Applied Math Faculty Research A special class of solutions are referred to as solitons, Solitons areimportant in physical application especially in nonlinear optics. http://amath.colorado.edu/people/faculty/fac_summ.html
Extractions: (Ph.D. MIT) An essential element in the study of Applied Mathematics is to explain physical phenomena by mathematical models. Frequently such models lead to nonlinear systems and in a surprisingly large number of cases certain prototypical systems are obtained. A central theme in Ablowitz' research is to understand by approximation, numerical and exact methods, solutions to these underlying equations and their properties. An important method used to solve certain nonlinear wave equations is the so called Inverse Scattering Transform: IST. The IST is conceptually analogous to the Fourier Transform; IST employs methods of direct and inverse scattering. These techniques were originally developed by physicists and mathematicians studying quantum mechanics. The IST allows one to construct general solutions to certain initial-boundary value problems that arise in a variety of physical problems such as nonlinear optics, water waves, plasma physics, lattice vibrations, and relativity. A special class of solutions are referred to as solitons , which are extremely stable localized waves. Solitons are important in physical application especially in nonlinear optics.
The Math Forum - Math Library - Chaos chaos research Group (CRG) University of Tennessee, Knoxville The chaos researchGroup is an interdisciplinary team of faculty, students and engineering http://mathforum.org/library/topics/chaos/
Extractions: Chaos is an advanced field of mathematics that involves the study of dynamical systems or systems in motion. Chaos Theory consists of the mathematical proofs and theories that attempt to describe processes in motion. Think of any mathematical system that changes over time, such as the weather, the stock market, or the genetic distribution of a population. Tour of Chaos: Basic Concepts (Iteration, Orbits, Attraction and Repulsion, Graphical Analysis, Bifurcations); Examples (Cantor Set, Sierpenski Triangle, Mandelbrot Set, Julia Set); Java Applets Involving Chaos (Mandelbrot/Julia Set Explorer, Mandelbrot Escape Sequences). more>> random.org - Mads Haahr Generate random numbers on the Internet by using a web form (comparable to throwing dice), randomized sequences (lottery tickets), raw random bytes, virtual coin flips, or bitmaps. All numbers are tested statistically and the results available in real-time. Read the introduction to randomness, random numbers, and how random.org generates random numbers. Source code available. more>> Topical Index of Internet Resources (The Chaos Hypertextbook) - Glenn Elert
Research Highlights Of R.Klages fractal transport coefficients, microscopic chaos, habilitation thesis. Physical systems of this class being accessible in experiments are, for example, http://www.maths.qmw.ac.uk/~klages/teaching/rkresearch.html
Extractions: During my Ph.D. thesis work I discovered the phenomenon that diffusion coefficients can be fractal functions of control parameters . At first view this finding appears to be counter-intuitive, since usually one expects physical quantities to change smoothly under parameter variation as, for example, in Ohm's law. Subsequently it was shown by colleagues, coworkers and myself that this behavior is quite typical not only for diffusion but also for other types of transport coefficients (e.g., electrical conductivities, chemical reaction rates) characterizing transport in low-dimensional deterministic dynamical systems exhibiting spatial periodicities . This class of systems thus exhibits properties that are at the borderline of traditional statistical physics revealing fingerprints of an underlying microscopic deterministic dynamics. Physical systems of this class being accessible in experiments are, for example, semiconductor devices like antidots and Josephson junctions, certain types of ratchets, and corrugated vibratory conveyors, the latter frequently being used in industrial applications for transporting granular entities. For all these systems there are theoretical predictions of fractal, or at least highly irregular, parameter dependencies of physical transport properties. Although hints on experimental observations of such irregularities already exist in the literature, it still remains to clearly match theory with experiments at this point.
Extractions: The concept of cosmogenesis only entered the field of science at that crucial and surprising moment for physicists when it became clear that the universe was evolutionary and, therefore, had a history. That occurred in 1929 when Hubble made the experimental discovery of the expansion of the universe. Previously, it had been seen as something fixed, static and immutable. The major challenge for the physicists was then to predict how the universe would develop in the future, to forecast our cosmological future, but also to understand its history, its cosmogenesis. The Milky Way as seen through the Very Large Telescope in Paranal (Chile), at the European Southern Observatory (ESO). This core of the Galaxy includes around 400 000 stars and is about 800 million years old. An analysis of the creation and development of the Milky Way is vital to our understanding of the universe.
Preface An experimental approach to nonlinear dynamics and chaos In our opinionnonlinear dynamics research illustrates the finest aspects of small science. http://cnls.lanl.gov/People/nbt/Book/node2.html
Extractions: Next: Introduction by An Experimental Approach to Nonlinear Dynamics and Chaos is a textbook and a reference work designed for advanced undergraduate and beginning graduate students. This book provides an elementary introduction to the basic theoretical and experimental tools necessary to begin research into the nonlinear behavior of mechanical, electrical, optical, and other systems. A focus of the text is the description of several desktop experiments, such as the nonlinear vibrations of a current-carrying wire placed between the poles of an electromagnet and the chaotic patterns of a ball bouncing on a vibrating table. Each of these experiments is ideally suited for the small-scale environment of an undergraduate science laboratory. In addition, the book includes software that simulates several systems described in this text. The software provides the student with the opportunity to immediately explore nonlinear phenomena outside of the laboratory. The feedback of the interactive computer simulations enhances the learning process by promoting the formation and testing of experimental hypotheses. Taken together, the text and associated software provide a hands-on introduction to recent theoretical and experimental discoveries in nonlinear dynamics. Studies of nonlinear systems are truly interdisciplinary, ranging from experimental analyses of the rhythms of the human heart and brain to attempts at weather prediction. Similarly, the tools needed to analyze nonlinear systems are also interdisciplinary and include techniques and methodologies from all the sciences. The tools presented in the text include those of:
The Mukamel Group Bio 1992, Guest Editor, special Issue of Journal of Physical Chemistry, Charge Transfer NATO Advanced research workshop on Stochasticity and Intramolecular http://bose.ps.uci.edu/bio.html
Boris "Malomed (Melamed)"- Additional Information An invited talk at the International School of Solid State physics 1994 aspecial research grant, $7700, from the research Office of the Tel Aviv http://www.eng.tau.ac.il/~malomed/other.html
Erik Mosekilde CV special issue on chaos in Economic Systems, System Dynamics Society, MIT, special issue on Nonlinear Dynamic Phenomena in Physical, Chemical and http://fys.dtu.dk/Centre/BioCom/Staff/EMs_CV.aspx
Extractions: DTU.dk Indeks Kontakt Telefonbog document.write(''); DTU netv¦rk CampusNet DTU Intranet (gl. dtu.dk) Alumneforening KUP DTU netv¦rk CampusNet DTU Intranet (gl. dtu.dk) Alumneforening KUP ... Staff > Erik Mosekilde Erik Mosekilde Research Recent publications Books ... Kirstine Berg-S¸rensen Print CURRICULUM VITAE FOR Erik Mosekilde Department of Physics Erik Mosekilde was born in rhus, Denmark on May 26, 1941. In March 1966 he graduated (summa cum laude) from The Technical University of Denmark as an electrical engineer specialized in solid state physics, and in September 1968 he completed his Ph.D. studies at Physics Laboratory III with a thesis on acoustoelectric effects in piezoelectric semiconductors. Having performed his military service Erik Mosekilde was offered a postdoctoral position at Physics Laboratory III and shortly after received a postdoctoral fellowship from IBM, which allowed him to spend 9 months at Thomas J. Watson Research Center, Yorktown Heights, New York. In July 1972 Erik Mosekilde was appointed associate professor in modern physics, and in August 1977 he defended a dissertation on "Linear and Nonlinear Acoustoelectric Effects in Heavily Doped GaAs Epitaxial Single Crystals" for the Danish Doctor's degree at The University of Copenhagen. In September 2000 he was appointed Professor in Biological Applications of Nonlinear Dynamics at The Technical University of Denmark.
Ultrasound Imaging Of Rayleigh Bènard Convection In Liquid Metal Some very nice images of convection patterns from the research group of GuenterAhlers Right spiral defect chaos (image courtesy of J. Liu, KMS Bajaj, http://wlcnt2.wlc.edu/intranet/faculty_staff/kuehn/research.html
Extractions: Kuehn Home Course Info Research Physics Links ... Press Release It is well known that heat flows spontaneously from warmer to colder places and is capable of thereby doing work. This is known as the second law of thermodynamics Carnot, 1824 ). Such work is responsible for the function of steam engines and nuclear power plants, for the ascension of clouds and the flow of ocean currents, and for volcanism on the earth and convection on the surface of the sun. Thermal convection also plays an important role in metal and semiconductor processing (see, for instance, Kafalas and Bellows, 1986), and quite recently it has been shown to drive a chain reaction of DNA replication ( Braun, Goddard and Libchaber, 2003 Due in part to how common and how technologically important it is, thermal convection has been studied intensely in the laboratory for years, beginning with Count Rumford in 1798, who observed thermal convection in wine spirits trapped in vertical heated thermometer tubes. Another relatively simple arrangement which is commonly used to study thermal convection is the following: a thin horizontal layer of fluid is sandwiched between flat horizontal plates and subjected to a vertical temperature gradient. By this I mean that the lower plate is held at a higher temperature than the upper plate so that the fluid near the bottom plate is warmer than the fluid near the top plate. In such an arrangement, when the temperature of the bottom plate exceeds that of the top plate by some critical value, the fluid layer becomes unstable and begins to convect. This phenomenon, depicted below in Fig. 1, is called
