Stable rotating dipole solitons in nonlocal optical media

We reveal that nonlocality can provide a simple physical mechanism for stabilization of multihump optical solitons and present what we believe to be the first example of stable rotating dipole solitons and soliton spiraling, which are known to be unstable in all types of realistic nonlinear media with a local response.     

Mathematical programming modeling of the Response Time Variability Problem

The Response Time Variability Problem (RTVP) is a scheduling problem that has recently been defined in the literature. The RTVP has a broad range of real-life applications from manufacturing to services and information technology. A previous study developed a position exchange heuristic to apply to initial sequences for the RTVP, and a MILP (Mixed Integer Linear Programming) to obtain optimal solutions with a practical limit of 25 units to be scheduled. This paper aims to improve the best mathematical programming model developed thus far in order to solve larger instances up to 40 units to optimality. The contribution of this paper is 4-fold: (i) larger instances can be solved to optimality by the off the shelf standard software; (ii) the new optimal solutions of the RTVP can be used to compare the results of heuristic procedures; (iii) the importance of modeling is demonstrated, as well as the huge impact that reformulation, redundant constraints and the elimination of symmetries have on the efficiency of MILPs is clearly established; finally (iv) a challenge to develop a customized optimization algorithm to rival the MILP solution efficiency for the RTVP is put forward.     

Synthesis,crystal structure solution and characterization of two organic–inorganic hybrid layered materials based on metal sulfates and 1,4‐phenylenediamine

Two organic–inorganic hybrid layered materials, namely poly[(μ‐1,4‐diaminobenzene‐κ²N:N′)[μ₃‐sulfato(VI)‐κ⁴O:O′:O′′,O′′′]manganese], [Mn(SO₄)(C₆H₈N₂)]_n, 1 , and poly[(μ‐1,4‐diaminobenzene‐κ²N:N′)[μ₃‐sulfato(VI)‐κ⁴O:O′:O′′,O′′′]copper], [Cu(SO₄)(C₆H₈N₂)]_n, 2 , have been synthesized using 1,4‐phenylenediamine (PPD) as an organic template and component (linker). Both materials form three‐dimensional frameworks. The crystal structures were determined using data from powder X‐ray diffraction measurements. The purity and morphology of the compounds were studied by elemental analyses and SEM investigations, and their thermal stabilities were determined by thermogravimetric and nonambient powder X‐ray diffraction measurements, which indicated that 1 is stable up to 537 K and 2 is stable up to 437 K.     

Mapping phases of singular scalar light fields

We implement experimentally a simple method for accurate measurements of phase distributions of scalar light fields. The method is based on the polarimetric technique for recording the polarization maps of vector fields, where coaxial superposition of orthogonally polarized reference and signal beams allows the signal phase to be reconstructed from the polarization map of the total field. We demonstrate this method by resolving topologically neutral pairs of closely positioned vortices in a speckle field and recovering the positions of vortices within a Laguerre-Gaussian beam with the topological charge three.     

Further studies of phosphine adducts of niobium(IV) and tantalum(IV) chlorides: New seven- and eight-coordinate compounds with trimethylphosphine: NbCl4(PMe3)3 and Ta2Cl8(PMe3)4

The reaction of NbCl₄(THF)₂ with an excess of PMe₃ in toluene solution afforded a 70% isolated yield of green NbCl₄(PMe₃)₃. When a slurry of TaCl₅ in toluene containing a slight excess of PMe₃ was reduced with sodium amalgam overnight, a 60% yield of orange to red (depending on crystal size) Ta₂Cl₈(PMe₃)₄ was obtained. Both compounds have been fully characterized by X-ray crystallography. NbCl₄(PMe₃)₃ forms monoclinic crystals (P2₁/c) with unit cell dimensions a = 15.061(3) Å, b = 11.677(4) Å, c = 11.583(4) Å, β = 91.71(3)°, V = 2036(2) ų, and Z = 4. It is isomorphous with its TaCl₄(PMe₃)₃ homolog, and the bond lengths and angles are very similar. Ta₂Cl₈(PMe₃)₄ forms cubic crystals (Im3) with a = 16.377(2), V = 4392(2) ų and Z = 6. It is thus isomorphous with its niobium homolog, and the internal dimensions are quite comparable. The Ta-Ta distance is 2.830(1) Å, consistent with the existence of a single bond.     

Noncommutative Unification of General Relativity and Quantum Mechanics

We propose a mathematical structure, based on anoncommutative geometry, which combines essentialaspects of general relativity with those of quantummechanics, and leads to correct limitingcases of both these physical theories. Thenoncommutative geometry of the fundamental level isnonlocal with no space and no time in the usual sense,which emerge only in the transition process to thecommutative case. It is shown that because of the originalnonlocality, quantum gravitational observables should belooked for among correlations of distant phenomenarather than among local effects. We compute the Einstein–Podolsky–Rosen effect; itcan be regarded as a remnant or a shadowof the noncommutative regime of the fundamental level.A toy model is computed predicting the value of thecosmological constant (in the quantum sector) which vanishes whengoing to the standard spacetime physics.     

Transverse second-harmonic generation from disordered nonlinear crystals

We investigate the transverse second-harmonic generation in as grown strontium barium niobate (SBN) crystals with a random structure of anti-parallel ferroelectric domains. We consider both, single and counter-propagating pulse geometries. We investigate polarization properties of the second harmonic signal and discuss applications of this process for short pulses characterization. Presented at 9-th International Workshop on Nonlinear Optics Applications, NOA 2007, May 17–20, 2007, Świnoujście, Poland     

Preparation,molecular structure and electronic structure of the rhombic,six-coordinate niobium(IV) complex NbCl2(ButC(O)CHC(O)But)2

The compound trans-NbCl₂(dpm)₂, Hdpm = 2,2,6,6-tetramethylheptane-3,5-dione, has been prepared and the molecular structure determined in each of two crystalline polymorphs by X-ray diffraction. The visible spectrum and the EPR spectrum have been measured and a Fenske—Hall calculation performed. The combined results give a reasonable and internally consistent picture of the electronic structure of the molecule. The HOMO is a b_3g-orbital (predominantly d_yz), while the two lowest-lying unoccupied orbitals (ca 16,000 cm^?1 higher) are b_2g(sim; d_xz) and a_g(sim; d_x²_?y²) orbitals, all in the D_2h-symmetry. The b_3g → b_2g and b_3g → a_g transitions are observed at 588.4 and 626.7 nm. The EPR spectrum in solution is a decet; the measured value of <g > is 1.930 and <A_iso > is 149 G. For the crystalline polymorph 1 the crystal data are: orthorhombic (P2₁2₁2₁), a = 13.649(3) Å, b = 18.166(4) Å, c = 11.425(4) Å, V = 2833(2) ų and Z = 4. Polymorph 2 is monoclinic (P2₁/n) with a = 12.288(5) Å, b = 9.226(4) Å, c = 12.545(4) Å, β = 94.24(3)°, V = 1418(2) ų and Z = 2. The molecule in 2 is centrosymmetric with virtual D_2h-symmetry. In 1 there are distortions in the chelate plane postulated to be due to packing forces. The two forms have comparable averaged values of interatomic dimensions.     

Attraction of nonlocal dark optical solitons

We study the formation and interaction of spatial dark optical solitons in materials with a nonlocal nonlinear response. We show that unlike in local materials, where dark solitons typically repel, the nonlocal nonlinearity leads to a long-range attraction and formation of stable bound states of dark solitons.