Spontaneous pattern formation with incoherent white light

We present the first experimental observation of modulation instability and spontaneous pattern formation with incoherent white light emitted from an incandescent light bulb. We show experimentally that modulation instability of white light propagating in a noninstantaneous self-focusing medium is a collective effect, where the entire temporal spectrum of the light beam becomes unstable at the same threshold value and collectively forms a pattern with a single periodicity. We experimentally demonstrate that the temporal spectrum of the evolving perturbation self-adjusts to match the collective pattern formation phenomenon.     

All-forward semiclassical simulations of nonlinear response functions

We propose a quantum trajectory algorithm for computing nonlinear response functions of condensed phase molecular systems based on a time-ordered expansion of the density matrix. The nth-order response function is expressed as a sum of 2(n) impulsive response pathways representing trajectories involving zero, one, and up to n interactions with short external pulses. These are evaluated using a forward propagation algorithm based upon a Liouville space extension of the Bohmian propagation method.     

Observation of discrete solitons in optically induced real time waveguide arrays

We report the first experimental observation of discrete solitons in an array of optically induced waveguides. The waveguide lattice is induced in real time by illuminating a photorefractive crystal with a pair of interfering plane waves. We demonstrate two types of bright discrete solitons: in-phase self-localized states and the staggered (pi out-of-phase) soliton family. This experiment is the first observation of bright staggered solitons in any physical system. Our scheme paves the way for reconfigurable focusing and defocusing photonic lattices where low-power (mW) discrete solitons can be thoroughly investigated.     

Weak beam control of multiple quadratic soliton generation

Theoretical predictions and experimental observations show that a weak harmonic seed beam can control the process of generating multiple quadratic solitons in periodically poled KTiOPO4 by inputting only a fundamental beam. This all-optical switching does not depend on the relative phase of the input beams, an unusual property for such coherent solitons.     

Shock waves in saturated thermoelastic porous media

The objective of this paper is to develop and present the macroscopic motion equations for the fluid and the solid matrix, in the case of a saturated porous medium, in the form of coupled, nonlinear wave equations for the fluid and solid velocities. The nonlinearity in the equations enables the generation of shock waves. The complete set of equations required for determining phase velocities in the case of a thermoelastic solid matrix, includes also the energy balance equation for the porous medium as a whole, as well as mass balance equations for the two phase. In the special case of a rigid solid matrix, the wave after an abrupt change in pressure propagates only through the fluid.     

β-Amino alcohol selectors for enantioselective separation of amino acids by ligand-exchange capillary zone electrophoresis in a low molecular weight organogel

A new family of copper ligand-exchange selectors, L- or D-β-amino alcohols, is employed for the chiral separation of D,L-dansyl-amino acids, unmodified amino acid racemates, phenylalanine and tryptophan, and β-blocker L,D-propranolol by SDS-micellar electrokinetic chromatography and by electrophoretic chromatography in a low molecular weight organogel (LMOG)-filled capillary. The LMOG comprised a self-assembled fibrillar gel of trans-(1S,2S)-1,2-bis-(dodecylamido) cyclohexane in methanol. The di-L-valinol-copper complex exhibited the best performance on LMOG-CE compared with all other β-amino alcohol-copper selectors. The dependence of chiral resolution on the pH*, the ratio between the copper and the L-valinol ligand and the concentration of added selector complex in the run buffer were investigated revealing a marked difference between the activity of the copper-valinol and the previously studied copper-valine selector. The optimal separation conditions were achieved using a 2:1 valinol/copper ratio, in accordance with the 2:1 structure of the complex, which was proven by single crystal and powder X-ray diffractions and by elemental analysis. Unlike the copper-valine selectors that could be used only under acidic conditions (pH* 3.5), the copper-valinol selectors could be used under near-neutral conditions and even at pH* 9.1. A comparison between SDS-micellar electrokinetic chromatography and LMOG-CE under otherwise identical conditions revealed a significant superior separation on the LMOG-filled capillaries.     

Completion by Derived Double Centralizer

Let A be a commutative ring, and let $\mathfrak{a}$ be a weakly proregular ideal in A. (If A is noetherian then any ideal in it is weakly proregular.) Suppose M is a compact generator of the category of cohomologically $\mathfrak{a}$ -torsion complexes. We prove that the derived double centralizer of M is isomorphic to the $\mathfrak{a}$ -adic completion of A. The proof relies on the MGM equivalence from Porta et al. (Algebr Represent Theor, 2013) and on derived Morita equivalence. Our result extends earlier work of Dwyer et al. (Adv Math 200:357–402, 2006) and Efimov (2010).     

Boundary force effects exerted on solitons in highly nonlinear media

We study the effects caused by remote boundaries on soliton dynamics in nonlinear media with a large range of nonlocality, and demonstrate theoretically and experimentally how asymmetric boundary forces can lead to soliton steering and oscillation in predetermined trajectories.     

Two-dimensional adaptive Eulerian-Lagrangian method for mass transport with spatial velocity distribution

A Eulerian-Lagrangian scheme is used to solve the two-dimensional advection-dispersion equation. Concentration and its partial differential operator are decomposed into advection and dispersion terms. Thus, advection is formally decoupled from dispersion and solved by continuous forward particle tracking. Dispersion is handled by implicit finite elements on a fixed Eulerian grid. Translation of steep gradients of concentration in advection-dominated flow regimes, is done without numerical distortion. Continuous spatial distribution of velocities are evaluated by using Galerkin's approach in conjunction with Darcy's law based on hydraulic input data from each element. The method was implemented on coarse FE grid with linear shape functions, demonstrating no over/under shooting and practically no numerical dispersion. Simulations, covering a wide range of Peclet numbers, yield high agreement with analytic and practical results.