Electron Transfer through a One-Dimensional Fractal Structure

An adequate model of electron tunneling through a self-similar fractal potential (SFP) defined on a Cantor set is extended to a generalized Cantor set. It is demonstrated that, as in a specific case, the Schrödinger equation for the SFP is reduced to a functional equation for the transfer matrix which admits solutions of three types. Two of them are single-parameter solutions corresponding to SFP barriers and lacunas with arbitrary powers. In both cases, the transfer matrices are nonanalytic in the long-wavelength region and have fractal dimensionalities there. The third solution type includes a unique solution corresponding to the SFP barrier with fixed power for a given barrier width. The corresponding transfer matrix is analytic at the point k = 0. It is shown that generally the SFP possesses only the property of approximate scale invariance on the generalized Cantor set in the long- and short-wavelength regions. Only the limiting SFP, whose fractal dimensionality is equal to unity, possesses the property of rigorous scale invariance irrespective of its power. It is shown that SFPs with identical fractal dimensionalities but different lacunas are described by different transfer matrices.     

First principles studies of elastic and thermodynamic properties of fcc-VH2 with pressure and temperature

In this work, we study elastic and thermodynamic properties of VH₂ at different pressures and temperatures. Elastic constants and bulk modulus of VH₂ decrease with increase in temperature, and hence increase with pressure. Thermal expansion of the crystal lattice will be suppressed by high pressure. When the temperature is 1500 K, 15.99 GPa of pressure can completely restrain the volume expansion caused by temperature. At a given pressure, the lower the temperature, the easier the cell compression. At low temperatures, C_v is proportional to T³, and C_v tends to the Dulong-Petit limit at higher temperatures. The Debye temperature increases with pressure, but decreases with temperature. At low temperature and low pressure, thermal expansion coefficient increases sharply with temperature. At high temperature and high pressure, the increasing trend slows down.     

Phase behaviour of polyethylene knotted ring chains

The phase behaviour of polyethylene knotted ring chains is investigated by using molecular dynamics simulations. In this paper, we focus on the collapse of the polyethylene knotted ring chain, and also present the results of linear and ring chains for comparison. At high temperatures, a fully extensive knot structure is observed. The mean-square radius of gyration per bond ² / (Nb²) and the shape factor <δ^*> depend on not only the chain length but also the knot type. With temperature decreasing, chain collapse is observed, and the collapse temperature decreases with the chain length increasing. The actual collapse transition can be determined by the specific heat capacity C_v, and the knotted ring chain undergoes gas-liquid-solid-like transition directly. The phase transition of a knotted ring chain is only one-stage collapse, which is different from the polyethylene linear and ring chains. This investigation can provide some insights into the statistical properties of knotted polymer chains.     

Evaluation of assumed-PDF methods in two-phase flows using direct numerical simulation

The hypothesis of uncorrelated temperature (T) and vapor-fuel mass fraction (Y_v), frequently made when modeling reaction rates using assumed-PDF models, is examined utilizing transitional databases from direct numerical simulation (DNS) of three-dimensional mixing-layers two-phase (TP) flows with evaporation. Because the databases do not contain chemical reaction, which would further correlate variables, finding here a correlation between T and Y_v is sufficient for invalidating reaction rate modeling of the joint (T, Y_v) probability distribution function (PDF) as a product of the marginal PDFs. The databases comprise four multicomponent fuels, two mass loadings and two free-stream gas temperatures. For comparison, databases for single-phase (SP) flows are also analyzed at two initial Reynolds numbers. The examination is conducted in the mixing layer excluding the free streams and in a more restricted part of the mixing layer constituting its core. The analysis is performed at the DNS and large eddy simulation (LES) scales, and subgrid scale (SGS). To obtain the LES database, the DNS database is filtered, and an evaluation of the examined correlation at the LES and SGS scales is made at two filter sizes. At the DNS scale, T and Y_v are practically uncorrelated for SP flows, showing the weak influence of the perfect-gas equation of state, whereas for TP flows the correlation is strong and increases with mass loading indicating the powerful effect of the phase change. At the LES scale, the findings emulate those at the DNS scale. The fluctuations of the SGS scale are uncorrelated for SP flows, but the product of the marginal PDFs is different from the joint PDF. For TP flows, the fluctuations are correlated and the correlation increases with temperature, casting doubt on current assumed PDFs used to model chemistry in reacting sprays. These results are independent of filter size. The joint PDFs for TP and SP fluctuations are successfully modeled.     

Coulomb zero bias anomaly for fractal geometry and conductivity of granular systems near the percolation threshold

A granular system slightly below the percolation threshold is a collection of finite metallic clusters, characterized by wide spectrum of sizes, resistances, and charging energies. Electrons hop from cluster to clusters via short insulating “links” of high resistance. At low temperatures all clusters are Coulomb blockaded and the dc-conductivity σ is exponentially suppressed. At lowest T the leading transport mechanism is variable range cotunneling via largest (critical) clusters, leading to the modified Efros-Shklovsky law. At intermediate temperatures the principal suppression of ρ originates from the Coulomb zero bias anomaly occurring, when electron tunnels between adjacent large clusters with large resistances. Such clusters are essentially extended objects and their internal dynamics should be taken into account. In this regime the T-dependence of ρ is stretched exponential with a nontrivial index, expressed through the indices of percolation theory. Due to the fractal structure of large clusters the anomaly is strongly enhanced: it arises not only in low dimensions, but also in d = 3 case.     

Bose-Einstein condensation of an ideal gas in a parabolic trap

The temperature-dependent velocity distribution function is found for the case of Bose-Einstein condensation of a finite number of noninteracting atoms trapped in a three-dimensional anisotropic parabolic trap. It is shown that at a temperature T of the order of the condensation temperature T ₀ the velocity distribution consists of an anisotropic part, reflecting the population of the ground state, and an isotropic part above the condensate. Pis’ma Zh. éksp. Teor. Fiz. 66, No. 8, 559–563 (25 October 1997)     

Monte-Carlo study of correlations in quantum spin chains at non-zero temperature

Antiferromagnetic Heisenberg spin chains with various spin values (S=1/2,1,3/2,2,5/2) are studied numerically with the quantum Monte-Carlo method. Effective spin S chains are realized by ferromagnetically coupling n=2S antiferromagnetic spin chains with S=1/2. The temperature dependence of the uniform susceptibility, the staggered susceptibility, and the static structure factor peak intensity are computed down to very low temperatures, . The correlation length at each temperature is deduced from numerical measurements of the instantaneous spin-spin correlation function. At high temperatures, very good agreement with exact results for the classical spin chain is obtained independent of the value of S. For the S=2 chain which has a gap , the correlation length and the uniform susceptibility in the temperature range are well predicted by the semi-classical theory of Damle and Sachdev. Received: 23 December 1997 / Revised and Accepted: 11 March 1998     

Effects of Carbon Black on Chain Mobility and Dynamic Mechanical Properties of Solution Polymerized Styrene-Butadiene Rubber

The structure of the bound rubber, the ¹H NMR (nuclear magnetic resonance) relaxation time, and the crosslink density of the physical network and the glass transition, were studied for solution polymerized styrene-butadiene rubber (SSBR) filled by carbon black, to investigate the effects of carbon black on the chain mobility and dynamic mechanical properties. It was found by ¹H NMR analysis that the rubber chains were adsorbed on the surface of carbon black to form physical crosslinks and restrict the mobility of the chains, especially for some high-mobility units such as chain ends. It was calculated, according to the molecular weight between adjacent crosslinks, that the main motion units of the tightly adsorbed chains appeared to be similar in size to the chain segments. The glass transition temperature (T _g) obtained by differential scanning calorimetry (DSC) could not be used to judge the effect of carbon black on chain mobility, while the appearance and change of the loss-tangent (tan δ) peak at high temperature in dynamic mechanical thermal spectrometry (DMTS) test showed that there were three chain states: free chains, loosely adsorbed chains, and tightly adsorbed chains. The dynamic rheology test showed that the unfilled SSBR compound had the rheological characteristics of entangled chain networks; however the nonlinear viscoelasticities of the filled SSBR were related to the gradual disentanglement of adsorbed chains and free chains. The peaks in tan δ vs. temperature curves implied that the motion unit size decreased with the increase of bound rubber content, and the modulus vs. temperature curve showed an apparently lower mobility of adsorbed chains than that of free chains through the very low dependence of modulus on temperature for the highly filled compounds. The extremely high tensile modulus of the vulcanizate with 63.6% carbon black at room temperature also implied that the adsorbed chains were in the glass state due to their restriction by the carbon black.     

Thermodynamic studies of the two dimensional Falicov-Kimball model on a triangular lattice

Thermodynamic properties of the spinless Falicov-Kimball model are studied on a triangular lattice using numerical diagonalization technique with Monte-Carlo simulation algorithm. Discontinuous metal-insulator transition is observed at finite temperature. Unlike the case of square lattice, here we observe that the finite temperature effect is not able to smear out the discontinuous metal-insulator transition seen in the ground state. Calculation of specific heat (C _v ) shows single and double peak structures for different values of parameters like on-site correlation strength (U), f-electron energy (E _f ) and temperature.     

Growth and thermal evolution of submonolayer Pt films on Ru(0 0 0 1) studied by STM

The growth of submonolayer Pt on Ru(0 0 0 1) has been studied with scanning tunneling microscopy. We focus on the island evolution depending on Pt coverage θ_Pt, growth temperature T_G and post-growth annealing temperature T_A. Dendritic trigonal Pt islands with atomically rough borders are observed at room temperature and moderate deposition rates of about 5 × 10⁻⁴ ML/s. Two types of orientation, rotated by 180° and strongly influenced by minute amounts of oxygen are observed which is ascribed to nucleation starting at either hcp or fcc hollow sites. The preference for fcc sites changes to hcp in the presence of about one percent of oxygen. At lower growth temperatures Pt islands show a more fractal shape. Generally, atomically rough island borders smooth down at elevated growth temperatures higher than 300 K, or equivalent annealing temperatures. Dendritic Pt islands, for example, transform into compact, almost hexagonal islands, indicating similar step energies of A- and B-type of steps. Depending on the Pt coverage the thermal evolution differs somewhat: While regular islands on Ru(0 0 0 1) are formed at low coverages, vacancy islands are observed close to completion of the Pt layer.     

Study of the solid-liquid-vapour phase equilibria of flexible chain molecules using Wertheim's thermodynamic perturbation theory

The phase diagram of flexible molecules formed by freely-jointed tangent spheres is studied using the first-order thermodynamic perturbation theory of Wertheim for both fluid and solid phases. A mean-field term is added to the free energy of the fluid and solid phase in order to account for attractive dispersion forces. The approach is used to determine the global (solid-liquid-vapour) phase diagrams and triple points of chain molecules of increasing chain length. It is found that the triple point temperature is not affected strongly by the length of the chain, whereas the gas-liquid critical temperature increases dramatically. The asymptotic limits of the phase diagram for infinitely long chains are discussed. The reduced critical temperature of infinitely long chains as given by the mean-field theory is 2/3, and the reduced triple point temperature is 0.048 56, so that an asymptotic value of T _t/T _c = 0.07284 for the ratio of the triple to critical point temperatures is obtained. This indicates that fully-flexible tangent chains present an enormous liquid range. The proposed theory, while being extremely simple, provides a useful insight into the phase behaviour of chain molecules, showing the existence of finite asymptotic limits for the triple and critical point temperatures. However, since n-alkanes present an asymptotic limit of about T _t/T _c, = 0.40, the agreement With experiment is not quantitative. This suggests that fully flexible models may not be appropriate to model the solid phases of real chain molecules.     

Aggregation of colloidal particles with a finite interparticle attraction energy

Aggregation of colloidal particles with a finite attraction energy was investigated with computer simulations and with gold particles coated with a surfactant. Computer simulations were carried out with the Shih-Aksay-Kikuchi (SAK) model, which incorporates a finite nearest-neighbor attraction energy-E into the diffusion-limited-cluster-aggregation (DLCA) model. Both the computer simulations and the experiments showed that (i) with a finite interparticle attraction energy, aggregates can still remain fractal, and (ii) the fractal dimension remains unchanged at large interparticle attraction energies and increases when the interparticle attraction energy is smaller than 4k _B T whereT is the temperature andK _B is the Boltzmann constant. The agreement between the simulations and the experimental results suggests that the reversible aggregation process in a colloidal system can be represented by the SAK model.     

Lattice bosons in a quasi-disordered environment

In this paper, we study non-interacting bosons in a quasi-disordered one-dimensional optical lattice in a harmonic potential. We consider the case of deterministic quasi-disorder produced by an Aubry–André potential. Using exact diagonalization, we investigate both the zero temperature and the finite temperature properties. We investigate the localization properties by using an entanglement measure. We find that the extreme sensitivity of the localization properties to the number of lattice sites in finite size closed chains disappear in open chains. This feature continues to be present in the presence of a harmonic confining potential. The quasi-disorder is found to strongly reduce the Bose–Einstein condensation temperature and the condensate fraction in open chains. The low temperature thermal depletion rate of the condensate fraction increases considerably with increasing quasi-disorder strength. We also find that the critical quasi-disorder strength required for localization increases with increasing strength of the harmonic potential. Further, we find that the low temperature condensate fraction undergoes a sharp drop to 0.5 in the localization transition region. The temperature dependence of the specific heat is found to be only marginally affected by the quasi-disorder.     

On quark matter in a strong magnetic field

The effect of strong magnetic field on the bulk properties of quark matter is reinvestigated takingu, d ands-quarks as well as electrons in the presence of magnetic field. Here the bag pressure is chosen such that in the absence of magnetic field and at zero temperature the binding energy of theuds-system is <930 MeV while that ofud-system is greater than 940 MeV. It is observed that the equation of state changes significantly in a strong magnetic field. At finite temperature the electron chemical potential varies between 6 and 50 MeV. Thus the expansion of thermodynamical quantities in powers ofT/(Μ _i ² -M _v ⁽ⁱ⁾² )^1/2 is valid only up to few MeV. For high temperatures ∼40 MeV the exact integral expressions are to be taken.     

Lower bounds on entropy for polymer chains on a square and a cubic lattice

Rigorous lower bounds on the entropy per particle as a function of the fractiong of thegauche bonds of a system of semiflexible polymer chains is obtained in the thermodynamic limit. Only square and cubic lattices are considered. For the case of a single chain havingl monomers, the bound is obtained for all gg=2/3. For the case of p>1 chains, each havingl monomers, wherel is a multiple of 4, the bound is obtained for all gg=13/90. In both cases, it is shown that the entropy is alwaysnonzero for all 0<gm(l), whereg _m(l) =(l-2)/l. Thiscontradicts the prediction from the Flory-Huggins approximations that the entropy is zero for allgg₀, whereg ₀ is some finite nonzero number. It is also pointed out that it isnot impossible to pack a lattice with disordered configurations of rodlike chains with finite entropy, again contradicting an assertion by Flory that it is impossible to do so. Finally, it is concluded that onecannot trust the Flory-Huggins approximations at least at low temperatures. The study also casts doubts on the validity of the Gibbs-DiMarzio theory of glass transitions in polymeric systems.     

On the Lifschitz singularity and the tailing in the density of states for random lattice systems

We prove rigorously the existence of a Lifschitz singularity in the density of states at zero energy in some random lattice systems of noninteracting bosons and fermions in any numberv of dimensions. The basic tool is a simple modification of the method of Fukushima to yield the correct upper and lower bounds for allv. We also comment on the mathematical difference between the models treated and the system of phonons with mass disorder in the harmonic approximation, whose behavior is known to be of Debye form, not Lifschitz, at low temperatures.Supported by the Swiss National Science Foundation.On leave of absence from the Institute de Fisica, University of São Paulo, Brazil.     

First-principles calculation of elastic and thermodynamic properties of Ni2MnGa Heusler alloy

The equilibrium lattice parameter, heat capacity, thermal expansion coefficient and bulk modulus of Ni 2 MnGa Heusler alloy are successfully obtained using the first-principles plane-wave pseudopotential (PW-PP) method as well as the quasi-harmonic Debye model. We analyse the relationship between bulk modulus B and temperature T up to 800 K and obtain the relationship between bulk modulus B and pressure at different temperatures. It is found that the bulk modulus B increases monotonically with increasing pressure and decreases with increasing temperature. The pressure dependence of heat capacity C v and thermal expansion α at various temperatures are also analysed. Finally, the Debye temperature of Ni 2 MnGa is determined from the non-equilibrium Gibbs function. Our calculated results are in excellent agreement with the experimental data.     

The melting phenomenon in random-walk model of DNA

The melting phenomenon in a double-stranded homopolypeptide is considered. The relative distance between the corresponding monomers of two polymer chains is modeled by the two-dimensional random walk on the square lattice. Returns of the random walk to the origin describe the formation of hydrogen bonds between complementary units. To take into account the two competing interactions of monomers inside the chains, we obtain a completely denatured state at finite temperature T _c .