Few artworks have been the subject of more extensive modern interpretation than Melencolia I by renowned artist, mathematician, and scientist Albrecht Durer (1514). And yet, did each of these art experts and historians miss a secret manifesto that Durer included within the engraving? This is the first work to decrypt secrets within Melencolia I based not on guesswork, but Durer's own writings, other subliminal artists that inspired him (i.e., Leonardo da Vinci), the Jewish and Christian Bibles, and books that inspired Durer (De Occulta Philosophia and the Hieorglyphica). To read the covert message of Melencolia I is to understand that Durer was a humanist in his interests in mathematics, science, poetry, and antiquity. This book recognizes his unparalleled power with the burin, his mathematical skill in perspective, his dedication to precise language, and his acute observation of nature. Melencolia I may also be one of the most controversial (and at the time most criminal) pieces of art as it hid Durer's disdain for the hierarchy of the Catholic Church, the Kaiser, and the Holy Roman Empire from the general public for centuries. This book closely ties the origins of philosophy (science) and the work of a Renaissance master together, and will be of interest for anyone who loves scientific history, art interpretation, and secret manifestos.

The book contains a detailed account of numerical solutions of differential equations of elementary problems of Physics using Euler and 2nd order Runge-Kutta methods and Mathematica 6.0. The problems are motion under constant force (free fall), motion under Hooke's law force (simple harmonic motion), motion under combination of Hooke's law force and a velocity dependent damping force (damped harmonic motion) and radioactive decay law. Also included are uses of Mathematica in dealing with complex numbers, in solving system of linear equations, in carrying out differentiation and integration, and in dealing with matrices.

This volume presents lectures given at the Wisła 20-21 Winter School and Workshop: Groups, Invariants, Integrals, and Mathematical Physics, organized by the Baltic Institute of Mathematics. The lectures were dedicated to differential invariants – with a focus on Lie groups, pseudogroups, and their orbit spaces – and Poisson structures in algebra and geometry and are included here as lecture notes comprising the first two chapters. Following this, chapters combine theoretical and applied perspectives to explore topics at the intersection of differential geometry, differential equations, and category theory. Specific topics covered include: The multisymplectic and variational nature of Monge-Ampère equations in dimension four Integrability of fifth-order equations admitting a Lie symmetry algebra Applications of the van Kampen theorem for groupoids to computation of homotopy types of striped surfaces A geometric framework to compare classical systems of PDEs in the category of smooth manifolds Groups, Invariants, Integrals, and Mathematical Physics is ideal for graduate students and researchers working in these areas. A basic understanding of differential geometry and category theory is assumed.

This book introduces the reader into the field of the physics of processes occurring in porous media. It targets Master and PhD students who need to gain fundamental understanding the impact of confinement on transport and phase change processes. The book gives brief overviews of topics like thermodynamics, capillarity and fluid mechanics in order to launch the reader smoothly into the realm of porous media. In-depth discussions are given of phase change phenomena in porous media, single phase flow, unsaturated flow and multiphase flow. In order to make the topics concrete the book contains numerous example calculations. Further, as much experimental data as possible is plugged in to give the reader the ability to quantify phenomena.

Synchrotron radiation is the name given to the radiation which occurs when charged particles are accelerated in a curved path or orbit. Classically, any charged particle which moves in a curved path or is accelerated in a straight-line path will emit electromagnetic radiation. Various names are given to this radiation in different contexts. Thus circular particle accelerators are called synchrotrons, this is where charged particles are accelerated to very high speeds and the radiation is referred to as synchrotron radiation.Suitable for a summer short course or one term lecture series this text introduces the subject, starting with some historical background then covering basic concepts such as flux, intensity, brilliance, emittance and Liouville's theorem. The book then covers the properties of synchrotron radiation, insertion devices, beamlines and monochromators before finishing with an introduction to free electron lasers and an overview of the most common techniques and applications of this technology.

For a physicist, "noise" is not just about sounds, but refers to any random physical process that blurs measurements, and in so doing stands in the way of scientific knowledge. This book deals with the most common types of noise, their properties, and some of their unexpected virtues. The text explains the most useful mathematical concepts related to noise. Finally, the book aims at making this subject more widely known and to stimulate the interest for its study in young physicists.

Physics and the Environment directly connects the physical world to environmental issues that the world is facing today and will face in the future. It shows how the first and second laws of thermodynamics limit the efficiencies of fossil fuel energy conversions to less than 100%, while also discussing how clever technologies can enhance overall performance. It also extensively discusses renewable forms of energy, their physical constraints and how we must use science and engineering as tools to solve problems instead of opinion and politics. Dr. Kyle Forinash takes you on a journey of understanding our mature and well developed technologies for using fossil fuel resources and how we are unlikely to see huge gains in their efficiency as well as why their role in climate change ought to be an argument for their replacement sooner rather than later. He also discusses the newest technologies in employing renewable resources and how it is important to understand their physical constrains in order to make a smooth transition to them. An entire chapter is dedicated to energy storage, a core question in renewable energy as well as another chapter on the technical issues of nuclear energy. The book ends with a discussion on how no environmental solution, no matter how clever from a technical aspect, will succeed if there are cheaper alternative, even if those alternatives have undesirable features associated with them.

This book is based on a commitment to teaching science to everybody. What may work for training professional scientists does not work for general science education. Students bring to the classrooms preconceived attitudes, as well as the emotional baggage called ""science anxiety."" Students may regard science as cold, unfriendly, and even inherently hostile and biased against women. This book has been designed to deal with each of these issues and results from research in both Denmark and the United States. The first chapter discusses student attitudes towards science and the second discusses science anxiety. The connection between the two is discussed before the introduction of constructivism as a pedagogy that can aid science learning if it also addresses attitudes and anxieties. Much of the book elucidates what the authors have learned as science teachers and science education researchers. They studied various groups including university students majoring in the sciences, mathematics, humanities, social sciences, business, nursing, and education; high school students; teachers' seminary students; science teachers at all levels from middle school through college; and science administrators. The insights of these groups constitute the most important feature of the book, and by sharing them, the authors hope to help their fellow science teachers to understand student attitudes about science, to recognize the connections between these and science anxiety, and to see how a pedagogy that takes these into account can improve science learning.

This book describes the advanced stability theories for magnetically confined fusion plasmas, especially in tokamaks. As the fusion plasma sciences advance, the gap between the textbooks and cutting-edge researches gradually develops.