179 research outputs found
A Symbolic Transformation Language and its Application to a Multiscale Method
The context of this work is the design of a software, called MEMSALab,
dedicated to the automatic derivation of multiscale models of arrays of micro-
and nanosystems. In this domain a model is a partial differential equation.
Multiscale methods approximate it by another partial differential equation
which can be numerically simulated in a reasonable time. The challenge consists
in taking into account a wide range of geometries combining thin and periodic
structures with the possibility of multiple nested scales.
In this paper we present a transformation language that will make the
development of MEMSALab more feasible. It is proposed as a Maple package for
rule-based programming, rewriting strategies and their combination with
standard Maple code. We illustrate the practical interest of this language by
using it to encode two examples of multiscale derivations, namely the two-scale
limit of the derivative operator and the two-scale model of the stationary heat
equation.Comment: 36 page
Computer-Aided Derivation of Multi-scale Models: A Rewriting Framework
We introduce a framework for computer-aided derivation of multi-scale models.
It relies on a combination of an asymptotic method used in the field of partial
differential equations with term rewriting techniques coming from computer
science.
In our approach, a multi-scale model derivation is characterized by the
features taken into account in the asymptotic analysis. Its formulation
consists in a derivation of a reference model associated to an elementary
nominal model, and in a set of transformations to apply to this proof until it
takes into account the wanted features. In addition to the reference model
proof, the framework includes first order rewriting principles designed for
asymptotic model derivations, and second order rewriting principles dedicated
to transformations of model derivations. We apply the method to generate a
family of homogenized models for second order elliptic equations with periodic
coefficients that could be posed in multi-dimensional domains, with possibly
multi-domains and/or thin domains.Comment: 26 page
The Omega Counter, a Frequency Counter Based on the Linear Regression
This article introduces the {\Omega} counter, a frequency counter -- or a
frequency-to-digital converter, in a different jargon -- based on the Linear
Regression (LR) algorithm on time stamps. We discuss the noise of the
electronics. We derive the statistical properties of the {\Omega} counter on
rigorous mathematical basis, including the weighted measure and the frequency
response. We describe an implementation based on a SoC, under test in our
laboratory, and we compare the {\Omega} counter to the traditional {\Pi} and
{\Lambda} counters. The LR exhibits optimum rejection of white phase noise,
superior to that of the {\Pi} and {\Lambda} counters. White noise is the major
practical problem of wideband digital electronics, both in the instrument
internal circuits and in the fast processes which we may want to measure. The
{\Omega} counter finds a natural application in the measurement of the
Parabolic Variance, described in the companion article arXiv:1506.00687
[physics.data-an].Comment: 8 pages, 6 figure, 2 table
The Parabolic variance (PVAR), a wavelet variance based on least-square fit
This article introduces the Parabolic Variance (PVAR), a wavelet variance
similar to the Allan variance, based on the Linear Regression (LR) of phase
data. The companion article arXiv:1506.05009 [physics.ins-det] details the
frequency counter, which implements the LR estimate.
The PVAR combines the advantages of AVAR and MVAR. PVAR is good for long-term
analysis because the wavelet spans over , the same of the AVAR wavelet;
and good for short-term analysis because the response to white and flicker PM
is and , same as the MVAR.
After setting the theoretical framework, we study the degrees of freedom and
the confidence interval for the most common noise types. Then, we focus on the
detection of a weak noise process at the transition - or corner - where a
faster process rolls off. This new perspective raises the question of which
variance detects the weak process with the shortest data record. Our
simulations show that PVAR is a fortunate tradeoff. PVAR is superior to MVAR in
all cases, exhibits the best ability to divide between fast noise phenomena (up
to flicker FM), and is almost as good as AVAR for the detection of random walk
and drift
Lessons From the Field: Community Anti-Drug Coalitions as Catalysts for Change
Analyzes the organization, operation, sustainability, and impact of community anti-drug coalitions. Examines characteristics shared among eight coalitions, including leadership, outcomes, planning, institutionalization, and funding diversification
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