2,624 research outputs found
Evidence from Rb–Sr mineral ages for multiple orogenic events in the Caledonides of Shetland, Scotland
Shetland occupies a unique central location within the North Atlantic Caledonides. Thirty-three new high-precision Rb–Sr mineral ages indicate a polyorogenic history. Ages of 723–702 Ma obtained from the vicinity of the Wester Keolka Shear Zone indicate a Neoproterozoic (Knoydartian) age and preclude its correlation with the Silurian Moine Thrust. Ordovician ages of c. 480–443 Ma obtained from the Yell Sound Group and the East Mainland Succession constrain deformation fabrics and metamorphic assemblages to have formed during Grampian accretionary orogenic events, broadly contemporaneously with orogenesis of the Dalradian Supergroup in Ireland and mainland Scotland. The relative paucity of Silurian ages is attributed to a likely location at a high structural level in the Scandian nappe pile relative to mainland Scotland. Ages of c. 416 and c. 411 Ma for the Uyea Shear Zone suggest a late orogenic evolution that has more in common with East Greenland and Norway than with northern mainland Scotland
Non equilibrium effects in fragmentation
We study, using molecular dynamics techniques, how boundary conditions affect
the process of fragmentation of finite, highly excited, Lennard-Jones systems.
We analyze the behavior of the caloric curves (CC), the associated thermal
response functions (TRF) and cluster mass distributions for constrained and
unconstrained hot drops. It is shown that the resulting CC's for the
constrained case differ from the one in the unconstrained case, mainly in the
presence of a ``vapor branch''. This branch is absent in the free expanding
case even at high energies . This effect is traced to the role played by the
collective expansion motion. On the other hand, we found that the recently
proposed characteristic features of a first order phase transition taking place
in a finite isolated system, i.e. abnormally large kinetic energy fluctuations
and a negative branch in the TRF, are present for the constrained (dilute) as
well the unconstrained case. The microscopic origin of this behavior is also
analyzed.Comment: 21 pages, 11 figure
The dispersive self-dual Einstein equations and the Toda lattice
The Boyer-Finley equation, or -Toda equation is both a reduction
of the self-dual Einstein equations and the dispersionlesslimit of the
-Toda lattice equation. This suggests that there should be a dispersive
version of the self-dual Einstein equation which both contains the Toda lattice
equation and whose dispersionless limit is the familiar self-dual Einstein
equation. Such a system is studied in this paper. The results are achieved by
using a deformation, based on an associative -product, of the algebra
used in the study of the undeformed, or dispersionless,
equations.Comment: 11 pages, LaTeX. To appear: J. Phys.
Multilevel regression modelling to investigate variation in disease prevalence across locations
In this article, we show how to investigate the role of individual (personal) risk factors in outcome prevalence in multicentre studies with multilevel modelling. The variation in outcome prevalence is modelled by introducing a random intercept. In the next step, the empty model is compared with the model containing the risk factor(s). Because the outcome is dichotomous, this comparison can only be carried out after having rescaled the models’ parameter values to the variance of an underlying continuous variable. We illustrate this approach with data from Phase Two of the International Study of Asthma and Allergies in Childhood (ISAAC) and provide a corresponding Stata do-file
The algebraic and Hamiltonian structure of the dispersionless Benney and Toda hierarchies
The algebraic and Hamiltonian structures of the multicomponent dispersionless
Benney and Toda hierarchies are studied. This is achieved by using a modified
set of variables for which there is a symmetry between the basic fields. This
symmetry enables formulae normally given implicitly in terms of residues, such
as conserved charges and fluxes, to be calculated explicitly. As a corollary of
these results the equivalence of the Benney and Toda hierarchies is
established. It is further shown that such quantities may be expressed in terms
of generalized hypergeometric functions, the simplest example involving
Legendre polynomials. These results are then extended to systems derived from a
rational Lax function and a logarithmic function. Various reductions are also
studied.Comment: 29 pages, LaTe
Hydrodynamic reductions of the heavenly equation
We demonstrate that Pleba\'nski's first heavenly equation decouples in
infinitely many ways into a triple of commuting (1+1)-dimensional systems of
hydrodynamic type which satisfy the Egorov property. Solving these systems by
the generalized hodograph method, one can construct exact solutions of the
heavenly equation parametrized by arbitrary functions of a single variable. We
discuss explicit examples of hydrodynamic reductions associated with the
equations of one-dimensional nonlinear elasticity, linearly degenerate systems
and the equations of associativity.Comment: 14 page
Effective temperatures in a simple model of non-equilibrium, non-Markovian dynamics
The concept of effective temperatures in nonequilibrium systems is studied
within an exactly solvable model of non-Markovian diffusion. The system is
coupled to two heat baths which are kept at different temperatures: one
('fast') bath associated with an uncorrelated Gaussian noise and a second
('slow') bath with an exponential memory kernel. Various definitions of
effective temperatures proposed in the literature are evaluated and compared.
The range of validity of these definitions is discussed. It is shown in
particular, that the effective temperature defined from the
fluctuation-dissipation relation mirrors the temperature of the slow bath in
parameter regions corresponding to a separation of time scales. On the
contrary, quasi-static and thermodynamic definitions of an effective
temperature are found to display the temperature of the fast bath in most
parameter regions
The Moyal bracket and the dispersionless limit of the KP hierarchy
A new Lax equation is introduced for the KP hierarchy which avoids the use of
pseudo-differential operators, as used in the Sato approach. This Lax equation
is closer to that used in the study of the dispersionless KP hierarchy, and is
obtained by replacing the Poisson bracket with the Moyal bracket. The
dispersionless limit, underwhich the Moyal bracket collapses to the Poisson
bracket, is particularly simple.Comment: 9 pages, LaTe
Hypercomplex Integrable Systems
In this paper we study hypercomplex manifolds in four dimensions. Rather than
using an approach based on differential forms, we develop a dual approach using
vector fields. The condition on these vector fields may then be interpreted as
Lax equations, exhibiting the integrability properties of such manifolds. A
number of different field equations for such hypercomplex manifolds are
derived, one of which is in Cauchy-Kovaleskaya form which enables a formal
general solution to be given. Various other properties of the field equations
and their solutions are studied, such as their symmetry properties and the
associated hierarchy of conservation laws.Comment: Latex file, 19 page
On the B\"acklund Transformation for the Moyal Korteweg-de Vries Hierarchy
We study the B\"acklund symmetry for the Moyal Korteweg-de Vries (KdV)
hierarchy based on the Kuperschmidt-Wilson Theorem associated with second
Gelfand-Dickey structure with respect to the Moyal bracket, which generalizes
the result of Adler for the ordinary KdV.Comment: 9 pages, Revte
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