Complete Solving for Explicit Evaluation of Gauss Sums in the Index 2 Case

Let $p$ be a prime number, $q=p^f$ for some positive integer $f$, $N$ be a positive integer such that $\gcd(N,p)=1$, and let \k be a primitive multiplicative character of order $N$ over finite field \fq. This paper studies the problem of explicit evaluation of Gauss sums in "\textsl{index 2 case}" (i.e. f=\f{\p(N)}{2}=[\zn:\pp], where \p(\cd) is Euler function). Firstly, the classification of the Gauss sums in index 2 case is presented. Then, the explicit evaluation of Gauss sums G(\k^\la) (1\laN-1) in index 2 case with order $N$ being general even integer (i.e. N=2^{r}\cd N_0 where $r,N_0$ are positive integers and $N_03$ is odd.) is obtained. Thus, the problem of explicit evaluation of Gauss sums in index 2 case is completely solved

Adjusting the melting point of a model system via Gibbs-Duhem integration: application to a model of Aluminum

Model interaction potentials for real materials are generally optimized with respect to only those experimental properties that are easily evaluated as mechanical averages (e.g., elastic constants (at T=0 K), static lattice energies and liquid structure). For such potentials, agreement with experiment for the non-mechanical properties, such as the melting point, is not guaranteed and such values can deviate significantly from experiment. We present a method for re-parameterizing any model interaction potential of a real material to adjust its melting temperature to a value that is closer to its experimental melting temperature. This is done without significantly affecting the mechanical properties for which the potential was modeled. This method is an application of Gibbs-Duhem integration [D. Kofke, Mol. Phys.78, 1331 (1993)]. As a test we apply the method to an embedded atom model of aluminum [J. Mei and J.W. Davenport, Phys. Rev. B 46, 21 (1992)] for which the melting temperature for the thermodynamic limit is 826.4 +/- 1.3K - somewhat below the experimental value of 933K. After re-parameterization, the melting temperature of the modified potential is found to be 931.5K +/- 1.5K.Comment: 9 pages, 5 figures, 4 table

Exciton bimolecular annihilation dynamics in supramolecular nanostructures of conjugated oligomers

We present femtosecond transient absorption measurements on $\pi$-conjugated supramolecular assemblies in a high pump fluence regime. Oligo(\emph{p}-phenylenevinylene) monofunctionalized with ureido-\emph{s}-triazine (MOPV) self-assembles into chiral stacks in dodecane solution below 75$^{\circ}$C at a concentration of $4\times 10^{-4}$ M. We observe exciton bimolecular annihilation in MOPV stacks at high excitation fluence, indicated by the fluence-dependent decay of $1^1$B$_{u}$-exciton spectral signatures, and by the sub-linear fluence dependence of time- and wavelength-integrated photoluminescence (PL) intensity. These two characteristics are much less pronounced in MOPV solution where the phase equilibrium is shifted significantly away from supramolecular assembly, slightly below the transition temperature. A mesoscopic rate-equation model is applied to extract the bimolecular annihilation rate constant from the excitation fluence dependence of transient absorption and PL signals. The results demonstrate that the bimolecular annihilation rate is very high with a square-root dependence in time. The exciton annihilation results from a combination of fast exciton diffusion and resonance energy transfer. The supramolecular nanostructures studied here have electronic properties that are intermediate between molecular aggregates and polymeric semiconductors

Development of a questionnaire measuring instrumental activities of daily living ( IADL) in patients with brain tumors: a pilot study

Neurolog

Flory-Huggins theory for athermal mixtures of hard spheres and larger flexible polymers

A simple analytic theory for mixtures of hard spheres and larger polymers with excluded volume interactions is developed. The mixture is shown to exhibit extensive immiscibility. For large polymers with strong excluded volume interactions, the density of monomers at the critical point for demixing decreases as one over the square root of the length of the polymer, while the density of spheres tends to a constant. This is very different to the behaviour of mixtures of hard spheres and ideal polymers, these mixtures although even less miscible than those with polymers with excluded volume interactions, have a much higher polymer density at the critical point of demixing. The theory applies to the complete range of mixtures of spheres with flexible polymers, from those with strong excluded volume interactions to ideal polymers.Comment: 9 pages, 4 figure

Image informatics strategies for deciphering neuronal network connectivity

Brain function relies on an intricate network of highly dynamic neuronal connections that rewires dramatically under the impulse of various external cues and pathological conditions. Among the neuronal structures that show morphologi- cal plasticity are neurites, synapses, dendritic spines and even nuclei. This structural remodelling is directly connected with functional changes such as intercellular com- munication and the associated calcium-bursting behaviour. In vitro cultured neu- ronal networks are valuable models for studying these morpho-functional changes. Owing to the automation and standardisation of both image acquisition and image analysis, it has become possible to extract statistically relevant readout from such networks. Here, we focus on the current state-of-the-art in image informatics that enables quantitative microscopic interrogation of neuronal networks. We describe the major correlates of neuronal connectivity and present workflows for analysing them. Finally, we provide an outlook on the challenges that remain to be addressed, and discuss how imaging algorithms can be extended beyond in vitro imaging studies

Middle and Late Pleistocene environmental history of the Marsworth area, south-central England

To elucidate the Middle and Late Pleistocene environmental history of south-central England, we report the stratigraphy, sedimentology, palaeoecology and geochronology of some deposits near the foot of the Chiltern Hills scarp at Marsworth, Buckinghamshire. The Marsworth site is important because its sedimentary sequences contain a rich record of warm stages and cold stages, and it lies close to the Anglian glacial limit. Critical to its history are the origin and age of a brown pebbly silty clay (diamicton) previously interpreted as weathered till. The deposits described infill a river channel incised into chalk bedrock. They comprise clayey, silty and gravelly sediments, many containing locally derived chalk and some with molluscan, ostracod and vertebrate remains. Most of the deposits are readily attributed to periglacial and fluvial processes, and some are dated by optically stimulated luminescence to Marine Isotope Stage (MIS) 6. Although our sedimentological data do not discriminate between a glacial or periglacial interpretation of the diamicton, amino-acid dating of three molluscan taxa from beneath it indicates that it is younger than MIS 9 and older than MIS 5e. This makes a glacial interpretation unlikely, and we interpret the diamicton as a periglacial slope deposit. The Pleistocene history reconstructed for Marsworth identifies four key elements: (1) Anglian glaciation during MIS 12 closely approached Marsworth, introducing far-travelled pebbles such as Rhaxella chert and possibly some fine sand minerals into the area. (2) Interglacial environments inferred from fluvial sediments during MIS 7 varied from fully interglacial conditions during sub-stages 7e and 7c, cool temperate conditions during sub-stage 7b or 7a, temperate conditions similar to those today in central England towards the end of the interglacial, and cool temperate conditions during sub-stage 7a. (3) Periglacial activity during MIS 6 involved thermal contraction cracking, permafrost development, fracturing of chalk bedrock, fluvial activity, slopewash, mass movement and deposition of loess and coversand. (4) Fully interglacial conditions during sub-stage 5e led to renewed fluvial activity, soil formation and acidic weathering

Mathematical and computational modelling of vegetated soil incorporating hydraulically-driven finite strain deformation

In this paper a new model for the hydro-mechanical behaviour of rooted soils is developed. It is a physically-based model that couples finite strain soil deformation with unsaturated water and air flow, while improving on existing cohesion-based approaches to mechanical root reinforcement and empirical soil water-uptake approaches typically used to deal with rooted slopes. The model is used to show that the dynamics of soil-water pressure and soil deformation depend strongly on the physics of the root-water uptake and the elasto-plastic soil mechanics. Root water uptake can cause suctions and corresponding soil shrinkage sufficiently large to necessitate a finite-strain approach. Although this deformation can change the intrinsic permeability, hydraulic conductivity remains dominated by the water content. The model incorporates simultaneous air-flow, but this is shown to be unimportant for soil-water dynamics under the conditions assumed in example simulations. The mechanical action of roots is incorporated via a root stress tensor and a simulation is used to show how root tension is mobilised within a swelling soil. The developed model may be used to simulate both laboratory experiments and full-scale vegetated slopes