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Ohne Zusammenfassung     

Structure and properties of Dinuclear [RuII([n]aneS4)] complexes of 3,6-Bis(2-pyridyl)-1,2,4,5-tetrazine

The synthesis of dinuclear [Ru(II)([n]aneS(4))] (where n = 12, 14) complexes of the bridging ligand 3,6-bis(2-pyridyl)-1,2,4,5-tetrazine are reported. The X-ray structures of both of the new complexes are compared to a newly obtained structure for a dinuclear [Ru(II)([9]aneS(3))]-based analogue, whose synthesis has previously been reported. A comparison of the electrochemistry of the three complexes reveals that the first oxidation of the [Ru(II)([n]aneS(4))]-based systems is a ligand-based couple, indicating that the formation of the radical anion form of the bridging ligand is stabilized by metal center coordination. Spectroelectrochemistry studies on the mixed-valence form of the new complexes suggest that they are Robin and Day Class II systems. The electrochemical and electronic properties of these complexes is rationalized by a consideration of the pi-bonding properties of thiacrown ligands.     

Phyllotactic patterns on plants

We demonstrate how phyllotaxis (the arrangement of leaves on plants) and the deformation configurations seen on plant surfaces may be understood as the energy-minimizing buckling pattern of a compressed shell (the plant's tunica) on an elastic foundation. The key new idea is that the strain energy is minimized by configurations consisting of special triads of almost periodic deformations. We reproduce a wide spectrum of plant patterns, all with the divergence angles observed in nature, and show how the occurrences of Fibonacci-like sequences and the golden angle are natural consequences.     

Dense atom clouds in a holographic atom trap

We demonstrate the production of high-density cold 87Rb samples (2 x 10(14) atoms/cm3) in a simple optical lattice formed with YAG light that is diffracted from a holographic phase plate. A loading protocol is described that results in 10,000 atoms per 10 microm x 10 microm x 100 microm unit cell of the lattice site. Rapid free evaporation leads to a temperature of 50 microK and phase space densities of 1/150 within 50 ms. The resulting small, high-density atomic clouds are very attractive for a number of experiments, including ultracold Rydberg atom physics.     

Kac-moody lie algebras and soliton equations: II. Lax equations associated with A1(1)

The soliton equations associated with sl(2) eigenvalue problems polynomial in the eigenvalue parameter are given a unified treatment; they are shown to be generated by a single family of commuting Hamiltonians on a subalgebra of the loop algebra of sl(2). The conserved densities and fluxes of the usual ANKS hierarchy are identified with conserved densities and fluxes for the polynomial eigenvalue problems. The Hamiltonian structures of the soliton equations associated with the polynomial eigenvalue problems are given a unified treatment.     

Kac-moody lie algebras and soliton equations: III. Stationary equations associated with A1(1)

The Hamiltonian structure of stationary soliton equations associated with the AKNS eigenvalue problem is derived in two ways. First, it is shown to arise from the Kostant-Kirillov symplectic structure on a coadjoint orbit in an infinite-dimensional Lie algebra. Second, it is obtained as the restriction to a finite-dimensional manifold of the infinite-dimensional Hamiltonian structure associated with a certain eigenvalue problem polynomial in the eigenvalue parameter.     

Propagation of solitary waves in channels of decreasing depth

The changes which occur in a right-going solitary wave as it travels a channel of decreasing depth are discussed. In addition to the changes in the solitary wave, we have found through a judicious use of the conservation laws two secondary structures (a shelf and a reflection). Each of these structures is small with respect to the solitary wave, though the mass flux associated with each is of the same order as that of the solitary wave. Of interest is that the amplitude of the reflected wave does not satisfy Green's law. But rather, the amplitude of the reflected wave is constant along left-going characteristics. This finding allows us to satisfy the mass flux conservation laws to leading order and establishes the perturbed Korteweg-deVries equation as a consistent approximation for the right-going profile.     

Task Specific and General Patterns of Joint Motion Variability in Upright- and Hand-Standing Postures

The preservation of static balance in both upright- and hand-stance is maintained by the projection of center of mass (CM) motion within the region of stability at the respective base of support. This study investigated, from a degrees of freedom (DF) perspective, whether the stability of the CM in both upright- and hand-stances was predicted by the respective dispersion and time-dependent regularity of joint (upright stance—ankle, knee, hip, shoulder, neck; hand stance—wrist, elbow, shoulder, neck) angle and position. Full body three-dimensional (3D) kinematic data were collected on 10 advanced level junior female gymnasts during 30 s floor upright- and hand-stands. For both stances the amount of the dispersion of joint angle and sway motion was higher than that of the CM and center of pressure (CP) with an inverse relation to time-dependent irregularity (SampEn). In upright-standing the variability of neck motion in the anterior–posterior direction was significantly greater than that of most joints consistent with the role of vision in the control of quiet upright posture. The findings support the proposition that there are both task specific and general properties to the global CM control strategy in the balance of upright- and hand-standing induced by the different active skeletal-muscular organization and the degeneracy revealed in the multiple distributional variability patterns of the joint angle and position in 3D.