Perspectives on Law and Legal Institutions As Complex Adaptive Systems
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Jump Bifurcation and Hysteresis in an Infinite-Dimensional Dynamical System of Coupled Spins*
SIAM J. APPL. MATH. (C) 1990 Society for Industrial and Applied Mathematics Vol. 50, No. 1, pp. 108-124, February 1990 008 JUMP BIFURCATION AND HYSTERESIS IN AN INFINITE-DIMENSIONAL DYNAMICAL SYSTEM OF COUPLED SPINS* RENATO E. MIROLLOt AND STEVEN H. STROGATZ: Abstract. This paper studies an infinite-dimensional dynamical system that models a collection of coupled spins in a random magnetic field. A state of the system is given by a self-map of the unit circle. Critical states for the dynamical system correspond to equilibrium configurations of the spins. Exact solutions are obtained for all the critical states and their stability is characterized by analyzing the second variation of the system's potential function at those states. It is proven rigorously that the system exhibits a jump bifurcation and hysteresis as the coupling between spins is varied. Key words, bifurcation, dynamical system, phase transition, spin system AMS(MOS) subject classifications. 58F14, 82A57, 34F05 1. Introduction. There is currently a great deal of interest in the collective behavior of dynamical systems with many interacting subunits [2]. Such systems are very difficult to analyze rigorously unless some simplifying assumptions are made. "Phase models," in which each subunit is characterized by a single phase angle Oi, provide an analytically tractable class of many-body systems. Phase models have been used in a wide variety of scientific contexts, including charge-density wave transport [8], [9], [23], [24], magnetic spin systems [3], [26], oscillating chemical reactions 15], 18], [28], networks of biological oscillators [4], [7], [14], [27], [28], and arrays of Josephson junctions [11], [25]. -
Question-And-Answer-Physics-Today
Questions and answers with Steven Strogatz An applied mathematician notes that for many physics topics, including general relativity and climate science, the whole is often not equal to the sum of the parts. By Jeremy N. A. Matthews April 2015 Bookends: Questions and answers with Steven Strogatz Questions and answers with Peter Pesic Questions and answers with Marcelo Gleiser Questions and answers with Amit Hagar Questions and answers with A. Douglas Stone Steven Strogatz is the Jacob Schurman Professor of Applied Mathematics at Cornell University in Ithaca, New York. He conducts research on dynamical systems in physics, biology, and social science. His 1998 Nature article “Collective dynamics of ‘small-world’ networks” is considered a seminal contribution to complexity research. Strogatz is also an active communicator of mathematics and related topics to the public. He frequently appears on public radio and writes for The New Yorker and other publications. A 2015 recipient of the Lewis Thomas Prize for Writing About Science, he has written books that include Sync: How Order Emerges from Chaos in the Universe, Nature, and Daily Life (Hyperion, 2003) and The Joy of x: A Guided Tour of Math, from One to Infinity (Houghton Mifflin Harcourt, 2012). Strogatz recently published the second edition of a text he wrote more than two decades ago. The new edition of Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering (Westview Press, 2015) contains new exercises on such topics as protein dynamics and superconductivity and covers applications in such emerging fields as sociophysics and systems biology. Physics Today reviewed the book in the April issue. -
Damien Fair, Never at Rest
Spectrum | Autism Research News https://www.spectrumnews.org PROFILES Rising Star: Damien Fair, never at rest BY SARAH DEWEERDT 9 JANUARY 2019 One day last April, Damien Fair chuckled along with the members of his 30-person lab at their monthly lunch meeting as he attempted to maneuver a bowl of soup, a plate of salad and a pair of crutches all at the same time. The associate professor of behavioral neuroscience at Oregon Health and Science University in Portland had broken his ankle in a city-league basketball game the evening before. Fair waved away offers of help and soon got down to business. “All right, teach us something,” he told the lab members who were presenting their work that day. He mostly let the presenters, a graduate student and a research associate, hold the floor. Fair is tall and trim, with a salt-and- pepper goatee and expressive eyebrows. He laughed appreciatively at the visual puns in their PowerPoint presentation — for example, a photograph of a toddler in a wetsuit, a play on the name ‘FreeSurfer,’ software for analyzing brain scans. “Damien never sweats anything — officially,” says Nico Dosenbach, assistant professor of pediatric neurology at Washington University in St. Louis, Missouri. Underneath his cool exterior, though, Fair is intense and driven, says Dosenbach, who has been Fair’s friend since the two were in graduate school. And Fair is not intimidated by conventional notions of status or rank: He doesn’t hesitate to ask other scientists for their data or time — or to offer his in return. These traits have made Fair one of the most productive and sought-after collaborators in the field of brain imaging. -
Truthiness and the Marble Palace
Emory Law Scholarly Commons Emory Law Journal Online Journals 2016 Truthiness and the Marble Palace Chad M. Oldfather Todd C. Peppers Follow this and additional works at: https://scholarlycommons.law.emory.edu/elj-online Recommended Citation Chad M. Oldfather & Todd C. Peppers, Truthiness and the Marble Palace, 65 Emory L. J. Online 2001 (2016). Available at: https://scholarlycommons.law.emory.edu/elj-online/17 This Essay is brought to you for free and open access by the Journals at Emory Law Scholarly Commons. It has been accepted for inclusion in Emory Law Journal Online by an authorized administrator of Emory Law Scholarly Commons. For more information, please contact [email protected]. OLDFATHER_PEPPERS GALLEYSFINAL 1/13/2016 10:12 AM TRUTHINESS AND THE MARBLE PALACE Chad M. Oldfather* Todd C. Peppers** INTRODUCTION Tucked inside the title page of David Lat’s Supreme Ambitions, just after a note giving credit for the cover design and before the copyright notice, sits a standard disclaimer of the sort that appears in all novels: “This is a work of fiction. Names, characters, places, and events either are the products of the author’s imagination or are used fictitiously. Any resemblance to actual persons, living or dead, events or locales is entirely coincidental.”1 These may be the most truly fictional words in the entire book. Its judicial characters are recognizable as versions of real judges, including, among others, Alex Kozinski, Goodwin Liu, Stephen Reinhardt, Antonin Scalia, and Clarence Thomas. Real-life bloggers including Tom Goldstein and Howard Bashman appear as themselves,2 and a blog called Beneath Their Robes, a clear reference to the blog that was Lat’s initial claim to fame3 (this time run by one of the protagonist’s bitter rivals) play a pivotal role in the plot.4 Supreme Ambitions’ observations about judging, clerking, prestige and the culture of elite law schools likewise reflect core truths, albeit via storylines and characters that are often exaggerated almost to the point of caricature. -
Judicial Clerkship Handbook 2013
Career Services Office | CLERKSHIPS JUDICIAL CLERKSHIP HANDBOOK 2013 - 2014 TABLE OF CONTENTS Overview of the Clerkship Program 2 Should I Seek a Clerkship? 3 Where Should I Apply to Clerk? 4 Type of Court 5 State Courts 5 Federal Courts 6 Federal District Court 7 Federal Appellate Court 7 Clerkships with Specialized Courts 8 Bankruptcy Courts 8 U.S. Magistrate Judges 8 U.S. Claims Court 9 U.S. Tax Court 9 Federal Circuit 9 U.S. Court of International Trade 9 U.S. Supreme Court 10 How Do I Apply for Clerkships? 11 Clerkship Application Materials 12 Cover Letter and Resume 13 Transcripts 14 Writing Sample 15 Letters of Recommendation 16 Envelopes and Labels 17 Step-by-Step Instructions 18 Clerkship Interviews, Offers and Acceptances 22 APPENDICES Appendix A: Timeline and Checklist Appendix B: USC Law School Graduates & Students with Clerkships Appendix C: USC Faculty Who Clerked Appendix D: California State Court Hiring Practices Appendix E: Optional Recommender Questionnaire Appendix F: Resources for Researching Judges and Courts Appendix G: Loan Repayment Assistance Program Appendix H: Supplemental Readings Appendix I: Sample Cover Letters Appendix J: Form of Address Appendix K: Mail-Merge Instructions Table of Contents OVERVIEW OF THE CLERKSHIP PROGRAM A judicial clerkship can be a very rewarding work experience for a recent law graduate, and it is a great way to begin your legal career in almost any area of practice. The Law School and the Clerkship Committee strongly support our students’ efforts to apply for judicial clerkships through several means, including the following: ASSIGNING YOU A CLERKSHIP ADVISOR If you participate in the Clerkship Program, we will assign a member of the Clerkship Committee or the Career Services Office to be your advisor throughout the application process. -
10-5-19 Workshop Announcement V2
Cornell University Department of Mathematics K-12 Education and Outreach MATH 5080 – Mathematics for Secondary School Teachers October 5, 2019 u 9:00 am – 2:30 pm (lunch provided) u 406 Malott Hall 8:45 – 9:00 am Bagels & Juice (provided) 9:00 – 9:20 am Introductions 9:20 – 10:20 am Business Math for Entrepreneurs Lee Kaltman, M.A.T. (New Roots Charter School) I will describe the course called Business Math for Entrepreneurs, share some student work, and explain how I use real-world experiences to engage and motivate students to want to learn more. 10:30 – 11:30 am The Beauty of Calculus Steven Strogatz, Ph.D. (Cornell University, Mathematics) Based on my new book, Infinite Powers: How Calculus Reveals the Secrets of the Universe, I will present a broad look at the story of calculus, focusing on the connections between calculus and the laws of nature. 11:30 – 12:00 pm Lunch (provided) 12:00 – 12:50 pm Teaching Statistics in the Age of Data Science Michael Nussbaum, Ph.D. (Cornell University, Mathematics) I will try to summarize my 20 years of experience teaching statistics at Cornell, focusing in particular on the basic undergraduate course, which is a slightly more advanced version of AP Statistics. This course always includes a computer component, but new challenges have arisen with the advent of “Data Science,” which promises to revolutionize both the practice and the teaching of statistics, and applied mathematics in general, by total integration with computing. I will conclude with a demonstration of how some of the new CS-inspired courses are taught at Cornell, with on-screen computing using software like R or Python. -
Judicial Genealogy (And Mythology) of John Roberts: Clerkships from Gray to Brandeis to Friendly to Roberts
The Judicial Genealogy (and Mythology) of John Roberts: Clerkships from Gray to Brandeis to Friendly to Roberts BRAD SNYDER* During his Supreme Court nomination hearings, John Roberts idealized and mythologized the first judge he clerkedfor, Second Circuit Judge Henry Friendly, as the sophisticated judge-as-umpire. Thus far on the Court, Roberts has found it difficult to live up to his Friendly ideal, particularlyin several high-profile cases. This Article addresses the influence of Friendly on Roberts and judges on law clerks by examining the roots of Roberts's distinguishedyet unrecognized lineage of former clerks: Louis Brandeis 's clerkship with Horace Gray, Friendly's clerkship with Brandeis, and Roberts's clerkships with Friendly and Rehnquist. Labeling this lineage a judicial genealogy, this Article reorients clerkship scholarship away from clerks' influences on judges to judges' influences on clerks. It also shows how Brandeis, Friendly, and Roberts were influenced by their clerkship experiences and how they idealized their judges. By laying the clerkship experiences and career paths of Brandeis, Friendly, and Roberts side-by- side in detailed primary source accounts, this Article argues that judicial influence on clerks is more professional than ideological and that the idealization ofjudges and emergence of clerks hips as must-have credentials contribute to a culture ofjudicial supremacy. * Assistant Professor, University of Wisconsin Law School. Thanks to Eleanor Brown, Dan Ernst, David Fontana, Abbe Gluck, Dirk Hartog, Dan -
Particle Dynamics in Inertial Microfluidics
PARTICLE DYNAMICS IN INERTIAL MICROFLUIDICS vorgelegt von Master of Science Christian Schaaf ORCID: 0000-0002-4154-5459 an der Fakultät II – Mathematik und Naturwissenschaften der Technischen Universität Berlin zur Erlangung des akademischen Grades Doktor der Naturwissenschaften – Dr. rer. nat. – genehmigte Dissertation Promotionsausschuss: Vorsitzender: Prof. Dr. Michael Lehmann Erster Gutachter: Prof. Dr. Holger Stark Zweiter Gutachter: Prof. Dr. Roland Netz Tag der wissenschaftlichen Aussprache: 17. September 2020 Berlin 2020 Zusammenfassung Die inertiale Mikrofluidik beschäftigt sich mit laminaren Strömungen von Flüssigkeiten durch mikroskopische Kanäle, bei denen die Trägheitseffekte der Flüssigkeit nicht vernach- lässigt werden können. Befinden sich Teilchen in diesen inertialen Strömungen, ordnen sie sich von selbst an bestimmten Positionen auf der Querschnittsfläche an. Da diese Gleich- gewichtspositionen von den Teilcheneigenschaften abhängen, können so beispielsweise Zellen voneinander getrennt werden. In dieser Arbeit beschäftigen wir uns mit der Dynamik mehrerer fester Teilchen, sowie dem Einfluss der Deformierbarkeit auf die Gleichgewichtsposition einer einzelnen Kapsel. Wir verwenden die Lattice-Boltzmann-Methode, um dieses System zu simulieren. Einen wichtigen Grundstein für das Verständnis mehrerer Teilchen bildet die Dynamik von zwei festen Partikeln. Zunächst klassifizieren wir die möglichen Trajektorien, von denen drei zu ungebundenen Zuständen führen und eine über eine gedämpfte Schwingung in einem gebundenem Zustand endet. Zusätzlich untersuchen wir die inertialen Hubkräfte, welche durch das zweite Teilchen stark beeinflusst werden. Dieser Einfluss hängt vor allem vom Abstand der beiden Teilchen entlang der Flussrichtung ab. Im Anschluss an die Dynamik beschäftigen wir uns genauer mit der Stabilität von Paaren und Zügen bestehend aus mehreren festen Teilchen. Wir konzentrieren uns auf Fälle, in denen die Teilchen sich lateral bereits auf ihren Gleichgewichtspositionen befinden, jedoch nicht entlang der Flussrichtung. -
The Size of the Sync Basin Daniel A
The size of the sync basin Daniel A. Wiley, Steven H. Strogatz, and Michelle Girvan Citation: Chaos: An Interdisciplinary Journal of Nonlinear Science 16, 015103 (2006); doi: 10.1063/1.2165594 View online: http://dx.doi.org/10.1063/1.2165594 View Table of Contents: http://scitation.aip.org/content/aip/journal/chaos/16/1?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Key role of time-delay and connection topology in shaping the dynamics of noisy genetic regulatory networks Chaos 21, 047522 (2011); 10.1063/1.3629984 Chaotic phase synchronization in small-world networks of bursting neurons Chaos 21, 013127 (2011); 10.1063/1.3565027 Coordinate transformation and matrix measure approach for synchronization of complex networks Chaos 19, 033131 (2009); 10.1063/1.3212941 Adaptive dynamical networks via neighborhood information: Synchronization and pinning control Chaos 17, 023122 (2007); 10.1063/1.2737829 Synchronizing weighted complex networks Chaos 16, 015106 (2006); 10.1063/1.2180467 This article is copyrighted as indicated in the article. Reuse of AIP content is subject to the terms at: http://scitation.aip.org/termsconditions. Downloaded to IP: 132.236.27.111 On: Wed, 26 Nov 2014 17:53:35 CHAOS 16, 015103 ͑2006͒ The size of the sync basin Daniel A. Wiley and Steven H. Strogatz Center for Applied Mathematics, Cornell University, Ithaca, New York 14853 Michelle Girvan Santa Fe Institute, Santa Fe, New Mexico 87501 ͑Received 30 September 2005; accepted 19 December 2005; published online 31 March 2006͒ We suggest a new line of research that we hope will appeal to the nonlinear dynamics community, especially the readers of this Focus Issue. -
The Love Song of J. Anthony Kennedy
THE LOVE SONG OF J. ANTHONY KENNEDY Steven M. Klepper† HE JUNE 2015 MARRIAGE equality decision in Obergefell v. Hodges1 fell during the same month as the 100th anniversary of the pub- lication of T.S. Eliot’s The Love Song of J. Alfred Prufrock. There has been a great recent debate over the value of a liberal arts Tdegree. I graduated from Goucher College, and I can tell you that a liberal arts degree can lead to spending your leisure time doing things like writing a Prufrock spoof from the perspective of a sitting justice. Whether that helps or hurts the cause, I do not know. The judiciary, on the contrary, has no influence over either the sword or the purse; no direction either of the strength or of the wealth of the society; and can take no active resolution whatever. It may truly be said to have neither FORCE nor WILL, but merely judgment.2 • • • † Steven Klepper is a principal at Kramon & Graham, P.A. and editor-in-chief of the Maryland Appellate Blog. 1 135 S. Ct. 2584 (2015). 2 Eliot began Prufrock with a quote (in Italian) from THE INFERNO. I’ll begin with a quote from Alexander Hamilton, writing as “Publius” in THE FEDERALIST NO. 78. The reason for these footnotes is that I suspect most or all of this piece will become hopelessly dated in the next ten years, and I wish to be able to inform the future reader and my future self what I was thinking. 19 GREEN BAG 2D 101 Steven M. -
Six Degrees: the Science of a Connected Age by Duncan J
Six degrees: The science of a connected age By Duncan J. Watts Brian Lewis INF 385Q December 1, 2005 Overview . About the author . About the book . Networks and network theory . Small world problem . Overview of some examples . Impressions Duncan J. Watts . From Australia . University College, University of New South Wales, Australian Defence Force Academy (Physics). Went to Cornell . Ph.D. 1997 Cornell University (Theoretical and Applied Mechanics) . Steven Strogatz - advisor (mathematician interested in biology, physics, and sociology) . Snowy tree crickets - biological oscillator . Lazarsfeld Center for the Social Sciences, Columbia University . Santa Fe Institute . Sloan School of Management, MIT. Department of Sociology, Columbia University . Collective Dynamics Group (research program in ISERP) Book Overview . Ch 1 - setup: how he became interested - key concepts . Ch 2 - background . Ch 3, 4, 5 - creation and implications of various models . Ch 6 - spreading of diseases and computer viruses . Ch 7, 8 - social contagion . Ch 9 - organizational robustness . Ch 10 - overview Networks A collection of objects connected to each other in some fashion . Properties of networks . Populations of components that are doing something . Structure of relationships affect behavior . Dynamic . Evolving and self constituting system . Affect multiple disciplines . Complex set of problems Small world problem . "six degrees" property . Six degrees from the President . Kevin Bacon . Party conversation . Stanley Milgram experiment - 1967 . Boston to Nebraska . First name basis . Results were about six A pure branching network Clustering Brief history of network theory . Paul Erdös & Alfred Rényi - random graphs . Anatol Rapoport - random-biased net . Stanley Milgram - "six degrees" . Mark Granovetter - "strength of weak ties" . Physicists - spin systems of magnetism . Social scientists . -
Book Review Essay the Supreme Court's Gatekeepers: the Role of Law Clerks in the Certiorari Process
Book Review Essay The Supreme Court’s Gatekeepers: The Role of Law Clerks in the Certiorari Process COURTIERS OF THE MARBLE PALACE: THE RISE AND INFLUENCE OF THE SUPREME COURT LAW CLERK. By Todd C. Peppers.† Stanford: Stanford University Press, 2006. Pp. 310. $21.95. SORCERERS’ APPRENTICES: 100 YEARS OF LAW CLERKS AT THE UNITED STATES SUPREME COURT. By Artemus Ward‡ & David L. Weiden.‡‡ New York: New York University Press, 2006. Pp. 336. $39.00. Reviewed by David R. Stras* Despite the shroud of secrecy surrounding the Supreme Court, it has become common knowledge that, to varying degrees, the Justices no longer tackle their work alone. Chief Justice Rehnquist, for instance, discussed the role of law clerks publicly, including describing the “cert pool,” in which many of the Justices combine their law clerks to draft memoranda analyzing each of the petitions for review under the Court’s discretionary jurisdiction.1 Other accounts, such as Bob Woodward and Scott Armstrong’s book The Brethren and Ed Lazarus’s book Closed Chambers, go a step further by suggesting that law clerks inappropriately influence their Justices and occa- 2 sionally impose their policy preferences on them. † Assistant Professor, Department of Public Affairs, Roanoke College. ‡ Assistant Professor of Political Science, Northern Illinois University. ‡‡ Assistant Professor of Politics and Government, Illinois State University. * Associate Professor, University of Minnesota Law School. I would like to thank Peggy Cordray, Rich Cordray, Allan Erbsen, Michael Gerhardt, Arthur Hellman, Toby Heytens, Kristin Hickman, Timothy Johnson, Orin Kerr, Trevor Morrison, and John Neiman for their comments and suggestions on an earlier draft.