519 research outputs found
The Cramer-Rao Bound and DMT Signal Optimisation for the Identification of a Wiener-Type Model
In linear system identification, optimal excitation signals can be determined using the Cramer-Rao bound. This problem has not been thoroughly studied for the nonlinear case. In this work, the Cramer-Rao bound for a factorisable Volterra model is derived. The analytical result is supported with simulation examples. The bound is then used to find the optimal excitation signal out of the class of discrete multitone signals. As the model is nonlinear in the parameters, the bound depends on the model parameters themselves. On this basis, a three-step identification procedure is proposed. To illustrate the procedure, signal optimisation is explicitly performed for a third-order nonlinear model. Methods of nonlinear optimisation are applied for the parameter estimation of the model. As a baseline, the problem of optimal discrete multitone signals for linear FIR filter estimation is reviewed
Relaxation oscillations and negative strain rate sensitivity in the Portevin - Le Chatelier effect
A characteristic feature of the Portevin - Le Chatelier effect or the jerky
flow is the stick-slip nature of stress-strain curves which is believed to
result from the negative strain rate dependence of the flow stress. The latter
is assumed to result from the competition of a few relevant time scales
controlling the dynamics of jerky flow. We address the issue of time scales and
its connection to the negative strain rate sensitivity of the flow stress
within the framework of a model for the jerky flow which is known to reproduce
several experimentally observed features including the negative strain rate
sensitivity of the flow stress. We attempt to understand the above issues by
analyzing the geometry of the slow manifold underlying the relaxational
oscillations in the model. We show that the nature of the relaxational
oscillations is a result of the atypical bent geometry of the slow manifold.
The analysis of the slow manifold structure helps us to understand the time
scales operating in different regions of the slow manifold. Using this
information we are able to establish connection with the strain rate
sensitivity of the flow stress. The analysis also helps us to provide a proper
dynamical interpretation for the negative branch of the strain rate
sensitivity.Comment: 7 figures, To appear in Phys. Rev.
Missing physics in stick-slip dynamics of a model for peeling of an adhesive tape
It is now known that the equations of motion for the contact point during
peeling of an adhesive tape mounted on a roll introduced earlier are singular
and do not support dynamical jumps across the two stable branches of the peel
force function. By including the kinetic energy of the tape in the Lagrangian,
we derive equations of motion that support stick-slip jumps as a natural
consequence of the inherent dynamics. In the low mass limit, these equations
reproduce solutions obtained using a differential-algebraic algorithm
introduced for the earlier equations. Our analysis also shows that mass of the
ribbon has a strong influence on the nature of the dynamics.Comment: Accepted for publication in Phys. Rev. E (Rapid Communication
High order amplitude equation for steps on creep curve
We consider a model proposed by one of the authors for a type of plastic
instability found in creep experiments which reproduces a number of
experimentally observed features. The model consists of three coupled
non-linear differential equations describing the evolution of three types of
dislocations. The transition to the instability has been shown to be via Hopf
bifurcation leading to limit cycle solutions with respect to physically
relevant drive parameters. Here we use reductive perturbative method to extract
an amplitude equation of up to seventh order to obtain an approximate analytic
expression for the order parameter. The analysis also enables us to obtain the
bifurcation (phase) diagram of the instability. We find that while
supercritical bifurcation dominates the major part of the instability region,
subcritical bifurcation gradually takes over at one end of the region. These
results are compared with the known experimental results. Approximate analytic
expressions for the limit cycles for different types of bifurcations are shown
to agree with their corresponding numerical solutions of the equations
describing the model. The analysis also shows that high order nonlinearities
are important in the problem. This approach further allows us to map the
theoretical parameters to the experimentally observed macroscopic quantities.Comment: LaTex file and eps figures; Communicated to Phys. Rev.
The Cramer-Rao bound and DMT signal optimisation for the identification of a Wiener-type model
PVDF/BaTiO3 composite foams with high content of β phase by thermally induced phase separation (TIPS)
Poly(vinylidene fluoride) (PVDF) displays ferroelectric, piezoelectric and pyroelectric behavior and it is widely used in high-tech applications including sensors, transducers, energy harvesting devices and actuators. The crystallization of this polymer into highly polar β phase is desirable but is hard to achieve without applying specific thermo-mechanical treatments. Indeed, fabrication processes directly affect PVDF molecular chain conformation, inducing distinct polymorphs. In this paper, we present the fabrication of PVDF/BaTiO3 composite foams by thermally induced phase separation method (TIPS). Different compositions are tested and characterized. The crystallinity, and in particular the development of electroactive β crystal phase is monitored by FTIR, DSC and XRD measurements. Dielectric properties are also evaluated. It turns out that TIPS is a straightforward method that clearly promotes the spontaneous growth of the β phase in PVDF and its composite foams, without the need to apply additional treatments, and also significantly improves the degree of crystallinity. BaTiO3 content gives additional value to the development of β phase and total crystallinity of the systems. The low permittivity values (between 2 and 3), combined with the cellular morphology makes these materials suitable as lightweight components of microelectronic circuits
Multifractal burst in the spatio-temporal dynamics of jerky flow
The collective behavior of dislocations in jerky flow is studied in Al-Mg
polycrystalline samples subjected to constant strain rate tests. Complementary
dynamical, statistical and multifractal analyses are carried out on the
stress-time series recorded during jerky flow to characterize the distinct
spatio-temporal dynamical regimes. It is shown that the hopping type B and the
propagating type A bands correspond to chaotic and self-organized critical
states respectively. The crossover between these types of bands is identified
by a large spread in the multifractal spectrum. These results are interpreted
on the basis of competing scales and mechanisms.Comment: 4 pages, 6 figures To be published in Phys. Rev. Lett. (2001
A dynamical approach to the spatiotemporal aspects of the Portevin-Le Chatelier effect: Chaos,turbulence and band propagation
Experimental time series obtained from single and poly-crystals subjected to
a constant strain rate tests report an intriguing dynamical crossover from a
low dimensional chaotic state at medium strain rates to an infinite dimensional
power law state of stress drops at high strain rates. We present results of an
extensive study of all aspects of the PLC effect within the context a model
that reproduces this crossover. A study of the distribution of the Lyapunov
exponents as a function of strain rate shows that it changes from a small set
of positive exponents in the chaotic regime to a dense set of null exponents in
the scaling regime. As the latter feature is similar to the GOY shell model for
turbulence, we compare our results with the GOY model. Interestingly, the null
exponents in our model themselves obey a power law. The configuration of
dislocations is visualized through the slow manifold analysis. This shows that
while a large proportion of dislocations are in the pinned state in the chaotic
regime, most of them are at the threshold of unpinning in the scaling regime.
The model qualitatively reproduces the different types of deformation bands
seen in experiments. At high strain rates where propagating bands are seen, the
model equations are reduced to the Fisher-Kolmogorov equation for propagative
fronts. This shows that the velocity of the bands varies linearly with the
strain rate and inversely with the dislocation density, consistent with the
known experimental results. Thus, this simple dynamical model captures the
complex spatio-temporal features of the PLC effect.Comment: 17 pages, 18 figure
Force-matched embedded-atom method potential for niobium
Large-scale simulations of plastic deformation and phase transformations in
alloys require reliable classical interatomic potentials. We construct an
embedded-atom method potential for niobium as the first step in alloy potential
development. Optimization of the potential parameters to a well-converged set
of density-functional theory (DFT) forces, energies, and stresses produces a
reliable and transferable potential for molecular dynamics simulations. The
potential accurately describes properties related to the fitting data, and also
produces excellent results for quantities outside the fitting range. Structural
and elastic properties, defect energetics, and thermal behavior compare well
with DFT results and experimental data, e.g., DFT surface energies are
reproduced with less than 4% error, generalized stacking-fault energies differ
from DFT values by less than 15%, and the melting temperature is within 2% of
the experimental value.Comment: 17 pages, 13 figures, 7 table
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