826 research outputs found
Linearization of nonlinear connections on vector and affine bundles, and some applications
A linear connection is associated to a nonlinear connection on a vector
bundle by a linearization procedure. Our definition is intrinsic in terms of
vector fields on the bundle. For a connection on an affine bundle our procedure
can be applied after homogenization and restriction. Several applications in
Classical Mechanics are provided
The Berwald-type linearisation of generalised connections
We study the existence of a natural `linearisation' process for generalised
connections on an affine bundle. It is shown that this leads to an affine
generalised connection over a prolonged bundle, which is the analogue of what
is called a connection of Berwald type in the standard theory of connections.
Various new insights are being obtained in the fine structure of affine bundles
over an anchored vector bundle and affineness of generalised connections on
such bundles.Comment: 25 page
Mode doubling and tripling in reaction-diffusion patterns on growing domains: A piece-wise linear model
Reaction-diffusion equations are ubiquitous as models of biological pattern formation. In a recent paper [4] we have shown that incorporation of domain growth in a reaction-diffusion model generates a sequence of quasi-steady patterns and can provide a mechanism for increased reliability of pattern selection. In this paper we analyse the model to examine the transitions between patterns in the sequence. Introducing a piecewise linear approximation we find closed form approximate solutions for steady-state patterns by exploiting a small parameter, the ratio of diffusivities, in a singular perturbation expansion. We consider the existence of these steady-state solutions as a parameter related to the domain length is varied and predict the point at which the solution ceases to exist, which we identify with the onset of transition between patterns for the sequence generated on the growing domain. Applying these results to the model in one spatial dimension we are able to predict the mechanism and timing of transitions between quasi-steady patterns in the sequence. We also highlight a novel sequence behaviour, mode-tripling, which is a consequence of a symmetry in the reaction term of the reaction-diffusion system
Lifetimes of electrons in the Shockley surface state band of Ag(111)
We present a theoretical many-body analysis of the electron-electron (e-e)
inelastic damping rate of electron-like excitations in the Shockley
surface state band of Ag(111). It takes into account ab-initio band structures
for both bulk and surface states. is found to increase more rapidly as
a function of surface state energy E than previously reported, thus leading to
an improved agreement with experimental data
Should haemoglobin A1C be used for diagnosis of diabetes mellitus in Malawi?
No abstract available
Stability analysis of non-autonomous reaction-diffusion systems: the effects of growing domains
By using asymptotic theory, we generalise the Turing diffusively-driven instability conditions for reaction-diffusion systems with slow, isotropic domain growth. There are two fundamental biological differences between the Turing conditions on fixed and growing domains, namely: (i) we need not enforce cross nor pure kinetic conditions and (ii) the restriction to activator-inhibitor kinetics to induce pattern formation on a growing biological system is no longer a requirement. Our theoretical findings are confirmed and reinforced by numerical simulations for the special cases of isotropic linear, exponential and logistic growth profiles. In particular we illustrate an example of a reaction-diffusion system which cannot exhibit a diffusively-driven instability on a fixed domain but is unstable in the presence of slow growth
Lifetimes of Shockley electrons and holes at the Cu(111) surface
A theoretical many-body analysis is presented of the electron-electron
inelastic lifetimes of Shockley electrons and holes at the (111) surface of Cu.
For a description of the decay of Shockley states both below and above the
Fermi level, single-particle wave functions have been obtained by solving the
Schr\"odinger equation with the use of an approximate one-dimensional
pseudopotential fitted to reproduce the correct bulk energy bands and
surface-state dispersion. A comparison with previous calculations and
experiment indicates that inelastic lifetimes are very sensitive to the actual
shape of the surface-state single-particle orbitals beyond the
() point, which controls the coupling between the Shockley
electrons and holes.Comment: 4 pages, 3 figures, to appear in Phys. Rev.
Feynman problem in the noncommutative case
In the context of the Feynman's derivation of electrodynamics, we show that
noncommutativity allows other particle dynamics than the standard formalism of
electrodynamics.Comment: latex, 7 pages, no figure
Driven cofactor systems and Hamilton-Jacobi separability
This is a continuation of the work initiated in a previous paper on so-called
driven cofactor systems, which are partially decoupling second-order
differential equations of a special kind. The main purpose in that paper was to
obtain an intrinsic, geometrical characterization of such systems, and to
explain the basic underlying concepts in a brief note. In the present paper we
address the more intricate part of the theory. It involves in the first place
understanding all details of an algorithmic construction of quadratic integrals
and their involutivity. It secondly requires explaining the subtle way in which
suitably constructed canonical transformations reduce the Hamilton-Jacobi
problem of the (a priori time-dependent) driven part of the system into that of
an equivalent autonomous system of St\"ackel type
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