Thermodynamic processes expressed in terms of nonlinear maps

2018 ◽  
Vol 6 (1) ◽  
pp. 83-88
Author(s):  
Yehuda Roth
Keyword(s):  
Nonlinear Maps ◽  
Thermodynamic Processes

Processes and Responses

2017 ◽  
Author(s):  
Jochen Rau
Keyword(s):  
Heat Engine ◽  
Cyclic Process ◽  
Free Enthalpy ◽  
Initial State ◽  
Thermodynamic Potentials ◽  
Grand Potential ◽  
Laws Of Thermodynamics ◽  
Cyclic Processes ◽  
Energy Exchanges ◽  
Thermodynamic Processes

Thermodynamic processes involve energy exchanges in the forms of work, heat, or particles. Such exchanges might be reversible or irreversible, and they might be controlled by barriers or reservoirs. A cyclic process takes a system through several states and eventually back to its initial state; it may convert heat into work (engine) or vice versa (heat pump). This chapter defines work and heat mathematically and investigates their respective properties, in particular their impact on entropy. It discusses the roles of barriers and reservoirs and introduces cyclic processes. Basic constraints imposed by the laws of thermodynamics are considered, in particular on the efficiency of a heat engine. The chapter also introduces the thermodynamic potentials: free energy, enthalpy, free enthalpy, and grand potential. These are used to describe energy exchanges and equilibrium in the presence of reservoirs. Finally, this chapter considers thermodynamic coefficients which characterize the response of a system to heating, compression, and other external actions.

scholarly journals An Algebraic Brascamp–Lieb Inequality

2021 ◽  
Author(s):  
Jennifer Duncan
Keyword(s):  
General Class ◽  
Recent Progress ◽  
Algebraic Groups ◽  
Hölder’S Inequality ◽  
Duke Math ◽  
Rational Maps ◽  
Affine Invariant ◽  
Linear Maps ◽  
Nonlinear Maps ◽  
Funct Anal

AbstractThe Brascamp–Lieb inequalities are a very general class of classical multilinear inequalities, well-known examples of which being Hölder’s inequality, Young’s convolution inequality, and the Loomis–Whitney inequality. Conventionally, a Brascamp–Lieb inequality is defined as a multilinear Lebesgue bound on the product of the pullbacks of a collection of functions $$f_j\in L^{q_j}(\mathbb {R}^{n_j})$$ f j ∈ L q j ( R n j ) , for $$j=1,\ldots ,m$$ j = 1 , … , m , under some corresponding linear maps $$B_j$$ B j . This regime is now fairly well understood (Bennett et al. in Geom Funct Anal 17(5):1343–1415, 2008), and moving forward there has been interest in nonlinear generalisations, where $$B_j$$ B j is now taken to belong to some suitable class of nonlinear maps. While there has been great recent progress on the question of local nonlinear Brascamp–Lieb inequalities (Bennett et al. in Duke Math J 169(17):3291–3338, 2020), there has been relatively little regarding global results; this paper represents some progress along this line of enquiry. We prove a global nonlinear Brascamp–Lieb inequality for ‘quasialgebraic’ maps, a class that encompasses polynomial and rational maps, as a consequence of the multilinear Kakeya-type inequalities of Zhang and Zorin-Kranich. We incorporate a natural affine-invariant weight that both compensates for local degeneracies and yields a constant with minimal dependence on the underlying maps. We then show that this inequality generalises Young’s convolution inequality on algebraic groups with suboptimal constant.

Defining the Thermodynamic Efficiency in a Wave Rotor

2016 ◽  
Vol 138 (11) ◽  
Author(s):  
Shining Chan ◽  
Huoxing Liu ◽  
Fei Xing
Keyword(s):  
Gas Turbine ◽  
Control Volume ◽  
Thermodynamic Efficiency ◽  
Wave Rotor ◽  
Wave Rotors ◽  
Compression And Expansion ◽  
Efficiency Estimation ◽  
Parametric Analyses ◽  
Control Volumes ◽  
Thermodynamic Processes

A wave rotor enhances the performance of a gas turbine with its internal compression and expansion, yet the thermodynamic efficiency estimation has been troubling because the efficiency definition is unclear. This paper put forward three new thermodynamic efficiency definitions to overcome the trouble: the adiabatic efficiency, the weighted-pressure mixed efficiency, and the pressure pre-equilibrated efficiency. They were all derived from multistream control volumes. As a consequence, they could correct the efficiency values and make the values for compression and expansion independent. Moreover, the latter two incorporated new models of pre-equilibration inside a control volume, and modified the hypothetical “ideal” thermodynamic processes. Parametric analyses based on practical wave rotor data demonstrated that the trends of those efficiency values reflected the energy losses in wave rotors. Essentially, different thermodynamic efficiency definitions indicated different ideal thermal cycle that an optimal wave rotor can provide for a gas turbine, and they were recommended to application based on that essence.

scholarly journals Summer Westerly Jet in Northern Hemisphere during the Mid-Holocene: A Multi-Model Study

Atmosphere ◽  
2020 ◽  
Vol 11 (11) ◽  
pp. 1193
Author(s):  
Chuchu Xu ◽  
Mi Yan ◽  
Liang Ning ◽  
Jian Liu
Keyword(s):  
Temperature Gradient ◽  
Northern Hemisphere ◽  
Hadley Cell ◽  
Dynamic Processes ◽  
Jet Stream ◽  
Meridional Temperature Gradient ◽  
The North ◽  
Westerly Jet ◽  
Poleward Shift ◽  
Thermodynamic Processes

The upper-level jet stream, a narrow band of maximum wind speed in the mid-latitude westerlies, exerts a considerable influence on the global climate by modulating the transport and distribution of momentum, heat and moisture. In this study by using four high-resolution models in the Paleoclimate Modelling Intercomparison Project phase 3, the changes of position and intensity of the northern hemisphere westerly jet at 200 hPa in summer during the mid-Holocene (MH), as well as the related mechanisms, are investigated. The four models show similar performance on the westerly jet. At the hemispheric scale, the simulated westerly jet has a poleward shift during the MH compared to the preindustrial period. The warming in arctic and cooling in the tropics during the MH are caused by the orbital changes of the earth and the precipitation changes, and it could lead to the weakened meridional temperature gradient and pressure gradient, which might account for the poleward shift of the westerly jet from the thermodynamic perspective. From the dynamic perspective, two maximum centers of eddy kinetic energy are simulated over the North Pacific and North Atlantic with the north deviation, which could cause the northward movement of the westerly jet. The weakening of the jet stream is associated with the change of the Hadley cell and the meridional temperature gradient. The largest weakening is over the Pacific Ocean where both the dynamic and the thermodynamic processes have weakening effects. The smallest weakening is over the Atlantic Ocean, and it is induced by the offset effects of dynamic processes and thermodynamic processes. The weakening over the Eurasia is mainly caused by the dynamic processes.

Stabilizing Feedback Controls for Nonlinear Hamiltonian Systems and Nonconservative Bilinear Systems in Elasticity

1982 ◽  
Vol 104 (1) ◽  
pp. 27-32 ◽  
Author(s):  
S. N. Singh
Keyword(s):  
Asymptotic Stability ◽  
Hamiltonian Systems ◽  
Attitude Control ◽  
Sufficient Conditions ◽  
Bilinear Systems ◽  
Feedback Controls ◽  
Control Laws ◽  
Nonlinear Maps ◽  
The Stability ◽  
Necessary And Sufficient

Using the invariance principle of LaSalle [1], sufficient conditions for the existence of linear and nonlinear control laws for local and global asymptotic stability of nonlinear Hamiltonian systems are derived. An instability theorem is also presented which identifies the control laws from the given class which cannot achieve asymptotic stability. Some of the stability results are based on certain results for the univalence of nonlinear maps. A similar approach for the stabilization of bilinear systems which include nonconservative systems in elasticity is used and a necessary and sufficient condition for stabilization is obtained. An application to attitude control of a gyrostat Satellite is presented.

Nonlinear Maps

1997 ◽  
pp. 251-290
Author(s):  
Richard H. Enns ◽  
George McGuire
Keyword(s):  
Nonlinear Maps
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