Математика
Различные книги в жанре МатематикаДвижение на плоскости и в пространстве. Теорема Шаля и аппарат кватернионов
Как можно представить любое движение на плоскости и в пространстве, используя всего два простых действия? В чём заключается теорема Шаля? Что такое углы Эйлера и почему с ними не всегда удобно работать? Существует ли аналог комплексных чисел в трёхмерном пространстве? Как четырёхмерное пространство «помогает» трёхмерному в описании движений? За счёт чего аппарат кватернионов так упрощает расчёты в компьютерной графике? Рассказывает Николай Николаевич Андреев кандидат физико-математических наук, заведующий лабораторией популяризации и пропаганды математики Математического института им. В.А. Стеклова РАН. наука, научпоп, николай андреев, математика, научпросвет, ран, пропаганда математики, популяризация математики, движение на плоскости, движение в пространстве, теорема шаля, углы эйлера, комплексные числа, трёхмерное пространство, четырёхмерное пространство, кватернионы, аппарат кватернионов, мехмат, математический институт
Atomic Physics
Atomic Physics provides a concise treatment of atomic physics and a basis to prepare for work in other disciplines that are underpinned by atomic physics such as chemistry, biology and several aspects of engineering science. The focus is mainly on atomic structure since this is what is primarily responsible for the physical properties of atoms. After a brief introduction to some basic concepts, the perturbation theory approach follows the hierarchy of interactions starting with the largest. The other interactions of spin, and angular momentum of the outermost electrons with each other, the nucleus and external magnetic fields are treated in order of descending strength. A spectroscopic perspective is generally taken by relating the observations of atomic radiation emitted or absorbed to the internal energy levels involved. X-ray spectra are then discussed in relation to the energy levels of the innermost electrons. Finally, a brief description is given of some modern, laser based, spectroscopic methods for the high resolution study of the nest details of atomic structure.
International Linear Collider (ILC)
The International Linear Collider (ILC) is a mega-scale, technically complex project, requiring large financial resources and cooperation of thousands of scientists and engineers from all over the world. Such a big and expensive project has to be discussed publicly, and the planned goals have to be clearly formulated. This book advocates for the demand for the project, motivated by the current situation in particle physics. The natural and most powerful way of obtaining new knowledge in particle physics is to build a new collider with a larger energy. In this approach, the Large Hadron Collider (LHC) was created and is now operating at the world record center of-mass energy of 13 TeV. Although the design of colliders with a larger energy of 50-100 TeV has been discussed, the practical realization of such a project is not possible for another 20-30 years. Of course, many new results are expected from LHC over the next decade. However, we must also think about other opportunities, and in particular, about the construction of more dedicated experiments. There are many potentially promising projects, however, the most obvious possibility to achieve significant progress in particle physics in the near future is the construction of a linear e+e- collider with energies in the range (250-1000) GeV. Such a project, the ILC, is proposed to be built in Kitakami, Japan. This book will discuss why this project is important and which new discoveries can be expected with this collider.
Spin-Wave Theory and its Applications to Neutron Scattering and THz Spectroscopy
Two of the most powerful tools used to study magnetic materials are inelastic neutron scattering and THz spectroscopy. Because the measured spectra provide a dynamical fingerprint of a magnetic material, those tools enable scientists to unravel the structure of complex magnetic states and to determine the microcscopic interactions that produce them. This book discusses the experimental techniques of inleastic neutron scattering and THz spectroscopy and provides the theoretical tools required to analyze their measurements using spin-wave theory. For most materials, this analysis can resolve the microscopic magnetic interactions such as exchange, anisotropy, and Dzyaloshinskii-Moriya interactions. Assuming a background in elementary statistical mechanics and a familiarity with the quantized harmonic oscillator, this book presents a comprehensive review of spin-wave theory and its applications to both inelastic neutron scattering and THz spectroscopy. Spin-wave theory is used to study several model magnetic systems, including non-collinear magnets such as spirals and cycloids that are produced by geometric frustration, competing exchange interactions, or Dzyaloshinskii-Moriya interactions. Several case studies utilizing spin-wave theory to analyze inelastic neutron-scattering and THz spectroscopy measurements are presented. These include both single crystals and powders and both oxides and molecule-based magnets. In addition to sketching the numerical techniques used to fit dynamical spectra based on microscopic models, this book also contains over 70 exercises that can be performed by beginning graduate students.
Truth and Traceability in Physics and Metrology
Metrological data is known to be blurred by the imperfections of the measuring process. In retrospect, for about two centuries regular or constant errors were no focal point of experimental activities, only irregular or random error were. Today's notation of unknown systematic errors is in line with this. Confusingly enough, the worldwide practiced approach to belatedly admit those unknown systematic errors amounts to consider them as being random, too. This book discusses a new error concept dispensing with the common practice to randomize unknown systematic errors. Instead, unknown systematic errors will be treated as what they physically are- namely as constants being unknown with respect to magnitude and sign. The ideas considered in this book issue a proceeding steadily localizing the true values of the measurands and consequently traceability.
Quantum Metrology with Photoelectrons
Since the turn of the century, the increasing availability of photoelectron imaging experiments, along with the increasing sophistication of experimental techniques, and the availability of computational resources for analysis and numerics, has allowed for significant developments in such photoelectron metrology. Quantum Metrology with Photoelectrons, Volume 2: Applications and Advances discusses the fundamental concepts along with recent and emerging applications. Volume 2 explores the applications and development of quantum metrology schemes based on photoelectron measurements. The author begins with a brief historical background on «complete» photoionization experiments, followed by the details of state reconstruction methodologies from experimental measurements. Three specific applications of quantum metrology schemes are discussed in detail. In addition, the book provides advances, future directions, and an outlook including (ongoing) work to generalise these schemes and extend them to dynamical many-body systems. Volume 2 will be of interest to readers wishing to see the (sometimes messy) details of state reconstruction from photoelectron measurements as well as explore the future prospects for this class of metrology.
Quantum Metrology with Photoelectrons
Since the turn of the century, the increasing availability of photoelectron imaging experiments, along with the increasing sophistication of experimental techniques, and the availability of computational resources for analysis and numerics, has allowed for significant developments in such photoelectron metrology. Quantum Metrology with Photoelectrons, Volume 1: Foundations discusses the fundamental concepts along with recent and emerging applications. The core physics is that of photoionization, and Volume 1 addresses this topic. The foundational material is presented in part as a tutorial with extensive numerical examples and also in part as a collected reference to the relevant theoretical treatments from the literature for a range of cases. Topics are discussed with an eye to developing general quantum metrology schemes, in which full quantum state reconstruction of the photoelectron wavefunction is the goal. In many cases, code and/or additional resources are available online. Consequently, it is hoped that readers at all levels will find something of interest and that the material provides something rather different from existing textbooks.
Gravity, Magnetic and Electromagnetic Gradiometry
Gradiometry is a multidisciplinary area that combines theoretical and applied physics, ultra-low noise electronics, precision engineering, and advanced signal processing. All physical fields have spatial gradients that fall with distance from their sources more rapidly than the field strength itself. This makes the gradient measurements more difficult. However, there has been a considerable investment, both in terms of time and money, into the development of various types of gradiometers driven by the extremely valuable type of information that is contained in gradients. Applications include the search for oil, gas, and mineral resources, GPS-free navigation, defence, space missions, medical research, and some other applications. The author describes gravity gradiometers, magnetic gradiometers, and electromagnetic (EM) gradiometers. The first two types do not require any active sources of the primary physical fields whose gradients are measured, such as gravity field and ambient magnetic field. EM gradiometers do require a primary EM field, pulsed, or sinusoidal, which propagates through media and creates a secondary EM field. The latter one contains information about the non uniformness of electromagnetically active media such as conductivity and magnetic permeability contrasts. These anomalies are the boundaries of mineral deposits, oil and gas traps, underground water reserves, buried artifacts, unexploded ordnance (UXO), nuclear submarines, and even cancerous human tissue. This book provides readers with a comprehensive introduction, history, potential applications, and current developments in relation to some of the most advanced technologies in the 21st Century. Most of the developments are strictly controlled by Defence Export Control rules and regulations, introduced in all developed countries that typically require permission to transfer relevant information from one country to another. The book is based on the materials that have been available in public domain such as scientific journals, conferences, extended abstracts, and online presentations. In addition, medical applications of EM gradiometers are exempt from any control, and some new results relevant to breast cancer early detection research are published in this book for the first time.
Lectures on Selected Topics in Mathematical Physics
This book provides an introduction to Lie Theory for first year graduate students and professional physicists who may not have across the theory in their studies. In particular, it is a summary overview of the theory of finite groups, a brief description of a manifold, and then an informal development of the theory of one-parameter Lie groups, especially as they apply to ordinary differential equations. The treatment is informal, but systematic and reasonably self-contained, as it assumes a familiarity with basic physics and applied calculus, but it does not assume additional mathematical training. Interested readers should have a fair chance of finding symmetries of a second order differential equation and should be able to use it to reduce the order of the differential equation.
Defining and Measuring Nature
Weights and measures form an essential part of our ingrained view of the world. It is just about impossible to function effectively without some internalized system of measurement. In this volume, I outline a history of the science of measurement, and the