Article
Mathematics, Applied
Alberto Montefusco, Christof Schuette, Stefanie Winkelmann
Summary: The reaction-diffusion master equation (RDME) is a lattice-based stochastic model used to describe spatially resolved cellular processes. In this study, we explore a method utilizing gradient structures to achieve the hydrodynamic limit of RDME and apply it to spatially extended systems with diffusion. Under the assumption of detailed balance, we establish a gradient structure for RDME and use the method to generate a gradient structure for its hydrodynamic limit, namely, the corresponding reaction-diffusion partial differential equation (RDPDE).
SIAM JOURNAL ON APPLIED MATHEMATICS
(2023)
Article
Mathematics, Applied
Wael W. Mohammed
Summary: This paper considers the approximate solutions of time-fractional reaction-diffusion equations forced by multiplicative noise on a bounded domain. When the diffusion is large, the solutions of the stochastic time-fractional reaction-diffusion equations with polynomial term can be approximated by the solutions of a stochastic time-fractional ordinary equations. Our results are illustrated by applying to time-fractional logistic and time-fractional Ginzburg-Landau equations.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Mathematics, Applied
Alberto Bressan, Maria Teresa Chiri, Najmeh Salehi
Summary: We study a controlled reaction-diffusion equation motivated by a pest eradication problem. In the first part, we investigate the optimal control of 1-dimensional traveling wave profiles and obtain explicit solutions using Stokes' formula. The last section focuses on optimizing a moving set and shows how these problems can be derived from the original parabolic problems by taking a sharp interface limit.
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
(2022)
Article
Engineering, Environmental
Stefano Rizzello, Raffaele Vitolo, Gaetano Napoli, Samuele De Bartolo
Summary: In this paper, a generalized system of diffusion equations in time and space is defined based on the conservation principles of mass and momentum. A numerical model for steady one-dimensional advection-dispersion equation in streams and channels with point-loading is presented. The numerical model parameter is determined by estimating the transition probability that characterizes the diffusion phenomenon. The findings in this paper represent the first part of a research project that has been extended to the basin scale.
STOCHASTIC ENVIRONMENTAL RESEARCH AND RISK ASSESSMENT
(2023)
Article
Mathematics, Applied
D. Burini, N. Chouhad
Summary: This paper discusses the micro-macro derivation of models based on the kinetic theory for active particles. It involves a survey and critical analysis of existing phenomenological models, such as virus transport models, social dynamics, and Keller-Segel in a fluid. A Hilbert-type approach is presented for deriving macroscopic models from the underlying description, and specific macroscopic models are derived for the selected case studies. The paper ends with a forward look into future research perspectives.
MATHEMATICAL MODELS & METHODS IN APPLIED SCIENCES
(2023)
Article
Mathematics
Keng Deng, Yixiang Wu
Summary: This paper investigates a reaction-diffusion equation with continuous delay and spatial variable coefficients, establishing a sharp threshold dynamic result for the global attractivity of positive steady state solutions. By analyzing the omega-limit set of the equation and proving it to be a singleton, the method is applied to demonstrate the global attractivity of the positive steady state of a spatially nonlocal diffusive logistic model.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2021)
Article
Polymer Science
Changhao Li, Jianfeng Li, Yuliang Yang
Summary: This work derives a more accurate reaction-diffusion equation for an A/B binary system by summing over microscopic trajectories and introduces the DRD diagram method. It is found that there are coupling terms between diffusion and reaction when there is intermolecular interaction, manifesting on the mesoscopic scale. This method can also be applied to describe chemical reactions in polymeric systems.
Article
Mathematics
Hirokazu Ninomiya, Hiroko Yamamoto
Summary: This paper introduces a reaction-diffusion system whose solutions approximate those of a semilinear wave equation under certain assumptions of a reaction term, with the proof based on the energy method.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2021)
Article
Mathematics
Boris Pena y Lillo, Sergei Trofimchuk, Vitaly Volpert
Summary: In this study, we propose a new model that describes the population density distribution with respect to genotype as a continuous variable. The model is based on a reaction-diffusion equation with a unique drift term due to random mutations. We demonstrate the existence and stability of a continuous family of positive stationary solutions, with the minimal solution resembling a normal distribution and all others decaying polynomially. Additionally, the minimal, quasi-normal, symmetric stationary solution serves as the ultimate destination for evolutionary processes starting with realistic initial data.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2023)
Article
Mathematics, Applied
Elaine Crooks, Yini Du
Summary: This paper presents an approach to characterize the fast-reaction limits of systems with nonlinear diffusion on unbounded domains, when there are either two reaction-diffusion equations or one reaction-diffusion equation and one ordinary differential equation. The approach replaces the linear diffusion terms with nonlinear diffusion terms, and proves the convergence in the fast-reaction limit determined by the unique solution of a certain scalar nonlinear diffusion problem.
COMMUNICATIONS IN CONTEMPORARY MATHEMATICS
(2023)
Article
Engineering, Electrical & Electronic
Malcolm Egan, Bayram Cevdet Akdeniz, Bao Quoc Tang
Summary: This paper provides an overview of stochastic models of reaction and diffusion systems and design schemes for molecular communication systems, with a focus on a robust equilibrium signaling method. The implementation of detection schemes and parameter estimation via stochastic chemical reaction networks is discussed, along with the interactions between molecular communication systems and biological systems as well as open problems.
DIGITAL SIGNAL PROCESSING
(2022)
Article
Mathematics, Applied
Hideki Murakawa
Summary: This paper investigates singular limit problems of reaction-diffusion systems, focusing on cases where the effects of reaction terms are significantly larger than those of other terms. By formulating the problem, deriving the limit equation, and establishing a rigorous mathematical theory, the study addresses various problems found in literature.
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S
(2021)
Article
Physics, Mathematical
Luca Fresta, Marcello Porta, Benjamin Schlein
Summary: This study investigates the quantum evolution of many-body Fermi gases in three dimensions, considering both non-relativistic and relativistic dispersion particles. The focus is on the high-density regime and a class of initial data describing zero-temperature states. In the non-relativistic case, the many-body evolution of the reduced one-particle density matrix converges to the solution of the time-dependent Hartree equation in short macroscopic times as the density approaches infinity. In the case of relativistic dispersion, the many-body evolution converges to the relativistic Hartree equation for all macroscopic times. The rate of convergence depends only on the density, allowing for the study of extensive many-body Fermi gases' quantum dynamics.
COMMUNICATIONS IN MATHEMATICAL PHYSICS
(2023)
Article
Computer Science, Interdisciplinary Applications
Martina Prugger, Lukas Einkemmer, Carlos F. Lopez
Summary: Solving the chemical master equation is crucial for understanding biological and chemical systems. However, directly solving it faces the curse of dimensionality. A low-rank approach based on partitioning the network into biologically relevant subsets is proposed to tackle this issue, successfully simulating large-scale biological networks.
JOURNAL OF COMPUTATIONAL PHYSICS
(2023)
Article
Mathematics, Applied
Gabriel G. da Rocha, Ervin K. Lenzi
Summary: In this study, we investigate a diffusion process by simultaneously considering stochastic resetting and linear reaction kinetics. We initially discuss the formalism for a single species and then extend it to multiple species. By analyzing a general probability density function for the random walk, we obtain diverse behaviors for the waiting time and jumping probability distributions. These distributions' behaviors have implications for the diffusion-like equations derived from this approach and can be connected to different fractional operators with singular or nonsingular kernels. We also demonstrate that diffusion-like equations can exhibit a wide range of behaviors associated with various processes, particularly anomalous diffusion.
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
(2023)
Article
Multidisciplinary Sciences
Michael J. Lawson, Linda Petzold, Andreas Hellander
Journal of the Royal Society Interface
(2015)
Article
Physics, Fluids & Plasmas
Stefan Hellander, Andreas Hellander, Linda Petzold
Article
Mathematics, Interdisciplinary Applications
Emilie Blanc, Stefan Engblom, Andreas Hellander, Per Lotstedt
MULTISCALE MODELING & SIMULATION
(2016)
Article
Mathematics, Applied
Lina Meinecke, Stefan Engblom, Andreas Hellander, Per Lotstedt
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2016)
Article
Mathematics, Applied
Brian Drawert, Michael Trogdon, Salman Toor, Linda Petzold, Andreas Hellander
SIAM JOURNAL ON SCIENTIFIC COMPUTING
(2016)
Article
Multidisciplinary Sciences
Marketa Kaucka, Evgeny Ivashkin, Daniel Gyllborg, Tomas Zikmund, Marketa Tesarova, Jozef Kaiser, Meng Xie, Julian Petersen, Vassilis Pachnis, Silvia K. Nicolis, Tian Yu, Paul Sharpe, Ernest Arenas, Hjalmar Brismar, Hans Blom, Hans Clevers, Ueli Suter, Andrei S. Chagin, Kaj Fried, Andreas Hellander, Igor Adameyko
Article
Biology
Sonja Mathias, Adrien Coulier, Anass Bouchnita, Andreas Hellander
BULLETIN OF MATHEMATICAL BIOLOGY
(2020)
Article
Chemistry, Physical
Adrien Coulier, Stefan Hellander, Andreas Hellander
Summary: Spatial stochastic models of single cell kinetics are crucial in capturing fluctuations in molecular numbers and spatial dependencies, but the computational cost is a limiting factor. Further approximation of spatial dynamics is necessary for improving computational efficiency in practical applications.
JOURNAL OF CHEMICAL PHYSICS
(2021)
Article
Biotechnology & Applied Microbiology
Philip J. Harrison, Hakan Wieslander, Alan Sabirsh, Johan Karlsson, Victor Malmsjo, Andreas Hellander, Carolina Wahlby, Ola Spjuth
Summary: This study demonstrates that considering temporal dynamics significantly improves performance in predicting cell expression using time-lapse data. The modeling approach used in this research highlights the practical significance of accounting for temporal dynamics when studying drug delivery.
Article
Biology
Ben Blamey, Salman Toor, Martin Dahlo, Hakan Wieslander, Philip J. Harrison, Ida-Maria Sintorn, Alan Sabirsh, Carolina Wahlby, Ola Spjuth, Andreas Hellander
Summary: The study introduces a pipeline model for scientific pipelines, which optimizes the use of limited computing resources through an interestingness function and policy; The HASTE Toolkit is a collection of tools for this approach, validated through two microscopy imaging case studies.
Review
Pharmacology & Pharmacy
Ola Spjuth, Jens Frid, Andreas Hellander
Summary: Cloud computing plays a crucial role in the machine learning life cycle of drug discovery, enhancing reproducibility and robustness of analysis through containerization and scientific workflows. The elasticity and flexibility of cloud infrastructures enable efficient access to compute resources, and cloud computing along with federated learning contribute towards collaborative drug discovery within organizations.
EXPERT OPINION ON DRUG DISCOVERY
(2021)
Article
Biochemical Research Methods
Richard Jiang, Prashant Singh, Fredrik Wrede, Andreas Hellander, Linda Petzold
Summary: In this work, a data-driven method is presented to infer the underlying biochemical reaction system governing a set of observed species concentrations over time. The method utilizes sparse Bayesian inference to produce robust, interpretable biochemical reaction networks, along with uncertainty estimates of parameters.
PLOS COMPUTATIONAL BIOLOGY
(2022)
Article
Biochemical Research Methods
Adrien Coulier, Prashant Singh, Marc Sturrock, Andreas Hellander
Summary: Quantitative stochastic models of gene regulatory networks are important tools for studying cellular regulation. Determining model fidelity is a practical challenge, as it affects the accuracy and computation cost of the results. Inference of true model parameters is often approximate and requires difficult choices, such as summary statistics selection and data quantity.
PLOS COMPUTATIONAL BIOLOGY
(2022)
Article
Chemistry, Physical
Stefan Hellander, Andreas Hellander
JOURNAL OF CHEMICAL PHYSICS
(2020)
Proceedings Paper
Computer Science, Hardware & Architecture
Christopher B. Horuk, Geoffrey Douglas, Anand Gupta, Chandra Krintz, Ben Bales, Giovanni Bellesia, Brian Drawert, Rich Wolski, Linda Petzold, Andreas Hellander
2014 INTERNATIONAL CONFERENCE ON HIGH PERFORMANCE COMPUTING & SIMULATION (HPCS)
(2014)
