Table of contents

The stochastic differential equations corresponding to the updating algorithm of Dissipative Particle Dynamics (DPD), and the corresponding Fokker-Planck equation are derived. It is shown that a slight modification to the algorithm is required before the Gibbs distribution is recovered as the stationary solution to the Fokker-Planck equation. The temperature of the system is then directly related to the noise amplitude by means of a fluctuation-dissipation theorem. However, the correspondingly modified, discrete DPD algorithm is only found to obey these predictions if the length of the time step is sufficiently reduced. This indicates the importance of time discretisation in DPD.

Polymers which are attached to a fluid membrane by a single anchor exhibit a dilute mushroom regime and a semi-dilute brush regime. Scaling arguments and explicit calculations for ideal polymers show that the membrane is bent by the anchored polymer: For smooth bends, an anchored mushroom with linear size R_po induces a spontaneous curvature of order ≃ T/κR_po, where T and κ are the temperature and the bending rigidity, respectively; for sharp cone-like bends, it induces a bending angle ≃ T/2πκ. A brush with mean anchor separation ξ_an leads to a curvature of order ≃ (R_po/ξ_an)^2/νT/κξ_an.

A Gaussian variational approach is applied to the random phase sine-Gordon model. The effect of the disorder appears through a scale-dependent random mass term. Some of the results of the replica-symmetry–broken variational solution are reproduced. This variational principle, however, gives a true upper bound to the free energy, and predicts new results. In particular, essential differences are found between the situation in which the phases are pinned on the boundary and that in which they are free.

The evolution of the surface temperature of materials exposed to a laser pulse or step heating is shown to display a "hyperdiffusive" anomalous power law behaviour at short times for samples whose boundary is a self-affine rough surface. A model is presented to account for this behaviour and to relate the anomalous-diffusion exponent to the self-affine roughness exponent of the surface. Experimental measurements exploring different surface roughness for the same composite material over more than five decades in time scales are shown to be consistent with our model.

We study structural phase transitions among modulated phases of liquid-crystal films. As a function of an applied electric field, we find that both square-lattice and hexagonal modulated phases are possible. The latter are similar to hexagonal phases predicted for smectic-C* films. In contrast with reconstructive transitions, however, we predict that the square-lattice modulated phase can undergo a continuous evolution to the hexagonal phase. Intermediate between these two phases is a phase of lower symmetry.

We discuss here a mechanism for the formation of Ca²⁺ circulations often observed before the germination of fertilized Fucus eggs. From the observation that, in a range of external Ca²⁺ concentrations, fertilized Fucus eggs germinate towards the low end of a Ca²⁺ gradient, it is deduced that the Ca²⁺ influx increases when the external Ca²⁺ concentration decreases. We show that this behaviour is associated to an instability of the cell state where the Ca²⁺ concentration is uniform in and outside the egg, at the origin of the Ca²⁺ circulation. However, in order that the circulation can develop at a reasonable cell size, the sensitivity of the Ca²⁺ influx with the inner concentration must be large, in correct order of magnitude with respect to the measured influx variation, owing to the small dependence of the inner Ca²⁺ concentration on the external one.

We report first experimental observation of quantum tunnelling of antiferromagnetic domain walls. The slow dynamics of domain walls in an antiferromagnetic TbFeO₃ single crystal has been studied. The magnetization shows exponential time relaxation due to the motion of the domain walls through the energy barrier of a single height U. Above 2.3 K, the rate of relaxation is pure exponential, exp [− U/T]. Below 2.3 K it becomes independent of temperature.

We have detected the ground state F = 4 → F = 3 hyperfine transition of cesium atoms implanted in a b.c.c. matrix of solid ⁴He using a microwave-optical double-resonance technique. The transition frequency is blue-shifted by ∼ 197 MHz (2.1%) with respect to the free atomic transition and grows with increasing pressure at a rate of ∼ 1.4 MHz/bar.

We present a novel computer simulation of bacterial-colony growth. The ingredients of the simulation are two local conditions: multiplication rate of bacteria in the interface, depending on agar concentration and agar plate moisture, and occupation rate of the sites of the cluster inside a small circle around the potential growth site, representing the nutrient concentration. Varying growth conditions, fractal, dense-branching morphology and compact-growth patterns have been observed, which is consistent with the experimental demonstrations.

Using the cavity method, I derive the microscopic equations and their stability condition for information learning in neural networks, optimized with arbitrary performance functions in terms of the aligning fields of the examples. In the thermodynamic limit the aligning fields are well-defined functions of the cavity fields. Iterating the microscopic equations provides a general algorithm for network learning, supported by simulations in the maximally stable perceptron and the committee tree. Macroscopic results agree with the replica theory and the Almeida-Thouless stability condition.

Erratum of Europhys. Lett.30 (2) pp 117