Self-avoiding walks on randomly diluted lattices

We discuss how the introduction of quenched impurities changes the exponents of a self-avoiding walk on a lattice. We find that , the exponent for the number of walks, does not change. On the other hand the exponent for the mean square end to end distance does change. This is caused by a singular normalization atp=p _c , which is necessary to compensate for the allowed number of walks on the diluted lattice.     

Excitations in randomly diluted two-dimensional ferromagnets

The dynamics of a randomly diluted Heisenberg ferromagnet on a two-dimensional square lattice is calculated using a CPA procedure introduced by Theumann and Tahir-Kheli. The density of states and frequency-wave-vector-dependent response functions at various symmetry points of the Brillouin zone are presented for several magnetic concentrations. Our results for the density of states are compared with those obtained from computer-experiment calculations of Huber and are found to be in good agreement with them. The spin-wave stiffness coefficient is calculated, and comparison is made with results on two-dimensional resistor networks given by Watson et al.     

Nonequilibrium phase transition on a randomly diluted lattice

We show that the interplay between geometric criticality and dynamical fluctuations leads to a novel universality class of the contact process on a randomly diluted lattice. The nonequilibrium phase transition across the percolation threshold of the lattice is characterized by unconventional activated (exponential) dynamical scaling and strong Griffiths effects. We calculate the critical behavior in two and three space dimensions, and we also relate our results to the recently found infinite-randomness fixed point in the disordered one-dimensional contact process.     

Entropic phase separation in polymer-microemulsion networks

We study theoretically a model system of a transient network of microemulsion droplets connected by telechelic polymers and explain recent experimental findings. Despite the absence of any specific interactions between either the droplets or polymer chains, we predict that as the number of polymers per drop is increased, the system undergoes a first-order phase separation into a dense, highly connected phase, in equilibrium with dilute droplets, decorated by polymer loops. The phase transition is purely entropic and is driven by the interplay between the translational entropy of the drops and the configurational entropy of the polymer connections between them. Because it is dominated by entropic effects, the phase behavior of the system is extremely robust and is independent of the detailed properties of either polymers or drops.     

Introducing CdS into two- and three-dimensional photonic crystals

SiO₂/air three-dimensional (3D) periodic structures were fabricated by removing Si layers partially from Si/SiO₂ 3D photonic crystals (PhCs) formed by using autocloning. CdS/SiO₂ 3D periodic structures were formed by introducing CdS into the SiO₂/air structures by the TEA method and photoluminescence (PL) was observed from the introduced CdS. TiO₂/air/CdS two-dimensional (2D) PhCs were also fabricated by introducing CdS into the voids of TiO₂/air 2D periodic structures, in which SiO₂ layers were partially etched out from TiO₂/SiO₂ 2D PhCs fabricated by using autocloning. PL radiating normal to the surface was measured and large polarization dependence was observed.     

Metal-insulator transition in two- and three-dimensional logarithmic plasmas

We consider the scaling of the mean square dipole moment in a plasma with logarithmic interactions in a two- and three-dimensional systems. In both cases, we establish the existence of a low-temperature regime where the mean square dipole moment does not scale with system size and a high-temperature regime where it does scale with system size. Thus, there is a nonanalytic change in the polarizability of the system as a function of temperature and hence a metal-insulator transition in both cases. The relevance of this transition in three dimensions to quantum phase transitions in (2+1)-dimensional systems is briefly discussed.     

q-Breathers in finite two- and three-dimensional nonlinear acoustic lattices

In their celebrated experiment, Fermi, Pasta, and Ulam (FPU) [Los Alamos Report No. LA-1940, 1955] observed that in simple one-dimensional nonlinear atomic chains the energy must not always be equally shared among the modes. Recently, it was shown that exact and stable time-periodic orbits, coined q-breathers (QBs), localize the mode energy in normal mode space in an exponential way, and account for many aspects of the FPU problem. Here we take the problem into more physically important cases of two- and three-dimensional acoustic lattices to find existence and principally different features of QBs. By use of perturbation theory and numerical calculations we obtain that the localization and stability of QBs are enhanced with increasing system size in higher lattice dimensions opposite to their one-dimensional analogues.     

Quantum transport in randomly diluted quantum percolation clusters in two dimensions

We study the hopping transport of a quantum particle through finite, randomly diluted percolation clusters in two dimensions. We investigate how the transmission coefficient T behaves as a function of the energy E of the particle, the occupation concentration p of the disordered cluster, the size of the underlying lattice, and the type of connection chosen between the cluster and the input and output leads. We investigate both the point-to-point contacts and the busbar type of connection. For highly diluted clusters we find the behavior of the transmission to be independent of the type of connection. As the amount of dilution is decreased we find sharp variations in transmission. These variations are the remnants of the resonances at the ordered, zero-dilution, limit. For particles with energies within 0.25≤E≤1.75 (relative to the hopping integral) and with underlying square lattices of size 20×20, the configurations begin transmitting near p_α=0.60 with T against p curves following a common pattern as the amount of dilution is decreased. Near p_β=0.90 this pattern is broken and the transmission begins to vary with the energy. In the asymptotic limit of very large clusters we find the systems to be totally reflecting in almost all cases. A few clear exceptions we find are when the amount of dilution is very low, when the particle has energy close to a resonance value at the ordered limit, and when the particle has energy at the middle of the band. These three cases, however, may not exhaust all possible exceptions.     

Generalization of the transfer-integral method for two- and three-dimensional crystals

The ground-state expectation value can be evaluated for arbitrary interactions (including those with a hard core) if all occurring many-body wavefunctions are assumed to be products of single-particle functions and nearest-neighbor correlation functions.     

Hybrid analysis of two- and three-dimensional solids composed of different materials

Modern methods in experimental mechanics require considerable expenditure of theoretical considerations with concern to the experimental methods themselves as well as with concern to reliable evaluation and interpretation of the measured data. Because of the high resolving power and the exact data recording it is necessary to consider comprehensively all, even very small effects, which may have influence on the results of measurement. Otherwise the impression of an apparent accuracy may arise. On the other hand it is necessary to transform the originally measured data into the finally wanted information, which generally do not coincide with the measured quantities. Therefore the conventional interpretation of observed phenomena, i.e. measured data, must be substituted by advanced mathematical algorithms, enabling correct evaluation of data into wanted information in order to better approaching the reality. As measurements yield discrete numerical procedures. Under these considerations application of modern experimental methods, especially optical methods, and the performance of experimental analysis consequently require proper computer capacity for controlling the measurement process, for digital image processing, data recording and evaluation and thus extensive software. Such entire concept of combining experiment and measurement, respectively, with numerical evaluation procedures to analyse problems in mechanics can be summarised under the notion “hybrid techniques”. The meaning of this notion will be demonstrated exemplarily by application in photoelastic/photoviscoelastic and holographic-interferometric experiments.     

Bessel X waves in two- and three-dimensional bidispersive optical systems

We show that new families of two- and three-dimensional nondiffracting Bessel X waves are possible in linear bidispersive optical systems. These X waves can be observed in both bulk and waveguide configurations as well as in photonic crystal lattices that simultaneously exhibit normal and anomalous dispersive-diffractive properties in different spatial or spatiotemporal coordinates.     

Entropic and conformational study of isolated double-tethered chains by three-dimensional lattice simulations

Double-tethered polymers are a kind of linear polymer with a peculiar topological constraint; that is, both of its end-points are attached to a plane which the polymer segments cannot penetrate. The effects of the constraint on the polymer's configurational and entropic properties were investigated by means of a three-dimensional lattice simulation that combined a previously proposed idea with a very efficient chain generation algorithm. In particular, the value of a topology-dependent critical exponent was estimated for the double-tethered configurations. This data is the first report on isolated and double-tethered chains. Also, two optional types of tethered-polymer were investigated as asymptotes of the double- and single-tethered configurations.     

Self-organization in two- and three-dimensional adsorbates with attractive lateral interactions

Self-consistent lattice gas models for the dynamics of monolayer and multilayer adsorbates with attractive lateral interactions are investigated. The existence of spinodal regions with uphill diffusion is shown. For monolayer growth, periodic stationary distributions of adsorbate density are found analytically. Generalized kinetic BET-model for multilayer growth is studied numerically. A possibility for surface transformation into self-organized arrays of quantum dot-like structures is shown.