UK Nonlinear News, August 2000.
Michel Pierre and Didier Schmitz. Blowup in Reaction-Diffusion Systems with Dissipation of Mass. SIAM Review Volume 42(1), March 2000, pages 93-106.
Abstract: We prove possible blowup in finite time of the solutions to reaction-diffusion systems which preserve nonegativity and for which the total mass of the components is nonincreasing in time (two natural properties in applications). This is done by presenting explicit counterexamples constructed with the help of formal computation software. Several partial results of global existence had been obtained previously in the literature. Our counterexamples explain a posteriori why extra conditions were needed. Negative results of independent interest are also provided as a by-product for linear parabolic equations in nondivergence form and with discontinuous coefficients and for nonlinear Hamilton-Jacobi evolution equations.
Rick Durrett. Stochastic Spatial Models. SIAM Review Volume 41(4), December 1999.
Abstract: In the models we will consider, space is represented by a grid of sites that can be in one of a finite number of states and that change at rates that depend on the states of a finite number of sites. Our main aim here is to explain an idea of Durrett and Levin (1994): the behaviour of these models can be predicted from the properties of the mean field ODE, i.e., the equations for the densities of the various types that result from pretending that all sites are always independent. We will illustrate this picture through a discussion of eight families of examples from statistical mechanics, genetics, population biology, epidemiology, and ecology. Some of our findings are only conjectures based on simulation, but in a number of cases we are able to prove results for systems with "fast stirring" by exploiting connections between the spatial model and an associated reaction diffusion equation.
The SIAM Activity Group on Dynamical Systems has recently released a new issue of their newsletter Dynamic Notes. It is available from their new web site: http://math.gmu.edu/html/ds/.
| Review Article | |
| Review of Virtual Distortion Method and Its Applications to Fast Redesign and Sensitivity Analysis | |
| Jan Holnicki-Szulc, Tomasz Bielecki | 71 |
| Technical Papers | |
| Optic Discrete Breathers in Euclidean Invariant Systems | |
| R.S.MacKay | 99 |
| Nonlinear Properties for Dynamic Behavior of Liquid with a Free Surface in a Rigid Moving Tank | |
| Oleg S. Imarchenko | |
| Dynamics of Stochastic Layers in Nonlinear Hamiltonian Systems | |
| Albert C.J. Luo and Ray P.S. Han | |
| A Classical Variational Model for Micropolar Elastodynamics | |
| Ji-Huan He | 133 |
| Letter | |
| A Variational Model for Micropolar Fluids in Lubrication Journal Bearing | |
| Ji-Huan He | 139 |
| Book Review | |
| Preprinciples of Mechanics (Veljko A. Vujicic) | |
| Katica (Stevanovic) Hedrih | 143 |
Source: Wen CHEN ( chenw@homer.shinshu-u.ac.jp).
Pages: 973--1424
| 973 | V. Afraimovich and B. Fernandez |
| Topological properties of linearly coupled expanding map lattices. | |
| 995 | H. Sumi |
| Skew product maps related to finitely generated rational semigroups | |
| 1021 | J. Palaci\'an and P. Yanguas |
| Reduction of polynomial Hamiltonians by the construction of formal integrals | |
| 1055 | L. Flatto and J.C. Lagarias |
| The lap-counting and zeta functions of the tent map | |
| 1073 | A. Ramani, Y. Ohta and B. Grammaticos |
| Discrete integrable systems from continuous Painlev\'e equations through limiting procedures | |
| 1087 | S. Yakovenko |
| On zeros of functions from Bernstein classes | |
| 1095 | G. Olivar, E. Fossas and C. Batlle |
| Bifurcations and chaos in converters. Discontinuous vector fields and singular Poincar\'e maps | |
| 1123 | V. Zharnitsky |
| Invariant curve theorem for quasiperiodic twist mappings and stability of motion in the Fermi--Ulam problem | |
| 1137 | A. Alonso Izquierdo, M.A. Gonz\'alez Le\'on and J. Mateos Guilarte |
| Kinks from dynamical systems: domain walls in a deformed O(N) linear sigma model | |
| 1171 | M. Dellnitz, G. Froyland and S. Sertl |
| On the isolated spectrum of the Perron--Frobenius operator | |
| 1189 | C. Fermanian Kammerer and H. Zaag |
| Boundedness up to blow-up of the difference between two solutions to a semilinear heat equation | |
| 1217 | T. Ioannidou |
| SU(N) skyrmions from instantons | |
| 1227 | N. Ju |
| The H1 compact global attractor for the solutions to the Navier--Stokes equations in two-dimensional unbounded domains | |
| 1239 | J-F Collet and T. Goudon |
| On solutions of the Lifshitz--Slyozov model | |
| 1263 | P. Collet, S. Mart\'{rm i} nez and V. Maume-Deschamps |
| On the existence of conditionally invariant probability measures in dynamical systems | |
| 1275 | M. Degli Esposti, G. Del Magno and M. Lenci |
| Escape orbits and ergodicity in infinite step billiards | |
| 1293 | P.C. Matthews and S.M. Cox |
| Pattern formation with a conservation law | |
| 1321 | K Josi\'c |
| Synchronization of chaotic systems and invariant manifolds | |
| 1337 | Yu Ilyashenko |
| Hilbert-type numbers for Abel equations, growth and zeros of holomorphic functions | |
| 1343 | G. Grammel |
| On the Van-der-Pol oscillator with noisy nonlinearity | |
| 1357 | B. Sandstede, S. Balasuriya, C.K.R.T. Jones and P. Miller |
| Melnikov theory for finite-time vector fields | |
| 1379 | F. Cantrijn, M. de Le\'on, J.C. Marrero and D. Mart\'{rm i}n de Diego |
| On almost-Poisson structures in nonholonomic mechanics: II. The time-dependent framework | |
| 1411 | P. Bizo\'n, T. Chmaj and Z. Tabor |
| Dispersion and collapse of wave maps |
Nonlinear phenomena appear everywhere in our daily life and in our scientific work, and today they represent one of the most important fields of research in science and technology. There exist innumerable hidden pearls in various nonlinear phenomena, these pearls can only be found by proper mathematical modelling, which may be simple and beautiful, or complex and exciting.
We feel that there is an urgent need for an International Journal of Nonlinear Modelling in Science and Engineering. The aim of this journal is to bring to the fore the many new and exciting nonlinear mathematical modelling applications in science and engineering, thereby capturing both the interest and imagination of the wider communities in various fields, such as in mathematics, physics, chemistry, earth science, computational science, biologics, economics, and nanotechnolgy. We hope by studying or improving the proposed modelling, new branches of science will occur, for example, nano-mathematics, nano-chemistry, nano-physics, nano-biotechnology and the like.
The emphasis of this journal, therefore, is placed on how to establish a proper nonlinear modelling for a real-life nonlinear problem, to search for pearls through complex phenomena by numerical or analytical solution. The numerical techniques for some special nonlinear modellings, for example, nonlinear fractional differential equations, are also welcome.
To make the journal accessible to a broad audience, the authors will, in the first Issue, present an overview of the current status of their fields with a speculative outlook on what are to come out in the future.
We are now seeking financial support from all sectors, and nominations of contributing editors specialized in various fields are mostly welcome. We cordially invite universities and institutes worldwide to sponsor this new journal.
My address is
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Source: Wen Chen ( chenw@homer.shinshu-u.ac.jp)
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