Research study for determination of liquid surface profile in a cryogenic tank during gas injection Quarterly progress report no. 9, Jun. 18 - Sep. 17, 1966

Determining liquid surface profiles in cryogenic tank during gas injectio

On the geometric boundaries of hyperbolic 4-manifolds

We provide, for hyperbolic and flat 3-manifolds, obstructions to bounding hyperbolic 4-manifolds, thus resolving in the negative a question of Farrell and Zdravkovska.Comment: 8 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTVol4/paper5.abs.htm

Real-time single image and video super-resolution using an efficient sub-pixel convolutional neural network

Recently, several models based on deep neural networks have achieved great success in terms of both reconstruction accuracy and computational performance for single image super-resolution. In these methods, the low resolution (LR) input image is upscaled to the high resolution (HR) space using a single filter, commonly bicubic interpolation, before reconstruction. This means that the super-resolution (SR) operation is performed in HR space. We demonstrate that this is sub-optimal and adds computational complexity. In this paper, we present the first convolutional neural network (CNN) capable of real-time SR of 1080p videos on a single K2 GPU. To achieve this, we propose a novel CNN architecture where the feature maps are extracted in the LR space. In addition, we introduce an efficient sub-pixel convolution layer which learns an array of upscaling filters to upscale the final LR feature maps into the HR output. By doing so, we effectively replace the handcrafted bicubic filter in the SR pipeline with more complex upscaling filters specifically trained for each feature map, whilst also reducing the computational complexity of the overall SR operation. We evaluate the proposed approach using images and videos from publicly available datasets and show that it performs significantly better (+0.15dB on Images and +0.39dB on Videos) and is an order of magnitude faster than previous CNN-based methods

Real-time single image and video super-resolution using an efficient sub-pixel convolutional neural network

Recently, several models based on deep neural networks have achieved great success in terms of both reconstruction accuracy and computational performance for single image super-resolution. In these methods, the low resolution (LR) input image is upscaled to the high resolution (HR) space using a single filter, commonly bicubic interpolation, before reconstruction. This means that the super-resolution (SR) operation is performed in HR space. We demonstrate that this is sub-optimal and adds computational complexity. In this paper, we present the first convolutional neural network (CNN) capable of real-time SR of 1080p videos on a single K2 GPU. To achieve this, we propose a novel CNN architecture where the feature maps are extracted in the LR space. In addition, we introduce an efficient sub-pixel convolution layer which learns an array of upscaling filters to upscale the final LR feature maps into the HR output. By doing so, we effectively replace the handcrafted bicubic filter in the SR pipeline with more complex upscaling filters specifically trained for each feature map, whilst also reducing the computational complexity of the overall SR operation. We evaluate the proposed approach using images and videos from publicly available datasets and show that it performs significantly better (+0.15dB on Images and +0.39dB on Videos) and is an order of magnitude faster than previous CNN-based methods

Profile blunting and flow blockage in a yield stress fluid: A molecular dynamics study

The flow of a simple glass forming system (a 80:20 binary Lennard-Jones mixture) through a planar channel is studied via molecular dynamics simulations. The flow is driven by an external body force similar to gravity. Previous studies show that the model exhibits both a static [Varnik et al. J. Chem. Phys. 120, 2788 (2004)] and a dynamic [F. Varnik and O. Henrich Phys. Rev. B 73, 174209 (2006)] yield stress in the glassy phase. \blue{These observations are corroborated by the present work, where we investigate how the presence of a yield stress may affect the system behavior in a Poiseuille-type flow geometry.} In particular, we observe a blunted velocity profile across the channel: A relatively wide region in the channel center flows with a constant velocity (zero shear rate) followed by a non linear change of the shear rate as the walls are approached. The observed velocity gradients are compared to those obtained from the knowledge of the shear stress across the channel and the flow-curves (stress versus shear rate), the latter being determined in our previous simulations of homogeneous shear flow. Furthermore, using the value of the (dynamic) yield stress known from previous simulations, we estimate the threshold body force for a complete arrest of the flow. Indeed, a blockage is observed as the imposed force falls below this threshold value. Small but finite shear rates are observed at stresses above the dynamic but below the static yield stress. We discuss the possible role of the \blue{stick-slip like motion} for this observation.Comment: 22 pages, 8 figure

Phase Transitions in the Spin-Half J_1--J_2 Model

The coupled cluster method (CCM) is a well-known method of quantum many-body theory, and here we present an application of the CCM to the spin-half J_1--J_2 quantum spin model with nearest- and next-nearest-neighbour interactions on the linear chain and the square lattice. We present new results for ground-state expectation values of such quantities as the energy and the sublattice magnetisation. The presence of critical points in the solution of the CCM equations, which are associated with phase transitions in the real system, is investigated. Completely distinct from the investigation of the critical points, we also make a link between the expansion coefficients of the ground-state wave function in terms of an Ising basis and the CCM ket-state correlation coefficients. We are thus able to present evidence of the breakdown, at a given value of J_2/J_1, of the Marshall-Peierls sign rule which is known to be satisfied at the pure Heisenberg point (J_2 = 0) on any bipartite lattice. For the square lattice, our best estimates of the points at which the sign rule breaks down and at which the phase transition from the antiferromagnetic phase to the frustrated phase occurs are, respectively, given (to two decimal places) by J_2/J_1 = 0.26 and J_2/J_1 = 0.61.Comment: 28 pages, Latex, 2 postscript figure

The beginnings of geography teaching and research in the University of Glasgow: the impact of J.W. Gregory

J.W. Gregory arrived in Glasgow from Melbourne in 1904 to take up the post of foundation Professor of Geology in the University of Glasgow. Soon after his arrival in Glasgow he began to push for the setting up of teaching in Geography in Glasgow, which came to pass in 1909 with the appointment of a Lecturer in Geography. This lecturer was based in the Department of Geology in the University's East Quad. Gregory's active promotion of Geography in the University was matched by his extensive writing in the area, in textbooks, journal articles and popular books. His prodigious output across a wide range of subject areas is variably accepted today, with much of his geomorphological work being judged as misguided to varying degrees. His 'social science' publications - in the areas of race, migration, colonisation and economic development of Africa and Australia - espouse a viewpoint that is unacceptable in the twenty-first century. Nonetheless, that viewpoint sits squarely within the social and economic traditions of Gregory's era, and he was clearly a key 'Establishment' figure in natural and social sciences research in the first half of the twentieth century. The establishment of Geography in the University of Glasgow remains enduring testimony of J.W. Gregory's energy, dedication and foresight

High-Order Coupled Cluster Method (CCM) Calculations for Quantum Magnets with Valence-Bond Ground States

In this article, we prove that exact representations of dimer and plaquette valence-bond ket ground states for quantum Heisenberg antiferromagnets may be formed via the usual coupled cluster method (CCM) from independent-spin product (e.g. N\'eel) model states. We show that we are able to provide good results for both the ground-state energy and the sublattice magnetization for dimer and plaquette valence-bond phases within the CCM. As a first example, we investigate the spin-half $J_1$--$J_2$ model for the linear chain, and we show that we are able to reproduce exactly the dimerized ground (ket) state at $J_2/J_1=0.5$. The dimerized phase is stable over a range of values for $J_2/J_1$ around 0.5. We present evidence of symmetry breaking by considering the ket- and bra-state correlation coefficients as a function of $J_2/J_1$. We then consider the Shastry-Sutherland model and demonstrate that the CCM can span the correct ground states in both the N\'eel and the dimerized phases. Finally, we consider a spin-half system with nearest-neighbor bonds for an underlying lattice corresponding to the magnetic material CaV$_4$O$_9$ (CAVO). We show that we are able to provide excellent results for the ground-state energy in each of the plaquette-ordered, N\'eel-ordered, and dimerized regimes of this model. The exact plaquette and dimer ground states are reproduced by the CCM ket state in their relevant limits.Comment: 34 pages, 13 figures, 2 table

A quantum Peierls-Nabarro barrier

Kink dynamics in spatially discrete nonlinear Klein-Gordon systems is considered. For special choices of the substrate potential, such systems support continuous translation orbits of static kinks with no (classical) Peierls-Nabarro barrier. It is shown that these kinks experience, nevertheless, a lattice-periodic confining potential, due to purely quantum effects anaolgous to the Casimir effect of quantum field theory. The resulting ``quantum Peierls-Nabarro potential'' may be calculated in the weak coupling approximation by a simple and computationally cheap numerical algorithm, which is applied, for purposes of illustration, to a certain two-parameter family of substrates.Comment: 13 pages LaTeX, 7 figure

Statistical Mechanics of Kinks in (1+1)-Dimensions

We investigate the thermal equilibrium properties of kinks in a classical $\phi^4$ field theory in $1+1$ dimensions. The distribution function, kink density, and correlation function are determined from large scale simulations. A dilute gas description of kinks is shown to be valid below a characteristic temperature. A double Gaussian approximation to evaluate the eigenvalues of the transfer operator enables us to extend the theoretical analysis to higher temperatures where the dilute gas approximation fails. This approach accurately predicts the temperature at which the kink description breaks down.Comment: 8 pages, Latex (4 figures available on request), LA-UR-92-399