Tomonaga-Luttinger liquid features in ballistic single-walled carbon nanotubes: conductance and shot noise

We study the electrical transport properties of well-contacted ballistic single-walled carbon nanotubes in a three-terminal configuration at low temperatures. We observe signatures of strong electron-electron interactions: the conductance exhibits bias-voltage-dependent amplitudes of quantum interference oscillation, and both the current noise and Fano factor manifest bias-voltage-dependent power-law scalings. We analyze our data within the Tomonaga-Luttinger liquid model using the nonequilibrium Keldysh formalism and find qualitative and quantitative agreement between experiment and theory.     

Microwave-assisted scavenging of electrophiles utilizing polymer-supported sequestration reagents. Application to the synthesis of N3-acylated dihydropyrimidine libraries

Different scavenging techniques using polymer-supported sequestration agents are described for the purification steps in the synthesis of N3-acylated dihydropyrimidines. For scavenging both excess anhydride and unwanted byproducts, polystyrene and silica supported diamines, aminomethyl-functionalized SynPhase Lanterns and diethylenetriamine StratoSpheres Plugs are used. In both synthesis and purification microwave flash heating was utilized, reducing reaction times from hours to minutes. These two steps coupled with an efficient solid-phase extraction (SPE) workup allowed the generation of a 28-member library of N3-acylated dihydropyrimidines using anhydrides. Using related protocols a 15-member library of N3-functionalized dihydropyrimidines utilizing acid chlorides as acylating reagents was also obtained.     

Stimulated Raman scattering in natural crystals of fluorapatite,Ca5(PO4)3F

Hexagonal Ca₅(PO₄)₃F, known as natural crystal fluorapatite and oldest host‐crystal for Ln³⁺‐lasant ions, is presented as a Raman‐active material. High‐order Raman‐induced χ⁽³⁾‐nonlinear processes are discovered in natural crystals of fluorapatite under picosecond pumping at 1.064 μm and 0.532 μm wavelength. A multitude of Stokes and anti‐Stokes components is generated in the ultraviolet, visible and near‐infrared spectral region by stimulated Raman scattering (SRS) and Raman four‐wave mixing (FWHM), resulting in a frequency comb with a width of 520 THz. The spectral lines are identified and attributed to the ν₁(A_g) vibration mode of the tetrahedral [PO₄] units which is related to a Raman shift of ω_SRS ≈ 965 cm⁻¹. The first Stokes steady‐state Raman gain coefficient in the near‐infrared spectral range is estimated to be >0.38 cm·GW⁻¹. Finally, a short review of SRS‐promoting vibration modes and observed χ⁽³⁾‐ nonlinear interactions in all known SRS‐active natural crystals (minerals) is given.

     

Diffractive beam splitter characterization via a power-recycled interferometer

We used the high-precision laser interferometer technique of power recycling to characterize the optical loss of an all-reflective grating beam splitter. This beam splitter was used to set up a Michelson interferometer with a power-recycling resonator with a finesse of 883. Analyzing the results obtained, we determined the beam splitter's total optical loss to be (0.193+/-0.019)%. Low loss all-reflective beam splitters might find application in future high-power laser interferometers for the detection of gravitational waves.     

The Cut Metric,Random Graphs,and Branching Processes

In this paper we study the component structure of random graphs with independence between the edges. Under mild assumptions, we determine whether there is a giant component, and find its asymptotic size when it exists. We assume that the sequence of matrices of edge probabilities converges to an appropriate limit object (a kernel), but only in a very weak sense, namely in the cut metric. Our results thus generalize previous results on the phase transition in the already very general inhomogeneous random graph model introduced by the present authors in Random Struct. Algorithms 31:3–122 (2007), as well as related results of Bollobás, Borgs, Chayes and Riordan (Ann. Probab. 38:150–183, 2010), all of which involve considerably stronger assumptions. We also prove corresponding results for random hypergraphs; these generalize our results on the phase transition in inhomogeneous random graphs with clustering (Random Struct. Algorithms, 2010, to appear).     

Magnetization reversal in textured NdFeB-Fe composites observed by domain imaging

Textured composite samples consisting of Nd_13.6Fe_73.6Ga_0.6Co_6.6B_5.6 (MQU-F™) and micron-sized Fe particles with weight ratios from 100:0 to 70:30 have been prepared by hot deformation. Microstructure studies revealed a layered structure of both phases with the layer normal parallel to the pressing direction. Magnetic measurements showed single-phase hysteresis curves for all samples when measured along the pressing direction, which is also the easy axis of magnetization. Coercivity decreased drastically from 1.32 T for pure NdFeB samples to 0.154 T for a sample with 30 wt% Fe. Magneto-optical Kerr microscopy with a digitally enhanced imaging technique has been used to examine the evolution of magnetic domains in the hard and soft phase during demagnetizing a sample consisting of 70 wt% NdFeB and 30 wt% Fe. It is shown that demagnetization takes place via domain rearrangements within the soft phase, which lead to and support the nucleation of reversed interaction domains at phase boundaries. Also nucleation of interaction domains within the hard magnetic phase could be revealed.     

Anomalous dispersion in the Belousov-Zhabotinsky reaction: Experiments and modeling

We report results on dispersion relations and instabilities of traveling waves in excitable systems. Experiments employ solutions of the 1,4-cyclohexanedione Belousov-Zhabotinsky reaction confined to thin capillary tubes which create a pseudo-one-dimensional system. Theoretical analyses focus on a three-variable reaction-diffusion model that is known to reproduce qualitatively many of the experimentally observed dynamics. Using continuation methods, we show that the transition from normal, monotonic to anomalous, single-overshoot dispersion curves is due to an orbit flip bifurcation of the solitary pulse homoclinics. In the case of “wave stacking”, this anomaly induces attractive pulse interaction, slow solitary pulses, and faster wave trains. For “wave merging”, wave trains break up in the wake of the slow solitary pulse due to an instability of wave trains at small wavelength. A third case, “wave tracking” is characterized by the non-existence of solitary waves but existence of periodic wave trains. The corresponding dispersion curve is a closed curve covering a finite band of wavelengths.     

Unbounded Entropy in Spacetimes with Positive Cosmological Constant

In theories of gravity with a positive cosmological constant, we consider product solutions with flux, of the form (A)dS _p ×S ^q . Most solutions are shown to be perturbatively unstable, including all uncharged dS _p ×S ^q spacetimes. For dimensions greater than four, the stable class includes universes whose entropy exceeds that of de Sitter space, in violation of the conjectured N-bound. Hence, if quantum gravity theories with finite-dimensional Hilbert space exist, the specification of a positive cosmological constant will not suffice to characterize the class of spacetimes they describe.