Thermoelastic Generalization of Isothermal Elastic Constitutive Models for Rubber-Like Materials

1996 ◽  
Vol 69 (2) ◽  
pp. 313-324 ◽  
Author(s):  
Nianning Zeng ◽  
Henry W. Haslach
Keyword(s):  
Free Energy ◽  
Thermal Properties ◽  
Helmholtz Free Energy ◽  
Constitutive Models ◽  
Temperature Dependent ◽  
Thermal Inversion ◽  
Entropic Elasticity ◽  
Deformation Dependence ◽  
Constant Deformation ◽  
Inversion Effects

Abstract Existing thermoelastic constitutive models are not able to predict important thermal properties of rubbers. For example, the modified entropic elasticity theory fails to predict that the temperature coefficient of stress, the energetic contribution to the stress, and the specific heat at constant deformation depend on both deformation and temperature. A class of thermoelastic constitutive equations is proposed that generalizes given isothermal models and predicts the temperature and deformation dependence. The Helmholtz free energy is written as the sum of the isothermal energy function, but with temperature-dependent material moduli, and a function of temperature. Conditions on the Helmholtz energy are given to ensure that three inversion effects which characterize rubber are predicted. As an application, an isotropic, homogeneous, mechanically incompressible thermoelastic constitutive equation is generalized from the isothermal Mooney-Rivlin model. The three uniaxial thermal inversion effects are successfully reproduced by this model.

scholarly journals Free Energy of Metals from Quasi-Harmonic Models of Thermal Disorder

Metals ◽  
2021 ◽  
Vol 11 (2) ◽  
pp. 195
Author(s):  
Pavel A. Korzhavyi ◽  
Jing Zhang
Keyword(s):  
Free Energy ◽  
First Principles ◽  
Density Functional ◽  
Helmholtz Free Energy ◽  
Complex Materials ◽  
Predictive Capability ◽  
Temperature Dependent ◽  
Disordered Alloys ◽  
Thermal Disorder ◽  
Structure Calculations

A simple modeling method to extend first-principles electronic structure calculations to finite temperatures is presented. The method is applicable to crystalline solids exhibiting complex thermal disorder and employs quasi-harmonic models to represent the vibrational and magnetic free energy contributions. The main outcome is the Helmholtz free energy, calculated as a function of volume and temperature, from which the other related thermophysical properties (such as temperature-dependent lattice and elastic constants) can be derived. Our test calculations for Fe, Ni, Ti, and W metals in the paramagnetic state at temperatures of up to 1600 K show that the predictive capability of the quasi-harmonic modeling approach is mainly limited by the electron density functional approximation used and, in the second place, by the neglect of higher-order anharmonic effects. The developed methodology is equally applicable to disordered alloys and ordered compounds and can therefore be useful in modeling realistically complex materials.

NONISOTHERMAL METASTABILITY IN MESOSCOPIC SYSTEMS

1991 ◽  
Vol 05 (06) ◽  
pp. 447-453 ◽  
Author(s):  
H. DEKKER
Keyword(s):  
Heat Capacity ◽  
Free Energy ◽  
Heat Exchange ◽  
Energy Barrier ◽  
Degrees Of Freedom ◽  
Helmholtz Free Energy ◽  
Nonequilibrium Thermodynamics ◽  
Magnetic Phase ◽  
Planck Equation ◽  
Temperature Dependent

Since the effective potential for noisy “macroscopic” degrees of freedom (e.g. the magnetic phase in Josephson junctions) in general depends on the (local) temperature, it is given thermodynamical significance as the Gibbs or Helmholtz free energy. Using the notions of nonequilibrium thermodynamics a generalized Kramers Fokker-Planck equation is then presented, which includes nonisothermal effects. The escape rate from a metastable state across a temperature-dependent energy barrier is investigated. A substantial entropic barrier enhancement is found for a specimen with small heat capacity and slow heat exchange with its environment (e.g. the helium reservoir).

A canonical ensemble derivation of the McMillan-Mayer solution theory

1983 ◽  
Vol 48 (10) ◽  
pp. 2888-2892 ◽  
Author(s):  
Vilém Kodýtek
Keyword(s):  
Free Energy ◽  
Partition Function ◽  
Energy Function ◽  
Special Function ◽  
Helmholtz Free Energy ◽  
Canonical Ensemble ◽  
Free Energy Function ◽  
Solution Theory ◽  
Pure Solvent ◽  
The Common

A special free energy function is defined for a solution in the osmotic equilibrium with pure solvent. The partition function of the solution is derived at the McMillan-Mayer level and it is related to this special function in the same manner as the common partition function of the system to its Helmholtz free energy.

scholarly journals The Dynamics of Subunit Rotation in a Eukaryotic Ribosome

Biophysica ◽  
2021 ◽  
Vol 1 (2) ◽  
pp. 204-221
Author(s):  
Frederico Campos Freitas ◽  
Gabriele Fuchs ◽  
Ronaldo Junio de Oliveira ◽  
Paul Charles Whitford
Keyword(s):  
Free Energy ◽  
Large Scale ◽  
Small Subunit ◽  
Free Energy Barrier ◽  
Temperature Dependent ◽  
Molecular Flexibility ◽  
Subunit Rotation ◽  
Biological Kinetics ◽  
Rate Limiting ◽  
Reversible Rotation

Protein synthesis by the ribosome is coordinated by an intricate series of large-scale conformational rearrangements. Structural studies can provide information about long-lived states, however biological kinetics are controlled by the intervening free-energy barriers. While there has been progress describing the energy landscapes of bacterial ribosomes, very little is known about the energetics of large-scale rearrangements in eukaryotic systems. To address this topic, we constructed an all-atom model with simplified energetics and performed simulations of subunit rotation in the yeast ribosome. In these simulations, the small subunit (SSU; ∼1 MDa) undergoes spontaneous and reversible rotation events (∼8∘). By enabling the simulation of this rearrangement under equilibrium conditions, these calculations provide initial insights into the molecular factors that control dynamics in eukaryotic ribosomes. Through this, we are able to identify specific inter-subunit interactions that have a pronounced influence on the rate-limiting free-energy barrier. We also show that, as a result of changes in molecular flexibility, the thermodynamic balance between the rotated and unrotated states is temperature-dependent. This effect may be interpreted in terms of differential molecular flexibility within the rotated and unrotated states. Together, these calculations provide a foundation, upon which the field may begin to dissect the energetics of these complex molecular machines.

scholarly journals Exploration of Free Energy Surface and Thermal Effects on Relative Population and Infrared Spectrum of the Be6B11− Fluxional Cluster

Materials ◽  
2020 ◽  
Vol 14 (1) ◽  
pp. 112
Author(s):  
Carlos Emiliano Buelna-Garcia ◽  
José Luis Cabellos ◽  
Jesus Manuel Quiroz-Castillo ◽  
Gerardo Martinez-Guajardo ◽  
Cesar Castillo-Quevedo ◽  
...  
Keyword(s):  
Free Energy ◽  
Infrared Spectrum ◽  
Infrared Spectra ◽  
Thermal Effects ◽  
Global Minimum ◽  
Energy Surface ◽  
Weighted Sums ◽  
Free Energy Surface ◽  
Temperature Dependent ◽  
Relative Population

The starting point to understanding cluster properties is the putative global minimum and all the nearby local energy minima; however, locating them is computationally expensive and difficult. The relative populations and spectroscopic properties that are a function of temperature can be approximately computed by employing statistical thermodynamics. Here, we investigate entropy-driven isomers distribution on Be6B11− clusters and the effect of temperature on their infrared spectroscopy and relative populations. We identify the vibration modes possessed by the cluster that significantly contribute to the zero-point energy. A couple of steps are considered for computing the temperature-dependent relative population: First, using a genetic algorithm coupled to density functional theory, we performed an extensive and systematic exploration of the potential/free energy surface of Be6B11− clusters to locate the putative global minimum and elucidate the low-energy structures. Second, the relative populations’ temperature effects are determined by considering the thermodynamic properties and Boltzmann factors. The temperature-dependent relative populations show that the entropies and temperature are essential for determining the global minimum. We compute the temperature-dependent total infrared spectra employing the Boltzmann factor weighted sums of each isomer’s infrared spectrum and find that at finite temperature, the total infrared spectrum is composed of an admixture of infrared spectra that corresponds to the spectra of the lowest-energy structure and its isomers located at higher energies. The methodology and results describe the thermal effects in the relative population and the infrared spectra.

Analysis of Tempering and Rehardening for Grinding of Hardened Steels

1991 ◽  
Vol 113 (4) ◽  
pp. 388-394 ◽  
Author(s):  
O. B. Fedoseev ◽  
S. Malkin
Keyword(s):  
Thermal Properties ◽  
Heat Source ◽  
Hardened Steel ◽  
Temperature History ◽  
Hardness Distribution ◽  
Temperature Dependent ◽  
Thermally Activated ◽  
Reaction Equations ◽  
Rate Controlling Step ◽  
Good Agreement

An analysis is presented to predict the hardness distribution in the subsurface of hardened steel due to tempering and rehardening associated with high temperatures generated in grinding. The grinding temperatures are modeled with a triangular heat source at the grinding zone and temperature-dependent thermal properties. The temperature history, including the effect of multiple grinding passes, is coupled with thermally activated reaction equations for tempering and for reaustenitization which is the rate controlling step in rehardening. Experimental results from the literature are found to be in good agreement with the analytical predictions.

Thermodynamics Energy for Both Supervised and Unsupervised Learning Neural Nets at a Constant Temperature

1999 ◽  
Vol 09 (03) ◽  
pp. 175-186 ◽  
Author(s):  
HAROLD SZU
Keyword(s):  
Free Energy ◽  
Constant Temperature ◽  
Helmholtz Free Energy ◽  
Principal Component ◽  
Neural Nets ◽  
Mixing Condition ◽  
Smart Cameras ◽  
Minimization Principle ◽  
Output Entropy ◽  
Artificial Neural Network Ann

Unified Lyaponov function is given for the first time to prove the learning methodologies convergence of artificial neural network (ANN), both supervised and unsupervised, from the viewpoint of the minimization of the Helmholtz free energy at the constant temperature. Early in 1982, Hopfield has proven the supervised learning by the energy minimization principle. Recently in 1996, Bell & Sejnowski has algorithmically demonstrated. Independent Component Analyses (ICA) generalizing the Principal Component Analyses (PCA) that the continuing reduction of early vision redundancy happens towards the "sparse edge maps" by maximization of the ANN output entropy. We explore the combination of both as Lyaponov function of which the proven convergence gives both learning methodologies. The unification is possible because of the thermodynamics Helmholtz free energy at a constant temperature. The blind de-mixing condition for more than two objects using two sensor measurement. We design two smart cameras with short term working memory to do better image de-mixing of more than two objects. We consider channel communication application that we can efficiently mix four images using matrices [AO] and [Al] to send through two channels.

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