5,112 research outputs found
Minimum Distance Estimation of Milky Way Model Parameters and Related Inference
We propose a method to estimate the location of the Sun in the disk of the
Milky Way using a method based on the Hellinger distance and construct
confidence sets on our estimate of the unknown location using a bootstrap based
method. Assuming the Galactic disk to be two-dimensional, the sought solar
location then reduces to the radial distance separating the Sun from the
Galactic center and the angular separation of the Galactic center to Sun line,
from a pre-fixed line on the disk. On astronomical scales, the unknown solar
location is equivalent to the location of us earthlings who observe the
velocities of a sample of stars in the neighborhood of the Sun. This unknown
location is estimated by undertaking pairwise comparisons of the estimated
density of the observed set of velocities of the sampled stars, with densities
estimated using synthetic stellar velocity data sets generated at chosen
locations in the Milky Way disk according to four base astrophysical models.
The "match" between the pair of estimated densities is parameterized by the
affinity measure based on the familiar Hellinger distance. We perform a novel
cross-validation procedure to establish a desirable "consistency" property of
the proposed method.Comment: 25 pages, 10 Figures. This version incorporates the suggestions made
by the referees. To appear in SIAM/ASA Journal on Uncertainty Quantificatio
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Damage detection using transient trajectories in phase-space with extended random decrement technique under non-stationary excitations
One-form superfluids and magnetohydrodynamics
We use the framework of generalised global symmetries to study various
hydrodynamic regimes of hot electromagnetism. We formulate the hydrodynamic
theories with an unbroken or a spontaneously broken U(1) one-form symmetry. The
latter of these describes a one-form superfluid, which is characterised by a
vector Goldstone mode and a two-form superfluid velocity. Two special limits of
this theory have been studied in detail: the string fluid limit where the U(1)
one-form symmetry is partly restored, and the electric limit in which the
symmetry is completely broken. The transport properties of these theories are
investigated in depth by studying the constraints arising from the second law
of thermodynamics and Onsager's relations at first order in derivatives. We
also construct a hydrostatic effective action for the Goldstone modes in these
theories and use it to characterise the space of all equilibrium
configurations. To make explicit contact with hot electromagnetism, the
traditional treatment of magnetohydrodynamics, where the electromagnetic photon
is incorporated as dynamical degrees of freedom, is extended to include
parity-violating contributions. We argue that the chemical potential and
electric fields are not independently dynamical in magnetohydrodynamics, and
illustrate how to eliminate these within the hydrodynamic derivative expansion
using Maxwell's equations. Additionally, a new hydrodynamic theory of
non-conducting, but polarised, plasmas is formulated, focusing primarily on the
magnetically dominated sector. Finally, it is shown that the different limits
of one-form superfluids formulated in terms of generalised global symmetries
are exactly equivalent to magnetohydrodynamics and the hydrodynamics of
non-conducting plasmas at the non-linear level.Comment: v3: 69 + 1 pages, 1 figure, added clarifications and appendix with
discrete symmetries, to be published in JHE
A phase-field study of elastic stress effects on phase separation in ternary alloys
Most of the commercially important alloys are multicomponent, producing
multiphase microstructures as a result of processing. When the coexisting
phases are elastically coherent, the elastic interactions between these phases
play a major role in the development of microstructures. To elucidate the key
effects of elastic stress on microstructural evolution when more than two
misfitting phases are present in the microstructure, we have developed a
microelastic phase-field model in two dimensions to study phase separation in
ternary alloy system. Numerical solutions of a set of coupled Cahn-Hilliard
equations for the composition fields govern the spatiotemporal evolution of the
three-phase microstructure. The model incorporates coherency strain
interactions between the phases using Khachaturyan's microelasticity theory. We
systematically vary the misfit strains (magnitude and sign) between the phases
along with the bulk alloy composition to study their effects on the
morphological development of the phases and the resulting phase separation
kinetics. We also vary the ratio of interfacial energies between the phases to
understand the interplay between elastic and interfacial energies on
morphological evolution. The sign and degree of misfit affect strain
partitioning between the phases during spinodal decomposition, thereby
affecting their compositional history and morphology. Moreover, strain
partitioning affects solute partitioning and alters the kinetics of coarsening
of the phases. The phases associated with higher misfit strain appear coarser
and exhibit wider size distribution compared to those having lower misfit. When
the interfacial energies satisfy complete wetting condition, phase separation
leads to development of stable core-shell morphology depending on the misfit
between the core (wetted) and the shell (wetting) phases
Probabilistic -mean with local alignment for clustering and motif discovery in functional data
We develop a new method to locally cluster curves and discover functional
motifs, i.e.~typical ``shapes'' that may recur several times along and across
the curves capturing important local characteristics. In order to identify
these shared curve portions, our method leverages ideas from functional data
analysis (joint clustering and alignment of curves), bioinformatics (local
alignment through the extension of high similarity seeds) and fuzzy clustering
(curves belonging to more than one cluster, if they contain more than one
typical ``shape''). It can employ various dissimilarity measures and
incorporate derivatives in the discovery process, thus exploiting complex
facets of shapes. We demonstrate the performance of our method with an
extensive simulation study, and show how it generalizes other clustering
methods for functional data. Finally, we provide real data applications to
Berkeley growth data, Italian Covid-19 death curves and ``Omics'' data related
to mutagenesis.Comment: 22 pages, 6 figures. This work has been presented at various
conference
Urban patterns, population density and optimal city dimension: The case of public infrastructure
Determination of the optimal city size underlies the economic rationality of infrastructure provision by local governments. We investigate the existence of decreasing average costs resulting from economies of scale, associated with larger urban dimensions in terms of population and housing, and economies of density, brought about by reductions in urban dispersion, and calculate optimal population densities when providing basic infrastructure. The methodology relies on novel definitions of scale and density economies and their estimation by way of flexible translog cost functions, extensively applied in the literature dealing with the provision of services—i.e., utilities, but extended here to their supporting infrastructure. Our results unveil the existence of latent economies of scale and density resulting in a cost excess in the provision of infrastructure due to the effect of urban sprawl that translates into suboptimal city sizes. Based on these findings several policy guidelines rationalizing urban development are suggested. The model is illustrated using Spanish statistical data collected from the nationwide local infrastructure and equipment survey, and prices from a new database that uses engineering cost benchmarks.Urban patterns; Optimal urban density; Scale and density economies; Translog cost function.
Regulation and efficiency incentives: evidence from the England and Wales water and sewerage industry
This paper evaluates the impact of the tightening in price cap by OFWAT and of other operational factors on the efficiency of water and sewerage companies in England and Wales using a mixture of data envelopment analysis and stochastic frontier analysis. Previous empirical results suggest that the regulatory system introduced at privatization was lax. The 1999 price review signaled a tightening in regulation which is shown to have led to a significant reduction in technical inefficiency. The new economic environment set by price-cap regulation acted to bring inputs closer to their cost-minimizing levels from both a technical and allocative perspective
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