Related papers: A thermodynamically consistent phenomenological mo…
A new supersymmetric model for electrons with generalized hopping terms and Hubbard interaction on a one-dimensional lattice is solved by means of the Bethe Ansatz. We investigate the phase diagram of this model by studying the ground state…
We propose a protocol to model accurately the electromechanical behavior of dielectric elastomer membranes using experimental data of stress-stretch and voltage-stretch tests. We show how the relationship between electric displacement and…
A model system inspired by recent experiments on the dynamics of a folded protein under the influence of a sinusoidal force is investigated and found to replicate many of the response characteristics of such a system. The essence of the…
Mathematical modeling of real-world physical systems requires the consistent combination of a multitude of physical laws and phenomenological models. This challenging task can be greatly simplified by hierarchically decomposing systems into…
We propose and investigate a model for the coexistence of Superconductivity (SC) and Ferroelectricity (FE) based on the dynamical symmetries $su(2)$ for the pseudo-spin SC sector, $h(4)$ for the displaced oscillator FE sector, and $su(2)…
Introducing structural and/or chemical heterogeneity into otherwise ordered crystals can dramatically alter material properties. Lead-based relaxor ferroelectrics are a prototypical example, with decades of investigation having connected…
Active symmetry control - a central challenge in materials science, particularly in ferroelectrics - is achieved via mechanically assisted poling (MAP) guided by thermodynamics and phase - field modeling. This approach yields extraordinary…
To achieve quantitative interpretation of Piezoresponse Force Microscopy (PFM), including resolution limits, tip bias- and strain-induced phenomena and spectroscopy, analytical representations for tip-induced electroelastic fields inside…
This paper investigates the stabilization of a coupled system comprising a parabolic PDE and an elliptic PDE with nonlinear terms. A rigorous backstepping design provides an explicit boundary control law and exponentially convergent…
Recently introduced model of magnetic hysteresis was extended into set of the following features: frequency, pick of induction and temperature of specimen. Group theoretical classification of hysteresis loops' sets is presented. An effect…
We present a thermodynamically based approach to the design of models for viscoelastic fluids with stress diffusion effect. In particular, we show how to add a stress diffusion term to some standard viscoelastic rate-type models (Giesekus,…
In this work, a result of exponential stability is obtained for solutions of a compressible flow-structure partial differential equation (PDE) model which has recently appeared in the literature. In particular, a compressible flow PDE and…
Electromechanical hysteresis loop formation in piezoresponse force microscopy of thin ferroelectric films is studied with special emphasis on the effects of tip size and film thickness, as well as dependence on the tip voltage frequency.…
The thermodynamical model of viscoelastic deformable solids at finite strains with Kelvin-Voigt rheology with a higher-order viscosity (using the concept of multipolar materials) is formulated in a fully Eulerian way in rates. Assumptions…
The thermodynamic formalism expresses chaotic properties of dynamical systems in terms of the Ruelle pressure $\psi(\beta)$. The inverse-temperature like variable $\beta$ allows one to scan the structure of the probability distribution in…
This paper provides a brief introduction to the phenomenological aspects of the polarization in ferrroelectric materials, and then an analysis of a few selected topics related to the modelling of ferroelectrics. The description of…
In this work, we are interested in the behaviour of a single ferromagnetic mono--domain particle submitted to an external field with a stochastic perturbation. This model is a step toward the mathematical understanding of thermal effects on…
The role of the surface during polarization switching in constrained ferroelectrics is investigated using the time-dependent Ginzburg-Landau theory. The model incorporates the elastic and electrostrictive effects in the form of a long-range…
This paper considers the backstepping state feedback and observer design for hyperbolic and parabolic PDEs, which are bidirectionally interconnected in a general coupling structure. Both PDE subsystems consist of coupled scalar PDEs with…
We apply the methodology of our recent paper 'The Dynamics of the Hubbard Model through Stochastic Calculus and Girsanov Transformation' [1] to thermodynamic correlation functions in the Fermi-Hubbard model. They can be obtained from a…