On the canonical character of the Sawada-Kotera equation

Recursion operators for solutions of two linear equations, associated with the SK equation, are given. A method to construct constants on the motion is described. The hamiltonian structure and the relation with the inverse scattering problem is indicated.     

Constants of the motion for the Benjamin-Ono and related equations

It is shown that the Benjamin-Ono equation and higher order equations of the same kind have an infinite series of infinite sets of constants of the motion. Apart from the, already known, first set these constants depend explicitly on time.     

Control of a coupled map lattice model for vortex shedding in the wake of a cylinder

The flow behind a vibrating flexible cable at low Reynolds numbers can exhibit complex wake structures such as lace-like patterns, vortex dislocations and frequency cells. These structures have been observed in experiments and numerical simulations, and are predicted by a previously developed low-order coupled map lattice (CML). The discrete (in time and space) CML models consist of a series of diffusively coupled circle map oscillators along the cable span. Motivated by a desire to modify the complex wake patterns behind flexible vibrating cables we have studied the addition of control terms into the highly efficient CML models and explored the resulting dynamics. Proportional, adaptive proportional and discontinuous non-linear (DNL) control methods were used to derive the control laws. The first method employed occasional proportional feedback. The adaptive method used spatio-temporal feedback control. The DNL method used a discontinuous feedback linearization procedure, and the controller was designed for the resulting linearized system using eigenvalue assignment. These techniques were applied to a modeled vortex dislocation structure in the wake of a vibrating cable in uniform freestream flow. Parallel shedding patterns were achieved for a range of forcing frequency-forcing amplitude combinations studied to validate the control theory. The adaptive proportional and DNL methods were found to be more effective than the proportional control method due to the incorporation of a spatially varying feedback gain across the cylinder span. The DNL method was found to be the most efficient controller of the low-order CML model. The required control level across the cable span was correlated to the 1/1 lock-on behavior of the temporal circle map.     

Conversion from material to local coordinates as a canonical transformation

It is shown that the conversion from material to local coordinates in continuum mechanics can be considered as a restricted canonical transformation. As a simple example the longitudinal motion of an elastic bar is discussed.     

Mononuclear, trinuclear, and hetero-trinuclear supramolecular complexes containing a new tri-sulfonate ligand and cobalt(II)/copper(II)-(1,10-phenanthroline)2 building blocks

Novel mononuclear, trinuclear, and hetero-trinuclear supermolecular complexes, [Co(phen)₂(H₂O)(HTST)]·2H₂O (1), [Co₃(phen)₆(H₂O)₂(TST)₂]·7H₂O (2), and [Co₂Cu(phen)₆(H₂O)₂(TST)₂]·10H₂O (3), have been synthesized by the reactions of a new tri-sulfonate ligand (2,4,6-tris(4-sulfophenylamino)-1,3,5-triazine, H₃TST) with the M²⁺ (M=Co, Cu) and the second ligand 1,10-phenanthroline (phen). Complex 1 contains a cis-Co(II)(phen)₂ building block and an HTST as monodentate ligand; complex 2 consists of two TST as bidentate ligands connecting one trans- and two cis-Co(II)(phen)₂ building blocks; complex 3 is formed by replacing the trans-Co(II)(phen)₂ in 2 with a trans-Cu(II)(phen)₂, which is the first reported hetero-trinuclear supramolecular complex containing both the Co(II)(phen)₂ and Cu(II)(phen)₂ as building blocks. The study shows the flexible multifunctional self-assembly capability of the H₃TST ligands presenting in these supramolecular complexes through coordinative, H-bonding and even π-π stacking interactions. The photoluminescent optical properties of these complexes are also investigated and discussed as well as the second-order nonlinear optical properties of 1.     

Role of charge transfer configurations in LaMnO3, CaMnO3, and CaFeO3

A simple scheme is proposed to analyze the N-electron wave function obtained in embedded cluster calculations in valence bond terms such as ligand-to-metal charge transfer and non-charge-transfer determinants. The analysis is based on a unitary transformation of pairs of natural orbitals to optimal atomiclike orbitals. The procedure is applied to compare the degree of ionicity in NiO and MnO and to explain the existence or absence of Jahn-Teller distortions in LaMnO3, CaMnO3, and CaFeO3. The authors find that the ground state of LaMnO3 is dominated by non-charge-transfer configurations, whereas the charge transfer configurations dominate the ground state wave function in the other two perovskites.     

Real time quantitative amplification detection on a microarray: towards high multiplex quantitative PCR

Quantitative real-time polymerase chain reaction (qrtPCR) is widely used as a research and diagnostic tool. Notwithstanding its many powerful features, the method is limited in the degree of multiplexing to about 6 due to spectral overlap of the available fluorophores. A new method is presented that allows quantitative amplification detection at higher multiplexing by the integration of amplification in solution and monitoring via hybridization to a microarray in real-time. This method does not require any manipulation of the PCR product and runs in a single closed chamber. Employing labeled primers, one of the main challenges is to measure surface signals against a high fluorescence background from solution. A compact, confocal scanner is employed, based on miniaturized optics from DVD technology and combined with a flat thermocycler for simultaneous scanning and heating. The feasibility of this method is demonstrated in singleplex with an analytical sensitivity comparable to routine qrtPCR.     

Electric field confinement effect on charge transport in organic field-effect transistors

While it is known that the charge-carrier mobility in organic semiconductors is only weakly dependent on the electric field at low fields, the experimental mobility in organic field-effect transistors using silylethynyl-substituted pentacene is found to be surprisingly field dependent at low source-drain fields. Corroborated by scanning Kelvin probe measurements, we explain this observation by the severe difference between local conductivities within grains and at grain boundaries. Redistribution of accumulated charges creates very strong local lateral fields in the latter regions. We further confirm this picture by verifying that the charge mobility in channels having no grain boundaries, made from the same organic semiconductor, is not significantly field dependent. We show that our model allows us to quantitatively model the source-drain field dependence of the mobility in polycrystalline organic transistors.     

Ultrafast Deactivation Mechanism of the Excited Singlet in the Light‐Induced Spin Crossover of [Fe(2,2′‐bipyridine)3]2+

The mechanism of the light‐induced spin crossover of the [Fe(bpy)₃]²⁺ complex (bpy=2,2′‐bipyridine) has been studied by combining accurate electronic‐structure calculations and time‐dependent approaches to calculate intersystem‐crossing rates. We investigate how the initially excited metal‐to‐ligand charge transfer (MLCT) singlet state deactivates to the final metastable high‐spin state. Although ultrafast X‐ray free‐electron spectroscopy has established that the total timescale of this process is on the order of a few tenths of a picosecond, the details of the mechanisms still remain unclear. We determine all the intermediate electronic states along the pathway from low spin to high spin and give estimates for the deactivation times of the different stages. The calculations result in a total deactivation time on the same order of magnitude as the experimentally determined rate and indicate that the complex can reach the final high‐spin state by means of different deactivation channels. The optically populated excited singlet state rapidly decays to a triplet state with an Fe d⁶(${{\rm t}{{5\hfill \atop {\rm 2g}\hfill}}}$ ${{\rm e}{{1\hfill \atop {\rm g}\hfill}}}$ ) configuration either directly or by means of a triplet MLCT state. This triplet ligand‐field state could in principle decay directly to the final quintet state, but a much faster channel is provided by internal conversion to a lower‐lying triplet state and subsequent intersystem crossing to the high‐spin state. The deactivation rate to the low‐spin ground state is much smaller, which is in line with the large quantum yield reported for the process.