A Stefan-Type Problem with Void Formation and its Explicit Solution

For most materials, the densities of the solid and liquid phasesare different. For some materials being considered as potentiallatent heat thermal energy storage materials, this density changeis large. When the solid phase is more dense than the liquid,solidification may result in the formation of vapour bubblesor voids. We have formulated a problem, representing a phasechange process with such a void, that has an explicit solution.We examine the solution to gain a further understanding of thethermal and phase change performance of a material in whichsuch voids form. We use the solution to analyse an example probleminvolving freezing lithium fluoride, a candidate phase-changematerial with a density change on freezing of about 25 per cent.     

Resonances in Dispersive Wave Systems

Weakly nonlinear wave interactions under the assumption of a continuous, as opposed to discrete, spectrum of modes is studied. In particular, a general class of one-dimensional (1-D) dispersive systems containing weak quadratic nonlinearity is investigated. It is known that such systems can possess three-wave resonances, provided certain conditions on the wavenumber and frequency of the constituent modes are met. In the case of a continuous spectrum, it has been shown that an additional condition on the group velocities is required for a resonance to occur. Nonetheless, such so-called double resonances occur in a variety of physical regimes. A direct multiple scale analysis of a general model system is conducted. This leads to a system of three-wave equations analogous to those for the discrete case. Key distinctions include an asymmetry between the temporal evolution of the modes and a longer time scale of as opposed to O (ε t ). Extensions to additional dimensions and higher-order nonlinearities are then made. Numerical simulations are conducted for a variety of dispersions and nonlinearities providing qualitative and quantitative agreement.     

A comparison of two methods for estimating DCE-MRI parameters via individual and cohort based AIFs in prostate cancer: A step towards practical implementation

Multi-parametric Magnetic Resonance Imaging, and specifically Dynamic Contrast Enhanced (DCE) MRI, play increasingly important roles in detection and staging of prostate cancer (PCa). One of the actively investigated approaches to DCE MRI analysis involves pharmacokinetic (PK) modeling to extract quantitative parameters that may be related to microvascular properties of the tissue. It is well-known that the prescribed arterial blood plasma concentration (or Arterial Input Function, AIF) input can have significant effects on the parameters estimated by PK modeling. The purpose of our study was to investigate such effects in DCE MRI data acquired in a typical clinical PCa setting. First, we investigated how the choice of a semi-automated or fully automated image-based individualized AIF (iAIF) estimation method affects the PK parameter values; and second, we examined the use of method-specific averaged AIF (cohort-based, or cAIF) as a means to attenuate the differences between the two AIF estimation methods.     

En route to Background Independence: Broken split-symmetry,and how to restore it with bi-metric average actions

The most momentous requirement a quantum theory of gravity must satisfy is Background Independence, necessitating in particular an ab initio derivation of the arena all non-gravitational physics takes place in, namely spacetime. Using the background field technique, this requirement translates into the condition of an unbroken split-symmetry connecting the (quantized) metric fluctuations to the (classical) background metric. If the regularization scheme used violates split-symmetry during the quantization process it is mandatory to restore it in the end at the level of observable physics. In this paper we present a detailed investigation of split-symmetry breaking and restoration within the Effective Average Action (EAA) approach to Quantum Einstein Gravity (QEG) with a special emphasis on the Asymptotic Safety conjecture. In particular we demonstrate for the first time in a non-trivial setting that the two key requirements of Background Independence and Asymptotic Safety can be satisfied simultaneously. Carefully disentangling fluctuation and background fields, we employ a ‘bi-metric’ ansatz for the EAA and project the flow generated by its functional renormalization group equation on a truncated theory space spanned by two separate Einstein–Hilbert actions for the dynamical and the background metric, respectively. A new powerful method is used to derive the corresponding renormalization group (RG) equations for the Newton- and cosmological constant, both in the dynamical and the background sector. We classify and analyze their solutions in detail, determine their fixed point structure, and identify an attractor mechanism which turns out instrumental in the split-symmetry restoration. We show that there exists a subset of RG trajectories which are both asymptotically safe and split-symmetry restoring: In the ultraviolet they emanate from a non-Gaussian fixed point, and in the infrared they loose all symmetry violating contributions inflicted on them by the non-invariant functional RG equation. As an application, we compute the scale dependent spectral dimension which governs the fractal properties of the effective QEG spacetimes at the bi-metric level. Earlier tests of the Asymptotic Safety conjecture almost exclusively employed ‘single-metric truncations’ which are blind towards the difference between quantum and background fields. We explore in detail under which conditions they can be reliable, and we discuss how the single-metric based picture of Asymptotic Safety needs to be revised in the light of the new results. We shall conclude that the next generation of truncations for quantitatively precise predictions (of critical exponents, for instance) is bound to be of the bi-metric type.     

Quantum chemical studies on (ZnO)n/(NiO)n heterostructured nanoclusters

The structural stability and electronic properties of (ZnO)_n, (NiO)_n, (ZnO)_n/(NiO)_n for n = (1 to 4) and 3D structures were studied using density functional theory. The geometrical optimisation of clusters implies that when the atoms in the cluster increase it leads to an increase in its stability. The stability drastically increases for the heterostructure of (ZnO)_n/(NiO)_n. The dipole moment of the clusters depends on the geometry of the cluster and it is found to be minimum for heterostructures representing more neutralised clusters. HOMO-LUMO energies, ionisation potential, electron affinity, chemical hardness, binding energies and vibrational analysis of different clusters are calculated and reported. The adsorption of CO on the different sites of nanoclusters are studied and discussed.     

Study of phase coexistence in YVO3 and LaVO3

The coexistence at low temperature in YVO₃ and LaVO₃ of two competing phases with defined orbital and spin orientations is studied by Raman spectroscopy. The temperature evolution of the phonons indicates that phase coexistence, due to strain in YVO₃ and fluctuations in LaVO₃, is not restricted to small R ionic radius in RVO₃ compounds. Also, a typical temperature at 50 K is inferred from the temperature dependence of the intensities in LaVO₃. Copyright © 2015 John Wiley & Sons, Ltd.     

Optimization of ozone generation

The generation of ozone under homogeneous conditions is described by a system of kinetic equations. We supposed a certain time dependence of electric field intensity inside a discharge gap. We computed the dependence of efficiency of the ozone generation on both the width and the maximum intensity of electric pulse.     

Irreducible representations of the quantum analogue of SU(2)

We give the complete set of irreducible representations of U(SU(2))_q when q is a mth root of unity. In particular, we show that their dimensions are less or equal to m. Some of them are not highest-weight representations.     

Role of exciton-phonon interactions and disordering processes in the formation of the absorption edge in Cu<Subscript>6</Subscript>P(S<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>Se<Subscript>x</Subscript>)<Subscript>5</Subscript>Br crystals

The absorption edge in Cu₆P(S_1?x Se_x)⁵Br crystals has been studied for strong absorption in the temperature range of 77–330 K. The parameters of the Urbach absorption edge and exciton-phonon interactions in Cu₆P(S_1-x Se_x)₅Br crystals are determined and their effect on the composition disorder is studied.     

Generation of Electrical Currents and Magnetic Fields by Grain Boundary Motion

The effect of an induced magnetic moment due to grain boundary motion in a magnetic field was studied theoretically in a microscopic and a mesoscopic approximation. It was found that the induced moment generates a drag force on the boundary, which depends on the orientation of the magnetic field with regard to the crystal axis, as observed experimentally. However, the magnitude of the theoretically predicted dependency is much smaller than experimentally observed and even opposite with regard to the orientation dependence. Therefore, the electromagnetic drag can be neglected in comparison with other driving forces for grain boundary motion, but the effect may play a role for fast moving dislocations in a magnetic field.