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.

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.

Sample size adaptive strategy for time-dependent Monte Carlo particle transport simulation

When multiphysics coupling calculations contain time-dependent Monte Carlo particle transport simulations, these simulations often account for the largest part of the calculation time, which is insufferable in certain important cases. This study proposes an adaptive strategy for automatically adjusting the sample size to fulfil more reasonable simulations. This is realized based on an extension of the Shannon entropy concept and is essentially different from the popular methods in timeindependent Monte Carlo particle transport simulations, such as controlling the sample size according to the relative error of a target tally or by experience. The results of the two models show that this strategy can yield almost similar results while significantly reducing the calculation time. Considering the efficiency, the sample size should not be increased blindly if the efficiency cannot be enhanced further. The strategy proposed herein satisfies this requirement.

Time-dependent variational approach to solve multi-dimensional time-dependent Schr?dinger equation

We present an efficient approach to solve multi-dimensional time-dependent Schr?dinger equation(TDSE)in an intense laser field.In this approach,each spatial degree of freedom is treated as a distinguishable quasi-particle.The non-separable Coulomb potential is regarded as a two-body operator between different quasi-particles.The time-dependent variational principle is used to derive the equations of motion.Then the high-order multi-dimensional problem is broken down into several lower-order coupled equations,which can be efficiently solved.As a demonstration,we apply this method to solve the two-dimensional TDSE.The accuracy is tested by comparing the direct solutions of TDSE using several examples such as the strong-field ionization and the high harmonic generation.The results show that the present method is much more computationally efficient than the conventional one without sacrificing accuracy.The present method can be straightforwardly extended to three-dimensional problems.Our study provides a flexible method to investigate the laser-atom interaction in the nonperturbative regime.

Non-harmonic resonance of viscoelastic structures subjected to time-dependent exponentially decreasing transverse distributed loads

In this paper,the non-harmonic resonance of Bernoulli viscoelastic beams,Kirchhoff viscoelastic plates,Timoshenko viscoelastic beams,and Mindlin viscoelastic plates subjected to time-dependent exponentially decreasing transverse distributed load is investigated for the first time.The constitutive equations are expressed utilizing Boltzmann integral law with a constant bulk modulus.The displacement vector is approximated by employing the separation of variables method.The Laplace transformation is used to transfer equations from the time domain to the Laplace domain and vice versa.The novel point of the proposed method is to express,prove and calculate the critical time in which the displacement will be several times the displacement at time zero.In addition,this new method calculates the maximum deflection at the critical time,explicitly and exactly,without any need to follow the time-displacement curve with a low computational cost.Additionally,the proposed method introduces the critical range of time so that the responses are greater than the responses at time zero.

Blowup of Solutions to the Non-Isentropic Compressible Euler Equations with Time-Dependent Damping and Vacuum

This paper mainly studies the blowup phenomenon of solutions to the compressible Euler equations with general time-dependent damping for non-isentropic fluids in two and three space dimensions. When the initial data is assumed to be radially symmetric and the initial density contains vacuum, we obtain that classical solution, especially the density, will blow up on finite time. The results also reveal that damping can really delay the singularity formation.

Extra Time Dimension: Deriving Relativistic Space-Time Transformations, Kinematics, and Example of Dimensional Compactification Using Time-Dependent Non-Relativistic Quantum Mechanics

We consider a five-dimensional Minkowski space with two time dimensions characterized by distinct speeds of causality and three space dimensions. Formulas for relativistic coordinate and velocity transformations are derived, leading to a new expression for the speed limit. Extending the ideas of Einstein’s Theory of Special Relativity, concepts of five-velocity and five-momenta are introduced. We get a new formula for the rest energy of a massive object. Based on a non-relativistic limit, a two-time dependent Schrödinger-like equation for infinite square-well potential is developed and solved. The extra time dimension is compactified on a closed loop topology with a period matching the Planck time. It generates interference of additional quantum states with an ultra-small period of oscillation. Some cosmological implications of the concept of four-dimensional versus five-dimensional masses are briefly discussed, too.

Determination of safe mud window considering time-dependent variations of temperature and pore pressure:Analytical and numerical approaches

Wellbore stability is a key to have a successful drilling operation.Induced stresses are the main factors affecting wellbore instability and associated problems in drilling operations.These stresses are significantly impacted by pore pressure variation and thermal stresses in the field.In order to address wellbore instability problems,it is important to investigate the mechanisms of rockefluid interaction with respect to thermal and mechanical aspects.In order to understand the induced stresses,different mathematical models have been developed.In this study,the field equations governing the problem have been derived based on the thermo-poroelastic theory and solved analytically in Laplace domain.The results are transferred to time domain using Fourier inverse method.Finite difference method is also utilized to validate the results.Pore pressure and temperature distributions around the wellbore have been focused and simulated.Next,induced radial and tangential stresses for different cases of cooling and heating of formation are compared.In addition,the differences between thermo-poroelastic and poroelastic models in situation of permeable and impermeable wellbores are described.It is observed that cooling and pore pressure distribution reinforce the induced radial stress.Whereas cooling can be a tool to control and reduce tangential stress induced due to invasion of drilling fluid.In the next step,safe mud window is obtained using Mohr-Coulomb,Mogi-Coulomb,and modified Lade failure criteria for different inclinations.Temperature and pore pressure distributions do not change the minimum allowable wellbore pressure significantly.However,upper limit of mud window is sensitive to induced stresses and it seems vital to consider changes in temperature and pore pressure to avoid any failures.The widest and narrowest mud windows are proposed by modified Lade and Mohr-Coulomb failure criteria,respectively.

Multiscale modeling of gas-induced fracturing in anisotropic clayey rocks

In the context of repositories for nuclear waste,understanding the behavior of gas migration through clayey rocks with inherent anisotropy is crucial for assessing the safety of geological disposal facilities.The primary mechanism for gas breakthrough is the opening of micro-fractures due to high gas pressure.This occurs at gas pressures lower than the combined strength of the rock and its minimum principal stress under external loading conditions.To investigate the mechanism of microscale mode-I ruptures,it is essential to incorporate a multiscale approach that includes subcritical microcracks in the modeling framework.In this contribution,we derive the model from microstructures that contain periodically distributed microcracks within a porous material.The damage evolution law is coupled with the macroscopic poroelastic system by employing the asymptotic homogenization method and considering the inherent hydro-mechanical(HM)anisotropy at the microscale.The resulting permeability change induced by fracture opening is implicitly integrated into the gas flow equation.Verification examples are presented to validate the developed model step by step.An analysis of local macroscopic response is undertaken to underscore the influence of factors such as strain rate,initial damage,and applied stress,on the gas migration process.Numerical examples of direct tension tests are used to demonstrate the model’s efficacy in describing localized failure characteristics.Finally,the simulation results for preferential gas flow reveal the robustness of the two-scale model in explicitly depicting gas-induced fracturing in anisotropic clayey rocks.The model successfully captures the common behaviors observed in laboratory experiments,such as a sudden drop in gas injection pressure,rapid build-up of downstream gas pressure,and steady-state gas flow following gas breakthrough.

Dirac method for nonlinear and non-homogenous boundary value problems of plates

The boundary value problem plays a crucial role in the analytical investigation of continuum dynamics. In this paper, an analytical method based on the Dirac operator to solve the nonlinear and non-homogeneous boundary value problem of rectangular plates is proposed. The key concept behind this method is to transform the nonlinear or non-homogeneous part on the boundary into a lateral force within the governing function by the Dirac operator, which linearizes and homogenizes the original boundary, allowing one to employ the modal superposition method for obtaining solutions to reconstructive governing equations. Once projected into the modal space, the harmonic balance method(HBM) is utilized to solve coupled ordinary differential equations(ODEs)of truncated systems with nonlinearity. To validate the convergence and accuracy of the proposed Dirac method, the results of typical examples, involving nonlinearly restricted boundaries, moment excitation, and displacement excitation, are compared with those of the differential quadrature element method(DQEM). The results demonstrate that when dealing with nonlinear boundaries, the Dirac method exhibits more excellent accuracy and convergence compared with the DQEM. However, when facing displacement excitation, there exist some discrepancies between the proposed approach and simulations;nevertheless, the proposed method still accurately predicts resonant frequencies while being uniquely capable of handling nonuniform displacement excitations. Overall, this methodology offers a convenient way for addressing nonlinear and non-homogenous plate boundaries.

Modelling the viscoplastic behaviour of Callovo-Oxfordian claystone with consideration of damage effect

In order to evaluate the performance of deep geological disposal of radioactive waste,an underground research laboratory(URL)was constructed by Andra in the Callovo-Oxfordian(COx)claystone formation at the Meuse/Haute-Marne(MHM).The construction of URL induced the excavation damage of host formations,and the ventilation in the galleries desaturated the host formation close to the gallery wall.Moreover,it is expected that the mechanical behaviour of COx claystone is time-dependent.This study presents a constitutive model developed to describe the viscoplastic behaviour of unsaturated and damaged COx claystone.In this model,the unsaturation effect is considered by adopting the Bishop effective stress and the van Genuchten(VG)water retention model.In terms of the viscoplastic behaviour,the nonstationary flow surface(NSFS)theory for unsaturated soils is used with consideration of the coupled effects of strain rate and suction on the yield stress.A progressive hardening law is adopted.Meanwhile,a non-associated flow rule is used,which is similar to that in Barcelona basic model(BBM).In addition,to describe the damage effect induced by suction change and viscoplastic loading,a damage function is defined based on the crack volume proportion.This damage function contains two variables:unsaturated effective stress and viscoplastic volumetric strain,with the related parameters determined based on the mercury intrusion porosimetry(MIP)tests.For the model validation,different tests on COx claystone under different loading paths are simulated.Comparisons between experimental and simulated results indicated that the present model is able to well describe the viscoplastic behaviour of damaged COx claystone,including swelling/shrinkage,triaxial extension and compression,and triaxial creep.

Microscopic mechanism of plasmon-mediated photocatalytic H_(2) splitting on Ag-Au alloy chain

Alloy nanostructures supporting localized surface plasmon resonances has been widely used as efficient photocatalysts,but the microscopic mechanism of alloy compositions enhancing the catalytic efficiency is still unclear.By using time-dependent density functional theory(TDDFT),we analyze the real-time reaction processes of plasmon-mediated H_(2) splitting on linear Ag-Au alloy chains when exposed to femtosecond laser pulses.It is found that H_(2) splitting rate depends on the position and proportion of Au atoms in alloy chains,which indicates that specially designed Ag-Au alloy is more likely to induce the reaction than pure Ag chain.Especially,more electrons directly transfer from the alloy chain to the anti-bonding state of H_(2),thereby accelerating the H_(2) splitting reaction.These results establish a theoretical foundation for comprehending the microscopic mechanism of plasmon-induced chemical reaction on the alloy nanostructures.

Plasmon-induced nonlinear response on gold nanoclusters

The plasmon-induced nonlinear response has attracted great attention in micro-nano optics and optoelectronics applications,yet the underlying microscopic mechanism remains elusive.In this study,the nonlinear response of gold nanoclusters when exposed to a femtosecond laser pulse was investigated using time-dependent density functional theory.It was observed that the third-order tunneling current was augmented in plasmonic dimers,owing to a greater number of electrons in the dimer being excited from occupied to unoccupied states.These findings provide profound theoretical insights and enable the realization of accurate regulation and control of nonlinear effects induced by plasmons at the atomic level.

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.

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.

Time-dependent safety of lining structures of circular tunnels in weak rock strata

Following tunnel excavation and lining completion,fractured surrounding rock deforms gradually over time;this results in a time-dependent evolution of the pressure applied to the lining structure by the surrounding rock.Thus,the safety of the tunnel lining in weak strata is strongly correlated with time.In this study,we developed an analytical method for determining the time-dependent pressure in the surrounding rock and lining structure of a circular tunnel under a hydrostatic stress field.Under the proposed method,the stress–strain relationship of the fractured surrounding rock is assumed to conform to that of the Burgers viscoelastic component,and the lining structure is assumed to be an elastomer.Based on these assumptions,the viscoelastic deformation of the surrounding rock,the elastic deformation of the lining structure,and the coordinated deformation between the surrounding rock and lining structure were derived.The proposed analytical method,which employs a time-dependent safety coefficient,was subsequently used to estimate the durability of the lining structure of the Foling Tunnel in China.The derived attenuation curve of the safety coefficient with respect to time can assist engineers in predicting the remaining viable life of the lining structure.Unlike existing analytical methods,the method derived in this study considers the time dependency of the interaction between the surrounding rock and tunnel lining;hence,it is more suitable for the evaluation of lining lifetime.

The characterization of the time-dependent nonlinear viscoelastic of an LDPE melt using a simple thixotropy model

A new simple thixotropy model was proposed in the present paper to characterize the thixotropy-loop experiments and the start-up experiment of an LDPE （PE-FSB23D0221Q200） melt. The thixotropy model is a combination of a viscoelastic-component and a postulated kinetics process of structure change, which is constituted in terms of the indirect microstructural approach usually adopted in the characterization of thixotropy. The descriptions of the thixotropy model on both the thixotropy-loop tests and the startup test show good agreement with the experimental values, indicating the good capability of the model in characterizing the time-dependent nonlinear viscoelastic. The stress overshoot phenomenon and the stress relaxation after cessation of the thixotropy loop test can be described well by the model, whereas both of the typical viscoelastic phenomena could not be described in our previous work with a variant Huang model.

Approximate solution to the time-dependent Kratzer plus screened Coulomb potential in the Feinberg–Horodecki equation

We obtain the quantized momentum eigenvalues Pn together with space-like coherent eigenstates for the space-like counterpart of the Schr¨odinger equation,the Feinberg–Horodecki equation,with a combined Kratzer potential plus screened coulomb potential which is constructed by temporal counterpart of the spatial form of these potentials.The present work is illustrated with two special cases of the general form:the time-dependent modified Kratzer potential and the time-dependent screened Coulomb potential.