Article
Mathematics, Applied
Fritz Colonius, Martin Rasmussen
Summary: This paper presents formulas for quasi-ergodic limits of finite absorbing Markov chains, focusing on the reducible case and based on a precise asymptotic analysis of growth behavior along admissible paths.
LINEAR ALGEBRA AND ITS APPLICATIONS
(2021)
Article
Mathematics
Vasiliki Bitsouni, Nikolaos Gialelis, Ioannis G. Stratis
Summary: This study examines the quasi-steady-state assumption in the fundamental mathematical model of enzymatic reactions from a purely quantitative perspective. The study introduces a simple yet generic scaling algorithm for the problem, quantitatively defines the two essential parts of the assumption (standard and reverse), and comments on the dispensable third part (total) that is commonly adopted.
Article
Mathematics
Shiping Cao
Summary: This article introduces partial loop-erasing operators and shows that they can be applied to finite Markov chains to obtain a process equivalent to the chronological loop-erased Markov chain. The article also constructs loop-erased random paths on bounded resistance spaces as the weak limit of the loop erasure of Markov chains on a sequence of finite sets approximating the space, with the limit being independent of the approximating sequences. Finally, the article demonstrates the existence of the scaling limit of loop-erased random walks on Sierpinski carpet graphs, equivalent to loop-erased random paths on the Sierpinski carpet.
ADVANCES IN MATHEMATICS
(2023)
Article
Engineering, Mechanical
Michail L. Pivovarov
Summary: In this study, a quasi-linear Mathieu-type equation is analyzed using the averaging method near the main resonance. Different types of phase portraits are identified and steady-state solutions are found. The periodic solutions of the primary equation that correspond to the steady-state solutions of the averaged equation are determined, along with analytical expressions for the probabilities of dissipation-induced capture into feasible steady-state solutions.
NONLINEAR DYNAMICS
(2021)
Article
Chemistry, Multidisciplinary
Xiaojian Wang, Xudong Zheng, Ingo R. Titze, Anil Palaparthi, Qian Xue
Summary: This study examined the limitations of the quasi-steady flow assumption (QSFA) in human phonation and found that the errors in predictions using QSFA increased significantly with higher phonation frequencies and growing flow unsteadiness. The air inertia in the vocal tract and flow unsteadiness negatively affected the validity of QSFA.
APPLIED SCIENCES-BASEL
(2023)
Article
Engineering, Mechanical
Petr Sidlof, David Simurda, Jan Lepicovsky, Martin Stepan, Vaclav Vomacko
Summary: This study investigates the limits of applicability of the quasi-steady approximation in a linear five-blade cascade and quantifies the degree of unsteadiness in airflow through a comparison of quasi-steady and time-resolved blade surface pressure measurements. The results show that the stationary and time-resolved profiles match almost perfectly for low reduced frequencies, with a degree of unsteadiness below 2%. However, the degree of unsteadiness increases quickly above 0.2 reduced frequencies, reaching up to 10% with local pressure profile differences of up to 40%.
JOURNAL OF FLUIDS AND STRUCTURES
(2023)
Article
Engineering, Mechanical
K. V. Swarnalatha, Sarma L. Rani
Summary: We propose novel solutions based on the method of multiple scales to solve the nonlinear equations governing the time-dependent amplitudes of coupled acoustic modes in a quasi one-dimensional duct. Our results show that both the MMS and KBMA approaches are in good agreement with numerical solutions, and the MMS method can eliminate low-frequency oscillations in the outer envelope under linear decoupling. The stability criteria are analyzed using the MMS and KBMA solutions, and the stability boundaries are illustrated.
NONLINEAR DYNAMICS
(2023)
Article
Mathematics, Applied
Hayate Suda
Summary: This study investigates one-dimensional infinite chains of harmonic oscillators with random exchanges of momenta and long-range interaction potentials. The research reveals that the systems evolve on different space-time scales, exhibiting superballistic, hyperbolic, and superdiffusive/diffusive behavior.
Article
Mathematics, Applied
Robin Chemnitz
Summary: This article studies the steady states of dynamics with an underlying network structure, and examines how these states respond to small perturbations in the network parameters and how this sensitivity is related to the network structure. The study introduces a prototypical linear response equation and determines its sensitivity. This abstract result is then applied to analyze the sensitivity of steady states in continuous-time Markov chains and deterministically modeled chemical reaction networks.
SIAM JOURNAL ON APPLIED MATHEMATICS
(2023)
Article
Statistics & Probability
George Liddle, Amanda Turner
Summary: We study the anisotropic version of the Hastings-Levitov model AHL(nu). Our results show that the harmonic measure on the cluster boundary converges to a deterministic ordinary differential equation on bounded time-scales. We also find that over logarithmic time-scales, the leading order behavior of the harmonic measure becomes random.
ELECTRONIC JOURNAL OF PROBABILITY
(2023)
Article
Geochemistry & Geophysics
Edouard Kravchinsky, Mirko van der Baan
Summary: This paper introduces a statistical analysis method using cellular automata for earthquakes and other physical applications, utilizing Markov chains to simplify the model and approximate the statistical characteristics of cellular automata by ignoring spatial components.
JOURNAL OF GEOPHYSICAL RESEARCH-SOLID EARTH
(2022)
Article
Mathematics
Vassili N. Kolokoltsov
Summary: Levy walks are important modeling tools for various real-life processes. They are described by material fractional derivatives, which are known to represent their natural scaling limits. In this study, we derive the limiting equations for Levy walks with position-dependent times and velocities, where Fourier transforms cannot be effectively applied. We find three different limits, corresponding to different boundary conditions for the related Feller semigroups and processes, leading to three different multi-dimensional versions of Caputo-Dzherbashian derivatives. We also analyze other extensions and generalizations.
Proceedings Paper
Automation & Control Systems
Stepan Papacek, Volodymyr Lynnyk
Summary: This paper focuses on mathematical models describing drug-induced enzyme production networks, aiming to develop an enhanced model for further analysis and optimization of drug delivery. The comparison of full and reduced models is presented along with future prospects, demonstrating the method with an example.
PROCESS CONTROL '21 - PROCEEDING OF THE 2021 23RD INTERNATIONAL CONFERENCE ON PROCESS CONTROL (PC)
(2021)
Article
Environmental Sciences
Tao Huang, Venkatesh Merwade
Summary: Bayesian model averaging (BMA) is a popular multi-model method used in flood modeling to account for uncertainties and generate robust predictions. This study compares the performances of the Expectation-Maximization (EM) algorithm and the Metropolis-Hastings (M-H) algorithm in estimating BMA parameters, and finds that the M-H algorithm yields results closer to the given values.
WATER RESOURCES RESEARCH
(2023)
Article
Statistics & Probability
Adrien Prodhomme
Summary: In this paper, we study the convergence of density-dependent Markov chains to the solution of an ODE with an exponentially stable equilibrium point as the scale parameter K tends to infinity. We propose a new strong approximation method for density using a Gaussian process, based on a construction by Kurtz using the Komlos-Major-Tusnady theorem. We prove that the time needed for the error to reach a threshold epsilon(K) greater than a multiple of log(K)/K is at least of order exp(V K epsilon(K)), for some V > 0. We also discuss the implications for moderate deviations and applications to logistic birth-and-death processes and epidemic models conditioned to survive.
STOCHASTIC PROCESSES AND THEIR APPLICATIONS
(2023)
