SURFACE PERTURBATIONS OF A SHALLOW VISCOUS-FLUID HEATED FROM BELOW AND THE (2+1)-DIMENSIONAL BURGERS-EQUATION

The (2 + 1)-dimensional Burgers equation is obtained as the equation of motion governing the surface perturbations of a shallow viscous fluid heated from below, provided the Rayleigh number of the system satisfies the condition R not-equal 30. A solution to this equation is explicitly exhibited and it is argued that it describes the nonlinear evolution of a nearly one-dimensional kink.

CAUSAL APPROACH TO (2+1)-DIMENSIONAL QED

It is shown that the causal approach to (2 + 1)-dimensional quantum electrodynamics yields a well-defined perturbative theory. In particular, and in contrast to renormalized perturbative quantum field theory, it is free of any ambiguities and ascribes a nonzero value to the dynamically generated, nonperturbative photon mass. (C) 1994 Academic Press, Inc.

Virial coefficients from (2+1)-dimensional QED effective actions at finite temperature and density

From spinor and scalar (2 + 1)-dimensional QED effective actions at finite temperature and density in a constant magnetic field background, we calculate the corresponding virial coefficients for particles in the lowest Landau level. These coefficients depend on a parameter theta related to the time-component of the gauge field, which plays an essential role for large gauge invariance. The variation of the parameter theta might lead to an interpolation between fermionic and bosonic virial coefficients, although these coefficients are singular for theta = pi/2.

Nonlinear (2+1)-dimensional systems solvable through asymptotic modules

Some nonlinear differential systems in (2+1) dimensions are characterized by means of asymptotic modules involving two poles and a ring of linear differential operators with scalar coefficients.Rational and soliton-like are exhibited. If these coefficients are rational functions, the formalism leads to nonlinear evolution equations with constraints. © 1989.

Two-matrix string model as constrained (2+1)-dimensional integrable system

We show that the 2-matrix string model corresponds to a coupled system of 2 + 1-dimensional KP and modified KP ((m)KP2+1) integrable equations subject to a specific symmetry constraint. The latter together with the Miura-Konopelchenko map for (m)KP2+1 are the continuum incarnation of the matrix string equation. The (m)KP2+1 Miura and Backhand transformations are natural consequences of the underlying lattice structure. The constrained (m)KP2+1 system is equivalent to a 1 + 1-dimensional generalized KP-KdV hierarchy related to graded SL(3,1). We provide an explicit representation of this hierarchy, including the associated W(2,1)-algebra of the second Hamiltonian structure, in terms of free currents.

Determination of 2-methylimidazole and 4-methylimidazole in caramel colors by capillary electrophoresis

The use of chemical preservative compounds is common in the food products industry. Caramel color is the most usual additive used in beverages, desserts, and breads worldwide. During its fabrication process, 2- and 4-methylimidazole (MeI), highly carcinogenic compounds, are generated. In these cases, the development of reliable analytical methods for the monitoring of undesirable compounds is necessary. The primary procedure for the analysis of 2- and 4-MeI is using LC- or GC-MS techniques. These procedures are time-consuming and require large amounts of organic solvents and several pretreatment steps. This prevents the routine use of this procedure. This paper describes a rapid, efficient, and simple method using capillary electrophoresis (CE) for the separation and determination of 2- and 4-MeI in caramel colors. The analyses were performed using a 75 μm i.d. uncoated fused-silica capillary with an effective length of 40 cm and a running electrolyte consisting of 160 mmol L-1 phosphate plus 30% acetonitrile. The pH was adjusted to 2.5 with triethylamine. The analytes were separated within 6 min at a voltage of 20 kV. Method validation revealed good repeatability of both migration time (<0.8% RSD) and peak area (<2% RSD). Analytical curves for 2- and 4-MeI were linear in the 0.4-40 mg L-1 concentration interval. Detection limits were 0.16 mg L-1 for 4-MeI and 0.22 mg L-1 for 2-MeI. The extraction recoveries were satisfactory. The developed method showed many advantages when compared to the previously used method. © 2013 American Chemical Society.

Lattice effects in the quasi-two-dimensional valence-bond-solid Mott insulator EtMe3P[Pd(dmit)(2)](2)

The organic charge-transfer salt EtMe3P[Pd(dmit)(2)](2) is a quasi-two-dimensional Mott insulator with localized spins S = 1/2 residing on a distorted triangular lattice. Here we report measurements of the uniaxial thermal expansion coefficients alpha(i) along the in-plane i = a and c axis as well as along the out-of-plane b axis for temperatures 1.4 K <= T <= 200 K. Particular attention is paid to the lattice effects around the phase transition at T-VBS = 25 K into a low-temperature valence-bond-solid phase and the paramagnetic regime above where effects of short-range antiferromagnetic correlations can be expected. The salient results of our study include (i) the observation of strongly anisotropic lattice distortions accompanying the formation of the valence-bond-solid phase, and (ii) a distinct anomaly in the thermal expansion coefficients in the paramagnetic regime around 40 K. Our results demonstrate that upon cooling through T-VBS the in-plane c axis, along which the valence bonds form, contracts while the second in-plane a axis elongates by the same relative amount. Surprisingly, the dominant effect is observed for the out-of-plane b axis which shrinks significantly upon cooling through T-VBS. The pronounced anomaly in alpha(i) around 40 K is attributed to short-range magnetic correlations. It is argued that the position of this maximum, relative to that in the magnetic susceptibility around 70 K, speaks in favor of a more anisotropic triangular-lattice scenario for this compound than previously thought.

Redução dimensional de partículas de spin s=0,s=1 e s=2 via mecanismo de Kaluza-Klein

In this graduate work we will perform the dimensional reduction of particles of spin s=0, s=1 and s=2 via Kaluza Klein mechanism. The method of Kaluza-Klein dimensional reduction is introduced by the dimensional reduction from D to D

Scalar-bipolar asymptotic modules for solving (2+1)-dimensional nonlinear evolution equations with constraints

An infinite hierarchy of solvable systems of purely differential nonlinear equations is introduced within the framework of asymptotic modules. Eacy system consists of (2+1)-dimensional evolution equations for two complex functions and of quite strong differential constraints. It may be interpreted formally as an integro-differential equation in (1+1) dimensions. © 1988.

BMP-2 induces the expression of chondrocyte-specific genes in bovine synovium-derived progenitor cells cultured in three-dimensional alginate hydrogel

OBJECTIVE: According to recent reports, the synovial membrane may contain mesenchymal stem cells with the potential to differentiate into chondrocytes under appropriate conditions. In order to assess the usefulness of synovium-derived progenitor cells for the purposes of cartilage tissue engineering, we explored their requirements for the expression of chondrocyte-specific genes after expansion in vitro. DESIGN: Mesenchymal progenitor cells were isolated from the synovial membranes of bovine shoulder joints and expanded in two-dimensions on plastic surfaces. They were then seeded either as micromass cultures or as single cells within alginate gels, which were cultured in serum-free medium. Under these three-dimensional conditions, chondrogenesis is known to be supported and maintained. Cell cultures were exposed either to bone morphogenetic protein-2 (BMP-2) or to isoforms of transforming growth factor-beta (TGF-beta). The levels of mRNA for Sox9, collagen types I and II and aggrecan were determined by RT-PCR. RESULTS: When transferred to alginate gel cultures, the fibroblast-like synovial cells assumed a rounded form. BMP-2, but not isoforms of TGF-beta, stimulated, in a dose-dependent manner, the production of messenger RNAs (mRNAs) for Sox9, type II collagen and aggrecan. Under optimal conditions, the expression levels of cartilage-specific genes were comparable to those within cultured articular cartilage chondrocytes. However, in contrast to cultured articular cartilage chondrocytes, synovial cells exposed to BMP-2 continued to express the mRNA for alpha1(I) collagen. CONCLUSIONS: This study demonstrates that bovine synovium-derived mesenchymal progenitor cells can be induced to express chondrocyte-specific genes. However, the differentiation process is not complete under the chosen conditions. The stimulation conditions required for full transformation must now be delineated.

Chiral Templating Activity of Tris(bipyridine)ruthenium(II) Cation in the Design of Three-Dimensional (3D) Optically Active Oxalate-Bridged {[Ru(bpy) 3 ][Cu 2 x Ni 2(1 - x ) (C 2 O 4 ) 3 ]} n (0 ≤ x ≤ 1; bpy = 2,2‘-bipyridine): Structural, Optical, and Magnetic Studies

Three-dimensional oxalate-based {[Ru(bpy)3][Cu2xNi2(1-x)(ox)3]}n (0≤ x ≤ 1, ox = C2O42-, bpy = 2,2‘bipyridine) were synthesized. The structure was determined for x = 1 by X-ray diffraction on single crystal. The compound crystallizes in the cubic space group P4132. It shows a three-dimensional 10-gon 3-connected (10,3) anionic network where copper(II) has an unusual tris(bischelated) environment. X-ray powder diffraction patterns and their Rietveld refinement show that all the compounds along the series are isostructural and single-phased. According to X-ray absorption spectroscopy, copper(II) and nickel(II) have an octahedral environment, respectively elongated and trigonally distorted. As shown by natural circular dichroism, the optically active forms of {[Ru(bpy)3][CuxNi2(1-x)(ox)3]}n are obtained starting from resolved Δ- or Λ-[Ru(bpy)3]2+. The Curie−Weiss temperatures range between −55 (x = 1) and −150 K (x = 0). The antiferromagnetic exchange interaction thus decreases when the copper contents increases in agreement with the crystallographic structure of the compounds and the electronic structure of the metal ions. At low temperature, the compounds exhibit complex long-range ordered magnetic behavior.

The Utilization of Classical Spin Monte Carlo Methods to Simulate the Magnetic Behavior of Extended Three-Dimensional Cubic Networks Incorporating M(II) Ions with an S = 5/2 Ground State Spin

The numerical simulations of the magnetic properties of extended three-dimensional networks containing M(II) ions with an S = 5/2 ground-state spin have been carried out within the framework of the isotropic Heisenberg model. Analytical expressions fitting the numerical simulations for the primitive cubic, diamond, together with (10−3) cubic networks have all been derived. With these empirical formulas in hands, we can now extract the interaction between the magnetic ions from the experimental data for these networks. In the case of the primitive cubic network, these expressions are directly compared with those from the high-temperature expansions of the partition function. A fit of the experimental data for three complexes, namely [(N(CH3)4][Mn(N3)] 1, [Mn(CN4)]n 2, and [FeII(bipy)3][MnII2(ox)3] 3, has been carried out. The best fits were those obtained using the following parameters, J = −3.5 cm-1, g = 2.01 (1); J = −8.3 cm-1, g = 1.95 (2); and J = −2.0 cm-1, g = 1.95 (3).