Time-dependent Parts Research Articles

Coercivity-based analysis and its application to an inverse source problem for a subdiffusion equation with time-dependent principal parts

Abstract In this article, we investigate an inverse source problem for subdiffusion equations with time-dependent principal parts using distributed observations. We analyze coercivity properties of fractional derivatives. As applications, we use a coercivity property to establish a Lipschitz stability estimate for an inverse problem of determining the temporal component in the source term, which is a new result to the best knowledge of the authors, Numerically, we transform the inverse source problem into an optimization framework, incorporating Tikhonov regularization to mitigate the ill-posedness of the inverse problem. We then propose an iterative thresholding algorithm to solve this optimization problem efficiently. Finally, we present several numerical experiments to validate the accuracy and the efficiency of our proposed algorithm.

Hybrid Hamiltonian Simulation for Excitation Dynamics.

Hamiltonian simulation is one of the most anticipated applications of quantum computing. Quantum circuit depth for implementing Hamiltonian simulation is commonly time dependent using Trotter-Suzuki product formulas so that long time quantum dynamic simulations (QDSs) become impratical for near-term quantum processors. Hamiltonian simulation based on Cartan decomposition (CD) provides an appealing scheme for QDSs with fixed-depth circuits, while it is limited to a time-independent Hamiltonian. In this work, we generalize this CD-based Hamiltonian simulation algorithm for studying time-dependent systems by combining it with variational quantum algorithms. The time-dependent and time-independent parts of the Hamiltonian are treated by using variational and CD-based Hamiltonian simulation algorithms, respectively. As such, this hybrid Hamiltonian simulation requires only fixed-depth quantum circuits to handle time-dependent cases while maintaining a high accuracy. We apply this new algorithm to study the response of spin and molecular systems to δ-kick electric fields and obtain accurate spectra for these excitation processes.

Non-Stationary Helical Flows for Incompressible Couple Stress Fluid

We explored here the case of three-dimensional non-stationary flows of helical type for the incompressible couple stress fluid with given Bernoulli-function in the whole space (the Cauchy problem). In our presentation, the case of non-stationary helical flows with constant coefficient of proportionality α between velocity and the curl field of flow is investigated. In the given analysis for this given type of couple stress fluid flows, an absolutely novel class of exact solutions in theoretical hydrodynamics is illuminated. Conditions for the existence of the exact solution for the aforementioned type of flows were obtained, for which non-stationary helical flow with invariant Bernoulli-function satisfying to the Laplace equation was considered. The spatial and time-dependent parts of the pressure field of the fluid flow should be determined via Bernoulli-function if components of the velocity of the flow are already obtained. Analytical and numerical findings are outlined, including outstanding graphical presentations of various types of constructed solutions, in order to elucidate dynamic snapshots that show the timely development of the topological behavior of said solutions.

Internal Heat Modulation on Darcy Convection in a Porous Media Saturated by Nanofluid

In this paper we investigate the effect of internal heat modulation over a nanofluid saturated porous medium. We consider a small variation in time dependant heat source and vary sinusoidally with slow time. An energy equation will be altered by adding time dependant internal heat source. This internal heat source has its time dependent and independent parts. Time dependent part shows that the internal heat modulation over a porous media and defines controls on heat/mass transfer in the layer. We have performed a nonlinear stability analysis to investigate heat/mass transfer in the system. The nonlinear system of partial differential equations are transformed into nonlinear ordinary differential equations under similarity transforms up to the second term. This system has different system parameters and they have been investigated on heat and mass transfer graphically. The dual nature, stabilize or destabilize is due to the significant effect of internal heating modulation of the system. Further, the effect of internal heating is to destabilize the system, as a consequence heat/mass transfer enhances. It is found that internal heating modulation can be used effectively to regulate heat/mass transfer in the system.

Experimental Investigation and Micromechanics-Based Analytical Modeling of Creep and Relaxation Behaviors of Beishan Granite

This paper investigates experimentally and numerically the short- and long-term strength and deformation behaviors of Beishan granite at room temperature. Single-stage creep, relaxation, and conventional triaxial compression tests were performed on cylindrical rock samples. Its typical brittle response is captured and the dependence of peak strength on confining pressure and time-dependent response on deviatoric stress are revealed. For constitutive modeling, a unified micromechanics-based plasticity-damage model is formulated based on the Mori–Tanaka method and the subcritical cracking theory postulate, with the focus on simulating both instantaneous strain and time-dependent deformation process over a broad range of time scales. Its unification is achieved by representing the evolution of damage, which is strongly coupled with plastic deformation induced by frictional sliding along closed cracks, as an internal variable that can be decomposed into instantaneous and time-dependent parts. The performance of the model with analytical predictions is well validated using the experimental results on Beishan granite.

A highly efficient explicit constitutive model for linear viscoelastic closed-cell porous materials

In this paper, a highly efficient explicit constitutive model for linear viscoelastic closed-cell porous materials is proposed based on micromechanics and homogenization method in the time domain. The deformation first is additively divided into volumetric and deviatoric parts and then the viscoelastic behaviors are decomposed into the time-dependent and time-independent parts. Finite element simulations based on representative volume element models are utilized to numerically verify the constitutive model. The effects of the void-shape, porosity, elastic and viscous parameters of the matrix, strain rate, and angular frequency on the effective linear viscoelastic responses are studied. The results demonstrate that the constitutive model can provide accurate estimation of the effective linear viscoelastic properties for the closed-cell porous materials in both time and frequency domains. The 3D printed nylon porous materials with various porosities are employed to experimentally validate the constitutive model through simple uniaxial compression tests, stress relaxation uniaxial compression tests, and uniaxial compression tests with different strain rates. The results reveal that the constitutive model can also predict well the behaviors of linear viscoelastic closed-cell porous materials with different porosities in the time domain under various loading conditions.

Modeling the resistance mechanism of passive knee joint flexion and extension for use in rehabilitation equipment.

The purpose of this study was to model the resistance mechanism of Passive Knee Joint Flexion and Extension to create a similar torque mechanism in rehabilitation equipment. In order to better model the behavior of passive knee tissues, it is necessary to exactly calculate the two coefficients of elasticity of time-independent and time-dependent parts. Ten healthy male volunteers (mean height 176.4+/-4.59 cm) participated in this study. Passive knee joint flexion and extension occurred at velocities of 15, 45, and 120 (degree/s), and in five consecutive cycles and within the range of 0 to 100° of knee movement on the sagittal plane on Cybex isokinetic dynamometer. To ensure that the muscles were relaxed, the electrical activity of knee muscles was recorded. The elastic coefficient, (KS) increased with elevating the passive velocity in flexion and extension. The elastic coefficient, (KP) was observed to grow with the passive velocity increase. While, the viscous coefficient (C) diminished with passive velocity rise in extension and flexion. The heightened passive velocity of the motion resulted in increased hysteresis (at a rate of 42%). The desired of passive velocity is lower so that there is less energy lost and the viscoelastic resistance of the tissue in the movement decreases. The Coefficient of Determination, R2 between the model-responses and experimental curves in the extension was 0.96 < R2 < 0.99 and in flexion was 0.95 < R2 < 0.99. This modeling is capable of predicting the true performance of the components of passive knee movement and we can create a resistance mechanism in the rehabilitation equipment to perform knee joint movement. Quantitative measurements of two elastic coefficients of Time-independent and Time-dependent parts passive knee joint coefficients should be used for better accurate simulation the behavior of passive tissues in the knee which is not seen in other studies.

Interrelation between polycrystalline structure and time-dependent magnetic anisotropies in exchange-biased bilayers

For polycrystalline exchange-biased thin films the macroscopic magnetic properties evolve from a complex interplay of different individual magnetic anisotropies which are directly connected to the grain volume distribution and to the crystal and interface structure of the layer system. A quantitative comparison of models describing a macroscopically observed exchange bias by the contributing anisotropies has in most cases been hampered by neglecting their time dependence with respect to data acquisition and storage times. Using a recently developed model we are able to connect time-dependent parts of the prevailing anisotropies with parameters describing the polycrystalline structure of the layer system. The model will be compared to experiments on a prototypical IrMn/CoFe bilayer, where structural and magnetic parameters have been systematically altered by varying the deposition rate of the antiferromagnetic layer and the field-cooling temperature. The combination of angular-resolved measurements obtained by vectorial magneto-optic Kerr magnetometry and a systematic analysis of the polycrystalline structure enables the disentanglement of the different anisotropy contributions to the macroscopic exchange bias and coercive fields and serves as a verification of the utilized model.

On finite bending of visco-hyperelastic materials: a novel analytical solution and FEM

In this paper, an analytical approach is proposed to examine the finite strain time-dependent behavior of incompressible, isotropic visco-hyperelastic elastomeric material under bending. Phenomenological hyperelastic invariant-based strain energy density function, Yeoh model, and N-termed Prony series are utilized to define the strain-dependent and time-dependent parts of the visco-hyperelastic constitutive model, respectively. 3D finite element analysis of the problem is carried out using ABAQUS/Visco to verify the analytical solution results. Material parameters of polyurea are calibrated using an optimization framework for experimental results under five different strain rates, simultaneously. Two well-known tests of viscoelastic materials, stress relaxation and creep tests, are investigated both analytically and numerically. Distribution of the Cauchy stress components and the resultant bending moment versus time, and the variation of the mentioned results with different rise times and ultimate bent angles are provided for the stress relaxation test. Moreover, the strain and bending angle results are plotted in a creep test for different rise times and applied moments. Besides, a multi-step relaxation test and creep recovery test are performed for different loading conditions. Finite element method results confirm the analytical approach with great compatibility.

Unitarity of the time-evolution and observability of non-Hermitian Hamiltonians for time-dependent Dyson maps

We present an strategy for the derivation of a time-dependent Dyson map which ensures simultaneously the unitarity of the time evolution and the observability of the whole time-dependent non-Hermitian Hamiltonian or parts of it. The time-dependent Dyson map is derived through a constructed Schrödinger-like equation governed, in one case, by the non-Hermitian Hamiltonian itself or, in another case, by its parts. In the former case, when the whole non-Hermitian Hamiltonian is considered, our scheme ensures the time-independence of the metric operator despite the time-dependence of the Dyson map, a necessary condition for the observability of the non-Hermitian Hamiltonian. In the later case, however, when parts of the non-Hermitian Hamiltonian is considered, our method ensures the simultaneous time-dependence of the Dyson map and the metric operator. In this latter case what is ensured is the observability of the remaining part of the non-Hermitian Hamiltonian that was not chosen for the derivation of the Dyson map. Illustrative examples, for both cases, are derived from a driven non-Hermitian Harmonic oscillator.

Operando X-Ray Diffraction of Lithium-Sulfur Batteries with Concurrent Resistance Measurement

Lithium-sulfur (Li-S) batteries have been viewed as one of the promising electric energy storage technologies due to the high theoretical energy density and the abundance of sulfur [1]. However, the utilization of sulfur is typically only 60-70% given the commonly reported reversible capacity of ~1000 mAh/g compared with the theoretical capacity of 1672 mAh/g [2]. The complicated reaction mechanism at the positive electrode is one of the causes for this discrepancy [3]. Though the charged (elemental sulfur, S) and discharged (lithium sulfide, Li2S) states are solid, the reaction intermediates (Li2Sx, x=4-8) are soluble in ether-based electrolytes, e.g. 1,3-dioxolane (DOL) [3]. Therefore, the active material goes through repeated dissolution and precipitation during cell operation. Furthermore, both S and Li2S are insulating, so a conductive porous carbon matrix is required as a host structure [1]. The precipitation of the insulating S and Li2S particles can decrease the electronically-conductive surface area or even block the pores in the carbon matrix, which leads to incomplete reaction and thus low utilization of active material [3]. In this work, the correlation between the evolution of the solid species and the electrochemical response of the porous electrode is investigated by operando X-ray diffraction (XRD) coupled with the Intermittent Current Interruption (ICI) method [4]. The ICI method is a facile way to follow the real-time internal resistance of a battery cycling at a constant current. Periodic transient current pauses are applied to obtain the potential response of the system [4]. From the potential-time relationship, both time-independent and time-dependent parts of the resistance can be derived. The time-independent resistance has been shown to correspond to the sum of the resistive elements in an equivalent circuit model of the electrochemical impedance spectroscopic (EIS) response [4]. In terms of the electrochemical process, the time-independent resistance includes the electronic, ionic and charge transfer resistances. In our recent work [5], the time-dependent part of the resistance from ICI measurements is analyzed by comparison with the existing porous electrode model. This enables us to characterize the mass transport in the positive electrode during the evolution of the solid species as captured by operando XRD. Along with the resistance profile, this work will present the results from in-house operando XRD of a Li-S cell with our cell design, which is dedicated to preserve the reproducible electrochemical properties while offering a satisfactory signal-to-noise ratio in the XRD data. With the information of the mass transport in porous electrode and evolution of crystalline species, the concurrent analyses of both techniques will illustrate the dynamic interaction between the solid sulfur species and the carbon matrix at the positive electrode of Li-S batteries. Figure: Operando XRD results with the diffraction pattern as the heatmap at the top, followed by the cell voltage (E), time-independent resistance (R) and time-dependent resistance (k). The legend for the colors used in the heatmap and following curves are labeled at the top and bottom of the graph.

Simultaneous study of molecular and micelle diffusion in a technical microemulsion system by dynamic light scattering

HypothesisThe application of dynamic light scattering (DLS) is well-established for measuring diffusion coefficients related to either molecular or translational micelle diffusion. The simultaneous determination of both transport properties should be feasible, but has not been reported in the literature yet. ExperimentsDifferent diffusion modes present in a microemulsion and selected subsystems consisting of a polyol mixture, a binary surfactant mixture, and carbon dioxide (CO2) were investigated systematically by DLS at temperatures of (314, 333, and 353) K and corresponding pressures of (10, 13, and 16) MPa. FindingsDiffusion coefficients related to molecular and translational micelle diffusion could be measured simultaneously and increase with increasing temperature. From the translational diffusion coefficients, an increase in the hydrodynamic diameter of the micelles from their non-swollen to the CO2-swollen state being in agreement with literature data for the same and similar microemulsions was found. The effective diffusion coefficients related to the faster molecular diffusion process only observable in the presence of CO2 are not affected significantly by the surfactant. The time-dependent parts of the recorded intensity correlation functions related to molecular diffusion processes are heterodyne because the scattered light modulated by molecular concentration fluctuations is superimposed with light scattered by the micelles.

Quantum field-theoretical description of neutrino and neutral kaon oscillations

It is shown that the neutrino and neutral kaon oscillation processes can be consistently described in quantum field theory using only plane waves of the mass eigenstates of neutrinos and neutral kaons. To this end, the standard perturbative S-matrix formalism is modified so that it can be used for calculating the amplitudes of the processes passing at finite distances and finite time intervals. The distance-dependent and time-dependent parts of the amplitudes of the neutrino and neutral kaon oscillation processes are calculated and the results turn out to be in accordance with those of the standard quantum mechanical description of these processes based on the notion of neutrino flavor states and neutral kaon states with definite strangeness. However, the physical picture of the phenomena changes radically: now, there are no oscillations of flavor or definite strangeness states, but, instead of it, there is interference of amplitudes due to different virtual mass eigenstates.

Hyperviscoelastic Constitutive Modelling of Solid Propellants with Damage and Compressibility

AbstractFilled elastomers especially composite solid propellants demonstrate strain rate dependent, large deformation/large strain, thermo‐rheological, stress relaxation, stress softening due to microstructural damage and compressible constitutive behavior. This paper presents a micromechanism inspired framework capturing all the above mentioned features by combining both continuum formulation of hyperelasticity, statistical formulation of viscoelasticity, compressibility and damage. The mechanical response is decomposed into equilibrium and time dependent parts. The equilibrium and time dependent parts are further decomposed into dilational and deviatoric parts. Deviatoric parts are modelled using Mooney‐ Rivlin hyperelastic strain energy density functions. Compressibility is modelled by considering dilatational part of strain energy density as the function of the dilation with quadratic and quartic terms. The stress softening during cyclic loading (Mullins effect) due to microstructural damage is described by polynomial function of the current strain energy density and its previous maximum value. The predictions based on the proposed model are in good agreement with the experimental results.

Weak nonlinear rotating Bénard convection with modulation using Ginzburg- Landau model

This article theoretically investigates the effect of modulated rotation speed on rotating Rayleigh- Bénard convection. The Rayleigh-Bénard momentum equation with Coriolis term has been used to describe the fluid flow in the medium. The system is consider to rotate about vertical axis with non-uniform rotational speed consisting of steady and time dependent parts. In particular, we assume that the rotation speed i.e time dependent part is varying sinusoidally with time. A nonlinear stability analysis has been performed to find the effect of modulation on heat transport. The heat transfer quotient, Nusselt number obtained in terms of amplitude and frequency of modulation, and depicted graphically with respect to slow time, showing the effect of various parameters of the system on heat transport. It is found that the effect of rotation speed modulation is to stabilize or destabilize the system depending on the amplitude and frequency of modulation. The corresponding streamlines and isotherms are presented at different states of slow time .

The unsteady flow of a third-grade fluid caused by the periodic motion of an infinite wall with transpiration

In this work, the unidirectional flow of an incompressible electrically conducting third-grade fluid past a vertical transpiration wall through a porous medium with time-dependent periodic motion is presented. The nonlinear partial differential equations are transformed to ordinary differential equation by means of symmetry reductions. The reduced equation is then solved analytically for steady-state and time-dependent transient parts. The time series of the transient flow velocity for different pertinent parameters are examined through plots. During the course of computation, it was observed that the time-dependent transient and steady-state solutions agree very well at large value of time when the ratio is related to fluid parameters γ∗γ>1.

Modeling quasar central engine as a relativistic radiating star

Long ago Hoyle & Fowler attempted to model the central engine of quasars as hot super-massive stars supported by radiation pressure. Whereas the model of Hoyle & Fowler was Newtonian, here we make a toy model of quasar central engines as ultra relativistic ultrahot plasma or as a ball of radiation. Accordingly, we consider general relativistic gravitational collapse including emission of radiation. More specifically, we discuss a new class of radiating fluid ball exact solution in conformally-flat metric which is quasi-static and contracting at negligible rate. The problem is solved by assuming that the metric potential is separable in to radial and time dependent parts. It is found the gravitational mass of the radiating ball M→0 as comoving time t→∞ in conformity of the idea of an “Eternally Collapsing Object” (ECO) which has been claimed to be the true nature of the so-called “Black Holes”. In particular, we consider here a quasi-static radiation ball having M≈9.507×107M⊙, a radius of ≈2×1014 km, and a luminosity L∞≈9.1×1046 erg/s. Prima-facie, such an ECO solution is compatible with the central compact object of a quasar having comoving lifetime of ≈107 yr and a distantly observed lifetime (u) which could be higher by many orders of magnitude.

Time-domain matched interface and boundary (MIB) modeling of Debye dispersive media with curved interfaces

A new finite-difference time-domain (FDTD) method is introduced for solving transverse magnetic Maxwell's equations in Debye dispersive media with complex interfaces and discontinuous wave solutions. Based on the auxiliary differential equation approach, a hybrid Maxwell–Debye system is constructed, which couples the wave equation for the electric component with Maxwell's equations for the magnetic components. This hybrid formulation enables the calculation of the time dependent parts of the interface jump conditions, so that one can track the transient changes in the regularities of the electromagnetic fields across a dispersive interface. Effective matched interface and boundary (MIB) treatments are proposed to rigorously impose the physical jump conditions which are not only time dependent, but also couple both Cartesian directions and both magnetic field components. Based on a staggered Yee lattice, the proposed MIB scheme can deal with arbitrarily curved interfaces and nonsmooth interfaces with sharped edges. Second order convergences are numerically achieved in solving dispersive interface problems with constant curvatures, general curvatures, and nonsmooth corners.

Nonlinear viscoelastic-degradation model for polymeric based materials

This study presents a phenomenological constitutive model for describing response of solid-like viscoelastic polymers undergoing degradation. The model is expressed in terms of recoverable and irrecoverable time-dependent parts. We use a time-integral function with a nonlinear integrand for the recoverable part and another time-integral function is used for the irrecoverable part, which is associated with the degradation evolution in the materials. Here, the degradation is attributed to the secondary and tertiary creep stages. An ‘internal clock’ concept in viscoelastic materials is used to incorporate the accelerated failure in the materials at high stress levels. We ignore the effect of heat generation due to the dissipation of energy and possible healing in predicting the long-term and failure response of the polymeric materials. Experimental data on polymer composites reported by Drozdov (2011) were used to characterize the material parameters and validate the constitutive model. The model is shown capable of predicting response of the polymer composites under various loading histories: creep, relaxation, ramp loading with a constant rate, and cyclic loadings. We observed that the failure time and number of cycles to failure during cyclic loadings are correlated to the duration of loading and magnitude of the prescribed mechanical loads. A scalar degradation variable is also introduced in order to determine the severity of the degradation in the materials, which is useful to predict the lifetime of the structures subject to various loading histories during the structural design stage.

Short- and long-term behaviors of drifts in the Callovo-Oxfordian claystone at the Meuse/Haute-Marne Underground Research Laboratory

Since 2000, the French National Radioactive Waste Management Agency (ANDRA) has been constructing an Underground Research Laboratory (URL) at Bure (east of the Paris Basin) to perform experiments in order to obtain in situ data necessary to demonstrate the feasibility of geological repository in the Callovo-Oxfordian claystone. An important experimental program is planned to characterize the response of the rock to different drift construction methods. Before 2008, at the main level of the laboratory, most of the drifts were excavated using pneumatic hammer and supported with rock bolts, sliding steel arches and fiber shotcrete. Other techniques, such as road header techniques, stiff and flexible supports, have also been used to characterize their impacts. The drift network is developed following the in situ major stresses. The parallel drifts are separated enough so as they can be considered independently when their hydromechanical (HM) behaviors are compared. Mine-by experiments have been performed to measure the HM response of the rock and the mechanical loading applied to the support system due to the digging and after excavation. Drifts exhibit extensional (mode I) and shear fractures (modes II and III) induced by excavation works. The extent of the induced fracture networks depends on the drift orientation versus the in situ stress field. This paper describes the drift convergence and deformation in the surrounding rock walls as function of time and the impact of different support methods on the rock mass behavior. An observation based method is finally applied to distinguish the instantaneous and time-dependent parts of the rock mass deformation around the drifts.