Self-written waveguides in photopolymerizable resins

We study the optically induced growth and interaction of self-written waveguides in a photopolymerizable resin. We investigate experimentally how the interaction depends on the mutual coherence and the relative power of the input beams and suggest an improved analytical model that describes the growth of single waveguides and the main features of their interaction in photosensitive materials.     

Depositing nanoparticles inside millimeter-size hollow tubing

The inner and the outer walls of hollow tubing with an inner diameter of 0.4-0.9 cm and an outer diameter of 0.6-1.3 cm were coated with silver nanoparticles (NPs) by a one-step process using ultrasound irradiation. The structure and morphology of the nanoparticles (NPs) inside the hollow tubing and on the outer surface were characterized using methods such as XRD, TEM, HR-TEM, and HRSEM. The inner surface of the tubing was found to be coated with more silver than the outer surface. The coating was done on tubing made of rubber, PVC, Teflon and polyethylene. Sonochemistry is demonstrated as a method for depositing nanoparticles on the inner wall of a tube.     

Surface bound states in the continuum

We introduce a novel concept of surface bound states in the continuum, i.e., surface modes embedded into the linear spectral band of a discrete lattice. We suggest an efficient method for creating such surface modes and the local bounded potential necessary to support the embedded modes. We demonstrate that the surface embedded modes are structurally stable, and the position of their eigenvalues inside the spectral band can be tuned continuously by adding weak nonlinearity.     

Structural investigations on YbRh2Si2: from the atomic to the macroscopic length scale

YbRh2Si2 has advanced to a prototype material for investigating physics related to the Kondo effect. An optimization of the synthesis resulted in single crystals of extraordinary crystalline quality. At the atomic scale, we utilize scanning tunneling microscopy to study the topography of cleaved single crystals. A structural and chemical analysis was conducted by highly accurate x-ray diffraction and wavelength dispersive x-ray spectroscopy measurements. The latter indicate a homogeneity range of the YbRh2Si2 phase between approximately 40.0–40.2 at.% Rh. For our high-quality samples the number of defects found on the atomic scale (of the order of 0.3% of the visible lattice sites) is in quantitative agreement with a very small off-stoichiometry within this homogeneity range. Comparing our results for these samples allows an assignment of the structural defects observed at the cleaved surfaces to Rh occupying Si sites and, even less numerous Si in Rh sites. Such an analysis is hampered for samples of lesser quality, but there seem to be numerous empty Si-sites. Based on these observations the results of scanning tunneling spectroscopy can be analyzed in further detail and provide insight into the Kondo physics.     

Symmetry breaking in plasmonic waveguides with metal nonlinearities

We studied nonlinear effects in plasmonic metal film waveguides and couplers stimulated by third-order optical response due to ponderomotive metal nonlinearities. We analyzed the structure and dispersion of nonlinear plasmonic guided modes and predicted the bifurcations and symmetry breaking of nonlinear modes for the critical powers, depending on the structure dimensions.     

A Hierarchical Model of Quantum Anharmonic Oscillators: Critical Point Convergence

We study the two-dimensional gauge theory of the symmetric group S_n describing the statistics of branched n-coverings of Riemann surfaces. We consider the theory defined on the disc and on the sphere in the large-n limit. A non trivial phase structure emerges, with various phases corresponding to different connectivity properties of the covering surface. We show that any gauge theory on a two-dimensional surface of genus zero is equivalent to a random walk on the gauge group manifold: in the case of S_n, one of the phase transitions we find can be interpreted as a cutoff phenomenon in the corresponding random walk. A connection with the theory of phase transitions in random graphs is also pointed out. Finally we discuss how our results may be related to the known phase transitions in Yang-Mills theory. We discover that a cutoff transition occurs also in two dimensional Yang-Mills theory on a sphere, in a large N limit where the coupling constant is scaled with N with an extra logN compared to the standard t Hooft scaling.     

On a Theorem of Høegh-Krohn

A theorem proved by R. Høegh-Krohn in Comm. Math. Phys. 38(1974), 195–224, which yields a possibility to define states of systems of quantum particles by their values on the products , where \mathfraka _t , t are time automorphisms and F _j are multiplication operators, is generalized and extended. In particular, it is shown that the algebras generated by such products with F _j taken from the families of multiplication operators satisfying certain conditions are dense in the algebras of observables in the -weak topology, in which normal states are continuous. This result was obtained for the systems with two types of kinetic energy: the usual one expressed by means of the Laplacian; the relativistic kinetic energy defined by a pseudo-differential operator.     

Self-regulation in infinite populations with fission-death dynamics

The evolution of an infinite population of interacting point entities placed in ${\mathbb{R}}^d$ is studied. The elementary evolutionary acts are death of an entity with rate that includes a competition term and independent fission into two entities. The population states are probability measures on the corresponding configuration space and the result is the construction of the evolution of states in the class of sub-Poissonian measures, that corresponds to the lack of clusters in such states. This is considered as a self-regulation in the population due to competition.     

Structure of trans-1,4-polybutadiene synthesized with a new catalyst system

Abstract

The structure, phase composition, and temperature behavior of two trans-1,4-polybutadienes (TPBs) were studied by means of x-ray scattering and differential scanning calorimetry (DSC) techniques. The two samples examined were (1) PB synthesized using an immobilized titanium-magnesium catalyst and (2) a random copolymer based on PB prepared with a homogeneous vanadium-containing catalyst used as a reference material. It was found that the nascent structure of the first PB involves three phases: crystalline, mesomorphic (low-temperature form), and amorphous. In the vicinity of 65°C, a first-order phase transition occurs. The system becomes biphasic and contains the high-temperature form of the mesophase, as well as the amorphous phase, component. Above 165°C, the polymer melts to form a single-phase isotropic melt with a structure typical of liquids. The lateral dimension of crystallites reversibly changes at the crystal-mesophase transition. It is suggested that during annealing of the mesophase formed by cooling of the isotropic melt, the chains acquire an extended conformation. Loss of regularity of the structure of macromolecules of TPB causes a reduction of phase transition temperatures, an increase of the imperfection of the crystalline phase, and a contraction of the temperature range of existence of the mesophase.