scholarly journals Hessian matrix, specific heats, Nambu brackets, and thermodynamic geometry

2015 ◽  
Vol 2015 (4) ◽  
Author(s):  
Seyed Ali Hosseini Mansoori ◽  
Behrouz Mirza ◽  
Mohamadreza Fazel
Keyword(s):  
Hessian Matrix ◽  
Specific Heats ◽  
Nambu Brackets ◽  
Thermodynamic Geometry

Constructing Quantum Mechanics

2019 ◽  
Author(s):  
Anthony Duncan ◽  
Michel Janssen
Keyword(s):  
Quantum Mechanics ◽  
Quantum Theory ◽  
Stark Effect ◽  
Zeeman Effect ◽  
Black Body ◽  
Black Body Radiation ◽  
Wave Mechanics ◽  
Specific Heats ◽  
Old Quantum Theory ◽  
Upper Level

This is the first of two volumes on the genesis of quantum mechanics. It covers the key developments in the period 1900–1923 that provided the scaffold on which the arch of modern quantum mechanics was built in the period 1923–1927 (covered in the second volume). After tracing the early contributions by Planck, Einstein, and Bohr to the theories of black‐body radiation, specific heats, and spectroscopy, all showing the need for drastic changes to the physics of their day, the book tackles the efforts by Sommerfeld and others to provide a new theory, now known as the old quantum theory. After some striking initial successes (explaining the fine structure of hydrogen, X‐ray spectra, and the Stark effect), the old quantum theory ran into serious difficulties (failing to provide consistent models for helium and the Zeeman effect) and eventually gave way to matrix and wave mechanics. Constructing Quantum Mechanics is based on the best and latest scholarship in the field, to which the authors have made significant contributions themselves. It breaks new ground, especially in its treatment of the work of Sommerfeld and his associates, but also offers new perspectives on classic papers by Planck, Einstein, and Bohr. Throughout the book, the authors provide detailed reconstructions (at the level of an upper‐level undergraduate physics course) of the cental arguments and derivations of the physicists involved. All in all, Constructing Quantum Mechanics promises to take the place of older books as the standard source on the genesis of quantum mechanics.

scholarly journals Skewed thermodynamic geometry and optimal free energy estimation

2020 ◽  
Vol 153 (24) ◽  
pp. 244119
Author(s):  
Steven Blaber ◽  
David A. Sivak
Keyword(s):  
Free Energy ◽  
Energy Estimation ◽  
Thermodynamic Geometry

scholarly journals Adjoint-based exact Hessian computation

2021 ◽  
Author(s):  
Shin-ichi Ito ◽  
Takeru Matsuda ◽  
Yuto Miyatake
Keyword(s):  
Krylov Subspace ◽  
Hessian Matrix ◽  
Adjoint System ◽  
Coefficient Matrix ◽  
Scalar Function ◽  
Second Order ◽  
Subspace Method ◽  
Initial Value ◽  
Research Fields ◽  
Memory Efficiency

AbstractWe consider a scalar function depending on a numerical solution of an initial value problem, and its second-derivative (Hessian) matrix for the initial value. The need to extract the information of the Hessian or to solve a linear system having the Hessian as a coefficient matrix arises in many research fields such as optimization, Bayesian estimation, and uncertainty quantification. From the perspective of memory efficiency, these tasks often employ a Krylov subspace method that does not need to hold the Hessian matrix explicitly and only requires computing the multiplication of the Hessian and a given vector. One of the ways to obtain an approximation of such Hessian-vector multiplication is to integrate the so-called second-order adjoint system numerically. However, the error in the approximation could be significant even if the numerical integration to the second-order adjoint system is sufficiently accurate. This paper presents a novel algorithm that computes the intended Hessian-vector multiplication exactly and efficiently. For this aim, we give a new concise derivation of the second-order adjoint system and show that the intended multiplication can be computed exactly by applying a particular numerical method to the second-order adjoint system. In the discussion, symplectic partitioned Runge–Kutta methods play an essential role.

scholarly journals On the measurement of the ratio of the specific heats using small volumes of gas.—The ratios of the specific heat of air and of hydrogen at atmospheric pressure and a temperatures between 20°C. and —183°C

1925 ◽  
Vol 107 (743) ◽  
pp. 510-543 ◽  
Keyword(s):  
Systematic Error ◽  
Low Temperatures ◽  
Room Temperature ◽  
Expansion Chamber ◽  
Small Vessels ◽  
Specific Heats ◽  
Large Expansion ◽  
Before And After ◽  
The One ◽  
Chamber Capacity

Introduction .—In nearly all the previous determinations of the ratio of the specific heats of gases, from measurements of the pressures and temperature before and after an adiabatic expansion, large expansion chambers of fror 50 to 130 litres capacity have been used. Professor Callendar first suggests the use of smaller vessels, and in 1914, Mercer (‘Proc. Phys. Soc.,’ vol. 26 p. 155) made some measurements with several gases, but at room temperature only, using volumes of about 300 and 2000 c. c. respectively. He obtained values which indicated that small vessels could be used, and that, with proper corrections, a considerable degree of accuracy might be obtained. The one other experimenter who has used a small expansion chamber, capacity about 1 litre, is M. C. Shields (‘Phys. Rev.,’ 1917), who measured this ratio for air and for hydrogen at room temperature, about 18° C., and its value for hydroger at — 190° C. The chief advantage gained by the use of large expansion chambers is that no correction, or at the most, a very small one, has to be made for any systematic error due to the size of the containing vessels, but it is clear that, in the determinations of the ratio of the specific heats of gases at low temperatures, the use of small vessels becomes a practical necessity in order that uniform and steady temperature conditions may be obtained. Owing, however, to the presence of a systematic error depending upon the dimensions of the expansion chamber, the magnitude of which had not been definitely settled by experiment, the following work was undertaken with the object of investigating the method more fully, especially with regard to it? applicability to the determination of this ratio at low temperatures.

scholarly journals Fluctuations and thermodynamic geometry of the chiral phase transition

2020 ◽  
Vol 102 (11) ◽  
Author(s):  
Paolo Castorina ◽  
Daniele Lanteri ◽  
Marco Ruggieri
Keyword(s):  
Phase Transition ◽  
Chiral Phase ◽  
Chiral Phase Transition ◽  
Thermodynamic Geometry

Effect of supplementary firing on the performance of an integrated gasification combined cycle power plant

2000 ◽  
Vol 214 (1) ◽  
pp. 53-60 ◽  
Author(s):  
S De ◽  
P K Nag
Keyword(s):  
Power Plant ◽  
Heat Recovery ◽  
Combined Cycle ◽  
Exergy Loss ◽  
Temperature Ratio ◽  
Integrated Gasification Combined Cycle ◽  
Specific Heats ◽  
Second Law Analysis ◽  
Integrated Gasification ◽  
Igcc Power Plant

The effect of supplementary firing on the performance of an integrated gasification combined cycle (IGCC) power plant is studied. The results are presented with respect to a simple ‘unfired’ IGCC power plant with single pressure power generation for both the gas and the steam cycles as reference. The gases are assumed as real with variable specific heats. It is found that the most favourable benefit of supplementary firing can be obtained for a low temperature ratio R T only. For higher R T, only a gain in work output is possible with a reverse effect on the overall efficiency of the plant. The second law analysis reveals that the exergy loss in the heat-recovery steam generator is most significant as the amount of supplementary firing increases. It is also noteworthy that, although the total exergy loss of the plant decreases with higher supplementary firing for a low R T (= 3.0), the reverse is the case for a higher R T (= 6.0).

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