517 research outputs found
Angular dependence of domain wall resistivity in artificial magnetic domain structures
We exploit the ability to precisely control the magnetic domain structure of
perpendicularly magnetized Pt/Co/Pt trilayers to fabricate artificial domain
wall arrays and study their transport properties. The scaling behaviour of this
model system confirms the intrinsic domain wall origin of the
magnetoresistance, and systematic studies using domains patterned at various
angles to the current flow are excellently described by an angular-dependent
resistivity tensor containing perpendicular and parallel domain wall
resistivities. We find that the latter are fully consistent with Levy-Zhang
theory, which allows us to estimate the ratio of minority to majority spin
carrier resistivities, rho-down/rho-up~5.5, in good agreement with thin film
band structure calculations.Comment: 14 pages, 3 figure
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
Twistor geometry of a pair of second order ODEs
We discuss the twistor correspondence between path geometries in three
dimensions with vanishing Wilczynski invariants and anti-self-dual conformal
structures of signature . We show how to reconstruct a system of ODEs
with vanishing invariants for a given conformal structure, highlighting the
Ricci-flat case in particular. Using this framework, we give a new derivation
of the Wilczynski invariants for a system of ODEs whose solution space is
endowed with a conformal structure. We explain how to reconstruct the conformal
structure directly from the integral curves, and present new examples of
systems of ODEs with point symmetry algebra of dimension four and greater which
give rise to anti--self--dual structures with conformal symmetry algebra of the
same dimension. Some of these examples are analogues of plane wave
space--times in General Relativity. Finally we discuss a variational principle
for twistor curves arising from the Finsler structures with scalar flag
curvature.Comment: Final version to appear in the Communications in Mathematical
Physics. The procedure of recovering a system of torsion-fee ODEs from the
heavenly equation has been clarified. The proof of Prop 7.1 has been
expanded. Dedicated to Mike Eastwood on the occasion of his 60th birthda
From kitchen to classroom: Assessing the impact of cleaner burning biomass-fuelled cookstoves on primary school attendance in Karonga district, northern Malawi
Household air pollution from burning solid fuels is responsible for an estimated 2.9 million premature deaths worldwide each year and 4.5% of global disability-adjusted life years, while cooking and fuel collection pose a considerable time burden, particularly for women and children. Cleaner burning biomass-fuelled cookstoves have the potential to lower exposure to household air pollution as well as reduce fuelwood demand by increasing the combustion efficiency of cooking fires, which may in turn yield ancillary benefits in other domains. The present paper capitalises on opportunities offered by the Cooking and Pneumonia Study (CAPS), the largest randomised trial of biomass-fuelled cookstoves on health outcomes conducted to date, the design of which allows for the evaluation of additional outcomes at scale. This mixed methods study assesses the impact of cookstoves on primary school absenteeism in Karonga district, northern Malawi, in particular by conferring health and time and resource gains on young people aged 5–18. The analysis combines quantitative data from 6168 primary school students with in-depth interviews and focus group discussions carried out among 48 students in the same catchment area in 2016. Negative binomial regression models find no evidence that the cookstoves affected primary school absenteeism overall [IRR 0.92 (0.71–1.18), p = 0.51]. Qualitative analysis suggests that the cookstoves did not sufficiently improve household health to influence school attendance, while the time and resource burdens associated with cooking activities—although reduced in intervention households—were considered to be compatible with school attendance in both trial arms. More research is needed to assess whether the cookstoves influenced educational outcomes not captured by the attendance measure available, such as timely arrival to school or hours spent on homework
Differential Calculi on Associative Algebras and Integrable Systems
After an introduction to some aspects of bidifferential calculus on
associative algebras, we focus on the notion of a "symmetry" of a generalized
zero curvature equation and derive Backlund and (forward, backward and binary)
Darboux transformations from it. We also recall a matrix version of the binary
Darboux transformation and, inspired by the so-called Cauchy matrix approach,
present an infinite system of equations solved by it. Finally, we sketch recent
work on a deformation of the matrix binary Darboux transformation in
bidifferential calculus, leading to a treatment of integrable equations with
sources.Comment: 19 pages, to appear in "Algebraic Structures and Applications", S.
Silvestrov et al (eds.), Springer Proceedings in Mathematics & Statistics,
202
Higher-order Abel equations: Lagrangian formalism, first integrals and Darboux polynomials
A geometric approach is used to study a family of higher-order nonlinear Abel
equations. The inverse problem of the Lagrangian dynamics is studied in the
particular case of the second-order Abel equation and the existence of two
alternative Lagrangian formulations is proved, both Lagrangians being of a
non-natural class (neither potential nor kinetic term). These higher-order Abel
equations are studied by means of their Darboux polynomials and Jacobi
multipliers. In all the cases a family of constants of the motion is explicitly
obtained. The general n-dimensional case is also studied
Scattering Theory of Kondo Mirages and Observation of Single Kondo Atom Phase Shift
We explain the origin of the Kondo mirage seen in recent quantum corral
Scanning Tunneling Microscope (STM) experiments with a scattering theory of
electrons on the surfaces of metals. Our theory combined with experimental data
provides the first direct observation of a single Kondo atom phase shift. The
Kondo mirage at the empty focus of an elliptical quantum corral is shown to
arise from multiple electron bounces off the walls of the corral in a manner
analagous to the formation of a real image in optics. We demonstrate our theory
with direct quantitive comparision to experimental data.Comment: 13 pages; significant clarifications of metho
Soliton equations and the zero curvature condition in noncommutative geometry
Familiar nonlinear and in particular soliton equations arise as zero
curvature conditions for GL(1,R) connections with noncommutative differential
calculi. The Burgers equation is formulated in this way and the Cole-Hopf
transformation for it attains the interpretation of a transformation of the
connection to a pure gauge in this mathematical framework. The KdV, modified
KdV equation and the Miura transformation are obtained jointly in a similar
setting and a rather straightforward generalization leads to the KP and a
modified KP equation.
Furthermore, a differential calculus associated with the Boussinesq equation
is derived from the KP calculus.Comment: Latex, 10 page
A class of Poisson-Nijenhuis structures on a tangent bundle
Equipping the tangent bundle TQ of a manifold with a symplectic form coming
from a regular Lagrangian L, we explore how to obtain a Poisson-Nijenhuis
structure from a given type (1,1) tensor field J on Q. It is argued that the
complete lift of J is not the natural candidate for a Nijenhuis tensor on TQ,
but plays a crucial role in the construction of a different tensor R, which
appears to be the pullback under the Legendre transform of the lift of J to
co-tangent manifold of Q. We show how this tangent bundle view brings new
insights and is capable also of producing all important results which are known
from previous studies on the cotangent bundle, in the case that Q is equipped
with a Riemannian metric. The present approach further paves the way for future
generalizations.Comment: 22 page
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