Lamellar-like structures in ferrofluids placed in strong magnetic fields

We consider a ferrofluid system consisting of magnetic particles interacting with a magnetic dipole–dipole interaction. We study the strong magnetic field regime where all magnetic dipoles are completely polarized in the direction of the magnetic field. We introduce a lattice gas model that serves to describe space ordering phenomena in such systems. It is found that, within mean field theory, this model predicts a second order phase transition to a phase with inhomogeneous lamellar-like ordering below a certain critical temperature.     

Coulomb self-energy of a uniformly charged three-dimensional cylinder

We calculate exactly the Coulomb self-energy of a uniformly charged three-dimensional cylinder. We derive a general analytical formula which, in the limit of zero length, gives also the correct result for the Coulomb self-energy of a uniformly charged two-dimensional disk. The exact analytical expression that we derive can be used in models that incorporate finite thickness effects in studies of two-dimensional electronic systems in the fractional quantum Hall regime as well as models that describe cylindrical beams of charged particles, certain colloidal suspensions of charged rigid rod-like particles and biological systems consisting of macromolecules with cylindrical symmetry.     

Anion-pi interaction augments halide binding in solution

1H NMR spectroscopic data and complementary theoretical predictions suggest that a designed receptor exhibits the anion-pi interaction in solution.     

Synthesis and characterization of pyridine- and thiophene-based platinacyclynes

Seven heterocyclic macrocycles, including the first platinacycles with pyridine and thiophene rings incorporated into the cyclyne system, are reported. Pt-acetylide cyclynes were assembled via tin transmetallation or amine-mediated oxidative addition with stoichiometric PtCl₂(PEt₃)₂ and CuI. The organometallic cyclynes exhibited enhanced electronic properties compared to previously described platinabenzocyclynes.     

Lithium cation enhances anion binding in a tripodal phosphine oxide-based ditopic receptor

A tripodal ditopic receptor presents H-bond donors and a phosphine oxide to potential guests. In the idealized binding conformation, an endohedral P=O functionality provides enhanced halide binding in the presence of lithium with the greatest ΔΔG° observed for bromide, while minimal changes in K(a) are observed in the presence of sodium.     

Design, synthesis and characterization of self-assembled As2L3 and Sb2L3 cryptands

The syntheses and X-ray crystal structures of six new self-assembled supramolecular As and Sb-containing cryptands are described. Analysis in the context of previously reported As(2)L(3) and Sb(2)L(3) cryptands reveals that small differences in ligand geometries result in significant differences in the helicity of the complexes and the stereochemistry of the metal coordination within the assembled complexes. Additionally, a new synthetic route is described which involves exposure of reactants to vacuum to help facilitate self-assembly.     

The electrostatic potential of a uniformly charged disk as the source of novel mathematical identities

We use two different frameworks to calculate the electrostatic potential created by a uniformly charged disk in its plane. We first implement a standard direct integration approach and carry out the calculations to the extent possible while keeping them simple. We then apply a different method that relies on Bessel function transformations. This method allows us to derive compact analytic expressions for the electrostatic potential in terms of complete elliptic integrals of the first and second kind. By comparing the results obtained through the application of the two different approaches, we uncover interesting transformation formulas and novel mathematical identities that might be of interest to a broad range of researchers in mathematical and physical sciences.     

Two-dimensional motion of a parabolically confined charged particle in a perpendicular magnetic field

The classical two-dimensional motion of a parabolically confined charged particle in presence of a perpendicular magnetic is studied. The resulting equations of motion are solved exactly by using a mathematical method which is based on the introduction of complex variables. The two-dimensional motion of a parabolically charged particle in a perpendicular magnetic field is strikingly different from either the two-dimensional cyclotron motion, or the oscillator motion. It is found that the trajectory of a parabolically confined charged particle in a perpendicular magnetic field is closed only for particular values of cyclotron and parabolic confining frequencies that satisfy a given commensurability condition. In these cases, the closed paths of the particle resemble Lissajous figures, though significant differences with them do exist. When such commensurability condition is not satisfied, path of particle is open and motion is no longer periodic. In this case, after a sufficiently long time has elapsed, the open paths of the particle fill a whole annulus, a region lying between two concentric circles of different radii.     

Finite clusters of fast-rotating spinless bosons in a harmonic trap

Rapidly rotating two-dimensional ultracold Bose–Einstein condensates of spinless bosons in a harmonic trap have attracted considerable interest during the recent years. It is expected that, in the fast-rotation limit, the system of bosons will exhibit collective behavior similar to that of two-dimensional electrons in the fractional quantum Hall effect regime. It is predicted that the most robust correlated bosonic state in this regime will be the Bose Laughlin state at a half filling factor. An exact treatment of such a state is generally a formidable task due to the inherent many-particle nature of the wave function. We report in this work that a transformation to Jacobi coordinates allows one to obtain much desirable exact analytic closed-form expressions for various quantities of interest corresponding to a Bose Laughlin wave function for various finite systems of particles.