Markov chains, R-trivial monoids and representation theory

We develop a general theory of Markov chains realizable as random walks on R-trivial monoids. It provides explicit and simple formulas for the eigenvalues of the transition matrix, for multiplicities of the eigenvalues via Mobius inversion along a lattice, a condition for diagonalizability of the transition matrix and some techniques for bounding the mixing time. In addition, we discuss several examples, such as Toom-Tsetlin models, an exchange walk for finite Coxeter groups, as well as examples previously studied by the authors, such as nonabelian sandpile models and the promotion Markov chain on posets. Many of these examples can be viewed as random walks on quotients of free tree monoids, a new class of monoids whose combinatorics we develop.

Theory Of Phase Transformation And Reorientation In Single Crystalline Shape Memory Alloys

A constitutive model, based on an (n + 1)-phase mixture of the Mori-Tanaka average theory, has been developed for stress-induced martensitic transformation and reorientation in single crystalline shape memory alloys. Volume fractions of different martensite lattice correspondence variants are chosen as internal variables to describe microstructural evolution. Macroscopic Gibbs free energy for the phase transformation is derived with thermodynamics principles and the ensemble average method of micro-mechanics. The critical condition and the evolution equation are proposed for both the phase transition and reorientation. This model can also simulate interior hysteresis loops during loading/unloading by switching the critical driving forces when an opposite transition takes place.

Lattice anomalies and magnetic states in Fe_5Si_3-Mn_5Si_3 alloys

The lattice anomalies and magnetic states in the (Fe_100-xMn_x)₅Si₃ alloys have been investigated. Contrary to what was previously reported, results of x-ray diffraction show a second phase (α') present in Fe-rich alloys and therefore strictly speaking a complete solid solution does not exist. Mössbauer spectra, measured as a function of composition and temperature, indicate the presence of two inequivalent sites, namely 6(g) site (designated as site I) and 4(d) (site II). A two-site model (TSM) has been introduced to interpret the experimental findings. The compositional variation of lattice parameters a and c, determined from the x-ray analysis, exhibits anomalies at x = 22.5 and x = 50, respectively. The former can be attributed to the effect of a ferromagnetic transition; while the latter is due to the effect of preferential substitution between Fe and Mn atoms according to TSM.

The reduced magnetization of these alloys deduced from magnetic hyperfine splittings has been correlated with the magnetic transition temperatures in terms of the molecular field theory. It has been found from both the Mössbauer effect and magnetization measurements that for composition 0 ≤ x ˂ 50 both sites I and II are ferromagnetic at liquid-nitrogen temperature and possess moments parallel to each other. In the composition range 50 ˂ x ≤ 100 , the site II is antiferromagnetic whereas site I is paramagnetic even at a temperature below the bulk Néel temperatures. In the vicinity of x = 50 however, site II is in a state of transition between ferromagnetism and antiferromagnetism. The present study also suggests that only Mn in site II are responsible for the antiferromagnetism in Mn₅Si₃ contrary to a previous report.

Electrical resistance has also been measured as a function of temperature and composition. The resistive anomalies observed in the Mn-rich alloys are believed to result from the effect of the antiferromagnetic Brillouin zone on the mobility of conduction electrons.

Scattering by two degenerate anisotropic modes in square-lattice dielectric photonic crystals

We systematically investigate the square-lattice dielectric photonic crystals that have been used to demonstrate flat slab imaging experimentally. A right-handed Bloch mode is found in the left-handed frequency region by using the plane wave expansion method to analyze the photonic band structure and equifrequency contours. Using the multiple scattering theory, numerical simulations demonstrate that the left-handed mode and the right-handed mode are excited simultaneously by a point source and result in two kinds of transmitted waves. Impacted by the evanescent waves, superposition of these transmitted waves brings on complicated near field distributions such as the so-called imaging and its disappearance.

Density-potential mapping in the standard and quantum electrodynamical time-dependent density functional theory

131 p.

Theory of defects in amorphous semiconductors

We review the electronic structure of defects in aSi:H, aGaAs and aSi3N4, emphasising in aSi:H the doping mechanism, the evidence that its dangling bond defect has a small electron-lattice coupling and a positive correlation energy, and possible atomic mechanisms for the Staebler-Wronski effect. © 1985.

Correcting the systematic error of the density functional theory calculation: the alternate combination approach of genetic algorithm and neural network

The alternate combinational approach of genetic algorithm and neural network (AGANN) has been presented to correct the systematic error of the density functional theory (DFT) calculation. It treats the DFT as a black box and models the error through external statistical information. As a demonstration, the AGANN method has been applied in the correction of the lattice energies from the DFT calculation for 72 metal halides and hydrides. Through the AGANN correction, the mean absolute value of the relative errors of the calculated lattice energies to the experimental values decreases from 4.93% to 1.20% in the testing set. For comparison, the neural network approach reduces the mean value to 2.56%. And for the common combinational approach of genetic algorithm and neural network, the value drops to 2.15%. The multiple linear regression method almost has no correction effect here.

Anisotropic strain in (100) ZnSe epilayers grown on lattice mismatched substrates

We show that part of the reflectance difference resonance near the E-0 energy of ZnSe is due to the anisotropic in-plane strain in the ZnSe thin films, as films grown on three distinctly different substrates, GaAs, GaP, and ZnS, all show the resonance at the same energy. Such anisotropic strain induced resonance is predicted and also observed near the E-1/E-1+Delta(1) energies in ZnSe grown on GaAs. The theory also predicts that there should be no resonance due to strain at, the E-0+Delta(0) energy, which is consistent with experiments. The strain anisotropy is rather independent of the ZnSe layer thickness, or whether the film is strain relaxed. For ZnSe films with large lattice mismatch with substrates, the resonance at the E-1/E-1+Delta(1) energies is absent, very likely due to the poor crystalline quality of the 20 nm or so surface layer. (C) 2000 American Vacuum Society. [S0734-211X(00)05604-3].

Anisotropic strain in (100) ZnSe epilayers grown on lattice mismatched substrates

We show that part of the reflectance difference resonance near the E-0 energy of ZnSe is due to the anisotropic in-plane strain in the ZnSe thin films, as films grown on three distinctly different substrates, GaAs, GaP, and ZnS, all show the resonance at the same energy. Such anisotropic strain induced resonance is predicted and also observed near the E-1/E-1+Delta(1) energies in ZnSe grown on GaAs. The theory also predicts that there should be no resonance due to strain at, the E-0+Delta(0) energy, which is consistent with experiments. The strain anisotropy is rather independent of the ZnSe layer thickness, or whether the film is strain relaxed. For ZnSe films with large lattice mismatch with substrates, the resonance at the E-1/E-1+Delta(1) energies is absent, very likely due to the poor crystalline quality of the 20 nm or so surface layer. (C) 2000 American Vacuum Society. [S0734-211X(00)05604-3].

Lattice Boltzmann study of hydrodynamic effects in lamellar ordering process of two-dimensional quenched block copolymers

By incorporating self-consistent field theory with lattice Boltzmann method, a model for polymer melts is proposed. Compared with models based on Ginzburg-Landau free energy, our model does not employ phenomenological free energies to describe systems and can consider the chain topological details of polymers. We use this model to study the effects of hydrodynamic interactions on the dynamics of microphase separation for block copolymers. In the early stage of phase separation, an exponential growth predicted by Cahn-Hilliard treatment is found. Simulation results also show that the effect of hydrodynamic interactions can be neglected in the early stage.

STUDY OF COARSENING OF MICRODOMAINS IN BLOCK COPOLYMERS BY LATTICE BOLTZMANN METHODS

In order to understand the coarsening of microdomains in symmetric diblock copolymers at the late stage, a model for block copolymers is proposed. By incorporating the self consistent field theory with the free energy approach Lattice Boltzmann model, hydrodynamic interactions can be considered. Compared with models based on Ginzburg-Landau free energy, this model does not employ phenomenological free energies to describe systems. The model is verified by comparing the simulation results obtained using this method with those of a dynamical version of the self consistent mean field theory. After that,the growth exponents of the characteristic domain size for symmetric block copolymers at late stage are studied. It is found that the viscosity of the system affects the growth exponents greatly, although the growth exponents are all less than 1/3 Furthermore, the relations between the growth exponent, the interaction parameter and the chain length are studied.

Active site structure of NO decomposition on perovskite(-like) oxides: An investigation from experiment and density functional theory

Active site structure for NO decomposition carried out on perovskite-like oxides were discussed based on the N-2 yield measured from LaSrNi1-x,AlxO4 with different B-site cations and from La2-ySryCuO4 with different crystal phases. Results show that the active site contains two oxygen vacancies, two transition metals, and one lattice-oxygen, with the oxygen vacancy locating on the apex of MO6 octahedron, and the lattice oxygen locating between the two transition metals (i.e., M-O-M plane). Density functional theory (DFT) analysis to the structure shows that this new active site is the most active structure for NO adsorbing, and hence, for NO decomposition. The similar trend of the relative energies that are required for the formation of oxygen vacancies with f form (calculated from DFT), the amount of oxygen vacancies, and the activities (N-2 yield) certifies this result further.

A self-consistent field theory study on the morphologies of linear ABCBA and H-shaped (AB)(2)C(BA)(2) block copolymers

By using a combinatorial screening method based on the self-consistent field theory, we investigate the equilibrium morphologies of linear ABCBA and H-shaped (AB)(2)C(BA)(2) block copolymers in two dimensions. The triangle phase diagrams of both block copolymers are constructed by systematically varying the volume fractions of blocks A, B, and C. In this study, the interaction energies between species A, B, and C are set to be equal. Four different equilibrium morphologies are identified, i.e., the lamellar phase (LAM), the hexagonal lattice phase (HEX), the core-shell hexagonal lattice phase (CSH), and the two interpenetrating tetragonal lattice phase (TET2). For the linear ABCBA block copolymer, the reflection symmetry is observed in the phase diagram except for some special grid points, and most of grid points are occupied by LAM morphology. However, for the H-shaped (AB)(2)C(BA)(2) block copolymer, most of the grid points in the triangle phase diagram are occupied by CSH morphology, which is ascribed to the different chain architectures of the two block copolymers. These results may help in the design of block copolymers with different microstructures.

Lattice energy estimation for inorganic ionic crystals

An empirical method based on chemical bond theory for the estimation of the lattice energy for ionic crystals has been proposed. The lattice energy contributions have been partitioned into bond dependent terms. For an individual bond, the lattice energy contribution made by it has been separated into ionic and covalent parts. Our calculated values of lattice energies agree well with available experimental and theoretical values for diverse ionic crystals. This method, which requires detailed crystallographic information and elaborate computation, might be extended and possibly yield further insights with respect to bond properties of materials.