The 2D Coulomb gas on a 1D lattice

The statistical mechanics of a two-dimensional Coulomb gas confined to one dimension is studied, wherein hard core particles move on a ring. Exact self-duality is shown for a version of the sine-Gordon model arising in this context, thereby locating the transition temperature exactly. We present asymptotically exact results for the correlations in the model and characterize the low- and high-temperature phases. Numerical simulations provide support to these renormalization group calculations. Connections with other interesting problems, such as the quantum Brownian motion of a panicle in a periodic potential and impurity problems, are pointed out.

EPR and photoluminescence studies of ZnO:Mn nanophosphors prepared by solution combustion route

Nanocrystalline ZnO:Mn (0.1 mol%) phosphors have been successfully prepared by self propagating, gas producing solution combustion method. The powder X-ray diffraction of as-formed ZnO:Mn sample shows, hexagonal wurtzite phase with particle size of similar to 40 nm. For Mn doped ZnO, the lattice parameters and volume of unit cell (a=3.23065 angstrom, c=5.27563 angstrom and V=47.684 (angstrom)(3)) are found to be greater than that of undoped ZnO (a=3.19993 angstrom, c=5.22546 angstrom and V=46.336 (angstrom)(3)). The SEM micrographs reveal that besides the spherical crystals, the powders also contained several voids and pores. The TEM photograph also shows the particles are approximately spherical in nature. The FTIR spectrum shows two peaks at similar to 3428 and 1598 cm(-1) which are attributed to O-H stretching and H-O-H bending vibration. The PL spectra of ZnO:Mn indicate a strong green emission peak at 526 nm and a weak red emission at 636 nm corresponding to T-4(1) -> (6)A(1) transition of Mn2+ ions. The EPR spectrum exhibits fine structure transition which will be split into six hyperfine components due to Mn-55 hyperfine coupling giving rise to all 30 allowed transitions. From EPR spectra the spin-Hamiltonian parameters have been evaluated and discussed. The magnitude of the hyperfine splitting (A) constant indicates that there exists a moderately covalent bonding between the Mn2+ ions and the surrounding ligands. The number of spins participating in resonance (N), its paramagnetic susceptibility (chi) have been evaluated. (C) 2011 Elsevier B.V. All rights reserved.

Traveling waves in a drifting flux lattice

Starting from the time-dependent Ginzburg-Landau equations for a type II superconductor, we derive the equations of motion for the displacement field of a moving vortex lattice ignoring pinning and inertia. We show that it is linearly stable and, surprisingly, that it supports wavelike long-wavelength excitations arising not from inertia or elasticity but from the strain-dependent mobility of the moving lattice. It should be possible to image these waves, whose speeds are a few mu m/s, using fast scanning tunneling microscopy.

A current error space vector based hysteresis controller with constant switching frequency and simple online boundary computation for VSI fed IM drive

This paper proposes a simple current error space vector based hysteresis controller for two-level inverter fed Induction Motor (IM) drives. This proposed hysteresis controller retains all advantages of conventional current error space vector based hysteresis controllers like fast dynamic response, simple to implement, adjacent voltage vector switching etc. The additional advantage of this proposed hysteresis controller is that it gives a phase voltage frequency spectrum exactly similar to that of a constant switching frequency space vector pulse width modulated (SVPWM) inverter. In this proposed hysteresis controller the boundary is computed online using estimated stator voltages along alpha and beta axes thus completely eliminating look up tables used for obtaining parabolic hysteresis boundary proposed in. The estimation of stator voltage is carried out using current errors along alpha and beta axes and steady state model of induction motor. The proposed scheme is simple and capable of taking inverter upto six step mode operation, if demanded by drive system. The proposed hysteresis controller based inverter fed drive scheme is simulated extensively using SIMULINK toolbox of MATLAB for steady state and transient performance. The experimental verification for steady state performance of the proposed scheme is carried out on a 3.7kW IM.

An organically templated iron sulfate with a distorted Kagome lattice exhibiting unusual magnetic properties

A layered iron sulfate of the composition [H3N(CH2)(2)NH2(CH2)(2)NH2(CH2)(2)NH3][(Fe3F6)-F-II(SO4)(2)], possessing a distorted Kagome lattice, prepared hydrothermally, is found to exhibit magnetic hysteresis like a ferrimagnet besides the characteristics of a frustrated system, like those of a spin glass.

Constant pressure laminar, transitional and turbulent flows - An approximate unified treatment

A nondimensional number that is constant in two-dimensional, incompressible and constant pressure laminar and fully turbulent boundary, layer flows has been proposed. An extension of this to constant pressure transitional flow is discussed.

Helical structures: The geometry of protein helices and nanotubes

In nature, helical structures arise when identical structural subunits combine sequentially, the orientational and translational relation between each unit and its predecessor remaining constant. A helical structure is thus generated by the repeated action of a screw transformation acting on a subunit. A plane hexagonal lattice wrapped round a cylinder provides a useful starting point for describing the helical conformations of protein molecules, for investigating the geometrical properties of carbon nanotubes, and for certain types of dense packings of equal spheres.

Phase diagram of a two-species lattice model with a linear instability

We discuss the properties of a one-dimensional lattice model of a driven system with two species of particles in which the mobility of one species depends on the density of the other. This model was introduced by Lahiri and Ramaswamy (Phys. Rev. Lett., 79, 1150 (1997)) in the context of sedimenting colloidal crystals, and its continuum version was shown to exhibit an instability arising from linear gradient couplings. In this paper we review recent progress in understanding the full phase diagram of the model. There are three phases. In the first, the steady state can be determined exactly along a representative locus using the condition of detailed balance. The system shows phase separation of an exceptionally robust sort, termed strong phase separation, which survives at all temperatures. The second phase arises in the threshold case where the first species evolves independently of the second, but the fluctuations of the first influence the evolution of the second, as in the passive scalar problem. The second species then shows phase separation of a delicate sort, in which long-range order coexists with fluctuations which do not damp down in the large-size limit. This fluctuation-dominated phase ordering is associated with power law decays in cluster size distributions and a breakdown of the Porod law. The third phase is one with a uniform overall density, and along a representative locus the steady state is shown to have product measure form. Density fluctuations are transported by two kinematic waves, each involving both species and coupled at the nonlinear level. Their dissipation properties are governed by the symmetries of these couplings, which depend on the overall densities. In the most interesting case,, the dissipation of the two modes is characterized by different critical exponents, despite the nonlinear coupling.

Effect of lattice orientation on crack tip constraint in ductile single crystals

In this work, the effect of lattice orientation on the fields prevailing near a notch tip is investigated pertaining to various constraint levels in FCC single crystals. A modified boundary layer formulation is employed and numerical solutions under mode I, plane strain conditions are generated by assuming an elastic-perfectly plastic FCC single crystal. The analysis is carried out corresponding to different lattice orientations with respect to the notch line. It is found that the near-tip deformation field, especially the development of kink or slip shear bands is sensitive to the constraint level. The stress distribution and the size and shape of the plastic zone near the notch tip are also strongly influenced by the level of T-stress. The present results clearly establish that ductile single crystal fracture geometries would progressively lose crack tip constraint as the T-stress becomes more negative irrespective of lattice orientation. Also, the near-tip field for a range of constraint levels can be characterized by two-parameters such as K-T or J-Q as in isotropic plastic solids.

Axisymmetric turbulent boundary layer along a circular cylinder at constant pressure

A constant-pressure axisymmetric turbulent boundary layer along a circular cylinder of radius a is studied at large values of the frictional Reynolds number a+ (based upon a) with the boundary-layer thickness δ of order a. Using the equations of mean motion and the method of matched asymptotic expansions, it is shown that the flow can be described by the same two limit processes (inner and outer) as are used in two-dimensional flow. The condition that the two expansions match requires the existence, at the lowest order, of a log region in the usual two-dimensional co-ordinates (u+, y+). Examination of available experimental data shows that substantial log regions do in fact exist but that the intercept is possibly not a universal constant. Similarly, the solution in the outer layer leads to a defect law of the same form as in two-dimensional flow; experiment shows that the intercept in the defect law depends on δ/a. It is concluded that, except in those extreme situations where a+ is small (in which case the boundary layer may not anyway be in a fully developed turbulent state), the simplest analysis of axisymmetric flow will be to use the two-dimensional laws with parameters that now depend on a+ or δ/a as appropriate.

Theory of Gas Hydrates: Effect of the Approximation of Rigid Water Lattice

One of the assumptions of the van der Waals and Platteeuw theory for gas hydrates is that the host water lattice is rigid and not distorted by the presence of guest molecules. In this work, we study the effect of this approximation on the triple-point lines of the gas hydrates. We calculate the triple-point lines of methane and ethane hydrates via Monte Carlo molecular simulations and compare the simulation results with the predictions of van der Waals and Platteeuw theory. Our study shows that even if the exact intermolecular potential between the guest molecules and water is known, the dissociation temperatures predicted by the theory are significantly higher. This has serious implications to the modeling of gas hydrate thermodynamics, and in spite of the several impressive efforts made toward obtaining an accurate description of intermolecular interactions in gas hydrates, the theory will suffer from the problem of robustness if the issue of movement of water molecules is not adequately addressed.

Modified lattice model for mode-I fracture analysis of notched plain concrete beam using probabilistic approach

A modified lattice model using finite element method has been developed to study the mode-I fracture analysis of heterogeneous materials like concrete. In this model, the truss members always join at points where aggregates are located which are modeled as plane stress triangular elements. The truss members are given the properties of cement mortar matrix randomly, so as to represent the randomness of strength in concrete. It is widely accepted that the fracture of concrete structures should not be based on strength criterion alone, but should be coupled with energy criterion. Here, by incorporating the strain softening through a parameter ‘α’, the energy concept is introduced. The softening branch of load-displacement curves was successfully obtained. From the sensitivity study, it was observed that the maximum load of a beam is most sensitive to the tensile strength of mortar. It is seen that by varying the values of properties of mortar according to a normal random distribution, better results can be obtained for load-displacement diagram.

Search on a Hypercubic Lattice using Quantum Random Walk

We investigate the spatial search problem on the two-dimensional square lattice, using the Dirac evolution operator discretized according to the staggered lattice fermion formalism. d=2 is the critical dimension for the spatial search problem, where infrared divergence of the evolution operator leads to logarithmic factors in the scaling behavior. As a result, the construction used in our accompanying article [ A. Patel and M. A. Rahaman Phys. Rev. A 82 032330 (2010)] provides an O(√NlnN) algorithm, which is not optimal. The scaling behavior can be improved to O(√NlnN) by cleverly controlling the massless Dirac evolution operator by an ancilla qubit, as proposed by Tulsi Phys. Rev. A 78 012310 (2008). We reinterpret the ancilla control as introduction of an effective mass at the marked vertex, and optimize the proportionality constants of the scaling behavior of the algorithm by numerically tuning the parameters.