Download or read book Dynamical Systems Associated with Particle Flow Models written by Roman V. Samulyak and published by . This book was released on 1999 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new class of integro - partial differential equation models is derived for the prediction of granular flow dynamics. These models are obtained using a novel limiting averaging method (inspired by techniques employed in the derivation of infinite-dimensional dynamical systems models) on the Newtonian equations of motion of a many-particle system incorporating widely used inelastic particle-particle force formulas. By using Taylor series expansions, these models can be approximated by a system of partial differential equations of the Navier-Stokes type. Solutions of the new models for granular flows down inclined planes and in vibrating beds are compared with known experimental and analytical results and good agreement is obtained. Theorems on the existence and uniqueness of a solution to the granular flow dynamical system are proved in the Faedo-Galerkin method framework. A class of one-dimensional models describing the dynamics of thin granular layers and some related problems of fluid mechanics was studied from the Liouville-Lax integrability theory point of view. The integrability structures for these dynamical systems were constructed using Cartan's calculus of differential forms, Grassman algebras over jet-manifolds associated with the granular flow dynamical systems, the gradientholonomic algorithm and generalized Hamiltonian methods. By proving the exact integrability of the systems, the quasi-periodicity of the solutions was explained as well as the observed regularity of the numerical solutions. A numerical algorithm based on the idea of higher and lower modes separation in the theory of approximate inertial manifolds for dissipative evolutionary equations is developed in a finite-difference framework. The method is applied to the granular flow dynamical system. Numerical calculations show that this method has several advantages compared to standard finite-difference schemes. A numerical solution to the granular flow in a hopper is obtained using the finite difference scheme in curvilinear coordinates. By making coefficients in the governing equations functionally dependent on the gradient of the velocity field, we were able to model the influence of the stationary friction phenomena in solids and reproduce in this way experimentally observable results. Some analytical and numerical solutions to the dynamical system describing granular flows in vibrating beds are also presented. We found that even in the simplest case where we neglect the arching phenomena and surface waves, these solutions exhibit some of the typical features that have been observed in simulation and experimental studies of vibrating beds. The approximate analytical solutions to the governing system of equations were found to share several important features with actual granular flows. Using this approach we showed the existence of the typical dynamical structures of chaotic motion. By employing Melnikov theory the bifurcation parameter values were estimated analytically. The vortex solutions we obtained for the perturbed motion and the solutions corresponding to the vortex disintegration agree qualitatively with the dynamics obtained numerically.

Download or read book Advances in Dynamical Systems Theory Models Algorithms and Applications written by Bruno Carpentieri and published by BoD – Books on Demand. This book was released on 2021-07-28 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of modern dynamical systems dates back to 1890 with studies by Poincaré on celestial mechanics. The tradition was continued by Birkhoff in the United States with his pivotal work on periodic orbits, and by the Moscow School in Russia (Liapunov, Andronov, Pontryagin). In the 1960s the field was revived by the emergence of the theory of chaotic attractors, and in modern years by accurate computer simulations. This book provides an overview of recent developments in the theory of dynamical systems, presenting some significant advances in the definition of new models, computer algorithms, and applications. Researchers, engineers and graduate students in both pure and applied mathematics will benefit from the chapters collected in this volume.

Download or read book Algebraic Integrability of Nonlinear Dynamical Systems on Manifolds written by A.K. Prykarpatsky and published by Springer Science & Business Media. This book was released on 2013-04-09 with total page 555 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent times it has been stated that many dynamical systems of classical mathematical physics and mechanics are endowed with symplectic structures, given in the majority of cases by Poisson brackets. Very often such Poisson structures on corresponding manifolds are canonical, which gives rise to the possibility of producing their hidden group theoretical essence for many completely integrable dynamical systems. It is a well understood fact that great part of comprehensive integrability theories of nonlinear dynamical systems on manifolds is based on Lie-algebraic ideas, by means of which, in particular, the classification of such compatibly bi Hamiltonian and isospectrally Lax type integrable systems has been carried out. Many chapters of this book are devoted to their description, but to our regret so far the work has not been completed. Hereby our main goal in each analysed case consists in separating the basic algebraic essence responsible for the complete integrability, and which is, at the same time, in some sense universal, i. e. , characteristic for all of them. Integrability analysis in the framework of a gradient-holonomic algorithm, devised in this book, is fulfilled through three stages: 1) finding a symplectic structure (Poisson bracket) transforming an original dynamical system into a Hamiltonian form; 2) finding first integrals (action variables or conservation laws); 3) defining an additional set of variables and some functional operator quantities with completely controlled evolutions (for instance, as Lax type representation).

Download or read book Differential Dynamical Systems Revised Edition written by James D. Meiss and published by SIAM. This book was released on 2017-01-24 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential equations are the basis for models of any physical systems that exhibit smooth change. This book combines much of the material found in a traditional course on ordinary differential equations with an introduction to the more modern theory of dynamical systems. Applications of this theory to physics, biology, chemistry, and engineering are shown through examples in such areas as population modeling, fluid dynamics, electronics, and mechanics.? Differential Dynamical Systems begins with coverage of linear systems, including matrix algebra; the focus then shifts to foundational material on nonlinear differential equations, making heavy use of the contraction-mapping theorem. Subsequent chapters deal specifically with dynamical systems concepts?flow, stability, invariant manifolds, the phase plane, bifurcation, chaos, and Hamiltonian dynamics. This new edition contains several important updates and revisions throughout the book. Throughout the book, the author includes exercises to help students develop an analytical and geometrical understanding of dynamics. Many of the exercises and examples are based on applications and some involve computation; an appendix offers simple codes written in Maple?, Mathematica?, and MATLAB? software to give students practice with computation applied to dynamical systems problems.

Download or read book Dynamics Models and Kinetic Methods for Non equilibrium Many Body Systems written by John Karkheck and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: Recent years have witnessed a resurgence in the kinetic approach to dynamic many-body problems. Modern kinetic theory offers a unifying theoretical framework within which a great variety of seemingly unrelated systems can be explored in a coherent way. Kinetic methods are currently being applied in such areas as the dynamics of colloidal suspensions, granular material flow, electron transport in mesoscopic systems, the calculation of Lyapunov exponents and other properties of classical many-body systems characterised by chaotic behaviour. The present work focuses on Brownian motion, dynamical systems, granular flows, and quantum kinetic theory.

Download or read book A Dynamical Systems Theory of Thermodynamics written by Wassim M. Haddad and published by Princeton University Press. This book was released on 2019-06-04 with total page 744 pages. Available in PDF, EPUB and Kindle. Book excerpt: A brand-new conceptual look at dynamical thermodynamics This book merges the two universalisms of thermodynamics and dynamical systems theory in a single compendium, with the latter providing an ideal language for the former, to develop a new and unique framework for dynamical thermodynamics. In particular, the book uses system-theoretic ideas to bring coherence, clarity, and precision to an important and poorly understood classical area of science. The dynamical systems formalism captures all of the key aspects of thermodynamics, including its fundamental laws, while providing a mathematically rigorous formulation for thermodynamical systems out of equilibrium by unifying the theory of mechanics with that of classical thermodynamics. This book includes topics on nonequilibrium irreversible thermodynamics, Boltzmann thermodynamics, mass-action kinetics and chemical reactions, finite-time thermodynamics, thermodynamic critical phenomena with continuous and discontinuous phase transitions, information theory, continuum and stochastic thermodynamics, and relativistic thermodynamics. A Dynamical Systems Theory of Thermodynamics develops a postmodern theory of thermodynamics as part of mathematical dynamical systems theory. The book establishes a clear nexus between thermodynamic irreversibility, the second law of thermodynamics, and the arrow of time to further unify discreteness and continuity, indeterminism and determinism, and quantum mechanics and general relativity in the pursuit of understanding the most fundamental property of the universe—the entropic arrow of time.

Download or read book Dynamical Systems Models of Wall bounded Shear flow Turbulence written by John Francis Gibson and published by . This book was released on 2002 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Geometrical Theory of Dynamical Systems and Fluid Flows revised Edition written by and published by World Scientific. This book was released on 2009 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This is an introductory textbook on the geometrical theory of dynamical systems, fluid flows and certain integrable systems. The topics are interdisciplinary and extend from mathematics, mechanics and physics to mechanical engineering, and the approach is very fundamental. The main theme of this book is a unified formulation to understand dynamical evolutions of physical systems within mathematical ideas of Riemannian geometry and Lie groups by using well-known examples. Underlying mathematical concepts include transformation invariance, covariant derivative, geodesic equation and curvature tensors on the basis of differential geometry, theory of Lie groups and integrability. These mathematical theories are applied to physical systems such as free rotation of a top, surface wave of shallow water, action principle in mechanics, diffeomorphic flow of fluids, vortex motions and some integrable systems. In the latest edition, a new formulation of fluid flows is also presented in a unified fashion on the basis of the gauge principle of theoretical physics and principle of least action along with new type of Lagrangians. A great deal of effort has been directed toward making the description elementary, clear and concise, to provide beginners easy access to the topics."-

Download or read book Traffic and Granular Flow 13 written by Mohcine Chraibi and published by Springer. This book was released on 2014-12-05 with total page 617 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book continues the biannual series of conference proceedings, which has become a classical reference resource in traffic and granular research alike, and addresses the latest developments at the intersection of physics, engineering and computational science. These involve complex systems, in which multiple simple agents, be they vehicles or particles, give rise to surprising and fascinating phenomena. The contributions collected in these proceedings cover several research fields, all of which deal with transport. Topics include highway, pedestrian and internet traffic; granular matter; biological transport; transport networks; data acquisition; data analysis and technological applications. Different perspectives, i.e., modeling, simulations, experiments, and phenomenological observations are considered.

Download or read book Introduction to Turbulent Dynamical Systems in Complex Systems written by Andrew J. Majda and published by Springer. This book was released on 2016-09-14 with total page 97 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a research expository article on the applied mathematics of turbulent dynamical systems through the paradigm of modern applied mathematics. It involves the blending of rigorous mathematical theory, qualitative and quantitative modeling, and novel numerical procedures driven by the goal of understanding physical phenomena which are of central importance to the field. The contents cover general framework, concrete examples, and instructive qualitative models. Accessible open problems are mentioned throughout. Topics covered include: · Geophysical flows with rotation, topography, deterministic and random forcing · New statistical energy principles for general turbulent dynamical systems, with applications · Linear statistical response theory combined with information theory to cope with model errors · Reduced low order models · Recent mathematical strategies for online data assimilation of turbulent dynamical systems as well as rigorous results for finite ensemble Kalman filters The volume will appeal to graduate students and researchers working mathematics, physics and engineering and particularly those in the climate, atmospheric and ocean sciences interested in turbulent dynamical as well as other complex systems.

Download or read book Dynamical Systems PDEs and Networks for Biomedical Applications Mathematical Modeling Analysis and Simulations written by André H. Erhardt and published by Frontiers Media SA. This book was released on 2023-02-15 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Chaotic Climate Dynamics written by A. Selvam and published by Luniver Press. This book was released on 2007-08 with total page 157 pages. Available in PDF, EPUB and Kindle. Book excerpt: Atmosphere is a chaotic system. As such it is inherently unpredictable. The book applies chaos theory to understand and predict climate systems. Author presents a cell dynamical system model for turbulent fluid flows. The model envisages the irregular space-time fluctuations of the atmospheric flow pattern generated as a consequence of the superimposition of a continuum of eddies. The natural space-time variability is quantified in terms of the universal inverse power-law form of the statistical normal distribution. A range of possible applications of the cell dynamical system model for weather and climate system is discussed. The book provides a comprehensive reference material for scientists and academicians working in the field of atmospheric sciences and related topics.

Download or read book Mathematical Modeling of Collective Behavior in Socio Economic and Life Sciences written by Giovanni Naldi and published by Springer Science & Business Media. This book was released on 2010-08-12 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: Using examples from finance and modern warfare to the flocking of birds and the swarming of bacteria, the collected research in this volume demonstrates the common methodological approaches and tools for modeling and simulating collective behavior. The topics presented point toward new and challenging frontiers of applied mathematics, making the volume a useful reference text for applied mathematicians, physicists, biologists, and economists involved in the modeling of socio-economic systems.

Download or read book IUTAM Symposium on Segregation in Granular Flows written by Anthony D. Rosato and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: Segregation is a pervasive phenomenon whereby a flowing granular mass consisting of particles with diverse physical properties becomes spatially inhomogeneous. In the industrial sector that deals with the handling and processing of bulk solids, this non-uniformity is highly undesirable since blend homogeneity is generally a stringent requirement of most products. In the arena of geophysical flows, segregation can enhance the destructive capabilities of natural events such as avalanches and landslides. During the last 15 years, these issues have provided motivation and fostered collaborations between the communities of mathematicians, engineers, industrial researchers, and physicists to develop predictive models of segregation by integrating the perspectives and approaches of each. The collection of unique papers brings to light many of the perplexing scientific and technical issues in our current understanding of this complex phenomenon. It addresses advances in experiment, computational modeling and theory. This volume is one of the very few books devoted entirely to problems of segregation of particulate solids.

Download or read book Statistical Physics and Dynamical Systems written by FRITZ and published by Springer Science & Business Media. This book was released on 2013-11-22 with total page 489 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Handbook of Dynamic Data Driven Applications Systems written by Erik P. Blasch and published by Springer Nature. This book was released on 2022-05-11 with total page 753 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Dynamic Data Driven Applications Systems establishes an authoritative reference of DDDAS, pioneered by Dr. Darema and the co-authors for researchers and practitioners developing DDDAS technologies. Beginning with general concepts and history of the paradigm, the text provides 32 chapters by leading experts in ten application areas to enable an accurate understanding, analysis, and control of complex systems; be they natural, engineered, or societal: The authors explain how DDDAS unifies the computational and instrumentation aspects of an application system, extends the notion of Smart Computing to span from the high-end to the real-time data acquisition and control, and manages Big Data exploitation with high-dimensional model coordination. The Dynamically Data Driven Applications Systems (DDDAS) paradigm inspired research regarding the prediction of severe storms. Specifically, the DDDAS concept allows atmospheric observing systems, computer forecast models, and cyberinfrastructure to dynamically configure themselves in optimal ways in direct response to current or anticipated weather conditions. In so doing, all resources are used in an optimal manner to maximize the quality and timeliness of information they provide. Kelvin Droegemeier, Regents’ Professor of Meteorology at the University of Oklahoma; former Director of the White House Office of Science and Technology Policy We may well be entering the golden age of data science, as society in general has come to appreciate the possibilities for organizational strategies that harness massive streams of data. The challenges and opportunities are even greater when the data or the underlying system are dynamic - and DDDAS is the time-tested paradigm for realizing this potential. Sangtae Kim, Distinguished Professor of Mechanical Engineering and Distinguished Professor of Chemical Engineering at Purdue University

Download or read book Fluid Vortices written by Sheldon Green and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 905 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fluid Vortices is a comprehensive, up-to-date, research-level overview covering all salient flows in which fluid vortices play a significant role. The various chapters have been written by specialists from North America, Europe and Asia, making for unsurpassed depth and breadth of coverage. Topics addressed include fundamental vortex flows (mixing layer vortices, vortex rings, wake vortices, vortex stability, etc.), industrial and environmental vortex flows (aero-propulsion system vortices, vortex-structure interaction, atmospheric vortices, computational methods with vortices, etc.), and multiphase vortex flows (free-surface effects, vortex cavitation, and bubble and particle interactions with vortices). The book can also be recommended as an advanced graduate-level supplementary textbook. The first nine chapters of the book are suitable for a one-term course; chapters 10--19 form the basis for a second one-term course.