A compact permanent magnet array with a remote homogeneous field

We present the design and construction of a single sided magnet array generating a homogeneous field in a remote volume. The compact array measures 11.5 cm by 10 cm by 6 cm and weights approximately 5 kg. It produces a B(0) field with a 'sweet spot' at a point 1cm above its surface, where its first and second spatial derivatives are approximately zero. Unlike other sweet spot magnets of this general type, our array has B(0) oriented parallel to its surface. This allows an ordinary surface coil to be used for unilateral measurements, giving the potential for dramatic SNR improvement.     

Superradiance of trapped atoms

A new method for calculating the total power of the spontaneous emission of a few motionless two-level atoms located at a distance of the order of the resonance-radiation wavelength with dipole-dipole interaction is suggested. The method is based on the Schrödinger representation. It is shown, as an example, that two trapped atoms cannot emit a pulse of superradiance under any conditions, while four atoms can emit such a pulse at certain conditions. Different ways of introducing the quasi-stationary states of atoms along with the generalization of the proposed method to other resonance systems are discussed.     

Mechanical properties of silk: interplay of deformation on macroscopic and molecular length scales

Using an in situ combination of tensile tests and x-ray diffraction, we have determined the mechanical properties of both the crystalline and the disordered phase of the biological nanocomposite silk by adapting a model from linear viscoelastic theory to the semicrystalline morphology of silk. We observe a strong interplay between morphology and mechanical properties. Silk's high extensibility results principally from the disordered phase; however, the crystals are also elastically deformed.     

Apodization‐Assisted Subdiffraction Near‐Field Localization in 2D Phase Diffraction Grating

Conventional phase diffraction gratings can be used to localize the incoming optical radiation in the near‐field region. A new design of the binary phase diffraction grating is proposed with embedded pupil opaque mask inside each stripe. By means of numerical simulations, it is shown that with this masked phase grating the spatial resolution of the near‐field localization can be substantially improved and brought even beyond the solid immersion limit (λ/2n). Moreover, due to anomalous apodization effect, the subdiffraction field localization is accompanied by intensity enhancement as compared to the non‐masked design. The pupil mask rearranges the optical fluxes within the stripes and promotes the Fano resonances excitation in the periodic step lattice. This can be important for advancing the phase grating‐based super‐resolution technologies, including subdiffraction imaging, interferometry, and surface fabrication.     

Boron-Containing Lipids and Liposomes: New Conjugates of Cholesterol with Polyhedral Boron Hydrides

A series of boron-containing lipids were prepared by reactions of cyclic oxonium derivatives of polyhedron boranes and metallacarboranes (closo-dodecaborate anion, cobalt and iron bis(dicarbollides)) with amine and carboxylic acids which are derived from cholesterol. Stable liposomal formulations, on the basis of synthesized boron-containing lipids, hydrogenated soybean l -α-phosphatidylcholine and (HSPC) 1,2-distearoyl-sn-glycero-3-phosphoethanolamine-N-[methoxy(polyethylene glycol)-2000] (DSPE-PEG) as excipients, were prepared and then characterized by dynamic light scattering (DLS) that revealed the formation of particles to be smaller than 200 nm in diameter. The resulting liposomal formulations showed moderate to excellent loading and entrapment efficiency, thus justifying the design of the compounds to fit in the lipid bilayer and ensuring ease of in vivo use for future application. The liposomal formulations based on cobalt and iron bis(dicarbollide)-based lipids were found to be nontoxic against both human breast normal epithelial cells MCF-10A and human breast cancer cells MCF-7.     

Effects of external global harmonic influence on chimera states

Nonlinear Dynamics - The effects of the global harmonic force on an ensemble of nonlocally coupled chaotic Rössler oscillators is studied. The autonomous ensemble without external force...     

Counting Singular Matrices with Primitive Row Vectors

We solve an asymptotic problem in the geometry of numbers, where we count the number of singular n×n matrices where row vectors are primitive and of length at most T. Without the constraint of primitivity, the problem was solved by Y. Katznelson. We show that as T, the number is asymptotic to for n3. The 3-dimensional case is the most problematic and we need to invoke an equidistribution theorem due to W. M. Schmidt.     

Lie point symmetries and some group invariant solutions of the quasilinear equation involving the infinity Laplacian

Using the classical Lie method we obtain the full Lie point symmetry group of the Aronsson equation in two independent variables. Some group invariant solutions of this equation are found and a conjecture on the Lie point symmetry group of the Aronsson equation in Rⁿ is presented.     

On the local asymptotics of Faber polynomials

We study a local asymptotics of the (generalized) Faber polynomials at the boundary of the associated domain, under certain mild smoothness conditions on the weight function and geometric conditions on the boundary. The main result exhibits how this asymptotics depends on the corners at the boundary. Its proof is based on the continuity properties of the Visser-Ostrowski quotient at the corners.