Tag: Hyperbolic

Free Download Fundamentals of Nano-Optics in Hyperbolic van der Waals Materials
English | 2024 | ISBN: 3031757661 | 563 Pages | PDF EPUB (True) | 103 MB
This thesis focuses on the study of phonon polaritons-hybrids of infrared light and lattice vibrations-in van der Waals polar materials, particularly strongly anisotropic (hyperbolic) ones. It combines experiments, analytical theory, and numerical simulations to explore nanoscale optical phenomena that challenge our conventional understanding, such as negative reflection, anomalous refraction and polariton canalization. These studies have paved the way for practical applications in integrated flat optics, such as planar lenses and resonators for nanoscale light. The thesis also introduces the emerging field of twistoptics, aimed at controlling the propagation of light at the nanoscale by stacking slabs of van der Waals materials at different rotation angles, and introduces innovative approaches to tune polariton properties both passively and actively. In addition to providing a solid foundation for future advancements in planar nano-optical devices and helping lay the fundamentals of light-matter interactions in hyperbolic van der Waals materials, the thesis’s didactic approach makes complex phenomena accessible to a broad audience.

Free Download Trigonometric And Hyperbolic Generated Approximation Theory
English | 2025 | ISBN: 9811293856 | 838 Pages | PDF (True) | 12 MB
This monograph is a testimony of the impact over Computational Analysis of some new trigonometric and hyperbolic types of Taylor’s formulae with integral remainders producing a rich collection of approximations of a very wide spectrum.This volume covers perturbed neural network approximations by themselves and with their connections to Brownian motion and stochastic processes, univariate and multivariate analytical inequalities (both ordinary and fractional), Korovkin theory, and approximations by singular integrals (both univariate and multivariate cases). These results are expected to find applications in the many areas of Pure and Applied Mathematics, Computer Science, Engineering, Artificial Intelligence, Machine Learning, Deep Learning, Analytical Inequalities, Approximation Theory, Statistics, Economics, amongst others. Thus, this treatise is suitable for researchers, graduate students, practitioners and seminars of related disciplines, and serves well as an invaluable resource for all Science and Engineering libraries.

Free Download Tushar Das, David Simmons, Mariusz Urbanski, "Geometry and Dynamics in Gromov Hyperbolic Metric Spaces: With an Emphasis on Non-proper Settings"
English | 2017 | ISBN: 1470434652 | PDF | pages: 321 | 4.0 mb
This book presents the foundations of the theory of groups and semigroups acting isometrically on Gromov hyperbolic metric spaces. Particular emphasis is paid to the geometry of their limit sets and on behavior not found in the proper setting. The authors provide a number of examples of groups which exhibit a wide range of phenomena not to be found in the finite-dimensional theory. The book contains both introductory material to help beginners as well as new research results, and closes with a list of attractive unsolved problems.

Free Download Introduction to Hyperbolic Geometry By Arlan Ramsay, Robert D. Richtmyer (auth.)
1995 | 289 Pages | ISBN: 0387943390 | PDF | 13 MB
This book is an introduction to hyperbolic and differential geometry that provides material in the early chapters that can serve as a textbook for a standard upper division course on hyperbolic geometry. For that material, the students need to be familiar with calculus and linear algebra and willing to accept one advanced theorem from analysis without proof. The book goes well beyond the standard course in later chapters, and there is enough material for an honors course, or for supplementary reading. Indeed, parts of the book have been used for both kinds of courses. Even some of what is in the early chapters would surely not be nec essary for a standard course. For example, detailed proofs are given of the Jordan Curve Theorem for Polygons and of the decomposability of poly gons into triangles, These proofs are included for the sake of completeness, but the results themselves are so believable that most students should skip the proofs on a first reading. The axioms used are modern in character and more "user friendly" than the traditional ones. The familiar real number system is used as an in gredient rather than appearing as a result of the axioms. However, it should not be thought that the geometric treatment is in terms of models: this is an axiomatic approach that is just more convenient than the traditional ones.

Free Download Introduction to the Thermomechanics of Continua and Hyperbolic Systems
English | 2024 | ISBN: 3031699505 | 203 Pages | PDF EPUB (True) | 11 MB
The primary aim of this book is to present a unified treatment of the thermomechanics of continua using the axiomatic approach typical of rational mechanics. While many books on continuum mechanics focus on specific types of continuous bodies, such as deformable solid bodies or fluids, this book adopts a general perspective. It presents the mathematical structure of balance laws and constitutive equations as a cohesive whole, with special attention given to the modern theory of constitutive equations. Notable principles such as the principle of material indifference and the contemporary interpretation of the principle of entropy are emphasized. This book will be beneficial not only to engineering students but also to students from other scientific disciplines where aspects of continuum mechanics are studied. It provides an opportunity to view traditionally distinct topics in a broader, interconnected context. To ensure self-consistency, the first part of the book addresses issues related to linear algebra, with a particular focus on linear operators within finite-dimensional vector spaces. The book then offers a detailed exploration of finite deformations of continua, followed by an overview of kinematics. It characterizes the various forces that can exist in a continuum, introduces the stress tensor, and presents the balance laws in both Eulerian and Lagrangian forms. Next, the modern theory of constitutive equations is defined, emphasizing the role of the general principles of material indifference and entropy as criteria for selecting physically acceptable classes of constitutive equations. The resulting field equations are specialized for various cases, including thermoelasticity, Eulerian fluids, Fourier-Navier‒Stokes fluids, and rigid heat conductors. In the final part of the book, partial differential equations in continuum mechanics are discussed, with particular attention given to hyperbolic systems. The method of characteristics is introduced in both linear and nonlinear cases, and the need to expand the class of solutions by introducing weak solutions is discussed, with shock waves being a significant case. As an illustrative example of a weak solution, the Riemann problem is presented for the fluid dynamic model of vehicular traffic, where cars are initially stopped at a red light and then start moving when the light turns green.

Free Download Theory of Electrostatic Waves in Hyperbolic Metamaterials by Afshin Moradi
English | PDF EPUB (True) | 2023 | 239 Pages | ISBN : 3031485955 | 54.8 MB
This book covers electrostatic properties of hyperbolic metamaterials (HMMs), a fascinating class of metamaterials which combine dielectric and metal components. Due to the hyperbolic topology of the isofrequency surface in HMMs, the so-called resonance cone direction exists, and as a result, propagation of quasi-electrostatic waves, or more commonly, electrostatic waves close to the resonance cone with large wave vectors, is possible. However, the investigation of electrostatic wave properties in HMMs is largely overlooked in most works on the subject, and the purpose of this monograph is to fill this gap. This book gives a thorough theoretical treatment of propagation, reflection, and refraction of electrostatic waves in HMMs of various dimensions and geometries. It will be of interest to students and researchers who work on electrical and optical properties of metamaterials.

Free Download Samir Sellami, "Hyperbolic Realism: A Wild Reading of Pynchon’s and Bolaño’s Late Maximalist Fiction"
English | ISBN: 1501360493 | 2024 | 248 pages | EPUB, PDF | 1105 KB + 3 MB
What comes after postmodernism in literature?