A truncation/recoupling method for eigenvalues and eigenvectors ideal for parallel computation

Summary We review a new truncation/recoupling method to obtain eigenvalues and eigenvectors of anF-mode vibrational Hamiltonian. In particular we focus on the block diagonalization aspects of the method which are ideal for massive parallelization, and we demonstrate this using H₂O₂ as an example. We then present vibrational energies for non-rotating HO₂ and HCN, which illustrate several key advantages of this method.     

Dynamics and Stability of Bose-Einstein Condensates: The Nonlinear Schrödinger Equation with Periodic Potential

Summary. The cubic nonlinear Schr?dinger equation with a lattice potential is used to model a periodic dilute-gas Bose-Einstein condensate. Both two- and three-dimensional condensates are considered, for atomic species with either repulsive or attractive interactions. A family of exact solutions and corresponding potential is presented in terms of elliptic functions. The dynamical stability of these exact solutions is examined using both analytical and numerical methods. For condensates with repulsive atomic interactions, all stable, trivial-phase solutions are off-set from the zero level. For condensates with attractive atomic interactions, no stable solutions are found, in contrast to the one-dimensional case [8].     

Finite dimensional approximation of Riemannian path space geometry

In this paper, we construct a finite dimensional approximation for the geometry on the path space over a compact Riemannian manifold. This approximation allows to construct the horizontal lift of the Ornstein-Uhlenbeck process on the path space through the Markovian connection. We also prove a representation formula for the heat semigroup on (adapted) vector fields as well as a commutation formula for its derivative.     

The excluded volume of hard sphero-zonotopes

Excluded volume effects can account for most ordering transitions in simple liquids and liquid crystals. Starting with the work of Onsager, this has been demonstrated in the case of liquid crystals for a number of simple convex bodies, e.g. sphero-cylinders, for which the orientation-dependent pair-excluded volume could be written down analytically. However, in recent years, experiments and simulations have been reported on ordering transitions in suspensions of more complex convex colloids. For these systems, theoretical understanding is hampered by the fact that no analytical expressions for the pair-excluded volume were available. Here we show that it is possible to obtain explicit expressions for the pair-excluded volume of a much larger class of convex bodies: the so-called sphero-zonotopes. These bodies are obtained by ‘padding’ a special class of convex polytopes with a blanket of uniform thickness. The resultant family of particles encompasses a wide range of shapes that have been considered as models for fluid and liquid crystalline behaviour e.g. spheres, cubes, sphero-cylinders, sphero-platelets. We discuss two explicit examples: sphero-cuboids, the 3D core generalization of the sphero-cylinder and the sphero-platelet, and hexagonal prisms that are models for the recently synthesized colloidal gibbsite platelets. Employing the fact that a cylinder is a zonoid, i.e. the limit of a sequence of right regular prisms, we are able to compute the excluded volume of the ‘true’ sphero-cylinder, a uniformly padded cylinder, of which the oblate-spherocylinder is a known example. Our approach en passant provides a relatively elementary rederivation of Onsager's classical result on cylinders.     

Deoxyfluorination with CuF2: Enabled by Using a Lewis Base Activating Group

Deoxyfluorination is a primary method for the formation of C−F bonds. Bespoke reagents are commonly used because of issues associated with the low reactivity of metal fluorides. Reported here is the development of a simple strategy for deoxyfluorination, using first-row transition-metal fluorides, and it overcomes these limitations. Using CuF₂ as an exemplar, activation of an O-alkylisourea adduct, formed in situ, allows effective nucleophilic fluoride transfer to a range of primary and secondary alcohols. Spectroscopic investigations have been used to probe the origin of the enhanced reactivity of CuF₂. The utility of the process in enabling ¹⁸F-radiolabeling is also presented.     

Rheological and electrical properties of EVA copolymer filled with bamboo charcoal

The electrical and rheological properties of an ethylene vinyl acetate (EVA) copolymer filled with bamboo charcoal were investigated. The composites were prepared by melt process in an internal batch mixer. Size distribution analysis showed that d₍₅₀₎ and d₍₉₀₎ values of the bamboo charcoal particles are 12.7 and 40 μm, respectively, with a mean diameter of 22 μm. Scanning electron microscopy proved that the particles of bamboo charcoal present a rectangular shape. The electrical percolation threshold was observed at 0.18 volume fraction (35 wt%) of bamboo. Beyond the percolation threshold, a considerable increase in electrical properties was observed up to a limit value of 10^-2 S/m. The rheological percolation was studied from different rheological models. As a result, the rheological percolation threshold was observed at 0.3 volume fraction (50 wt%) of bamboo charcoal contents. So, the electrical percolation occurs before the rheological percolation. This is principally due to the filler’s characteristics such as the specific surface area, the aspect ratio, and the surface properties. Finally, the bamboo charcoal confers high electrical properties to the EVA composite without inducing strong changes in its viscoelastic properties.     

Plasticizer effect on the dynamics of polyvinylchloride studied by dielectric spectroscopy and quasielastic neutron scattering

We have studied the influence of plasticization on the microscopic dynamics of a glass-forming polymer. For this purpose we studied polyvinylchloride (PVC) with and without the commercially used plasticizer dioctylphthalate (DOP). We used dielectric spectroscopy and inelastic neutron scattering employing the neutron spin echo (NSE) technique. For both kinds of spectra the alpha relaxation could be consistently described by a model involving a distribution of individual relaxations of the Kohlrausch type. In contrast to earlier studies it turned out that an asymmetric distribution is necessary to fit the data at the lower temperatures investigated here. The shape parameters of the distribution (width, skewness) for PVC and PVC/DOP turned out to coincide when the characteristic relaxation times were the same. This means that the plasticizer only induces a remapping of the temperature dependence of the alpha relaxation. Comparison of NSE spectra S(Q,t)S(Q) at different scattering vectors Q gave the result that the slowing down at the structure factor peak Q(max) is surprisingly small for PVC while it is in the normal range for PVC/DOP.     

L^p-gradient Estimates of Symmetric Markov Semigroups for 1 〈 p ≤ 2

For 1 〈 p ≤2, an L^p-gradient estimate for a symmetric Markov semigroup is derived in a general framework, i.e. ‖Γ^/2（Ttf）‖p≤Cp/√t‖p, where F is a carre du champ operator. As a simple application we prove that F1/2（（I- L） ^-α） is a bounded operator from L^p to L^v provided that 1 〈 p 〈 2 and 1/2〈α〈1. For any 1 〈 p 〈 2, q 〉 2 and 1/2 〈α 〈 1, there exist two positive constants cq,α,Cp,α such that ‖Df‖p≤ Cp,α‖（I - L）^αf‖p,Cq,α（I-L）^（1-α）‖Df‖q＋‖f‖q, where D is the Malliavin gradient （[2]） and L the Ornstein-Uhlenbeck operator.     

Sub‐Micromolar Pulse Dipolar EPR Spectroscopy Reveals Increasing CuII‐labelling of Double‐Histidine Motifs with Lower Temperature

Electron paramagnetic resonance (EPR) distance measurements are making increasingly important contributions to the studies of biomolecules by providing highly accurate geometric constraints. Combining double‐histidine motifs with Cu^II spin labels can further increase the precision of distance measurements. It is also useful for proteins containing essential cysteines that can interfere with thiol‐specific labelling. However, the non‐covalent Cu^II coordination approach is vulnerable to low binding‐affinity. Herein, dissociation constants (K_D) are investigated directly from the modulation depths of relaxation‐induced dipolar modulation enhancement (RIDME) EPR experiments. This reveals low‐ to sub‐μm Cu^II K_Ds under EPR distance measurement conditions at cryogenic temperatures. We show the feasibility of exploiting the double‐histidine motif for EPR applications even at sub‐μm protein concentrations in orthogonally labelled Cu^II–nitroxide systems using a commercial Q‐band EPR instrument.