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Fundamentals of Thermodynamics
This book provides a concise coverage of the basic concepts of thermodynamics, as it is used to solve the energy, power, and propulsion related issues. Reversible and regenerative principles from thermodynamics, high-pressure combustion processes, fuel cells, and renewable energy sources find application today in mitigating waste heat. The modeling can be used for prediction of cyclones, tornadoes, and other phenomena taking place in nature. It also derives the mathematical expressions about reversibility, work, and equilibrium from physical and intuitive considerations. The treatment is not restricted to ideal gases, and ideal gas assumption is imposed as a particular case of a real gas. Reversible paths between equilibrium states are obtained using reversible heat engines and reversible heat pumps to determine the entropy changes and obtain reversible work. The conditions of thermodynamic equilibrium are addressed for different systems. The molecular basis for temperature, internal energy changes, entropy, reversibility, and equilibrium are discussed. The book serves as a reference for undergraduate and graduate students alongside thermodynamics textbooks.
Book
Experimental test of a predicted dynamics–structure–thermodynamics connection in molecularly complex glass-forming liquids
Understanding in a unified manner the generic and chemically specific aspects of activated dynamics in diverse glass-forming liquids over 14 or more decades in time is a grand challenge in condensed matter physics, physical chemistry, and materials science and engineering. Large families of conceptually distinct models have postulated a causal connection with qualitatively different “order parameters” including various measures of structure, free volume, thermodynamic properties, short or intermediate time dynamics, and mechanical properties. Construction of a predictive theory that covers both the noncooperative and cooperative activated relaxation regimes remains elusive. Here, we test using solely experimental data a recent microscopic dynamical theory prediction that although activated relaxation is a spatially coupled local–nonlocal event with barriers quantified by local pair structure, it can also be understood based on the dimensionless compressibility via an equilibrium statistical mechanics connection between thermodynamics and structure. This prediction is found to be consistent with observations on diverse fragile molecular liquids under isobaric and isochoric conditions and provides a different conceptual view of the global relaxation map. As a corollary, a theoretical basis is established for the structural relaxation time scale growing exponentially with inverse temperature to a high power, consistent with experiments in the deeply super-cooled regime. A criterion for the irrelevance of collective elasticity effects is deduced and shown to be consistent with viscous flow in low-fragility inorganic network-forming melts. Finally, implications for relaxation in the equilibrated deep glass state are briefly considered.
Journal Article
Quasinormal modes, thermodynamics and shadow of black holes in Hu-Sawicki Formula omitted gravity theory
We derive novel black hole solutions in a modified gravity theory, namely the Hu-Sawicki model of f(R) gravity. After obtaining the black hole solution, we study the horizon radius of the black hole from the metric and then analyse the dependence of the model parameters on the horizon. We then use the 6th order WKB method to study the quasinormal modes of oscillations (QNMs) of the black hole perturbed by a scalar field. The dependence of the amplitude and damping part of the QNMs are analysed with respect to variations in model parameters and the error associated with the QNMs are also computed. After that we study some thermodynamic properties associated with the black hole such as its thermodynamic temperature as well as greybody factors. It is found that the black hole has the possibility of showcasing negative temperatures and is thermodynamically unstable for feasible values of model parameters. Then we analyse the geodesics and derive the photon sphere radius as well as the shadow radius of the black hole. The photon radius is independent of the model parameters while shadow radius showed fair amount of dependence on the model parameters. We tried to constrain the parameters with the help of Keck and VLTI observational data and obtained some bounds on m and [Formula omitted] parameters.
Journal Article
Conformal Graph Directed Markov Systems on Carnot Groups
We develop a comprehensive theory of conformal graph directed Markov systems in the non-Riemannian setting of Carnot groups equipped
with a sub-Riemannian metric. In particular, we develop the thermodynamic formalism and show that, under natural hypotheses, the limit
set of an Carnot conformal GDMS has Hausdorff dimension given by Bowen’s parameter. We illustrate our results for a variety of examples
of both linear and nonlinear iterated function systems and graph directed Markov systems in such sub-Riemannian spaces. These include
the Heisenberg continued fractions introduced by Lukyanenko and Vandehey as well as Kleinian and Schottky groups associated to the
non-real classical rank one hyperbolic spaces.
eBook
Impact of swaps on Mössbauer characteristics of Ni.sub.2MnSn: an experimental and quantum-mechanical study
We report on a combined experimental and theoretical study of stoichiometric Heusler-structure Ni.sub.2MnSn. Our detected Mössbauer spectrum of Sn atoms can be fitted as a combination of four components. As only a single component is expected in the defect-free Ni.sub.2MnSn, we have performed quantum-mechanical calculations of Ni.sub.2MnSn with selected point defects, in particular, all three fundamental types of swaps (Mn-Ni, Mn-Sn and Ni-Sn). Our phonon and elasticity calculations indicate that the swaps result in (i) magnitudes of local magnetic moments of Sn atoms within four ranges of values and (ii) mean square displacements of Sn atoms falling within four intervals of values. Further, we used calculations of phonons and elastic properties to assess mechanical, dynamical and thermodynamic stability of swap-containing states. Our results indicate that a majority of the studied swaps is reducing the stability of Ni.sub.2MnSn and need to be stabilized by the surrounding matrix.
Journal Article
Analytically approximation solution to Formula omitted gravity
In this paper, we obtain analytical approximate black hole solutions in the framework of f(R) gravity and the absence of a cosmological constant. In this area, we apply the equations of motion of the theory to a spherically symmetric spacetime with one unknown function and derive black hole solutions without any constraints on the Ricci scalar. To do so, first, we obtain the near horizon and asymptotic solutions and then use both of them to obtain a complete solution by utilizing a continued-fraction expansion. Finally, we investigate the stability of the solutions by employing the thermodynamics and quasi-normal modes.
Journal Article