Equilibrium and equivariant triangulations of some small covers with minimum number of vertices

Small covers were introduced by Davis and Januszkiewicz in 1991. We introduce the notion of equilibrium triangulations for small covers. We study equilibrium and vertex minimal 4-equivariant triangulations of 2-dimensional small covers. We discuss vertex minimal equilibrium triangulations of RP3#RP3, S-1 x RP2 and a nontrivial S-1 bundle over RP2. We construct some nice equilibrium triangulations of the real projective space RPn with 2(n) + n 1 vertices. The main tool is the theory of small covers.

Detection of a quantum particle on a lattice under repeated projective measurements

We consider a quantum particle, moving on a lattice with a tight-binding Hamiltonian, which is subjected to measurements to detect its arrival at a particular chosen set of sites. The projective measurements are made at regular time intervals tau, and we consider the evolution of the wave function until the time a detection occurs. We study the probabilities of its first detection at some time and, conversely, the probability of it not being detected (i.e., surviving) up to that time. We propose a general perturbative approach for understanding the dynamics which maps the evolution operator, which consists of unitary transformations followed by projections, to one described by a non-Hermitian Hamiltonian. For some examples of a particle moving on one-and two-dimensional lattices with one or more detection sites, we use this approach to find exact expressions for the survival probability and find excellent agreement with direct numerical results. A mean-field model with hopping between all pairs of sites and detection at one site is solved exactly. For the one-and two-dimensional systems, the survival probability is shown to have a power-law decay with time, where the power depends on the initial position of the particle. Finally, we show an interesting and nontrivial connection between the dynamics of the particle in our model and the evolution of a particle under a non-Hermitian Hamiltonian with a large absorbing potential at some sites.

Majorana modes and transport across junctions of superconductors and normal metals

We study Majorana modes and transport in one-dimensional systems with a p-wave superconductor (SC) and normal metal leads. For a system with an SC lying between two leads, it is known that there is a Majorana mode at the junction between the SC and each lead. If the p-wave pairing Delta changes sign or if a strong impurity is present at some point inside the SC, two additional Majorana modes appear near that point. We study the effect of all these modes on the sub-gap conductance between the leads and the SC. We derive an analytical expression as a function of Delta and the length L of the SC for the energy shifts of the Majorana modes at the junctions due to hybridization between them; the shifts oscillate and decay exponentially as L is increased. The energy shifts exactly match the location of the peaks in the conductance. Using bosonization and the renormalization group method, we study the effect of interactions between the electrons on Delta and the strengths of an impurity inside the SC or the barriers between the SC and the leads; this in turn affects the Majorana modes and the conductance. Finally, we propose a novel experimental realization of these systems, in particular of a system where Delta changes sign at one point inside the SC.

Anomalous transport at weak coupling

We evaluate the contribution of chiral fermions in d = 2, 4, 6, chiral bosons, a chiral gravitino like theory in d = 2 and chiral gravitinos in d = 6 to all the leading parity odd transport coefficients at one loop. This is done by using finite temperature field theory to evaluate the relevant Kubo formulae. For chiral fermions and chiral bosons the relation between the parity odd transport coefficient and the microscopic anomalies including gravitational anomalies agree with that found by using the general methods of hydrodynamics and the argument involving the consistency of the Euclidean vacuum. For the gravitino like theory in d = 2 and chiral gravitinos in d = 6, we show that relation between the pure gravitational anomaly and parity odd transport breaks down. From the perturbative calculation we clearly identify the terms that contribute to the anomaly polynomial, but not to the transport coefficient for gravitinos. We also develop a simple method for evaluating the angular integrals in the one loop diagrams involved in the Kubo formulae. Finally we show that charge diffusion mode of an ideal 2 dimensional Weyl gas in the presence of a finite chemical potential acquires a speed, which is equal to half the speed of light.

Formation of composite organic thin film transistors with nanotubes and nanowires

Plastic electronics is a rapidly expanding topic, much of which has been focused on organic semiconductors. However, it is also of interest to find viable ways to integrate nanomaterials, such as silicon nanowires (SiNWs) and carbon nanotubes (CNTs), into this technology. Here, we present methods of fabrication of composite devices incorporating such nanostructured materials into an organic matrix. We investigate the formation of polymer/CNT composites, for which we use the semiconducting polymer poly(3,3‴-dialkyl-quaterthiophene) (PQT). We also report a method of fabricating polymer/SiNW TFTs, whereby sparse arrays of parallel oriented SiNWs are initially prepared on silicon dioxide substrates from forests of as-grown gold-catalysed SiNWs. Subsequent ink-jet printing of PQT on these arrays produces a polymer/SiNW composite film. We also present the electrical characterization of all composite devices. © 2007 Elsevier B.V. All rights reserved.

Size effects on the melting of nickel nanowires: a molecular dynamics study

The melting process of nickel nanowires are simulated by using molecular dynamics with the quantum Sutten-Chen many-body force field. The wires studied were approximately cylindrical in cross-section and periodic boundary conditions were applied along their length; the atoms were arranged initially in a face-centred cubic structure with the [0 0 1] direction parallel to the long axis of the wire. The size effects of the nanowires on the melting temperatures are investigated. We find that for the nanoscale regime, the melting temperatures of Ni nanowires are much lower than that of the bulk and are linear with the reciprocal of the diameter of the nanowire. When a nanowire is heated up above the melting temperature, the neck of the nanowire begins to arise and the diameter of neck decreases rapidly with the equilibrated running time. Finally, the breaking of nanowire arises, which leads to the formation of the spherical clusters. (C) 2004 Elsevier B.V. All rights reserved.

A new method of studying the dynamical behavior of the sine-gordon equation

We try to connect the theory of infinite dimensional dynamical systems and nonlinear dynamical methods. The sine-Gordon equation is used to illustrate our method of discussing the dynamical behaviour of infinite dimensional systems. The results agree with those of Bishop and Flesch [SLAM J. Math. Anal. 21 (1990) 1511].

Approximate theory of natural-convection with small grashof number

To gain some insight into the behaviour of low-gravity flows in the material processing in space, an approximate theory has been developed for the convective motion of fluids with a small Grashof number Gr. The expansion of the variables into a series of Gr reduces the Boussinesq equation to a system of weakly coupled linearly inhomogeneous equations. Moreover, the analogy concept is proposed and utilized in the study of the plate bending problems in solid mechanics. Two examples are investigated in detail, i. e. the 2-dimensional steady flows in either circular or square infinite closed cylinder, which is horizontally imposed at a specified temperature of linear distribution on the boundaries. The results for stream function ψ, velocity u and temperature T are provided. The analysis of the influences of some parameters such as the Grashof number Gr and the Prandtl number Pr, on motions will lead to several interesting conclusions. The theory seems to be useful for seeking for an analytical solutions. At least, it will greatly simplify the complicated problems originally governed by the Navier-Stokes equation including buoyancy. It is our hope that the theory might be applicable to unsteady or 3-dimensional cases in future.

Magnetostatic relations including fluctuation fields - the local expansion

Using the approach of local expansion, we analyze the magnetostatic relations in the case of conventional turbulence. The turbulent relations are obtained consisten tly for themomentum equation and induction equation of both the average and fluctuation relations.In comparison with the magnetostatic relations as discussed usually, turbulent fluctuationfields produce forces, one of which 1/(4π)(α1×B0)×B0 may have parallel and perpendicular components in the direction of magnetic field, the other of which 1/(4π)K×B0 is introduced by the boundary value of turbulence and is perpendicular to the magnetic field. In the case of 2-dimensional configuration of magnetic field, the basic equation will be reduced into a second-order elliptic equation, which includes some linear and nonlinear terms introduced by turbulent fluctuation fields. Turbulent fields may change the configuration of magnetic field and even shear it non-uniformly. The study on the influence of turbulent fields is significant since they are observed in many astrophysical environments.

Some comments on the stability theory of mhd shock waves

The stability (evolutionarity) problem for a kind of MHD shock waves is discussed in this paper. That is to solve the interaction problem of MHD shock waves with (2-dimensional) oblique incident disturbances. In other words, the result of gasdynamic shocks is generalized to the case of MHD shocks. The previous conclusion of stability theory of MHD shock waves obtained from the solution of interaction problem of MHD shock wave with (one-dimensional) normal shock wave is that only fast and slow shocks are stable, and intermediate shocks are unstable. However, the results of this paper show that when the small disturbances are the Alfven waves a new stability condition which is related to the parameters in front of and behind the shock wave is derived. When the disturbances are entropy wave and fast and slow magneto acoustic waves the stability condition is related to the frequency of small disturbances. As the limiting ease, i. e. when a normal incident (reflection, refraction) is consid...更多ered, the fast and slow shocks are unstable. The results also show that the conclusion drawn by Kontorovich is invalid for the stability theory of shock waves.

Triangle Evolution-A Hybrid Heuristic for Global Optimization

Abstract This paper presents a hybrid heuristic{triangle evolution (TE) for global optimization. It is a real coded evolutionary algorithm. As in di®erential evolution (DE), TE targets each individual in current population and attempts to replace it by a new better individual. However, the way of generating new individuals is di®erent. TE generates new individuals in a Nelder- Mead way, while the simplices used in TE is 1 or 2 dimensional. The proposed algorithm is very easy to use and e±cient for global optimization problems with continuous variables. Moreover, it requires only one (explicit) control parameter. Numerical results show that the new algorithm is comparable with DE for low dimensional problems but it outperforms DE for high dimensional problems.

High Order Multi-Moment Constrained Finite Volume Method. Part I: Basic Formulation

A new high-order finite volume method based on local reconstruction is presented in this paper. The method, so-called the multi-moment constrained finite volume (MCV) method, uses the point values defined within single cell at equally spaced points as the model variables (or unknowns). The time evolution equations used to update the unknowns are derived from a set of constraint conditions imposed on multi kinds of moments, i.e. the cell-averaged value and the point-wise value of the state variable and its derivatives. The finite volume constraint on the cell-average guarantees the numerical conservativeness of the method. Most constraint conditions are imposed on the cell boundaries, where the numerical flux and its derivatives are solved as general Riemann problems. A multi-moment constrained Lagrange interpolation reconstruction for the demanded order of accuracy is constructed over single cell and converts the evolution equations of the moments to those of the unknowns. The presented method provides a general framework to construct efficient schemes of high orders. The basic formulations for hyperbolic conservation laws in 1- and 2D structured grids are detailed with the numerical results of widely used benchmark tests. (C) 2009 Elsevier Inc. All rights reserved.

Attenuation tomography. Modelling regional love waves: Imperial Valley to Pasadena

Abstract to Part I

The inverse problem of seismic wave attenuation is solved by an iterative back-projection method. The seismic wave quality factor, Q, can be estimated approximately by inverting the S-to-P amplitude ratios. Effects of various uncertain ties in the method are tested and the attenuation tomography is shown to be useful in solving for the spatial variations in attenuation structure and in estimating the effective seismic quality factor of attenuating anomalies.

Back-projection attenuation tomography is applied to two cases in southern California: Imperial Valley and the Coso-Indian Wells region. In the Coso-Indian Wells region, a highly attenuating body (S-wave quality factor (Q_β ≈ 30) coincides with a slow P-wave anomaly mapped by Walck and Clayton (1987). This coincidence suggests the presence of a magmatic or hydrothermal body 3 to 5 km deep in the Indian Wells region. In the Imperial Valley, slow P-wave travel-time anomalies and highly attenuating S-wave anomalies were found in the Brawley seismic zone at a depth of 8 to 12 km. The effective S-wave quality factor is very low (Q_β ≈ 20) and the P-wave velocity is 10% slower than the surrounding areas. These results suggest either magmatic or hydrothermal intrusions, or fractures at depth, possibly related to active shear in the Brawley seismic zone.

No-block inversion is a generalized tomographic method utilizing the continuous form of an inverse problem. The inverse problem of attenuation can be posed in a continuous form , and the no-block inversion technique is applied to the same data set used in the back-projection tomography. A relatively small data set with little redundancy enables us to apply both techniques to a similar degree of resolution. The results obtained by the two methods are very similar. By applying the two methods to the same data set, formal errors and resolution can be directly computed for the final model, and the objectivity of the final result can be enhanced.

Both methods of attenuation tomography are applied to a data set of local earthquakes in Kilauea, Hawaii, to solve for the attenuation structure under Kilauea and the East Rift Zone. The shallow Kilauea magma chamber, East Rift Zone and the Mauna Loa magma chamber are delineated as attenuating anomalies. Detailed inversion reveals shallow secondary magma reservoirs at Mauna Ulu and Puu Oo, the present sites of volcanic eruptions. The Hilina Fault zone is highly attenuating, dominating the attenuating anomalies at shallow depths. The magma conduit system along the summit and the East Rift Zone of Kilauea shows up as a continuous supply channel extending down to a depth of approximately 6 km. The Southwest Rift Zone, on the other hand, is not delineated by attenuating anomalies, except at a depth of 8-12 km, where an attenuating anomaly is imaged west of Puu Kou. The Ylauna Loa chamber is seated at a deeper level (about 6-10 km) than the Kilauea magma chamber. Resolution in the Mauna Loa area is not as good as in the Kilauea area, and there is a trade-off between the depth extent of the magma chamber imaged under Mauna Loa and the error that is due to poor ray coverage. Kilauea magma chamber, on the other hand, is well resolved, according to a resolution test done at the location of the magma chamber.

Abstract to Part II

Long period seismograms recorded at Pasadena of earthquakes occurring along a profile to Imperial Valley are studied in terms of source phenomena (e.g., source mechanisms and depths) versus path effects. Some of the events have known source parameters, determined by teleseismic or near-field studies, and are used as master events in a forward modeling exercise to derive the Green's functions (SH displacements at Pasadena that are due to a pure strike-slip or dip-slip mechanism) that describe the propagation effects along the profile. Both timing and waveforms of records are matched by synthetics calculated from 2-dimensional velocity models. The best 2-dimensional section begins at Imperial Valley with a thin crust containing the basin structure and thickens towards Pasadena. The detailed nature of the transition zone at the base of the crust controls the early arriving shorter periods (strong motions), while the edge of the basin controls the scattered longer period surface waves. From the waveform characteristics alone, shallow events in the basin are easily distinguished from deep events, and the amount of strike-slip versus dip-slip motion is also easily determined. Those events rupturing the sediments, such as the 1979 Imperial Valley earthquake, can be recognized easily by a late-arriving scattered Love wave that has been delayed by the very slow path across the shallow valley structure.