Supersymmetric Backgrounds and Black Holes in N=(1,1){\cal N}=(1,1) Cosmological New Massive Supergravity

Using an off-shell Killing spinor analysis we perform a systematic investigation of the supersymmetric background and black hole solutions of the ${\cal N}=(1,1)$ Cosmological New Massive Gravity model. The solutions with a null Killing vector are the same pp-wave solutions that one finds in the ${\cal N}=1$ model but we find new solutions with a time-like Killing vector that are absent in the ${\cal N}=1$ case. An example of such a solution is a Lifshitz spacetime. We also consider the supersymmetry properties of the so-called rotating hairy BTZ black holes and logarithmic black holes in an $AdS_3$ background. Furthermore, we show that under certain assumptions there is no supersymmetric Lifshitz black hole solution.Comment: 27 pages, v2: Typos Corrected, Version appeared in JHE

Measurement of the ground-state distributions in bistable mechanically interlocked molecules using slow scan rate cyclic voltammetry

In donor–acceptor mechanically interlocked molecules that exhibit bistability, the relative populations of the translational isomers—present, for example, in a bistable [2]rotaxane, as well as in a couple of bistable [2]catenanes of the donor–acceptor vintage—can be elucidated by slow scan rate cyclic voltammetry. The practice of transitioning from a fast scan rate regime to a slow one permits the measurement of an intermediate redox couple that is a function of the equilibrium that exists between the two translational isomers in the case of all three mechanically interlocked molecules investigated. These intermediate redox potentials can be used to calculate the ground-state distribution constants, K. Whereas, (i) in the case of the bistable [2]rotaxane, composed of a dumbbell component containing π-electron-rich tetrathiafulvalene and dioxynaphthalene recognition sites for the ring component (namely, a tetracationic cyclophane, containing two π-electron-deficient bipyridinium units), a value for K of 10 ± 2 is calculated, (ii) in the case of the two bistable [2]catenanes—one containing a crown ether with tetrathiafulvalene and dioxynaphthalene recognition sites for the tetracationic cyclophane, and the other, tetrathiafulvalene and butadiyne recognition sites—the values for K are orders (one and three, respectively) of magnitude greater. This observation, which has also been probed by theoretical calculations, supports the hypothesis that the extra stability of one translational isomer over the other is because of the influence of the enforced side-on donor–acceptor interactions brought about by both π-electron-rich recognition sites being part of a macrocyclic polyether

Donor-Acceptor Oligorotaxanes Made to Order

Five donor–acceptor oligorotaxanes made up of dumbbells composed of tetraethylene glycol chains, interspersed with three and five 1,5-dioxynaphthalene units, and terminated by 2,6-diisopropylphenoxy stoppers, have been prepared by the threading of discrete numbers of cyclobis(paraquat-p-phenylene) rings, followed by a kinetically controlled stoppering protocol that relies on click chemistry. The well-known copper(I)-catalyzed alkyne–azide cycloaddition between azide functions placed at the ends of the polyether chains and alkyne-bearing stopper precursors was employed during the final kinetically controlled template-directed synthesis of the five oligorotaxanes, which were characterized subsequently by ^1H NMR spectroscopy at low temperature (233 K) in deuterated acetonitrile. The secondary structures, as well as the conformations, of the five oligorotaxanes were unraveled by spectroscopic comparison with the dumbbell and ring components. By focusing attention on the changes in chemical shifts of some key probe protons, obtained from a wide range of low-temperature spectra, a picture emerges of a high degree of folding within the thread protons of the dumbbells of four of the five oligorotaxanes—the fifth oligorotaxane represents a control compound in effect— brought about by a combination of C-H···O and π–π stacking interactions between the p-electron-deficient bipyridinium units in the rings and the π-electron-rich 1,5-dioxynaphthalene units and polyether chains in the dumbbells. The secondary structures of a foldamer-like nature have received further support from a solid-state superstructure of a related [3]pseudorotaxane and density functional calculations performed thereon

A Parallel Monte Carlo Code for Simulating Collisional N-body Systems

We present a new parallel code for computing the dynamical evolution of collisional N-body systems with up to N~10^7 particles. Our code is based on the the Henon Monte Carlo method for solving the Fokker-Planck equation, and makes assumptions of spherical symmetry and dynamical equilibrium. The principal algorithmic developments involve optimizing data structures, and the introduction of a parallel random number generation scheme, as well as a parallel sorting algorithm, required to find nearest neighbors for interactions and to compute the gravitational potential. The new algorithms we introduce along with our choice of decomposition scheme minimize communication costs and ensure optimal distribution of data and workload among the processing units. The implementation uses the Message Passing Interface (MPI) library for communication, which makes it portable to many different supercomputing architectures. We validate the code by calculating the evolution of clusters with initial Plummer distribution functions up to core collapse with the number of stars, N, spanning three orders of magnitude, from 10^5 to 10^7. We find that our results are in good agreement with self-similar core-collapse solutions, and the core collapse times generally agree with expectations from the literature. Also, we observe good total energy conservation, within less than 0.04% throughout all simulations. We analyze the performance of the code, and demonstrate near-linear scaling of the runtime with the number of processors up to 64 processors for N=10^5, 128 for N=10^6 and 256 for N=10^7. The runtime reaches a saturation with the addition of more processors beyond these limits which is a characteristic of the parallel sorting algorithm. The resulting maximum speedups we achieve are approximately 60x, 100x, and 220x, respectively.Comment: 53 pages, 13 figures, accepted for publication in ApJ Supplement

Mechanically Stabilized Tetrathiafulvalene Radical Dimers

Two donor−acceptor [3]catenanes—composed of a tetracationic molecular square, cyclobis(paraquat-4,4′-biphenylene), as the π-electron deficient ring and either two tetrathiafulvalene (TTF) and 1,5-dioxynaphthalene (DNP) containing macrocycles or two TTF-butadiyne-containing macrocycles as the π-electron rich components—have been investigated in order to study their ability to form TTF radical dimers. It has been proven that the mechanically interlocked nature of the [3]catenanes facilitates the formation of the TTF radical dimers under redox control, allowing an investigation to be performed on these intermolecular interactions in a so-called “molecular flask” under ambient conditions in considerable detail. In addition, it has also been shown that the stability of the TTF radical-cation dimers can be tuned by varying the secondary binding motifs in the [3]catenanes. By replacing the DNP station with a butadiyne group, the distribution of the TTF radical-cation dimer can be changed from 60% to 100%. These findings have been established by several techniques including cyclic voltammetry, spectroelectrochemistry and UV−vis−NIR and EPR spectroscopies, as well as with X-ray diffraction analysis which has provided a range of solid-state crystal structures. The experimental data are also supported by high-level DFT calculations. The results contribute significantly to our fundamental understanding of the interactions within the TTF radical dimers

Comparison of Current Balancing Configurations for Primary Parallel Isolated Boost Converter

Different current balancing configurations have been investigated for Primary Parallel Isolated Boost Converter (PPIBC). It has been shown that parallel branch current balancing is possible with several configurations of coupled/uncoupled inductors. Analytical expressions for branch currents have been derived for different cases of gate signal mismatch causing current imbalance. It has been observed that turn-on and turn-off delays in parallel power stages of the PPIBC have different effects in the branch currents deviating from ideal. It has also been observed that in some configurations inductance differences due to core tolerances play an important role in current imbalance. Analytical and simulation results have shown that another side effect of the gate signal delay and inductor value difference is additional voltage stress over the switches during the mismatch times. Advantages of each configuration in terms of effective current balancing, efficiency and manufacturing simplicity have been highlighted. Simulations with ideal components for each case have been carried out to confirm the analytical derivations. Experimental results have also been included to show the performances of different configurations where component non-idealities like transformer leakage inductances also become effective