Second-harmonic generation by intense beams containing phase dislocations:self-breaking into sets of solitons

Second-harmonic generation of light in bulk quadratic non-linear media with intense input beams containing phase dislocations is studied numerically under conditions for TypeI phase-matching. We investigate how, above a threshold light intensity, the input beams self-split along the azimuthal direction into a pattern of separate beams which then form a set of spatial solitons. The mechanism of such a behaviour is the azimuthal modulational instability of the ring-shaped, mutually trapped fundamental and second-harmonic beams containing the phase dislocations. This revised version was published online in November 2006 with corrections to the Cover Date.     

Negative Goos-Hänchen shift in periodic media

We show that, under certain conditions, a negative Goos-H?nchen shift-a longitudinal displacement of a totally internally reflected wave packet-occurs in periodic media such as waveguide arrays.     

On the integral cohomology of a sylow subgroup of the symmetric group

Projectivity classes, which dualize injectivity classes (cf.[ll]), are introduced and some examples are given. Characterizations of hereditary rings, semisimple rings, Noetherian rings, (semi-)perfect rings, quasi-perfect rings, semiregular rings, semiregular modules and F- semiperfect modules using projectivity classes are given. Finally, for a projectivity class P, P-projective covers are defined and similar results with “quasi-projective cover” substituted by “T-projective cover” will still hold. Our results unify and generalize several well known results by Golan, Huynh and Smith, Rangaswamy and Vanaja, Tiwary and Pandeya, and Xue.     

Myth,language, and complex ideologies

Ideologies use for their conservation and propagation persuasive methods of communication: rhetoric. Rhetoric is analyzed from the semiotic and logical‐mathematical points of view. The following hypotheses are established: (1) language L is a self‐explanatory system, mediated by a successive series of systems of cultural conventions, (2) connotative significances of an ideological advertising rhetoric must be known, and (3) the notion of ideological information is a neutral notion that does not imply the valuation of ideology or its conditions of veracity or falsification. Rhetorical figures like metonymy, metaphor, parable analogy, and allegory are defined as relations. Metaphor and parable are order relations. Operations of metonymic and metaphoric substitution are defined and several theorems derived from these operations have been deduced. © 2014 Wiley Periodicals, Inc. Complexity 20: 63–81, 2014     

Shaping soliton properties in Mathieu lattices

We address basic properties and stability of two-dimensional solitons in photonic lattices induced by the nondiffracting Mathieu beams. Such lattices allow for smooth topological transformation of radially symmetric Bessel lattices into quasi-one-dimensional periodic ones. The transformation of lattice topology drastically affects the properties of ground-state and dipole-mode solitons, including their shape, stability, and transverse mobility.     

Multipole vector solitons in nonlocal nonlinear media

We show that multipole solitons can be made stable via vectorial coupling in bulk nonlocal nonlinear media. Such vector solitons are composed of mutually incoherent nodeless and multipole components jointly inducing a nonlinear refractive index profile. We found that stabilization of the otherwise highly unstable multipoles occurs below certain maximum energy flow. Such a threshold is determined by the nonlocality degree.     

Observation of two-dimensional lattice interface solitons

We report on the experimental observation of two-dimensional solitons at the interface between square and hexagonal waveguide arrays. In addition to the different symmetries of the lattices, the influence of a varying refractive index modulation depth is investigated. Such variation strongly affects the properties of surface solitons residing at different sides of the interface.     

Bragg guiding of domainlike nonlinear modes and kink arrays in lower-index core structures

We introduce a novel class of stable nonlinear modes trapped in a lower-index film core sandwiched between two optical lattices, or in the cylindrical core of a radial lattice, imprinted in defocusing media. Such a family of nonlinear modes transforms into defect lattice solitons when the core width is sufficiently small or into an array of kinks when the width is large enough. We find that higher-order modes with multiple zeros inside the guiding core can be stable in one-dimensional settings.     

New waveguide modes in anisotropic structures

The existence of new hybrid waveguide modes of properly tailored integrated optical waveguides consisting of ultrathin films clad by positive birefringent media is pointed out.     

Determination of the power and load parameters of rubber extruders

The power input and screw loads are theoretically determined for the extrusion of materials with anomalous viscosity. The drive power is expended on the translational and circulatory flow of material in the helical channel. The axial load can be treated as the sum of the rubber pressure on the front of the screw and the axial component of the reaction. Circulatory flow results in an axial load component associated with the presence of a transverse pressure gradient.NOTATION D_o outside screw diameter - h depth of helical channel - helix angle - w width of helical channel along normal to its side walls - gap - e width of land - t helix pitch - i number of flights - w_f effective flow width - L axial length of filled section of screw channel - ₀=y₀/h dimensionless quantity - v peripheral speed of screw - shear stress - _a effective viscosity - m flow melt index - f _cy andf _s coefficients of friction of rubber compound against cylinder and screw - F_cy force of friction between cylinder and rubber compound - F_s force of friction between screw and rubber compound - F_n component of F_cy along normal to side wall of helical channel - F_z component of F_cy along axis of helical channel - p and P_h pressure of rubber compound in extruder head - Q_a axial load - dimensionless quantity - N power. Mekhanika Polimerov, Vol. 4, No. 2, pp. 349–357, 1968