Scaling behaviour in the Bose gas

The scaling behaviour of fluctuations of the Bose field (f) in the ergodic infinite volume equilibrium states of ad-dimensional Bose gas at temperatureT and density , can be classified in terms of the testfunctionsf. In the low density regime, the space of testfunctions splits up in two subspaces, leading to two different types of non-commuting macroscopic field fluctuation observables. Testfunctionsf with Fourier transform yield normal fluctuation observables. The local fluctuations of the field operators (f) must be scaled subnormally (i.e. with a negative scaling index) if the testfunctionf has . The macroscopic fluctuations of these fields can then again be described by a Bose field. The situation changes when the density of the gas exceeds the critical density. The field operators which have normal fluctuations in the low density regime need to be scaled abnormally in the high density regime, yielding classical macroscopic fluctuation observables. Another difference with the low density regime is that the space of testfunctions with splits up in two subspaces when the critical density is reached: for a first subspace the algebraic character of the macroscopic field fluctuation observables in also classical because it is necessary to scale the fluctuations of the field operators normally, while for the remaining subclass, the same negative scaling index is required as in the low density regime and hence also the algebraic character of these macroscopic fluctuations is again CCR.     

Scaling behaviour in the truncated Zel'dovich approximation

Summary We analyse the scaling properties of the matter distribution generated by the truncated Zel'dovich approximation (TZA) for a universe dominated by a mixture of cold+hot non-baryonic dark matter. At the present epoch, the dark-matter distribution generated by TZA displays an intermediate scaling behaviour between about 4 and 60h ⁻¹ Mpc with a correlation dimensionD _q∼2 forq≥2. The possible implications of these results are considered.     

Scaling behaviour of polyelectrolytes and polyelectrolyte brushes

Summary Simulation results as well as experimental data indicate that full stretching of flexible polyelectrolytes will not occur under experimentally realizable conditions. Using density-dependent swelling exponents ν(ϕ) as suggested by Stevens and Kremer from the results of a MD simulation study, we present an Alexander-de Gennes-like scaling picture for the behaviour of charged brushes. The brush height is found to become dependent on the grafting density as soon as internal stretching is incomplete. For a particular anchoring technique used in experimental studies the grafting density itself becomes dependent on the chain length. The resulting modified overall chain length dependence of the brush height is discussed. Paper presented at the I International Conference on Scaling Concepts and Complex Fluids, Copanello, Italy, July 4–8, 1994.     

Scaling of Lévy-Student processes

Student’s t-distributions are widely used in financial studies as heavy-tailed alternatives to normal distributions. As these distributions are not closed under convolution, there exist no Lévy processes with Student’s t-marginals at all points in time. In this article we show that a Student’s t-approximation of these marginals is still suitable, while not exact. Using this approximation, we are able to describe the scaling behavior of such Lévy-Student processes and the parameters of its marginal distributions by a simple analytical scaling law. This scaling law drastically simplifies the use of Lévy-Student processes as a general diffusion process in various interdisciplinary applications. We explicitly provide an application in the context of modelling high-frequency price returns.     

Scaling limit for interacting Ornstein-Uhlenbeck processes

The problem of describing the bulk behavior of an interacting system consisting of a large number of particles comes up in different contexts. See for example [1] for a recent exposition. In [4] one of the authors considered the case of interacting diffusions on a circle and proved that the density of particles evolves according to a nonlinear diffusion equation. The interacting particles evolved according to a generator that was symmetric in equilibrium. In this article we consider interacting Ornstein-Uhlenbeck processes. Here the diffusion generator is not symmetric relative to the equilibrium and the earlier methods have to be modified considerably. We use some ideas that were employed in [3] to extend the central limit theorem from the symmetric to nonsymmetric cases.This research is supported in part by the National Science Foundation, grant nos. DMS 89-01682 and DMS-88-06727     

Scaling behaviour of inner-shell ionization in superheavy quasi-molecules

We derive an approximate analytical formula for theK-shell ionization in collisions of very heavy atoms. The impact parameter and bombarding energy dependence are well described. The binding energy of the bound state at closest approach enters in a simple way, which could provide an experimental method for a spectroscopy of quasimolecular states.     

Scaling behaviour in the fracture of fibrous materials

We study the existence of distinct failure regimes in a model for fracture in fibrous materials. We simulate a bundle of parallel fibers under uniaxial static load and observe two different failure regimes: a catastrophic and a slowly shredding. In the catastrophic regime the initial deformation produces a crack which percolates through the bundle. In the slowly shredding regime the initial deformations will produce small cracks which gradually weaken the bundle. The boundary between the catastrophic and the shredding regimes is studied by means of percolation theory and of finite-size scaling theory. In this boundary, the percolation density scales with the system size L, which implies the existence of a second-order phase transition with the same critical exponents as those of usual percolation. Received 24 June 1999     

Scaling analysis of phase transition in Hg-based superconductor

With the vibrating-reed technique, the internal friction (IF) Q⁻¹ is measured for sing-phase (Hg_0.66Pb_0.34)Ba₂Ca₂Cu₃O_8+x superconductor as a function of temperature at low applied magnetic field up to 0.5 T and as a function of frequency at normal state temperatures. An IF peak associated with flux motion can be found below T_C. The IF peak becomes higher and shifts towards lower temperature with increasing magnetic field. In addition an IF peak is found near 200 K. By scaling analysis we have demonstrated that the internal friction around the peak temperature can be collapsed into a single curve, indicating that the IF peak below T_C is originated from a phase transition associated with a vortex glass transition and a structural phase transition occurs at around 200 K in the superconductor.     

Electronic phase separation in La-Cuprates

The mechanisms driving the phase separation in high-T _c La cuprates is studied by magnetic susceptibility and electrical resistivity measurements. The experiments are performed under different thermal treatment. Three temperature ranges can be resolved characteristic for different physical processes: At 150T170K a space limited diffusion of superparamagnetic clusters (single hole clusters) occurs leading to the formation of a small but rather tight percolative subphase which at highT _c values becomes superconducting. Above 180 K the cluster motion becomes unrestricted in space and a more extended subphase is built up, however, with lowerT _c values. Above 230 K oxygen diffusion starts leading to an unexpected destruction of the conducting/superconducting phase.     

Scaling behaviour of charged spin-one partons in a gauge model

In a hadron model in which the fermion constituents are bound by vector-isovector gauge fields, electromagnetism is introduced; by spontaneously breaking the strong (SU(2)) gauge symmetry, the gauge fields become massive. We identify the spinors and vectors with partons, and, assuming the naive parton model hypothesis, we calculate the cross section e⁺e^?→ hadrons and the structure functions of the nucleon; scaling is obtained desoite induces presence of an anomalous magnetic moment term in the coupling of the photon with the charged vector fields; the reason is that the spontaneous breaking of the symmetry indices a vector-meson dominance type of coupling between the photon and the neutral vector, which is just what is necessary to restore scaling.     

Displacive processes and phase transformations

Two basic displacive processes can be considered, namely displacements of crystal parts as rigid blocks and shuffling of atomic planes. The many-body potentials are used for the interatomic forces. General displacements of atomic planes are examined, i.e. γ-surface type calculations are applied to single plane shuffling and alternate shuffling of every other atomic plane producing in combination with homogeneous deformation the hcp structure.     

Scaling analysis of phase fluctuations in experimental three-phase flows

The characterization of complex patterns arising from three-phase (e.g., oil-gas-water) flows is an important problem with significant engineering and industrial applications. Based solely on measured conductance fluctuation signals from experimental three-phase flows, we propose a method to characterize and distinguish three commonly observed flow patterns. Using the phase characterization method, we first calculate the instantaneous phase from the signals. Then, through performing a scaling analysis, detrended fluctuation analysis (DFA), we extract scaling behaviors associated with the phase fluctuations and find that the DFA scaling exponent is sensitive to the transition among different flow patterns, which can be used to characterize nonlinear dynamics of the three-phase flow. From a novel perspective, we investigate the three-phase flow in terms of phase characterization and scaling analysis. The results indicate that our method can provide new insights into the exploration of complex mechanism in flow pattern transition. The effectiveness of the method is demonstrated and its broader applicability is articulated.     

Direct-energy processes and phase transitions in silicon

Summary The phase transition of amorphous to single-crystal silicon has been investigated not only by conventional heating in a furnace but under direct-energy processes like pulsed-laser and ion beam irradiation. The first method allows the experimental determination of the free-energy-temperature diagram for amorphous, liquid and crystalline silicon. Due to the very fast heating and cooling the amorphous-to-liquid transition can be investigated in both directions. Ion beam irradiation induces either a layer-by-layer amorphization or crystallization by the movement of the initial α-Si/c-Si interface according to the substrate temperature. The two processes are governed by different types of defects created by the beam in the amorphous and in the crystalline side of the interface. The existence of a native-oxide layer at the interface between single crystal and deposited layer retards the ion beam crystallization until oxygen atoms are dispersed by beam mixing in the matrix. A recent alternative way of crystallizing deposited layers is by short high-temperature anneals obtained by incoherent-light irradiations. In this case the rupture of the native-oxide layer is achieved by the agglomeration of oxide into beads, thus allowing the realignment. This technique appears to be particularly promising for several technological applications. In honour of Prof. Fausto Fumi on the occasion of his retirement from teaching.     

Adhesion-induced lateral phase separation in membranes

Adhesion between membranes is studied using a phenomenological model, where the inter-membrane distance is coupled to the concentration of sticker molecules on the membranes. The model applies to both adhesion of two flexible membranes and to adhesion of one flexible membrane onto a second membrane supported on a solid substrate. We mainly consider the case where the sticker molecules form bridges and adhere directly to both membranes. The calculated mean-field phase diagrams show an upward shift of the transition temperature indicating that the lateral phase separation in the membrane is enhanced due to the coupling effect. Hence the possibility of adhesion-induced lateral phase separation is predicted. For a particular choice of the parameters, the model exhibits a tricritical behavior. We also discuss the non-monotonous shape of the inter-membrane distance occurring when the lateral phase separation takes place. The inter-membrane distance relaxes to the bulk values with two symmetric overshoots. Adhesion mediated by other types of stickers is also considered. Received 12 January 2000 and Received in final form 15 May 2000     

Field-induced phase separation in one dimension

Phase separation is induced in the one-dimensional Ising chain (or lattice-gas model of a fluid) by means of an external field that changes sign in the middle of the chain. The magnetization profile (or density profile of the analogous fluid) is obtained analytically. It is found to decay exponentially rapidly to the bulk-phase magnetizations (or densities), the exponential decay parameter being the correlation length in the bulk phases in the presence of the field. This is in accord with earlier theoretical ideas. The interfacial tension is also obtained analytically. In an appropriately defined limit of large neighboring-site spin-spin interactions and small external field the interface becomes infinitely broad while the amplitude of the profile and the interfacial tension both vanish, in close imitation of the approach to a critical point in a real fluid. In this asymptotic limit the interfacial tension is related to the amplitude of the profile in the way that is predicted by earlier theories of interfaces near critical points, with critical-point exponents now those appropriate to one dimension. The exact interfacial profile and tension are used to test several approximations, including a corrected form of the barometric law and local (square-gradient) and nonlocal forms of the van der Waals theory.     

Wetting and phase separation at surfaces

We study the problem ofsurfacedirected spinodal decomposition, viz., the dynamical interplay of wetting and phase separation at surfaces. In particular, we focus on the kinetics of wetting-layer growth in a semi-infinite geometry for arbitrary surface potentials and mixture compositions. We also present representative results for phase separation in confined geometries, e.g., cylindrical pores, thin films, etc.