Hot Molecules Cold Electrons

Author : Paul J. Nahin
Publisher : Princeton University Press
Page : 232 pages
File Size : 44,5 Mb
Release : 2022-05-10
Category : Science
ISBN : 9780691207841

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Hot Molecules, Cold Electrons by Paul J. Nahin Pdf

An entertaining mathematical exploration of the heat equation and its role in the triumphant development of the trans-Atlantic telegraph cable Heat, like gravity, shapes nearly every aspect of our world and universe, from how milk dissolves in coffee to how molten planets cool. The heat equation, a cornerstone of modern physics, demystifies such processes, painting a mathematical picture of the way heat diffuses through matter. Presenting the mathematics and history behind the heat equation, Hot Molecules, Cold Electrons tells the remarkable story of how this foundational idea brought about one of the greatest technological advancements of the modern era. Paul Nahin vividly recounts the heat equation’s tremendous influence on society, showing how French mathematical physicist Joseph Fourier discovered, derived, and solved the equation in the early nineteenth century. Nahin then follows Scottish physicist William Thomson, whose further analysis of Fourier’s explorations led to the pioneering trans-Atlantic telegraph cable. This feat of engineering reduced the time it took to send a message across the ocean from weeks to minutes. Readers also learn that Thomson used Fourier’s solutions to calculate the age of the earth, and, in a bit of colorful lore, that writer Charles Dickens relied on the trans-Atlantic cable to save himself from a career-damaging scandal. The book’s mathematical and scientific explorations can be easily understood by anyone with a basic knowledge of high school calculus and physics, and MATLAB code is included to aid readers who would like to solve the heat equation themselves. A testament to the intricate links between mathematics and physics, Hot Molecules, Cold Electrons offers a fascinating glimpse into the relationship between a formative equation and one of the most important developments in the history of human communication.

Author : Paul J. Nahin
Publisher : Unknown
Page : 128 pages
File Size : 43,8 Mb
Release : 2020
Category : Heat equation
ISBN : 0691191271

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Hot Molecules & Cold Electrons by Paul J. Nahin Pdf

"This book is a testament to the intimate, mutual embrace of mathematics and physics. It achieves that by telling the story of an historical event of tremendous impact upon society, both spiritually and technically - the mid-19th century construction of the trans-Atlantic telegraph cable, which reduced the time to send a message across the ocean from weeks to minutes. The story of the cable actually begins decades earlier, at the start of the century, with the French mathematical physicist Joseph Fourier's development of the mathematics that the Scottish physicist William Thomson (later Lord Kelvin) would use to analyze the electrical physics of the cable. The story of Fourier opens the book, that of Thomson completes it, and in-between the reader will learn how to derive Fourier's second-order partial differential equation for the flow of heat energy in matter, how Fourier solved the heat equation, how Thomson used Fourier's solutions to calculate the age of the Earth (imagined to be the result of the of an initially molten sphere of blinding brilliance) and, finally, how Thomson showed that the heat equation also describes the Atlantic cable. An epilogue describing the post-Thomson developments completes the book. All readers who have completed first courses at the level of AP-calculus and AP-physics will be able to read this book. This is a perhaps surprising feature of the book, as the mathematics discussed is normally not encountered until the second year (or even later) of college-level work. This book shows that, in fact, the technical material is fully graspable by a college freshman. Unlike a pure technical book, readers will also find a lot of fascinating history in this book (including the bizarre story of how the English novelist Charles Dickens used the Atlantic cable to send a coded message - during his 1867 American reading tour - to avoid a career-damaging scandal concerning his mistress)"--

Author : Ian W. M. Smith,World Scientific (Firm)
Publisher : Imperial College Press
Page : 578 pages
File Size : 40,6 Mb
Release : 2008
Category : Science
ISBN : 9781848162105

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Low Temperatures and Cold Molecules by Ian W. M. Smith,World Scientific (Firm) Pdf

This book brings together, for the first time, the results of recent research in areas ranging from the chemistry of cold interstellar clouds (10-20 K), through laboratory studies of the spectroscopy and kinetics of ions, radicals and molecules, to studies of molecules in liquid helium droplets, to attempts to create molecular (as distinct from atomic) Bose-Einstein condensates.

Author : Paul J. Nahin
Publisher : Princeton University Press
Page : 342 pages
File Size : 43,5 Mb
Release : 2021-10-19
Category : Mathematics
ISBN : 9780691206073

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In Pursuit of Zeta-3 by Paul J. Nahin Pdf

"For centuries, mathematicians have tried, and failed, to solve the zeta-3 problem. This problem is simple in its formulation, but remains unsolved to this day, despite the attempts of some of the world's greatest mathematicians to solve it. The problem can be stated as follows: is there a simple symbolic formula for the following sum: 1+(1/2)^3+(1/3)^3+(1/4)^3+...? Although it is possible to calculate the approximate numerical value of the sum (for those interested, it's 1.20205...), there is no known symbolic expression. A symbolic formula would not only provide an exact value for the sum, but would allow for greater insight into its characteristics and properties. The answers to these questions are not of purely academic interest; the zeta-3 problem has close connections to physics, engineering, and other areas of mathematics. Zeta-3 arises in quantum electrodynamics and in number theory, for instance, and it is closely connected to the Riemann hypothesis. In In Pursuit of zeta-3, Paul Nahin turns his sharp, witty eye on the zeta-3 problem. He describes the problem's history, and provides numerous "challenge questions" to engage readers, along with Matlab code. Unlike other, similarly challenging problems, anyone with a basic mathematical background can understand the problem-making it an ideal choice for a pop math book"--

Author : Paul J. Nahin
Publisher : Springer Nature
Page : 205 pages
File Size : 43,9 Mb
Release : 2024-05-17
Category : Electronic
ISBN : 9783031384165

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The Probability Integral by Paul J. Nahin Pdf

Author : Paul J. Nahin
Publisher : Princeton University Press
Page : 377 pages
File Size : 52,5 Mb
Release : 2024-01-16
Category : Technology & Engineering
ISBN : 9780691235325

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The Mathematical Radio by Paul J. Nahin Pdf

How a modern radio works, told through mathematics, history, and selected puzzles The modern radio is a wonder, and behind that magic is mathematics. In The Mathematical Radio, Paul Nahin explains how radios work, deploying mathematics and historical discussion, accompanied by a steady stream of intriguing puzzles for math buffs to ponder. Beginning with oscillators and circuits, then moving on to AM, FM, and single-sideband radio, Nahin focuses on the elegant mathematics underlying radio technology rather than the engineering. He explores and explains more than a century of key developments, placing them in historical and technological context. Nahin, a prolific author of books on math for the general reader, describes in fascinating detail the mathematical underpinnings of a technology we use daily. He explains and solves, for example, Maxwell’s equations for the electromagnetic field. Readers need only a familarity with advanced high school–level math to follow Nahin’s mathematical discussions. Writing with the nonengineer in mind, Nahin examines topics including impulses in time and frequency, spectrum shifting at the transmitter, the superheterodyne, the physics of single-sideband radio, and FM sidebands. Chapters end with “challenge problems” and an appendix offers solutions, partial answers, and hints. Readers will come away with a new appreciation for the beauty of even the most useful mathematics.

Author : Paul J. Nahin
Publisher : Springer Nature
Page : 542 pages
File Size : 40,5 Mb
Release : 2020-06-27
Category : Science
ISBN : 9783030437886

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Inside Interesting Integrals by Paul J. Nahin Pdf

What’s the point of calculating definite integrals since you can’t possibly do them all? What makes doing the specific integrals in this book of value aren’t the specific answers we’ll obtain, but rather the methods we’ll use in obtaining those answers; methods you can use for evaluating the integrals you will encounter in the future. This book, now in its second edition, is written in a light-hearted manner for students who have completed the first year of college or high school AP calculus and have just a bit of exposure to the concept of a differential equation. Every result is fully derived. If you are fascinated by definite integrals, then this is a book for you. New material in the second edition includes 25 new challenge problems and solutions, 25 new worked examples, simplified derivations, and additional historical discussion.

Author : Paul J. Nahin
Publisher : Princeton University Press
Page : 424 pages
File Size : 46,7 Mb
Release : 2009-08-17
Category : Mathematics
ISBN : 9781400833467

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Mrs. Perkins's Electric Quilt by Paul J. Nahin Pdf

An incomparable collection of stimulating math puzzles from bestselling author Paul Nahin What does quilting have to do with electric circuit theory? The answer is just one of the fascinating ways that best-selling popular math writer Paul Nahin illustrates the deep interplay of math and physics in the world around us in his latest book of challenging mathematical puzzles, Mrs. Perkins's Electric Quilt. With his trademark combination of intriguing mathematical problems and the historical anecdotes surrounding them, Nahin invites readers on an exciting and informative exploration of some of the many ways math and physics combine to create something vastly more powerful, useful, and interesting than either is by itself. In a series of brief and largely self-contained chapters, Nahin discusses a wide range of topics in which math and physics are mutually dependent and mutually illuminating, from Newtonian gravity and Newton's laws of mechanics to ballistics, air drag, and electricity. The mathematical subjects range from algebra, trigonometry, geometry, and calculus to differential equations, Fourier series, and theoretical and Monte Carlo probability. Each chapter includes problems—some three dozen in all—that challenge readers to try their hand at applying what they have learned. Just as in his other books of mathematical puzzles, Nahin discusses the historical background of each problem, gives many examples, includes MATLAB codes, and provides complete and detailed solutions at the end. Mrs. Perkins's Electric Quilt will appeal to students interested in new math and physics applications, teachers looking for unusual examples to use in class—and anyone who enjoys popular math books.

Author : N. N. Sobolev
Publisher : Nova Publishers
Page : 296 pages
File Size : 41,9 Mb
Release : 1989
Category : Low temperature plasmas
ISBN : UVA:X001404640

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Electron-excited Molecules in Nonequilibrium Plasma by N. N. Sobolev Pdf

A translation of studies published in Russian in 1985 (Nauka House) the results from research conducted principally between 1972 and 1982 at the Laboratory of Low-Temperature Plasma Optics, Lebedev Physics Institute. Primary attention is on issues fundamental for a physical substantiation of spectra

Author : Roman Krems,Bretislav Friedrich,William C Stwalley
Publisher : CRC Press
Page : 756 pages
File Size : 45,6 Mb
Release : 2009-06-25
Category : Science
ISBN : 9781420059045

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Cold Molecules by Roman Krems,Bretislav Friedrich,William C Stwalley Pdf

The First Book on Ultracold MoleculesCold molecules offer intriguing properties on which new operational principles can be based (e.g., quantum computing) or that may allow researchers to study a qualitatively new behavior of matter (e.g., Bose-Einstein condensates structured by the electric dipole interaction). This interdisciplinary book discusse

Author : Anonim
Publisher : Unknown
Page : 834 pages
File Size : 50,5 Mb
Release : 1977
Category : Periodicals
ISBN : CHI:18210312

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Soviet Physics by Anonim Pdf

Author : Vadim Kaloshin,Ke Zhang
Publisher : Princeton University Press
Page : 218 pages
File Size : 54,6 Mb
Release : 2020-11-03
Category : Mathematics
ISBN : 9780691202525

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Arnold Diffusion for Smooth Systems of Two and a Half Degrees of Freedom by Vadim Kaloshin,Ke Zhang Pdf

The first complete proof of Arnold diffusion—one of the most important problems in dynamical systems and mathematical physics Arnold diffusion, which concerns the appearance of chaos in classical mechanics, is one of the most important problems in the fields of dynamical systems and mathematical physics. Since it was discovered by Vladimir Arnold in 1963, it has attracted the efforts of some of the most prominent researchers in mathematics. The question is whether a typical perturbation of a particular system will result in chaotic or unstable dynamical phenomena. In this groundbreaking book, Vadim Kaloshin and Ke Zhang provide the first complete proof of Arnold diffusion, demonstrating that that there is topological instability for typical perturbations of five-dimensional integrable systems (two and a half degrees of freedom). This proof realizes a plan John Mather announced in 2003 but was unable to complete before his death. Kaloshin and Zhang follow Mather's strategy but emphasize a more Hamiltonian approach, tying together normal forms theory, hyperbolic theory, Mather theory, and weak KAM theory. Offering a complete, clean, and modern explanation of the steps involved in the proof, and a clear account of background material, this book is designed to be accessible to students as well as researchers. The result is a critical contribution to mathematical physics and dynamical systems, especially Hamiltonian systems.

Author : Paul J. Nahin
Publisher : Princeton University Press
Page : 281 pages
File Size : 52,8 Mb
Release : 2011-05-04
Category : Mathematics
ISBN : 9781400839292

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Digital Dice by Paul J. Nahin Pdf

Some probability problems are so difficult that they stump the smartest mathematicians. But even the hardest of these problems can often be solved with a computer and a Monte Carlo simulation, in which a random-number generator simulates a physical process, such as a million rolls of a pair of dice. This is what Digital Dice is all about: how to get numerical answers to difficult probability problems without having to solve complicated mathematical equations. Popular-math writer Paul Nahin challenges readers to solve twenty-one difficult but fun problems, from determining the odds of coin-flipping games to figuring out the behavior of elevators. Problems build from relatively easy (deciding whether a dishwasher who breaks most of the dishes at a restaurant during a given week is clumsy or just the victim of randomness) to the very difficult (tackling branching processes of the kind that had to be solved by Manhattan Project mathematician Stanislaw Ulam). In his characteristic style, Nahin brings the problems to life with interesting and odd historical anecdotes. Readers learn, for example, not just how to determine the optimal stopping point in any selection process but that astronomer Johannes Kepler selected his second wife by interviewing eleven women. The book shows readers how to write elementary computer codes using any common programming language, and provides solutions and line-by-line walk-throughs of a MATLAB code for each problem. Digital Dice will appeal to anyone who enjoys popular math or computer science.

Author : Anonim
Publisher : Unknown
Page : 1144 pages
File Size : 48,8 Mb
Release : 2006
Category : Nuclear fusion
ISBN : UIUC:30112079625627

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Nuclear Fusion by Anonim Pdf

Author : Brady
Publisher : Unknown
Page : 952 pages
File Size : 50,9 Mb
Release : 1990-01-02
Category : Electronic
ISBN : 0471520632

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General Chemistry by Brady Pdf