11,462 research outputs found
The surface-tension-driven evolution of a two-dimensional annular viscous tube
We consider the evolution of an annular two-dimensional region occupied by viscous fluid driven by surface tension and applied pressure at the free surfaces. We assume that the thickness of the domain is small compared with its circumference so that it may be described as a thin viscous sheet whose ends are joined to form a closed loop. Analytical and numerical solutions of the resulting model are obtained and we show that it is well posed whether run forwards or backwards in time. This enables us to determine, in many cases explicitly, which initial shapes will evolve into a desired final shape. We also show how the application of an internal pressure may be used to control the evolution. This work is motivated by the production of non-axisymmetric capillary tubing via the Vello process. Molten glass is fed through a die and drawn off vertically, while the shape of the cross-section evolves under surface tension and any applied pressure as it flows downstream. Here the goal is to determine the die shape required to achieve a given desired final shape, typically square or rectangular. We conclude by discussing the role of our two-dimensional model in describing the three-dimensional tube-drawing process
Mathematical modelling of non-axisymmetric capillary tube drawing
This paper concerns the manufacture of non-axisymmetric capillary tubing via the Velloprocess, in which molten glass is fed through a die and drawn off vertically. The shapeof the cross-section evolves under surface tension as it flows downstream. The aim is to achieve a given desired final shape, typically square or rectangular, and our goal is to determine the required die shape. We use the result that, provided the tube is slowly varying in the axial direction, each cross-section evolves like a two-dimensional Stokes flow when expressed in suitably scaled Lagrangian coordinates. This allows us to use a previously derived model for the surface- tension-driven evolution of a thin two-dimensional viscous tube. We thus obtain, and solve analytically, equations governing the axial velocity, thickness and circumference of the tube, as well as its shape. The model is extended to include non-isothermal effects
An experimental and theoretical investigation of particle–wall impacts in a T-junction
Understanding the behaviour of particles entrained in a fluid flow upon changes in flow direction is crucial in problems where particle inertia is important, such as the erosion process in pipe bends.We present results on the impact of particles in a T-shaped channel in the laminar-turbulent transitional regime. The impacting event for a given system is described in terms of the Reynolds number and the particle Stokes number. Experimental results for the impact are compared with the trajectories predicted by theoretical particle tracing models for a range of configurations to determine the role of the viscous boundary layer in retarding the particles and reducing the rate of collision with the substrate. In particular a 2D model based on a stagnation point flow is used together with 3D numerical simulations. We show how the simple 2D model provides a tractable way of understanding the general collision behaviour, while more advanced 3D simulation can be helpful in understanding the details of the flow
The angular spin current and its physical consequences
We find that in order to completely describe the spin transport, apart from
spin current (or linear spin current), one has to introduce the angular spin
current. The two spin currents respectively describe the translational and
rotational motion of a spin. The definitions of these spin current densities
are given and their physical properties are discussed. Both spin current
densities appear naturally in the spin continuity equation. Moreover we predict
that the angular spin current can also induce an electric field , and
in particular scales as at large distance , whereas the
field generated from the linear spin current goes as .Comment: 7 pages, 2 figure
On the predictions and limitations of the BeckerDoring model for reaction kinetics in micellar surfactant solutions
We investigate the breakdown of a system of micellar aggregates in a surfactant solution following an order-one dilution. We derive a mathematical model based on the Becker–Döring system of equations, using realistic expressions for the reaction constants fit to Molecular Dynamics simulations. We exploit the largeness of typical aggregation numbers to derive a continuum model, substituting a large system of ordinary differential equations for a partial differential equation in two independent variables: time and aggregate size. Numerical solutions demonstrate that re-equilibration occurs in two distinct stages over well-separated time-scales, in agreement with experiment and with previous theories. We conclude by exposing a limitation in the Becker–Döring theory for re-equilibration and discuss potential resolutions
Interaction between U/UO2 bilayers and hydrogen studied by in-situ X-ray diffraction
This paper reports experiments investigating the reaction of H with
uranium metal-oxide bilayers. The bilayers consist of 100 nm of
epitaxial -U (grown on a Nb buffer deposited on sapphire) with a
UO overlayer of thicknesses of between 20 and 80 nm. The oxides were made
either by depositing via reactive magnetron sputtering, or allowing the uranium
metal to oxidise in air at room temperature. The bilayers were exposed to
hydrogen, with sample temperatures between 80 and 200 C, and monitored via
in-situ x-ray diffraction and complimentary experiments conducted using
Scanning Transmission Electron Microscopy - Electron Energy Loss Spectroscopy
(STEM-EELS). Small partial pressures of H caused rapid consumption of the
U metal and lead to changes in the intensity and position of the diffraction
peaks from both the UO overlayers and the U metal. There is an
orientational dependence in the rate of U consumption. From changes in the
lattice parameter we deduce that hydrogen enters both the oxide and metal
layers, contracting the oxide and expanding the metal. The air-grown oxide
overlayers appear to hinder the H-reaction up to a threshold dose, but
then on heating from 80 to 140 C the consumption is more rapid than for the
as-deposited overlayers. STEM-EELS establishes that the U-hydride layer lies at
the oxide-metal interface, and that the initial formation is at defects or
grain boundaries, and involves the formation of amorphous and/or
nanocrystalline UH. This explains why no diffraction peaks from UH
are observed. {\textcopyright British Crown Owned Copyright 2017/AWE}Comment: Submitted for peer revie
Photon-Number-Splitting versus Cloning Attacks in Practical Implementations of the Bennett-Brassard 1984 protocol for Quantum Cryptography
In practical quantum cryptography, the source sometimes produces multi-photon
pulses, thus enabling the eavesdropper Eve to perform the powerful
photon-number-splitting (PNS) attack. Recently, it was shown by Curty and
Lutkenhaus [Phys. Rev. A 69, 042321 (2004)] that the PNS attack is not always
the optimal attack when two photons are present: if errors are present in the
correlations Alice-Bob and if Eve cannot modify Bob's detection efficiency, Eve
gains a larger amount of information using another attack based on a 2->3
cloning machine. In this work, we extend this analysis to all distances
Alice-Bob. We identify a new incoherent 2->3 cloning attack which performs
better than those described before. Using it, we confirm that, in the presence
of errors, Eve's better strategy uses 2->3 cloning attacks instead of the PNS.
However, this improvement is very small for the implementations of the
Bennett-Brassard 1984 (BB84) protocol. Thus, the existence of these new attacks
is conceptually interesting but basically does not change the value of the
security parameters of BB84. The main results are valid both for Poissonian and
sub-Poissonian sources.Comment: 11 pages, 5 figures; "intuitive" formula (31) adde
Boson stars and oscillatons in an inflationary universe
Spherically symmetric gravitationally bound, oscillating scalar lumps (boson
stars and oscillatons) are considered in Einstein's gravity coupled to massive
scalar fields in 1+D dimensional de Sitter-type inflationary space-times. We
show that due to inflation bosons stars and oscillatons lose mass through
scalar radiation, but at a rate that is exponentially small when the expansion
rate is slow.Comment: 19 pages, 5 figure
An asymptotic theory for the re-equilibration of a micellar surfactant solution
Micellar surfactant solutions are characterized by a distribution of aggregates comprised predominantly of pre-micellar aggregates (monomers, dimers, trimers, etc.) and a region of proper micelles close to the peak aggregation number, connected by an intermediate region containing a very low concentration of aggregates. Such a distribution gives rise to a distinct two-timescale re-equilibration following a system dilution, known as the 1 and 2 processes, whose dynamics may be described by the Becker–Döring equations. We use a continuum version of these equations to develop a reduced asymptotic description that elucidates the behavior during each of these processes
P,T-Violating Nuclear Matrix Elements in the One-Meson Exchange Approximation
Expressions for the P,T-violating NN potentials are derived for ,
and exchange. The nuclear matrix elements for and
exchange are shown to be greatly suppressed, so that, under the assumption of
comparable coupling constants, exchange would dominate by two orders of
magnitude. The ratio of P,T-violating to P-violating matrix elements is found
to remain approximately constant across the nuclear mass table, thus
establishing the proportionality between time-reversal-violation and
parity-violation matrix elements. The calculated values of this ratio suggest a
need to obtain an accuracy of order for the ratio of the
PT-violating to P-violating asymmetries in neutron transmission experiments in
order to improve on the present limits on the isovector pion coupling constant.Comment: 17 pages, LaTeX, no figure
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