Michael Grinfeld
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View article: Interpreting convex integration results in hydrodynamics
Interpreting convex integration results in hydrodynamics Open
The aim of this article is to encourage debate of issues of the applications of modern methods of mathematical analysis in fluid dynamics. A recent surprising result derived by convex integration techniques shows non-uniqueness of weak sol…
View article: A Rate-Dependent Probabilistic Model of Hysteresis
A Rate-Dependent Probabilistic Model of Hysteresis Open
Instead of modelling an economic agent by a hysteron, we suggest a fluid–mechanical notion of rate-dependent hysteretic agents based on the theory of Poisson counters. It leads to a simple representation of assemblies of such agents. We di…
View article: On singular behaviour in a plane linear elastostatics problem
On singular behaviour in a plane linear elastostatics problem Open
A vector field similar to those separately introduced by Artstein and Dafermos is constructed from the tangent to a monotone increasing one-parameter family of non-concentric circles that touch at the common point of intersection taken as …
View article: The Least Action Admissibility Principle
The Least Action Admissibility Principle Open
This paper provides a new admissibility criterion for choosing physically relevant weak solutions of the equations of Lagrangian and continuum mechanics when non-uniqueness of solutions to the initial value problem occurs. The criterion is…
View article: Travelling waves in a dispersion-saturating diffusion equation
Travelling waves in a dispersion-saturating diffusion equation Open
In the framework of hyperbolic conservation laws regularised by including diffusive and dispersive terms, we study monotone travelling waves for the generalised Rosenau-Korteweg de Vries equation. We establish existence as well as linear a…
View article: Pendent steady rivulets and droplets: from lubrication to bifurcation
Pendent steady rivulets and droplets: from lubrication to bifurcation Open
We consider the shape of the free surface of steady pendent rivulets (or equivalently, two-dimensional droplets) beneath a planar substrate. We formulate the governing equations in terms of two closely related dynamical systems and use cla…
View article: Decomposing diversity into measures of evenness, similarity, and richness
Decomposing diversity into measures of evenness, similarity, and richness Open
It has long been recognized that diversity has many measurable aspects, such as richness, evenness, and similarity among species. However, given a diversity index, it is unclear whether it necessarily can be decomposed into components that…
View article: Vaccination, asymptomatics and public health information in COVID-19
Vaccination, asymptomatics and public health information in COVID-19 Open
The dynamics of the COVID-19 pandemic is greatly influenced by vaccine quality, as well as by vaccination rates and the behaviour of infected individuals, both of which reflect public health policies. We develop a model for the dynamics of…
View article: Pyroelectric Plate with Magnetoelectric Effect
Pyroelectric Plate with Magnetoelectric Effect Open
In dynamic problems the electric and magnetic fields are inseparable. At the same time, a multitude of electrostatic and magnetostatic effects permit mutually independent description. This separation appears to be possible and thermodynami…
View article: Toward Modeling of Coulomb Explosions of an Elastic Plate
Toward Modeling of Coulomb Explosions of an Elastic Plate Open
Under the action of electromagnetic irradiation or high inertial forces accompanying some ballistic phenomena, the solids are able to accumulate net electric charges.These charges can, in turn, generate sufficiently high macroscopic forces…
View article: Energy-Constrained Random Walk with Boundary Replenishment
Energy-Constrained Random Walk with Boundary Replenishment Open
We study an energy-constrained random walker on a length- N interval of the one-dimensional integer lattice, with boundary reflection. The walker consumes one unit of energy for every step taken in the interior, and energy is replenished u…
View article: Energy-constrained random walk with boundary replenishment
Energy-constrained random walk with boundary replenishment Open
We study an energy-constrained random walker on a length-$N$ interval of the one-dimensional integer lattice, with boundary reflection. The walker consumes one unit of energy for every step taken in the interior, and energy is replenished …
View article: Pendent Steady Rivulets: From Lubrication to Bifurcation
Pendent Steady Rivulets: From Lubrication to Bifurcation Open
We consider the shape of the free surface of steady pendent rivulets beneath a planar substrate. We formulate the governing equations in terms of two closely related dynamical systems and use classical phase-plane techniques to develop the…
View article: Non-Uniqueness in Plane Fluid Flows
Non-Uniqueness in Plane Fluid Flows Open
Examples of dynamical systems proposed by Z. Artstein and C. M. Dafermos admit non-unique solutions that track a one parameter family of closed circular orbits contiguous at a single point. Switching between orbits at this single point pro…
View article: Morphological Instability of Phase Interface between Pyroelectric Domains
Morphological Instability of Phase Interface between Pyroelectric Domains Open
The Gibbs-like variational methodology is applied to the heterogeneous systems with rigid pyroelectric or pyromagnetic domains. The processes of depolarization/demagnetization are taken into account by assuming the spatial mobility of the …
View article: Deformable Permanent Ferroelectric or Ferromagnetic Media
Deformable Permanent Ferroelectric or Ferromagnetic Media Open
In the framework of continuum mechanics, one of possible consistent definitions of deformable permanent magnets is introduced and explored. Similar model can be used for ferroelectric substances. Based on the suggested definition, we estab…
View article: Decomposition of the Leinster-Cobbold Diversity Index
Decomposition of the Leinster-Cobbold Diversity Index Open
The Leinster and Cobbold diversity index possesses a number of merits; in particular, it generalises many existing indices and defines an effective number. We present a scheme to quantify the contribution of richness, evenness, and taxonom…
View article: Weak Wavefront Solutions of Maxwell’s Equations in Conducting Media
Weak Wavefront Solutions of Maxwell’s Equations in Conducting Media Open
We analyze the propagation of electromagnetic fronts in unbounded electric conductors. Our analysis is based on the Maxwell model of electromagnetism that includes the displacement current and Ohm’s law in its simplest forms. A weak electr…
View article: Exact Solution for Equilibrium Configurations of Two-Component Plasma Confined between Parallel Plates
Exact Solution for Equilibrium Configurations of Two-Component Plasma Confined between Parallel Plates Open
It is the fifth part of the study published under the common umbrella of “The Gibbs Variational Method in Thermodynamics of Equilibrium Plasma”. In Parts 1 - 4, we formulated a novel approach to thermodynamics of one- and two-component het…
View article: Shock Fronts in Non-Polar Electro-Conducting Media
Shock Fronts in Non-Polar Electro-Conducting Media Open
We analyze the propagation of electromagnetic fronts in unbounded electric conductors. Our model is based on the Maxwell model of electromagnetism, which includes the displacement current and Ohm’s law in its simplest forms. The shock-like…
View article: Characterising Spectral Anomalies in Rotating Machine Sensors
Characterising Spectral Anomalies in Rotating Machine Sensors Open
Several spectral analysis algorithms have been developed to identify spectral anomalies. A careful literature analysis is undertaken of sources of nonlinearity through bearing distress and other contacts and rubs within rotor dynamics. Sev…
View article: Patterns formed in a thin film with spatially homogeneous and non-homogeneous Derjaguin disjoining pressure
Patterns formed in a thin film with spatially homogeneous and non-homogeneous Derjaguin disjoining pressure Open
We consider patterns formed in a two-dimensional thin film on a planar substrate with a Derjaguin disjoining pressure and periodic wettability stripes. We rigorously clarify some of the results obtained numerically by Honisch et al. [ Lang…
View article: Variational Method in Thermodynamics of Two-Component Charged Gas
Variational Method in Thermodynamics of Two-Component Charged Gas Open
Based on appropriately generalized Gibbsâ variational methodology, we analyzed two-component systems with electrostatic interaction. We begin by formulating isoperimetric-type variational problems, and then proceed with calculation of th…
View article: Homeless populations
Homeless populations Open
Numbers of people on housing waiting lists and the size of the homeless population within a local authority area are modelled by a system of coupled ordinary differential equations. The effects on list sizes and levels of homelessness brou…
View article: Boundary Charge Layer and Current for Spherical Inclusion in Conducting System
Boundary Charge Layer and Current for Spherical Inclusion in Conducting System Open
The steady-state current in heterogeneous conducting system is considered. One of the goals is to generate a battery of establish exact solutions for the analysis of steady-state currents in the current-conducting heterogeneous system. The…
View article: A General Model of Structured Cell Kinetics
A General Model of Structured Cell Kinetics Open
We present a modelling framework for the dynamics of cells structured by the concentration of a micromolecule they contain. We derive general equations for the evolution of the cell population and of the extra-cellular concentration of the…
View article: Pattern formation in a thin-film equation with spatially homogeneous and non-homogeneous Derjaguin disjoining pressure
Pattern formation in a thin-film equation with spatially homogeneous and non-homogeneous Derjaguin disjoining pressure Open
We consider pattern formation in a two-dimensional thin film on a planar substrate with a Derjaguin disjoining pressure and periodic wettability stripes in one of the directions. We rigorously clarify some of the results obtained numerical…
View article: Patterns formed in a thin film with spatially homogeneous and non-homogeneous Derjaguin disjoining pressure
Patterns formed in a thin film with spatially homogeneous and non-homogeneous Derjaguin disjoining pressure Open
We consider patterns formed in a two-dimensional thin film on a planar substrate with a Derjaguin disjoining pressure and periodic wettability stripes. We rigorously clarify some of the results obtained numerically by Honisch et al. and em…
View article: An enzymatic hormesis box
An enzymatic hormesis box Open
We present a simple enzymatic system that is capable of a biphasic response under competitive inhibition. This is arguably the simplest system that can be said to be hormetic
View article: Second-Order Discontinuities for Simple and Double Layers
Second-Order Discontinuities for Simple and Double Layers Open
Simple and double layers first appeared in electrostatics and later found various applications in mathematical physics. In this paper, we present the jump discontinuity conditions for their second-order spatial derivatives.