Phase diagram and spectral properties of a new exactly integrable spin-1 quantum chain

The spectral properties and phase diagram of the exactly integrable spin-1 quantum chain introduced by Alcaraz and Bariev are presented. The model has a U(1) symmetry and its integrability is associated with an unknown R-matrix whose dependence on the spectral parameters is not of a different form. The associated Bethe ansatz equations that fix the eigenspectra are distinct from those associated with other known integrable spin models. The model has a free parameter t(p). We show that at the special point t(p) = 1, the model acquires an extra U(1) symmetry and reduces to the deformed SU(3) Perk-Schultz model at a special value of its anisotropy q = exp(i2 pi/3) and in the presence of an external magnetic field. Our analysis is carried out either by solving the associated Bethe ansatz equations or by direct diagonalization of the quantum Hamiltonian for small lattice sizes. The phase diagram is calculated by exploring the consequences of conformal invariance on the finite-size corrections of the Hamiltonian eigenspectrum. The model exhibits a critical phase ruled by the c = 1 conformal field theory separated from a massive phase by first-order phase transitions.

NMR investigation of phenolphthalein polyether ether ketone .1. The chain structure and assignments of H-1, C-13 NMR lines of PEK-C

Amorphous samples of polyether ketone with cardo(PEK-C) have been studied in the solution state by C-13, H-1 high-resolution NMR, The H-1 and C-13 1D NMR spectra were assigned using two dimensional chemical shift correlated spectroscopy, 2D homonuclear correlated(COSY) and heteronuclear correlated (HETCOR) spectroscopy present important information. In this work, the structural units of PEK-C was determined by NMR. For some peaks, these assignments are confirmed by two dimensional long-range heteronuclear correlation experiments, A little modification is made on the original C-13 peak assignments for the main chain, The symmetry and the isotacticity of the chain structure for PEK-C are obvious on NMR data.

Self-assembly of three new coordination complexes: Formation of 2-D square grid, 1-D chain and tape structures

Three distinct coordination complexes, viz., [Co(imi)(2)(tmb)(2)] (1) [where imi = imidazole], {[Ni(tmb)(2)(H2O)(3)]center dot 2H(2)O}(n) (2) and [Cu-2(mu-tmb)(4)(CH3OH)(2)] (3), have been synthesized hydrothermally by the reactions of metal acetates,2,4,6-trimethylbenzoic acid (Htmb) and with or without appropriate amine. The Ni analogue of 1 and the Co analogue of 2 have also been synthesized. X-ray single-crystal diffraction suggests that complex 1 represents discrete mononuclear species and complex 2 represents a 1D chain coordination polymer in which the Ni(H) ions are connected by the bridging water molecules. Complex 3 represents a neutral dinuclear complex. In 1, the central metal ions are associated by the carboxylate moiety and imidazole ligands, whereas the central metal atom is coordinated to the carboxylate moiety and the respective solvent molecules in 2 and 3. In 3, the four 2,4,6-trimethylbenzoate moieties act as a bridge connecting two copper (11) ions and the 0 atoms of methanol coord geometry, with the methanol molecule at the apical position. In all the three structures the central metal atom sits on a crystallographic inversion centre. In all the cases, the coordination entities are further organized via hydrogen bonding interactions to generate multifarious supramolecular networks. Complexes 1, 2 and 3 have also been characterized by spectroscopic (UV/Vis and IR) and thermal analysis (TGA). In addition, the complexes were found to exhibit antimicrobial activity. The magnetic susceptibility measurements, measured from 8 to 300 K, revealed antiferromagnetic interactions between the Co(II) ions in compound 1 and the Ni(II) ions in la, respectively.

Modified density matrix renormalization group algorithm for the zigzag spin-1/2 chain with frustrated antiferromagnetic exchange: Comparison with field theory at large J(2)/J(1)

A modified density matrix renormalization group (DMRG) algorithm is applied to the zigzag spin-1/2 chain with frustrated antiferromagnetic exchange J(1) and J(2) between first and second neighbors. The modified algorithm yields accurate results up to J(2)/J(1) approximate to 4 for the magnetic gap Delta to the lowest triplet state, the amplitude B of the bond order wave phase, the wavelength lambda of the spiral phase, and the spin correlation length xi. The J(2)/J(1) dependences of Delta, B, lambda, and xi provide multiple comparisons to field theories of the zigzag chain. The twist angle of the spiral phase and the spin structure factor yield additional comparisons between DMRG and field theory. Attention is given to the numerical accuracy required to obtain exponentially small gaps or exponentially long correlations near a quantum phase transition.

Infrared divergences and confinement in massive (2+1)-dimensional QED

In (2+1)-dimensional quantum electrodynamics with massless photons and massive matter fields, it is shown that the mass renormalization of the latter is infrared divergent at one loop. This result remains unchanged at two loops. A simple argument based on a similar divergence of the Coulomb potential leads us to conjecture that charged states are not observable in this model. This argument holds in 1+1 dimensions also.

Transient population and polarization gratings induced by (1+1)-dimensional ultrashort dipole soliton

An ultrafast transient population grating induced by a (1+1)-dimensional, ultrashort dipole soliton is demonstrated by solving the full-wave Maxwell-Bloch equations. The number of lines and the period of the grating can be controlled by the beam waist and the area of the pulse. Of interest is that a polarization grating is produced. A coherent control scheme based on these phenomena can be contemplated as ultrafast transient grating techniques.

New doubly periodic waves of the (2+1)-dimensional double sine-Gordon equation

New exact solutions of the (2 + 1)-dimensional double sine-Gordon equation are studied by introducing the modified mapping relations between the cubic nonlinear Klein-Gordon system and double sine-Gordon equation. Two arbitrary functions are included into the Jacobi elliptic function solutions. New doubly periodic wave solutions are obtained and displayed graphically by proper selections of the arbitrary functions.

BRST invariant theory of a generalized 1+1 Dimensional nonlinear sigma model with topological term

We give a generalized Lagrangian density of 1 + 1 Dimensional O( 3) nonlinear sigma model with subsidiary constraints, different Lagrange multiplier fields and topological term, find a lost intrinsic constraint condition, convert the subsidiary constraints into inner constraints in the nonlinear sigma model, give the example of not introducing the lost constraint. N = 0, by comparing the example with the case of introducing the lost constraint, we obtain that when not introducing the lost constraint, one has to obtain a lot of various non-intrinsic constraints. We further deduce the gauge generator, give general BRST transformation of the model under the general conditions. It is discovered that there exists a gauge parameter beta originating from the freedom degree of BRST transformation in a general O( 3) nonlinear sigma model, and we gain the general commutation relations of ghost field.

Magnet-assisted assembly of 1-dimensional hollow PtCo nanomaterials on an electrode surface

In this work, rapid and controllable confinement of one-dimensional (1D) hollow PtCo nanomaterials on an indium tin oxide (ITO) electrode surface was simply realized via magnetic attraction. The successful assembly was verified by scanning electron microscopy (SEM) and cyclic voltammetry, which showed that a longer exposure time of the electrode to the suspension of these 1D hollow nanomaterials (magnetic suspension) led to a larger amount of attached 1D hollow PtCo nanomaterials.

Fabrication, characterisation and electroanalysis at 1-dimensional nanostructures

Integrated nanowire electrodes that permit direct, sensitive and rapid electrochemical based detection of chemical and biological species are a powerful emerging class of sensor devices. As critical dimensions of the electrodes enter the nanoscale, radial analyte diffusion profiles to the electrode dominate with a corresponding enhancement in mass transport, steady-state sigmoidal voltammograms, low depletion of target molecules and faster analysis. To optimise these sensors it is necessary to fully understand the factors that influence performance limits including: electrode geometry, electrode dimensions, electrode separation distances (within nanowire arrays) and diffusional mass transport. Therefore, in this thesis, theoretical simulations of analyte diffusion occurring at a variety of electrode designs were undertaken using Comsol Multiphysics®. Sensor devices were fabricated and corresponding experiments were performed to challenge simulation results. Two approaches for the fabrication and integration of metal nanowire electrodes are presented: Template Electrodeposition and Electron-Beam Lithography. These approaches allow for the fabrication of nanowires which may be subsequently integrated at silicon chip substrates to form fully functional electrochemical devices. Simulated and experimental results were found to be in excellent agreement validating the simulation model. The electrochemical characteristics exhibited by nanowire electrodes fabricated by electronbeam lithography were directly compared against electrochemical performance of a commercial ultra-microdisc electrode. Steady-state cyclic voltammograms in ferrocenemonocarboxylic acid at single ultra-microdisc electrodes were observed at low to medium scan rates (≤ 500 mV.s-1). At nanowires, steady-state responses were observed at ultra-high scan rates (up to 50,000 mV.s-1), thus allowing for much faster analysis (20 ms). Approaches for elucidating faradaic signal without the requirement for background subtraction were also developed. Furthermore, diffusional process occurring at arrays with increasing inter-electrode distance and increasing number of nanowires were explored. Diffusion profiles existing at nanowire arrays were simulated with Comsol Multiphysics®. A range of scan rates were modelled, and experiments were undertaken at 5,000 mV.s-1 since this allows rapid data capture required for, e.g., biomedical, environmental and pharmaceutical diagnostic applications.

The technical merits of turbogenerating shown through the design, validation and implementation of a 1 dimensional engine model

Turbocompounding is the process of recovering a proportion of an engine’s fuel energy that would otherwise be lost in the exhaust process and adding it to the output power. This was first seen in the 1930s and is carried out by coupling an exhaust gas turbine to the crankshaft of a reciprocating engine. It has since been recognised that coupling the power turbine to an electrical generator instead of the crankshaft has the potential to reduce the fuel consumption further with the added flexibility of being able to decide how this recovered energy is used. The electricity generated can be used in automotive applications to assist the crankshaft using a flywheel motor generator or to power ancillaries that would otherwise have run off the crankshaft. In the case of stationary power plants, it can assist the electrical power output. Decoupling the power turbine from the crankshaft and coupling it to a generator allows the power electronics to control the turbine speed independently in order to optimise the specific fuel consumption for different engine operating conditions. This method of energy recapture is termed ‘turbogenerating’.

This paper gives a brief history of turbocompounding and its thermodynamic merits. It then moves on to give an account of the validation of a turbogenerated engine model. The model is then used to investigate what needs to be done to an engine when a turbogenerator is installed. The engine being modelled is used for stationary power generation and is fuelled by an induced biogas with a small portion of palm oil being injected into the cylinder to initiate combustion by compression ignition. From these investigations, optimum settings were found that result in a 10.90% improvement in overall efficiency. These savings relate to the same engine without a turbogenerator installed operating with fixed fuelling.

Stabilization of a (3+1)-dimensional soliton in a Kerr medium by a rapidly oscillating dispersion coefficient

Using the numerical solution of the nonlinear Schrodinger equation and a variational method it is shown that (3 + 1)-dimensional spatiotemporal optical solitons can be stabilized by a rapidly oscillating dispersion coefficient in a Kerr medium with cubic nonlinearity. This has immediate consequence in generating dispersion-managed robust optical soliton in communication as well as possible stabilized Bose-Einstein condensates in periodic optical-lattice potential via an effective-mass formulation. We also critically compare the present stabilization with that obtained by a rapid sinusoidal oscillation of the Kerr nonlinearity parameter.