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Mathematical Model of a Two-Temperature Medium of Gas–Solid Nanoparticles with Laser Methane Pyrolysis
AbstractA mathematical model of a two-phase chemically active medium of gas and solid ultrafine particles in the field of laser radiation with...
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Phenomenological models and their analysis
The role of mathematical neuroscience, of which neurodynamics is a subset, is to explore the mechanisms underlying the behaviour observed in real...
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A Mathematical Model for the Determination of Hydrogen Concentration Corresponding to Changes in the Mechanism of Deformation
We propose a three-dimensional mathematical model of hydrogen diffusion in a polycrystalline body taking into account the heterogeneity of diffusion...
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A mathematical model with aberrant growth correction in tissue homeostasis and tumor cell growth
Cancer is usually considered a genetic disease caused by alterations in genes that control cellular behaviors, especially growth and division. Cancer...
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Phenomenological Models of Three Scenarios of Local SARS-COV-2 Coronavirus Epidemics in New York, Brazil, and Japan
AbstractThe COVID-19 pandemic did not end in the summer of 2023 but moved into the stage of a dynamic confrontation between a mutating pathogen and...
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The Algorithmic-Device View of Informal Rigorous Mathematical Proof
A new approach to informal rigorous mathematical proof is offered. To this end, algorithmic devices are characterized and their central role in...
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Predicting Radiotherapy Patient Outcomes with Real-Time Clinical Data Using Mathematical Modelling
Longitudinal tumour volume data from head-and-neck cancer patients show that tumours of comparable pre-treatment size and stage may respond very...
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Analysis of Keynes’s Mathematical Model—Effect of Spatial Factors
AbstractOur primary aims are to investigate a specific version of the classical macroeconomics model, known as the Keynes business cycle model...
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Pattern formation of vascular network in a mathematical model of angiogenesis
We discuss the characteristics of the patterns of the vascular networks in a mathematical model for angiogenesis. Based on recent in vitro...
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Mathematical Model of Permanent Magnets and Superconducting Coils
A Lagrangian formalism is developed, which allows finding the magnetic potential energy of interactions in a system of superconducting inductors...
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The Social Constitution of Mathematical Knowledge: Objectivity, Semantics, and Axiomatics
The philosophy of mathematical practice sometimes investigates the social constitution of mathematics but does not always make explicit the...
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Computers as a Novel Mathematical Reality: I. A Personal Account
AbstractMuch ink has been spilled in the last few decades on computer proofs, computer-assissted proofs, computer-verified proofs, etc. It is obvious...
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A Mathematical Analysis of the Intermediate Behaviour of the Energy Cascades of Quantum Turbulence
We propose a mathematical interpolation between several regimes of energy cascade in quantum turbulence in He II. On the basis of a physical...
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The Social Constitution of Mathematical Knowledge. Objectivity, Semantics, and Axiomatics
The philosophy of mathematical practice sometimes investigates the social constitution of mathematics but does not always make explicit the...
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Signs as a Theme in the Philosophy of Mathematical Practice
Why study notations, diagrams, or more broadly the variety of nonverbal “representations” or “signs” that are used in mathematical practice? This...
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Multi-period Optimization for Long-Term Oilfield Production Planning
In this work, a multi-period nonlinear programming formulation is presented to obtain the optimal long-term oilfield production planning, based on a...
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Generalized Functions and Generalized Regular Solutions for Traditionally Singular Problems of Mathematical Physics
AbstractThe paper is concerned with the equations of mathematical physics which describe the actual physical processes. The actual are the processes...
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Invasiveness of a Growth-Migration System in a Two-dimensional Percolation cluster: A Stochastic Mathematical Approach
We developed a framework based on the software Unstructured Reaction-Diffusion Master Equation (URDME) to address tumor cells’ proliferation and...
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Mathematical Modeling of Gas Filtration in the Bottomhole Zone of Underground Gas Storage Wells Using Fractional Derivatives
The finite-element method is applied for the numerical simulation of gas filtration in porous inhomogeneous media. The model is based on the...
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Phase-field model of bilipid membrane electroporation
This paper proposes a new model of membrane electropermeabilisation that combines the water content of the membrane and the transmembrane voltage....
