32,003 research outputs found
Renormalisation of parabolic stochastic PDEs
We give a survey of recent result regarding scaling limits of systems from
statistical mechanics, as well as the universality of the behaviour of such
systems in so-called cross-over regimes. It transpires that some of these
universal objects are described by singular stochastic PDEs. We then give a
survey of the recently developed theory of regularity structures which allows
to build these objects and to describe some of their properties. We place
particular emphasis on the renormalisation procedure required to give meaning
to these equations.
These are expanded notes of the 20th Takagi lectures held at Tokyo University
on November 4, 2017
Damage monitoring in sandwich beams by modal parameter shifts: a comparative study of burst random and sine dwell vibration testing
This paper presents an experimental study on the effects of multi-site damage on the vibration response of honeycomb sandwich beams, damaged by two different ways i.e., impact damage and core-only damage simulating damage due to bird or stone impact or due to mishandling during assembly and maintenance. The variation of the modal parameters with different levels of impact energy and density of damage is studied. Vibration tests have been carried out with both burst random and sine dwell testing in order to evaluate the damping estimation efficiency of these methods in the presence of damage. Sine dwell testing is done in both up and down frequency directions in order to detect structural non-linearities. Results show that damping ratio is a more sensitive parameter for damage detection than the natural frequency. Design of experiments (DOE) highlighted density of damage as the factor having a more significant effect on the modal parameters and also proved that sine dwell testing is more suitable for damping estimation in the presence of damage as compared to burst random testing
Optimal Rate of Direct Estimators in Systems of Ordinary Differential Equations Linear in Functions of the Parameters
Many processes in biology, chemistry, physics, medicine, and engineering are
modeled by a system of differential equations. Such a system is usually
characterized via unknown parameters and estimating their 'true' value is thus
required. In this paper we focus on the quite common systems for which the
derivatives of the states may be written as sums of products of a function of
the states and a function of the parameters.
For such a system linear in functions of the unknown parameters we present a
necessary and sufficient condition for identifiability of the parameters. We
develop an estimation approach that bypasses the heavy computational burden of
numerical integration and avoids the estimation of system states derivatives,
drawbacks from which many classic estimation methods suffer. We also suggest an
experimental design for which smoothing can be circumvented. The optimal rate
of the proposed estimators, i.e., their -consistency, is proved and
simulation results illustrate their excellent finite sample performance and
compare it to other estimation approaches
Mobile impurities in integrable models
We use a mobile impurity or depleton model to study elementary excitations in
one-dimensional integrable systems. For Lieb-Liniger and bosonic Yang-Gaudin
models we express two phenomenological parameters characterising renormalised
inter- actions of mobile impurities with superfluid background: the number of
depleted particles, and the superfluid phase drop in terms of the
corresponding Bethe Ansatz solution and demonstrate, in the leading order, the
absence of two-phonon scattering resulting in vanishing rates of inelastic
processes such as viscosity experienced by the mobile impuritiesComment: 25 pages, minor corrections made to the manuscrip
Modelling and identification of a six axes industrial robot
This paper deals with the modelling and identification of a six axes industrial St šaubli RX90 robot. A non-linear finite element method is used to generate the dynamic equations of motion in a form suitable for both simulation and identification. The latter requires that the equations of motion are linear in the inertia parameters. Joint friction is described by a friction model that describes the friction behaviour in the full velocity range necessary for identification. Experimental parameter identification by means of linear least squares techniques showed to be very suited for identification of the unknown parameters, provided that the problem is properly scaled and that the influence of disturbances is sufficiently analysed and managed. An analysis of the least squares problem by means of a singular value decomposition is preferred as it not only solves the problem of rank deficiency, but it also can correctly deal with measurement noise and unmodelled dynamics
Lam\'e Parameter Estimation from Static Displacement Field Measurements in the Framework of Nonlinear Inverse Problems
We consider a problem of quantitative static elastography, the estimation of
the Lam\'e parameters from internal displacement field data. This problem is
formulated as a nonlinear operator equation. To solve this equation, we
investigate the Landweber iteration both analytically and numerically. The main
result of this paper is the verification of a nonlinearity condition in an
infinite dimensional Hilbert space context. This condition guarantees
convergence of iterative regularization methods. Furthermore, numerical
examples for recovery of the Lam\'e parameters from displacement data
simulating a static elastography experiment are presented.Comment: 29 page
From synchronization to Lyapunov exponents and back
The goal of this paper is twofold. In the first part we discuss a general
approach to determine Lyapunov exponents from ensemble- rather than
time-averages. The approach passes through the identification of locally stable
and unstable manifolds (the Lyapunov vectors), thereby revealing an analogy
with generalized synchronization. The method is then applied to a periodically
forced chaotic oscillator to show that the modulus of the Lyapunov exponent
associated to the phase dynamics increases quadratically with the coupling
strength and it is therefore different from zero already below the onset of
phase-synchronization. The analytical calculations are carried out for a model,
the generalized special flow, that we construct as a simplified version of the
periodically forced Rossler oscillator.Comment: Submitted to Physica
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