Determinism in the one-way model

We introduce a flow condition on open graph states (graph states with inputs and outputs) which guarantees globally deterministic behavior of a class of measurement patterns defined over them. Dependent Pauli corrections are derived for all such patterns, which equalize all computation branches, and only depend on the underlying entanglement graph and its choice of inputs and outputs. The class of patterns having flow is stable under composition and tensorization, and has unitary embeddings as realizations. The restricted class of patterns having both flow and reverse flow, supports an operation of adjunction, and has all and only unitaries as realizations.Comment: 8 figures, keywords: measurement based quantum computing, deterministic computing; Published version, including a new section on circuit decompositio

Direct velocity measurement of a turbulent shear flow in a planar Couette cell

In a plane Couette cell a thin fluid layer consisting of water is sheared between a transparent band at Reynolds numbers ranging from 300 to 1400. The length of the cells flow channel is large compared to the film separation. To extract the flow velocity in the experiments a correlation image velocimetry (CIV) method is used on pictures recorded with a high speed camera. The flow is recorded at a resolution that allows to analyze flow patterns similar in size to the film separation. The fluid flow is then studied by calculating flow velocity autocorrelation functions. The turbulent pattern that arise on this scale above a critical Reynolds number of Re=360 display characteristic patterns that are proven with the calculated velocity autocorrelation functions. The patterns are metastable and reappear at different positions and times throughout the experiments. Typically these patterns are turbulent rolls which are elongated in the stream direction which is the direction the band is moving. Although the flow states are metastable they possess similarities to the steady Taylor vortices known to appear in circular Taylor Couette cells

Magnetic fields and flows between 1 AU and 0.3 AU during the primary mission of HELIOS 1

The recurrent flow and field patterns observed by HELIOS 1, and the relation between these patterns and coronal holes are discussed. Four types of recurrent patterns were observed: a large recurrent stream, a recurrent slow (quiet) flow, a rapidly evolving flow, and a recurrent compound stream. There recurrent streams were not stationary, for although the sources recurred at approximately the same longitudes on successive rotations, the shapes and latitudinal patterns changed from one rotation to the next. A type of magnetic field and plasma structure characterized by a low ion temperature and a high magnetic field intensity is described as well as the structures of stream boundaries between the sun at approximately 0.3 AU

Principal Flow Patterns across renewable electricity networks

Using Principal Component Analysis (PCA), the nodal injection and line flow patterns in a network model of a future highly renewable European electricity system are investigated. It is shown that the number of principal components needed to describe 95$\%$ of the nodal power injection variance first increases with the spatial resolution of the system representation. The number of relevant components then saturates at around 76 components for network sizes larger than 512 nodes, which can be related to the correlation length of wind patterns over Europe. Remarkably, the application of PCA to the transmission line power flow statistics shows that irrespective of the spatial scale of the system representation a very low number of only 8 principal flow patterns is sufficient to capture 95$\%$ of the corresponding spatio-temporal variance. This result can be theoretically explained by a particular alignment of some principal injection patterns with topological patterns inherent to the network structure of the European transmission system

Self-organised droplet flow patterns in microchannels

This paper was presented at the 2nd Micro and Nano Flows Conference (MNF2009), which was held at Brunel University, West London, UK. The conference was organised by Brunel University and supported by the Institution of Mechanical Engineers, IPEM, the Italian Union of Thermofluid dynamics, the Process Intensification Network, HEXAG - the Heat Exchange Action Group and the Institute of Mathematics and its Applications.In this work, we have investigated the generation and behaviour of self-organised droplet flow patterns in microchannels. The water droplets, which are generated at a T-junction where the carrier is oil, move into an expanded channel and are self reorganised into various flow patterns: single-profile, double-helix-profile, triple-helix-profile, and more. We find that increasing water/oil flow rate ratio and Capillary number lead to more densely packed droplet flow patterns. The channel geometry also plays an essential role where the 300-μm-deep expansion channel can form multiple layers of droplets while only single layer of droplets can be observed in the 200-μm-deep expansion channel

Analysis of Kolmogorov Flow and Rayleigh-B\'enard Convection using Persistent Homology

We use persistent homology to build a quantitative understanding of large complex systems that are driven far-from-equilibrium; in particular, we analyze image time series of flow field patterns from numerical simulations of two important problems in fluid dynamics: Kolmogorov flow and Rayleigh-B\'enard convection. For each image we compute a persistence diagram to yield a reduced description of the flow field; by applying different metrics to the space of persistence diagrams, we relate characteristic features in persistence diagrams to the geometry of the corresponding flow patterns. We also examine the dynamics of the flow patterns by a second application of persistent homology to the time series of persistence diagrams. We demonstrate that persistent homology provides an effective method both for quotienting out symmetries in families of solutions and for identifying multiscale recurrent dynamics. Our approach is quite general and it is anticipated to be applicable to a broad range of open problems exhibiting complex spatio-temporal behavior

Two-phase flow patterns in turbulent flow through a dose diffusion pipe

A numerical investigation is carried out for turbulent particle-laden flow through a dose diffusion pipe for a model reactor system. A Lagrangian Stochastic Monte-Carlo particle-tracking approach and the averaged Reynolds equations with a k-e turbulence model, with a two-layer zonal method in the boundary layer, are used for the disperse and continuous phases. The flow patterns coupled with the particle dynamics are predicted. It is observed that the coupling of the continuous phase with the particle dynamics is important in this case. It was found that the geometry of the throat significantly influences the particle distribution, flow patterns and length of the recirculation region. The accuracy of the simulations depends on the numerical prediction and correction of the fluid phase velocity during a characteristic time interval of the particles. A numerical solution strategy for the computation of two-way momentum coupled flow is discussed. The three test cases show different flow features in the formation of a recirculation region behind the throat. The method will be useful for the qualitative analysis of conceptual designs and their optimisation