Table of contents

Kauffman's model is a random complex automata where nodes are randomly assembled. Each node σ_i receives K inputs from K randomly chosen nodes and the values of σ_i at time t + 1 is a random Boolean function of the K inputs at time t. Numerical simulations have shown that the behaviour of this model is very different for K > 2 and K ⩽ 2. It is the purpose of this work to give a simple annealed approximation which predicts K = 2 as the critical value of K. This approximation gives also quantitative predictions for distances between iterated configurations. These predictions agree rather well with the numerical simulations. A possible way of improving this annealed approximation is proposed.

We examine a modification of Newton's law to a potential G_NMm/r^1+ε as would follow if, e.g., we had 3 + ε noncompact spatial dimensions. This would cause a precession of the periastron of orbiting bodies. From data on Mercury we get |ε| < 1.7 · 10^-9, and from the binary PRS 1913 + 16, |ε| < 1.5 · 10^-9. This is to be compared with a recent bound |ε_e.m.| < 5 · 10^-7 from the electron g - 2. Note that, for the Coulomb potential, the negative outcome of Cavendish-like experiments show that if the Coulomb law is α_C/r^2+εC, then |ε - ε_C| < 10^-16, which does not give a bound on ε_C but supports the assumption ε = ε_C.

The possibility of observing an ordered condensed state in beam of fast charged particles to be contained within presently planned heavy-ion storage rings is pointed out, with particular attention to recently proposed application of laser cooling techniques to such beams. Some relevant considerations are mentioned.

A general analysis of dislocations in a 2d Penrose pattern is given in terms of an inhomogeneous order parameter space, which provides for their topological invariants. The corresponding Volterra processes are described. Dislocations of smallest Burgers' vector in usual Penrose patterns are characterized by stacking faults, or by the appearance of specific tilings belonging to generalized Penrose patterns. In that sense they are partial or imperfect dislocations. They are probably of great physical importance. Our order parameter space provides us also with a characterization of the canonical modes of deformation, which involve 4 hydrodynamic modes and one mode which corresponds to localized structural transitions.

Measurements are reported on the electrical resistivity ρ(B, T) in a wide range of parameters for the heavy-fermion compound UBe₁₃. In addition to known results concerning a very strong dependence of ρ on both magnetic field and temperature, the present results shed new light on the low-temperature, low-field behaviour of the magnetoresistivity Δρ(B, T) = ρ(B, T) - ρ(0, T). As T → 0, Δρ becomes very small, and the results suggest that a change of sign of Δρ from negative to positive takes place below 100 mK. Thus, from the viewpoint of magnetoresistivity, UBe₁₃ appears to behave similarly to the Ce-based heavy-fermion compounds CeAl₃ and CeCu₂Si₂, though important differences remain.

We introduce a new method, which does not use replicas, from which we recover all the results of the replica symmetry-breaking solution of the Sherrington-Kirkpatrick model.

The relaxation times, T₁ and T₂, of liquid ³He confined by fluorocarbon microspheres have been measured over a wide spectrum of frequencies (125 kHz to 100 MHz) and over a large range of temperatures. Below approximately 100 mK, T₁ and T₂ have a linear temperature dependence. In the linear temperature regime, T₁ varies linearly with frequency over the entire frequency range, whereas T₂ is frequency independent. The results are discussed in terms of existing theoretical models.