Article
Materials Science, Multidisciplinary
C. Ravichandran, K. Logeswari, Aziz Khan, Thabet Abdeljawad, J. F. Gomez-Aguilar
Summary: The era of data is transforming into a Big Data model, where storing massive amounts of data and protecting it from viruses becomes crucial. This study focuses on optimal control analysis using the Atangana-Baleanu derivative and analyzes solutions for a fractional order computer virus model. The results are verified numerically and presented graphically.
RESULTS IN PHYSICS
(2023)
Article
Materials Science, Multidisciplinary
Muhammad Farman, Maryam Batool, Kottakkaran Sooppy Nisar, Abdul Sattar Ghaffari, Aqeel Ahmad
Summary: This research proposes a mathematical model of cancer treatment with chemotherapy using a fractal fractional Mittag-Leffler operator with non-integer order. The model is analyzed both qualitatively and quantitatively. The control of cancer treatment with chemotherapy effects is established using a fractal fractional operator with a Mittag-Leffler kernel and control theory.
RESULTS IN PHYSICS
(2023)
Article
Mathematics, Interdisciplinary Applications
Mati Ur Rahman, Shabir Ahmad, Muhammad Arfan, Ali Akgul, Fahd Jarad
Summary: This article describes the dynamics of a fractional mathematical model of serial killing using the Mittag-Leffler kernel. Through the fixed point theory approach, a qualitative analysis is conducted and a result is established to ensure the existence of at least one solution. Ulam's stability of the model is demonstrated using nonlinear concepts. The iterative fractional-order Adams-Bashforth approach is employed to find an approximate solution. The suggested method is numerically simulated at various fractional orders, and the simulation shows that all compartments achieve convergence and stability over time, with lower fractional orders achieving stability sooner.
FRACTAL AND FRACTIONAL
(2022)
Article
Mathematics, Applied
Ali Akgul, Muhammad Sajid Iqbal, Umbreen Fatima, Nauman Ahmed, Zafar Iqbal, Ali Raza, Muhammad Rafiq, Muhammad Aziz-ur Rehman
Summary: This article analyzes the fractional order computer epidemic model, extending a classical model using the Atangana-Baleanu fractional differential operator. The regularity condition and existence of solutions in the Banach space are described, with stability at steady states studied using the Jacobian matrix method. The significance of the basic reproduction number on stability analysis is highlighted, with numerical designs and graphical solutions presented through computer simulations.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Mathematics, Interdisciplinary Applications
Mohammad Partohaghighi, Abdullahi Yusuf, Yeliz Karaca, Yong-Min Li, Tarek F. Ibrahim, B. A. Younis, Bahaa Saleh, Ayman A. Aly
Summary: In this study, we modeled the fractal-fractional system of the Computer virus problem using the Atangana-Baleanu operator and verified the existence and uniqueness of the results by applying the Schauder fixed point and Banach fixed theorems. We obtained approximate solutions using the Atangana-Toufik technique by choosing different values of orders and examined the performance of the suggested numerical method on the new fractal-fractional system by selecting different values of fractal-fractional orders and initial conditions.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2022)
Article
Mathematics, Applied
Madasamy Vellappandi, Venkatesan Govindaraj
Summary: This paper investigates the fractional optimal control problem with a single delay in the state using the operator theoretic approach. It establishes the existence of an optimal pair for the abstract system by reducing the delay fractional dynamical system into an equivalent operator equation and providing sufficient conditions to the operators. The optimality system for the quadratic cost functional is derived using the Frechet derivative and related to the Hamiltonian system of Pontryagin's minimum principle. The article demonstrates the existence of an optimal pair for the fractional-order delay dynamical system and provides numerical examples to support the theoretical findings.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Applied
X. Y. Li, X. Y. Liu
Summary: In this letter, a hybrid kernel functions collocation approach for boundary value problems with Caputo fractional derivative is proposed. The approach combines the advantages of the Sobolev and Mittag-Leffler kernel functions to improve the stability and accuracy of existing methods. The results demonstrate the effectiveness of the proposed approach.
APPLIED MATHEMATICS LETTERS
(2023)
Article
Mathematics, Applied
Velusamy Kavitha, Mani Mallika Arjunan, Dumitru Baleanu
Summary: In this manuscript, we examine the existence of fractional-order functional differential equations with non-instantaneous impulses within the Mittag-Leffler kernel. Non-instantaneous impulses are involved in such equations, resulting in a non-compact solution semigroup in Banach spaces. We propose assumptions on the nonlinear term and the non-instantaneous impulsive functions to justify the theoretical results. Additionally, an example is provided to illustrate the validity of the results.
Article
Engineering, Multidisciplinary
Muhammad Irfan Ullah, Qura Tul Ain, Aziz Khan, Thabet Abdeljawad, Manar A. Alqudah
Summary: Compared to fossil fuels, the sun has abundant energy to meet the global energy demand, but the challenge lies in efficiently and economically converting solar energy into electricity. This study utilizes fractional derivatives to introduce the dynamics of a solar heating model and investigates the existence and uniqueness of solutions for the fractional system. A novel numerical method is employed to visualize the dynamics of different parameters in the nonlinear ordinary differential equation system, demonstrating the validity and efficiency of the proposed ODE models for fractional order data in a solar heating system.
ALEXANDRIA ENGINEERING JOURNAL
(2023)
Article
Mathematics, Interdisciplinary Applications
Mohammed Al-Refai, Muhammed I. Syam, Dumitru Baleanu
Summary: This paper discusses the solutions of systems of fractional differential equations, providing closed-form solutions for linear systems involving the modified Atangana-Baleanu derivative and numerical approximations for nonlinear systems using the collocation method. The applicability of the results is tested through several examples, highlighting the absence of solutions for certain systems with the Atangana-Baleanu derivative but not with the modified derivative.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2023)
Article
Mathematics, Interdisciplinary Applications
Auwal Abdullahi
Summary: This study formulates a new integer-order ordinary differential equation (ODE) Lassa fever model, and devises its corresponding fractional-order differential equation (FODE) using the Caputo fractional-order derivative. The study explores the existence and uniqueness of the solution of the proposed FODE through fixed point theory, and determines the positivity of the FODE model using the Mittag-Leffler function. The results show that although a culling strategy on the population of rodents can reduce the number of infected rodents, it cannot completely eradicate the disease in humans.
CHAOS SOLITONS & FRACTALS
(2021)
Article
Mathematics, Interdisciplinary Applications
Changjin Xu, Muhammad Farman
Summary: The primary objective of this study is to investigate a mathematical model of cancer using a novel fractional operator, focusing on the dynamics of cancer cells during treatment with a combination of cytokines and inhibitors. The study aims to analyze the model qualitatively and quantitatively using nonlinear differential equations, establish the existence and uniqueness of solutions using fixed-point theorems, and analyze the stability of the system through stability concepts and functions. The study also explores the impact of the fractional operator on the dynamical system and presents numerical simulations to provide practical insights.
CHAOS SOLITONS & FRACTALS
(2023)
Article
Mathematics, Applied
Xing -Yu Li, Kai-Ning Wu, Xiao-Zhen Liu
Summary: In this study, the Mittag-Leffler stabilization of short memory fractional reaction-diffusion systems (SMFRDSs) is investigated using a designed intermittent boundary controller. By employing the Lyapunov functional method and various inequalities, a sufficient criterion is derived to ensure the Mittag-Leffler stability of SMFRDSs. The robust Mittag-Leffler stability is also considered in the presence of uncertainties in SMFRDSs. Furthermore, the influence of control gains and diffusion coefficient matrix on stability is analyzed. Numerical simulations are conducted to validate the proposed approach based on the obtained results.
APPLIED MATHEMATICS AND COMPUTATION
(2023)
Article
Mathematics, Applied
Berat Karaagac, Kolade M. Owolabi
Summary: The study aims to analyze and obtain a new numerical approach for polio, an important mathematical model. By using noninteger-order derivative modeling, the study finds that the model is more accurate and reliable. A new numerical approximation method is proposed and validated through experiments.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Interdisciplinary Applications
Rajarama Mohan Jena, Snehashish Chakraverty, Shengda Zeng, Van Thien Nguyen
Summary: A new definition of fractional differentiation of nonlocal and non-singular kernels has been developed recently to overcome the shortcomings of traditional fractional derivatives. This study explores the dynamic behaviors of a fractional financial chaotic model using both singular and non-singular kernel fractional derivatives. The proposed model is solved using the fractional Adams-Bashforth method, and the existence, uniqueness, error analysis, and stability of the solution are examined.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2023)
Article
Computer Science, Artificial Intelligence
Zulqurnain Sabir, Mohamed R. Ali, Muhammad Asif Zahoor Raja, R. Sadat, Dumitru Baleanu
Summary: The present study introduces a novel heuristic computing design for solving the second kind of Three-point singular boundary value problems (TPS-BVPs) by combining Feed forward Gudermannian neural networks (GNN) with Genetic algorithms (GA) and Active-set method (ASM). The proposed intelligent computing solver, FF-GNN-GAASM, is integrated into the hidden layer structure of FF-GNN systems, optimizing the error based Merit function (MF) with the hybrid-combined heuristics of GAASM. The performance of FF-GNN-GAASM is evaluated through statistical assessments, demonstrating consistent stability, accuracy, and convergence.
EVOLUTIONARY INTELLIGENCE
(2023)
Article
Engineering, Multidisciplinary
Muhammad Jawaz, Muhammad Aziz-Ur Rehman, Nauman Ahmed, Dumitru Baleanu, Muhammad Sajid Iqbal, Muhammad Rafiq, Ali Raza
Summary: This work investigates disease dynamics and numerical modeling for the delay diffusion infectious rabies model. It considers a non-linear diffusive rabies model with a delay count and describes the parameters involved. Equilibrium points are determined and their role in studying disease dynamics is identified. The basic reproduction number is also studied. The solution's existence is ensured using the Schauder fixed point theorem and uniqueness is established. A finite difference method is introduced and its stability is analyzed using the Von-Neumann method. The consistency of the method is examined using Taylor's expansion approach. The numerical test example and computer simulations investigate the important aspects of the proposed numerical device, including the effect of tau on infected individuals. A fruitful conclusion of the study is presented.
INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION
(2023)
Article
Mathematics
R. Rajagopalan, Abass H. Abdel Kader, Mohamed S. Abdel Latif, Dumitru Baleanu, Amr El Sonbaty
Summary: In this paper, the variable coefficients KdV equation with general power nonlinearities is transformed into a generalized KdV equation with constant coefficients using a point transformation. Then, the traveling wave transformation is utilized to convert the equation into a generalized ordinary differential equation. A classification is given for the obtained equation using an integrating factor, and new solutions are obtained for the equation. All the solutions obtained in this paper are new.
JOURNAL OF MATHEMATICS AND COMPUTER SCIENCE-JMCS
(2023)
Article
Mathematics
Manickam Jayapriya, Anumanthappa Ganesh, Shyam Sundar Santra, Reem Edwan, Dumitru Baleanu, Khaled Mohamed Khedher
Summary: This study investigates the Hyers-Ulam stability of nth order differential equations using the Sawi transform, aiming to derive a generalized stability result for linear homogeneous and non-homogeneous differential equations.
JOURNAL OF MATHEMATICS AND COMPUTER SCIENCE-JMCS
(2023)
Article
Physics, Applied
Hanumesh Vaidya, Rajashekhar Choudhari, Dumitru Baleanu, K. Prasad, Shivaleela, M. Ijaz Khan, Kamel Guedri, Mohammed Jameel, Ahmed M. Galal
Summary: This study investigates phenomena such as electro-osmosis, peristalsis, and heat transfer and proposes the possibility of constructing biomimetic thermal pumping systems. A mathematical model is developed to examine the mechanisms of magnetohydrodynamics non-Newtonian flow. The findings suggest that electro-osmosis may improve peristaltic flow.
INTERNATIONAL JOURNAL OF MODERN PHYSICS B
(2023)
Article
Physics, Applied
Tukur A. Sulaiman, Abdullahi Yusuf, Ali S. Alshomrani, Dumitru Baleanu
Summary: The novel wave profiles for the (2+1)-dimensional Boussinesq equation are established using the powerful Sardar sub-equation technique. The explanations for several physical difficulties have been studied in depth. These technological advancements have proven to be beneficial for long-wave and high-power communications networks. The circumstances that led to the emergence of these solutions are described in detail. The physical characteristics of the governing equation have been depicted using contour plots and three-dimensional figures.
INTERNATIONAL JOURNAL OF MODERN PHYSICS B
(2023)
Article
Mathematics, Applied
Sayooj Aby Jose, Raja Ramachandran, Dumitru Baleanu, Hasan S. Panigoro, Jehad Alzabut, Valentina E. Balas
Summary: This paper presents a mathematical model for dynamic systems of substance addiction using the ABC fractional derivative. The stability of the equilibrium points and the basic reproduction number are investigated. The theoretical results of solution existence and uniqueness for the proposed model are verified using fixed point theory and nonlinear analytic techniques. A numerical technique is established to obtain the approximate solution of the model, and numerical graphs corresponding to different fractional orders are provided. Furthermore, a numerical simulation is conducted to study the transmission of substance addiction in scenarios with different basic reproduction numbers.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Applied
Dumitru Baleanu, Pshtiwan Othman Mohammed, Hari Mohan Srivastava, Eman Al-Sarairah, Thabet Abdeljawad, Y. S. Hamed
Summary: This paper focuses on the analytical and numerical convexity analysis of discrete delta Riemann-Liouville fractional differences. In the analytical part, a new definition for the discrete delta Riemann-Liouville fractional difference is proposed and a formula for delta(2) is established. The correlation between the positivity of ((RL)(w0)delta(alpha)f)(t) and the convexity of the function is examined. Two decreasing subsets H(k,E) and M-k,M-E are defined based on basic lemmas to obtain the relationship between the negative lower bound of ((RL)(w0)delta(alpha)f)(t) and convexity of the function on a finite time set N-w0(P).
JOURNAL OF INEQUALITIES AND APPLICATIONS
(2023)
Article
Nanoscience & Nanotechnology
J. Leo Amalraj, M. Maria Susai Manuel, Dumitru Baleanu, D. S. Dilip
Summary: This research aims to discuss the existence, global stability, periodicity, and bifurcation analysis of a modified version of the ecological model proposed by Tilman and Wedlin [Nature 353, 653-655 (1991)].
Article
Multidisciplinary Sciences
Hari Mohan Srivastava, Pshtiwan Othman Mohammed, Juan Luis G. Guirao, Dumitru Baleanu, Eman Al-Sarairah, Rashid Jan
Summary: The class of symmetric function interacts extensively with other types of functions, particularly with the class of positivity of functions. In this study, we propose a positive analysis technique to analyze a specific class of Liouville-Caputo difference equations of fractional-order with extremal conditions. By utilizing difference conditions, we derive relative minimum and maximum through monotonicity results. The obtained monotonicity results are verified by solving two numerical examples.
Article
Engineering, Multidisciplinary
Sanjay Bhatter, Kamlesh Jangid, Shyamsunder Kumawat, Sunil Dutt Purohit, Dumitru Baleanu, D. L. Suthar
Summary: In this study, we investigated calcium fluctuations in cellular environments using the Hilfer fractional advection-diffusion equation. We simulated calcium signalling with different buffers, including calcium-binding buffers, and set limits and start conditions. The results showed that the modified Hilfer calcium model, considering time, position, and the Hilfer fractional derivative, provided a richer physical explanation than the classical calcium model.
APPLIED MATHEMATICS IN SCIENCE AND ENGINEERING
(2023)
Article
Mathematics, Applied
Yasemin Basci, Dumitru Baleanu
Summary: In this manuscript, we discuss various new Hilbert-Pachpatte type inequalities that imply the left sided psi-Hilfer fractional derivatives with a general kernel. Our results generalize the inequalities of Pecaric and Vukovic. Additionally, by considering the limits of the parameters alpha and beta and selecting specific cases of the psi-Hilfer fractional derivative, we explore a wide class of fractional derivatives.
Article
Mathematics, Interdisciplinary Applications
Zulqurnain Sabir, Dumitru Baleanu, Muhammad Asif Zahoor Raja, Ali S. S. Alshomrani, Evren Hincal
Summary: This study designs Meyer wavelet neural networks (WNNs) for the numerical solutions of the spread of computer virus with kill signals (SEIR-KS system). The SEIR-KS system is optimized using Meyer WNNs in combination with genetic algorithm (GA) and sequential quadratic (SQ) programming, referred to as Meyer WNNs-GASQ programming. A sigmoidal-based log-sigmoid function is used as the activation function, with 10 neurons and 120 variables. The correctness and reliability of the proposed Meyer WNNs-GASQ programming is validated through comparison with reference numerical solutions and statistical analysis.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2023)
Article
Mathematics, Interdisciplinary Applications
Zulqurnain Sabir, Dumitru Baleanu, Muhammad Asif Zahoor Raja, Ali S. Alshomrani, Evren Hincal
Summary: The aim of this study is to design a novel stochastic solver using Morlet wavelet neural networks (MWNNs) for solving the mathematical Layla and Majnun (LM) system. The numerical representations of the system are optimized using a hybrid of global and local search schemes. The correctness and stability of the MWNNs are evaluated through comparison with a reference solution and statistical performance analysis.
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
(2023)
Article
Mathematics, Applied
Velusamy Kavitha, Mani Mallika Arjunan, Dumitru Baleanu, Jeyakumar Grayna
Summary: The main motivation of this paper is to study weighted pseudo almost automorphic (WPAA) functions and establish existence results of piecewise continuous mild solution for fractional order integro-differential equations with instantaneous impulses. Traditional WPAA functions may not work due to possible discontinuity in solutions of impulsive differential equations, hence a broader concept is introduced. Main results are established using the Banach contraction mapping principle and Sadovskii's fixed point theorem. An example is presented to illustrate the analytical findings.
ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA
(2023)
Article
Physics, Multidisciplinary
Xiaoyu Shi, Jian Zhang, Xia Jiang, Juan Chen, Wei Hao, Bo Wang
Summary: This study presents a novel framework using offline reinforcement learning to improve energy consumption in road transportation. By leveraging real-world human driving trajectories, the proposed method achieves significant improvements in energy consumption. The offline learning approach demonstrates generalizability across different scenarios.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2024)
Article
Physics, Multidisciplinary
Junhyuk Woo, Soon Ho Kim, Hyeongmo Kim, Kyungreem Han
Summary: Reservoir computing (RC) is a new machine-learning framework that uses an abstract neural network model to process information from complex dynamical systems. This study investigates the neuronal and network dynamics of liquid state machines (LSMs) using numerical simulations and classification tasks. The findings suggest that the computational performance of LSMs is closely related to the dynamic range, with a larger dynamic range resulting in higher performance.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2024)
Article
Physics, Multidisciplinary
Yuwei Yang, Zhuoxuan Li, Jun Chen, Zhiyuan Liu, Jinde Cao
Summary: This paper proposes an extreme learning machine (ELM) algorithm based on residual correction and Tent chaos sequence (TRELM-DROP) for accurate prediction of traffic flow. The algorithm reduces the impact of randomness in traffic flow through the Tent chaos strategy and residual correction method, and avoids weight optimization using the iterative method. A DROP strategy is introduced to improve the algorithm's ability to predict traffic flow under varying conditions.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2024)
Article
Physics, Multidisciplinary
Chengwei Dong, Min Yang, Lian Jia, Zirun Li
Summary: This work presents a novel three-dimensional system with multiple types of coexisting attractors, and investigates its dynamics using various methods. The mechanism of chaos emergence is explored, and the periodic orbits in the system are studied using the variational method. A symbolic coding method is successfully established to classify the short cycles. The flexibility and validity of the system are demonstrated through analogous circuit implementation. Various chaos-based applications are also presented to show the system's feasibility.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2024)
Article
Physics, Multidisciplinary
Viorel Badescu
Summary: This article discusses the maximum work extraction from confined particles energy, considering both reversible and irreversible processes. The results vary for different types of particles and conditions. The concept of exergy cannot be defined for particles that undergo spontaneous creation and annihilation. It is also noted that the Carnot efficiency is not applicable to the conversion of confined thermal radiation into work.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2024)
Article
Physics, Multidisciplinary
P. M. Centres, D. J. Perez-Morelo, R. Guzman, L. Reinaudi, M. C. Gimenez
Summary: In this study, a phenomenological investigation of epidemic spread was conducted using a model of agent diffusion over a square region based on the SIR model. Two possible contagion mechanisms were considered, and it was observed that the number of secondary infections produced by an individual during its infectious period depended on various factors.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2024)
Article
Physics, Multidisciplinary
Zuan Jin, Minghui Ma, Shidong Liang, Hongguang Yao
Summary: This study proposes a differential variable speed limit (DVSL) control strategy considering lane assignment, which sets dynamic speed limits for each lane to attract vehicle lane-changing behaviors before the bottleneck and reduce the impact of traffic capacity drop. Experimental results show that the proposed DVSL control strategy can alleviate traffic congestion and improve efficiency.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2024)
Article
Physics, Multidisciplinary
Matthew Dicks, Andrew Paskaramoorthy, Tim Gebbie
Summary: In this study, we investigate the learning dynamics of a single reinforcement learning optimal execution trading agent when it interacts with an event-driven agent-based financial market model. The results show that the agents with smaller state spaces converge faster and are able to intuitively learn to trade using spread and volume states. The introduction of the learning agent has a robust impact on the moments of the model, except for the Hurst exponent, which decreases, and it can increase the micro-price volatility as trading volumes increase.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2024)
Article
Physics, Multidisciplinary
Zhouzhou Yao, Xianyu Wu, Yang Yang, Ning Li
Summary: This paper developed a cooperative lane-changing decision system based on digital technology and indirect reciprocity. By introducing image scoring and a Q-learning based reinforcement learning algorithm, drivers can continuously evaluate gains and adjust their strategies. The study shows that this decision system can improve driver cooperation and traffic efficiency, achieving over 50% cooperation probability under any connected vehicles penetration and traffic density, and reaching 100% cooperation probability under high penetration and medium to high traffic density.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2024)
Article
Physics, Multidisciplinary
Josephine Nanyondo, Henry Kasumba
Summary: This paper presents a multi-class Aw-Rascle (AR) model with area occupancy expressed in terms of vehicle class proportions. The qualitative properties of the proposed equilibrium velocity and the stability conditions of the model are established. The numerical results show the effect of proportional densities on the flow of vehicle classes, indicating the realism of the proposed model.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2024)
Article
Physics, Multidisciplinary
Oliver Smirnov
Summary: This study proposes a new method for simultaneously estimating the parameters of the 2D Ising model. The method solves a constrained optimization problem, where the objective function is a pseudo-log-likelihood and the constraint is the Hamiltonian of the external field. Monte Carlo simulations were conducted using models of different shapes and sizes to evaluate the performance of the method with and without the Hamiltonian constraint. The results demonstrate that the proposed estimation method yields lower variance across all model shapes and sizes compared to a simple pseudo-maximum likelihood.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2024)
Article
Physics, Multidisciplinary
Przemyslaw Chelminiak
Summary: The study investigates the first-passage properties of a non-linear diffusion equation with diffusivity dependent on the concentration/probability density through a power-law relationship. The survival probability and first-passage time distribution are determined based on the power-law exponent, and both exact and approximate expressions are derived, along with their asymptotic representations. The results pertain to diffusing particles that are either freely or harmonically trapped. The mean first-passage time is finite for the harmonically trapped particle, while it is divergent for the freely diffusing particle.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2024)
Article
Physics, Multidisciplinary
Hidemaro Suwa
Summary: The choice of transition kernel is crucial for the performance of the Markov chain Monte Carlo method. A one-parameter rejection control transition kernel is proposed, and it is shown that the rejection process plays a significant role in determining the sampling efficiency.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2024)
Article
Physics, Multidisciplinary
Xudong Wang, Yao Chen
Summary: This article investigates the joint influence of expanding medium and constant force on particle diffusion. By starting from the Langevin picture and introducing the effect of external force in two different ways, two models with different force terms are obtained. Detailed analysis and derivation yield the Fokker-Planck equations and moments for the two models. The sustained force behaves as a decoupled force, while the intermittent force changes the diffusion behavior with specific effects depending on the expanding rate of the medium.
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS
(2024)