Related papers: Development of three dimensional constitutive theo…
In all structural models, the section or fiber response is a relation between the strain measures and the stress resultants. This relation can only be expressed in a simple analytical form when the material response is linear elastic. For…
A constitutive model is developed to predict the viscoelastic response of polyimide resins that are used in high temperature applications. This model is based on a thermodynamic framework that uses the notion that the `natural…
This article concludes a three-part series developing a self-consistent theoretical framework of the electromechanics of lipid membranes at the continuum scale. Owing to their small thickness, lipid membranes are commonly modeled as…
When constructing models of the world, we aim for optimal compressions: models that include as few details as possible while remaining as accurate as possible. But which details -- or features measured in data -- should we choose to include…
The role of thermodynamics in continuum mechanics and the derivation of the proper constitutive relations is a discussed subject of Rational Mechanics. The classical literature did not use the accumulated knowledge of thermostatics and was…
We propose a model for thermo-elastic beams, consistent with the theory of linear three-dimensional thermo-elasticity and deduced by a suitable version of the Principle of Virtual Powers. Dimensional reduction is achieved by postulating…
The selection of an equilibrium state by maximising the entropy of a system, subject to certain constraints, is often powerfully motivated as an exercise in logical inference, a procedure where conclusions are reached on the basis of…
The thermodynamic definition of entropy can be extended to nonequilibrium systems based on its relation to information. To apply this definition in practice requires access to the physical system's microstates, which may be prohibitively…
We present some existence results for three-dimensional quasistatic morphoelasticity. The state of the growing body is described by its deformation and the underlying growth tensor and is ruled by the interplay of hyperelastic energy…
Recently the formation of an expanding universe from the (1+3+6)-dimensional space-times has been proposed on the basis of super-string theory. The serious entropy problem must be solved for it to be realistic from the cosmological…
Theory of multi-dimensional representation of free energy surface of protein folding is developed by adopting structural order parameters of multiple regions in protein as multiple coordinates. Various scenarios of folding are classified in…
The dynamics of molecular collisions in a macroscopic body are encoded by the parameter Thermodynamic entropy - a statistical measure of the number of molecular configurations that correspond to a given macrostate. Directionality in the…
We describe a thought experiment using an isolated system of known parameters and assuming the correctness of Clausius and Boltzmann descriptions of entropy. The experiment produced an astronomical increase in the number of possible ways…
The three-dimensional electron-gas model has been a major focus for many-body theory applied to the electronic properties of metals and semiconductors. Because the model neglects band effects, whereas electronic systems are generally more…
Reduced dimensionality has long been regarded as an important strategy for increasing thermoelectric performance, for example in superlattices and other engineered structures. Here we point out and illustrate by examples that three…
Depending on context, the term entropy is used for a thermodynamic quantity, a~measure of available choice, a quantity to measure information, or, in the context of statistical inference, a maximum configuration predictor. For systems in…
In this note we discuss a common misconception, namely that embeddings are always used to reduce the dimensionality of the item space. We show that when we measure dimensionality in terms of information entropy then the embedding of sparse…
Many theoretical expressions of dissipation along non-equilibrium processes have been proposed. However, they have not been fully verified by experiments. Especially for systems strongly interacting with environments the connection between…
The recent Letter by Wissner-Gross and Freer [1] proposes a relationship between intelligence and entropy maximization based on a causal generalization of entropic forces over configuration space paths, which may beautifully induce…
We construct a configurational entropy measure in functional space. We apply it to several nonlinear scalar field models featuring solutions with spatially-localized energy, including solitons and bounces in one spatial dimension, and…