A molecular theory of the dielectric permittivity of a nematic liquid crystal

We present a theory of the dielectric permittivity in which the intermolecular dipole-dipole correlations are treated explicitly. The results for the static permittivity agree with those which have previously been obtained by continuum calculations. The frequency dependence of the permittivity is related to two relaxation times which contain the effects of only short range intermolecular correlations. Approximate relationships are derived between these times and independently measurable properties.     

On the calculation of the orientational correlation parameter g 2

The g ₂ factor for a model of liquid carbon disulphide has been calculated by molecular dynamics simulation. The values of g ₂ for the model at three points along the orthobaric curve are: 1·17 ± 0·04 (298 K), 1·27 ± 0·03 (245 K), 1·39 ± 0·06 (193 K). These values are in good agreement with available experimental values. By calculating g ₂ in shells of cubic symmetry it is found that the value of g ₂ is determined by the orientational correlation of a molecule with neighbours within a few (two to three) molecular diameters. Spurious orientational correlations are introduced by the periodic boundary conditions and the calculation of collective correlation functions by averaging over the whole cube is shown to be unreliable. A theoretical calculation of g ₂ using RISM + SSA fails to reproduce the state dependence of the g ₂ values calculated from the simulation. This failure is not due to the small differences between the simulation and RISM g _αβ(r) for r < 4·5 Å but to inaccuracies in the SSA in the intermediate region r ～ 6 Å.     

Guided modes of integrated optical guides. A mathematical study

A waveguide in integrated optics is defined by its refractiveindex. The guide is assumed to be invariant in the propagationdirection while in the transverse direction it is supposed tobe a compact perturbation of an unbounded stratified medium.We are interested in the modes guided by this device, whichare waves with a transverse energy confined in a neighbourhoodof the perturbation. Our goal is to analyse the existence of such guided modes. Underthe assumptions of weak guidance the problem reduces to a two-dimensionaleigenvalue problem for a scalar field. The associated operatoris unbounded, selfadjoint, and bounded from below. Its spectrumconsists of the discrete spectrum corresponding to the guidedmodes and of the essential spectrum corresponding to the radiationmodes. We present existence results of guided modes and an asymptoticstudy at high frequencies, which shows that contrarily to thecase of optical fibers, the number of guided modes can remainbounded. The major tools are the min-max principle and comparisonof results between different eigenvalue problems. The originalityof the present study lies in the stratified character of theunbounded reference medium.     

Interaction of the mu-opioid receptor with GPR177 (Wntless) inhibits Wnt secretion: potential implications for opioid dependence

Background  

Opioid agonist drugs produce analgesia. However, long-term exposure to opioid agonists may lead to opioid dependence. The analgesic and addictive properties of opioid agonist drugs are mediated primarily via the mu-opioid receptor (MOR). Opioid agonists appear to alter neuronal morphology in key brain regions implicated in the development of opioid dependence. However, the precise role of the MOR in the development of these neuronal alterations remains elusive. We hypothesize that identifying and characterizing novel MOR interacting proteins (MORIPs) may help to elucidate the underlying mechanisms involved in the development of opioid dependence.     

Simulation of the pressure-driven wurtzite to rock salt phase transition in nanocrystals

Nanocrystals in the size range 12-21 nm of a model binary ionic material in the wurtzite (B4) structure were constructed with morphologies which minimize the surface energy. These were then embedded in a pressurization medium, consisting of a binary Lennard-Jones-type fluid and progressively pressurized in "constant pressure" molecular dynamics simulation runs. Phase transitions to the rocksalt (B1) phase were confirmed by examining calculated powder diffraction patterns, which show the same changes in features as seen for experimental systems. By directly observing the atomic trajectories throughout the duration of the transition the local mechanism has been identified. The transition proceeds via a trigonal bipyramidal intermediate, denoted as the h-MgO structure. It is initiated by a single nucleation event at a [1120]B4 surface with subsequent growth of the B1 region throughout the remainder of the nanocrystal. The consequences of this mechanism for the particle shape of the product phase are detailed and contrasted with those previously found for initially zincblende (B3) structured nanoparticles, using the same interaction potential. The observed transition pressures are elevated relative to the thermodynamically predicted pressure for the bulk, but there is no observable system size effect on the transition pressure across the size range of nanocrystals investigated.     

Ionic motion in crystalline cryolite

The character of the ion dynamics in crystalline cryolite, Na(3)AlF(6), a model double perovskite-structured mineral, has been examined in computer simulations using a polarizable ionic potential obtained by force-fitting to ab initio electronic structure calculations. NMR studies, and conductivity measurements, have indicated a high degree of mobility, in both Na(+) ion diffusion and reorientation of the AlF(6) octahedral units. The simulations reproduce the low-temperature (tilted) crystal structure and the existence of a transition to a cubic structure at elevated temperatures, in agreement with diffraction measurements, though the calculated transition temperature is too low. The reorientational dynamics of the AlF(6) octahedra is shown to consist of a hopping motion between the various tilted positions of the low-temperature form, even above the transition temperature. The rate of reorientation estimated by extrapolation to the temperature régime of the NMR measurements is consistent with the experimental data. In addition, we report a novel cooperative "tilt-swapping" motion of the differently tilted sublattices, just below the transition temperature. The perfect crystals show no Na(+) diffusion, in apparent disagreement with observation. We argue, following previous analyses of the cryolite phase diagram, that the diffusion observed in the experimental studies is a consequence of defects that are intrinsic to the thermodynamically stable form of cryolite. By introducing defects into the simulation cell, we obtain diffusion rates that are consistent with the NMR and conductivity measurements. Finally, we demonstrate a link between diffusion of the Na(+) ions and the reorientation of AlF(6) units, though the correlation between the two is not very strong.     

Bayesian networks for mathematical models: Techniques for automatic construction and efficient inference

Expert knowledge in the form of mathematical models can be considered sufficient statistics of all prior experimentation in the domain, embodying generic or abstract knowledge of it. When used in a probabilistic framework, such models provide a sound foundation for data mining, inference, and decision making under uncertainty.We describe a methodology for encapsulating knowledge in the form of ordinary differential equations (ODEs) in dynamic Bayesian networks (DBNs). The resulting DBN framework can handle both data and model uncertainty in a principled manner, can be used for temporal data mining with noisy and missing data, and can be used to re-estimate model parameters automatically using data streams. A standard assumption when performing inference in DBNs is that time steps are fixed. Generally, the time step chosen is small enough to capture the dynamics of the most rapidly changing variable. This can result in DBNs having a natural time step that is very short, leading to inefficient inference; this is particularly an issue for DBNs derived from ODEs and for systems where the dynamics are not uniform over time.We propose an alternative to the fixed time step inference used in standard DBNs. In our algorithm, the DBN automatically adapts the time step lengths to suit the dynamics in each step. The resulting system allows us to efficiently infer probable values of hidden variables using multiple time series of evidence, some of which may be sparse, noisy or incomplete.We evaluate our approach with a DBN based on a variant of the van der Pol oscillator, and demonstrate an example where it gives more accurate results than the standard approach, but using only one tenth the number of time steps.We also apply our approach to a real-world example in critical care medicine. By incorporating knowledge in the form of an existing ODE model, we have built a DBN framework for efficiently predicting individualised patient responses using the available bedside and lab data.     

Efficient CO2 Removal for Ultra‐Pure CO Production by Two Hybrid Ultramicroporous Materials

Removal of CO₂ from CO gas mixtures is a necessary but challenging step during production of ultra‐pure CO as processed from either steam reforming of hydrocarbons or CO₂ reduction. Herein, two hybrid ultramicroporous materials (HUMs), SIFSIX‐3‐Ni and TIFSIX‐2‐Cu‐i , which are known to exhibit strong affinity for CO₂, were examined with respect to their performance for this separation. The single‐gas CO sorption isotherms of these HUMs were measured for the first time and are indicative of weak affinity for CO and benchmark CO₂/CO selectivity (>4000 for SIFSIX‐3‐Ni ). This prompted us to conduct dynamic breakthrough experiments and compare performance with other porous materials. Ultra‐pure CO (99.99 %) was thereby obtained from CO gas mixtures containing both trace (1 %) and bulk (50 %) levels of CO₂ in a one‐step physisorption‐based separation process.     

A parameter-uniform Schwarz method for a coupled system of reaction–diffusion equations

We consider an arbitrarily sized coupled system of one-dimensional reaction–diffusion problems that are singularly perturbed in nature. We describe an algorithm that uses a discrete Schwarz method on three overlapping subdomains, extending the method in [H. MacMullen, J.J.H. Miller, E. O’Riordan, G.I. Shishkin, A second-order parameter-uniform overlapping Schwarz method for reaction-diffusion problems with boundary layers, J. Comput. Appl. Math. 130 (2001) 231–244] to a coupled system. On each subdomain we use a standard finite difference operator on a uniform mesh. We prove that when appropriate subdomains are used the method produces ε-uniform results. Furthermore we improve upon the analysis of the above-mentioned reference to show that, for small ε, just one iteration is required to achieve the expected accuracy.