44,173 research outputs found
Observations on Unstable Quantons, Hyperplane Dependence and Quantum Fields
There is persistent heterodoxy in the physics literature concerning the
proper treatment of those quantons that are unstable against spontaneous decay.
Following a brief litany of this heterodoxy, I develop some of the consequences
of assuming that such quantons can exist, undecayed and isolated, at definite
times and that their treatment can be carried out within a standard quantum
theoretic state space. This assumption requires hyperplane dependence for the
unstable quanton states and leads to clarification of some recent results
concerning deviations from relativistic time dilation of decay lifetimes. In
the course of the discussion I make some observations on the relationship of
unstable quantons to quantum fields.Comment: 29 pages, 4 figures, revised with added references, section 4 revise
On the Quantum Deviations from Einstein Dilation of Unstable Quanton Decay Evolution and Lifetimes
For over a decade several workers have argued for the existence of quantum
deviations from the classical, Einstein dilation of the decay evolution of
moving or Lorentz boosted unstable particles. While the general claim is
correct, the discussions have been incomplete and, sometimes, misleading. The
discussions have been of three kinds. Type 1 examines the time dependence of
the survival probability for 3-momentum eigenstates of the unstable quanton
(Khalfin). Type 2 does the same for velocity eigenstates, obtaining an
outrageous result which then discredits velocity eigenstates (Shirokov /
Hegerfeldt). Type 3 examines arbitrary boosts of 3-momentum eigenstates
(Stefanovich). Type 1 is incomplete since the momentum eigenstates are not the
boosts of one another. Type 2 is misleading since the outrageous result is due
to misinterpreting the initial conditions of the velocity eigenstates (as I
have previously argued). Type 3 is the most satisfactory, but has failed to
recognize and implement the unification of all three types of discussion that
can be achieved. In this paper I will provide that unified treatment, beginning
with a recapitulation of Type 1 and offering further clarification of Type 2 in
the process. The unified treatment fully reinstates velocity eigenstates as
essential contributors to unstable quanton states. Besides discussing the time
evolution of survival probabilities I also focus on the concept of lifetime
defined as the average time of decay. This quantity is helpful in order to
display the inequivalent dependence of dilation on momentum and boosts most
sharply and the deviation from Einstein dilation most cleanly.Comment: 40 pages, 2 figure
Key lessons from the RESET programme: Recommendations for the resettlement of young offenders
Reoffending rates for young offenders released from custody are high. Of approximately 6000 young people sentenced to custody each year, between 70% and 90% will reoffend within 12 months. Effective resettlement is vital to achieving better outcomes. RESET was a major experimental project led by Catch 22 and funded by European Equal, designed to improve outcomes.
This executive briefing summarises the findings from the evaluation of RESET by CSR-Salford and ARCS UK. It explores lessons for mainstream resettlement support, making key recommendations about: coordinating resources and staff, making local partnerships, preparing young people for release, and communication and information flow between custody and community. It concludes that successful resettlement crucially requires: (1) widespread partnership coordination to address offenders' multiple needs; and (2) effective cooperation between custodial institutions and community agencies to ensure preparedness for release
Hydrodynamic instability in warped astrophysical discs
Warped astrophysical discs are usually treated as laminar viscous flows,
which have anomalous properties when the disc is nearly Keplerian and the
viscosity is small: fast horizontal shearing motions and large torques are
generated, which cause the warp to evolve rapidly, in some cases at a rate that
is inversely proportional to the viscosity. However, these flows are often
subject to a linear hydrodynamic instability, which may produce small-scale
turbulence and modify the large-scale dynamics of the disc. We use a warped
shearing sheet to compute the oscillatory laminar flows in a warped disc and to
analyse their linear stability by the Floquet method. We find widespread
hydrodynamic instability deriving from the parametric resonance of inertial
waves. Even very small, unobservable warps in nearly Keplerian discs of low
viscosity can be expected to generate hydrodynamic turbulence, or at least wave
activity, by this mechanism.Comment: 17 pages, 7 figures, revised version, to be published in MNRA
The linear stability of dilute particulate rings
Irregular structure in planetary rings is often attributed to the intrinsic
instabilities of a homogeneous state undergoing Keplerian shear. Previously
these have been analysed with simple hydrodynamic models. We instead employ a
kinetic theory, in which we solve the linearised moment equations derived in
Shu and Stewart 1985 for a dilute ring. This facilitates an examination of
velocity anisotropy and non-Newtonian stress, and their effects on the viscous
and viscous/gravitational instabilities thought to occur in Saturn's rings.
Because we adopt a dilute gas model, the applicability of our results to the
actual dense rings of Saturn are significantly curtailled. Nevertheless this
study is a necessary preliminary before an attack on the difficult problem of
dense ring dynamics. We find the Shu and Stewart formalism admits analytic
stability criteria for the viscous overstability, viscous instability, and
thermal instability. These criteria are compared with those of a hydrodynamic
model incorporating the effective viscosity and cooling function computed from
the kinetic steady state. We find the two agree in the `hydrodynamic limit'
(i.e. many collisions per orbit) but disagree when collisions are less
frequent, when we expect the viscous stress to be increasingly non-Newtonian
and the velocity distribution increasingly anisotropic. In particular,
hydrodynamics predicts viscous overstability for a larger portion of parameter
space. We also numerically solve the linearised equations of the more accurate
Goldreich and Tremaine 1978 kinetic model and discover its linear stability to
be qualitatively the same as that of Shu and Stewart's. Thus the simple
collision operator adopted in the latter would appear to be an adequate
approximation for dilute rings, at least in the linear regime
Viscous overstability and eccentricity evolution in three-dimensional gaseous discs
We investigate the growth or decay rate of the fundamental mode of even
symmetry in a viscous accretion disc. This mode occurs in eccentric discs and
is known to be potentially overstable. We determine the vertical structure of
the disc and its modes, treating radiative energy transport in the diffusion
approximation. In the limit of very long radial wavelength, an analytical
criterion for viscous overstability is obtained, which involves the effective
shear and bulk viscosity, the adiabatic exponent and the opacity law of the
disc. This differs from the prediction of a two-dimensional model. On shorter
wavelengths (a few times the disc thickness), the criterion for overstability
is more difficult to satisfy because of the different vertical structure of the
mode. In a low-viscosity disc a third regime of intermediate wavelengths
appears, in which the overstability is suppressed as the horizontal velocity
perturbations develop significant vertical shear. We suggest that this effect
determines the damping rate of eccentricity in protoplanetary discs, for which
the long-wavelength analysis is inapplicable and overstability is unlikely to
occur on any scale. In thinner accretion discs and in decretion discs around Be
stars overstability may occur only on the longest wavelengths, leading to the
preferential excitation of global eccentric modes.Comment: 11 pages, 8 figure
Local and global dynamics of warped astrophysical discs
Astrophysical discs are warped whenever a misalignment is present in the
system, or when a flat disc is made unstable by external forces. The evolution
of the shape and mass distribution of a warped disc is driven not only by
external influences but also by an internal torque, which transports angular
momentum through the disc. This torque depends on internal flows driven by the
oscillating pressure gradient associated with the warp, and on physical
processes operating on smaller scales, which may include instability and
turbulence. We introduce a local model for the detailed study of warped discs.
Starting from the shearing sheet of Goldreich & Lynden-Bell, we impose the
oscillating geometry of the orbital plane by means of a coordinate
transformation. This warped shearing sheet (or box) is suitable for analytical
and computational treatments of fluid dynamics, magnetohydrodynamics, etc., and
it can be used to compute the internal torque that drives the large-scale
evolution of the disc. The simplest hydrodynamic states in the local model are
horizontally uniform laminar flows that oscillate at the orbital frequency.
These correspond to the nonlinear solutions for warped discs found in previous
work by Ogilvie, and we present an alternative derivation and generalization of
that theory. In a companion paper we show that these laminar flows are often
linearly unstable, especially if the disc is nearly Keplerian and of low
viscosity. The local model can be used in future work to determine the
nonlinear outcome of the hydrodynamic instability of warped discs, and its
interaction with others such as the magnetorotational instability.Comment: 17 pages, 10 figures, revised version, to be published in MNRA
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