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Geophysical methods of prospecting for oil and gas resources are based on observations of elastic wave fields, treated to a first approximation as acoustic waves. Emitted pressure impulses penetrate the crust and then are backscattered to the surface where they are detected by an array of receivers. The goal of seismic processing is to recover from the recorded wave field as much information as possible about the earth subsurface. Migration is an acoustic image reconstruction technique based on the inversion of the scalar wave equation. In the migration process the recorded pressure waves are used as initial conditions for a wave field governed by the scalar wave equation which propagates downward and in reverse time. [ABSTRACT FROM AUTHOR]

We translate a standard approach of Field Theory into the framework of Cellular Automata (CA) to construct a parametrised class of stochastic 2D CA models simulating general explosion phenomena. The models exhibit morphological instabilities and phase transitions from bounded to unbounded growth. [ABSTRACT FROM AUTHOR]

Using elementary differential algebraic techniques, we prove that the 3-D Lotka-Volterra dynamical system has no other nontrivial polynomial first integrals than the previously known ones. [ABSTRACT FROM AUTHOR]

Pioneering leads the way in science and is essential to those who follow, who reap the benefits. Plasma simulation, begun in the 1950s, has had numerous pioneering efforts over the past five decades. This short paper recalls some of these, apropos to recognizing the early contributions by Marc Feix. The next decade will probably see science simulations done in high schools with simulations of whole devices, small and large, accelerating immensely. [ABSTRACT FROM AUTHOR]

We consider the Schrödinger equation as the reversible approximation of a more general irreversible equation whose expression is derived. It becomes, therefore, possible to describe continously any quantum transition. [ABSTRACT FROM AUTHOR]

An analytical and local expression of the semiclassical Wigner distribution is performed using the Airy uniform approximation in the neighbourhood of a turning point. At the classical limit the one-dimensional Wigner distribution leads to the microcanonical distribution. For the two-dimensional systems the variables separable problems (nonchaotic dynamics) and the variables nonseparable problems (possibility of chaos) are not locally distinguishable by using the uniform approximation. Meanwhile the examination of a section of the phase space allows us to see that the apparent complexity of the Wigner distribution is not a proof of chaos. [ABSTRACT FROM AUTHOR]

The subject of this paper concerns the design of telecommunication networks. Through a simple model of competition in the local access network, we illustrate the interest of some statistical physics concepts. In particular, simulated annealing as a computing method and dimensional analysis for optimal solution behaviour are physical contributions to such network studies. Moreover one can demonstrate a phase transition phenomenon while optimising two technology networks. [ABSTRACT FROM AUTHOR]

The generalised second order Riccati equation is a nonlinear differential equation which can be transformed into a linear third order ODE. We are interested here in the search for asymptotic solutions of this equation in the case that there is a transition point (turning point). Then we consider the analytical solutions of y‴−xy′−μy=0, which involve and generalise Airy functions. [ABSTRACT FROM AUTHOR]

A branch and bound algorithm for the flow-shop scheduling problem is proposed. Dominated nodes are removed from the tree. [ABSTRACT FROM AUTHOR]

We study the generalised Chazy equation, $$\dddot x + x^q \ddot x + kx^{q - 1} \dot x^2 = 0$$ , which is characterised by the symmetries of time translation and rescaling. For a large class of initial conditions numerical computations reveal the asymptotic appearance of periodic solutions for k=q+1. These solutions are identical after rescaling and, in this sense, exhibit the property of a limit cycle in the three dimensional phase space. The periodic solutions are related to a conventional limit cycle of a class of second order ordinary differential equations which are connected to the existence of a first integral of the generalised Chazy equation. [ABSTRACT FROM AUTHOR]

We propose a model of tropical rain forests over large time scales. Discrete rate equations are derived from the elementary physical phenomena, which drive the evolution of the ecosystems, using methods from quantum field theory. This leads to a set of equations essentially similar to the Lotka-Volterra system — though more complex because of the presence of transport terms. Considerations on the integrability of this system are also given. [ABSTRACT FROM AUTHOR]

Let S be an orientable compact connected surface without boundary and let X be a C2 vector field such that its flow is area preserving on S. Assume that X has finitely many singular points, satisfies a Lojasiewicz condition at all its singular points and has singular points if S is the 2-dimensional torus. Then every singular point is either a center or it has a neighbourhood which splits into a finite union of an even number of hyperbolic sectors and all orbits of X are closed except finitely many of them which are either singular points or separatrices joining singular points. The same result is true for measure preserving flows on S. In this case it is not necessary that S be orientable. [ABSTRACT FROM AUTHOR]

The singularity analysis of ordinary differential equations is based on the concept of the balance of the dominant terms. The equivalence of these terms is reflected by the possession of the same similarity symmetry. Different possible singular behaviours are reflected by different similarity symmeties. Hierarchal structures are observed. The generalised Chazy equation provides a simple example of this structure. The singularity analysis is based on the recently introduced ‘g function' method. [ABSTRACT FROM AUTHOR]

Hamilton's principal function for an N-degree-of-freedom non autonomous Hamiltonian system is expressed in terms of quadratures involving N, possibly time-dependent, invariants in involution. This determines a set of 2N canonical coordinates and momenta, each of which is an invariant. [ABSTRACT FROM AUTHOR]

The Lie point symmetry analysis of Ermakov systems is extended to the case where the frequency function in the equations of motion depends also on the dynamical variables and their derivatives. From this new standpoint, a quite general class of two dimensional oscillators with nonlinear coupling can be viewed as a Hamiltonian Ermakov system possessing a Lie point symmetry and is shown to be completely integrable. [ABSTRACT FROM AUTHOR]

We study the two-dimensional autonomous systems of differential equations of the form $$\dot x$$ =y+a20x2+a11xy+a02y2, $$\dot y$$ =b20x2+b11xy+b02y2, where aij and bij are arbitrary real constants. The origin is a degenerate critical point of this system. In this work we give a sufficient conditions for local integrability at the origin. [ABSTRACT FROM AUTHOR]

In this paper we study isochronous centers of reversible two-dimensional autonomous system with linear part of center type and nonlinear part given by polynomials of third degree. Firstly we find necessary conditions for such isochronous centers in polar coordinates and finally we give a proof of the isochronicity of these systems using different methods. [ABSTRACT FROM AUTHOR]

We apply the method of Darboux to study the integrability of the 2d Lotka-Volterra system. The method of Darboux, which consists of finding first integrals by using algebraic solutions, is reduced in the case of the Lotka-Volterra system to obtaining only one algebraic solution different from the two axes, which can be a polynomial of arbitrary degree. Here we are concerned with polynomials of degree less than five. We find that all the essential parameters of the Lotka-Volterra system must be fixed for the existence of a polynomial solution of degree greater than or equal to three whereas, for degrees one and two respectively, only one and two conditions on the parameters are required. [ABSTRACT FROM AUTHOR]

A semi-lagrangian relativistic Vlasov model is described for a hierarchy of applications of increasing complexity, in one and two dimensions. Attention is focused on its accuracy, stability, efficiency properties and implementation facilities on massively parallel computers. Such a code provides good resolution all over phase space, including very low density regions where Particles-In-Cell PIC codes simply run out of particles for which to compute. Recent developments in applying semi-lagrangian Vlasov codes to 1D and 2D problems in an electromagnetic regime (including Forward Raman Scattering and Relativistic Modulational Instability) are then reviewed. [ABSTRACT FROM AUTHOR]

We determine the general expression for the interaction force between point elements or vector elements, based on symmetry group properties in space. In a particular case this expression is then shown to derive from a scalar form of energy. [ABSTRACT FROM AUTHOR]

We show analytically that it is natural to develop a hierarchy of structures in a one dimensional self-gravitating gas exploded from an initial Gaussian space distribution and a smooth symmetric momentum distribution. We also conjecture the occurrence of an instability for some combination of time and gravitational coupling constant. [ABSTRACT FROM AUTHOR]

The coupling between collective and individual modes for a meta-equilibrium one-dimensional gravitating gas is studied. The one-dimensional water-bag model allows the calculation of the theoretical values of these modes and they are compared with those obtained by simulations realised with an N Body code. Finally the influence on the time evolution and stability of holes localised in the water-bag equilibrium is numerically investigated. [ABSTRACT FROM AUTHOR]

We review the results of recent investigations of the dynamics of one-dimensional gravitational systems carried out at Texas Christian University. Two types of systems are considered: (1) parallel mass sheets of infinite spatial extent and (2) concentric, spherically symmetric, irrotational mass shells confined between two rigid spherical barriers. By studying the kinetic energy equipartition of a sheet system consisting of two distinct populations with a fixed mass ratio, we show that the system approaches equilibrium on a long time scale. We show that the system of spherical shells has stronger ergodic properties than the planar sheets and that it approaches equilibrium on a much shorter time scale. In addition, for sufficiently small inner barrier radius, it undergoes a phase transition to a state with a greatly condensed core as the energy passes through its phase equilibrium value. [ABSTRACT FROM AUTHOR]

In this paper, we derive a Jeans' criterion for the dynamical spherical collapse of a gravitational polytropic medium with constant γ. In opposition to the classical (static configuration) Jeans' criterion where a threshold for stability appears, it is shown that the stability of the dynamical solution depends on the value of γ. For γ=4/3, the existence of a threshold is also obtained. However, for γ≠4/3, the system is always unstable with an instability growing according to a time-power, instead of the usual exponential law. In addition, two types of instabilities are obtained: the large wavelengths are unstable from the very beginning of the evolution, whereas the small ones, produce oscillations on a finite range of time and, finally, the system becomes unstable (oscillations stop). In this stage the pressure can be neglected. Since the collapse is unstable, we examine the fragmentation problem. The dynamical Jeans' criterion suggests a cascade in which the mass M and the radius R of the pieces are connected by a relation of the type M∞R2. [ABSTRACT FROM AUTHOR]

We propose a functional framework for some nonlinear dynamics, where the nonlinearities are (very) short-range perturbation of a given Hamiltonian. In this framework one can prove the global in time existence and uniqueness of a solution for the time dependent problem and the existence of steady states of the form which can be specified. This problem arises from the modeling of semiconductors and covers different applications. [ABSTRACT FROM AUTHOR]

The simultaneous balance of nonlinear spatial self-focusing with diffraction and the compensation of dispersion with nonlinear temporal self-focusing, in a saturating nonlinear medium, gives stable spatiotemporal solitons — light bullets. An analytical approach for arbitrary saturating nonlinearity is established in order to investigate the dynamics of such light bullets. The analytically predicted exceptional robustness of light bullets, which can be generated over a large range of values of the parameters, is confirmed by numerical simulations. [ABSTRACT FROM AUTHOR]

We study the statistical properties of nonlinear wave-wave interaction in a system consisting of three Langmuir waves and one ion-sound wave. Such a system describes either a cascade of two decay instabilties or a modified decay instability. We pay a particular attention to the phases which in some cases exhibit a chaotic synchronization, showing a transition from three-wave to four-wave interaction. [ABSTRACT FROM AUTHOR]

It is shown that "Liouville's theorem" on integrability still holds in the case of time-dependent Hamiltonian systems; when they have n independent possibly time-dependent invariants in involution the solution can be found by quadratures and no chaos can take place. This is applied to the relativistic motion of a charged particle in a homogeneous constant magnetic field and a transverse circularly polarized homogeneous electric field. [ABSTRACT FROM AUTHOR]

Playing with the geometrical dimensionality of plasmas models gives us the opportunity to explore models with different properties. In particular, a lower dimensionality allows us to avoid a quantum description of interactions between oppositely charged particles, totally in one dimension and partially in two dimensions. We will describe some models; from the One and Two Component Plasma in one and two dimensions to the "true" three dimensional plasma combined with a Thomas-Fermi description of the electrons. [ABSTRACT FROM AUTHOR]

The Crank-Nicolson scheme is widely used to solve numerically the diffusion equation, because of its good stability properties. It is, however, ill-behaved when large time-steps are used: the short wave-lengths may happen to be less damped than the long ones. A detailed analysis of this flaw is performed and an alternative scheme is proposed, which removes this difficulty while preserving all other good properties (unconditional stability and second-order accuracy). [ABSTRACT FROM AUTHOR]

A negative ion plasma expansion into vacuum is simulated by use of a one-dimensional, fully Eulerian code. As for the case of a two species plasma, the time-asymptotic regime is found to be self-similar with the temperature decreasing as t−2. The numerical results exhibit clearly the physically expected effects of mass separation. [ABSTRACT FROM AUTHOR]

We consider transport equations with a second member which is a full space derivative. This structure coresponds to numerous models of fluid dynamics and to the kinetic formulation of isentropic gas dynamics and, for the case of scalar conservation laws, averaging lemmas prove regularizing effects. We extend the averaging lemmas to second members which are a full space derivative. Our method uses Calderón-Zygmund theory. [ABSTRACT FROM AUTHOR]

The splitting schemes of the 1D and 2D Vlasov equations are presented for the electrostatic (with an external magnetic field in 2D) problem. A solution of the split equations by a Flux Balance Method (F.B.) is shown and extended to cases where the transport coefficient depends upon the variable (as in the relativistic Vlasov problem). A short comparison with a 1D spline model is given and a 2D phase space visualisation of an electrostatic simulation is presented. [ABSTRACT FROM AUTHOR]

Both one-and-a-half and two-dimensional simulations of a dense neutral plasma impinged upon by a ultra-intense laser pulse are presented. The various scenarii of plasma interaction are reviewed. [ABSTRACT FROM AUTHOR]

Numerical simulation has long been recognised has an essential tool to study the complex nature of plasma physics. For those who are involved in this field it is essential to identify the pioneering work of some contributors. The purpose of this short paper is to recall the early contributions by Marc Feix to numerical plasma simulation and also to more general problems in other areas of mathematical physics. [ABSTRACT FROM AUTHOR]

A self-consistent treatment of reaction-diffusion processes is surveyed. Dynamic response to heating processes as well as the phenomenon of profile consistency is analysed. [ABSTRACT FROM AUTHOR]