2,641 research outputs found
A survey of the follow-up studies carried out by recognized educational clinics in the United States.
Thesis (Ed.M.)--Boston Universit
Local and nonlocal solvable structures in ODEs reduction
Solvable structures, likewise solvable algebras of local symmetries, can be
used to integrate scalar ODEs by quadratures. Solvable structures, however, are
particularly suitable for the integration of ODEs with a lack of local
symmetries. In fact, under regularity assumptions, any given ODE always admits
solvable structures even though finding them in general could be a very
difficult task. In practice a noteworthy simplification may come by computing
solvable structures which are adapted to some admitted symmetry algebra. In
this paper we consider solvable structures adapted to local and nonlocal
symmetry algebras of any order (i.e., classical and higher). In particular we
introduce the notion of nonlocal solvable structure
Bayesian parameter estimation in the second LISA Pathfinder Mock Data Challenge
A main scientific output of the LISA Pathfinder mission is to provide a noise
model that can be extended to the future gravitational wave observatory, LISA.
The success of the mission depends thus upon a deep understanding of the
instrument, especially the ability to correctly determine the parameters of the
underlying noise model. In this work we estimate the parameters of a simplified
model of the LISA Technology Package (LTP) instrument. We describe the LTP by
means of a closed-loop model that is used to generate the data, both injected
signals and noise. Then, parameters are estimated using a Bayesian framework
and it is shown that this method reaches the optimal attainable error, the
Cramer-Rao bound. We also address an important issue for the mission: how to
efficiently combine the results of different experiments to obtain a unique set
of parameters describing the instrument.Comment: 14 pages, 4 figures, submitted to PR
Seismic retrofit of an existing reinforced concrete building with buckling-restrained braces
Background: The seismic retrofitting of frame structures using hysteretic dampers is a very effective strategy to mitigate earthquake-induced risks. However, its application in current practice is rather limited since simple and efficient design methods are still lacking, and the more accurate time-history analysis is time-consuming and computationally demanding. Aims: This paper develops and applies a seismic retrofit design method to a complex real case study: An eight-story reinforced concrete residential building equipped with buckling-restrained braces. Methods: The design method permits the peak seismic response to be predicted, as well as the dampers to be added in the structure to obtain a uniform distribution of the ductility demand. For that purpose, a pushover analysis with the first mode load pattern is carried out. The corresponding story pushover curves are first idealized using a degrading trilinear model and then used to define the SDOF (Single Degree-of-Freedom) system equivalent to the RC frame. The SDOF system, equivalent to the damped braces, is designed to meet performance criteria based on a target drift angle. An optimal damper distribution rule is used to distribute the damped braces along the elevation to maximize the use of all dampers and obtain a uniform distribution of the ductility demand. Results: The effectiveness of the seismic retrofit is finally demonstrated by non-linear time-history analysis using a set of earthquake ground motions with various hazard levels. Conclusion: The results proved the design procedure is feasible and effective since it achieves the performance objectives of damage control in structural members and uniform ductility demand in dampers
Calibrating spectral estimation for the LISA Technology Package with multichannel synthetic noise generation
The scientific objectives of the Lisa Technology Package (LTP) experiment, on
board of the LISA Pathfinder mission, demand for an accurate calibration and
validation of the data analysis tools in advance of the mission launch. The
levels of confidence required on the mission outcomes can be reached only with
an intense activity on synthetically generated data. A flexible procedure
allowing the generation of cross-correlated stationary noise time series was
set-up. Multi-channel time series with the desired cross correlation behavior
can be generated once a model for a multichannel cross-spectral matrix is
provided. The core of the procedure is the synthesis of a noise coloring
multichannel filter through a frequency-by-frequency eigendecomposition of the
model cross-spectral matrix and a Z-domain fit. The common problem of initial
transients in noise time series is solved with a proper initialization of the
filter recursive equations. The noise generator performances were tested in a
two dimensional case study of the LTP dynamics along the two principal channels
of the sensing interferometer.Comment: Accepted for publication in Physical Review D (http://prd.aps.org/
Local Isometric immersions of pseudo-spherical surfaces and evolution equations
The class of differential equations describing pseudo-spherical surfaces,
first introduced by Chern and Tenenblat [3], is characterized by the property
that to each solution of a differential equation, within the class, there
corresponds a 2-dimensional Riemannian metric of curvature equal to . The
class of differential equations describing pseudo-spherical surfaces carries
close ties to the property of complete integrability, as manifested by the
existence of infinite hierarchies of conservation laws and associated linear
problems. As such, it contains many important known examples of integrable
equations, like the sine-Gordon, Liouville and KdV equations. It also gives
rise to many new families of integrable equations. The question we address in
this paper concerns the local isometric immersion of pseudo-spherical surfaces
in from the perspective of the differential equations that give
rise to the metrics. Indeed, a classical theorem in the differential geometry
of surfaces states that any pseudo-spherical surface can be locally
isometrically immersed in . In the case of the sine-Gordon
equation, one can derive an expression for the second fundamental form of the
immersion that depends only on a jet of finite order of the solution of the
pde. A natural question is to know if this remarkable property extends to
equations other than the sine-Gordon equation within the class of differential
equations describing pseudo-spherical surfaces. In an earlier paper [11], we
have shown that this property fails to hold for all other second order
equations, except for those belonging to a very special class of evolution
equations. In the present paper, we consider a class of evolution equations for
of order describing pseudo-spherical surfaces. We show that
whenever an isometric immersion in exists, depending on a jet of
finite order of , then the coefficients of the second fundamental forms are
functions of the independent variables and only.Comment: Fields Institute Communications, 2015, Hamiltonian PDEs and
Applications, pp.N
Time domain maximum likelihood parameter estimation in LISA Pathfinder Data Analysis
LISA is the upcoming space-based Gravitational Wave telescope. LISA
Pathfinder, to be launched in the coming years, will prove and verify the
detection principle of the fundamental Doppler link of LISA on a flight
hardware identical in design to that of LISA. LISA Pathfinder will collect a
picture of all noise disturbances possibly affecting LISA, achieving the
unprecedented pureness of geodesic motion necessary for the detection of
gravitational waves. The first steps of both missions will crucially depend on
a very precise calibration of the key system parameters. Moreover, robust
parameters estimation is of fundamental importance in the correct assessment of
the residual force noise, an essential part of the data processing for LISA. In
this paper we present a maximum likelihood parameter estimation technique in
time domain being devised for this calibration and show its proficiency on
simulated data and validation through Monte Carlo realizations of independent
noise runs. We discuss its robustness to non-standard scenarios possibly
arising during the real-life mission, as well as its independence to the
initial guess and non-gaussianities. Furthermore, we apply the same technique
to data produced in mission-like fashion during operational exercises with a
realistic simulator provided by ESA.Comment: 16 pages (two columns), 15 figures, 5 tables, submitted to Phys. Rev.
Parameter estimation in LISA Pathfinder operational exercises
The LISA Pathfinder data analysis team has been developing in the last years
the infrastructure and methods required to run the mission during flight
operations. These are gathered in the LTPDA toolbox, an object oriented MATLAB
toolbox that allows all the data analysis functionalities for the mission,
while storing the history of all operations performed to the data, thus easing
traceability and reproducibility of the analysis. The parameter estimation
methods in the toolbox have been applied recently to data sets generated with
the OSE (Off-line Simulations Environment), a detailed LISA Pathfinder
non-linear simulator that will serve as a reference simulator during mission
operations. These operational exercises aim at testing the on-orbit experiments
in a realistic environment in terms of software and time constraints. These
simulations, so called operational exercises, are the last verification step
before translating these experiments into tele-command sequences for the
spacecraft, producing therefore very relevant datasets to test our data
analysis methods. In this contribution we report the results obtained with
three different parameter estimation methods during one of these operational
exercises.Comment: 10 pages, 3 figures, prepared for the Proceedings of the 9th Edoardo
Amaldi Conference on Gravitational Waves, JPC
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