180 degree unidirectional bond rotation in a biaryl lactone artificial molecular motor prototype

A bifunctional biaryl lactone has been synthesized that should be capable of iterative unidirectional aryl-aryl bond rotation via: (1) a diastereoselective lactone ring opening, (S)-1 to (P,S)-2 or (M,S)-2; (2) a chemoselective lactonization, (P,S)-2 or (M,S)-2 to (S)-3; and (3) a chemoselective hydrolysis, (S)-3 to (S)-1. Preliminary results of a racemic sample have indicated unidirectional 180 degrees rotation with very high directional selectivity per individual artificial molecular motor molecule through the first two steps of this sequence. [reaction: see text]     

Tunneling of an energy eigenstate through a parabolic barrier viewed from Wigner phase space

We analyze the tunneling of a particle through a repulsive potential resulting from an inverted harmonic oscillator in the quantum mechanical phase space described by the Wigner function. In particular, we solve the partial differential equations in phase space determining the Wigner function of an energy eigenstate of the inverted oscillator. The reflection or transmission coefficients R or T are then given by the total weight of all classical phase-space trajectories corresponding to energies below, or above the top of the barrier given by the Wigner function.     

Surgery and the Spinorial τ-Invariant

We associate to a compact spin manifold M a real-valued invariant τ(M) by taking the supremum over all conformal classes of the infimum inside each conformal class of the first positive Dirac eigenvalue, when the metrics are normalized to unit volume. This invariant is a spinorial analogue of Schoen's σ-constant, also known as the smooth Yamabe invariant. We prove that if N is obtained from M by surgery of codimension at least 2 then τ(N) ≥ min{τ(M), Λ _n }, where Λ _n is a positive constant depending only on n = dim M. Various topological conclusions can be drawn, in particular that τ is a spin-bordism invariant below Λ _n . Also, below Λ _n the values of τ cannot accumulate from above when varied over all manifolds of dimension n.     

Pricing of Claims in Discrete Time with Partial Information

We consider the pricing problem of a seller with delayed price information. By using Lagrange duality, a dual problem is derived, and it is proved that there is no duality gap. This gives a characterization of the seller’s price of a contingent claim. Finally, we analyze the dual problem, and compare the prices offered by two sellers with delayed and full information respectively.     

Brownian Approximation and Monte Carlo Simulation of the Non-Cutoff Kac Equation

The non-cutoff Boltzmann equation can be simulated using the DSMC method, by a truncation of the collision term. However, even for computing stationary solutions this may be very time consuming, in particular in situations far from equilibrium. By adding an appropriate diffusion, to the DSMC-method, the rate of convergence when the truncation is removed, may be greatly improved. We illustrate the technique on a toy model, the Kac equation, as well as on the full Boltzmann equation in a special case.     

Switching from "absorption within transparency" to "transparency within transparency" in an electromagnetically induced absorption dominated transition

The absorption of a resonant coupling laser driving a closed degenerate two-level system in an atomic cesium beam was investigated as a function of the detuning of a second laser probing the same transition. The measurements were performed for four different polarization combinations of the two laser beams. Except for the beams of counterrotating polarizations all coupling-laser absorption profiles showed "absorption within transparency," i.e., the absorption in the region around the two-photon resonance was smaller than the absorption corresponding to the one-photon transition induced by the coupling laser, and an extra absorption peak was observed on this curve at the two-photon resonance. With regard to the beams of counterrotating polarizations we observed a switch from absorption within transparency to "transparency within transparency" when the probe-laser power exceeded the constant coupling-laser power. In other words, the cesium ensemble became mostly transparent to the coupling-laser beam at the two-photon resonance.     

Two-dimensional thermometry using temperature-induced line shifts of ZnO:Zn and ZnO:Ga fluorescence

Sensitive temperature-induced line shifts of the near-band-edge emission from ZnO:Ga and ZnO:Zn are investigated for two-dimensional (2D) thermometry with nanosecond time resolution. Spectral and temporal concerns for 2D measurements and the feasibility for utilizing the line shifts for temperature measurements using a spectral ratio are investigated. Owing to the high temperature sensitivity, a precision of 1% at 800 K is reported for spectral ratio measurements. The technique is demonstrated by 2D measurements of the liquid temperature of burning methanol droplets.     

Brans–Dicke geometry

We reveal the non-metric geometry underlying ω→0$\omega \to 0$ Brans–Dicke theory by unifying the metric and scalar field into a single geometric structure. Taking this structure seriously as the geometry to which matter universally couples, we show that the theory is fully consistent with solar system tests. This is in striking contrast with the standard metric coupling, which grossly violates post-Newtonian experimental constraints.     

The interaction between model biomaterial coatings and nylon microparticles as measured with a quartz crystal microbalance with dissipation monitoring

The interaction between cells and biomaterials has been mimicked using nylon microparticles as pseudo-cells and PLMA and PIBMA as biomaterial model acrylate polymers. The shift of fundamental resonance frequencies was negative for both polymers, indicating mass-coupling to the sensor surface. The shifts of the 3rd, 5th and 7th overtone frequencies were initially positive for both polymers, indicating a particle slip or wobbling on the surface. The QCM technique could discriminate between the two different polymers, showing increased interaction between microparticle and PLMA. The dissipation shift was positive for all overtones on both polymers, but again with faster and more prominent response for PLMA.