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The Formation of Planets |
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This paper reviews the dynamics of the growth of solid particles from micron-sized dust grains to planets in protostellar accretion disks. The formation and orbital evolution of giant protoplanets is also discussed. . . . . |
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Many-body Correlation Effects in the Ultrafast Nonlinear Optical Response of Confined Fermi Seas |
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The dynamics of electrons and atoms interacting with intense and ultrashort optical pulses presents an important problem in physics that cuts across different materials such as semiconductors and metals. The currently available laser pulses, as short as 5 fs, provide a time resolution shorter than the dephasing and relaxation times in many materials. This allows for a systematic study of many-body effects using nonlinear optical spectroscopy. In this review article, we discuss the role of Coulomb correlations in the ultrafast dynamics of modula . . . . |
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Quantum Principles and Particles |
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This is a two semester, 550 page introductory text, plus a 10 page index. It includes material which overlaps with particle physics, including a number of interesting models as well as material on identical particles. I use a bra-ket notation which I learned from Schwinger, which is much simpler and easier to understand than the standard bra-ket notation. Included are about 160 end of the chapter problems. The ideas of quantum mechanics are introduced via “Process Diagrams”, which are filter/transition devices which help students visualize the . . . . |
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Methods in Industrial Biotechnology for Chemical Engineers |
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In keeping with the definition that biotechnology is really no more than a name given to a set of techniques and processes, the authors apply some set of fuzzy techniques to chemical industry problems such as finding the proper proportion of raw mix to control pollution, to study flow rates, to find out the better quality of products. We use fuzzy control theory, fuzzy neural networks, fuzzy relational equations, genetic algorithms to these problems for solutions. When the solution to the problem can have certain concepts or attributes as indet . . . . |
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Complex and Adaptive Dynamical Systems: A Primer |
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An thorough introduction is given at an introductory level to the field of quantitative complex system science, with special emphasis on emergence in dynamical systems based on network topologies. Subjects treated include graph theory and small-world networks, a generic introduction to the concepts of dynamical system theory, random Boolean networks, cellular automata and self-organized criticality, the statistical modeling of Darwinian evolution, synchronization phenomena and an introduction to the theory of cognitive systems. . . . . |
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Super Linear Algebra |
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In this book, the authors introduce the notion of Super linear algebra and super vector spaces using the definition of super matrices defined by Horst (1963). This book expects the readers to be well-versed in linear algebra. Many theorems on super linear algebra and its properties are proved. Some theorems are left as exercises for the reader. These new class of super linear algebras which can be thought of as a set of linear algebras, following a stipulated condition, will find applications in several fields using computers. The authors feel . . . . |
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Elementary Mechanics from a Mathematician's Viewpoint |
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Contents: The Hardest Part of Mechanics (The Fundamentals); Further Remarks on the Fundamentals; How Newton Analyzed Planetary Motion; Systems of Particles; Conservation Laws; Rigid Bodies; Constraints; Holonomic and Non-Holonomic Constraints; Statically Indeterminate Structures. . . . . |
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Graph Theory Lessons |
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Graph Theory Lessons in html and java. Contents: # Lesson 1: Null graphs
# Lesson 2: Handshaking Lemma
# Lesson 3: Isomorphism
# Lesson 4: Complete Graphs, Subgraphs
# Lesson 5: Regular Graphs
# Lesson 6: Platonic Graphs
# Lesson 7: Adjacency Matrices
# Lesson 8: Graph Coloring
# Lesson 9: Bipartite Graphs
# Lesson 10: Stars and Tripartite Graphs
# Lesson 11: Circuits and Wheels
# Lesson 12: Euler Circuits, Hamilton Circuits and Directed Graphs
# Lesson 13: Trees and Searches
# Lesson 14: Unions and Sums
# Lesson 15: Complements
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Dynamical vertex approximation -- an introduction |
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We give an elementary introduction to a recent diagrammatic extension of dynamical mean field theory (DMFT) coined dynamical vertex approximation (D$\Gamma$A). This approach contains the important local correlations of DMFT, giving, among others, rise to quasiparticle renormalizations, Mott-Hubbard transitions and magnetism, but also non-local correlations beyond. The latter are at the very essence of many physical phenomena in strongly correlated elecectron systems. As correlations are treated equally on all length scales, D$\Gamma$A allo . . . . |
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Introduction to the Pinch Technique |
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These notes are a short introduction to the pinch technique. We present the one-loop calculations for basic QCD Green's functions. The equivalence between the pinch technique and the background field method is explicitly shown at the one-loop level. We review the absorptive pinch technique in the last sections. These lectures are a compilation of relevant papers on this subject and are prepared for the third Modave Summer School in Mathematical Physics. . . . . |
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Tensor categories: A selective guided tour |
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These are the -- only lightly edited -- lecture notes for a short course on tensor categories. The coverage in these notes is relatively non-technical, focussing on the essential ideas. They are meant to be accessible for beginners, but it is hoped that also some of the experts will find something interesting in them.
Once the basic definitions are given, the focus is mainly on k-linear categories with finite dimensional hom-spaces. Connections with quantum groups and low dimensional topology are pointed out, but these notes have no pretension . . . . |
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From Deterministic Chaos to Deterministic Diffusion |
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This is a set of easy-to-read lecture notes for a short first-year Ph.D. student course on Applied Dynamical Systems, which was given at the London Taught Course Centre in Spring 2008. The notes cover five hours of lectures and do not require any preknowledge on dynamical systems. The first part introduces to deterministic chaos in one-dimensional maps in form of Ljapunov exponents and the metric entropy. The second part first outlines the concept of deterministic diffusion. Then the escape rate formalism for deterministic diffusion, which expr . . . . |
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Green function techniques in the treatment of quantum transport at the molecular scale |
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The theoretical investigation of charge (and spin) transport at nanometer length scales requires the use of advanced and powerful techniques able to deal with the dynamical properties of the relevant physical systems, to explicitly include out-of-equilibrium situations typical for electrical/heat transport as well as to take into account interaction effects in a systematic way. Equilibrium Green function techniques and their extension to non-equilibrium situations via the Keldysh formalism build one of the pillars of current state-of-the-art ap . . . . |
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Theory of Dynamical Thermal Transport Coefficients in Correlated Condensed Matter |
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We present a recently developed formalism for computing certain dynamical transport coefficients for standard models of correlated matter, such as the Hubbard and the $t-J$ model. The case of the Hall constant in correlated matter is used to motivate the method of high frequency. This method is pointed out to be closer to DC results for models describing low energy properties after eliminating high energy degrees of freedom. Successful predictions of this method are also noted. The extension of this method is made to evaluate and estimate the S . . . . |
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Nature of the 5f states in actinide metals |
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Actinide elements produce a plethora of interesting physical behaviors due to the 5f states. This review compiles and analyzes progress in understanding of the electronic and magnetic structure of the 5f states in actinide metals. Particular interest is given to electron energy-loss spectroscopy and many-electron atomic spectral calculations, since there is now an appreciable library of core d -> valence f transitions for Th, U, Np, Pu, Am, and Cm. These results are interwoven and discussed against published experimental data, such as x-ray pho . . . . |
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Title: Introduction to Monte Carlo methods for an Ising Model of a Ferromagnet |
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This discussion serves as an introduction to the use of Monte Carlo simulations as a useful way to evaluate the observables of a ferromagnet. Key background is given about the relevance and effectiveness of this stochastic approach and in particular the applicability of the Metropolis-Hastings algorithm. Importantly the potentially devastating effects of spontaneous magnetization are highlighted and a means to avert this is examined.
An Ising model is introduced and used to investigate the properties of a two dimensional ferromagnet with respe . . . . |
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Ekpyrotic and Cyclic Cosmology |
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Ekpyrotic and cyclic cosmologies provide theories of the very early and of the very late universe. In these models, the big bang is described as a collision of branes - and thus the big bang is not the beginning of time. Before the big bang, there is an ekpyrotic phase with equation of state w=P/rho >> 1 (where P is the average pressure and rho the average energy density) during which the universe slowly contracts. This phase resolves the standard cosmological puzzles and generates a nearly scale-invariant spectrum of cosmological perturbations . . . . |
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Title: An introduction to quantum cluster methodsThese lecture notes provide an introduction to quantum cluster methods for stro |
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These lecture notes provide an introduction to quantum cluster methods for strongly correlated systems. Cluster Perturbation Theory (CPT), the Variational Cluster Approximation (VCA) and Cellular Dynamical Mean Field Theory (CDMFT) are described, as well as the exact diagonalization solver for the cluster. Potthoff's self-energy functional formalism is reviewed. Some numerical procedures, in particular regarding the exact diagonalization method and the frequency-momentum integrals needed in VCA, are discussed in detail. . . . . |
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Optical Metamagnetism and Negative Index Metamaterials |
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A new class of artificially structured materials called metamaterials makes it possible to achieve electromagnetic properties that do not exist in nature. In this paper we review the recent progress made in the area of optical metamaterials. It was predicted that nanostructured metamaterials could provide us with artificial magnetic response and negative refractive index at optical frequencies. To date, optical metamagnetics have been already fabricated to demonstrate artificial magnetic response in the infrared and across the entire visible sp . . . . |
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Cosmic Rays and the Search for a Lorentz Invariance Violation |
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This is an introductory review about the on-going search for a signal of Lorentz Invariance Violation (LIV) in cosmic rays. We first summarise basic aspects of cosmic rays, focusing on rays of ultra high energy (UHECRs). We discuss the Greisen-Zatsepin-Kuz'min (GZK) energy cutoff for cosmic protons, which is predicted due to photopion production in the Cosmic Microwave Background (CMB). This is a process of modest energy in the proton rest frame. It can be investigated to a high precision in the laboratory, if Lorentz transformations apply even . . . . |
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Microscopic approaches for nuclear Many-Body dynamics |
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These lecture notes are addressed to PhD student and/or researchers who want a general overview of microscopic approaches based on mean-field and applied to nuclear dynamics. Our goal is to provide a good description of low energy heavy-ion collisions. We present both formal aspects and practical applications of the time-dependent Hartree-Fock (TDHF) theory. The TDHF approach gives a mean field dynamics of the system under the assumption that particles evolve independently in their self-consistent average field. As an example, we study the . . . . |
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Chimie Inorganique |
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Contenu: Chapitre I : Principes généraux; Chapitre II : Eléments des blocs s et p; Chapitre III : Eléments du bloc d. . . . . |
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Algebraic Combinatorics |
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Algebraic Combinatorics in Mathematical Chemistry. Methods and Algorithms. I. Permutation Groups and Coherent (Cellular) Algebras. . . . . |
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An introduction to quantum cluster methods |
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Posted on 0000-00-00
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These lecture notes provide an introduction to quantum cluster methods for strongly correlated systems. Cluster Perturbation Theory (CPT), the Variational Cluster Approximation (VCA) and Cellular Dynamical Mean Field Theory (CDMFT) are described, as well as the exact diagonalization solver for the cluster. Potthoff's self-energy functional formalism is reviewed. Some numerical procedures, in particular regarding the exact diagonalization method and the frequency-momentum integrals needed in VCA, are discussed in detail. . . . . |
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MPI: The Complete Reference |
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This book is about the Message Passing Interface (MPI), an important and increasingly popular standarized and portable message passing system that brings us closer to the potential development of practical and cost-effective large-scale parallel applications. It gives a complete specification of the MPI standard and provides illustrative programming examples. . . . . |
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A Field Guide to Recent Work on the Foundations of Statistical Mechanics |
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This is an extensive review of recent work on the foundations of statistical mechanics. Subject matters discussed include: interpretation of probability, typicality, recurrence, reversibility, ergodicity, mixing, coarse graining, past hypothesis, reductionism, phase average, thermodynamic limit, interventionism, entropy. . . . . |
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Spectroscopy of Conjugated Polymers |
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Contents: Correlations in Conjugated Polymers; Nature of the Primary Photo-Excitations in Poly(Arylene-Vinylenes): Bound Neutral Excitons or Charged Polaron Pairs; Excitons in Conjugated Polymers; Intramolecular Excitons and Intermolecular Polaron Pairs as Primary Photoexcitations in Conjugated Polymers; Excitonic Effects in the Linear and Nonlinear Optical Properties of Conjugated Polymers; Bound Polaron Pair Formation in Poly (Phenylenevinylenes); Luminescence Efficiency and Time-Dependence: Insights into the Nature of the Emitting Specie . . . . |
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Theory of Spin Hall Effects in Semiconductors |
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Spin Hall effects are a collection of phenomena, resulting from spin-orbit coupling, in which an electrical current flowing through a sample can lead to spin transport in a perpendicular direction and spin accumulation at lateral boundaries. These effects, which do not require an applied magnetic field, can originate in a variety of intrinsic and extrinsic spin-orbit coupling mechanisms and depend on geometry, dimension, impurity scattering, and carrier density of the system--making the analysis of these effects a diverse field of research. In . . . . |
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