Optical beam instabilities in nonlinear nanosuspensions

We investigate the modulation instability of plane waves and the transverse instabilities of soliton stripe beams propagating in nonlinear nanosuspensions. We show that in these systems the process of modulational instability depends on the input beam conditions. On the other hand, the transverse instability of soliton stripes can exhibit new features as a result of 1D collapse caused by the exponential nonlinearity.     

Random-phase surface-wave solitons in nonlocal nonlinear media

We demonstrate, theoretically and experimentally, incoherent surface solitons in a noninstantaneous nonlocal nonlinear media. These incoherent surface waves are located at the interface between a nonlinear medium with long-range nonlocality and a linear dielectric medium (air).     

The finite quotients of the multiplicative group of a division algebra of degree 3 are solvable

LetD be a finite dimensional division algebra. It is known that in a variety of cases, questions about the normal subgroup structure ofD ^x (the multiplicative group ofD) can be reduced to questions about finite quotients ofD ^x. In this paper we prove that when deg(D)=3, finite quotients ofD ^x are solvable. the proof uses Wedderburn’s Factorization Theorem. Partially supported by grant no. 427-97-1 from the Israeli Science Foundation and by grant no. 6782-1-95 from the Israeli Ministry of Science and Art.     

Force theory for multiphase bodies

We present a framework for the study of bodies wherein the deformation gradient may suffer a jump across an evolving nonmaterial interface. To formulate the kinematics relevant to such a situation, we use a global approach in which the configuration space has the structure of an infinite dimensional bundle. We show that a force, defined as an element of the cotangent bundle of the configuration manifold, may be represented by bulk and interfacial stress measures. The invariant decomposition of that force into bulk and interfacial components is discussed and we show that, in the case where the stress measures representing the force are given in terms of smooth densities, such a decomposition is determined by the average stress on the interface.     

Miyamoto involutions in axial algebras of Jordan type half

Nonassociative commutative algebras A, generated by idempotents e whose adjoint operators ad _e : A → A, given by x ? xe, are diagonalizable and have few eigenvalues, are of recent interest. When certain fusion (multiplication) rules between the associated eigenspaces are imposed, the structure of these algebras remains rich yet rather rigid. For example, vertex operator algebras give rise to such algebras. The connection between the Monster algebra and Monster group extends to many axial algebras which then have interesting groups of automorphisms.Axial algebras of Jordan type η are commutative algebras generated by idempotents whose adjoint operators have a minimal polynomial dividing (x-1)x(x-η), where η ? {0, 1} is fixed, with well-defined and restrictive fusion rules. The case of η ≠1/2 was thoroughly analyzed by Hall, Rehren and Shpectorov in a recent paper, in which axial algebras were introduced. Here we focus on the case where η = 1/2, which is less understood and is of a different nature.     

Nonabelian free subgroups in homomorphic images of valued quaternion division algebras

Given a quaternion division algebra a noncentral element is called pure if its square belongs to the center. A theorem of Rowen and Segev (2004) asserts that for any quaternion division algebra of positive characteristic and any pure element the quotient of by the normal subgroup generated by is abelian-by-nilpotent-by-abelian. In this note we construct a quaternion division algebra of characteristic zero containing a pure element such that contains a nonabelian free group. This demonstrates that the situation in characteristic zero is very different.

     

Evolution of conformational changes in the dynamics of small biological molecules: a hybrid MD/RRK approach

The dynamics of long timescale evolution of conformational changes in small biological molecules is described by a hybrid molecular dynamics/RRK algorithm. The approach employs classical trajectories for transitions between adjacent structures separated by a low barrier, and the classical statistical RRK approximation when the barrier involved is high. In determining the long-time dynamics from an initial structure to a final structure of interest, an algorithm is introduced for determining the most efficient pathways (sequence of the intermediate conformers). This method uses the Dijkstra algorithm for finding optimal paths on networks. Three applications of the method using an AMBER force field are presented: a detailed study of conformational transitions in a blocked valine dipeptide; a multiple reaction path study of the blocked valine tripeptide; and the evolution in time from the beta hairpin to alpha helix structure of a blocked alanine hexapeptide. Advantages and limitations of the method are discussed in light of the results.     

Interaction between vector solitons and solitonic gluons

We describe a physical mechanism for creating multisoliton bound states by which optical solitons are glued together by attraction between the nonsoliton beams that they guide, solitonic gluons. We verify the concept of the solitonic gluons experimentally, observing a suppression of the repulsion between dark solitons owing to an attractive force acting between out-of-phase bright guided beams.     

Amorphous photonic lattices: band gaps, effective mass, and suppressed transport

We study, experimentally and numerically, amorphous photonic lattices and the existence of band gaps therein. Our amorphous system comprises 2D waveguides distributed randomly according to a liquidlike model responsible for the absence of Bragg peaks, as opposed to ordered lattices with disorder which always exhibit Bragg peaks. In amorphous lattices the bands comprise localized states, but we find that defect states residing in the gap are more localized than the localization length of states within the band. Finally, we show how the concept of effective mass carries over to amorphous photonic lattices.