On the dynamics of a discrete reaction-diffusion system

We investigate various aspects of the dynamics of a discrete reaction-diffusion system. First, we examine the effect of the boundary conditions on the spatially uniform fixed point at locations far from the boundaries by using an asymptotic expansion. We show that, except for a few computational cells adjacent to the boundary, the fixed point practically coincides with the one calculated by using reflective boundary conditions (equivalent to an infinite domain). Next, we introduce a classification of the fixed points based on the wavelength in the infinite-medium approximation of the system. We use the symbolic manipulator MACSYMA to analytically calculate the amplitude of several such classes of fixed points and we generate bifurcation diagrams for their members. Also, we consider two special classes of periodic solutions; we calculate their amplitude analytically in the infinite-medium approximation, and generate bifurcation diagrams that shed new light on some previous confusing results. Finally, we present an analysis of fictitious periodic solutions that have been previously reported and incorrectly interpreted.     

Evidence for resonant structure near 1780 MeV in e+ e− annihilations observed with the new colliding beam ring at Orsay

We present evidence for the existence of a new J^PC = 1^?? resonance with a mass of 1778 ± 14 (±12) MeV and 150 ± 40 (±30) MeV wide. We tentatively conclude that it is an I = 0 state.     

Amplitude analyses of the reactions π+p → (ϱ0, ω) Δ++ at 7.1 GeV/c

New data are presented, in the form of statistical tensors, for the reactions π⁺p → (?⁰, ω)Δ⁺⁺ at 7.1 GeV/c. Using these data, two types of model-dependent amplitude analyses have been performed. Both analyses, though based on different sets of assumptions, yield results which are in agreement with each other. The structure observed in the magnitudes and phases of the extracted amplitudes is consistent with that expected on the basis of currently accepted phenomenological ideas.     

Hadronic cross sections study in e+e− collisions from 1.350 GeV to 2.125 GeV

The results of the first experiment performed at DCI in e⁺e^? annihilations in the c.m. energy range 1.350–2.125 GeV region are presented. The cross sections of various multipion channels are extracted. Significant structure appears in some specific channels. A relatively narrow resonance around 1.660 GeV decaying into 3π's is found. Charged and neutral multiplicities, and also the ratio R are given.     

A study of inclusive vector meson production

Data are presented on the reactions π⁺n → ?⁰+X and $\text{K}{}^{\mathrm{?}}\text{p}\text{→}\text{K}{}^1\text{0}\text{(890)+}\text{X}\text{at 6.0}\text{and}\text{7.3}\text{GeV}\text{/c}$, respectively. Comparisons are made with related reactions at higher energies.     

A weight-function approach for determining watershed initial conditions for combustion waves

In many generic combustion models, one finds that a combustionwave will develop with a specific wave speed. However, thereare possible initial temperature profiles which do not evolveinto such waves, but rather die out to the ambient temperature.There can exist, in some models, a clear distinction betweenthose initial conditions that do evolve into combustion wavesand those that do not; this is sometimes referred to as thewatershed initial condition. When fuel consumption is consideredto be negligible, analytical methods can be used to obtain theexact watershed. In this paper, we consider the problem of determiningpseudo-watersheds and ascertaining the relationship betweenthese pseudo-watersheds and the exact watersheds. In the processa novel weight-function approach for infinite spatial domainsis developed.     

Optimal control for parabolic systems with competitive interactions

We consider a two-dimensional parabolic system with general competitive interactions as a two-player game with conflicting objectives and with controls on the inhomogencous (source) terms. We show the existence of an optimal solution of the game as the saddle point of a suitable objective functional.     

On the spectrum of the linear transport operator with generalized boundary conditions

The spectrum of the linear transport operator under generalized boundary conditions proposed by Belleni-Morante (1970 a) contains in the right half-plane (|Re>–1) only a finite number of real eigenvalues. Its essential spectrum consists of a fan of continuous spectrum lines with apex at =–1.