The Recursion Operator of the Kadomtsev-Petviashvili Equation and the Squared Eigenfunctions of the Schrödinger Operator

The recursion operator of the Kadomtsev-Petviashvili equation is algorithmically derived. This recursion operator is the two-spatial-dimensional analogue of the Lenard operator of the Korteweg-deVries equation. It is also the “squared” eigenfunction operator of the time-dependent Schrödinger operator. The existence of the recursion operator suggests that the Kadomtsev-Petviashvili equation is a hi-Hamiltonian system.     

Recursion operators and bi-Hamiltonian structures in multidimensions. I

The algebraic properties of exactly solvable evolution equations in one spatial and one temporal dimensions have been well studied. In particular, the factorization of certain operators, called recursion operators, establishes the bi-Hamiltonian nature of all these equations. Recently, we have presented the recursion operator and the bi-Hamiltonian formulation of the Kadomtsev-Petviashvili equation, a two spatial dimensional analogue of the Korteweg-deVries equation. Here we present the general theory associated with recursion operators for bi-Hamiltonian equations in two spatial and one temporal dimensions. As an application we show that general classes of equations, which include the Kadomtsev-Petviashvili and the Davey-Stewartson equations, possess infinitely many commuting symmetries and infinitely many constants of motion in involution under two distinct Poisson brackets. Furthermore, we show that the relevant recursion operators naturally follow from the underlying isospectral eigenvalue problems.     

Quantum magneto-oscillations in a supramolecular Mn(II)-[3 x 3] grid

The magnetic grid molecule Mn(II)-[3 x 3] has been studied by high-field torque magnetometry at 3He temperatures. At fields above 5 T, the torque versus field curves exhibit an unprecedented oscillatory behavior. A model is proposed which describes these magneto-oscillations well.     

Secondary atomization of water and isooctane drops impinging on tilted heated surfaces

The present paper reports an experimental study aimed at characterizing the effects of heat transfer on the secondary atomization, which occurs during droplet impact on hot surfaces at conditions reproducing those occurring at fuel injection in internal combustion engines. The experiments consider single isooctane and water droplets impacting at different angles on a stainless steel surface with known roughness and encompass a range of Weber numbers from 240 to 600 and heat transfer regimes from the film-vaporization up to the Leidenfrost regime. The mechanisms of secondary breakup are inferred from the temporal evolution of the morphology of the impact imaged with a CCD camera, together with instantaneous measurements of droplet size and velocity. The combination of a technique for image processing with a phase Doppler instrument allows evaluating extended size distributions from 5.5 μm up to a few millimetres and to cover the full range of secondary droplet sizes observed at all heat transfer regimes and impaction angles. Temporal evolution of the size and velocity distributions are then determined. The experiments are reported at impact conditions at which disintegration does not occur at ambient temperature. So, any alteration observed in droplet impact behavior is thermally induced. The analysis is relevant for port fuel injection systems, where droplets injected to impact on the back surface of the valves, behave differently depending on fuel properties, particularly when the use of alcohols is considered, even as an additive to gasoline.     

Small scorpionate ligands: silver(I)-organophosphane complexes of 5-CF(3)-substituted scorpionate ligand combining a B-H...Ag coordination motif

The first 5-substituted trihydro(azolyl)borate system, the sodium trihydro(5-CF3-pyrazol-1-yl)borate, Na[H3B(5-(CF3)pz)], has been synthesized by the reaction of 3-trifuoromethyl-pyrazole with NaBH4 in high yield. Na[H3B(5-(CF3)pz)] reacts with AgNO3 in the presence of monodentate tertiary phosphanes PR3 (PR3=P(C6H5)3, P(p-C6H4CH3)3, P(m-C6H4CH3)3, P(o-C6H4CH3)3, or PCH3(C6H5)2) to afford silver(I) bis(phosphane) adducts. These compounds have been characterized by elemental analyses, FTIR, ESI-MS, and multinuclear (1H, 19F, and 31P) NMR spectroscopy. Solid-state structures of {[H3B(5-(CF3)pz)]Ag[P(C6H5)3]2} and {[H3B(5-(CF3)pz)]Ag[P(p-C6H4CH3)3]2} are also reported. They feature kappa2-N,H-bonded trihydro(pyrazolyl)borate ligands and pseudo-tetrahedral silver atoms.     

Silver(I)-organophosphane complexes of electron withdrawing CF3- or NO2-substituted scorpionate ligands

New silver(I) complexes have been synthesized from the reaction of AgNO(3), monodentate tertiary phosphanes PR(3) (PR(3) = P(C(6)H(5))(3), P(o-C(6)H(4)CH(3))(3), P(m-C(6)H(4)CH(3))(3), P(p-C(6)H(4)CH(3))(3), PCH(3)(C(6)H(5))(2)) and two novel electron withdrawing ligands: potassium dihydrobis(3-nitropyrazol-1-yl)borate and potassium dihydrobis(3-trifluoromethylpyrazol-1-yl)borate. These compounds have been characterized by elemental analyses, FT-IR, ESI-MS and multinuclear ((1)H, (19)F and (31)P) NMR spectroscopy. Solid state structures of the potassium salts K[H(2)B(3-(NO(2))pz)(2)] and K[H(2)B(3-(CF(3))pz)(2)] have been reported. They form polymeric networks due to intermolecular contacts of various types between the potassium ion and atoms of the neighboring molecules. The silver adducts [H(2)B(3-(NO(2))pz)(2)]Ag[P(C(6)H(5))(3)](2) and [H(2)B(3-(NO(2))pz)(2)]Ag[P(p-C(6)H(4)CH(3))(3)] have pseudo tetrahedral and trigonal planar silver sites, respectively. The bis(pyrazolyl)borate ligand acts as a kappa(2)-N(2) donor. The nitro-substituents are coplanar with the pyrazolyl rings in all these adducts indicating efficient electron delocalization between the two units. The [H(2)B(3-(CF(3))pz)(2)]Ag[P(C(6)H(5))(3)] complex has been obtained from re-crystallization of {[H(2)B(3-(CF(3))pz)(2)]Ag[P(C(6)H(5))(3)](2)} in a dichloromethane-diethyl ether solution; it is a three-coordinate, trigonal planar silver complex.     

: A quantitative measure of NMR signal receiving efficiency

Recognizing that the sensitivity of NMR is influenced by factors such as conductance and dielectric constant of the sample, we propose the receiving efficiency to characterize how efficiently the NMR signal can be observed from a unit transverse magnetization in a sample under optimal probe tuning and matching conditions. Conveniently, the relative receiving efficiency can be defined as the ratio of the NMR signal induced by a unit transverse magnetization in a sample of interest and a reference solution. Based on the reciprocal relationship between excitation and observation in NMR, the relative receiving efficiency can be correlated with the 90° pulse length (τ₉₀). In the special case of perfect probe tuning (impedance matched to 50 Ω), is inversely proportional to τ₉₀. Application of the NMR receiving efficiency in quantitative analysis potentially enables a single external concentration reference for almost any sample, eliminating the need to know its exact chemical composition or detailed electromagnetic properties.     

A branch-and-price approach to the feeder network design problem

In this paper we consider the problem of designing a container liner shipping feeder network. The designer has to choose which port to serve during many rotations that start and end at a central hub. Many operational characteristics are considered, such as variable leg-by-leg speeds and cargo transit times. Realistic instances are generated from the LinerLib benchmark suite. The problem is solved with a branch-and-price algorithm, which can solve most instances to optimality within one hour. The results also provide insights on the cost structure and desirable features of optimal routes. These insights were obtained by means of an analysis where scenarios are generated varying internal and external conditions, such as fuel costs and port demands.     

Quadrupolar waves in uranium dioxide

In presence of active orbital degrees of freedom, elementary excitations around a broken-symmetry state may include multipolar waves, but none of these exotic dispersive excitation branches has ever been identified. We show that quadrupolar waves constitute a major component of the dynamics of uranium dioxide in its magnetoquadrupolar ordered phase, and that many unexplained features in existing inelastic neutron scattering data, including a whole excitation branch, are associated with these propagating quadrupolar fluctuations. Our model permits us to separate the role of Jahn-Teller and superexchange mechanisms as sources of quadrupolar interactions.     

Hidden order and low-energy excitations in NpO2

We investigate the nature of the hidden order parameter in the ordered phase of NpO2, which had been identified with a staggered arrangement of Gamma5 magnetic multipoles. By analyzing the existing experimental data, we show that the most likely driving order parameter is not provided by octupoles, as usually assumed, but rather by the rank-5 triakontadipoles. Calculations of the coupled dynamics of spins, Gamma5 quadrupoles, and Gamma5 triakontadipoles in the ordered phase enable us to analyze the resulting structure of low-energy excitations. We show that the powder inelastic neutron scattering cross section should contain, in addition to the already-observed peak at 6.5 meV, a second weaker peak at about 14 meV.