Isolation of the novel dirhodium(II/II) thiolate compound Rh(2)(eta(1)-C(6)H(5)S)(2)(mu-C(6)H(5)S)(2)(bpy)(2)

The reaction of the anticancer active compound [Rh(2)(mu-O(2)CCH(3))(2)(bpy)(2)(CH(3)CN)(2)][BF(4)](2) (1) (bpy = 2,2'-bipyridine) with NaC(6)H(5)S under anaerobic conditions yields Rh(2)(eta(1)-C(6)H(5)S)(2)(mu-C(6)H(5)S)(2)(bpy)(2).CH(3)OH (2), which was characterized by UV-visible, IR, and (1)H NMR spectroscopies as well as single-crystal X-ray crystallography. Compound 2 crystallizes as dark red platelets in the monoclinic space group C2/c with cell parameters a = 20.398(4) A, b = 11.861(2) A, c = 17.417(4) A, beta = 108.98 degrees, V = 3984.9(14) A(3), Z = 4. The main structural features are the presence of a [Rh(2)](4+) core with a Rh-Rh distance of 2.549(2) A bridged by two benzene thiolate ligands in a butterfly-type arrangement. The axial positions of the [Rh(2)](4+) core are occupied by two terminal benzene thiolates. Cyclic voltammetric studies of 2 reveal that the compound exhibits an irreversible oxidation at +0.046 V in CH(3)CN, which is in accord with the fact that the compound readily oxidizes in the presence of O(2). The fact that this unusual dirhodium(II/II) thiolate compound is formed under these conditions is an important first step in understanding the metabolism of dirhodium anticancer active compounds with thiol-containing peptides and proteins.     

Nonlinear vertical accelerations of a floating torus in regular waves

The longitudinal motions and vertical accelerations of a floating torus as well as wave motion inside the torus are studied by model tests in regular deep-water waves. Comparisons are made with linear and partly with second-order potential-flow theory for the smallest examined experimental wave height-to-wave length ratio 1/120. Reasonable agreement is obtained, in particular for the linear problem. The importance of 3D flow, hydroelasticity and strong hydrodynamic frequency dependency is documented. Experimental precision errors and bias errors, for instance, due to tank-wall interference are discussed. Numerical errors due to viscous effects are found to be secondary. Experiments show that the third and fourth harmonic accelerations of the torus matter and cannot be explained by a perturbation method with the wave steepness as a small parameter.     

On clique relaxation models in network analysis

Increasing interest in studying community structures, or clusters in complex networks arising in various applications has led to a large and diverse body of literature introducing numerous graph-theoretic models relaxing certain characteristics of the classical clique concept. This paper analyzes the elementary clique-defining properties implicitly exploited in the available clique relaxation models and proposes a taxonomic framework that not only allows to classify the existing models in a systematic fashion, but also yields new clique relaxations of potential practical interest. Some basic structural properties of several of the considered models are identified that may facilitate the choice of methods for solving the corresponding optimization problems. In addition, bounds describing the cohesiveness properties of different clique relaxation structures are established, and practical implications of choosing one model over another are discussed.     

Additive twists of Fourier coefficients of symmetric-square lifts

We study the sum of additively twisted Fourier coefficients of a symmetric-square lift of a Maass form invariant under the full modular group. Our bounds are uniform in terms of the spectral parameter of the Maass form, as well as in terms of the additive twist.     

A thermodynamic framework to model thixotropic materials

Thixotropic materials are widely used in a variety of industrial applications. The constitutive relations to describe these materials are based on one-dimensional experiments in which the material is subjected to a shear motion and there is no unique methodology to obtain proper three-dimensional models. The path towards generalization to a three-dimensional framework is invariably carried out in a ad hoc manner. Here we propose a three-dimensional model that stems from a general thermodynamic framework that has proved to be quite robust in the development of constitutive relations, namely the application of the second law of thermodynamics together with the maximization of the entropy production. This leads to a constitutive equation that has the same form of a generalized Upper Convected Maxwell equation, if we require that changes of microstructure due to the deformation of each Maxwell element that comprises the model are reversible. Changes in microstructure are governed by a potential that is a measure of the difference between the current structure and the equilibrium structure associated with it. The equilibrium structure associated with the current structure is determined by the current value of stress, considered the main break up agent. We assume that the state of equilibrium would be achieved in a Motion With Constant Stress History, starting from the current stress state, until a steady state where the kinematics is not changing.     

Frame dragging with optical vortices

General Relativistic calculations in the linear regime have been made for electromagnetic beams of radiation known as optical vortices. These exotic beams of light carry a physical quantity known as optical orbital angular momentum. It is found that when a massive spinning neutral particle is placed along the optical axis, a phenomenon known as inertial frame dragging occurs. Our results are compared with those found previously for a ring laser and an order of magnitude estimate of the laser intensity needed for a precession frequency of 1 Hz is given for these “steady” beams of light.     

Schubert varieties as variations of Hodge structure

We (1) characterize the Schubert varieties that arise as variations of Hodge structure (VHS); (2) show that the isotropy orbits of the infinitesimal Schubert VHS ‘span’ the space of all infinitesimal VHS; and (3) show that the cohomology classes dual to the Schubert VHS form a basis of the invariant characteristic cohomology associated with the infinitesimal period relation (a.k.a. Griffiths’ transversality).     

Liquid Bridges Between Balls: The Small Volume Instability

Stability for a liquid bridge between two solid balls is studied by cutting and scaling pieces of a standardized family of Delaunay surfaces. This theoretical framework is used to analyze the problem numerically.     

Residual‐based artificial viscosity for simulation of turbulent compressible flow using adaptive finite element methods

In this paper, we present a finite element method with a residual‐based artificial viscosity for simulation of turbulent compressible flow, with adaptive mesh refinement based on a posteriori error estimation with sensitivity information from an associated dual problem. The artificial viscosity acts as a numerical stabilization, as shock capturing, and as turbulence capturing for large eddy simulation of turbulent flow. The adaptive method resolves parts of the flow indicated by the a posteriori error estimates but leaves shocks and turbulence under‐resolved in a large eddy simulation. The method is tested for examples in 2D and 3D and is validated against experimental data. Copyright © 2012 John Wiley & Sons, Ltd.