4,938 research outputs found
Microstructure from ferroelastic transitions using strain pseudospin clock models in two and three dimensions: a local mean-field analysis
We show how microstructure can arise in first-order ferroelastic structural
transitions, in two and three spatial dimensions, through a local meanfield
approximation of their pseudospin hamiltonians, that include anisotropic
elastic interactions. Such transitions have symmetry-selected physical strains
as their -component order parameters, with Landau free energies that
have a single zero-strain 'austenite' minimum at high temperatures, and
spontaneous-strain 'martensite' minima of structural variants at low
temperatures. In a reduced description, the strains at Landau minima induce
temperature-dependent, clock-like hamiltonians, with
-component strain-pseudospin vectors pointing to
discrete values (including zero). We study elastic texturing in five such
first-order structural transitions through a local meanfield approximation of
their pseudospin hamiltonians, that include the powerlaw interactions. As a
prototype, we consider the two-variant square/rectangle transition, with a
one-component, pseudospin taking values of , as in a
generalized Blume-Capel model. We then consider transitions with two-component
() pseudospins: the equilateral to centred-rectangle ();
the square to oblique polygon (); the triangle to oblique ()
transitions; and finally the 3D cubic to tetragonal transition (). The
local meanfield solutions in 2D and 3D yield oriented domain-walls patterns as
from continuous-variable strain dynamics, showing the discrete-variable models
capture the essential ferroelastic texturings. Other related hamiltonians
illustrate that structural-transitions in materials science can be the source
of interesting spin models in statistical mechanics.Comment: 15 pages, 9 figure
Inverse Spectral-Scattering Problem with Two Sets of Discrete Spectra for the Radial Schroedinger Equation
The Schroedinger equation on the half line is considered with a real-valued,
integrable potential having a finite first moment. It is shown that the
potential and the boundary conditions are uniquely determined by the data
containing the discrete eigenvalues for a boundary condition at the origin, the
continuous part of the spectral measure for that boundary condition, and a
subset of the discrete eigenvalues for a different boundary condition. This
result extends the celebrated two-spectrum uniqueness theorem of Borg and
Marchenko to the case where there is also a continuous spectru
Multidimensional Borg-Levinson Theorem
We consider the inverse problem of the reconstruction of a Schr\"odinger
operator on a unknown Riemannian manifold or a domain of Euclidean space. The
data used is a part of the boundary and the eigenvalues corresponding
to a set of impedances in the Robin boundary condition which vary on .
The proof is based on the analysis of the behaviour of the eigenfunctions on
the boundary as well as in perturbation theory of eigenvalues. This reduces the
problem to an inverse boundary spectral problem solved by the boundary control
method
Effect of suspension systems on the physiological and psychological responses to sub-maximal biking on simulated smooth and bumpy tracks
The aim of this study was to compare the physiological and psychological responses of cyclists riding on a hard tail bicycle and on a full suspension bicycle. Twenty males participated in two series of tests. A test rig held the front axle of the bicycle steady while the rear wheel rotated against a heavy roller with bumps (or no bumps) on its surface. In the first series of tests, eight participants (age 19 – 27 years, body mass 65 – 82 kg) were tested on both the full suspension and hard tail bicycles with and without bumps fitted to the roller. The second series of test repeated the bump tests with a further six participants (age 22 – 31 years, body mass 74 – 94 kg) and also involved an investigation of familiarization effects with the final six participants (age 21 – 30 years, body mass 64 – 80 kg). Heart rate, oxygen consumption (VO<sub>2</sub>), rating of perceived exertion (RPE) and comfort were recorded during 10 min sub-maximal tests. Combined data for the bumps tests show that the full suspension bicycle was significantly different (P < 0.001) from the hard tail bicycle on all four measures. Oxygen consumption, heart rate and RPE were lower on average by 8.7 (s = 3.6) ml · kg<sup>-1</sup> · min<sup>-1</sup>, 32.1 (s = 12.1) beats · min<sup>-1</sup> and 2.6 (s = 2.0) units, respectively. Comfort scores were higher (better) on average by 1.9 (s = 0.8) units. For the no bumps tests, the only statistically significant difference (P = 0.008) was in VO<sub>2</sub>, which was lower for the hard tail bicycle by 2.2 (s = 1.7) ml · kg-1 · min<sup>-1</sup>. The results indicate that the full suspension bicycle provides a physiological and psychological advantage over the hard tail bicycle during simulated sub-maximal exercise on bumps
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Infrared, UV/VIS and Raman Spectroscopy of Comet Wild-2 Samples Returned by the Stardust Mission
Results from the preliminary examination of Stardust samples obtained using various spectroscopic methods will be presented
On the (Non)-Integrability of KdV Hierarchy with Self-consistent Sources
Non-holonomic deformations of integrable equations of the KdV hierarchy are
studied by using the expansions over the so-called "squared solutions" (squared
eigenfunctions). Such deformations are equivalent to perturbed models with
external (self-consistent) sources. In this regard, the KdV6 equation is viewed
as a special perturbation of KdV equation. Applying expansions over the
symplectic basis of squared eigenfunctions, the integrability properties of the
KdV hierarchy with generic self-consistent sources are analyzed. This allows
one to formulate a set of conditions on the perturbation terms that preserve
the integrability. The perturbation corrections to the scattering data and to
the corresponding action-angle variables are studied. The analysis shows that
although many nontrivial solutions of KdV equations with generic
self-consistent sources can be obtained by the Inverse Scattering Transform
(IST), there are solutions that, in principle, can not be obtained via IST.
Examples are considered showing the complete integrability of KdV6 with
perturbations that preserve the eigenvalues time-independent. In another type
of examples the soliton solutions of the perturbed equations are presented
where the perturbed eigenvalue depends explicitly on time. Such equations,
however in general, are not completely integrable.Comment: 16 pages, no figures, LaTe
Force acting on a rough disk spinning in a flow of noninteracting particles
Pressure force exerted on a rough disk spinning in a flow of noninteracting particles is determined by considering that a flow of point particles impinges on a body spinning around a fixed point. The rough disk is identical with the sequence of sets and thus the sets can be viewed as successive approximations of the rough disk. A proper choice of sequence of sets shows that the characteristic of billiard scattering is independent of n, and the billiard scattering on the rough set is defined. The pressure force exerted on the disk is independent of its angular velocity and that the characteristic of the interaction that is the moment of the pressure force slows down the rotation of the rough disk. The transverse force aligned with the instantaneous velocity of the front point of the body results in Magnus effect
Neutrino propagation in a random magnetic field
The active-sterile neutrino conversion probability is calculated for neutrino
propagating in a medium in the presence of random magnetic field fluctuations.
Necessary condition for the probability to be positive definite is obtained.
Using this necessary condition we put constraint on the neutrino magnetic
moment from active-sterile electron neutrino conversion in the early universe
hot plasma and in supernova.Comment: 11 page
In search of phylogenetic congruence between molecular and morphological data in bryozoans with extreme adult skeletal heteromorphy
peerreview_statement: The publishing and review policy for this title is described in its Aims & Scope. aims_and_scope_url: http://www.tandfonline.com/action/journalInformation?show=aimsScope&journalCode=tsab20© Crown Copyright 2015. This document is the author's final accepted/submitted version of the journal article. You are advised to consult the publisher's version if you wish to cite from it
Scaled free energies, power-law potentials, strain pseudospins and quasi-universality for first-order structural transitions
We consider ferroelastic first-order phase transitions with
order-parameter strains entering Landau free energies as invariant polynomials,
that have structural-variant Landau minima. The total free energy
includes (seemingly innocuous) harmonic terms, in the {\it
non}-order-parameter strains. Four 3D transitions are considered,
tetragonal/orthorhombic, cubic/tetragonal, cubic/trigonal and
cubic/orthorhombic unit-cell distortions, with respectively, and 2; and and 6. Five 2D transitions are also considered, as
simpler examples. Following Barsch and Krumhansl, we scale the free energy to
absorb most material-dependent elastic coefficients into an overall prefactor,
by scaling in an overall elastic energy density; a dimensionless temperature
variable; and the spontaneous-strain magnitude at transition .
To leading order in the scaled Landau minima become
material-independent, in a kind of 'quasi-universality'. The scaled minima in
-dimensional order-parameter space, fall at the centre and at the
corners, of a transition-specific polyhedron inscribed in a sphere, whose
radius is unity at transition. The `polyhedra' for the four 3D transitions are
respectively, a line, a triangle, a tetrahedron, and a hexagon. We minimize the
terms harmonic in the non-order-parameter strains, by substituting
solutions of the 'no dislocation' St Venant compatibility constraints, and
explicitly obtain powerlaw anisotropic, order-parameter interactions, for all
transitions. In a reduced discrete-variable description, the competing minima
of the Landau free energies induce unit-magnitude pseudospin vectors, with values, pointing to the polyhedra corners and the (zero-value) center.Comment: submitted to PR
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