Sornette, Didier 1957
Overview
Works:  124 works in 267 publications in 3 languages and 5,479 library holdings 

Genres:  History Conference papers and proceedings 
Roles:  Author, Editor, Author of introduction, Thesis advisor 
Classifications:  HB3722, 332.63222 
Publication Timeline
.
Most widely held works about
Didier Sornette
Most widely held works by
Didier Sornette
Why stock markets crash : critical events in complex financial systems by
Didier Sornette(
Book
)
21 editions published between 2003 and 2011 in English and Undetermined and held by 829 WorldCat member libraries worldwide
Most attempts to explain market failure seek  with little hard science  to pinpoint triggering mechanisms that occur hours, days, or weeks before the collapse. Sornette proposes a radically different view: the underlying cause can be sought months and even years before the abrupt, catastrophic event in the buildup of cooperative speculation, which often translates into an accelerating rise of the market price, otherwise known as a "bubble". Anchoring his stepbystep analysis in leadingedge physical and statistical modelling techniques, he unearths insights and some predictions  among them, that the "end of the growth era" will occur around 2050
21 editions published between 2003 and 2011 in English and Undetermined and held by 829 WorldCat member libraries worldwide
Most attempts to explain market failure seek  with little hard science  to pinpoint triggering mechanisms that occur hours, days, or weeks before the collapse. Sornette proposes a radically different view: the underlying cause can be sought months and even years before the abrupt, catastrophic event in the buildup of cooperative speculation, which often translates into an accelerating rise of the market price, otherwise known as a "bubble". Anchoring his stepbystep analysis in leadingedge physical and statistical modelling techniques, he unearths insights and some predictions  among them, that the "end of the growth era" will occur around 2050
Critical phenomena in natural sciences : chaos, fractals, selforganization, and disorder : concepts and tools by
Didier Sornette(
Book
)
39 editions published between 2000 and 2007 in English and held by 603 WorldCat member libraries worldwide
"The emphasis of the book is on a clear understanding of concepts and methods, while it also provides the tools that can be of immediate use in applications. Although this book evolved out of a course for graduate students, it will be of great interest to researchers and engineers, as well as to postdocs in geophysics and meteorology."Jacket
39 editions published between 2000 and 2007 in English and held by 603 WorldCat member libraries worldwide
"The emphasis of the book is on a clear understanding of concepts and methods, while it also provides the tools that can be of immediate use in applications. Although this book evolved out of a course for graduate students, it will be of great interest to researchers and engineers, as well as to postdocs in geophysics and meteorology."Jacket
Extreme financial risks : from dependence to risk management by
Yannick Malevergne(
Book
)
20 editions published between 2006 and 2012 in English and held by 228 WorldCat member libraries worldwide
Offering an original treatment of the domains of Portfolio analysis and optimization, along with the associated risk assessment and management, this book focuses mainly on the concepts and tools that remain valid for large and extreme price moves. It also places strong emphasis on the theory of copulas and their empirical testing and calibration
20 editions published between 2006 and 2012 in English and held by 228 WorldCat member libraries worldwide
Offering an original treatment of the domains of Portfolio analysis and optimization, along with the associated risk assessment and management, this book focuses mainly on the concepts and tools that remain valid for large and extreme price moves. It also places strong emphasis on the theory of copulas and their empirical testing and calibration
Scale invariance and beyond : Les Houches Workshop, March 1014, 1997 by
Les Houches Workshop(
Book
)
6 editions published in 1997 in English and held by 127 WorldCat member libraries worldwide
This book is an excellent introduction to the concept of scale invariance, which is a growing field of research with wide applications. It describes where and how symmetry under scale transformation (and its various forms of partial breakdown) can be used to analyze solutions of a problem without the need to explicitly solve it. The first part gives descriptions of tools and concepts; the second is devoted to recent attempts to go beyond the invariance or symmetry breaking, to discuss causes and consequences, and to extract useful information about the system. Examples are carefully worked out in fields as diverse as condensed matter physics, population dynamics, earthquake physics, turbulence, cosmology and finance
6 editions published in 1997 in English and held by 127 WorldCat member libraries worldwide
This book is an excellent introduction to the concept of scale invariance, which is a growing field of research with wide applications. It describes where and how symmetry under scale transformation (and its various forms of partial breakdown) can be used to analyze solutions of a problem without the need to explicitly solve it. The first part gives descriptions of tools and concepts; the second is devoted to recent attempts to go beyond the invariance or symmetry breaking, to discuss causes and consequences, and to extract useful information about the system. Examples are carefully worked out in fields as diverse as condensed matter physics, population dynamics, earthquake physics, turbulence, cosmology and finance
Theory of Zipf's law and beyond by
A. I Saichev(
Book
)
15 editions published between 2009 and 2010 in English and German and held by 83 WorldCat member libraries worldwide
"Zipf's law is one of the few quantitative reproducible regularities found in economics. It states that, for most countries, the size distributions of city sizes and of firms are power laws with a specific exponent: the number of cities and of firms with sizes greater than S is inversely proportional to S. Zipf's law also holds in many other scientific fields. Most explanations start with Gibrat's law of proportional growth (also known as "preferential attachment'' in the application to network growth) but need to incorporate additional constraints and ingredients introducing deviations from it. This book presents a general theoretical derivation of Zipf's law, providing a synthesis and extension of previous approaches. The general theory is presented in the language of firm dynamics for the sake of convenience but applies to many other systems. It takes into account (i) timevarying firm creation, (ii) firm's exit resulting from both a lack of sufficient capital and sudden external shocks, (iii) the coupling between firm's birth rate and the growth of the value of the population of firms. The robustness of Zipf's law is understood from the approximate validity of a general balance condition. A classification of the mechanisms responsible for deviations from Zipf's law is also offered."Publisher's website
15 editions published between 2009 and 2010 in English and German and held by 83 WorldCat member libraries worldwide
"Zipf's law is one of the few quantitative reproducible regularities found in economics. It states that, for most countries, the size distributions of city sizes and of firms are power laws with a specific exponent: the number of cities and of firms with sizes greater than S is inversely proportional to S. Zipf's law also holds in many other scientific fields. Most explanations start with Gibrat's law of proportional growth (also known as "preferential attachment'' in the application to network growth) but need to incorporate additional constraints and ingredients introducing deviations from it. This book presents a general theoretical derivation of Zipf's law, providing a synthesis and extension of previous approaches. The general theory is presented in the language of firm dynamics for the sake of convenience but applies to many other systems. It takes into account (i) timevarying firm creation, (ii) firm's exit resulting from both a lack of sufficient capital and sudden external shocks, (iii) the coupling between firm's birth rate and the growth of the value of the population of firms. The robustness of Zipf's law is understood from the approximate validity of a general balance condition. A classification of the mechanisms responsible for deviations from Zipf's law is also offered."Publisher's website
Market risk and financial markets modeling by
Didier Sornette(
Book
)
17 editions published between 2012 and 2014 in English and held by 53 WorldCat member libraries worldwide
Annotation
17 editions published between 2012 and 2014 in English and held by 53 WorldCat member libraries worldwide
Annotation
Risk management : gestion des risques en entreprise, banque et assurance by
Laurent Pierandrei(
Book
)
1 edition published in 2015 in French and held by 38 WorldCat member libraries worldwide
Ce manuel propose un cours de référence pour la formation au management des risques dans une perspective globale et transdisciplinaire. Après avoir posé le cadre théorique (concepts fondamentaux, origines, stratégies face au risque), il présente les outils (cartographie, évaluation, instruments d'assurance et de financement) et les liens avec l'audit et le contrôle interne. Enfin, la gestion des risques est largement déployée dans les banques et les entreprises d'assurance, avec un contexte réglementaire (Bâle 3, Solvency 2) et des méthodes spécifiques. Ce manuel permet de mettre en pratique les techniques de gestion du risque opérationnel et financier au travers de nombreux exemples et études de cas [4e de couv.]
1 edition published in 2015 in French and held by 38 WorldCat member libraries worldwide
Ce manuel propose un cours de référence pour la formation au management des risques dans une perspective globale et transdisciplinaire. Après avoir posé le cadre théorique (concepts fondamentaux, origines, stratégies face au risque), il présente les outils (cartographie, évaluation, instruments d'assurance et de financement) et les liens avec l'audit et le contrôle interne. Enfin, la gestion des risques est largement déployée dans les banques et les entreprises d'assurance, avec un contexte réglementaire (Bâle 3, Solvency 2) et des méthodes spécifiques. Ce manuel permet de mettre en pratique les techniques de gestion du risque opérationnel et financier au travers de nombreux exemples et études de cas [4e de couv.]
Market Risk and Financial Markets Modeling Perm Winter School(
)
1 edition published in 2012 in English and held by 16 WorldCat member libraries worldwide
1 edition published in 2012 in English and held by 16 WorldCat member libraries worldwide
Physics of black holes : a guided tour by
W Beiglbck(
)
3 editions published in 2009 in English and held by 15 WorldCat member libraries worldwide
This volume serves as a tutorial, highlevel guided tour through the black hole landscape: information paradox and blackhole thermodynamics, numerical simulations of black hole formation and collisions, braneworld scenarios and stability of black holes with respect to perturbations are treated in great detail
3 editions published in 2009 in English and held by 15 WorldCat member libraries worldwide
This volume serves as a tutorial, highlevel guided tour through the black hole landscape: information paradox and blackhole thermodynamics, numerical simulations of black hole formation and collisions, braneworld scenarios and stability of black holes with respect to perturbations are treated in great detail
Earthquakes : from chemical alteration to mechanical rupture by
Didier Sornette(
Book
)
5 editions published in 1999 in English and held by 13 WorldCat member libraries worldwide
5 editions published in 1999 in English and held by 13 WorldCat member libraries worldwide
Professor Zipf goes to Wall Street by
Yannick Malevergne(
Book
)
8 editions published between 2009 and 2010 in English and held by 10 WorldCat member libraries worldwide
The heavytailed distribution of firm sizes first discovered by Zipf (1949) is one of the best established empirical facts in economics. We show that it has strong implications for asset pricing. Due to the concentration of the market portfolio when the distribution of the capitalization of firms is sufficiently heavytailed, an additional risk factor generically appears even for very large economies. Our twofactor model is as successful empirically as the threefactor FamaFrench model
8 editions published between 2009 and 2010 in English and held by 10 WorldCat member libraries worldwide
The heavytailed distribution of firm sizes first discovered by Zipf (1949) is one of the best established empirical facts in economics. We show that it has strong implications for asset pricing. Due to the concentration of the market portfolio when the distribution of the capitalization of firms is sufficiently heavytailed, an additional risk factor generically appears even for very large economies. Our twofactor model is as successful empirically as the threefactor FamaFrench model
Xray and neutron reflectivity : principles and applications by
J Daillant(
)
2 editions published in 2009 in English and held by 4 WorldCat member libraries worldwide
This book is the first comprehensive introduction to Xray and neutron reflectivity techniques and illustrates them with many examples. After a pedagogical introduction on the interaction of Xrays and neutrons with matter, the interplay between the statistics of rough surfaces and interfaces and the scattering of radiation is considered in detail. Specular reflectivity and diffuse scattering are discussed next, in chapters 3 and 4 . The approximations are rigorously introduced and many experimental effects are discussed. The specific aspects of neutron reflectivity require separate treatment, given in chapter 5. Chapter 6 turns to Xray reflectivity by rough multilayers. Eventually, chapter 7 introduces and discusses the by now wellestablished method of grazing incidence small angle Xray scattering to investigate nanostructures. For the second edition, the material has been completely reorganized so as to meet the demand for a modern multiauthor textbook for PhD students and young researchers. All chapters have further been throughly revised, updated and, where appropriate, suitably augmented. The first edition was been published as Lect. Notes Phys. m58 in the same series
2 editions published in 2009 in English and held by 4 WorldCat member libraries worldwide
This book is the first comprehensive introduction to Xray and neutron reflectivity techniques and illustrates them with many examples. After a pedagogical introduction on the interaction of Xrays and neutrons with matter, the interplay between the statistics of rough surfaces and interfaces and the scattering of radiation is considered in detail. Specular reflectivity and diffuse scattering are discussed next, in chapters 3 and 4 . The approximations are rigorously introduced and many experimental effects are discussed. The specific aspects of neutron reflectivity require separate treatment, given in chapter 5. Chapter 6 turns to Xray reflectivity by rough multilayers. Eventually, chapter 7 introduces and discusses the by now wellestablished method of grazing incidence small angle Xray scattering to investigate nanostructures. For the second edition, the material has been completely reorganized so as to meet the demand for a modern multiauthor textbook for PhD students and young researchers. All chapters have further been throughly revised, updated and, where appropriate, suitably augmented. The first edition was been published as Lect. Notes Phys. m58 in the same series
The Cambridge Nbody lectures by
W Beiglbck(
)
2 editions published in 2008 in English and held by 3 WorldCat member libraries worldwide
Published under the auspices of the Royal Astronomical Society, this volume contains a set of extensive school tested lectures, with the aim to give a coherent and thorough background knowledge of the subject and to introduce the latest developments in Nbody computational astrophysics. The topics cover a wide range from the classical fewbody problem with discussions of resonance, chaos and stability to realistic modelling of star clusters as well as descriptions of codes, algorithms and special hardware for Nbody simulations. This collection of topics, related to the gravitational Nbody problem, will prove useful to both students and researchers in years to come
2 editions published in 2008 in English and held by 3 WorldCat member libraries worldwide
Published under the auspices of the Royal Astronomical Society, this volume contains a set of extensive school tested lectures, with the aim to give a coherent and thorough background knowledge of the subject and to introduce the latest developments in Nbody computational astrophysics. The topics cover a wide range from the classical fewbody problem with discussions of resonance, chaos and stability to realistic modelling of star clusters as well as descriptions of codes, algorithms and special hardware for Nbody simulations. This collection of topics, related to the gravitational Nbody problem, will prove useful to both students and researchers in years to come
Jets from young stars III : numerical MHD and instabilities by
Silvano Massaglia(
)
1 edition published in 2008 in English and held by 0 WorldCat member libraries worldwide
This volume contains the lecture notes of the Third JETSET School on Jets from Young Stars focussing on Numerical MHD and Instabilities. The introductory lectures presented here cover the basic concepts of the numerical methods for the integration of hydrodynamic and magnetohydrodynamic equations and of the applications of these methods to the treatment of the instabilities relevant for the physics of stellar jets. The first part of the book contains an introduction to the finite difference and finite volume methods for computing the solutions of hyperbolic partial differential equations and a discussion of approximate Riemann solvers for both hydrodynamic and magnetohydrodynamic problems. The second part is devoted to the discussion of some of the main instability processes that may take place in stellar jets, namely: the KelvinHelmholtz, the radiative shock, the pressure driven and the thermal instabilities. Graduate students and young scientists will benefit from this book by learning how to use the fundamental tools used in computational astrophysical jet research
1 edition published in 2008 in English and held by 0 WorldCat member libraries worldwide
This volume contains the lecture notes of the Third JETSET School on Jets from Young Stars focussing on Numerical MHD and Instabilities. The introductory lectures presented here cover the basic concepts of the numerical methods for the integration of hydrodynamic and magnetohydrodynamic equations and of the applications of these methods to the treatment of the instabilities relevant for the physics of stellar jets. The first part of the book contains an introduction to the finite difference and finite volume methods for computing the solutions of hyperbolic partial differential equations and a discussion of approximate Riemann solvers for both hydrodynamic and magnetohydrodynamic problems. The second part is devoted to the discussion of some of the main instability processes that may take place in stellar jets, namely: the KelvinHelmholtz, the radiative shock, the pressure driven and the thermal instabilities. Graduate students and young scientists will benefit from this book by learning how to use the fundamental tools used in computational astrophysical jet research
Theory and simulation of hardsphere fluids and related systems(
)
1 edition published in 2008 in English and held by 0 WorldCat member libraries worldwide
Hard spheres and related objects (hard disks and mixtures of hard systems) are paradigmatic systems: indeed, they have served as a basis for the theoretical and numerical development of a number of fields, such as general liquids and fluids, amorphous solids, liquid crystals, colloids and granular matter, to name but a few. The present volume introduces and reviews some important basics and progress in the study of such systems. Their structure, thermodynamic properties, equations of state, as well as kinetic and transport properties are considered from different and complementary points of view. This book addresses graduate students, lecturers as well as researchers in statistical mechanics, physics of liquids, physical chemistry and chemical engineering
1 edition published in 2008 in English and held by 0 WorldCat member libraries worldwide
Hard spheres and related objects (hard disks and mixtures of hard systems) are paradigmatic systems: indeed, they have served as a basis for the theoretical and numerical development of a number of fields, such as general liquids and fluids, amorphous solids, liquid crystals, colloids and granular matter, to name but a few. The present volume introduces and reviews some important basics and progress in the study of such systems. Their structure, thermodynamic properties, equations of state, as well as kinetic and transport properties are considered from different and complementary points of view. This book addresses graduate students, lecturers as well as researchers in statistical mechanics, physics of liquids, physical chemistry and chemical engineering
Applications of nonlinear dynamics : model and design of complex systems by
Visarath In(
)
1 edition published in 2009 in English and held by 0 WorldCat member libraries worldwide
This edited book is aimed at interdisciplinary deviceoriented applications of nonlinear science theory and methods in complex systems. In particular, applications directed to nonlinear phenomena with space and time characteristics. The examples include: complex networks of magnetic sensor systems, coupled nanomechanical oscillators, nanodetectors, microscale devices, stochastic resonance in multidimensional chaotic systems, biosensors, and stochastic signal quantization. "Applications of Nonlinear Dynamics: Model and Design of Complex Systems" brings together the work of scientists and engineers that are applying ideas and methods from nonlinear dynamics to design and fabricate complex systems
1 edition published in 2009 in English and held by 0 WorldCat member libraries worldwide
This edited book is aimed at interdisciplinary deviceoriented applications of nonlinear science theory and methods in complex systems. In particular, applications directed to nonlinear phenomena with space and time characteristics. The examples include: complex networks of magnetic sensor systems, coupled nanomechanical oscillators, nanodetectors, microscale devices, stochastic resonance in multidimensional chaotic systems, biosensors, and stochastic signal quantization. "Applications of Nonlinear Dynamics: Model and Design of Complex Systems" brings together the work of scientists and engineers that are applying ideas and methods from nonlinear dynamics to design and fabricate complex systems
Complex systems and selforganization modelling(
)
1 edition published in 2009 in English and held by 0 WorldCat member libraries worldwide
The concern of this book is the use of emergent computing and selforganization modelling within various applications of complex systems. The authors focus their attention both on the innovative concepts and implementations in order to model selforganizations, but also on the relevant applicative domains in which they can be used efficiently. This book is the outcome of a workshop meeting within ESM 2006 (Eurosis), held in Toulouse, France in October 2006
1 edition published in 2009 in English and held by 0 WorldCat member libraries worldwide
The concern of this book is the use of emergent computing and selforganization modelling within various applications of complex systems. The authors focus their attention both on the innovative concepts and implementations in order to model selforganizations, but also on the relevant applicative domains in which they can be used efficiently. This book is the outcome of a workshop meeting within ESM 2006 (Eurosis), held in Toulouse, France in October 2006
Aspects of physical biology : biological water, protein solutions, transport and replication by
W Beiglbck(
)
2 editions published in 2008 in English and held by 0 WorldCat member libraries worldwide
The application to Biology of the methodologies developed in Physics is attracting an increasing interest from the scientific community. It has led to the emergence of a new interdisciplinary field, called Physical Biology, with the aim of reaching a better understanding of the biological mechanisms at molecular and cellular levels. Statistical Mechanics in particular plays an important role in the development of this new field. For this reason, the XXth session of the famous Sitges Conference on Statistical Physics was dedicated to "Physical Biology: from Molecular Interactions to Cellular Behavior". As is by now tradition, a number of lectures were subsequently selected, expanded and updated for publication as lecture notes, so as to provide both a stateoftheart introduction and overview to a number of subjects of broader interest and to favor the interchange and crossfertilization of ideas between biologists and physicists. The present volume focuses on three main subtopics (biological water, protein solutions as well as transport and replication), presenting for each of the them the ongoing debates on recent results. The role of water in biological processes, the mechanisms of protein folding, the phases and cooperative effects in biological solutions, the thermodynamic description of replication, transport and neural activity, all are subjects that are revised in this volume, based on new experiments and new theoretical interpretations
2 editions published in 2008 in English and held by 0 WorldCat member libraries worldwide
The application to Biology of the methodologies developed in Physics is attracting an increasing interest from the scientific community. It has led to the emergence of a new interdisciplinary field, called Physical Biology, with the aim of reaching a better understanding of the biological mechanisms at molecular and cellular levels. Statistical Mechanics in particular plays an important role in the development of this new field. For this reason, the XXth session of the famous Sitges Conference on Statistical Physics was dedicated to "Physical Biology: from Molecular Interactions to Cellular Behavior". As is by now tradition, a number of lectures were subsequently selected, expanded and updated for publication as lecture notes, so as to provide both a stateoftheart introduction and overview to a number of subjects of broader interest and to favor the interchange and crossfertilization of ideas between biologists and physicists. The present volume focuses on three main subtopics (biological water, protein solutions as well as transport and replication), presenting for each of the them the ongoing debates on recent results. The role of water in biological processes, the mechanisms of protein folding, the phases and cooperative effects in biological solutions, the thermodynamic description of replication, transport and neural activity, all are subjects that are revised in this volume, based on new experiments and new theoretical interpretations
The rotation of sun and stars(
)
1 edition published in 2009 in English and held by 0 WorldCat member libraries worldwide
The Sun and stars rotate in different ways and at different rates of velocity, and knowledge of how they rotate is important in understanding the formation and evolution of stars and their structure. The wide variety of stars offers an equally wide variety of rotation rates and rotational evolution. From the slowly rotating stars to stars rotating close to their breakup velocities, different techniques and models have to be developed to study rotation and its effects on physical aspects of stars. In fact, one currently witnesses a complete renewal of astrophysical ideas about stellar rotation, mainly due to the development of new models including highorder effects of rotation and magnetism. This book, while not attempting to answer all questions about rotation, given that many issues still have to be further investigated, focuses on the basics and some particular aspects while aiming to show why it is important, from a physical point of view, to study stellar rotation. Based on courses given at a graduate school, these tutorial lectures will be of interest and useful to a rather broad audience of scientists and students
1 edition published in 2009 in English and held by 0 WorldCat member libraries worldwide
The Sun and stars rotate in different ways and at different rates of velocity, and knowledge of how they rotate is important in understanding the formation and evolution of stars and their structure. The wide variety of stars offers an equally wide variety of rotation rates and rotational evolution. From the slowly rotating stars to stars rotating close to their breakup velocities, different techniques and models have to be developed to study rotation and its effects on physical aspects of stars. In fact, one currently witnesses a complete renewal of astrophysical ideas about stellar rotation, mainly due to the development of new models including highorder effects of rotation and magnetism. This book, while not attempting to answer all questions about rotation, given that many issues still have to be further investigated, focuses on the basics and some particular aspects while aiming to show why it is important, from a physical point of view, to study stellar rotation. Based on courses given at a graduate school, these tutorial lectures will be of interest and useful to a rather broad audience of scientists and students
Integrable Hamiltonian hierarchies : spectral and geometric methods by
V. S Gerdjikov(
)
2 editions published in 2008 in English and held by 0 WorldCat member libraries worldwide
This text presents a detailed derivation of the spectral properties of the Recursion Operators allowing one to derive all the fundamental properties of the soliton equations and to study their hierarchies
2 editions published in 2008 in English and held by 0 WorldCat member libraries worldwide
This text presents a detailed derivation of the spectral properties of the Recursion Operators allowing one to derive all the fundamental properties of the soliton equations and to study their hierarchies
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Related Identities
 Malevergne, Yannick Thesis advisor Author
 Saichev, A. I. Author
 Woodard, Hilary Editor
 Ivliev, Sergey Editor
 Zittartz, J.
 Weise, W.
 Raimond, J.M
 Mangano, Michelangelo L.
 Beig, R.
 Hasinger, G.
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Assets (Accounting)PricesEconometric models Astrophysical jets Astrophysics Biophysics Black holes (Astronomy) Cities and townsGrowthMathematical models Complexity (Philosophy) Consciousness Critical phenomena (Physics) Distribution (Probability theory) Dynamics Earthquakes Econometrics Economic geographyMathematical models Economics Finance Financial crises Financial crisesMathematical models Fluid mechanics Fractals Fracture mechanics Hamiltonian systems Investment analysisMathematical models Magnetohydrodynamic instabilities Manybody problem Mathematical geography Mechanics NeutronsScattering Nonlinear systems Particle acceleration Particles (Nuclear physics) Physics Quantum theory Relativity (Physics) Risk managementMathematical models Scaling laws (Statistical physics) Selforganizing systemsData processing StarsRotation Statistical physics Stellar dynamics Stochastic models Stock exchanges StocksPrices Sun Surfaces (Physics) System analysis United States Urban economicsMathematical models XraysScattering Zipf's law