Flat surfaces of finite type in the 3-sphere

We introduce the notion of flat surfaces of finite type in the 3- sphere, give the algebro-geometric description in terms of spectral curves and polynomial Killing fields, and show that finite type flat surfaces generated by curves on S2 with periodic curvature functions are dense in the space of all flat surfaces generated by curves on S2 with periodic curvature functions.

Robust gap repair in the contractile ring ensures timely completion of cytokinesis

Cytokinesis in animal cells requires the constriction of an actomyosin contractile ring, whose architecture and mechanism remain poorly understood. We use laser microsurgery to explore the biophysical properties of constricting rings in Caenorhabditis elegans embryos. Laser cutting causes rings to snap open. However, instead of disintegrating, ring topology recovers and constriction proceeds. In response to severing, a finite gap forms and is repaired by recruitment of new material in an actin polymerization-dependent manner. An open ring is able to constrict, and rings repair from successive cuts. After gap repair, an increase in constriction velocity allows cytokinesis to complete at the same time as controls. Our analysis demonstrates that tension in the ring increases while net cortical tension at the site of ingression decreases throughout constriction and suggests that cytokinesis is accomplished by contractile modules that assemble and contract autonomously, enabling local repair of the actomyosin network. Consequently, cytokinesis is a highly robust process impervious to discontinuities in contractile ring structure.

Liquid alloy semiconductors revisited - Discussion

In 1990 Enderby and Barnes reviewed the electrical properties of liquid alloys which show features associated with semiconducting behaviour. They proposed an empirical classification scheme based on the notion that some liquid semiconductors are characterized by a finite gap in σ (E), the energy-dependent conductivity (narrow definition), whereas in others σ (E) is continuous (broad definition). Interesting behaviour occurs for systems at the narrow/broad boundary and further analysis of these liquid alloys will form the subject matter of this paper. Particular attention will be focused on liquid silver chalcogenides as these offer a severe test of current theories.

Broken symmetry and pseudogaps in ropes of carbon nanotubes

Since the discovery of carbon nanotubes, it has been speculated that these materials should behave like nanoscale wires with unusual electronic properties and exceptional strength. Recently, 'ropes' of close-packed single-wall nanotubes have been synthesized in high yield. The tubes in these ropes are mainly of the (10,10) type3, which is predicted to be metallic. Experiments on individual nanotubes and ropes indicate that these systems indeed have transport properties that qualify them to be viewed as nanoscale quantum wires at low temperature. It has been expected that the close-packing of individual nanotubes into ropes does not change their electronic properties significantly. Here, however, we present first-principles calculations which show that a broken symmetry of the (10,10) tube caused by interactions between tubes in a rope induces a pseudogap of about 0.1 eV at the Fermi level. This pseudogap strongly modifies many of the fundamental electronic properties: we predict a semimetal-like temperature dependence of the electrical conductivity and a finite gap in the infrared absorption spectrum. The existence of both electron and hole charge carriers will lead to qualitatively different thermopower and Hall-effect behaviours from those expected for a normal metal.

Cutoff-independent regularization of four-fermion interactions for color superconductivity

We implement a cutoff-independent regularization of four-fermion interactions to calculate the color-superconducting gap parameter in quark matter. The traditional cutoff regularization has difficulties for chemical potentials mu of the order of the cutoff Lambda, predicting in particular a vanishing gap at mu similar to Lambda. The proposed cutoff-independent regularization predicts a finite gap at high densities and indicates a smooth matching with the weak coupling QCD prediction for the gap at asymptotically high densities.

Periodic waves and solitons in a nonlinear fibre with resonant impurities

We shall consider a coupled nonlinear Schrodinger equation- Bloch system of equations describing the propagation of a single pulse through a nonlinear dispersive waveguide in the presence of resonances; this could be, for example, a doped optical fibre. By making use of the integrability of the dynamic equations, we shall apply the finite-gap integration method to obtain periodic solutions for this system. Next, we consider the problem of the formation of solitons at a sharp front pulse and, by means of the Whitham modulational theory, we derive the amplitude and velocity of the largest soliton.

ELECTRON TRANSPORT IN LOW-DIMENSIONAL NANOSTRUCTURES - THEORETICAL STUDY WITH APPLICATION

Graphene as a carbon monolayer has attracted extensive research interest in recent years. My research work within the frame of density functional theory has suggested that positioning graphene in proximity to h-BN may induce a finite energy gap in graphene, which is important for device applications. For an AB-stacked graphene/BN bilayer, a finite gap is induced at the equilibrium configuration. This induced gap shows a linear relationship with the applied strain. For a graphene/BN/graphene trilayer, a negligible gap is predicted in the ground state due to the overall symmetry of the system. When an electric field is applied, a tunable gap can be obtained for both AAA and ABA stackings. Enhanced tunneling current in the AA-stacked bilayer nanoribbons is predicted compared to either single-layer or AB-stacked bilayer nanoribbons. Interlayer separation between the nanoribbons is shown to have a profound impact on the conducting features. The effect of boron or nitrogen doping on the electronic transport properties of C60 fullerene is studied. The BC59 fullerene exhibits a considerably higher current than the pristine or nitrogen doped fullerenes beyond the applied bias of 1 V, suggesting it can be an effective semiconductor in p-type devices. The interaction between nucleic acid bases - adenine (A), guanine (G), cytosine (C), thymine (T) and uracil (U) - and a hydrogen-passivated silicon nanowire (SiNW) is investigated. The binding energy of the bases with the SiNW shows the order: G > A~C~T~U. This suggests that the interaction strength of a hydrogen passivated SiNW with the nucleic acid bases is nearly the same-G being an exception. The nature of the interaction is suggested to be electrostatic.

Two-dimensional Cartesian air-gap element (CAGE) for dynamic finite-element modeling of electrical machines with a flat air gap

This paper extends the air-gap element (AGE) to enable the modeling of flat air gaps. AGE is a macroelement originally proposed by Abdel-Razek et al.for modeling annular air gaps in electrical machines. The paper presents the theory of the new macroelement and explains its implementation within a time-stepped finite-element (FE) code. It validates the solution produced by the new macroelement by comparing it with that obtained by using an FE mesh with a discretized air gap. It then applies the model to determine the open-circuit electromotive force of an axial-flux permanent-magnet machine and compares the results with measurements.

On the forbidden gap of finite graphene nanoribbons

The electronic structure of isolated finite graphene nanoribbons is investigated by solving, at the Hartree-Fock (HF) level, the Pariser, Parr and Pople (PPP) many-body Hamiltonian. The study is mainly focused on 7-AGNR and 13-AGNR (Armchair Graphene Nano-Ribbons), whose electronic structures have been recently experimentally investigated. Only paramagnetic solutions are considered. The characteristics of the forbidden gap are studied as a function of the ribbon length. For a 7-AGNR, the gap monotonically decreases from a maximum value of ~6.5 eV for short nanoribbons to a very small value of ~0.12 eV for the longer calculated systems. Gap edges are defined by molecular orbitals that are spatially localized near the nanoribbon extremes, that is, near both zig-zag edges. On the other hand, two delocalized orbitals define a much larger gap of about 5 eV. Conductance measurements report a somewhat smaller gap of ~3 eV. The small real gap lies in the middle of the one given by extended states and has been observed by STM and reproduced by DFT calculations. On the other hand, the length dependence of the gap is not monotonous for a 13-AGNR. It decreases initially but sharply increases for lengths beyond 30 Å remaining almost constant thereafter at a value of ~2.1 eV. Two additional states localized at the nanoribbon extremes show up at energies 0.31 eV below the HOMO (Highest Occupied Molecular Orbital) and above the LUMO (Lowest Unoccupied Molecular Orbital). These numbers compare favorably with those recently obtained by means of STS for a 13-AGNR sustained by a gold surface, namely 1.4 eV for the energy gap and 0.4 eV for the position of localized band edges. We show that the important differences between 7- and 13-AGNR should be ascribed to the charge rearrangement near the zig-zag edges obtained in our calculations for ribbons longer than 30 Å, a feature that does not show up for a 7-AGNR no matter its length.

Finite Symmetric Functions with Non-Trivial Arity Gap

Given an n-ary k-valued function f, gap(f) denotes the essential arity gap of f which is the minimal number of essential variables in f which become fictive when identifying any two distinct essential variables in f. In the present paper we study the properties of the symmetric function with non-trivial arity gap (2 ≤ gap(f)). We prove several results concerning decomposition of the symmetric functions with non-trivial arity gap with its minors or subfunctions. We show that all non-empty sets of essential variables in symmetric functions with non-trivial arity gap are separable. ACM Computing Classification System (1998): G.2.0.

Directional coupler using gap plasmon waveguides

Here, we demonstrate that efficient nano-optical couplers can be developed using closely spaced gap plasmon waveguides in the form of two parallel nano-sized rectangular slots in a thin metal film or membrane. Using the rigorous numerical finite-difference and finite element algorithms, we investigate the physical mechanisms of coupling between two neighboring gap plasmon waveguides and determine typical coupling lengths for different structural parameters of the coupler. Special attention is focused onto the analysis of the effect of such major coupler parameters, such as thickness of the metal film/membrane, slot width, and separation between the plasmonic waveguides. Detailed physical interpretation of the obtained unusual dependencies of the coupling length on slot width and film thickness is presented based upon the energy consideration. The obtained results will be important for the optimization and experimental development of plasmonic sub-wavelength compact directional couplers and other nano-optical devices for integrated nanophotonics.

Ratchetting of railhead in the vicinity of the gap of the insulated rail joints

Insulated Rail Joints (IRJs) are designed to electrically isolate two rails in rail tracks to control the signalling system for safer train operations. Unfortunately the gapped section of the IRJs is structurally weak and often fails prematurely especially in heavy haul tracks, which adversely affects service reliability and efficiency. The IRJs suffer from a number of failure modes; the railhead ratchetting at the gap is, however, regarded as the root cause and attended to in this thesis. Ratchetting increases with the increase in wheel loads; in the absence of a life prediction model, effective management of the IRJs for increased wagon wheel loads has become very challenging. Therefore, the main aim of this thesis is to determine method to predict IRJs' service life. The distinct discontinuity of the railhead at the gap makes the Hertzian theory and the rolling contact shakedown map, commonly used in the continuously welded rails, not applicable to examine the metal ratchetting of the IRJs. Finite Element (FE) technique is, therefore, used to explore the railhead metal ratchetting characteristics in this thesis, the boundary conditions of which has been determined from a full scale study of the IRJ specimens under rolling contact of the loaded wheels. A special purpose test set up containing full-scale wagon wheel was used to apply rolling wheel loads on the railhead edges of the test specimens. The state of the rail end face strains was determined using a non-contact digital imaging technique and used for calibrating the FE model. The basic material parameters for this FE model were obtained through independent uniaxial, monotonic tensile tests on specimens cut from the head hardened virgin rails. The monotonic tensile test data have been used to establish a cyclic load simulation model of the railhead steel specimen; the simulated cyclic load test has provided the necessary data for the three decomposed kinematic hardening plastic strain accumulation model of Chaboche. A performance based service life prediction algorithm for the IRJs was established using the plastic strain accumulation obtained from the Chaboche model. The predicted service lives of IRJs using this algorithm have agreed well with the published data. The finite element model has been used to carry out a sensitivity study on the effects of wheel diameter to the railhead metal plasticity. This study revealed that the depth of the plastic zone at the railhead edges is independent of the wheel diameter; however, large wheel diameter is shown to increase the IRJs' service life.

Optimizing the quantum dot: Plasmon interaction in a nano gap waveguide

Spontaneous emission (SE) of a Quantum emitter depends mainly on the transmission strength between the upper and lower energy levels as well as the Local Density of States (LDOS)[1]. When a QD is placed in near a plasmon waveguide, LDOS of the QD is increased due to addition of the non-radiative decay and a plasmonic decay channel to free space emission[2-4]. The slow velocity and dramatic concentration of the electric field of the plasmon can capture majority of the SE into guided plasmon mode (Гpl ). This paper focused on studying the effect of waveguide height on the efficiency of coupling QD decay into plasmon mode using a numerical model based on finite elemental method (FEM). Symmetric gap waveguide considered in this paper support single mode and QD as a dipole emitter. 2D simulation models are done to find normalized Гpl and 3D models are used to find probability of SE decaying into plasmon mode ( β) including all three decay channels. It is found out that changing gap height can increase QD-plasmon coupling, by up to a factor of 5 and optimally placed QD up to a factor of 8. To make the paper more realistic we briefly studied the effect of sharpness of the waveguide edge on SE emission into guided plasmon mode. Preliminary nano gap waveguide fabrication and testing are already underway. Authors expect to compare the theoretical results with experimental outcomes in the future