Stochastic Numerical Simulations Research Articles

A novel approach for fractional pharmacokinetics modeling and integrating stochastic simulation techniques using Sibuya distribution

Fractional compartment models are widely used to simulate pharmacokinetics with power-law behavior. In this work, we study an approach, previously mainly used in Epidemiology for the age model, employing the Sibuya distribution, a discrete-time, non-Markov probability distribution, to effectively emulate Mittag-Leffler functions. We demonstrate the validity of our method by applying it to various pharmacokinetic datasets and comparing the results with traditional methods like the Numerical Inverse Laplace Transform (NILT) algorithm. Additionally, we propose two stochastic simulation algorithms, where the Monte Carlo SSA allows us to capture the randomness of data and the Gillespie-like stochastic numerical simulation technique can optimize computational resources in fractional analysis.

Numerical Stochastic Simulation of Spatially Heterogeneous Population

Numerical Stochastic Simulation of Spatially Heterogeneous Population

Mapping and resource evaluation of deep high-temperature geothermal resources in the Jiyang Depression, China

In China, geothermal resource utilization has mainly focused on resources at shallow and medium depths. Yet, the exploration of deep, high-temperature geothermal resources holds significant importance for achieving the “dual carbon” goals and the transition of energy structure. The Jiyang Depression in the Bohai Bay Basin has vast potential for deep, high-temperature geothermal resources. By analyzing data from 2187 wells with temperature logs and 270 locations for temperature measurement in deep strata, we mapped the geothermal field of shallow to medium-deep layers in the Jiyang Depression using ArcGIS and predicted the temperatures of deep layers with a burial depth of 4000 m. Through stochastic modeling and numerical simulation, a reservoir attribute parameter database for favorable deep, high-temperature geothermal areas was developed, systematically characterizing the spatial distribution of geothermal resources within a play fairway of 139.5 km2 and estimating the exploitable deep geothermal resource potential by using the heat storage method and Monte Carlo data analysis. The study reveals that the Fan 54 well block in the Boxing-Jijia region is of prime significance to develop deep, high-temperature geothermal resources in the Jiyang Depression. Strata from the Cenozoic to the Upper Paleozoic are identified as effective cap layers for these deep geothermal resources. The Lower Paleozoic capable of effectively storing thermal energy and possessing an exploitable resource volume up to 127 million tons of standard coal, is identified as a target system for the development of deep high-temperature geothermal resources, providing significant insights for the efficient development of geothermal resources in the Jiyang Depression.

Stochastic CFD numerical model, algorithm, and simulation on regular wave fields

This paper invites higher-order derivative numerical technology to research the stochastic characteristics in regular wave fields. The randomness of the parameters vector was incorporated during the stochastic space establishment, by which, the stochastic CFD numerical model and algorithm were developed in the study. Meantime, Taylor expansion coupled with the perturbation was also utilized to realize the investigation on the random behaviours of the regular wave fields where the perturbative values of the parameters vector included 1%, 2%, and 3%. The results indicated the merit of the stochastic CFD numerical model and algorithm in wave field research.

Mbit/s-range alkali vapour spin noise quantum random number generators

Spin noise based quantum random number generators first appeared in 2008 and have since then garnered little further interest, in part because their bit rate is limited by the transverse relaxation time T2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$T_{2}$\\end{document} which for coated alkali vapour cells is typically in the kbit/s range. Here we present two advances. The first is an improved bit generation protocol that allows generating bits at rates exceeding 1/T2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$1/T_{2}$\\end{document} with only a minor increase of serial correlations. The second is a significant reduction of the time T2\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$T_{2}$\\end{document} itself by removing the coating, increasing the vapour temperature and introducing a magnetic-field gradient. In this way we managed to increase the bit generation rate to 1.04 Mbit/s. We analyse the quality of the generated random bits using entropy estimation and we discuss the extraction methods to obtain high-entropy bitstreams. We accurately predict the entropy output of the device backed with a stochastic model and numerical simulations.

Experiments in micro-patterned model membranes support the narrow escape theory

The narrow escape theory (NET) predicts the escape time distribution of Brownian particles confined to a domain with reflecting borders except for one small window. Applications include molecular activation events in cell biology and biophysics. Specifically, the mean first passage time bar{tau } can be analytically calculated from the size of the domain, the escape window, and the diffusion coefficient of the particles. In this study, we systematically tested the NET in a disc by variation of the escape opening. Our model system consisted of micro-patterned lipid bilayers. For the measurement of bar{tau }, we imaged diffusing fluorescently-labeled lipids using single-molecule fluorescence microscopy. We overcame the lifetime limitation of fluorescent probes by re-scaling the measured time with the fraction of escaped particles. Experiments were complemented by matching stochastic numerical simulations. To conclude, we confirmed the NET prediction in vitro and in silico for the disc geometry in the limit of small escape openings, and we provide a straightforward solution to determine bar{tau } from incomplete experimental traces.

Exact solution of the Langmuir rate equation: New Insights into pseudo-first-order and pseudo-second-order kinetics models for adsorption

The Langmuir adsorption rate equation was obtained in its exact, linear, and simple form. Using Stochastic Numerical Simulation, it was demonstrated that this equation can accurately calculate the adsorption rate constant (ka), which is more precise than the values obtained using pseudo-first-order (PFO) and pseudo-second-order (PSO) models. The derivation conditions of the PFO and PSO kinetics models from Langmuir kinetics were also investigated. The results showed that the PFO model can be obtained at two limit states: at Ce≅C0 and at Ce≪C0 with a very low fractional coverage. Also, the PSO model is derived under the condition Ce→0 and θe→1. The accuracy of the exact Langmuir model, both linear and nonlinear, and the theoretical derivation conditions of the PFO and PSO models were examined using several sets of kinetics data generated by the Stochastic Numerical Simulation method. The simulation results supported the theoretical approaches of this study.

A stochastic numerical model for wave-induced dynamic response in a spatially heterogeneous seabed around structures

The interaction between waves, seabed, and structures is a complex phenomenon that involves multiple physical domains and processes. The spatial variability of properties in marine sediment can significantly affect the dynamic response of seabed. A stochastic numerical model is developed to investigate the response in a spatially heterogeneous poro-elastic seabed around a submerged breakwater. The model is implemented using the COMSOL platform, which allows for solving the wave and seabed sub-models within the same framework. The spatial variability of soil properties is simulated using the random field method employing the Karhunen-Loève expansion. To couple the generated random fields in MATLAB with the integrated model in COMSOL, a LiveLink program is developed, which incorporates a cycle algorithm for stochastic finite element analysis, enabling hundreds or thousands of runs. The model is validated by comparing its results with analytical solutions and experimental data from literature. Probabilistic analysis is performed using the stochastic numerical model and Monte Carlo simulations. The effects of coefficient of variation and correlation lengths in random field on the probabilistic analysis are investigated. The present study provides a valuable tool and insights for the probabilistic assessment of soil response in a spatially heterogeneous seabed around structures.

Modeling the space-time correlation of pulsed twin beams

Entangled twin-beams generated by parametric down-conversion are among the favorite sources for imaging-oriented applications, due their multimodal nature in space and time. However, a satisfactory theoretical description is still lacking. In this work we propose a semi-analytic model which aims to bridge the gap between time-consuming numerical simulations and the unrealistic plane-wave pump theory. The model is used to study the quantum correlation and the coherence in the angle-frequency domain of the parametric emission, and demonstrates a g^{{1/2}} growth of their size as the gain g increases, with a corresponding contraction of the space-time distribution. These predictions are systematically compared with the results of stochastic numerical simulations, performed in the Wigner representation, of the full model equations: an excellent agreement is shown even for parameters well outside the expected limit of validity of the model.

Simulation of Inertial Droplet Dispersion and the Spray Mediated Fluxes in the Atmospheric Boundary Layer Above Waved Water Surface: A Lagrangian Stochastic Model Versus Direct Numerical Simulation

Simulation of Inertial Droplet Dispersion and the Spray Mediated Fluxes in the Atmospheric Boundary Layer Above Waved Water Surface: A Lagrangian Stochastic Model Versus Direct Numerical Simulation

A Kermack–McKendrick model with age of infection starting from a single or multiple cohorts of infected patients

The infectiousness of infected individuals is known to depend on the time since the individual was infected, called the age of infection. Here, we study the parameter identifiability of the Kermack–McKendrick model with age of infection which takes into account this dependency. By considering a single cohort of individuals, we show that the daily reproduction number can be obtained by solving a Volterra integral equation that depends on the flow of newly infected individuals. We test the consistency of the method by generating data from deterministic and stochastic numerical simulations. Finally, we apply our method to a dataset from SARS-CoV-1 with detailed information on a single cluster of patients. We stress the necessity of taking into account the initial data in the analysis to ensure the identifiability of the problem.

Mathematical Analysis of Epidemic Models with Treatment in Heterogeneous Networks.

In this paper, we formulate two different network-based epidemic models to investigate the effect of partly effective treatment on disease dynamics. The first network model represents the individuals with heterogeneous number of contacts in a population as choosing a new partner at each moment, whereas the second one assumes the individuals have fixed or stable neighbors. The basic reproduction number [Formula: see text] is computed for each model, using the next generation matrix method. In particular, the critical treatment rate is defined for the model, above which the disease can be eliminated through the treatment. The final epidemic size relations are derived, and the solvability of these implicit equations is studied. In particular, a unique solution of the implicit equation for the final epidemic size is determined, and by rewriting the implicit equation as a suitable fixed point problem, it is proved that the iteration of the fixed point problem converges to the unique solution. Stochastic simulations and numerical simulations, including in comparison with the model outputs and the joint influence of network topology and treatment on the final epidemic size, are conducted to illustrate the theoretical results.

Stochastic P-Bifurcation in a Delayed Myc/E2F/miR-17-92 Network

In this paper, Myc/E2F/miR-17-92 network under Gaussian white noise is studied. Taking the time delay as the parameter, the Hopf bifurcation of the system is obtained, which causes the protein concentration to oscillate periodically. Under the influence of time delay and noise, the stochastic D-bifurcation of the system is obtained. It is worth noting that the occurrence of stochastic P-bifurcation is successfully captured. Thus a pattern of coexistence of high and low protein concentrations is founded in the network. The specific research methods of this paper are as follows: firstly, the system is reduced to a finite dimensional system by using stochastic center manifold and normal form theory. Then, using the stochastic averaging method, the Fokker–Planck–Kolmogorov equation of the system is constructed in which the statistical response in the stationary state is the probability density. Finally, the stochastic bifurcation analysis and numerical simulation are carried out. The agreements between the analytical method and those obtained numerically validate the effectiveness of the analytical investigations.

Stability analysis of stochastic second-order macroscopic continuum models and numerical simulations

Second-order macroscopic continuum models have been constantly improving for decades to reproduce the empirical observations. Recently, a series of experimental studies have suggested that the stochastic factors contribute significantly to destabilizing traffic flow. Nevertheless, the traffic flow stability of the stochastic second-order macroscopic continuum model has not received the attention it deserves in past studies. More importantly, we have found that the destabilizing aspect of stochasticity is still not correctly validated in the existing theoretical stability analysis. In this paper, we analytically study the impact of stochasticity on traffic flow stability for a general stochastic second-order macroscopic model by using the direct Lyapunov method. Numerical simulations have been carried out for different typical stochastic second-order macroscopic models. Our analytical stability analysis has been validated, and our methodology has been proved more efficient. Our study has theoretically revealed that the presence of stochasticity has a destabilizing effect in usual stochastic macroscopic models.

Core Surface Flow Changes Associated With the 2017 Pacific Geomagnetic Jerk.

A geomagnetic jerk was seen in Swarm satellite data in 2017 over the Pacific region. We invert time series of spatial gradient secular variation data between 2014 and 2020, reduced to a grid of points at satellite altitude, for spatially‐ and temporally‐regularized core surface flow. Pacific region flow acceleration was almost constant before and after the jerk, with a sharp change, especially in the azimuthal component, at the jerk epoch, despite the temporal regularization. Azimuthal acceleration is oppositely signed either side of 160°W, where it effectively vanishes, and also reverses sign at the jerk epoch. Acceleration features drift westward at about 900 km year−1. Unlike previous studies, the evidence presented here for low latitude waves does not depend on imposing flow equatorial symmetry, quasi‐ or tangential geostrophy, or band‐pass filtering, and has no reliance on stochastic models or numerical simulations.

Constraints for the Vs profiles from engineering-geological qualitative characterization of shallow subsoil in seismic microzonation studies

A statistical analysis has been performed aiming at determining to what extent a qualitative engineering-geological characterization of subsoil may provide constraints to the shear wave velocity (Vs) profile. For this purpose, a large database of experimental values provided by seismic microzonation studies carried out in the last 10 years in Italy has been considered. This analysis suggests that statistical constraints can be provided to Vs values as a function of depth by considering main lithological characteristics of cover terrains and geological bedrock. The effectiveness and unbiasedness of resulting relationships are tested against some experimental situations. This information can be used to feed stochastic numerical simulations aiming at preliminary assessment of probability distribution of the expected seismic response in wide areas where an experimental geophysical/geotechnical characterization of the local subsoil is scarce or unavailable.

Modeling social media addiction with case detection and treatment

Introduction This paper discusses the problem of social media addiction that pose a major threat to the human population especially children and teenagers. It is well known that Cognitive Behavioral Therapy (CBT) is an effective treatment to treat the addict individuals and delay in the treatment leads the patient to worst stage even to death. Therefore, it is important to identify the individuals who has addiction symptoms at early stage and to provide proper counseling. Method We propose and analyze a nonlinear mathematical model for social media addiction problem using case detection strategy to reduce the addiction. The basic reproduction number and equilibria of the model are computed. Further, the deterministic model is extended to delay differential equation model by incorporating transmission delay and treatment delay in the system. The local stability of different equilibria is discussed in detail. Additionally, the model is converted to stochastic model and numerical simulation is carried out to compare the results of both deterministic and stochastic model. Results Numerical result shows that the introduction of time delays can destabilize the model system and Hopf bifurcation occurs due to periodic oscillations when certain equilibrium point crosses the delay threshold limit. Our results of stochastic model show a smaller number of social media users and addict population when compared with deterministic model. Also, our results reveal that detection and counseling parameters play a vital role in reducing addiction population. Discussion Presented results clearly suggest that there is a need to use effective detection strategy and suitable counseling program to reduce the social media addiction level.

Stochastic models of bioclimatic indices time series in the Arctic zone of the Russian Federation

In this paper, an approach to the numerical stochastic simulation of time series of two bioclimatic indices (wind chill index and the equivalent-effective temperature) at weather stations located in the Arctic zone of the Russian Federation is considered. The approach is based on the use of so-called “defining formulas”. On the basis of the considered approach, stochastic models of the time series of the considered bioclimatic indices were constructed, numerically implemented and verified. The models are developed on the assumption that the real bioclimatic processes are periodically correlated. The use of this assumption makes it possible to take into account the daily variation of the real processes. We also use the assumption that the real series of the wind chill index and the equivalent-effective temperature are non-Gaussian. To simulate non-stationary non-Gaussian time series, the method of inverse distribution functions is applied. The results of verification of the developed stochastic models showed that many statistical characteristics of simulated trajectories are close to the corresponding characteristics of the real series.

Study on stationary probability density of a stochastic tumor-immune model with simulation by ANN algorithm

In this paper, the theoretic analysis by stochastic dynamics and numerical simulation by ANN algorithm for tumor-immune models driven by random noises are studied. Firstly, a mathematical model about the competition between tumor cells and immune system is established based on the Michaelis-Menten enzyme kinetics. Secondly, the microenvironmental fluctuations are modeled as Gaussian white noises and Gaussian coloured noises, respectively. Then the corresponding Fokker-Planck equation (FPE) and the approximated Fokker-Planck equation (AFPE) are obtained to explore the stationary probability density (SPD) of the tumor cells. The innovation of this paper is that artificial neural network (ANN) algorithm is introduced to solve the SPD based on FPE or AFPE, which has higher robustness and accuracy. The SPDs of tumor cells show that the greater the intensity of Gaussian white noises, the more beneficial the prevention of tumor growth. In other words, the microenvironmental fluctuations could accelerate the extinction of tumor to a certain extent. For the case of Gaussian coloured noises, the existence of the cross-correlation time between multiplicative and additive Gaussian coloured noises lead the tumor to be large concentrations with probability of almost 1. All the theoretical results are examined by ANN algorithm and they are all in good agreement. In addition, we discuss the mean first passage time (MFPT) from the metastable state to the state of extinction of tumor cells, and discover the phenomena of the noise-enhanced stability (NES) as well as stochastic resonant activation (SRA). At last, the best parameters including penalty factors, the number of layers and nodes in ANN algorithm are also discussed in order to get the optimal accuracy.

Outbreak or extinction of bovine cysticercosis and human taeniasis: A Stochastic modelling approach

Bovine cysticercosis and human taeniasis are neglected food-borne infections that pose challenges to food safety, peoples’ health and the economy of rural farmers who depend on livestock keeping. In this paper, the continuous time Markov chain (CTMC) stochastic model is formulated based on its corresponding deterministic model and rigorously analyzed to study the dynamics of cysticercosis in cattle and taeniasis in humans. The multitype branching process is adopted to compute the stochastic threshold and numerical simulations for the CTMC model with 10,000 sample paths are used to compute probabilities of diseases’ extinction when initial conditions for infected classes are varied. The results show that when there is disease outbreak, the solutions of CTMC stochastic model are relatively close to deterministic model solutions. The analytical and numerical results for probability of diseases’ extinction are in good agreement when initially there is no infectious human. Some variations in probability of diseases’ extinction are due to infectious beef being considered a discrete number in CTMC model. The results show further that the diseases' extinction probability is high when the diseases emerge from a small number of T. saginata eggs or from infected cattle. However, the probability becomes low when there is at least an infectious beef at the beginning of the diseases' outbreak.