Time-dependent Function Research Articles

Neolignans from Myristica fragrans seeds, revision of their absolute configurations, reduction products and biological activities

Chromatographic purification of the CH2Cl2 extract of Myristica fragrans seeds provided 19 known compounds, four dihydrofuran neolignans, licarines A, B and maceneolignans A, B were among the isolates. Prior to hydrogenation, in order to obtain their di- and tetrahydrogenated products, the absolute configuration of these compounds was thoroughly investigated based on their optical rotations and ECD spectra. This report provides evidences concerning the disagreement between the use of an aromatic quadrant rule and time-dependent density function theory calculation for the prediction of the absolute configurations at C-7 and C-8 in these dihydrobenzofuran neolignans. The absolute configurations of licarines A, B and maceneolignans A, B were subsequently redefined. The antimicrobial and cytotoxic activities of the isolates and reduction products of licarines A, B and maceneolignans A, B were also investigated.

Power functional theory for many-body dynamics

The rich and diverse dynamics of particle-based systems ultimately originates from the coupling of their degrees of freedom via internal interactions. To arrive at a tractable approximation of such many-body problems, coarse-graining is often an essential step. Power functional theory provides a unique and microscopically sharp formulation of this concept. The approach is based on an exact one-body variational principle to describe the dynamics of both overdamped and inertial classical and quantum many-body systems. In equilibrium, density functional theory is recovered, and hence spatially inhomogeneous systems are described correctly. The dynamical theory operates on the level of time-dependent one-body correlation functions. Two- and higher-body correlation functions are accessible via the dynamical test particle limit and the nonequilibrium Ornstein-Zernike route. We describe the structure of this functional approach to many-body dynamics, including much background as well as applications to a broad range of dynamical situations, such as the van Hove function in liquids, flow in nonequilibrium steady states, motility-induced phase separation of active Brownian particles, lane formation in binary colloidal mixtures, and both steady and transient shear phenomena.

Machine learning-based multiscale constitutive modelling: Development and application to dual-porosity mass transfer

In multiscale modelling, multiple models are used simultaneously to describe scale-dependent phenomena in a system of interest. Here we introduce a machine learning (ML)-based multiscale modelling framework for modelling hierarchical multiscale problems. In these problems, closure relations are required for the macroscopic problem in the form of constitutive relations. However, forming explicit closures for nonlinear and hysteretic processes remains challenging. Instead, we provide a framework for learning constitutive mappings given microscale data generated according to micro and macro transitions governed by two-scale homogenisation rules. The resulting data-driven model is then coupled to a macroscale simulator leading to a hybrid ML-physics-based modelling approach. Accordingly, we apply the multiscale framework within the context of transient phenomena in dual-porosity geomaterials. In these materials, the inter-porosity flow is a complex time-dependent function making its adoption within flow simulators challenging. We explore nonlinear feedforward autoregressive ML strategies for the constitutive modelling of this sequential problem. We demonstrate how to inject the resulting surrogate constitutive model into a simulator. We then compare the resulting hybrid approach to traditional dual-porosity and microscale models on a variety of tests. We show the hybrid approach to give high-quality results with respect to explicit microscale simulations without the computational burden of the latter. Lastly, the steps provided by the multiscale framework herein are sufficiently general to be applied to a variety of multiscale settings, using different data generation and learning techniques accordingly.

Multi-objective water-sediment optimal operation of cascade reservoirs in the Yellow River Basin

Sediment deposition in sediment-laden rivers seriously restricts the normal operation of reservoirs and the socioeconomic development of the basin. Studying the water–sediment joint operation of cascade reservoirs is important for extending the life of reservoirs. The objective of this paper is to provide a sound scientific approach to optimize the water–sediment operation of cascade reservoirs considering multiple objectives. An innovative time-dependent objective function was proposed, in which the sediment release efficiency equations suitable for different sediment inflow scenarios were introduced for sediment flushing calculation. The Sanmenxia (SMX) and Xiaolangdi (XLD) Reservoirs on the Yellow River were selected as case studies to test the proposed method. First, two typical data sets, including high and low flow magnitudes, were taken as model input scenarios. Second, the multiple-objective joint optimal operation model was established. Discrete differential dynamic programming (DDDP) was used to solve the operation model. Finally, the operation results based on different weights were discussed. Results indicate that, for sediment-laden rivers, such as the Yellow River, the proposed model can achieve the maximization of the hydropower generation and sediment flushing benefits for the high flow and low flow series. And the proposed model can guarantee the flood control, ice flood control, water supply, and ecological objectives. For the SMX-XLD cascade reservoirs, when the water resources are abundant, the hydropower generation reservoirs increase significantly. And in flood season, the weight for sediment flushing can be increased appropriately to improve the comprehensive benefits of the reservoir in sediment-laden rivers. In addition, the time-dependent objective function can provide a reference for the multi-objective optimal operation of cascade reservoirs. The optimal operation model provides a model basis for the water–sediment-energy joint operation of large-scale reservoir group in the sediment-laden basins.

RL based hyper-parameters optimization algorithm (ROA) for convolutional neural network

AbstractMany real-world applications necessitate optimization in dynamic situations, where the difficulty is to locate and follow the optima of a time-dependent objective function. To solve dynamic optimization problems (DOPs), many evolutionary techniques have been created. However, more efficient solutions are still required. Recently, a new intriguing trend in dealing with optimization in dynamic environments has developed, with new reinforcement learning (RL) algorithms predicted to breathe fresh life into the DOPs community. In this paper, a new Q-learning RL-based optimization algorithm (ROA) for CNN hyperparameter optimization is proposed. Two datasets were used to test the proposed RL model (MNIST dataset, and CIFAR-10 dataset). Due to the use of RL for hyperparameter optimization, very competitive results and good performance were produced. From the experimental results, it is observed that the CNN optimized by ROA has higher accuracy than CNN without optimization. When using the MNIST dataset, it is shown that the accuracy of the CNN optimized by ROA when learning 5 epoch is 98.97%, which is greater than the 97.62% of the CNN without optimization. When using the CIFAR-10 dataset, it is shown that the accuracy of the CNN optimized by ROA when learning 10 epoch is 73.40 percent, which is greater than 71.73% of the CNN without optimization.

Second-order peculiar velocity field as a novel probe of scalar-tensor theories

We investigate the galaxy bispectrum induced by the nonlinear gravitational evolution as a possible probe to constrain degenerate higher-order scalar tensor (DHOST) theories. We find that the signal obtained from the leading kernel of second-order density fluctuations is partially hidden by the uncertainty in the nonlinear galaxy bias, and that the kernel of second-order velocity fields instead provides unbiased information on the modification of gravity theory. Based on this fact, we propose new phenomenological time-dependent functions, written as a combination of the coefficients of the second-order kernels, which is expected to trace the higher-order growth history. We then present approximate expressions for these variables in terms of parameters that characterize the DHOST theories. We also show that the resultant formulae provides new constraints on the parameter space of the DHOST theories.

Intermittent Pinning Synchronization for Directed Networks With Switching Technique

This research concerns the pinning synchronization of directed networks from the perspective of switched systems. Some vertices are appropriately selected to be pinned in accordance with an aperiodically intermittent pinning (AIP) strategy. The resultant synchronization error systems are then regarded as switching between two different connection topologies. Under the proposed novel piecewise time-dependent multiple Lyapunov function (PTDMLF) approach, the corresponding synchronization conditions with less conservativeness are formulated. Finally, the provided Chua’s circuit model substantiate the superiority and applicability of the theoretical results.

Population dynamics under climate change: persistence criterion and effects of fluctuations.

The present paper is devoted to the investigation of population dynamics under climate change. The evolution of species is modelled by a reaction-diffusion equation in a spatio-temporally heterogeneous environment described by a climate envelope that shifts with a time-dependent speed function. For a general almost-periodic speed function, we establish the persistence criterion in terms of the sign of the approximate top Lyapunov exponent and, in the case of persistence, prove the existence of a unique forced wave solution that dominates the population profile of species in the long run. In the setting for studying the effects of fluctuations in the shifting speed or location of the climate envelope, we show by means of matched asymptotic expansions and numerical simulations that the approximate top Lyapunov exponent is a decreasing function with respect to the amplitude of fluctuations, yielding that fluctuations in the shifting speed or location have negative impacts on the persistence of species, and moreover, the larger the fluctuation is, the more adverse the effect is on the species. In addition, we assert that large fluctuations can always drive a species to extinction. Our numerical results also show that a persistent species under climate change is invulnerable to mild fluctuations, and becomes vulnerable when fluctuations are so large that the species is endangered. Finally, we show that fluctuations of amplitude less than or equal to the speed difference between the shifting speed and the critical speed are too weak to endanger a persistent species.

Field calibration and validation of a pavement aging model

ABSTRACT A pavement aging model (PAM) is established by calibrating and validating the NCHRP 09–54 kinetics model's predictions against field core measurements. Field cores, laboratory-mixed loose mixtures, and binders from a wide range of pavement sections are used, including both conventional hot mix asphalt (HMA) mixtures and modern materials (i.e. reclaimed asphalt pavement (RAP), warm mix asphalt (WMA), and polymer modified asphalt (PMA)). Field aging levels are measured at different depths from binder extracted and recovered from in-service field cores. The original component materials of these pavement sections are aged in the laboratory and used to calibrate the kinetics model. The measured field aging levels are compared against those predicted from the kinetics model to inform a depth and time dependent field calibration function for the PAM. The validation of PAM using an independent set of field sections shows that, within the limited data used in this study, the calibrated PAM may be able to predict the aging of the conventional HMA, RAP, WMA, and PMA mixtures. The PAM predictions are lastly found to outmatch the predictions by the Global Aging System (GAS) model.

Autocorrelation functions and ergodicity in diffusion with stochastic resetting

Diffusion with stochastic resetting is a paradigm of resetting processes. Standard renewal or master equation approach are typically used to study steady state and other transport properties such as average, mean squared displacement etc. What remains less explored is the two time point correlation functions whose evaluation is often daunting since it requires the implementation of the exact time dependent probability density functions of the resetting processes which are unknown for most of the problems. We adopt a different approach that allows us to write a stochastic solution for a single trajectory undergoing resetting. Moments and the autocorrelation functions between any two times along the trajectory can then be computed directly using the laws of total expectation. Estimation of autocorrelation functions turns out to be pivotal for investigating the ergodic properties of various observables for this canonical model. In particular, we investigate two observables (i) sample mean which is widely used in economics and (ii) time-averaged-mean-squared-displacement (TAMSD) which is of acute interest in physics. We find that both diffusion and drift–diffusion processes with resetting are ergodic at the mean level unlike their reset-free counterparts. In contrast, resetting renders ergodicity breaking in the TAMSD while both the stochastic processes are ergodic when resetting is absent. We quantify these behaviors with detailed analytical study and corroborate with extensive numerical simulations. Our results can be verified in experimental set-ups that can track single particle trajectories and thus have strong implications in understanding the physics of resetting.

A creep model coupling moisture and mechanical damage for water-bearing concrete

The influence of moisture content and overstress on the creep of concrete was investigated from the perspective of damage rheology theory. The weakening effects of moisture and overstress were characterized by a time-independent and a time-dependent damage functions, respectively, and then combined and applied to a modified creep model that can represent the elasto-visco-plastic creep deformation of concrete. Hence, a damage creep model is proposed to describe the creep behavior of water-bearing concrete. Theoretical and statistical analyses, as well as a comparison with the ACI-209 model were performed to examine the validity and superiority of the proposed model. Further analyses showed that not only the deformation parameters, but also the long-term strength parameters degraded with time and increasing moisture. Experiments were then conducted on saturated cement mortar with different static moisture holding durations to investigate the time correlation of moisture-induced damage on the mechanical properties of the material. The experimental results proved that moisture-induced damage was independent of time.

Time domain potential and source methods and their application to twin-hull high-speed crafts

ABSTRACT The numerical accuracy of time dependent potential and source methods is compared against analytical and other numerical results using an in-house transient wave-body interaction three-dimensional wave Green function computational tool of ITU-WAVE. The time dependent Impulse Response Functions (IRFs) are used to predict the behaviour of radiation forces, exciting forces, and response of floating bodies. For radiation force IRFs, the numerical results show that potential method converges with less numbers of panels compared to source method, while in the case of diffraction force IRFs, the convergence is achieved with the same number of elements for both potential and source methods. As potential method achieves convergence faster than source method for radiation force IRFs prediction, potential method is applied for the hydrodynamic and response parameters of a twin-hull high-speed craft. The present ITU-WAVE numerical results, which are compared with experimental, analytical, and other numerical results for validation purposes show satisfactory agreements.

Time-Dependent Friction Effects on Vibrational Infrared Frequencies and Line Shapes of Liquid Water.

From ab initio simulations of liquid water, the time-dependent friction functions and time-averaged nonlinear effective bond potentials for the OH stretch and HOH bend vibrations are extracted. The obtained friction exhibits not only adiabatic contributions at and below the vibrational time scales but also much slower nonadiabatic contributions, reflecting homogeneous and inhomogeneous line broadening mechanisms, respectively. Intermolecular interactions in liquid water soften both stretch and bend potentials compared to the gas phase, which by itself would lead to a red-shift of the corresponding vibrational bands. In contrast, nonadiabatic friction contributions cause a spectral blue shift. For the stretch mode, the potential effect dominates, and thus, a significant red shift when going from gas to the liquid phase results. For the bend mode, potential and nonadiabatic friction effects are of comparable magnitude, so that a slight blue shift results, in agreement with well-known but puzzling experimental findings. The observed line broadening is shown to be roughly equally caused by adiabatic and nonadiabatic friction contributions for both the stretch and bend modes in liquid water. Thus, the quantitative analysis of the time-dependent friction that acts on vibrational modes in liquids advances the understanding of infrared vibrational frequencies and line shapes.

Multi-objective optimisation of in-service asphalt pavement maintenance schedule considering system reliability estimated via LSTM neural networks

This article presents a novel system reliability-based framework for multi-objective optimisation of preventive maintenance (PM) management of in-service asphalt pavement. To accurately predict the international roughness index (IRI) sequence of pavement sections, a long short-term memory (LSTM) neural network that considers the spatiotemporal correlations between IRI sequences is trained with data retrieved from the long-term pavement performance (LTPP) program. Based on time-dependent limit-state functions (LSFs) incorporating the uncertainty associated with LSTM neural network prediction and the observational error involved in IRI measurement, Monte Carlo simulation (MCS) with importance sampling (IS) is adopted to calculate the reliability of pavement sections. Pavement sections located in New Mexico and Montana are selected as illustrative examples. Tri-objective optimisation processes are investigated by maximising user benefits (i.e. improved system reliability) and agency benefits (i.e. extended service life) while minimising the associated life-cycle cost (LCC) (i.e. user and agency costs) with multi-objective genetic algorithms (GAs). The obtained Pareto solution sets may assist decision-makers in the selection of well-balanced solutions to identify the optimal timing for applying PM treatments to in-service asphalt pavement.

Exact Time-Dependent Solutions and Information Geometry of a Rocking Ratchet

The noise-induced transport due to spatial symmetry-breaking is a key mechanism for the generation of a uni-directional motion by a Brownian motor. By utilising an asymmetric sawtooth periodic potential and three different types of periodic forcing G(t) (sinusoidal, square and sawtooth waves) with period T and amplitude A, we investigate the performance (energetics, mean current, Stokes efficiency) of a rocking ratchet in light of thermodynamic quantities (entropy production) and the path-dependent information geometric measures. For each G(t), we calculate exact time-dependent probability density functions under different conditions by varying T, A and the strength of the stochastic noise D in an unprecedentedly wide range. Overall similar behaviours are found for different cases of G(t). In particular, in all cases, the current, Stokes efficiency and the information rate normalised by A and D exhibit one or multiple local maxima and minima as A increases. However, the dependence of the current and Stokes efficiency on A can be quite different, while the behaviour of the information rate normalised by A and D tends to resemble that of the Stokes efficiency. In comparison, the irreversibility measured by a normalised entropy production is independent of A. The results indicate the utility of the information geometry as a proxy of a motor efficiency.

Haste Makes Waste: An Optimization Problem

Summary We pose the following optimization problem: given a fixed distance to be traveled in one dimension and a known time-dependent velocity function, what departure time minimizes the time spent traveling? We determine a method to solve this problem with computer assistance, and along the way we discover a nice geometric characterization of the candidates for the solution.

Simulation of COVID-19 outbreaks via Graphical User Interface (GUI).

Background: This research aimed to model the outbreak of COVID-19 in Malaysia and develop a GUI-based model.Design and methods: The model is an improvement of the susceptible, infected, recovery, and death (SIRD) compartmental model. The epidemiological parameters of the infection, recovery, and death rates were formulated as time dependent piecewise functions by incorporating the control measures of lockdown, social distancing, quarantine, lockdown lifting time and the percentage of people who abide by the rules. An improved SIRD model was solved via the 4th order Runge-Kutta (RK4) method and 14 unknown parameters were estimated by using Nelder- Mead algorithm and pattern-search technique. The publicly available data for COVID-19 outbreak in Malaysia was used to validate the performance of the model. The GUI-based SIRD model was developed to simulate the number of active cases of COVID-19 over time by considering movement control order (MCO) lifted date and the percentage of people who abide the rules.Results: The simulator showed that the improved SIRD model adequately fitted Malaysia COVID-19 data indicated by low values of root mean square error (RMSE) as compared to other existing models. The higher the percentage of people following the SOP, the lower the spread of disease. Another key point is that the later the lifting time after the lockdown, the lower the spread of disease.Conclusions: These findings highlight the importance of the society to obey the intervention measures in preventing the spread of the COVID-19 disease. Significance for public health This research is in line with critical areas in Malaysia that are in close association with the community in dealing with the COVID-19 pandemic. This study contributes to the understanding of COVID-19 contagion in Malaysia. This model guides the policymakers to plan the 'exit strategy' of the COVID-19 outbreak as it can forecast the spreading dynamics of the disease in the population accompanied by the intervention measures of quarantine, isolation, lockdown lifting time and the percentage of the people who follow the SOP. The key ingredients to win the battle against the pandemic are embracing the new normal and community responsibility empowerment. This research showed that the individual act of following SOP can prevent the spread of the disease.

A production inventory model for the deteriorating goods under COVID-19 disruption risk

The rapid onset of the COVID-19 epidemic has brought the manufacturing process to a halt. The problem is especially serious for deteriorating products because demand for these items is not consistent and the product's worth has diminished with time. Many deteriorating product industries are now looking for an appropriate and effective disruption recovery plan to help them recover. However, a survey of the literature suggests that there has been little research done on developing an effective inventory production model for deteriorating products exposed to COVID-19 pandemic risks. This research intends to develop a disruption recovery model that considers demand as a time-dependent quadratic function to find out the optimum number of orders. Two different heuristic algorithms named: Genetic Algorithm (GA) and Whale Optimization Algorithm (WOA) have been employed to solve the model and it has been found that WOA performs better in terms of convergence. The numerical findings indicate that the price inclination rate for the component price and selling price played a pivotal role to maximize net profit. It is expected that by employing the proposed model of this research, the industry managers will be greatly benefitted to obtain quick recovery from the COVID-19 disruption risk for the deteriorating goods and retain financial stability.

Impact response of a thin shallow doubly curved linear viscoelastic shell rectangular in plan

In this paper, we consider the problem on a transverse impact of a viscoelastic sphere upon a viscoelastic shallow doubly curved shell with rectangular platform, the viscoelastic features of which are defined via the fractional derivative standard linear solid models; in so doing, only Young’s time-dependent operators are preassigned, while the bulk moduli are considered to be constant values, since the bulk relaxation for the majority of materials is far less than the shear relaxation. Shallow panel’s displacement subjected to the concentrated contact force is found by the method of expansion in terms of eigen functions, and the sphere’s displacement under the action of the contact force, which is the sum of the shell’s displacement at the place of contact and local bearing of impactor and target’s materials, is defined from the equation of motion of the material point with the mass equal to sphere’s mass. Within the contact domain, the contact force is defined by the modified Hertzian contact law with the time-dependent rigidity function. For decoding the viscoelastic operators involving the problem under consideration, the algebra of Rabotnov’s fractional operators is employed. A nonlinear integro-differential equation is obtained either in terms of the contact force or in the local bearing of the target and impactor materials. Using the duration of contact as a small parameter, approximate analytical solutions have been found, which allow one to define the key characteristics of impact process.

Optimal control and comprehensive cost-effectiveness analysis for COVID-19

Cost-effectiveness analysis is a mode of determining both the cost and economic health outcomes of one or more control interventions. In this work, we have formulated a non-autonomous nonlinear deterministic model to study the control of COVID-19 to unravel the cost and economic health outcomes for the autonomous nonlinear model proposed for the Kingdom of Saudi Arabia. We calculated the strength number and noticed the strength number is less than zero, meaning the proposed model does not capture multiple waves, hence to capture multiple wave new compartmental model may require for the Kingdom of Saudi Arabia. We proposed an optimal control problem based on a previously studied model and proved the existence of the proposed optimal control model. The optimality system associated with the non-autonomous epidemic model is derived using Pontryagin’s maximum principle. The optimal control model captures four time-dependent control functions, thus, u1-practising physical or social distancing protocols; u2-practising personal hygiene by cleaning contaminated surfaces with alcohol-based detergents; u3-practising proper and safety measures by exposed, asymptomatic and symptomatic infected individuals; u4-fumigating schools in all levels of education, sports facilities, commercial areas and religious worship centres. We have performed numerical simulations to investigate extensive cost-effectiveness analysis for fourteen optimal control strategies. Comparing the control strategies, we noticed that; Strategy 1 (practising physical or social distancing protocols) is the most cost-saving and most effective control intervention in Saudi Arabia in the absence of vaccination. But, in terms of the infection averted, we saw that strategy 6, strategy 11, strategy 12, and strategy 14 are just as good in controlling COVID-19.