratio approached l, significant Kaiser effect was observed. In-situ stress should be determined by the limestone measurements when the delay time was 40-120 days. Finally, the in-situ stress in a limestone formation could be successfully measured in practice.

Memory effect on the pressure-temperature condition and induction time of gas hydrate nucleation

The focus of this study is to investigate the influence of memory effect and the relation of its existence with the dissociation temperature,using gas hydrate formation and dissociation experiments.This is beneficial because memory effect is considered as an effective approach to promote the thermodynamic and dynamic conditions of gas hydrate nucleation.Seven experimental systems （twenty tests in total） were performed in a 1 L pressure cell.Three types of hydrate morphology,namely massive,whiskery and jelly crystals were present in the experiments.The pressures and temperatures at the time when visual hydrate crystals appeared were measured.Furthermore,the influence of memory effect was quantified in terms of pressure-temperature-time （p-T-t） relations.The results revealed that memory effect could promote the thermodynamic conditions and shorten the induction time when the dissociation temperature was not higher than 25℃.In this study,the nucleation superpressure and induction time decrease gradually with time of tests,when the earlier and the later tests are compared.It is assumed that the residual structure of hydrate dissociation,as the source of the memory effect,provides a site for mass transfer between host and guest molecules.Therefore,a driving force is created between the residual structures and its surrounding bulk phase to promote the hydrate nucleation.However,when the dissociation temperature was higher than 25 ℃,the memory effect vanished.These findings provide references for the application of memory effect in hydrate-based technology.

Modeling of Fluid Turbulence Modification Using Two-time-scale Dissipation Models and Accounting for the Particle Wake Effect

Presently developed two-phase turbulence models under-predict the gas turbulent fluctuation, because their turbulence modification models cannot fully reflect the effect of particles. In this paper, a two-time-scale dis- sipation model of turbulence modification, developed for the two-phase velocity correlation and for the dissipation rate of gas turbulent kinetic energy, is proposed and used to simulate sudden-expansion and swirling gas-particle flows. The proposed two-time scale model gives better results than the single-time scale model. Besides, a gas tur- bulence augmentation model accounting for the finite-size particle wake effect in the gas Reynolds stress equation is proposed. The proposed turbulence modification models are used to simulate two-phase pipe flows. It can prop- erly predict both turbulence reduction and turbulence enhancement for a certain size of particles observed in ex- periments.

Monitoring models for base flow effect and daily variation of dam seepage elements considering time lag effect

Affected by external environmental factors and evolution of dam performance, dam seepage behavior shows nonlinear time-varying characteristics. In this study, to predict and evaluate the long-term development trend and short-term fluctuation of the dam seepage behavior, two monitoring models were developed, one for the base flow effect and one for daily variation of dam seepage elements. In the first model, to avoid the influence of the time lag effect on the evaluation of seepage variation with the time effect component of seepage elements, the base values of the seepage element and the reservoir water level were extracted using the wavelet multi-resolution analysis method, and the time effect component was separated by the established base flow effect monitoring model. For the development of the daily variation monitoring model for dam seepage elements, all the previous factors, of which the measured time series prior to the dam seepage element monitoring time may have certain influence on the monitored results, were considered. Those factors that were positively correlated with the analyzed seepage element were initially considered to be the support vector machine(SVM) model input factors, and then the SVM kernel function-based sensitivity analysis was performed to optimize the input factor set and establish the optimized daily variation SVM model. The efficiency and rationality of the two models were verified by case studies of the water level of two piezometric tubes buried under the slope of a concrete gravity dam.Sensitivity analysis of the optimized SVM model shows that the influences of the daily variation of the upstream reservoir water level and rainfall on the daily variation of piezometric tube water level are processes subject to normal distribution.

Modeling of Fluid Turbulence Modification Using Two-time-scale Dissipation Models and Accounting for the Particle Wake Effect

Presently developed two-phase turbulence models under-predict the gas turbulent fluctuation, because their turbulence modification models cannot fully reflect the effect of particles. In this paper, a two-time-scale dissipation model of turbulence modification, developed for the two-phase velocity correlation and for the dissipation rate of gas turbulent kinetic energy, is proposed and used to simulate sudden-expansion and swirling gas-particle flows. The proposed two-time scale model gives better results than the single-time scale model. Besides, a gas turbulence augmentation model accounting for the f＇mite-size particle wake effect in the gas Reynolds stress equation is proposed. The proposed turbulence modification models are used to simulate two-phase pipe flows. It can properly predict both turbulence reduction and turbulence enhancement for a certain size of particles observed in experiments.

A new approach for time effect analysis of settlement for single pile based on virtual soil-pile model

A new approach is proposed to analyze the settlement behavior for single pile embedded in layered soils. Firstly, soil layers surrounding pile shaft are simulated by using distributed Voigt model, and finite soil layers under the pile end are assumed to be virtual soil-pile whose cross-section area is the same as that of the pile shaft. Then, by means of Laplace transform and impedance function transfer method to solve the static equilibrium equation of pile, the analytical solution of the displacement impedance fimction at the pile head is derived. Furthermore, the analytical solution of the settlement at the head of single pile is theoretically derived by virtue of convolution theorem. Based on these solutions, the influences of parameters of soil-pile system on the settlement behavior for single pile are analyzed. Also, comparison of the load-settlement response for two well-instrumented field tests in multilayered soils is given to demonstrate the effectiveness and accuracy of the proposed approach. It can be noted that the presented solution can be used to calculate the settlement of single pile for the preliminary design of pile foundation.

Mathematical Model for Tempering Time Effect on Quenched Steel Based on Hollomon Parameter

Through the differentiating and integrating process, a mathematical model for tempering time effect on quenched steel was derived based on the attribute of state function and the general equation of Hollomon parameter, which correlates the tempering hardness with the tempering time at different tempering temperature. Using the established model, the linear relationship between the tempering hardness and the tempering time in logarithm was proved theoretically, and the tempering hardness for various tempering time was reduced to the measurement and calculation of a hardness experiment tempered for 1 h at different tempering temperatures. Moreover, the hardness of steel 42CrMo and T8Mn tempered for various times at 200-600℃ was calculated using this method. The predicted results are in good agreement with those of the available experiments.

Time effect and prediction of broken rock bulking coefficient on the base of particle discrete element method

Bulking characteristics of gangue are of great significance for the stability of goafs in mining overburden in the caving zones.In this paper,a particle discrete element method with clusters to represent gangue was adopted to explore the bulking coefficient time effect of the broken rock in the caving zone under three-dimensional triaxial compression condition.The phenomena of stress corrosion,deformation,and failure of rock blocks were simulated in the numerical model.Meanwhile,a new criterion of rock fragments damage was put forward.It was found that the broken rock has obvious viscoelastic properties.A new equation based on the Burgers creep model was proposed to predict the bulking coefficient of broken rock.A deformation characteristic parameter of the prediction equation was analyzed,which can be set as a fixed value in the mid-and long-term prediction of the bulking coefficient.There are quadratic function relationships between the deformation characteristic parameter value and Talbot gradation index,axial pressure and confining pressure.