Modeling time-dependent mechanical behavior of hard rock considering excavation-induced damage and complex 3D stress states

To investigate the long-term stability of deep rocks,a three-dimensional(3D)time-dependent model that accounts for excavation-induced damage and complex stress state is developed.This model comprises three main components:a 3D viscoplastic isotropic constitutive relation that considers excavation damage and complex stress state,a quantitative relationship between critical irreversible deformation and complex stress state,and evolution characteristics of strength parameters.The proposed model is implemented in a self-developed numerical code,i.e.CASRock.The reliability of the model is validated through experiments.It is indicated that the time-dependent fracturing potential index(xTFPI)at a given time during the attenuation creep stage shows a negative correlation with the extent of excavationinduced damage.The time-dependent fracturing process of rock demonstrates a distinct interval effect of the intermediate principal stress,thereby highlighting the 3D stress-dependent characteristic of the model.Finally,the influence of excavation-induced damage and intermediate principal stress on the time-dependent fracturing characteristics of the surrounding rocks around the tunnel is discussed.

Impact of different interaction behavior on epidemic spreading in time-dependent social networks

We investigate the impact of pairwise and group interactions on the spread of epidemics through an activity-driven model based on time-dependent networks.The effects of pairwise/group interaction proportion and pairwise/group interaction intensity are explored by extensive simulation and theoretical analysis.It is demonstrated that altering the group interaction proportion can either hinder or enhance the spread of epidemics,depending on the relative social intensity of group and pairwise interactions.As the group interaction proportion decreases,the impact of reducing group social intensity diminishes.The ratio of group and pairwise social intensity can affect the effect of group interaction proportion on the scale of infection.A weak heterogeneous activity distribution can raise the epidemic threshold,and reduce the scale of infection.These results benefit the design of epidemic control strategy.

A process-oriented approach for identifying potential landslides considering time-dependent behaviors beyond geomorphological features

Geomorphological features are commonly used to identify potential landslides.Nevertheless,overemphasis on these features could lead to misjudgment.This research proposes a process-oriented approach for potential landslide identification that considers time-dependent behaviors.The method integrates comprehensive remote sensing and geological analysis to qualitatively assess slope stability,and employs numerical analysis to quantitatively calculate aging stability.Specifically,a time-dependent stability calculation method for anticlinal slopes is developed and implemented in discrete element software,incorporating time-dependent mechanical and strength reduction calculations.By considering the time-dependent evolution of slopes,this method highlights the importance of both geomorphological features and time-dependent behaviors in landslide identification.This method has been applied to the Jiarishan slope(JRS)on the Qinghai-Tibet Plateau as a case study.The results show that the JRS,despite having landslide geomorphology,is a stable slope,highlighting the risk of misjudgment when relying solely on geomorphological features.This work provides insights into the geomorphological characterization and evolution history of the JRS and offers valuable guidance for studying slopes with similar landslide geomorphology.Furthermore,the process-oriented method incorporating timedependent evolution provides a means to evaluate potential landslides,reducing misjudgment due to excessive reliance on geomorphological features.

A GENERALIZED SCALAR AUXILIARY VARIABLE METHOD FOR THE TIME-DEPENDENT GINZBURG-LANDAU EQUATIONS

This paper develops a generalized scalar auxiliary variable(SAV)method for the time-dependent Ginzburg-Landau equations.The backward Euler method is used for discretizing the temporal derivative of the time-dependent Ginzburg-Landau equations.In this method,the system is decoupled and linearized to avoid solving the non-linear equation at each step.The theoretical analysis proves that the generalized SAV method can preserve the maximum bound principle and energy stability,and this is confirmed by the numerical result,and also shows that the numerical algorithm is stable.

Momentum Eigensolutions of Feinberg-Horodecki Equation with Time-Dependent Screened Kratzer-Hellmann Potential

We obtain an approximate value of the quantized momentum eigenvalues, Pn, together with the space-like coherent eigenvectors for the space-like counterpart of the Schrödinger equation, the Feinberg-Horodecki equation, with a screened Kratzer-Hellmann potential which is constructed by the temporal counterpart of the spatial form of this potential. In addition, we got exact eigenvalues of the momentum and the eigenstates by solving Feinberg-Horodecki equation with Kratzer potential. The present work is illustrated with three special cases of the screened Kratzer-Hellman potential: the time-dependent screened Kratzer potential, time-dependent Hellmann potential and, the time-dependent screened Coulomb potential.

Sensitivity Analysis of Electromagnetic Scattering from Dielectric Targets with Polynomial Chaos Expansion and Method of Moments

In this paper,an adaptive polynomial chaos expansion method(PCE)based on the method of moments(MoM)is proposed to construct surrogate models for electromagnetic scattering and further sensitivity analysis.The MoM is applied to accurately solve the electric field integral equation(EFIE)of electromagnetic scattering from homogeneous dielectric targets.Within the bistatic radar cross section(RCS)as the research object,the adaptive PCE algorithm is devoted to selecting the appropriate order to construct the multivariate surrogate model.The corresponding sensitivity results are given by the further derivative operation,which is compared with those of the finite difference method(FDM).Several examples are provided to demonstrate the effectiveness of the proposed algorithm for sensitivity analysis of electromagnetic scattering from homogeneous dielectric targets.

The deterministic condition for the ground reaction force acting point on the combined knee valgus and tibial internal rotation moments in early phase of cutting maneuvers in female athletes

Background:Combined knee valgus and tibial internal rotation(VL+IR)moments have been shown to stress the anterior cruciate ligament(ACL)in several in vitro cadaveric studies.To utilize this knowledge for non-contact ACL injury prevention in sports,it is necessary to elucidate how the ground reaction force(GRF)acting point(center of pressure(CoP))in the stance foot produces combined knee VL+IR moments in risky maneuvers,such as cuttings.However,the effects of the GRF acting point on the development of the combined knee VL+IR moment in cutting are still unknown.Methods:We first established the deterministic mechanical condition that the CoP position relative to the tibial rotational axis differentiates the GRF vector’s directional probability for developing the combined knee VL+IR moment,and theoretically predicted that when the CoP is posterior to the tibial rotational axis,the GRF vector is more likely to produce the combined knee VL+IR moment than when the CoP is anterior to the tibial rotational axis.Then,we tested a stochastic aspect of our theory in a lab-controlled in vivo experiment.Fourteen females performed 60˚cutting under forefoot/rearfoot strike conditions(10 trials each).The positions of lower limb markers and GRF data were measured,and the knee moment due to GRF vector was calculated.The trials were divided into anterior-and posterior-CoP groups depending on the CoP position relative to the tibial rotational axis at each 10 ms interval from 0 to 100 ms after foot strike,and the occurrence rate of the combined knee VL+IR moment was compared between trial groups.Results:The posterior-CoP group showed significantly higher occurrence rates of the combined knee VL+IR moment(maximum of 82.8%)at every time point than those of the anterior-CoP trials,as theoretically predicted by the deterministic mechanical condition.Conclusion:The rearfoot strikes inducing the posterior CoP should be avoided to reduce the risk of non-contact ACL injury associated with the combined knee VL+IR stress.

Thermomechanical Dynamics (TMD) and Bifurcation-Integration Solutions in Nonlinear Differential Equations with Time-Dependent Coefficients

The new independent solutions of the nonlinear differential equation with time-dependent coefficients (NDE-TC) are discussed, for the first time, by employing experimental device called a drinking bird whose simple back-and-forth motion develops into water drinking motion. The solution to a drinking bird equation of motion manifests itself the transition from thermodynamic equilibrium to nonequilibrium irreversible states. The independent solution signifying a nonequilibrium thermal state seems to be constructed as if two independent bifurcation solutions are synthesized, and so, the solution is tentatively termed as the bifurcation-integration solution. The bifurcation-integration solution expresses the transition from mechanical and thermodynamic equilibrium to a nonequilibrium irreversible state, which is explicitly shown by the nonlinear differential equation with time-dependent coefficients (NDE-TC). The analysis established a new theoretical approach to nonequilibrium irreversible states, thermomechanical dynamics (TMD). The TMD method enables one to obtain thermodynamically consistent and time-dependent progresses of thermodynamic quantities, by employing the bifurcation-integration solutions of NDE-TC. We hope that the basic properties of bifurcation-integration solutions will be studied and investigated further in mathematics, physics, chemistry and nonlinear sciences in general.

Time-dependent magnetometric resistivity anomalies of groundwater contamination: Synthetic results from computational hydro-geophysical modeling

We present a forward-modeling investigation of time-dependent ground magnetometric resistivity （MMR） anomalies associated with transient leachate transport in groundwater systems. Numerical geo-electrical models are constructed based on the hydrological simulation results of leachate plumes from a highly conceptualized landfill system and the resultant MMR responses are computed using a modified finite difference software MMR2DFD. Three transmitter configurations （i.e., single source, MMR-TE, and MMR-TM modes） and two hydrological models （i.e., uniform and faulted porous media） are considered. Our forward modeling results for the uniform porous medium indicates that the magnetic field components perpendicular to the dominant current flow contain the most information of the underground targets and the MMR-TE mode is an appropriate configuration for detecting contaminant plumes. The modeling experiments for the faulted porous medium also confirm that the MMR method is capable of mapping and monitoring the extent of contaminant plumes in aroundwater systems.

Construction of a complete set of similarity invariants using pseudo-Zernike moments

To resolve the completeness and independence of an invariant set derived by the traditional method, a systematic method for deriving a complete set of pseudo-Zernike moment similarity （translation, scale and rotation） invariants is described. First, the relationship between pseudo-Zernike moments of the original image and those of the image having the same shape but distinct orientation and scale is established. Based on this relationship, a complete set of similarity invariants can be expressed as a linear combination of the original pseudo-Zernike moments of the same order and lower order. The problem of image reconstruction from a finite set of the pseudo-Zernike moment invariants （PZMIs） is also investigated. Experimental results show that the proposed PZMIs have better performance than complex moment invariants.

Retrieving Microphysical Properties and Air Motion of Cirrus Clouds Based on the Doppler Moments Method Using Cloud Radar

Radar parameters including radar reflectivity, Doppler velocity, and Doppler spectrum width were obtained from Doppler spectrum moments. The Doppler spectrum moment is the convolution of both the particle spectrum and the mean air vertical motion. Unlike strong precipitation, the motion of particles in cirrus clouds is quite close to the air motion around them. In this study, a method of Doppler moments was developed and used to retrieve cirrus cloud microphysical properties such as the mean air vertical velocity, mass-weighted diameter, effective particle size, and ice content. Ice content values were retrieved using both the Doppler spectrum method and classic Z-IWC （radar reflectivity-ice water content） relationships; however, the former is a more reasonable method.

On the Spectral Moments of Wind Waves

In order to obtain high order spectral moments, the residual moment M(w(n))(i) = integral(0)(wn) w(i)S(w)dw, as proposed by Denis s, is presented for approximate estimation of spectral moment m(i) = integral(0)(infinity) w(i)S(w)dw. Glazman's partial averaging idea is discussed. It is pointed out that Glazman's method and definition of non-dimensional spectral moment can not be used to estimate spectral moments for engineering purposes and that method is not supported by theory and computation. The non-dimensional spectral moment of PM spectrum, which should be expressed as [GRAPHICS] is related to wind speed. The 0 - 8th moments of PM spectrum are estimated for wind speeds of 10, 20 and 30 m/s and some discussions are given.

Series expansion feasibility of singular integral in method of moments

When calculating electromagnetic scattering using method of moments （MoM）, integral of the singular term has a significant influence on the results. This paper transforms the singular surface integral to the contour integral. The integrand is expanded to Taylor series and the integral results in a closed form. The cut-off error is analyzed to show that the series converges fast and only about 2 terms can agree wel with the accurate result. The comparison of the perfect electric conductive （PEC） sphere＇s bi-static radar cross section （RCS） using MoM and the accurate method validates the feasibility in manipulating the singularity. The error due to the facet size and the cut-off terms of the series are analyzed in examples.

Numerical investigation into pillar failure induced by time-dependent skin degradation

This paper focuses on the instability mechanism of an isolated pillar, caused by time-dependent skin degradation and strength heterogeneity. The time-dependent skin degradation is simulated with a non-linear rheological model capable of simulating tertiary creep, whereby two different pillar failure cases are investigated. The first case is of an isolated pillar in a deep hard rock underground mine and subjected to high stresses. The results show that pillar degradation is limited to the regions near the surface or the skin until two months after ore extraction. Afterwards degradation starts to extend deeper into the pillar, eventually leaving a highly-stressed pillar core due to stress transfer from the failed skin.Rockburst potential indices show that the risk increases exponentially at the core as time goes by. It is then demonstrated that the progressive skin degradation cannot be simulated with conventional strain-softening model assuming brittle failure. The parametric study with respect to the degree of heterogeneity reveals that heterogeneity is key to the occurrence of progressive skin degradation. The second case investigated in this study is pillar failure taking place in a very long period. Such failure becomes significantly important when assessing the risk for ground subsidence caused by pillar collapse in an abandoned mine. The analysis results demonstrate that the employed non-linear rheological model can simulate gradual skin degradation taking place over several hundred years. The percentage of damage zone volume within the pillar is merely 1% after a lapse of one days and increases to 50% after one hundred years, indicating a high risk for pillar collapse in the long term. The vertical displacements within the pillar also indicate the risk of subsidence. The proposed method is suitable for evaluating the risk of ground surface subsidence above an abandoned mine.

CALCULATING RESPONSE SPECTRAL MOMENTS BY COMPLEX MODAL ANALYSIS

Response spectral moments are useful for system reliability analysis.Usually,spectral mo- ments are calculated by the frequency domain method.Based on the time domain modal analysis of random vibrations,the authors present a new method for calculating response spectral moments through response correlation functions.The method can be applied to both classical and non-classical damping cases and to three kinds of random excitations,i.e.,white noise,band-limited white noise, and filtered white noise.

THE FINITE DIFFERENCE STREAMLINE DIFFUSION METHODS FOR TIME-DEPENDENT CONVECTION-DIFFUSION EQUATIONS

In this paper, two finite difference streamline diffusion (FDSD) schemes for solving two-dimensional time-dependent convection-diffusion equations are constructed. Stability and optimal order error estimati-ions for considered schemes are derived in the norm stronger than L^2-norm.

Fast Non-Local Means Algorithm Based on Krawtchouk Moments

Non-local means(NLM)method is a state-of-the-art denoising algorithm, which replaces each pixel with a weighted average of all the pixels in the image. However, the huge computational complexity makes it impractical for real applications. Thus, a fast non-local means algorithm based on Krawtchouk moments is proposed to improve the denoising performance and reduce the computing time. Krawtchouk moments of each image patch are calculated and used in the subsequent similarity measure in order to perform a weighted averaging. Instead of computing the Euclidean distance of two image patches, the similarity measure is obtained by low-order Krawtchouk moments, which can reduce a lot of computational complexity. Since Krawtchouk moments can extract local features and have a good antinoise ability, they can classify the useful information out of noise and provide an accurate similarity measure. Detailed experiments demonstrate that the proposed method outperforms the original NLM method and other moment-based methods according to a comprehensive consideration on subjective visual quality, method noise, peak signal to noise ratio(PSNR), structural similarity(SSIM) index and computing time. Most importantly, the proposed method is around 35 times faster than the original NLM method.

NONLINEAR STOCHASTIC HEAT EQUATION DRIVEN BY SPATIALLY COLORED NOISE:MOMENTS AND INTERMITTENCY

In this article, we study the nonlinear stochastic heat equation in the spatial domain R^d subject to a Gaussian noise which is white in time and colored in space. The spatial correlation can be any symmetric, nonnegative and nonnegative-definite function that satisfies Dalang's condition. We establish the existence and uniqueness of a random field solution starting from measure-valued initial data. We find the upper and lower bounds for the second moment. With these moment bounds, we first establish some necessary and sufficient conditions for the phase transition of the moment Lyapunov exponents, which extends the classical results from the stochastic heat equation on Z^d to that on R^d.Then, we prove a localization result for the intermittency fronts, which extends results by Conus and Khoshnevisan [9] from one space dimension to higher space dimension. The linear case has been recently proved by Huang et al [17] using different techniques.

Ghost images reconstructed from fractional-order moments with thermal light

We present the joint probability density function(PDF) between the bucket signals and reference signals in thermal light ghost imaging, by regarding these signals as stochastic variables. The joint PDF allows us to examine the fractional-order moments of the bucket and the reference signals, in which the correlation orders are fractional numbers,other than positive integers in previous studies. The experimental results show that various images can be reconstructed from fractional-order moments. Negative(positive) ghost images are obtained with negative(positive) orders of the bucket signals. The visibility and peak signal-to-noise ratios of the diverse ghost images depend greatly on the fractional orders.

Simulation of Vacuum Arc Characteristics at Different Moments Under Power-Frequency Current

In this paper, based on the quasi-stationary magneto-hydrodynamic （MHD） model, vacuum arc characteristics are simulated and analyzed at different moments under power-frequency current. For a vacuum arc with sinusoidal current under a uniform axial magnetic field （AMF）, simulation results show that at the moment of peak value current, maximal values appear in the ion number density, axial current density, heat flux density, electron temperature, plasma pressure and azimuthal magnetic field. At the same time, the distributions of these parameters along the radial position are mostly nonuniform as compared with those at other moments. In the first 1/4 cycle, the ion number density, axial current density and plasma pressure increase with time, but the growth rate decreases with time. Simulation results are partially compared with experimental results published in other papers. Simulations and light intensity near the cathode side is stronger than arcs. experimental results both show that the arc that near the anode side for diffusing vacuum