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Large Finite Systems
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Book Synopsis Large Finite Systems by : Joshua Jortner
Download or read book Large Finite Systems written by Joshua Jortner and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 391 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Twentieth Jerusalem Symposium reflected the high standards of these distinguished scientific meetings which convene once a year at the Israel Academy of Sciences and Humanities in Jerusalem to discuss a specific topic in the broad area of quantum chemistry and biochemistry. The Twentieth Jerusalem Symposium marked an auspicious occasion. commemorating two decades of this scientific endeavour. The topic at this year's Jerusalem Symposium was Large Finite Systems which constitutes a truly interdisciplinary subject of central interest in the broad areas of chemistry. physics. astrophysics and biophysics. The main theme of the Symposium was built around bridging the gap between molecular. surface and condensed matter chemical physics. Emphasis was placed on the interrelationship between the properties of large molecules. van der Waals complexes and clusters. focusing on the structure. dynamics of nuclear motion. quantum and thermodynamics size effects. the nature of electronic states and excited-state energetics and dynamics of large finite systems. The interdisciplinary nature of these research areas was deliberated by intensive and extensive interactions between scientists from different disciplines and between theory and experiment. This volume provides a record of the invited lectures at the Symposium.
Book Synopsis Mutually Catalytic Super Branching Random Walks: Large Finite Systems and Renormalization Analysis by : J. T. Cox
Download or read book Mutually Catalytic Super Branching Random Walks: Large Finite Systems and Renormalization Analysis written by J. T. Cox and published by American Mathematical Soc.. This book was released on 2004 with total page 97 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study features of the longtime behavior and the spatial continuum limit for the diffusion limit of the following particle model. Consider populations consisting of two types of particles located on sites labeled by a countable group. The populations of each of the types evolve as follows: each particle performs a random walk and dies or splits in two with probability $\frac{1} {2}$ and the branching rates of a particle of each type at a site $x$ at time $t$ is proportional to the size of the population at $x$ at time $t$ of the other type. The diffusion limit of ''small mass, large number of initial particles'' is a pair of two coupled countable collections of interacting diffusions, the mutually catalytic super branching random walk.Consider now increasing sequences of finite subsets of sites and define the corresponding finite versions of the process. We study the evolution of these large finite spatial systems in size-dependent time scales and compare them with the behavior of the infinite systems, which amounts to establishing the so-called finite system scheme. A dichotomy is known between transient and recurrent symmetrized migrations for the infinite system, namely, between convergence to equilibria allowing for coexistence in the first case and concentration on monotype configurations in the second case.Correspondingly we show in the recurrent case both large finite and infinite systems behave similar in all time scales, in the transient case we see for small time scales a behavior resembling the one of the infinite system, whereas for large time scales the system behaves as in the finite case with fixed size and finally in intermediate scales interesting behavior is exhibited, the system diffuses through the equilibria of the infinite system which are indexed by the pair of intensities and this diffusion process can be described as mutually catalytic diffusion on $(\R^ )^2$. At the same time, the above finite system asymptotics can be applied to mean-field systems of $N$ exchangeable mutually catalytic diffusions. This is the building block for a renormalization analysis of the spatially infinite hierarchical model and leads to an association of this system with the so-called interaction chain, which reflects the behavior of the process on large space-time scales.Similarly we introduce the concept of a continuum limit in the hierarchical mean field limit and show that this limit always exists and that the small-scale properties are described by another Markov chain called small scale characteristics. Both chains are analyzed in detail and exhibit the following interesting effects. The small scale properties of the continuum limit exhibit the dichotomy, overlap or segregation of densities of the two populations, as a function of the underlying random walk kernel. A corresponding concept to study hot spots is presented. Next we look in the transient regime for global equilibria and their equilibrium fluctuations and in the recurrent regime on the formation of monotype regions.For particular migration kernels in the recurrent regime we exhibit diffusive clustering, which means that the sizes (suitable defined) of monotype regions have a random order of magnitude as time proceeds and its distribution is explicitly identifiable. On the other hand in the regime of very large clusters we identify the deterministic order of magnitude of monotype regions and determine the law of the random size. These two regimes occur for different migration kernels than for the cases of ordinary branching or Fisher-Wright diffusion. Finally we find a third regime of very rapid deterministic spatial cluster growth which is not present in other models just mentioned. A further consequence of the analysis is that mutually catalytic branching has a fixed point property under renormalization and gives a natural example different from the trivial case of multitype models consisting of two independent versions of the fixed points for the one type case.
Author :Christian A. Schenk Publisher :Springer Science & Business Media ISBN 13 :9783540253433 Total Pages :184 pages Book Rating :4.2/5 (534 download)
Book Synopsis Uncertainty Assessment of Large Finite Element Systems by : Christian A. Schenk
Download or read book Uncertainty Assessment of Large Finite Element Systems written by Christian A. Schenk and published by Springer Science & Business Media. This book was released on 2005-06-08 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: The treatment of uncertainties in the analysis of engineering structures remains one of the premium challenges in modern structural mechanics. It is only in recent years that the developments in stochastic and deterministic computational mechanics began to be synchronized. To foster these developments, novel computational procedures for the uncertainty assessment of large finite element systems are presented in this monograph. The stochastic input is modeled by the so-called Karhunen-Loève expansion, which is formulated in this context both for scalar and vector stochastic processes as well as for random fields. Particularly for strongly non-linear structures and systems the direct Monte Carlo simulation technique has proven to be most advantageous as method of solution. The capabilities of the developed procedures are demonstrated by showing some practical applications.
Book Synopsis Physics and Chemistry of Finite Systems: From Clusters to Crystals by : Peru Jena
Download or read book Physics and Chemistry of Finite Systems: From Clusters to Crystals written by Peru Jena and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 1414 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent innovations in experimental techniques such as molecular and cluster beam epitaxy, supersonic jet expansion, matrix isolation and chemical synthesis are increasingly enabling researchers to produce materials by design and with atomic dimension. These materials constrained by sire, shape, and symmetry range from clusters containing as few as two atoms to nanoscale materials consisting of thousands of atoms. They possess unique structuraI, electronic, magnetic and optical properties that depend strongly on their size and geometry. The availability of these materials raises many fundamental questions as weIl as technological possibilities. From the academic viewpoint, the most pertinent question concerns the evolution of the atomic and electronic structure of the system as it grows from micro clusters to crystals. At what stage, for example, does the cluster look as if it is a fragment of the corresponding crystal. How do electrons forming bonds in micro-clusters transform to bands in solids? How do the size dependent properties change from discrete quantum conditions, as in clusters, to boundary constrained bulk conditions, as in nanoscale materials, to bulk conditions insensitive to boundaries? How do the criteria of classification have to be changed as one goes from one size domain to another? Potential for high technological applications also seem to be endless. Clusters of otherwise non-magnetic materials exhibit magnetic behavior when constrained by size, shape, and dimension. NanoscaIe metal particles exhibit non-linear opticaI properties and increased mechanical strength. SimiIarly, materials made from nanoscale ceramic particIes possess plastic behavior.
Book Synopsis Advances in Cryptology - CRYPTO '90 by : Alfred J. Menezes
Download or read book Advances in Cryptology - CRYPTO '90 written by Alfred J. Menezes and published by Springer. This book was released on 2003-06-30 with total page 630 pages. Available in PDF, EPUB and Kindle. Book excerpt: Crypto '90 marked the tenth anniversary of the Crypto conferences held at the University of California at Santa Barbara. The conference was held from August 11 to August 15, 1990 and was sponsored by the International Association for Cryptologic Research, in cooperation with the IEEE Computer Society Technical Committee on Security and Privacy and the Department of Computer Science of the University of California at Santa Barbara. 227 participants from twenty countries around the world. Crypto '90 attracted Roughly 35% of attendees were from academia, 45% from industry and 20% from government. The program was intended to provide a balance between the purely theoretical and the purely practical aspects of cryptography to meet the needs and diversified interests of these various groups. The overall organization of the conference was superbly handled by the general chairperson Sherry McMahan. All of the outstanding features of Crypto, which we have come to expect over the years, were again present and, in addition to all of this, she did a magnificent job in the preparation of the book of abstracts. This is a crucial part of the program and we owe her a great deal of thanks.
Book Synopsis Finite and Profinite Quantum Systems by : Apostolos Vourdas
Download or read book Finite and Profinite Quantum Systems written by Apostolos Vourdas and published by Springer. This book was released on 2017-07-17 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides an introduction to finite quantum systems, a field at the interface between quantum information and number theory, with applications in quantum computation and condensed matter physics. The first major part of this monograph studies the so-called `qubits' and `qudits', systems with periodic finite lattice as position space. It also discusses the so-called mutually unbiased bases, which have applications in quantum information and quantum cryptography. Quantum logic and its applications to quantum gates is also studied. The second part studies finite quantum systems, where the position takes values in a Galois field. This combines quantum mechanics with Galois theory. The third part extends the discussion to quantum systems with variables in profinite groups, considering the limit where the dimension of the system becomes very large. It uses the concepts of inverse and direct limit and studies quantum mechanics on p-adic numbers. Applications of the formalism include quantum optics and quantum computing, two-dimensional electron systems in magnetic fields and the magnetic translation group, the quantum Hall effect, other areas in condensed matter physics, and Fast Fourier Transforms. The monograph combines ideas from quantum mechanics with discrete mathematics, algebra, and number theory. It is suitable for graduate students and researchers in quantum physics, mathematics and computer science.
Book Synopsis Theory of Critical Phenomena in Finite-size Systems by : ?ordan Brankov
Download or read book Theory of Critical Phenomena in Finite-size Systems written by ?ordan Brankov and published by World Scientific. This book was released on 2000 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to familiarise the reader with the rich collection of ideas, methods and results available in the theory of critical phenomena in systems with confined geometry. The existence of universal features of the finite-size effects arising due to highly correlated classical or quantum fluctuations is explained by the finite-size scaling theory. This theory (1) offers an interpretation of experimental results on finite-size effects in real systems; (2) gives the most reliable tool for extrapolation to the thermodynamic limit of data obtained by computer simulations; (3) reveals the intimate mechanism of how the critical singularities build up in the thermodynamic limit; and (4) can be fruitfully used to explain the low-temperature behaviour of quantum critical systems. The exposition is given in a self-contained form which presumes the reader's knowledge only in the framework of standard courses on the theory of phase transitions and critical phenomena. The instructive role of simple models, both classical and quantum, is demonstrated by putting the accent on the derivation of rigorous and exact analytical results.
Book Synopsis Quantum Theory of Finite Systems by : Jean-Paul Blaizot
Download or read book Quantum Theory of Finite Systems written by Jean-Paul Blaizot and published by Mit Press. This book was released on 1986 with total page 657 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive and pedagogical account of the various methods used in the quantum theory of finite systems, including molecular, atomic, nuclear, and particle phenomena. Covering both background material and advanced topics and including nearly 200 problems, Quantum Theory of Finite Systems has been designed to serve primarily as a text and will also prove useful as a reference in research. The first of the book's four parts introduces the basic mathematical apparatus: second quantization, canonical transformations, Wick theorems and the resulting diagram expansions, and oscillator models. The second part presents mean field approximations and the recently developed path integral methods for the quantization of collective modes. Part three develops perturbation theory in terms of both time-dependent Feynman diagrams and time-independent Goldstone diagrams. A fourth part discusses variational methods based on correlated wavefunctions, including spin correlations. The approximation schemes are formulated for fermions and bosons at eigher zero or non-zero temperature. Although the formalism developed applies to both finite and infinite systems, the book stresses those aspects of the theory that are specific to the description of finite systems. Thus special attention is given to mean field approximations, the ensuing broken symmetries, and the associated collective motions such as rotations. Conversely, some specific features of systems with infinite numbers of degrees of freedom (such as the thermodynamic limit, critical phenomena, and the elimination of ultraviolet divergencies) are deliberately omitted. Jean-Paul Blaizot and Georges Ripka are associated with the Centre d'Etudes Nucleaires de Saclay.
Book Synopsis Automation of Finite Element Methods by : Jože Korelc
Download or read book Automation of Finite Element Methods written by Jože Korelc and published by Springer. This book was released on 2016-06-08 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: New finite elements are needed as well in research as in industry environments for thedevelopment of virtual prediction techniques. The design and implementation of novel finiteelements for specific purposes is a tedious and time consuming task, especially for nonlinearformulations. The automation of this process can help to speed up this processconsiderably since the generation of the final computer code can be accelerated by order ofseveral magnitudes.This book provides the reader with the required knowledge needed to employ modernautomatic tools like AceGen within solid mechanics in a successful way. It covers the rangefrom the theoretical background, algorithmic treatments to many different applications. Thebook is written for advanced students in the engineering field and for researchers ineducational and industrial environments.
Book Synopsis Technology for Large Space Systems by :
Download or read book Technology for Large Space Systems written by and published by . This book was released on 1986 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Fifty Years of Nuclear BCS by : Ricardo A Broglia
Download or read book Fifty Years of Nuclear BCS written by Ricardo A Broglia and published by World Scientific. This book was released on 2013-01-18 with total page 692 pages. Available in PDF, EPUB and Kindle. Book excerpt: This unique volume reviews more than fifty years of theoretical and experimental developments of the concept that properties of atomic nuclei up to a great extent are defined by the pair correlations of nuclear constituents — protons and neutrons. Such correlations in condensed matter are responsible for quantum phenomena on a macroscopic level — superfluidity and superconductivity. After introducing Bardeen–Cooper–Schrieffer (BCS) theory of superconductivity of metals, it became clear that atomic nuclei have properties of superfluid drops, and practically all features of nuclei strongly depend on the pair correlations. Presenting a comprehensive overview of the progress of nuclear science, the contributions from leading physicists around the world, cover the whole spectrum of studies in nuclear physics and physics of other small systems. With the most updated information written in an accessible way, the volume will serve as an irreplaceable source of references covering many years of development and insight into several new problems at the frontiers of science. It will be useful not only for physicists working in nuclear and condensed matter physics, astrophysicists, chemists and historians of science, but will also help students understand the current status and perspectives for the future. Contents:BCS Pairing (and Beyond) in Nuclear Structure and DynamicsThe Nuclear Pairing Interaction in Finite Nuclei and in Neutron StarsSingle- and Multiple-Pair Tunneling in Nuclear Reactions (Experiment and Theory)Pairing in Nuclei in An External Time-Reversal Violating Field: Rapidly Rotating NucleiThe Nuclear BCS (Pairing) Paradigm in Other Many-Body Systems Readership: Nuclear and theoretical physicists, chemists and astrophysicists. Keywords:Nuclear Structure;Transfer Reactions;Nuclear Superfluidity;Nuclear Matter;Neutron Star Crust;Pairing In Fermi SystemsKey Features:Currently there are no competing titles on the market, the books of this breadth and depth were not published beforeThe contributors are experts from leading institutions of the world
Book Synopsis Nonlinear Finite Element Methods by : Peter Wriggers
Download or read book Nonlinear Finite Element Methods written by Peter Wriggers and published by Springer Science & Business Media. This book was released on 2008-11-04 with total page 566 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finite element methods have become ever more important to engineers as tools for design and optimization, now even for solving non-linear technological problems. However, several aspects must be considered for finite-element simulations which are specific for non-linear problems: These problems require the knowledge and the understanding of theoretical foundations and their finite-element discretization as well as algorithms for solving the non-linear equations. This book provides the reader with the required knowledge covering the complete field of finite element analyses in solid mechanics. It is written for advanced students in engineering fields but serves also as an introduction into non-linear simulation for the practising engineer.
Book Synopsis Classical Systems in Quantum Mechanics by : Pavel Bóna
Download or read book Classical Systems in Quantum Mechanics written by Pavel Bóna and published by Springer Nature. This book was released on 2020-06-23 with total page 243 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book investigates two possibilities for describing classical-mechanical physical systems along with their Hamiltonian dynamics in the framework of quantum mechanics.The first possibility consists in exploiting the geometrical properties of the set of quantum pure states of "microsystems" and of the Lie groups characterizing the specific classical system. The second approach is to consider quantal systems of a large number of interacting subsystems – i.e. macrosystems, so as to study the quantum mechanics of an infinite number of degrees of freedom and to look for the behaviour of their collective variables. The final chapter contains some solvable models of “quantum measurement" describing dynamical transitions from "microsystems" to "macrosystems".
Book Synopsis Oscillations in Finite Quantum Systems by : George F. Bertsch
Download or read book Oscillations in Finite Quantum Systems written by George F. Bertsch and published by Cambridge University Press. This book was released on 1994-04-21 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: Appendix A: Mean field theory
Download or read book Finite-Size Scaling written by J. Cardy and published by Elsevier. This book was released on 2012-12-02 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the past few years, finite-size scaling has become an increasingly important tool in studies of critical systems. This is partly due to an increased understanding of finite-size effects by analytical means, and partly due to our ability to treat larger systems with large computers. The aim of this volume was to collect those papers which have been important for this progress and which illustrate novel applications of the method. The emphasis has been placed on relatively recent developments, including the use of the &egr;-expansion and of conformal methods.
Download or read book Forever Finite written by Kip K. Sewell and published by Rond Books. This book was released on 2023-08-01 with total page 828 pages. Available in PDF, EPUB and Kindle. Book excerpt: INFINITY IS NOT WHAT IT SEEMS… Infinity is commonly assumed to be a logical concept, reliable for conducting mathematics, describing the Universe, and understanding the divine. Most of us are educated to take for granted that there exist infinite sets of numbers, that lines contain an infinite number of points, that space is infinite in expanse, that time has an infinite succession of events, that possibilities are infinite in quantity, and over half of the world’s population believes in a divine Creator infinite in knowledge, power, and benevolence. According to this treatise, such assumptions are mistaken. In reality, to be is to be finite. The implications of this assessment are profound: the Universe and even God must necessarily be finite. The author makes a compelling case against infinity, refuting its most prominent advocates. Any defense of the infinite will find it challenging to answer the arguments laid out in this book. But regardless of the reader’s position, Forever Finite offers plenty of thought-provoking material for anyone interested in the subject of infinity from the perspectives of philosophy, mathematics, science, and theology.
Author :Konstantinos N. Anagnostopoulos Publisher :Konstantinos Anagnostopoulos ISBN 13 :1312464887 Total Pages :678 pages Book Rating :4.3/5 (124 download)
Book Synopsis Computational Physics, Vol II by : Konstantinos N. Anagnostopoulos
Download or read book Computational Physics, Vol II written by Konstantinos N. Anagnostopoulos and published by Konstantinos Anagnostopoulos. This book was released on 2014-07-27 with total page 678 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to the computational methods used in physics and other scientific fields. It is addressed to an audience that has already been exposed to the introductory level of college physics, usually taught during the first two years of an undergraduate program in science and engineering. The book starts with very simple problems in particle motion and ends with an in-depth discussion of advanced techniques used in Monte Carlo simulations in statistical mechanics. The level of instruction rises slowly, while discussing problems like the diffusion equation, electrostatics on the plane, quantum mechanics and random walks. The book aims to provide the students with the background and the experience needed in order to advance to high performance computing projects in science and engineering. But it also tries to keep the students motivated by considering interesting applications in physics, like chaos, quantum mechanics, special relativity and the physics of phase transitions. The book and the accompanying software is available for free in electronic form at http://goo.gl/SGUEkM (www.physics.ntua.gr/%7Ekonstant/ComputationalPhysics) and a printed copy can be purchased from lulu.com at http://goo.gl/XsSBdP (vol I at http://goo.gl/Pg1zHc )
