Intercommutation of semilocal strings and Skyrmions

We study the intercommuting of semilocal strings and Skyrmions for a wide range of internal parameters, velocities, and intersection angles by numerically evolving the equations of motion. We find that the collisions of strings and strings, strings and Skyrmions, and Skyrmions and Skyrmions all lead to intercommuting for a wide range of parameters. Even the collisions of unstable Skyrmions and strings lead to intercommuting, demonstrating that the phenomenon of intercommuting is very robust, extending to dissimilar field configurations that are not stationary solutions. Even more remarkably, at least for the semilocal U(2) formulation considered here, all intercommutations trigger a reversion to Nielsen-Olesen strings.     

Analytical theory of gamma-encoded double-quantum recoupling sequences in solid-state nuclear magnetic resonance

Many important double-quantum recoupling techniques in solid-state NMR are classified as being gamma-encoded. This means that the phase of the double-quantum effective Hamiltonian, but not its amplitude, depends on the third Euler angle defining the orientation of the molecular spin system in the frame of the magic-angle-spinning rotor. In this paper, we provide closed analytical solutions for the dependence of the powder-average double-quantum-filtered signal on the recoupling times, within the average Hamiltonian approximation for gamma-encoded pulse sequences. The validity of the analytical solutions is tested by numerical simulations. The internuclear distance in a (13)C(2)-labelled retinal is estimated by fitting the analytical curves to experimental double-quantum data.     

3D MRI of non-Gaussian (3)He gas diffusion in the rat lung

In (3)He magnetic resonance images of pulmonary air spaces, the confining architecture of the parenchymal tissue results in a non-Gaussian distribution of signal phase that non-exponentially attenuates image intensity as diffusion weighting is increased. Here, two approaches previously used for the analysis of non-Gaussian effects in the lung are compared and related using diffusion-weighted (3)He MR images of mechanically ventilated rats. One approach is model-based and was presented by Yablonskiy et al., while the other approach utilizes the second order decay contribution that is predicted from the cumulant expansion theorem. Total lung coverage is achieved using a hybrid 3D pulse sequence that combines conventional phase encoding with sparse radial sampling for efficient gas usage. This enables the acquisition of nine 3D images using a total of only approximately 1 L of hyperpolarized (3)He gas. Diffusion weighting ranges from 0 s/cm(2) to 40 s/cm(2). Results show that the non-Gaussian effects of (3)He gas diffusion in healthy rat lungs are directly attributed to the anisotropic geometry of lung microstructure as predicted by the Yablonskiy model, and that quantitative analysis over the entire lung can be reliably repeated in time-course studies of the same animal.     

Silicon nanowire grid polarizer for very deep ultraviolet fabricated from a shear-aligned diblock copolymer template

A silicon (Si) nanowire grid ultraviolet (UV) transmission polarizer has been fabricated, and its performance was measured over the visible to deep UV range. A cylinder-forming polystyrene-b-poly(hexylmethacrylate) diblock copolymer was coated onto an amorphous Si layer supported on a fused silica substrate, then shear aligned and employed as a mask for reactive-ion etching, resulting in a Si grid of 33 nm period and multi-centimeter-squared area. Due to the high plasma frequency and UV reflectance of the deposited Si, this nanowire grid was able to polarize light down into the deep UV, including 193 nm.     

Eigenvalue amplitudes of the Potts model on a torus

We consider the Q-state Potts model in the random-cluster formulation, defined on finite   two-dimensional lattices of size L×N$L\times N$ with toroidal boundary conditions. Due to the non-locality of the clusters, the partition function Z(L,N)$Z(L,N)$ cannot be written simply as a trace of the transfer matrix TL${\mathrm{T}}_L$. Using a combinatorial method, we establish the decomposition Z(L,N)=_∑l,Dkb(l,Dk)K_l,Dk$Z(L,N)={\sum }_{l,D_k}{b}^{(l,D_k)}{K}_{l,D_k}$, where the characters K_l,Dk=i_∑N(λi)$K_{l,D_k}={\sum }_i{({\lambda }_i)}^N$ are simple traces. In this decomposition, the amplitudes b(l,Dk)$b^{(l,D_k)}$ of the eigenvalues λi${\lambda }_i$ of TL${\mathrm{T}}_L$ are labelled by the number l=0,1,…,L$l=0,1,\dots ,L$ of clusters which are non-contractible with respect to the transfer (N  ) direction, and a representation Dk$D_k$ of the cyclic group Cl$C_l$. We obtain rigorously a general expression for b(l,Dk)$b^{(l,D_k)}$ in terms of the characters of Cl$C_l$, and, using number theoretic results, show that it coincides with an expression previously obtained in the continuum limit by Read and Saleur.     

The anxiolytic effects of midazolam during anticipation to pain revealed using fMRI

BACKGROUND AND PURPOSE: Functional neuroimaging can distinguish components of the pain experience associated with anticipation to pain from those associated with the experience of pain itself. Anticipation to pain is thought to increase the suffering of chronic pain patients. Inappropriate anxiety, of which anticipation is a component, is also a cause of disability. We present a pharmacological functional magnetic resonance imaging (fMRI) study in which we investigate the selective modulation by midazolam of brain activity associated with anticipation to pain compared to pain itself. METHODS: Eight right-handed male volunteers underwent fMRI combined with a thermal pain conditioning paradigm and midazolam (30 mug/kg) or saline administration on different occasions, with order randomized across volunteers. Volunteers learned to associate a colored light with either painful, hot stimulation or nonpainful, warm stimulation to the back of the left hand. RESULTS: Comparison of the period during thermal stimulation (pain-warm) revealed a network of brain activity commonly associated with noxious stimulation, including activities in the anterior cingulate cortex (ACC), the bilateral insular cortices (anterior and posterior), the thalamus, S1, the motor cortex, the brainstem, the prefrontal cortex and the cerebellum. Comparison of the periods preceding thermal stimulation (anticipation to pain-anticipation to warm) revealed activity principally in the ACC, the contralateral anterior insular cortex and the ipsilateral S2/posterior insula. Detected by a region-of-interest analysis, midazolam reduced the activity associated specifically with anticipation to pain while controlling for anticipation to warm. This was most significant in the contralateral anterior insula (P<.05). There were no significant drug effects on the activity associated with pain itself. CONCLUSION: In identifying a pharmacological effect on activity preceding but not during pain, we have successfully demonstrated an fMRI assay that can be used to study the action of anxiolytic agents in a relatively small cohort of humans.     

Twisted Poincaré Duality for some Quadratic Poisson Algebras

We exhibit a Poisson module restoring a twisted Poincaré duality between Poisson homology and cohomology for the polynomial algebra endowed with Poisson bracket arising from a uniparametrised quantum affine space. This Poisson module is obtained as the semiclassical limit of the dualising bimodule for Hochschild homology of the corresponding quantum affine space. As a corollary we compute the Poisson cohomology of R, and so retrieve a result obtained by direct methods (so completely different from ours) by Monnier. This research of the first author was supported by a Marie Curie Intra-European Fellowship within the 6th European Community Framework Programme. The second author was supported by EPSRC Grant EP/D034167/1.     

Synthesis and Ambiphilic Reactivity of Metalated Diorgano-Phosphonite Boranes

Unprecedented metalated phosphonite boranes were prepared from PH-substituted precursors and silyl amides. Although potassium derivatives were thermally stable and could even be isolated and structurally characterised, lithiated analogues proved to be unstable towards self-condensation under cleavage of LiOR at ambient temperature. Reaction studies revealed that the metalated phosphonite boranes exhibit ambiphilic character. Their synthetic potential as nucleophilic building blocks was demonstrated in the synthesis of the first stannylated phosphonite representing a new structural motif in phosphine chemistry.     

Azimuthal Dipolar Rotor Arrays on Surfaces

A set of dipolar molecular rotor compounds was designed, synthesized and adsorbed as self-assembled 2D arrays on Ag(111) surfaces. The title molecules are constructed from three building blocks: (a) 4,8,12-trioxatriangulene (TOTA) platforms that are known to physisorb on metal surfaces such as Au(111) and Ag(111), (b) phenyl groups attached to the central carbon atom that function as pivot joints to reduce the barrier to rotation, (c) pyridine and pyridazine units as small dipolar units on top. Theoretical calculations and scanning tunneling microscopy (STM) investigations hint at the fact that the dipoles of neighboring rotors interact through space through pairs of energetically favorable head-to-tail arrangements.