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In this paper, we survey our recent results on the variational formulation of nonequilibrium thermodynamics for the finite-dimensional case of discrete systems, as well as for the infinite-dimensional case of continuum systems. Starting with the fundamental variational principle of classical mechanics, namely, Hamilton’s principle, we show, with the help of thermodynamic systems with gradually increasing complexity, how to systematically extend it to include irreversible processes. In the finite dimensional cases, we treat systems experiencing the irreversible processes of mechanical friction, heat, and mass transfer in both the adiabatically closed cases and open cases. On the continuum side, we illustrate our theory using the example of multicomponent Navier–Stokes–Fourier systems.

In this monograph we consider the general setting of conformal graph directed Markov systems modeled by countable state symbolic subshifts of finite type. We deal with two classes of such systems: attracting and parabolic. The latter being treated by means of the former. We prove fairly complete asymptotic counting results for multipliers and diameters associated with preimages or periodic orbits ordered by a natural geometric weighting. We also prove the corresponding Central Limit Theorems describing the further features of the distribution of their weights. These results have direct applications to a wide variety of examples, including the case of Apollonian Circle Packings, Apollonian Triangle, expanding and parabolic rational functions, Farey maps, continued fractions, Mannenville-Pomeau maps, Schottky groups, Fuchsian groups, and many more. This gives a unified approach which both recovers known results and proves new results. Our new approach is founded on spectral properties of complexified Ruelle–Perron–Frobenius operators and Tauberian theorems as used in classical problems of prime number theory.

This comprehensive book provides the first unified framework for stability and dissipativity analysis and control design for nonnegative and compartmental dynamical systems, which play a key role in a wide range of fields, including engineering, thermal sciences, biology, ecology, economics, genetics, chemistry, medicine, and sociology. Using the highest standards of exposition and rigor, the authors explain these systems and advance the state of the art in their analysis and active control design. Nonnegative and Compartmental Dynamical Systemspresents the most complete treatment available of system solution properties, Lyapunov stability analysis, dissipativity theory, and optimal and adaptive control for these systems, addressing continuous-time, discrete-time, and hybrid nonnegative system theory. This book is an indispensable resource for applied mathematicians, dynamical systems theorists, control theorists, and engineers, as well as for researchers and graduate students who want to understand the behavior of nonnegative and compartmental dynamical systems that arise in areas such as biomedicine, demographics, epidemiology, pharmacology, telecommunications, transportation, thermodynamics, networks, heat transfer, and power systems.

Modern complex large-scale dynamical systems exist in virtually every aspect of science and engineering, and are associated with a wide variety of physical, technological, environmental, and social phenomena, including aerospace, power, communications, and network systems, to name just a few. This book develops a general stability analysis and control design framework for nonlinear large-scale interconnected dynamical systems, and presents the most complete treatment on vector Lyapunov function methods, vector dissipativity theory, and decentralized control architectures. Large-scale dynamical systems are strongly interconnected and consist of interacting subsystems exchanging matter, energy, or information with the environment. The sheer size, or dimensionality, of these systems necessitates decentralized analysis and control system synthesis methods for their analysis and design. Written in a theorem-proof format with examples to illustrate new concepts, this book addresses continuous-time, discrete-time, and hybrid large-scale systems. It develops finite-time stability and finite-time decentralized stabilization, thermodynamic modeling, maximum entropy control, and energy-based decentralized control. This book will interest applied mathematicians, dynamical systems theorists, control theorists, and engineers, and anyone seeking a fundamental and comprehensive understanding of large-scale interconnected dynamical systems and control.

Fracture networks constitute essential conduits for fluid and heat transport in enhanced geothermal systems (EGSs), yet their characterization is challenging due to the inherent geological complexities. This study develops an integrated inversion framework for effective fracture network characterization. The framework consists of a novel fracture network parameterization method, the covariance matrix adaptation‐evolution strategy (CMA‐ES) for fracture parameter inversion, and the embedded discrete fracture model (EDFM) for robust forward simulation of flow and transport in fractured reservoirs. The proposed fracture network parameterization method uses a background fracture network with fixed geometries and non‐uniform fracture apertures to approximate real‐world fracture networks. CMA‐ES is employed to infer fracture parameters by matching both conservative and sorptive tracer measurements, and multiple parallel CMA‐ES runs are executed to obtain an ensemble of model realizations for uncertainty assessment. Three synthetic EGS case studies with varying complexities demonstrate the effectiveness of the inversion framework in capturing major flow and transport characteristics in fracture networks. The long‐term thermal performances of the EGS reservoirs are appropriately predicted with the inferred fracture network models. This integrated framework offers a feasible solution for fracture network characterization and thermal performance prediction in EGS and also has potential applications in unconventional gas/oil reservoir explorations.

The material properties of thermoplastic polymer parts manufactured by the extrusion-based additive manufacturing process are highly dependent on the thermal history. Different numerical models have been proposed to simulate the thermal history of a 3D-printed part. However, they are limited due to limited geometric applicability; low accuracy; or high computational demand. Can the time–temperature history of a 3D-printed part be simulated by a computationally less demanding, fast numerical model without losing accuracy? This paper describes the numerical implementation of a simplified discrete-event simulation model that offers accuracy comparable to a finite element model but is faster by two orders of magnitude. Two polymer systems with distinct thermal properties were selected to highlight differences in the simulation of the orthotropic response and the temperature-dependent material properties. The time–temperature histories from the numerical model were compared to the time–temperature histories from a conventional finite element model and were found to match closely. The proposed highly parallel numerical model was approximately 300–500 times faster in simulating thermal history compared to the conventional finite element model. The model would enable designers to compare the effects of several printing parameters for specific 3D-printed parts and select the most suitable parameters for the part.

The present work aims to characterize the radiative thermal properties albedo and optical thickness of Juncus maritimus fibers using a FTIR spectrometer. Measurements of normal/directional transmittance and normal and hemispherical reflectance are performed. The numerical determination of the radiative properties is conducted through the computational treatment of the Radiative Transfer Equation (RTE) using the Discrete Ordinate Method (DOM), together with the inverse method, which is done through Gauss linearization. As it is a non-linear system, iterative calculations are necessary, which demand a significant computational cost, and, to optimize this problem, the Neumann method is used for the numerical determination of the parameters. These radiative properties are useful to quantify the radiative effective conductivity.

One of the most challenging tasks in studying precipitation is quantifying how the complexities of individual components contribute to the overall system complexity. To address this, we employed information measures based on Kolmogorov complexity (KC), specifically the Kolmogorov complexity spectrum (KC spectrum) and the Kolmogorov complexity plane (KC plane). We applied these measures to monthly time series data, both measured and simulated by the EBU POM regional climate model, spanning the period from 1982 to 2005 for Sombor (45.78° N, 19.12° E) in Serbia. The variables analyzed included precipitation—a complex physical system—and its individual components: mean temperature, minimum and maximum temperatures, humidity, wind speed, and global radiation. By applying the listed measures to all time series, we calculated normalized KC spectra for each position in the KC plane, displaying interactive master amplitudes against individual amplitudes. We proposed a simplified four-step method to compute the relative change in complexities within the overlapping area beneath the KC spectra. Our results facilitated a discussion on the relationship between the complexity of precipitation and that of its individual components.

Solar Air Heater (SAH) absorbs the irradiation and converts it into thermal energy, which is supplied to flowing fluid for the purpose of drying agricultural products, curing of industrial products, space heating applications and so on. An experimental examination has been conducted to assess the thermal performance of SAH having discrete arc shaped rib element in the absorber plate and analyzed against Flat Plate Solar Air Heater (FPSAH). Performance has been assessed by identifying the various parameters like useful heat gain, surface temperatures of collector plate, flow rate of working fluid, temperatures of air at inlet and exit. Investigation has been performed for flow rates of 0.028 kg/s and 0.045 kg/s. The results indicate that the absorber plate with artificial roughness element shows considerable increase in exit air temperature, heat transfer rate and thermal efficiency. Thermal efficiency of about 70 % is obtained for 0.045 kg/s, which is 13.1% more than that of FPSAH.

We propose a numerical scheme to approximate the weak solutions of the 10-moment Gaussian closure. The moment Gaussian closure for gas dynamics is governed by a conservative hyperbolic system supplemented by entropy inequalities whose solutions satisfy positiveness of density and tensorial pressure. We consider a Suliciu-type relaxation numerical scheme to approximate the solutions. These methods are proved to satisfy all the expected positiveness properties and all the discrete entropy inequalities. The scheme is illustrated by several numerical experiments.