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The Critical Thickness of Dislocation-Free Stranski-Krastanov Growth Atop a Deform Able Substrate
We investigate the influence of mass forces (in particular, of gravitation and van der Waals forces) on the critical film thickness of thin films attached to solid substrates and establish corresponding correc...
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Article
A Test for Strong Hysteresis
The mathematical definition of systems withhysteresis, that is nonlinear input-output systemswith memory, is different from the definition usuallyapplied to economic systems. Economic theory andmodelling pract...
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Article
The Stress Driven Rearrangement Instabilities in Electronic Materials and in Helium Crystals
At present, there is a consensus that various Stress Driven Rearrangement Instabilities (SDRI) are the implications of the mathematically rigorous theoretical Gibbs thermodynamics. Many applied researchers and...
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Article
Stress Driven Rearrangement Instability of Crystalline Films with Electromechanical Interaction
It was demonstrated, on general thermodynamic grounds, that, in non-hydrostatically stressed elastic systems, phase and grain interfaces undergo morphological destabilization due to different mechanisms of “ma...
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Article
Introduction to the special issue
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Article
Rank-Driven Markov Processes
We study a class of Markovian systems of N elements taking values in [0,1] that evolve in discrete time t via randomized replacement rules based on the ranks of the elements. These rank-driven processes are inspi...
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Chapter and Conference Paper
Operational Equations of State for Modeling High-Rate Phenomena
The concept of operational equations of state (EOS) is discussed and illustrated with several examples. We discuss several related concepts: (1) the complete and incomplete equations of state, (2) the skeleton...
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Book and Conference Proceedings
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Chapter and Conference Paper
The Hugoniot Relationships for Nonlinear Elastic Substances
The classical theory of shock waves in liquid and gases is the prototype for similar developments in the theory of shock waves in nonlinear elastic media. In this paper, we explore the weak shock waves in soli...
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Chapter and Conference Paper
Dynamics and Shock Waves in Media with Second Order Phase Transformations
We study free oscillations and the weak shock waves in the Ehrenfest liquids, i.e., in the liquids undergoing second order phase transformations. Also, we discuss the second order phase transformations in crys...
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Article
Finite kinetics effects in the problems of oscillations of two-phase liquid heterogeneous systems
For centuries, statics and dynamics of two-phase heterogeneous systems were and remain to be in the focus of multiple academic and engineering disciplines. Phase transformations phenomena include both strong r...
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Chapter and Conference Paper
Toward Paradoxical Inconsistency in Electrostatics of Metallic Conductors
In a recent report, we drew attention to the paradoxical inconsistency of classical electrostatics with the model of a crystalline conductor. There are different ways to avoid this inconsistency. Mostly, they ...
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Article
Open AccessPressure-driven changes to spontaneous flow in active nematic liquid crystals
We consider the effects of a pressure gradient on the spontaneous flow of an active nematic liquid crystal in a channel, subject to planar anchoring and no-slip conditions on the boundaries of the channel. We ...
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Article
Steady state solutions in a model of a cholesteric liquid crystal sample
Motivated by recent mathematical studies of Fréedericksz transitions in twist cells and helix unwinding in cholesteric liquid crystal cells [(da Costa et al. in Eur J Appl Math 20:269–287, 2009), (da Costa et ...
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Article
Open AccessEnergy-Constrained Random Walk with Boundary Replenishment
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, a...
