15,663 research outputs found
IGS: an IsoGeometric approach for Smoothing on surfaces
We propose an Isogeometric approach for smoothing on surfaces, namely
estimating a function starting from noisy and discrete measurements. More
precisely, we aim at estimating functions lying on a surface represented by
NURBS, which are geometrical representations commonly used in industrial
applications. The estimation is based on the minimization of a penalized
least-square functional. The latter is equivalent to solve a 4th-order Partial
Differential Equation (PDE). In this context, we use Isogeometric Analysis
(IGA) for the numerical approximation of such surface PDE, leading to an
IsoGeometric Smoothing (IGS) method for fitting data spatially distributed on a
surface. Indeed, IGA facilitates encapsulating the exact geometrical
representation of the surface in the analysis and also allows the use of at
least globally continuous NURBS basis functions for which the 4th-order
PDE can be solved using the standard Galerkin method. We show the performance
of the proposed IGS method by means of numerical simulations and we apply it to
the estimation of the pressure coefficient, and associated aerodynamic force on
a winglet of the SOAR space shuttle
Generalized Spatial Regression with Differential Regularization
We aim at analyzing geostatistical and areal data observed over irregularly
shaped spatial domains and having a distribution within the exponential family.
We propose a generalized additive model that allows to account for
spatially-varying covariate information. The model is fitted by maximizing a
penalized log-likelihood function, with a roughness penalty term that involves
a differential quantity of the spatial field, computed over the domain of
interest. Efficient estimation of the spatial field is achieved resorting to
the finite element method, which provides a basis for piecewise polynomial
surfaces. The proposed model is illustrated by an application to the study of
criminality in the city of Portland, Oregon, USA
Theoretical analysis of continuously driven dissipative solid-state qubits
We study a realistic model for driven qubits using the numerical solution of
the Bloch-Redfield equation as well as analytical approximations using a
high-frequency scheme. Unlike in idealized rotating-wave models suitable for
NMR or quantum optics, we study a driving term which neither is orthogonal to
the static term nor leaves the adiabatic energy value constant. We investigate
the underlying dynamics and analyze the spectroscopy peaks obtained in recent
experiments. We show, that unlike in the rotating-wave case, this system
exhibits nonlinear driving effects.We study the width of spectroscopy peaks and
show, how a full analysis of the parameters of the system can be performed by
comparing the first and second resonance. We outline the limitations of the NMR
linewidth formula at low temperature and show, that spectrocopic peaks
experience a strong shift which goes much beyond the Bloch-Siegert shift of the
Eigenfrequency.Comment: Accepted for publication in Phys. Rev.
Energy Growth in Schrödinger's Equation with Markovian Forcing
Schrödinger's equation is considered on a one-dimensional torus with time dependent potential v(θ,t)=λV(θ)X(t), where V(θ) is an even trigonometric polynomial and X(t) is a stationary Markov process. It is shown that when the coupling constant λ is sufficiently small, the average kinetic energy grows as the square-root of time. More generally, the H^s norm of the wave function is shown to behave as t^(s/4A)
Meson retardation in deuteron photodisintegration above pi-threshold
Photodisintegration of the deuteron above pi-threshold is studied in a
coupled channel approach including N Delta- and pi d-channels with pion
retardation in potentials and exchange currents. A much improved description of
total and differential cross sections in the energy region between pi-threshold
and 400-450 MeV is achieved.Comment: 12 pages revtex including 5 postscript figure
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