Modified <i>f(R)</i>Gravity and Thermodynamics of Time-Dependent Wormholes at Event Horizon

In the context of modified gravity theory, we study time-dependent wormhole spacetimes in the radiation background. In this framework, we attempt to generalize the thermodynamic properties of time-dependent wormholes in gravity. Finally, at event horizon, the rate of change of total entropy has been 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.

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.

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.

Thin-Shell Wormholes Admitting Conformal Motions in Spacetimes of Embedding Class One

This paper discusses the feasibility of thin-shell wormholes in spacetimes of embedding class one admitting a one-parameter group of conformal motions. It is shown that the surface energy density σis positive, while the surface pressure is negative, resulting in , thereby signaling a violation of the null energy condition, a necessary condition for holding a wormhole open. For a Morris-Thorne wormhole, matter that violates the null energy condition is referred to as “exotic”. For the thin-shell wormholes in this paper, however, the violation has a physical explanation since it is a direct consequence of the embedding theory in conjunction with the assumption of conformal symmetry. These properties avoid the need to hypothesize the existence of the highly problematical exotic matter.

Macroscopic Traversable Wormholes: Minimum Requirements

While wormholes are just as good a prediction of Einstein’s theory as black holes, they are subject to severe restrictions from quantum field theory. To allow for the possibility of interstellar travel, a macroscopic wormhole would need to maintain sufficiently low radial tidal forces. It is proposed in this paper that the assumption of zero tidal forces, i.e., the limiting case, is sufficient for overcoming the restrictions from quantum field theory. The feasibility of this approach is subsequently discussed by 1) introducing the additional conditions needed to ensure that the radial tidal forces can indeed be sufficiently low and 2) by viewing traversable wormholes as emergent phenomena, thereby increasing the likelihood of their existence.

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.

Noncommutative-Geometry Wormholes Based on the Casimir Effect

While wormholes are as good a prediction of Einstein’s theory as black holes, they are subject to severe restrictions from quantum field theory. In particular, holding a wormhole open requires a violation of the null energy condition, calling for the existence of exotic matter. The Casimir effect has shown that this physical requirement can be met on a small scale, thereby solving a key conceptual problem. The Casimir effect does not, however, guarantee that the small-scale violation is sufficient for supporting a macroscopic wormhole. The purpose of this paper is to connect the Casimir effect to noncommutative geometry, which also aims to accommodate small-scale effects, the difference being that these can now be viewed as intrinsic properties of spacetime. As a result, the noncommutative effects can be implemented by modifying only the energy momentum tensor in the Einstein field equations, while leaving the Einstein tensor unchanged. The wormhole can therefore be macroscopic in spite of the small Casimir effect.

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.

Exploration of Traversable Wormholes Sustained by an Extra Spatial Dimension

The main goal of this paper is to determine the effect of an extra dimension on a traversable wormhole. Here an earlier study by the author [Phys. Rev. D 98, 064041 (2018)] is extended in several significant ways. To begin with, the extra spatial dimension is assumed to be time dependent, while the redshift and shape functions, as well as the extra dimension, are functions of both r and l, the respective radial and extra coordinates;the last of these is therefore a function of r, l, and t. The main objective is to determine the conditions that allow the throat of the wormhole to be threaded with ordinary matter (by respecting the null energy condition) and that the same conditions lead to a violation of the null energy condition in the fifth dimension, which is therefore responsible for sustaining the wormhole. The dependence of the extra dimension on l and t is subject to additional conditions that are subsequently analyzed in this paper. Finally, the extra dimension may be extremely small or even curled up.

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.

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.

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.