A Self-Consistent Ornstein–Zernike Approximation for the Edwards–Anderson Spin-Glass Model

We propose a self-consistent Ornstein–Zernike approximation for studying the Edwards–Anderson spin glass model. By performing two Legendre transforms in replica space, we introduce a Gibbs free energy depending on both the magnetizations and the overlap order parameters. The correlation functions and the thermodynamics are then obtained from the solution of a set of coupled partial differential equations. The approximation becomes exact in the limit of infinite dimension and it provides a potential route for studying the stability of the high-temperature phase against replica-symmetry breaking fluctuations in finite dimensions. As a first step, we present the predictions for the freezing temperature T _f and for the zero-field thermodynamic properties and correlation length above T _f as a function of dimensionality.     

Dynamical dark energy models – dynamical system approach

We study the Friedmann-Robertson-Walker model with dynamical dark energy modelled in terms of the equation of state p _X = w _X (a(z)) ρ _X in which the coefficient w _X is parameterized by the scale factor a or redshift z. We use methods of qualitative analysis of differential equations to investigate the space of all admissible solutions for all initial conditions on the two-dimensional phase plane. We show advantages of representing this dynamics as a motion of a particle in the one-dimensional potential V(a). One of the features of this reduction is the possibility of investigating how typical big rip singularities are in the future evolution of the model. The properties of potential function V can serve as a tool for qualitative classification of all evolution paths. Some important features like resolution of the acceleration problem can be simply visualized as domains on the phase plane. Then one is able to see how large is the class of solutions (labelled by the inset of the initial conditions) leading to the desired property.     

Luttinger liquids with boundaries: Power-laws and energy scales

We present a study of the one-particle spectral properties for a variety of models of Luttinger liquids with open boundaries. We first consider the Tomonaga-Luttinger model using bosonization. For weak interactions the boundary exponent of the power-law suppression of the spectral weight close to the chemical potential is dominated by a term linear in the interaction. This motivates us to study the spectral properties also within the Hartree-Fock approximation. It already gives power-law behavior and qualitative agreement with the exact spectral function. For the lattice model of spinless fermions and the Hubbard model we present numerically exact results obtained using the density-matrix renormalization-group algorithm. We show that many aspects of the behavior of the spectral function close to the boundary can again be understood within the Hartree-Fock approximation. For the repulsive Hubbard model with interaction U the spectral weight is enhanced in a large energy range around the chemical potential. At smaller energies a power-law suppression, as predicted by bosonization, sets in. We present an analytical discussion of the crossover and show that for small U it occurs at energies exponentially (in -1/U) close to the chemical potential, i.e. that bosonization only holds on exponentially small energy scales. We show that such a crossover can also be found in other models. Received 8 February 2000 and Received in final form 25 April 2000     

Localization of a pair of bound particles in a random potential

We study the localization length l_c of a pair of two attractively bound particles moving in a one-dimensional random potential. We show in which way it depends on the interaction potential between the constituents of this composite particle. For a pair with many bound states N the localization length is proportional to N, independently of the form of the two particle interaction. For the case of two bound states, we present an exact solution for the corresponding Fokker–Planck equation and demonstrate that l_c depends sensitively on the shape of the interaction potential and the symmetry of the bound state wave functions.     

Monte Carlo studies of a driven lattice gas. I. Growth and asymmetry during phase segregation

We investigate the effects of an external field on the kinetics of phase segregation in systems with conservative diffusive dynamics. We find that, in contrast to the situation without a field, there are now qualitative differences between the results of microscopic simulations of a 2D lattice model with biased Kawasaki exchanges and those obtained from various modifications of the macroscopic Cahn-Hilliard equation (mCH). While both microscopic simulations and numerical solutions of MCH yield triangular domains, we find that in the former the triangles mainly pointopposite to the field, while in the latter and in new calculations with the mCH they pointalong the field. On the other hand, the rate of growth of the clusters and their final state, bands parallel to the field, are similar. This issue and the question of the mesoscopic behavior of cell dynamical systems is discussed but not resolved.     

Plastic Versus Glass Support for an Immunoassay on Metal-Coated Surfaces in Optically Dense Samples Utilizing Directional Surface Plasmon-Coupled Emission

We compared plastic (polycarbonate) and high-quality glass support materials for gold-coated slides, when performing a model immunoassay against rabbit IgG using fluorescently labeled (AlexaFluor-647) anti-rabbit IgG, and detecting surface plasmon-coupled emission (SPCE) signals. Both, glass and plastic slides were simultaneously coated with a 48-nm layer of gold and protected with a 10-nm layer of silica. The maximum SPCE signal of AlexaFluor-647 was only two- to three-fold smaller on plastic slides than on glass slides. A small difference in the SPCE angles on glass (θ _F = 55°) and plastic (θ _F = 52.5°) slides was observed and can be explained with a slightly smaller refractive index of the plastic. We have not found any difference in the angle distribution (sharpness of the fluorescence signal at optimal SPCE angle) for the plastic slide compared to the glass slide. The kinetics of binding was monitored on the plastic slide as well as on the glass slide. Optically dense samples, a 4% red blood cell suspension and a 15% hemoglobin solution, are causing a reduction in the immunoassay SPCE signal by approximately 15% and three times, respectively, and the percentage of the reduction is the same for plastic and for glass slides. We believe that plastic substrates can be readily used in any SPCE assay, with only marginally lower total signal compared to high-quality glass slides.     

Guest Charges in an Electrolyte: Renormalized Charge, Long- and Short-Distance Behavior of the Electric Potential and Density Profiles

We complement a recent exact study by L. Šamaj on the properties of a guest charge Q immersed in a two-dimensional electrolyte with charges +1/−1. In particular, we are interested in the behavior of the density profiles and electric potential created by the charge and the electrolyte, and in the determination of the renormalized charge which is obtained from the long-distance asymptotics of the electric potential. In Šamaj’s previous work, exact results for arbitrary coulombic coupling β were obtained for a system where all the charges are points, provided β Q < 2 and β < 2. Here, we first focus on the mean field situation which we believe describes correctly the limit β→ 0 but β Q large. In this limit we can study the case when the guest charge is a hard disk and its charge is above the collapse value β Q > 2. We compare our results for the renormalized charge with the exact predictions and we test on a solid ground some conjectures of the previous study. Our study shows that the exact formulas obtained by Šamaj for the renormalized charge are not valid for β Q > 2, contrary to a hypothesis put forward by Šamaj. We also determine the short-distance asymptotics of the density profiles of the coions and counterions near the guest charge, for arbitrary coulombic coupling. We show that the coion density profile exhibit a change of behavior if the guest charge becomes large enough (β Q≥ 2−β). This is interpreted as a first step of the counterion condensation (for large coulombic coupling), the second step taking place at the usual Manning–Oosawa threshold β Q = 2.     

Raman spectroscopy as a rapid screening method for ancient plain window glass

The aim of this paper is to highlight the potential of Raman spectroscopy as a fast screening method for large amounts of glass samples. Besides the dedicated research of specific glass collections during the last ten years, a broad corpus of archaeological window glass still needs to be investigated. For many sites, the amount of excavated glass artefacts is enormous and a selection of the most appropriate samples for chemical analysis is necessary. A classification can be made on the basis of the typical Raman signatures for the different kinds of glasses (alkali glass, high‐lime low‐alkali (HLLA) glass, Pb‐rich glass). Even in case of strong fluorescence, an uncomplicated treatment (normalisation) of the measured signals makes it possible to distinguish between the different types of glass. The preliminary screening of glass artefacts with Raman spectroscopy is a useful tool in the study of historical glass and can already answer some questions about provenance, period of production and authenticity of the glass samples. Copyright © 2010 John Wiley & Sons, Ltd.     

Dynamic domain networks

A model for a dynamic network consisting of changing local interactions is presented in this work. While the network maintains solely local connections, certain properties known only to Small World Networks may be extracted due to the dynamic nature of the model. At each time step the individuals are grouped into clusters creating neighborhoods or domains of fully connected agents. The boundaries of these domains change in time, corresponding to a situation where the links between individuals are dynamic only throughout the history of the network. A question that we pose is whether our model, which maintains a local structure such that diffusion calculations are possible, might lead to analytic or conceptual advances for the much more complicated case of diffusion on a static disordered network that exhibits the same macroscopic properties as our dynamic ordered network. To answer this, we compare certain properties which characterize the dynamic domain network to those of a Small World Network, and then analyze the diffusion coefficients for three possible domain mutations. We close with a comparison and confirmation of previous epidemiological work carried out on networks.     

Critical fluctuations of a binary fluid mixture confined in a porous medium

We have performed small angle neutron scattering experiments on the binary fluid mixture n-C₆H₁₄+n-C₈F₁₈ imbibed inside porous Vycor glass in the thermodynamic region corresponding to the bulk critical one. The resulting structure can be represented as the sum of a temperature dependent Lorentzian term and a term describing the interference between the porous matrix, a shell part richer in one component coating the glass surface, and a core part richer in the other component. We observe critical fluctuations extending over distances markedly larger than the mean pore size. Received 20 May 1999     

Two-Dimensional Coulomb Systems in a Disk with Ideal Dielectric Boundaries

We study two-dimensional Coulomb systems confined in a disk with ideal dielectric boundaries. In particular we consider the two-component plasma in detail. When the coulombic coupling constant =2 the model is exactly solvable. We compute the grand potential, densities and correlations. We show that the grand potential has a universal logarithmic finite-size correction as predicted in previous works. This logarithmic finite-size correction is also found in the free energy of another solvable model: the one-component plasma.     

Part II. Algebraic tails in three-dimensional quantum plasmas

We review various exact results concerning the presence of algebraic tails in three-dimensional quantum plasmas. First, we present a solvable model of two quantum charges immersed in a classical plasma. The effective potential between the quantum charges is shown to decay as 1/r ⁶ at large distances r. Then, we mention semiclassical expansions of the particle correlations for charged systems with Maxwell-Boltzmann statistics and short-ranged regularization of the Coulomb potential. The quantum corrections to the classical quantities, from orderh ⁴ on, also decay as 1/r ⁶. We also give the result of an analysis of the charge correlation for the one-component plasma in the framework of the usual many-body perturbation theory; some Feynman graphs beyond the random phase approximation display algebraic tails. Finally, we sketch a diagrammatic study of the correlations for the full many-body problem with quantum statistics and pure 1/r interactions. The particle correlations are found to decay as 1/r ⁶, while the charge correlation decays faster, as 1/r ¹⁰. The coefficients of these tails can be exactly computed in the low-density limit. The absence of exponential screening arises from the quantum fluctuations of partially screened dipolar interactions.     

Dynamics of the Schlögl models on lattices of low spatial dimension

The steady states and dynamics of the two Schlögl models on one- and two-dimensional lattices are studied using master equation techniques in tandem with simulations. It is found that the classic bistable behavior of model II is modified to monostable behavior at low dimension. An explanation of this modification is proposed in terms of the effective potential that appears in the dynamical equations on considering the significant effect of fluctuation correlations. The behavior can be modeled by replacing the transient average fluctuation correlation by its asymptotic value plus Gaussian white noise and analyzing the resulting effective potential obtained from the Fokker-Planck equation with multiplicative noise. For model I the transcritical bifurcation point is shifted to lower values of the forward ratek ₂ of the second step of the reaction scheme and this shift can also be explained via an effective potential as a function of the average asymptotic fluctuation correlation. Further addition of noise to the asymptotic value is irrelevant for this model since the noise term in the corresponding Fokker-Planck equation turns out to be purely additive.     

Copper blue in an ancient glass bead: a XANES study

The blue colour in ancient soda-lime glasses has been attributed to the presence of copper and/or cobalt but the origin of different shades is not yet fully interpreted. As a contribution to this question, a non-destructive X-ray absorption study at [ _Cu]K-edge was undertaken on the blue (turquoise) layer from a “Nueva Cadiz” type tubular glass bead dated pre-XVII century where copper is the unique colouring agent. Minerals configuring two distinct blue tonalities due to Cu (2+) in similar square coordination were selected as basic model compounds: azurite, which is a classical navy-blue pigment used in ancient wall paintings over plaster, and chalcanthite, displaying exactly the same turquoise-blue tonality of tubular glass beads manufactured since the Egyptian Antiquity. Theoretical modelling of the XAFS spectra was undertaken using the FEFF code. The IFEFFIT software package was used for fitting the calculated spectra to experimental data. EXAFS results are discussed in view of the crystal structures of copper minerals chosen to model the speciation state and structural situation of that element prevailing in the turquoise-blue archaeological glass. Special attention is focused on the difficulties in theoretical modelling [ _Cu]K-XANES spectra of ancient glasses with different colourings. PACS 61.43.Fs; 61.46.+w; 41.60.Ap; 61.10.Ht.     

Granular packing as model glass formers

Static granular packings are model hard-sphere glass formers. The nature of glass transition has remained a hotly debated issue. We review recent experimental progresses in using granular materials to study glass transitions. We focus on the growth of glass order with five-fold symmetry in granular packings and relate the findings to both geometric frustration and random first-order phase transition theories.     

Fermionic Ising glasses with BCS pairing interaction. Tricritical behaviour

We have examined the role of the BCS pairing mechanism in the formation of the magnetic moment and henceforth a spin glass (SG) phase by studying a fermionic Sherrington-Kirkpatrick model with a local BCS coupling between the fermions. This model is obtained by using perturbation theory to trace out the conduction electrons degrees of freedom in conventional superconducting alloys. The model is formulated in the path integral formalism where the spin operators are represented by bilinear combinations of Grassmann fields and it reduces to a single site problem that can be solved within the static approximation with a replica symmetric ansatz. We argue that this is a valid procedure for values of temperature above the de Almeida-Thouless instability line. The phase diagram in the T-g plane, where g is the strength of the pairing interaction, for fixed variance J ² /N of the random couplings J_ij, exhibits three regions: a normal paramagnetic (NP) phase, a spin glass (SG) phase and a pairing (PAIR) phase where there is formation of local pairs.The NP and PAIR phases are separated by a second order transition line g=g _c (T) that ends at a tricritical point T ₃ =0.9807J, g ₃ =5,8843J, from where it becomes a first order transition line that meets the line of second order transitions at T _c =0.9570J that separates the NP and the SG phases. For T<T _c the SG phase is separated from the PAIR phase by a line of first order transitions. These results agree qualitatively with experimental data in . Received 14 May 1998     

Toward a Raman/FORS discrimination between Art Nouveau and contemporary stained glasses from CdSxSe1 − x nanoparticles signatures

CdS_xSe_{1 − x} quantum dots received considerable attention in academic studies and as cut‐off filters and indirect‐gap semiconductors. These later compounds have also been used for artistic purposes to produce colored glass since the 1920s thanks to their bright colors. Because non‐invasive conditions are now mandatory when considering objects belonging to the cultural heritage, the use of Raman and fiber optics reflectance spectroscopy has been identified as potential ones to obtain information about the nanostructure of six samples of historical glass produced between the late 1920s and modern days. The average elemental composition of the nanocrystals has been deduced processing both optical and vibrational data, and the result arising has been compared taking into account the several factors affecting the experimental results. The diffusion of zinc inside the nanocrystals has also been questioned by the shift caused on the CdS‐ and CdSe‐like phonon band wavenumber and on the absorption edge wavelength. An investigation of the size distribution and crystallinity of CdS_xSe_{1 − x} nanoparticles has been also performed considering those parameters that are mainly influenced by the disorder of the system, such as the extent of the Urbach tail and the Raman bandwidth. Thanks to the results obtained, discrimination between the more recent glass and the older Art Nouveau ones has been verified, leading to the identification of a useful analytical protocol for conservation purposes. Copyright © 2015 John Wiley & Sons, Ltd.     

The simplest spin glass

We study a system of Ising spins with quenched random infinite ranged p-spin interactions. For p → ∞, we can solve this model exactly either by a direct microcanonical argument, or through the introduction of replicas and Parisi's ultrametric ansatz for replica symmetry breaking, or by means of TAP mean field equations. Although the model is extremely simple it retains the characteristic features of a spin glass. We use it to confirm the methods that have been applied in more complicated situations and to explicitlu exhibit the structure of the spin glass phase.     

Permeability of mixed soft and hard granular material: Hydrogels as drainage modifiers

We measure the flow of water through mixed packings of glass spheres and soft swellable hydrogel grains, at constant sample volume. Permeability values are obtained at constant sample volume and at porosities smaller than random close packing, for different glass bead diameters D and for variable gel grain diameter d, as controlled by the salinity of the water. The gel content is also varied. We find that the permeability decays exponentially in n(D/d ) ^b , where n = N _gel/N _glass is the gel to glass bead number ratio and b is approximately 3. Therefore, flow properties are determined by the volume fraction of gel beads. A simple model based on the porosity of overlapping spheres is used to account for these observations.