Потенциальные поля свободной энергии на стадиях упрочнения и разупрочнения среды Генки при неположительности объемной деформации

In general, materials with linear memory constitutive relations are characterized by a relaxation function. This leads to a situation where the free energy for most materials with memory is not unique. There is a convex set of free energy functionals with a minimum and a maximum element. An alternative procedure is proposed which characterizes a material by the kernel of the rate of dissipation functional. Using some recent results, we find that a unique free energy and relaxation function may then be deduced. An example is given for discrete spectrum materials. Also, the new results are used to show that a previously derived general representation of rate of dissipation and free energy functionals is not complete, in the sense that there are valid functionals which cannot be described by this general formula.

The interactions of amino acid side-chains confer diverse energetic contributions and physical properties to a protein's stability and function. Various computational tools estimate the effect of changing a given amino acid on the protein's stability based on parametrized (free) energy functions. When parametrized for the prediction of protein stability in water, such energy functions can lead to suboptimal results for other solvents, such as ionic liquids (IL), aqueous ionic liquids (aIL), or salt solutions. However, to our knowledge, no comprehensive data are available describing the energetic effects of aIL on intramolecular protein interactions. Here, we present the most comprehensive set of potential of mean force (PMF) profiles of pairwise protein-residue interactions to date, covering 50 relevant interactions in water, the two biotechnologically relevant aIL [BMIM/Cl] and [BMIM/TfO], and [Na/Cl]. These results are based on a cumulated simulation time of >1 ms. aIL and salt ions can weaken, but also strengthen, specific residue interactions by more than 3 kcal mol-1, depending on the residue pair, residue-residue configuration, participating ions, and concentration, necessitating considering such interactions specifically. These changes originate from a complex interplay of competitive or cooperative noncovalent ion-residue interactions, changes in solvent structural dynamics, or unspecific charge screening effects and occur at the contact distance but also at larger, solvent-separated distances. This data provide explanations at the atomistic and energetic levels for complex IL effects on protein stability and should help improve the prediction accuracies of computational tools that estimate protein stability based on (free) energy functions.

The modern materials undergoing large elastic deformations and exhibiting strong magnetostrictive effect are modelled here by free energy functionals for nonlinear and non-local magnetoelastic behaviour. The aim of this work is to prove a new theorem which claims that a sequence of free energy functionals of slightly compressible magnetostrictive materials with a non-local elastic behaviour, converges to an energy functional of a nearly incompressible magnetostrictive material. This convergence is referred to as a Γ -convergence. The non-locality is limited to non-local elastic behaviour which is modelled by a term containing the second gradient of deformation in the energy functional.

In many aspects, elastomers and soft biological tissues exhibit similar mechanical properties such as a pronounced nonlinear stress–strain relation and a viscoelastic response to external loads. Consequently, many models use the same rheological framework and material functions to capture their behavior. The viscosity function is thereby often assumed to be constant and the corresponding free energy function follows that one of the long-term equilibrium response. This work questions this assumption and presents a detailed study on non-Newtonian viscosity functions for elastomers and brain tissues. The viscosity functions are paired with several commonly used free energy functions and fitted to two different types of elastomers and brain tissues in cyclic and relaxation experiments, respectively. Having identified suitable viscosity and free energy functions for the different materials, numerical aspects of viscoelasticity are addressed. From the multiplicative decomposition of the deformation gradient and ensuring a non-negative dissipation rate, four equivalent viscoelasticity formulations are derived that employ different internal variables. Using an implicit exponential map as time integration scheme, the numerical behavior of these four formulations are compared among each other and numerically robust candidates are identified. The fitting results demonstrate that non-Newtonian viscosity functions significantly enhance the fitting quality. It is shown that the choice of a viscosity function is even more important than the choice of a free energy function and the classical neo-Hooke approach is often a sufficient choice. Furthermore, the numerical investigations suggest the superiority of two of the four viscoelasticity formulations, especially when complex finite element simulations are to be conducted.

In this paper, we investigate the influence of the extended uncertainty principle (EUP) on the thermodynamics of a charged rotating Bañados, Teitelboim and Zanelli (BTZ) black hole in ([Formula: see text])-dimensional anti-de Sitter (AdS) space–time. To this end, we derive EUP-corrected Hawking temperature, pressure, entropy, Gibbs free energy and heat capacity functions. We observe that EUP-based quantum corrections decrease pressure and entropy functions in AdS space–time. Such decreases show up itself only in physically meaningful region for Gibbs free energy and specific heat functions.

The aim of this work is to determine what free energy functionals are expressible as quadratic forms of the state functional \(I^t\) which is discussed in earlier papers. The single integral form is shown to include the functional \(\psi _F\) proposed a few years ago, and also a further category of functionals which are easily described but more complicated to construct. These latter examples exist only for certain types of materials. The double integral case is examined in detail, against the background of a new systematic approach developed recently for double integral quadratic forms in terms of strain history, which was used to uncover new free energy functionals. However, while, in principle, the same method should apply to free energies which can be given by quadratic forms in terms of \(I^t\), it emerges that this requirement is very restrictive; indeed, only the minimum free energy can be expressed in such a manner.

The octanol-water partition coefficient is an important physical-chemical characteristic widely used to describe hydrophobic/hydrophilic properties of chemical compounds. The partition coefficient is related to the transfer free energy of a compound from water to octanol. Here, we introduce a new protocol for prediction of the partition coefficient based on the statistical-mechanical, 3D-RISM-KH molecular theory of solvation. It was shown recently that with the compound-solvent correlation functions obtained from the 3D-RISM-KH molecular theory of solvation, the free energy functional supplemented with the correction linearly related to the partial molar volume obtained from the Kirkwood-Buff/3D-RISM theory, also called the "universal correction" (UC), provides accurate prediction of the hydration free energy of small compounds, compared to explicit solvent molecular dynamics [ Palmer , D. S. ; J. Phys.: Condens. Matter 2010 , 22 , 492101 ]. Here we report that with the UC reparametrized accordingly this theory also provides an excellent agreement with the experimental data for the solvation free energy in nonpolar solvent (1-octanol) and so accurately predicts the octanol-water partition coefficient. The performance of the Kovalenko-Hirata (KH) and Gaussian fluctuation (GF) functionals of the solvation free energy, with and without UC, is tested on a large library of small compounds with diverse functional groups. The best agreement with the experimental data for octanol-water partition coefficients is obtained with the KH-UC solvation free energy functional.

The free energy functions for electron transfer reactions in solution are explored using a previously developed microscopic simulation approach that provides a clear definition of these functions and the variable (the reaction coordinate) used as their argument. The issue of whether the curvatures of the two functions (which correspond to states with nonpolar and polar solutes) are different is given special attention. It is found, in contrast to some previous suggestions, that the curvatures of the two functions are quite similar, even when one would expect differences due to dielectric saturation effects, and that Marcus’ approximation (and, in fact, the linear response theory inherent in this approximation) provides a valid description of the solvent’s role in electron transfer reactions over a wide range of conditions. The present study demonstrates that direct simulations of the reactant and product states do not provide the data needed for determination of the free energy functions in high energy regions. On the other hand, a free energy perturbation approach developed in our early studies does allow one to obtain statistically significant data for these regions of high free energy. Inclusion of the solvent electronic polarizabilities in the potential results in a marked lowering of the solvent reorganization energy, but does not change the ratio of the curvatures of the free energy functions for the nonpolar and polar states. Finally, the effect of solvent tunneling is evaluated with the dispersed polaron method and shown to be rather small, and it is argued that the observed deviations from the classical Marcus theory in the inverted region are due to quantum mechanical tunneling associated with the solute vibrations, rather than to differences in the curvatures of the solvent free energy functions.

We develop a novel data-driven approach to the inverse problem of classical statistical mechanics: Given the experimental data on the collective motion of a classical many-body system, how does one characterize the free energy landscape of that system? By combining non-parametric Bayesian inference with physically motivated constraints, we develop an efficient learning algorithm that automates the construction of approximate free-energy functionals. In contrast to optimization-based machine learning approaches, which seek to minimize a cost function, the central idea of the proposed Bayesian inference is to propagate a set of prior assumptions through the model, derived from physical principles. The experimental data are used to probabilistically weigh the possible model predictions. This naturally leads to humanly interpretable algorithms with full uncertainty quantification of predictions. In our case, the output of the learning algorithm is a probability distribution over a family of free energy functionals, consistent with the observed particle data. We find that surprisingly small data samples contain sufficient information for inferring highly accurate analytic expressions of the underlying free-energy functionals, making our algorithm highly data efficient. In particular, we consider classical particle systems with excluded volume interactions, which are ubiquitous in nature, while being highly challenging in terms of free energy modeling. We validate our approach on the paradigmatic case of one-dimensional fluid and develop inference algorithms for the canonical and grand-canonical statistical-mechanical ensembles. Extensions to higher dimensional systems are conceptually straightforward, while standard coarse-graining techniques allow one to easily incorporate attractive interactions.

The paper presents a continuum mechanics approach in a mathematical formulation of a class of constitutive relations which tend to descibe mechanical as well as thermo-rheological behavior of a material with two limiting cases of consitutive behavior: thermo-hyperelastic representing the rate independent behavior and thermo-viscoelastic in a general rheological sense. In the rate-independent limit the mechanical part can be represented by appropriate strain energy functions. We consider potential functions of Murnagan’s type for compressible and Signorini’s type for incompressible materials. In addition to the standard kinematical variables, the time dependent part of the assumed general form of constitutive relation is postulated to depend on an internal variable similar to the reduced time scaled by a shift function as in classical thermo-viscoelasticity, but with much broader functional relationship. The corresponding expressions for stress, entropy, and dissipation inequality are derived from strict thermodynamic considerations and are given in an explicit form. Development is based on the principle of fading memory established by (Coleman 1961), (Coleman & Noll 1964) which was subsequently specialized for the class of viscoelastic materials by (Lianis 1965, 1970). A fundamental assumption of the proposed procedure is that in the expansion of the rheological time-dependent part of a free energy function small differences in histories of strain and temperature fields enter the thermodynamic potential or the free energy function only up to quadratic terms. Consequently, the derived expressions are quite amenable for further development. We discuss a thermo-rheologically simple constitutive model of a material which is described by a constitutive relation of a single-integral equation type.

Smart materials are active and multifunctional materials, which play an important part for sensor and actuator applications. These materials have the potential to transform passive structures into adaptive systems. However, a prerequisite for the design and the optimization of these materials is, that reliable models exist, which incorporate the interaction between the different combinations of thermal, electrical, magnetic, optical and mechanical effects. Polymeric electroelastic materials, so-called (EAP), own the characteristic to deform if an electric field is applied. EAP's possesses the benefit that they share the characteristic of polymers, these are lightweight, inexpensive, fracture tolerant, elastic, and the chemical and physical structure is well understood. However, the description electroactive polymer is a generic term for many kinds of different microscopic mechanisms and polymeric materials. Based on the laws of electromagnetism and elasticity, a visco-electroelastic model is developed and implemented into the finite element method (FEM). The presented three-dimensional solid element has eight nodes and trilinear interpolation functions for the displacement and the electric potential. The continuum mechanics model contains finite deformations, the time dependency and the nearly incompressible behavior of the material. To describe the possible, large time dependent deformations, a finite viscoelastic model with a split of the deformation gradient is used. Thereby the time dependent characteristic of polymeric materials is incorporated through the free energy function. The electromechanical interactions are considered by the electrostatic forces and inside the energy function.

Monte Carlo simulations are used to study the translocation of a polymer into and out of an ellipsoidal cavity through a narrow pore. We measure the polymer free energy F as a function of a translocation coordinate, s, defined to be the number of bonds that have entered the cavity. To study polymer insertion, we consider the case of a driving force acting on monomers inside the pore, as well as monomer attraction to the cavity wall. We examine the changes to F(s) upon variation in the shape anisometry and volume of the cavity, the polymer length, and the strength of the interactions driving the insertion. For athermal systems, the free energy functions are analyzed using a scaling approach, where we treat the confined portion of the polymer to be in the semi-dilute regime. The free energy functions are used with the Fokker-Planck (FP) equation to calculate mean translocation times, as well as translocation time distributions. We find that both polymer ejection and insertion are faster for ellipsoidal cavities than for spherical cavities. The results are in qualitative agreement with those of a Langevin dynamics study in the case of ejection but not for insertion. The discrepancy is likely due to out-of-equilibrium conformational behaviour that is not accounted for in the FP approach.

The heat capacities of the sesquioxides of yttrium, lanthanum, and neodymaium have been determined in the temperature range 16 to 300 deg K. The entropies, e thalpies, and free energy functions have been calculated from the heat capacity data and are tabulated for several temperatures. Yttriuma oxide and lanthanum oxide exhibit typical sigmoidal heat capacity curves with no auomalies in the temperature range studied. The shape of the heat capacity curve for neodymium oxide is similar except that at the lowest temperature there is evidence for the existence of an anomaly. At 298.16 deg K. the entropies are 23.693 deg 0.07 and 30.580 deg 0.07 cal. mole/sup -1/ deg./sup -1/ for yttrium oxide and lanthaum oxide, respectively. For neodymium oxide S/sub 298// sub .16/ is 33-607 cal- mole/sup -1/ deg./sup -1/. Th e free energy functions have been extended to 2500 deg K. by the use of some higher temperature heat capacity data available in the literature. (auth)

We study a model of active particles that perform a simple random walk and on top of that have a preferred direction determined by an internal state which is modelled by a stationary Markov process. First we calculate the limiting diffusion coefficient. Then we show that the ‘active part’ of the diffusion coefficient is in some sense maximal for reversible state processes. Further, we obtain a large deviations principle for the active particle in terms of the large deviations rate function of the empirical process corresponding to the state process. Again we show that the rate function and free energy function are (pointwise) optimal for reversible state processes. Finally, we show that in the case with two states, the Fourier–Laplace transform of the distribution, the moment generating function and the free energy function can be computed explicitly. Along the way we provide several examples.

Influence of microstructural parameters on mechanical behavior of polymer gels