Lattice Boltzmann simulations of 2D laminar flows past two tandem cylinders

We apply the lattice Boltzmann equation (LBE) with multiple-relaxation-time (MRT) collision model to simulate laminar flows in two-dimensions (2D). In order to simulate flows in an unbounded domain with the LBE method, we need to address two issues: stretched non-uniform mesh and inflow and outflow boundary conditions. We use the interpolated grid stretching method to address the need of non-uniform mesh. We demonstrate that various inflow and outflow boundary conditions can be easily and consistently realized with the MRT-LBE. The MRT-LBE with non-uniform stretched grids is first validated with a number of test cases: the Poiseuille flow, the flow past a cylinder asymmetrically placed in a channel, and the flow past a cylinder in an unbounded domain. We use the LBE method to simulate the flow past two tandem cylinders in an unbounded domain with Re = 100. Our results agree well with existing ones. Through this work we demonstrate the effectiveness of the MRT-LBE method with grid stretching.     

Lie Conformal Algebra Cohomology and the Variational Complex

We find an interpretation of the complex of variational calculus in terms of the Lie conformal algebra cohomology theory. This leads to a better understanding of both theories. In particular, we give an explicit construction of the Lie conformal algebra cohomology complex, and endow it with a structure of a \mathfrakg{\mathfrak{g}}-complex. On the other hand, we give an explicit construction of the complex of variational calculus in terms of skew-symmetric poly-differential operators.     

Local Minimizers of the Ginzburg-Landau Energy with Magnetic Field in Three Dimensions

We establish the existence of locally minimizing vortex solutions to the full Ginzburg-Landau energy in three dimensional simply-connected domains with or without the presence of an applied magnetic field. The approach is based upon the theory of weak Jacobians and applies to nonconvex sample geometries for which there exists a configuration of locally shortest line segments with endpoints on the boundary.Research partially supported by NSERC grant number 261955     

Magnetoelastic instability in molecular antiferromagnetic rings

Lattice stability in a model of an antiferromagnetic ring coupled to adiabatic phonons is investigated for different values of the spin and numbers of magnetic sites. The magnetoelastic transition is shown to be heavily affected by the spin value, displaying a qualitative difference in the nature of the instability for spin one-half. Among the different synthesized materials, Cu8 seems to be the best candidate to observe lattice dimerization in these systems. Our analysis excludes stable lattice distortions in higher spin rings. The effects of thermal fluctuations are studied in the Cu8 model, where a characteristic crossover temperature is estimated.     

Quantum Conservative Gates for Finite-Valued Logics

We introduce some conservative gates for finite-valued logics which are able to realize all the main connectives of the many-valued logics of ?ukasiewicz, the MV-algebras of Chang and Brower–Zadeh algebras. After a brief exposition of the motivations for this work, the gates are defined and their properties are explored. Finally, a possible quantum realization of them is proposed, using three techniques: a “brute force” method--an extension of the Conditional Quantum Control argument, and a new technique which we call the Constants Method. For all these techniques, the unitary operator which describes the gate is a sum of local operators.     

An open volume, high isolation, radio frequency surface coil system for pulsed magnetic resonance

We present an open volume, high isolation, RF system suitable for pulsed NMR and EPR spectrometers with reduced dead time. It comprises a set of three RF surface coils disposed with mutually parallel RF fields and a double-channel receiver (RX). Theoretical and experimental results obtained with a prototype operating at about 100 MHz are reported. Each surface RF coil (diameter 5.5 cm) was tuned to f₀ = 100.00 ± 0.01 MHz when isolated. Because of the mutual coupling and the geometry of the RF coils, only two resonances at f₁ = 97.94 MHz and f₂ = 101.85 MHz were observed. We show they are associated with two different RF field spatial distributions. In continuous mode (CW) operation the isolation between the TX coil and one of the RX coils (single-channel) was about −10 dB. By setting the double-channel RF assembly in subtraction mode the isolation values at f₁ or f₂ could be optimised to about −75 dB. Following a TX RF pulse (5 μs duration) an exponential decay with time constant of about 600 ns was observed. The isolation with single-channel RX coil was about −11 dB and it increased to about −47 dB with the double-channel RX in subtraction mode. Similar results were obtained with the RF pulse frequency selected to f₂ and also with shorter (500 ns) RF pulses. The above geometrical parameters and operating frequency of the RF assembly were selected as a model for potential applications in solid state NMR and in free radical EPR spectroscopy and imaging.     

Micro‐Raman and stratigraphic studies of the paintings on the ‘Cembalo’ model musical instrument (A.D. 1650) and laser‐induced degradation of the detected pigments

Micro‐fragments of the painted part of the ‘Cembalo’ model by Michele Todini (1625–1689) are investigated. The technique used for painting the terracotta base was studied via the stratigraphic analyses. No background layer of inorganic materials, e.g. gypsum, was found. To prevent absorption effects due to the terracotta porosity, a very thin layer of proteinaceous material was probably used. The micro‐Raman analyses have revealed the use of pigments currently used in the post‐Renaissance period (lead white, indigo, yellow of iron hydroxide, gypsum, hematite and carbon black) mixed with a pigment, the Prussian blue, discovered in A.D . 1704. This raises the authenticity problem of the work of art, a problem analysed and discussed in presenting the history of the work of art, and after the pigment study. The presence of degraded lead white is recognized via the laser‐induced degradation of the irradiated material. The possibility of a restoring action of the painted parts, as opposite to the non‐originality of the work, is considered and discussed. Since most part of the investigated pigments shows laser‐induced effects, a careful study of this phenomenon is performed by using the modern counterparts of the ancient pigments. For different laser powers, the temperatures of the investigated zones have been obtained via the detailed balance principle and connected to the laser‐induced degradation effects. Copyright © 2007 John Wiley & Sons, Ltd.     

Abelian BF Theories and Knot Invariants

In the context of the Batalin–Vilkovisky formalism, a new observable for the Abelian BF theory is proposed whose vacuum expectation value is related to the Alexander–Conway polynomial. The three-dimensional case is analyzed explicitly, and it is proved to be anomaly free. Moreover, at the second order in perturbation theory, a new formula for the second coefficient of the Alexander–Conway polynomial is obtained. An account on the higher-dimensional generalizations is also given. Received: 2 October 1996 / Accepted: 21 March 1997