1,843 research outputs found
Regression-based variance reduction approach for strong approximation schemes
In this paper we present a novel approach towards variance reduction for
discretised diffusion processes. The proposed approach involves specially
constructed control variates and allows for a significant reduction in the
variance for the terminal functionals. In this way the complexity order of the
standard Monte Carlo algorithm () can be reduced down to
in case of the Euler
scheme with being the precision to be achieved. These theoretical
results are illustrated by several numerical examples.Comment: arXiv admin note: text overlap with arXiv:1510.0314
Learning to change: Climate action pedagogy
This article considers higher education’s role in climate crisis, reflecting on the potential of action-oriented pedagogy. As a reflection on practice, the authors consider a new postgraduate course, Climate Crisis and Action (CCA), launched in 2022 as one of a suite of new courses using inside-out pedagogy in one of the oldest (and most recently holistically redesigned) Master of Environmental Management (MEM) programs in Australia, at the University of New South Wales (UNSW). Over ten weeks, while building foundational climate literacy underscored by imperatives of justice and education, CCA prioritises student leadership, active citizenship, and professional agency for real-world impact. We detail four key elements of the course design: 1) repositioning the course convenor as academic-facilitator to empower students to see climate crisis as a shared challenge addressed through joint contribution, 2) establishing an atmosphere of collective intelligence, shared accountability, and affect-based learning, 3) designing assessments that embed solutions and pedagogy to position students as climate innovators and educators, and 4) providing leadership opportunities in real-time to support students to experience their own growing expertise and professional agency. The approach reflects two motivations: to engage students with the immediacy and urgency of climate crisis, and to extend the core function of teaching academics to support real-world problem solving, social innovation and societal transformation
Finite nuclear size effect on Lamb shift of s1/2, p1/2, and p3/2 atomic states
We consider one-loop self-energy and vacuum polarization radiative
corrections to the shift of atomic energy level due to finite nuclear size.
Analytic expressions for vacuum polarization corrections are derived. For the
self-energy of p1/2 and p3/2 states in addition to already known terms we
derive next-to-leading nonlogarithmic Z\alpha-terms. Together with
contributions obtained earlier the terms derived in the present work give
explicit analytic expressions for s1/2 and p1/2 corrections which agree with
results of previous numerical calculations up to Z=100 (Z is the nuclear charge
number). We also show that the finite nuclear size radiative correction for a
p3/2 state is not small compared to the similar correction for a p1/2 state at
least for small Z.Comment: 12 pages, 7 figure
Local spin spirals in the Neel phase of La_{2-x}Sr_xCuO_4
Experimental observations of lightly doped La_{2-x}Sr_xCuO_4, x < 0.02,
revealed remarkable magnetic properties such as the incommensurate noncollinear
ordering (additional to the Neel ordering) and a tremendous doping dependence
of the uniform longitudinal susceptibility. We show that the spiral solution of
the t-t'-t''-J model obtained by taking into account the Coulomb trapping of
holes by Sr ions describes these puzzling data perfectly well. Our solution
firstly explains why the incommensurate structure is directed along the
orthorhombic b-axis, and secondly allows a numerical calculation of the
positions and shapes of the incommensurate neutron scattering peaks. Thirdly,
we calculate the doping dependence of the spin-wave gap, and lastly, we study
the longitudinal magnetic susceptibility and show that its doping dependence is
due to the noncollinearity of the spin spiral.Comment: 13 pages, 8 figure
Finite nuclear size and Lamb shift of p-wave atomic states
We consider corrections to the Lamb shift of p-wave atomic states due to the
finite nuclear size (FNS). In other words, these are radiative corrections to
the atomic isotop shift related to FNS. It is shown that the structure of the
corrections is qualitatively different from that for s-wave states. The
perturbation theory expansion for the relative correction for a -state
starts from -term, while for -states it starts
from term. Here is the fine structure constant and is
the nuclear charge. In the present work we calculate the -terms for
-states, the result for -state reads
. Even more interesting are
-states. In this case the ``correction'' is by several orders of
magnitude larger than the ``leading'' FNS shift.Comment: 4 pages, 2 figure
Corrections to deuterium hyperfine structure due to deuteron excitations
We consider the corrections to deuterium hyperfine structure originating from
the two-photon exchange between electron and deuteron, with the deuteron
excitations in the intermediate states. In particular, the motion of the two
intermediate nucleons as a whole is taken into account. The problem is solved
in the zero-range approximation. The result is in good agreement with the
experimental value of the deuterium hyperfine splitting.Comment: 7 pages, LaTe
Virtual light-by-light scattering and the g factor of a bound electron
The contribution of the light-by-light diagram to the g factor of electron
and muon bound in Coulomb field is obtained. For electron in a ground state,
our results are in good agreement with the results of other authors obtained
numerically for large Z. For relatively small Z our results have essentially
higher accuracy as compared to the previous ones. For muonic atoms, the
contribution is obtained for the first time with the high accuracy in whole
region of Z.Comment: 10 pages, 3 figures, RevTe
Ab initio Investigation of Elasticity and Stability of Metal Aluminum
On the basis of the pseudopotential plane-wave(PP-PW) method in combination
with the local-density-functional theory(LDFT), complete stress-strain curves
for the uniaxial loading and uniaxial deformation along the [001] and [111]
directions, and the biaxial proportional extension along [010] and [001] of
aluminium are obtained. During the uniaxial loading, certain general behaviors
of energy versus stretch and the load versus the stretch are confirmed; in each
acse, there exist three special unstressed structures: f.c.c., b.c.c. and
f.c.t. for [001]; f.c.c., s.c. and b.c.c. for [111]. Using stability criteria,
we find that all of these state are unstable, and always occur together with
shear instability, except the natural f.c.c. structure. A Bain transformation
from the stable f.c.c. structure to the stable b.c.c. configuration cannot be
obtained by uniaxial compression along any equivalent [001] and [111]
direction. The tensile strength are similar for the two directions. For the
higher energy barrier of [111] direction, the compressive strength is greater
than that for the [001] direction. With increase in the ratio of the biaxial
proportional extension, the stress and tensile strength increase; however, the
critical strain does not change significantly. Our results add to the existing
ab initio database for use in fitting and testing interatomic potentials.Comment: 9 Pages in Revtex and 11 Eps figure
Strained tetragonal states and Bain paths in metals
Paths of tetragonal states between two phases of a material, such as bcc and
fcc, are called Bain paths. Two simple Bain paths can be defined in terms of
special imposed stresses, one of which applies directly to strained epitaxial
films. Each path goes far into the range of nonlinear elasticity and reaches a
range of structural parameters in which the structure is inherently unstable.
In this paper we identify and analyze the general properties of these paths by
density functional theory. Special examples include vanadium, cobalt and
copper, and the epitaxial path is used to identify an epitaxial film as related
uniquely to a bulk phase.Comment: RevTeX, 4 pages, 4 figures, submitted to Phys. Rev. Let
Feshbach resonances and collapsing Bose-Einstein condensates
We investigate the quantum state of burst atoms seen in the recent Rb-85
experiments at JILA. We show that the presence of a resonance scattering state
can lead to a pairing instability generating an outflow of atoms with energy
comparable to that observed. A resonance effective field theory is used to
study this dynamical process in an inhomogeneous system with spherical
symmetry
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