Charge transfer between alkali cluster ions and atoms in the 1 to 10 keV collisional energy range

The cross-sections for collisional charge transfer between singly charged free clusters M _n ⁺ (M = Li, Na; n=1...50) and atomic targets A (cesium, potassium) have been measured as a function of collisional relative velocity in laboratory energy range 1–10 keV. For each cluster size, the experimental values of the charge transfer cross-section are fitted with an universal parametric curve with two independent parameters and v_m, the maximum cross-section and the corresponding velocity. For small size clusters (), the characteristic parameters show strong variations with the number of atoms in the cluster. Abrupt dips observed for n=10 and n=22 are attributed to electronic properties. Charge transfer patterns observed for various collisional systems present similarities, which appear more sensitive to cluster quantum size effects than to collision energy defects. In their whole, the and v_m parameters show differences in both their size evolution and their absolute values discussed in term of projectile and target electronic structures. Received 13 April 2000 and Received in final form 29 June 2000     

Dielectric resonances in three-dimensional binary disordered media

Powdered solids often present very specific properties due to their granular nature. Such powders are often obtained by mixing two ingredients in variable proportions: conductor and insulator, or conductor and super-conductor. In a very natural way, these systems are modeled by regular lattices, whose sites or bonds are randomly chosen with given probabilities. It is known that the electrical and optical properties of random bi-dimensional (2D) networks are well described by their conductance's poles (resonances) and residues (amplitudes). The numerical implementation of a spectral method gave the spectral density, the AC conductivity, the multi-fractal properties of the moments for the local electric field (or currents), and spectrum of resonances characteristic of some small clusters (animals). This work extends the spectral method to the three-dimensional (3D) case where the problem is more complicated because the duality property and the corresponding symmetries are broken. As in the 2D-case, the two significant parameters are the ratio of the complex conductances and of both phases, and the probability p (resp. 1-p) of (resp. ). All the resonances lie on the negative real h-axis, i.e. for pure non resistive networks in the AC case. For a static (DC) system, only the value h=0 (corresponding to a binary system with finite and , or and finite) can give a resonance. Some applications are proposed, in particular the ability for small clusters (animals with one, two or three bonds) to present a singular response for well identified frequencies of the incident electromagnetic field. Received 24 March 1999     

Roughness scaling and sensitivity to initial conditions in a symmetric restricted ballistic deposition model

In this work, we introduce a restricted ballistic deposition model with symmetric growth rules that favors the formation of local finite slopes. It is the simplest model which, even without including a diffusive relaxation mode of the interface, leads to a macroscopic groove instability. By employing a finite-size scaling of numerical simulation data, we determine the scaling behavior of the surface structure grown over a one-dimensional substrate of linear size L. We found that the surface profile develops a macroscopic groove with the asymptotic surface width scaling as , with . The early-time dynamics is governed by the scaling law , with . We further investigate the sensitivity to initial conditions of the present model by applying damage spreading techniques. We find that the early-time distance between two initially close surface configurations grows in a ballistic fashion as , but a slower Brownian-like scaling () sets up for evolution times much larger than a characteristic time scale . Received 26 May 2000     

Thermodynamics of small systems embedded in a reservoir: a detailed analysis of finite size effects

We present a detailed study on the finite size scaling behaviour of thermodynamic properties for small systems of particles embedded in a reservoir. Previously, we derived that the leading finite size effects of thermodynamic properties for small systems scale with the inverse of the linear length of the small system, and we showed how this can be used to describe systems in the thermodynamic limit [Chem. Phys. Lett. 504, 199 (2011)]. This approach takes into account an effective surface energy, as a result of the non-periodic boundaries of the small embedded system. Deviations from the linear behaviour occur when the small system becomes very small, i.e. smaller than three times the particle diameter in each direction. At this scale, so-called nook- and corner effects will become important. In this work, we present a detailed analysis to explain this behaviour. In addition, we present a model for the finite size scaling when the size of the small system is of the same order of magnitude as the reservoir. The developed theory is validated using molecular simulations of systems containing Lennard-Jones and WCA particles, and leads to significant improvements over our previous approach. Our approach eventually leads to an efficient method to compute the thermodynamic factor of macroscopic systems from finite size scaling, which is for example required for converting Fick and Maxwell–Stefan transport diffusivities.     

Surface flows of granular mixtures: II. Segregation with grains of different size

We present the generalization of a theoretical model for segregation of granular mixtures due to surface flows, published in J. Phys. I France 6, 1295 (1996). Our generalized model is valid for grains differing by their size and/or their surface properties; in the present paper, we describe the case of two species with the same surface properties but two different sizes. The rolling stream is assumed to be homogeneous. Exchanges between the grains at rest and the rolling stream are modelized via binary collisions. The model predicts that during the filling of a two-dimensional silo, continuous segregation appears inside the static phase: small (respectively large) grains tend to stop uphill (respectively downhill), although both species remain present everywhere. This fits the observations when the size difference between the species is small. When the size difference is large, a different regime is observed. We argue that in this case, segregation occurs directly inside the rolling stream. Received: 25 February 1998 / Received in final form and Accepted: 6 July 1998     

Slowing down in the three-dimensional three-state Potts glass with nearest neighbor exchange ± J: A Monte Carlo study

,Static and dynamic properties of the Potts model on the simple cubic lattice with nearest neighbor -interaction are obtained from Monte Carlo simulations in a temperature range where full thermal equilibrium still can be achieved (). For a lattice size L = 16, in this range finite size effects are still negligible, but the data for the spin glass susceptibility agree with previous extrapolations based on finite size scaling of very small lattices. While the static properties are compatible with a zero temperature transition, they certainly do not prove it. Unlike the Ising spin glass, the decay of the time-dependent order parameter is compatible with a simple Kohlrausch function, , while a power law prefactor cannot be distinguished. The Kohlrausch exponent y ( T ) decreases from at [0pt] to at [0pt] however. The relaxation time is compatible with the exponential divergence postulated by McMillan for spin glasses at their lower critical dimension, but the exponent that can be extracted still differs significantly from the theoretical value, . Thus the present results support the conclusion that the Potts spin glass in d = 3 dimensions differs qualitatively from the Ising spin glass. Received: 8 October 1997 / Accepted: 27 November 1997     

On the properties of small-world network models

We study the small-world networks recently introduced by Watts and Strogatz [Nature 393, 440 (1998)], using analytical as well as numerical tools. We characterize the geometrical properties resulting from the coexistence of a local structure and random long-range connections, and we examine their evolution with size and disorder strength. We show that any finite value of the disorder is able to trigger a “small-world” behaviour as soon as the initial lattice is big enough, and study the crossover between a regular lattice and a “small-world” one. These results are corroborated by the investigation of an Ising model defined on the network, showing for every finite disorder fraction a crossover from a high-temperature region dominated by the underlying one-dimensional structure to a mean-field like low-temperature region. In particular there exists a finite-temperature ferromagnetic phase transition as soon as the disorder strength is finite. [0.5cm] Received 29 March 1999 and Received in final form 21 May 1999     

Dynamical properties of low-dimensional and spin-Peierls systems

Properties of low-dimensional spin-Peierls systems are described by using a one-dimensional S =1/2 antiferromagnetic Heisenberg chain linearly coupled to a single phonon mode of wave vector (whose contribution is expected to be dominant). By exact diagonalizations of small rings with up to 24 sites supplemented by a finite size scaling analysis, static and dynamical properties are investigated. Numerical evidences are given for a spontaneous discrete symmetry breaking towards a spin gapped phase with a frozen lattice dimerization. Special emphasis is put on the comparative study of the two inorganic spin-Peierls compounds CuGeO₃ and NaV₂O₅ and the model parameters are determined from a fit of the experimental spin gaps. We predict that the spin-phonon coupling is 2 or 3 times larger in NaV₂O₅ than in CuGeO₃. Inelastic neutron scattering spectra are calculated and similar results are found in the single phonon mode approximation and in the model including a static dimerization. In particular, the magnon S =1 branch is clearly separated from the continuum of triplet excitations by a finite gap. Received: 30 July 1997 / Revised: 16 September 1997 / Accepted: 10 October 1997     

Microcanonical scaling in small systems

A microcanonical finite-size scaling ansatz is discussed. It exploits the existence of a well-defined transition point for systems of finite size in the microcanonical ensemble. The best data collapse obtained for small systems yields values for the critical exponents in good agreement with other approaches. The exact location of the infinite system critical point is not needed when extracting critical exponents from the microcanonical finite-size scaling theory.     

Coarsening and self-organization in dilute diblock copolymer melts and mixtures

This paper explores the evolution of a sharp interface model for phase separation of copolymers in the limit of low volume fraction. Particles both exchange material as in usual Ostwald ripening, and migrate because of an effectively repulsive nonlocal energetic term. Coarsening via mass diffusion only occurs while particle radii are small, and they eventually approach a finite equilibrium size. Migration, on the other hand, is responsible for producing self-organized patterns.We construct approximations based upon an ansatz of spherical particles similar to the classical LSW theory to derive finite dimensional dynamics for particle positions and radii. For large systems, kinetic-type equations which describe the evolution of a probability density are constructed. For systems larger than the screening length, we obtain an analog of the homogenization result of Niethammer & Otto [B. Niethammer, F. Otto, Ostwald ripening: The screening length revisited, Calc. Var. Partial Differential Equations 13-1 (2001) 33-68]. A separation of timescales between particle growth and migration allows for a variational characterization of spatially inhomogeneous quasi-equilibrium states.     

Finite size scale invariance

We develop a new approach to scale symmetry, which takes into account the possible finite cut-offs of the fields or the parameters. This new symmetry, called finite size scale symmetry: i) includes the traditional self-similarity as a limiting case, when the cut-offs are set to infinity (infinite size-system); ii) is consistent with the traditional finite size scaling approach already used in critical phenomena; iii) enables the computation of some of the universal functions appearing in the finite size scaling formulation; iv) allows scale transformations leaving the cut-offs invariant, like in the traditional renormalization approach; v) can be formulated to allow for positive or negative fields and parameters; vi) leads to new predictions about the shape of some distributions in critical phenomena or turbulence which are in very good agreement with the experimental or numerical findings. Received 26 January 1999 and Received in final form 25 October 1999     

Noise-induced bifurcations and chaos in the average motion of globally-coupled oscillators

A system of coupled master equations simplified from a model of noise-driven globally coupled bistable oscillators under periodic forcing is investigated. In the thermodynamic limit, the system is reduced to a set of two coupled differential equations. Rich bifurcations to subharmonics and chaotic motions are found. This behavior can be found only for certain intermediate noise intensities. Noise with intensities which are too small or too large will certainly spoil the bifurcations. In a system with large though finite size, the bifurcations to chaos induced by noise can still be detected to a certain degree. Received 6 April 1999 and Received in final form 1 November 1999     

The smooth structural change in mesoscopic Peierls chains

We investigate the Peierls transition in finite chains by exact (Lanczos) diagonalization and within a seminumerical method based on the factorization of the electron-phonon wave function (Adiabatic Ansatz, AA). AA can be applied for mesoscopic chains up to micrometer sizes and its reliability can be checked self-consistently. Our study demonstrates the important role played for finite systems by the tunneling in the double well potential. The chains are dimerized only if their size N exceeds a critical value N_c which increases with increasing phonon frequency. Quantum phonon fluctuations yield a broad transition region. This smooth Peierls transition contrasts not only to the sharp mean field transition, but also with the sharp RPA soft mode instability, although RPA partially accounts for quantum phonon fluctuations. For weak coupling the dimerization disappears below micrometer sizes; therefore, this effect could be detected experimentally in mesoscopic systems. Received: 3 January 1998 / Revised: 13 March 1998 / Accepted: 3 April 1998     

Convective and absolute instabilities in the subcritical Ginzburg-Landau equation

We study the nature of the instability of the homogeneous steady states of the subcritical real Ginzburg-Landau equation in the presence of group velocity. The shift of the absolute instability threshold of the trivial steady state, induced by the destabilizing cubic nonlinearities, is confirmed by the numerical analysis of the evolution of its perturbations. It is also shown that the dynamics of these perturbations is such that finite size effects may suppress the transition from convective to absolute instability. Finally, we analyze the instability of the subcritical middle branch of steady states, and show, analytically and numerically, that this branch may be convectively unstable for sufficiently high values of the group velocity. Received 17 December 1998     

QCD Phase Transitions and Bag Constants at Finite Chemical Potential

The global colour model at finite temperature is further extended to study the systems at finite chemical potential. The deconfinement and chiral phase transition at finite chemical potential and at temperature T = 0 K are studied simultaneously. Meanwhile the evolution of the bag constants at finite chemical potential is calculated. The dependences of results on the model parameters are discussed in detail     

Globally coupled systems with prescribed synchronized dynamics

A system of globally coupled maps whose synchronized dynamics differs from the individual (chaotic) evolution is considered. For nonchaotic synchronized dynamics, the synchronized state becomes stable at a critical coupling intensity lower than that of the fully chaotic case. Below such critical point, synchronization is also stable in a set of finite intervals. Moreover, the system is shown to exhibit multistability, so that even when the synchronized state is stable not all the initial conditions lead to synchronization of the ensemble. Received 22 October 1999     

Competing species dynamics: Qualitative advantage versus geography

A simple cellular automata model for a two-group war over the same “territory” is presented. It is shown that a qualitative advantage is not enough for a minority to win. A spatial organization as well a definite degree of aggressiveness are instrumental to overcome a less fitted majority. The model applies to a large spectrum of competing groups: smoker-non smoker war, epidemic spreading, opinion formation, competition for industrial standards and species evolution. In the last case, it provides a new explanation for punctuated equilibria. Received: 21 April 1998 / Revised and Accepted: 22 April 1998     

Mesoscopic charge density wave in a magnetic flux

The stability of a Charge Density Wave (CDW) in a one-dimensional ring pierced by a Aharonov-Bohm flux is studied in a mean-field picture. It is found that the stability depends on the parity of the number N of electrons. When the size of the ring becomes as small as the coherence length , the CDW gap increases for even N and decreases for odd N. Then when N is even, the CDW gap decreases with flux but it increases when N is odd. The variation of the BCS ratio with size and flux is also calculated. We derive the harmonics expansion of the persistent current in a presence of a finite gap. Received: 16 September 1997 / Received in final form: 12 November 1997 / Accepted: 13 November 1997