In situ X-ray diffraction investigation of porous silicon strains induced by the freezing of a confined organic fluid

High resolution X-ray diffraction is used to perform an in situ measurement of the variations of the lattice parameter of the nanometer size crystallites of porous silicon, induced by the freezing of a confined organic fluid, dodecane. Two p⁺ type PS layers of 60 and 70% porosity are investigated, and the variations of their lattice parameter with the temperature (in the range 150–300 K) are measured. The experimental curves are discussed in relation with the results of a previous calorimetric study of the freezing of confined dodecane. We explain the observed strains by the presence of capillary stresses, that appear in the layer due to the formation of internal liquid-vapour meniscus during the freezing process of the confined fluid. Received 22 October 1999 and Received in final form 25 March 2000     

Electro-optical phase shift in polymer dispersed liquid crystals

An anisotropic version of the Maxwell Garnett approximation is applied for studying the electro-optical phase modulation by polymer dispersed liquid crystals (PDLC). The PDLC contain bipolar liquid crystal droplets that can be reoriented by an external field causing a change in the optical birefringence. This approach provides an explicit link between the droplet orientation distribution and the electro-optical phase shift. For aligned droplets we find that the sharpness of the change in the birefringence may be controlled by selecting the initial orientation. For a planar distribution we find sharp transitions with a hysteresis loop whose width depends on the droplet concentration. For a random distribution, the droplet orientation and the optical phase shift change more gradually with the applied field. These results demonstrate that PDLC may be suitable for a wide range of electro-optic applications based on their field-induced phase modulation properties. In addition, it is apparent that the optical phase shift is quite sensitive to changes in droplet orientation. It should therefore be useful for studying reorientation phenomena in PDLC, overcoming the problems due to light scattering in these materials. Received 25 November 1999 and Received in final form 20 January 2000     

The self-consistent diagram approximation for lattice systems

We apply the self-consistent diagram approximation to calculate equilibrium properties of lattice systems. The free energy of the system is represented by a diagram expansion in Mayer-like functions with averaging over states of a reference system. The latter is defined by one-particle mean potentials, which are calculated using the variational condition formulated. As an example, numerical computations for a two-dimensional lattice gas on a square lattice with attractive interaction between nearest neighbours were carried out. The critical temperature, the phase coexistence curve, the chemical potential and particle and vacancy distribution functions coincide within a few per cent with exact or with Monte Carlo data. Received 18 March 1999 and Received in final form 8 November 1999     

Experimental observation of lattice distortions due to a flux line lattice in niobium

A polarized neutron scattering investigation of the flux line lattice in the type-II superconductor niobium is reported. A modulation of the nuclear lattice has been detected, and the magnitude of the first Fourier component of the lattice distortion established relative to the magnitude of the magnetic scattering. This constitutes the first experimental observation of lattice distortions due to the presence of magnetic flux lines within the bulk of a type-II superconductor. Using a simple microscopic model the lattice distortion in niobium is estimated. A new mechanism is suggested for the coupling of the flux line lattice to the crystallographic lattice. The experimental technique opens up the possibility of investigating the microscopic mechanism of flux line - nuclear lattice interactions, in particular the pinning of flux lines within the bulk of a type-II superconductor. Received: 8 August 1997 / Accepted: 16 October 1997     

The Penna model for biological ageing on a lattice: spatial consequences of child-care

We introduce a square lattice into the Penna bit-string model for biological ageing and study the evolution of the spatial distribution of the population considering different strategies of child-care. Two of the strategies are related to the movements of a whole family on the lattice: in one case the mother cannot move if she has any child younger than a given age, and in the other case if she moves, she brings these young children with her. A stronger condition has also been added to the second case, considering that young children die with a higher probability if their mothers die, this probability decreasing with age. We show that a highly non uniform occupation can be obtained when child-care is considered, even for an uniform initial occupation per site. We also compare the standard survival rate of the model with that obtained when the spacial lattice is considered (without any kind of child-care). Received 30 October 1998 and Received in final form 27 November 1998     

Low frequency, low temperature properties of the spin-boson problem

Low temperature and low frequency properties of a spin-boson model are investigated within a super operator and Liouville space formulation. The leading contributions are identified with the help of projection operators projecting onto the equilibrium state. The quantities of interest are expressed in terms of weighted bath propagators and static linear and nonlinear susceptibilities. In particular the generalized Shiba relation and Wilson ratio are recovered. Received 7 July 2000 and Received in final form 8 August 2000     

Spin-liquid state for two-dimensional Heisenberg antiferromagnets on a kagomé lattice

The magnetic properties of the spin liquid state of the antiferromagnetic Heisenberg model on the kagomé lattice are investigated within the self-consistent mean-field theory. The results show that the spin liquid ground-state energy per site is , which is in very good agreement with the best numerical estimates. The spin structure factor and spin susceptibility are also discussed. Received 1 December 1998 and Received in final form 12 April 1999     

Influence of high-energy electron irradiation on the transport properties of La1-xCaxMnO3 films ($$(x \approx 1/3)$$ )

The effect of crystal lattice disorder on the conductivity and colossal magnetoresistance in La_1-xCa_xMnO₃ ( ) films has been examined. The lattice defects are introduced by irradiating the film with high-energy ( MeV) electrons with a maximal fluence of about cm^-2. This comparatively low dose of irradiation produces rather small radiation damage in the films. The number of displacements per atom (dpa) in the irradiated sample is about 10^-5. Nevertheless, this results in an appreciable increase in the film resistivity. The percentage of the resistivity increase in the ferromagnetic metallic state (below the Curie temperature ) was much greater than that observed in the insulating state (above ). At the same time irradiation has much less effect on or on the magnitude of the colossal magnetoresistance. A possible explanation of such behavior is proposed. Received 21 July 1999 and Received in final form 27 December 1999     

Tracer diffusion and correlations in ordered adsorption systems with defect-controlled transport mechanisms

In this study we develop a theory of tracer diffusion in 2D lattice-gas systems with strongly repulsive nearest neighbor interactions. The study is performed for a square lattice in the vicinity of half monolayer coverage. In this case the lattice gas forms a highly-ordered c phase. The adatom kinetics is reduced to the problem of random walks of long-living structural defects. The correlated motion of tracer-defect pairs is considered. Equations for correlation functions of tracer-vacancy, tracer-excessive adatoms and tracer-dimer pairs are derived and solved in terms of microscopic jump probabilities of defects. The solutions are exact in the case of dominant single defect transport mechanisms. In the case of dimer transport we applied the approximation of short-range correlation length. The values obtained for the correlation factor are in good agreement with the results of computer simulations in the over-stoichiometric range, while for sub-stoichiometric coverages the agreement is not very good. Received 20 September 1999 and Received in final form 14 April 2000     

Lattice-Boltzmann study of spontaneous emulsification

We study the dynamics of spontaneous emulsification of an initially planar oil-water interface when surfactants are added. The thermodynamic properties of the ternary oil-water-surfactant system are modeled by a Ginzburg-Landau-type free energy. The lattice Boltzmann method is used to solve the dynamic equations. The dynamics is found to be governed by a complicated interplay of convection and diffusion as the two relevant transport mechanisms. As long as the interface is almost flat, we find the interfacial area to grow first exponentially and then linearly in time. Later finger-like structures form which grow with a constant velocity. The tip velocity is found to increase roughly linearly with the mobility of the amphiphile, and to decrease as with the solvent viscosity . Received 5 January 1999     

Moving nonlinear localized vibrational modes for a one-dimensional homogenous lattice with quartic anharmonicity

Moving nonlinear localized vibrational modes (i.e. discrete breathers) for the one-dimensional homogenous lattice with quartic anharmonicity are obtained analytically by means of a semidiscrete approximation plus an integration. In addition to the pulse-envelope type of moving modes which have been found previously both analytically and numerically, we find that a kink-envelope type of moving mode which has not been reported before can also exist for such a lattice system. The two types of modes in both right- and left-moving form can occur with different carrier wavevectors and frequencies in separate parts of the plane. Numerical simulations are performed and their results are in good agreement with the analytical predictions. Received 13 October 1999 and Received in final form 15 May 2000     

Water droplets in a spherically confined nematic solvent: A numerical investigation

Recently, it was observed that water droplets suspended in a nematic liquid crystal form linear chains [Poulin et al., Science 275, 1770 (1997)]. The chaining occurs, e.g., in a large nematic drop with homeotropic boundary conditions at all the surfaces. Between each pair of water droplets a point defect in the liquid crystalline order was found in accordance with topological constraints. This point defect causes a repulsion between the water droplets. In our numerical investigation we limit ourselves to a chain of two droplets. For such a complex geometry we use the method of finite elements to minimize the Frank free energy. We confirm an experimental observation that the distance d of the point defect from the surface of a water droplet scales with the radius r of the droplet like .When the water droplets are moved apart, we find that the point defect does not stay in the middle between the droplets, but rather forms a dipole with one of them. This confirms a theoretical model for the chaining. Analogies to a second order phase transition are drawn. We also find the dipole when one water droplet is suspended in a bipolar nematic drop with two boojums, i.e., surface defects at the outer boundary. Finally, we present a configuration where two droplets repel each other without a defect between them. Received 11 December 1998     

Lattice model for translational and rotational motions based on generalised diffusion equations: I. General formalism

A simple lattice model based on generalised diffusion equations and Gaussian statistics, aimed at describing diffusive translational and rotational motions, is presented. It is shown that it allows the generation of correlation functions relevant to spectroscopic techniques that are very similar to those experimentally observed in a large variety of complex systems. For some ranges of values of the model parameters, these functions, which can be expressed in closed mathematical forms, can be approximately represented by the sum of two exponentials or by “stretched" exponentials. Received 17 September 1999 and Received in final form 10 February 2000     

Collapse transitions of a periodic hydrophilic hydrophobic chain

We study a single self avoiding hydrophilic hydrophobic polymer chain, through Monte-Carlo lattice simulations. The affinity of monomer i for water is characterized by a (scalar) charge , and the monomer-water interaction is short-ranged. Assuming incompressibility yields an effective short ranged interaction between monomer pairs (i,j), proportional to . In this article, we take (resp. ()) for hydrophilic (resp. hydrophobic) monomers and consider a chain with (i) an equal number of hydro-philic and -phobic monomers (ii) a periodic distribution of the along the chain, with periodicity 2p. The simulations are done for various chain lengths N, in d=2 (square lattice) and d=3 (cubic lattice). There is a critical value p _c (d,N) of the periodicity, which distinguishes between different low temperature structures. For p >p _c , the ground state corresponds to a macroscopic phase separation between a dense hydrophobic core and hydrophilic loops. For p <p _c (but not too small), one gets a microscopic (finite scale) phase separation, and the ground state corresponds to a chain or network of hydrophobic droplets, coated by hydrophilic monomers. We restrict our study to two extreme cases, and to illustrate the physics of the various phase transitions. A tentative variational approach is also presented. Received: 10 March 1998 / Received in final form: 25 June 1998 / Accepted: 1st July 1998     

Theoretical description of adatom migration in two-dimensional highly-ordered states

Analytical expressions for chemical, jump, and tracer diffusion coefficients are obtained for interacting lattice gases on a square lattice. Strongly repulsive nearest neighbor interactions cause the formation of a highly-ordered c() state in the vicinity of half coverage. It is shown that only strongly correlated successive adatom jumps contribute to the particle flow. This allows to describe the adatom kinetics by considering an almost ideal lattice gas of defects. Two types of defects are considered, adatoms in the empty sublattice and vacancies in the filled sublattice of the c() ordered state. The diffusion equations for these defects are developed considering the generation and recombination of defects. In addition we have considered adatom transport caused by the motion of defect pairs (dimers). Dimer transport mechanism prevails in the high coverage region. The characteristic features of the various diffusion coefficients near half coverage are analyzed and discussed. The theory is compared with the results of sophisticated Monte-Carlo simulations which have been executed with the use of a fully parallelized algorithm on a Cray T3E (LC784-128). The agreement between theoretical and MC results is excellent if the motion of dimers at is taken into account. Received 24 June 1998     

Interaction versus dimerization in one-dimensional Fermi systems

In order to study the effect of interaction and lattice distortion on quantum coherence in one-dimensional Fermi systems, we calculate the ground state energy and the phase sensitivity of a ring of interacting spinless fermions on a dimerized lattice. Our numerical DMRG studies, in which we keep up to 1000 states for systems of about 100 sites, are supplemented by analytical considerations using bosonization techniques. We find a delocalized phase for an attractive interaction, which differs from that obtained for random lattice distortions. The extension of this delocalized phase depends strongly on the dimerization induced modification of the interaction. Taking into account the harmonic lattice energy, we find a dimerized ground state for a repulsive interaction only. The dimerization is suppressed at half filling, when the correlation gap becomes large. Received: 11 February 1998 / Revised: 1st April 1998 / Accepted: 30 April 1998     

Resonance effects in nonlinear lattices

We study a class of one-dimensional nonlinear lattices with nearest-neighbour interactions described by a potential of the binomial type. This potential contains a free parameter which can be chosen to reproduce a variety of models, such as the Toda, the Fermi-Pasta-Ulam and the Coulomb-like lattices. Carrying out essentially numerical experiments, the effects of soliton propagation on a lattice with defects are investigated. In particular, the properties of the localized mode, generated by the propagation of the soliton through the defect, are discussed with respect to the defect mass and the potential parameter, in the light of a simple theoretical model. Furthermore, an interesting phenomenon is observed: the amplitude of the speed of the mass defect shows a sequel of resonance peaks in terms of the mass defect. The positions of these peaks appear to be independent of the potential parameter. Received 16 August 1999 and Received in final form 3 February 2000     

Force distribution in an inhomogeneous sandpile

The force perturbation field in a two-dimensional pile of frictionless gravity-loaded discs or spheres arising from lattice distortions is derived to first order. The starting point is the model proposed by Liffman et al. (Powder Technology (1992) pp. 255-267) and Hong (Phys. Rev. E 47, 760-762 (1993)) in which discs of uniform size are arranged on a regular lattice: this predicts a uniform normal stress distribution at the base of the pile. The analysis is applied to two problems: (i) deformable (rather than rigid) grains that undergo Hertzian deformation at the points of contact; (ii) a pile containing a gradient in particle size from the centre to the free surfaces. The former results in the classical pressure dip at the centre; the latter also produces a dip if the larger particles are at the centre. Received 29 January 1998 and Received in final form 7 September 1998     

Bright optical lattices in a longitudinal magnetic field. Experimental study of the oscillating and jumping regimes

All the bright optical lattices studied so far have been designed to obtain a circularly polarized light at the bottom of the optical potential wells. This condition minimizes the departure rate of the atoms from the fundamental adiabatic surface and permits an oscillating regime in a large range of parameters. We present here an experimental study of cesium atoms in a three-dimensional optical lattice, where the light is linearly polarized at the bottom of the potential wells. Temperature measurements and pump-probe spectroscopy give similar results for this lattice and for the conventional lin lin lattice (which have circular polarizations at the bottom of the wells) despite the fact that one lattice operates in the jumping regime and the other in the oscillating regime. We study the behaviour of the two types of lattices in a longitudinal magnetic field, with particular emphasis on the zero field and strong field regimes. The strong field situation is very simple because the eigenstates are then almost pure Zeeman substates and the adiabatic and diabatic potential surfaces are identical. The comparison between the zero-field and the high-field situations shows that the diabatic potentials are more appropriate to account for experimental observations in the novel lattice. Received: 9 October 1997 / Accepted: 6 November 1997