Time-dependent Function Research Articles

Two-step multi-resolution reconstruction-based compact gas-kinetic scheme on tetrahedral mesh

This paper presents the development of a third-order compact gas-kinetic scheme (GKS) for compressible Euler and Navier-Stokes solutions, constructed particularly for an unstructured tetrahedral mesh. The scheme utilizes a time-dependent gas distribution function at a cell interface to not only calculate the fluxes needed for updating the cell-averaged flow variables but also to evaluate the flow variables at the cell interface. This leads to the evolution of cell-averaged gradients of flow variables. The success of this scheme heavily relies on the initial data reconstruction techniques, with an emphasis on their application to the tetrahedral mesh. Employing a conventional second-order unlimited least-square reconstruction directly on the cell-averaged flow variables of von Neumann neighbouring cells can introduce linear instability into the scheme. However, by using the updated cell-averaged gradients, the GKS with a third-order compact smooth reconstruction remains linearly stable under a large CFL number when applied to a tetrahedral mesh. To enhance the robustness of the high-order compact GKS for capturing a discontinuous solution, we propose a novel two-step multi-resolution weighted essentially non-oscillatory (WENO) reconstruction. This innovative approach overcomes the stability issues associated with a second-order compact reconstruction by incorporating a pre-reconstruction step. Additionally, it simplifies the third-order non-linear reconstruction process by adding a single large stencil to those used in the second-order one. A high-order wall boundary condition is achieved by fusing the constrained least-square technique with the WENO procedure, where a quadratic element is used in the reconstruction for cells with a curved boundary. Numerical tests involving both the second-order and third-order compact GKS are presented, encompassing both inviscid and viscous flows at both low and high speeds. The results demonstrate that the proposed third-order compact scheme possesses robustness in high-speed flow computation and exhibits excellent adaptability to meshes with complex geometrical configurations.

Data-Driven Deep Learning Neural Networks for Predicting the Number of Individuals Infected by COVID-19 Omicron Variant.

Infectious disease epidemics are challenging for medical and public health practitioners. They require prompt treatment, but it is challenging to recognize and define epidemics in real time. Knowing the prediction of an infectious disease epidemic can evaluate and prevent the disease's impact. Mathematical models of epidemics that work in real time are important tools for preventing disease, and data-driven deep learning enables practical algorithms for identifying parameters in mathematical models. In this paper, the SIR model was reduced to a logistic differential equation involving a constant parameter and a time-dependent function. The time-dependent function leads to constant, rational, and birational models. These models use several constant parameters from the available data to predict the time and number of people reported to be infected with the COVID-19 Omicron variant. Two out of these three models, rational and birational, provide accurate predictions for countries that practice strict mitigation measures, but fail to provide accurate predictions for countries that practice partial mitigation measures. Therefore, we introduce a time-series model based on neural networks to predict the time and number of people reported to be infected with the COVID-19 Omicron variant in a given country that practices both partial and strict mitigation measures. A logistics-informed neural network algorithm was also introduced. This algorithm takes as input the daily and cumulative number of people who are reported to be infected with the COVID-19 Omicron variant in the given country. The algorithm helps determine the analytical solution involving several constant parameters for each model from the available data. The accuracy of these models is demonstrated using error metrics on Omicron variant data for Portugal, Italy, and China. Our findings demonstrate that the constant model could not accurately predict the daily or cumulative infections of the COVID-19 Omicron variant in the observed country because of the long series of existing data of the epidemics. However, the rational and birational models accurately predicted cumulative infections in countries adopting strict mitigation measures, but they fell short in predicting the daily infections. Furthermore, both models performed poorly in countries with partial mitigation measures. Notably, the time-series model stood out for its versatility, effectively predicting both daily and cumulative infections in countries irrespective of the stringency of their mitigation measures.

A new solution framework for time-dependent reliability-based design optimization

Time-dependent reliability-based design optimization (TRBDO) has attracted intensive research attentions in recent years by virtue of its unique ability to allow consideration of dynamic uncertainties caused by stochastic processes and material property degradation. However, existing TRBDO methods are generally too intricate to be practically applicable for practical engineering application. On top of that, extremely high computational cost for complex TRBDO problems further hinders its practicability. To facilitate smooth implementation via enhancing computational efficiency in solving TRBDO problems, this study proposes an innovative and efficient solution framework. The strategy is that time-dependent performance function in each probabilistic constraint is discretized into a series of instantaneous performance functions to transform the original TRBDO problem into a RBDO problem. The reliability of each probabilistic constraint in the transformed RBDO problem is then considered under extreme value condition. With engagement of the first-order reliability method, the RBDO problem is transformed into two different triple-loop timeindependent RBDO problem. However, the issue of expensive computational cost still persists due to the triple-loop structure and identification of temporal variables under extreme value condition. To this gap, a decoupled strategy is adopted to resolve the triple-loop structure into a series of cycles of double-loop reliability analyses and deterministic optimization. Two numerical examples and three engineering applications are employed to demonstrate the supreme computational performance of the currently proposed solution framework. Results show that the proposed framework is capable of achieving a reliable optimal design at a fast convergence speed.

Upscaling solute transport in rough single-fractured media with matrix diffusion using a time fractional advection-dispersion equation

Complex structures in fractures and the rock matrix, which are difficult to map exhaustively at the local scale, can dominate contaminant transport in fractured aquifers. An upscaled model is therefore needed to effectively characterize solute transport in a heterogeneous fracture-matrix system on a large spatiotemporal scale. Most existing upscaling methods, however, do not specifically quantify the influence of matrix diffusion and fracture surface roughness on solute transport, and their upscaling parameters are usually difficult to obtain. To fill this knowledge gap, first, a time fractional advection–dispersion equation (t-FADE) model, which can accurately describe solute transport in straight fractured media, is proposed. Next, the influence of local roughness and tortuosity of fractures on transport is comprehensively considered by introducing trend lines. The t-FADE is used to characterize solute transport in each segment of rough fractures, and an upscaled model describing solute transport in rough fractures is established by averaging the governing equations of each segment. Finally, a time-dependent attenuation function is introduced into the convolutional function of the upscaled model to overcome the error caused by overlapping diffusion regions. Model comparison and analysis reveal that the rough wall of fractures strengthens matrix retention capacity, leading to a delayed peak of the breakthrough curve (BTC) with a lower peak concentration, which can be quantitatively characterized by the ratio of the actual fracture length to its longitudinal length; however, the fracture structure does not affect the solute BTC’s trailing concentration at the constant fracture mean flow velocity without considering mechanical dispersion, so the relatively simple straight fracture model can be used to describe the trailing stage of transport in rough-walled fracture media.

Gauss-Bonnet Dark Energy and the speed of gravitational waves

Gauss-Bonnet Dark Energy has been a popular model to explainthe accelerated expansion of the Universe. Quite generically it alsopredicts the speed of gravitational waves c GW to be differentfrom the speed of light. This fact alone led some authors to excludesuch models in view of the new tight observational constraints on c GW. However, the behaviour of c GW depends on the choice ofthe Gauss-Bonnet (GB) coupling function. It is possible to constructmodels where c GW is always equal to the speed of light. More generally, c GW is a time dependent function with instances where both speedscoincide. Nevertheless, we observe that the bound on c GW excludesscenarios where the GB term directly affects the expansion of theUniverse, even if the constraint on the variation of the couplingfunction does not appear to be strong. We perform the dynamical systemsanalysis to see if the expansion of the Universe could be affectedindirectly by modulating the behaviour of the scalar field, whichmodulates the GB coupling. It is shown that either the bounds on c GWare violated by many orders of magnitude, or it might be very difficultto find models that are consistent with other cosmological observations.

Time-dependent probability density functions, information geometry and entropy production in a stochastic prey–predator model of fusion plasmas

A stochastic, prey–predator model of the L–H transition in fusion plasma is investigated. The model concerns the regulation of turbulence by zonal and mean flow shear. Independent delta-correlated Gaussian stochastic noises are used to construct Langevin equations for the amplitudes of turbulence and zonal flow shear. We then find numerical solutions of the equivalent Fokker–Planck equation for the time-dependent joint probability distribution of these quantities. We extend the earlier studies [Kim and Hollerbach, Phys. Rev. Res. 2, 023077 (2020) and Hollerbach et al., Phys. Plasmas 27, 102301 (2020)] by applying different functional forms of the time-dependent external heating (input power), which is increased and then decreased in a symmetric fashion to study hysteresis. The hysteresis is examined through the probability distribution and statistical measures, which include information geometry and entropy. We find strongly non-Gaussian probability distributions with bi-modality being a persistent feature across the input powers; the information length to be a better indicator of distance to equilibrium than the total entropy. Both dithering transitions and direct L-–H transitions are (also) seen when the input power is stepped in time. By increasing the number of steps, we see less hysteresis (in the statistical measures) and a reduced probability of H-mode access; intermittent zonal flow shear is seen to have a role in the initial suppression of turbulence by zonal flow shear and stronger excitation of intermittent zonal flow shear for a faster changing input power.

A Parallelized Input Matching LMS Adaptive Filter for the Rejection of Spatially Cyclic Disturbances

Spatially cyclic disturbances exist widely in rotating machines. They usually have fixed spatial cycles rather than constant time periods, which affect the stationarity of angular speed tracking. An input matching least mean square (LMS) adaptive filter (IMLMS-AF) is proposed to cope with the effects of spatially cyclic disturbances. The IMLMS-AF sets a part of the inputs as spatially cyclic signals for disturbance rejection and forms another part as a time-dependent function for reference tracking. Furthermore, an updated law and convergence of the pending weights are given. The system's stability is proved by combining the instantaneous gradient with Lyapunov theory. Moreover, the IMLMS-AFs are parallelized to reject disturbance with multiple components and reference tracking. The effectiveness and superiority of the proposed control method are verified and compared with other methods by simulations and experiments.

Life-Cycle Seismic Reliability Analysis of a Railway Cable-Stayed Bridge Considering Material Corrosion and Degradation

To study the life-cycle seismic reliability analysis (SRA) of cable-stayed bridges (CSBs) taking into account chloride-induced corrosion and degradation of components, an actual railway CSB with uncertainties in structural geometry and material corrosion coefficients was employed in this investigation, and time-dependent models of CSB components at different service times were studied. Based on the OpenSees batch program, we adapted a mass numerical computation to obtain time-dependent non-linear seismic response and probability density function (PDF) of response via the multiplier dimensional-reduction method (MDRM) and the maximum entropy method with fractional moments (FM-MEM). Next, the time-dependent failure possibility of every component and the association coefficient between the failure modes of different parts were acquired. In the end, the product of the conditional marginal (PCM) approach was employed to obtain the life-cycle failure possibility of the CSB system. The results showed that the system failure possibility of the CSB in a corrosive environment increases significantly with increasing servicing time.

Improved analysis for impact response prediction of reinforced concrete structures considering stress wave propagation and time dependent shape function

In the design of reinforced concrete (RC) structures subjected to impulsive loading, usually an equivalent Single-Degree-of-Freedom (SDOF) system is derived based on a constant deflection shape assumption corresponding to static-loading condition. It is commonly known that this idealized assumption may not necessarily lead to accurate predictions of structural responses. This paper presents an improved analytical approach to predict the dynamic response of RC beams with consideration of stress wave propagation effect in the beam in the initial stage upon impact load application, and time-dependent shape function for SDOF analysis. The response of a structural component is divided into two phases: local response phase which is calculated using governing equations of stress wave propagations; and global response phase analyzed using the equivalent SDOF systems with considerations of time-dependent deformation shapes. Laboratory drop-weight impact tests are performed on RC beams, which are used to validate the developed method. Further validation is carried out against existing testing results by other researchers, demonstrating the proposed approach offers more accurate predictions of RC beam responses under impact loading compared to the conventional SDOF method.

Risk-Sensitive Markov Decision Processes of USV Trajectory Planning with Time-Limited Budget.

Trajectory planning plays a crucial role in ensuring the safe navigation of ships, as it involves complex decision making influenced by various factors. This paper presents a heuristic algorithm, named the Markov decision process Heuristic Algorithm (MHA), for time-optimized avoidance of Unmanned Surface Vehicles (USVs) based on a Risk-Sensitive Markov decision process model. The proposed method utilizes the Risk-Sensitive Markov decision process model to generate a set of states within the USV collision avoidance search space. These states are determined based on the reachable locations and directions considering the time cost associated with the set of actions. By incorporating an enhanced reward function and a constraint time-dependent cost function, the USV can effectively plan practical motion paths that align with its actual time constraints. Experimental results demonstrate that the MHA algorithm enables decision makers to evaluate the trade-off between the budget and the probability of achieving the goal within the given budget. Moreover, the local stochastic optimization criterion assists the agent in selecting collision avoidance paths without significantly increasing the risk of collision.

Designing of banana shaped chromophores via molecular engineering of terminal groups to probe photovoltaic behavior of organic solar cell materials

To meet the rising requirement of photovoltaic compounds for modernized hi-tech purpose, we designed six new molecules (DTPD1-DTPD6) from banana shaped small fullerene free chromophore (DTPR) by structural tailoring at terminal acceptors. Frontier molecular orbitals (FMOs), density of states (DOS), open circuit voltage (Voc), transition density matrix (TDM) analysis, optical properties, reorganization energy value of hole and electron were determined utilizing density function theory (DFT) and time-dependent density function theory (TD-DFT) approaches, to analyze photovoltaic properties of said compounds. Band gap contraction (∆E = 2.717–2.167 eV) accompanied by larger bathochromic shift (λmax = 585.490–709.693 nm) was observed in derivatives contrary to DTPR. The FMOs, DOS and TDMs investigations explored that central acceptor moiety played significant role for charge transformation. The minimum binding energy values for DTPD1-DTPD6 demonstrated the higher exciton dissociation rate with greater charge transferal rate than DTPR, which was further endorsed by TDM and DOS analyses. A comparable Voc (1.49–2.535 V) with respect to the HOMOPBDBT–LUMOacceptor for entitled compounds was investigated. In a nutshell, all the tailored chromophores can be considered as highly efficient compounds for promising OSCs with a good Voc response.

Gaussian solitary wave solutions for nonlinear perturbed Schrödinger equations with applications in nanofibers

This paper presents an investigation into solutions of two types of nonlinear Schrödinger equations of logarithmic form. This model is of particular interest to researchers due to its vast application in the field of the implication of nanofibers. Through a comprehensive analysis, it was found that the solutions take the form of Gaussian-type solitary solutions. These solutions possess a variety of new structures due to the presence of many arbitrary constants and time-dependent functions in their general expressions. By fixing these constants and functions appropriately, Gaussian solitary waves for nonlinear perturbed Schrödinger equations can be represented, which could be beneficial in understanding the dynamics of these equations in nanooptical fibers. The results obtained from this study may provide a useful tool for further research into nonlinear Schrödinger equations and can be extended to fit more applications.

Mixed-model moving assembly line material placement optimization for a shorter time-dependent worker walking time

Car mass production commonly involves a moving assembly line that mixes several car models. This requires plenty of material supplies at the line side, but available space is scarce. Thus, material is placed apart from ideal positions. Then, picking it up involves walking along the line. This time is non-productive and can encompass 10–15% of total production time. Thus, it is important to estimate and minimize it during production planning. However, the calculations are difficult because the conveyor continuously moves. Therefore, most literature bounds walking time by a constant, but this discards valuable potential. To better approximate it, we use a time-dependent V-shaped function. A comparison indicates that for a majority of instances, constant walking time estimates of 95% confidence are at least 51% higher. Then, we introduce a model to optimize material positions such that the model-mix walking time is minimized. This poses an NP-hard sequencing problem with a recursive and nonlinear objective function. Our key discovery is a lower bound on the objective of partial solutions, established by a Lagrangian relaxation that can be solved in quadratic time. Resulting branch and bound based algorithms allow to quickly and reliably optimize up to the largest real-world sized instances.

On the development of physiologically based toxicokinetic (PBTK) models for cardiovascular implants

Local and systemic contamination caused by metal ions leaching from medical device materials is a significant and continuing health problem. The increasing need for verification and validation, and the imposition of stringent government regulations to ensure that the products comply with the quality, safety, and performance standards, have led regulatory bodies worldwide to strongly recommend the use of modeling and simulation tools to support medical device submissions. A previously published physiologically based toxicokinetic (PBTK) model, is here expanded and enriched by an additional separate tissue compartment to better resemble normal physiology and by the introduction of time-dependent functions to describe all biokinetic parameters. The new model is exercised in conjunction with state-of-the-art probabilistic, Monte Carlo methodology to calculate the predictions' confidence intervals and incorporate variability associated with toxicological biodistribution studies. The quantitative consistency of the model-derived predictions is validated against reported data following the implantation of nickel-containing cardiovascular devices in humans and minipigs. Finally, a new methodology for compartmental toxicological risk assessment is presented that can be used for forward or reverse dosimetry. Our work is aimed at providing a computational tool to optimize the device design characteristics and safeguard that the substances released do not exceed permissible exposure limits.

Digital twins of multiple energy networks based on real-time simulation using holomorphic embedding method, Part I: Mechanism-driven modeling

Digital twins can provide system operators with a new way to design, operate, and maintain highly-interconnected multiple energy networks (MEN) by integrating interdisciplinary models using the co-simulation technique and implementing faster-than-real-time simulation enabled by powerful modern computing facilities. This series of papers presents digital twins of MEN capable of real-time simulation facilitated by the holomorphic embedding method. As Part I of this series of papers, mechanism-driven modeling is concentrated to guarantee that high-resolution solutions are computationally accessible. A holomorphic embedding-based model (HEM) for MEN is proposed, which uses time-dependent holomorphic functions to depict the time-varying dynamics of gas and heat flows. A convergence radius model (CRM) is proposed to obtain the essential convergence information of HEM, thereby improving its computational performance to match the real-time requirement. Finally, the effectiveness of the proposed method is validated in a medium-sized study case. The results show that the proposed method offers a significant computational benefit with competent precision when compared to standard differential methods, laying the groundwork for the realization of MEN’s digital twins.

Eliminating solution singularity of variably distributed-order time-fractional diffusion equation via strongly singular initial distribution

We investigate a distributed-order time-fractional diffusion equation with a time-dependent density function and its support. The well-posedness and regularity of the equation are analyzed. In particular, by proposing appropriate assumptions on the density function, which may lead to a strongly singular initial distribution instead of smooth distributions that are usually imposed in the literature, we prove smoothing properties of the solutions and eliminate their nonphysical initial singularities without affecting the memory and hereditary properties of the model, i.e. the current state of the model depends on its states at previous time instants, away from the initial time. The results generalize the solution theory of distributed-order equations and provide a model correction for problems that do not exhibit initial singularities.

A microscopic derivation of Gibbs measures for the 1D focusing cubic nonlinear Schrödinger equation

In this paper, we give a microscopic derivation of Gibbs measures for the focusing cubic nonlinear Schrödinger equation on the one-dimensional torus from many-body quantum Gibbs states. Since we are not making any positivity assumptions on the interaction, it is necessary to introduce a truncation of the mass in the classical setting and of the rescaled particle number in the quantum setting. Our methods are based on a perturbative expansion of the interaction, similarly as in [1]. Due to the presence of the truncation, the obtained series have infinite radius of convergence. We treat the case of bounded, L 1 and delta function interaction potentials, without any sign assumptions. Within this framework, we also study time-dependent correlation functions. This is the first such known result in the focusing regime.

Data-Driven Finite-Horizon Tracking Control With Event-Triggered Mechanism for the Continuous-Time Nonlinear Systems.

In this article, the neural network (NN)-based adaptive dynamic programming (ADP) event-triggered control method is presented to obtain the near-optimal control policy for the model-free finite-horizon optimal tracking control problem with constrained control input. First, using available input-output data, a data-driven model is established by a recurrent NN (RNN) to reconstruct the unknown system. Then, an augmented system with event-triggered mechanism is obtained by a tracking error system and a command generator. We present a novel event-triggering condition without Zeno behavior. On this basis, the relationship between event-triggered Hamilton-Jacobi-Isaacs (HJI) equation and time-triggered HJI equation is given in Theorem 3. Since the solution of the HJI equation is time-dependent for the augmented system, the time-dependent activation functions of NNs are considered. Moreover, an extra error is incorporated to satisfy the terminal constraints of cost function. This adaptive control pattern finds, in real time, approximations of the optimal value while also ensuring the uniform ultimate boundedness of the closed-loop system. Finally, the effectiveness of the proposed near-optimal control pattern is verified by two simulation examples.

Time-dependent probability density function for partial resetting dynamics

Stochastic resetting is a rapidly developing topic in the field of stochastic processes and their applications. It denotes the occasional reset of a diffusing particle to its starting point and effects, inter alia, optimal first-passage times to a target. Recently the concept of partial resetting, in which the particle is reset to a given fraction of the current value of the process, has been established and the associated search behaviour analysed. Here we go one step further and we develop a general technique to determine the time-dependent probability density function (PDF) for Markov processes with partial resetting. We obtain an exact representation of the PDF in the case of general symmetric Lévy flights with stable index . For Cauchy and Brownian motions (i.e. ), this PDF can be expressed in terms of elementary functions in position space. We also determine the stationary PDF. Our numerical analysis of the PDF demonstrates intricate crossover behaviours as function of time.

Dynamical behavior and transport coefficients of the pseudo hard-sphere fluid

In this work, we employ a recent approach to characterize the hard-sphere (HS) fluid by means of a continuous interaction potential, commonly referred to as pseudo hard-sphere potential, in order to determine HS transport coefficients as a function of the volume fraction for the three-dimensional mono disperse fluid. Using equilibrium molecular dynamics simulations, we determine time-dependent velocity, shear stress, and energy flux autocorrelation functions in order to use them within the Green–Kubo framework to compute the self-diffusion, shear viscosity, and thermal conductivity coefficients, respectively. Results are discussed as a function of the volume fraction and were compared to theoretical and simulations results previously reported by other authors. The main purpose of this work is twofold: first, testing the continuous approach of the HS fluid for the computation of dynamic properties and second, performing a systematic determination of aforementioned transport coefficients to analyze them as a function of fluid volume fraction. Furthermore, our results are used to provide a practical correction to the Chapman–Enskog equations for the HS self-diffusion, shear viscosity, and thermal conductivity predictions in a wide range of volume fractions.