438 research outputs found
Incomplete approach to homoclinicity in a model with bent-slow manifold geometry
The dynamics of a model, originally proposed for a type of instability in
plastic flow, has been investigated in detail. The bifurcation portrait of the
system in two physically relevant parameters exhibits a rich variety of
dynamical behaviour, including period bubbling and period adding or Farey
sequences. The complex bifurcation sequences, characterized by Mixed Mode
Oscillations, exhibit partial features of Shilnikov and Gavrilov-Shilnikov
scenario. Utilizing the fact that the model has disparate time scales of
dynamics, we explain the origin of the relaxation oscillations using the
geometrical structure of the bent-slow manifold. Based on a local analysis, we
calculate the maximum number of small amplitude oscillations, , in the
periodic orbit of type, for a given value of the control parameter. This
further leads to a scaling relation for the small amplitude oscillations. The
incomplete approach to homoclinicity is shown to be a result of the finite rate
of `softening' of the eigen values of the saddle focus fixed point. The latter
is a consequence of the physically relevant constraint of the system which
translates into the occurrence of back-to-back Hopf bifurcation.Comment: 14 Figures(Postscript); To Appear in Physica D : Nonlinear Phenomen
Projecting Low Dimensional Chaos from Spatio-temporal Dynamics in a Model for Plastic Instability
We investigate the possibility of projecting low dimensional chaos from
spatiotemporal dynamics of a model for a kind of plastic instability observed
under constant strain rate deformation conditions. We first discuss the
relationship between the spatiotemporal patterns of the model reflected in the
nature of dislocation bands and the nature of stress serrations. We show that
at low applied strain rates, there is a one-to-one correspondence with the
randomly nucleated isolated bursts of mobile dislocation density and the stress
drops. We then show that the model equations are spatiotemporally chaotic by
demonstrating the number of positive Lyapunov exponents and Lyapunov dimension
scale with the system size at low and high strain rates. Using a modified
algorithm for calculating correlation dimension density, we show that the
stress-strain signals at low applied strain rates corresponding to spatially
uncorrelated dislocation bands exhibit features of low dimensional chaos. This
is made quantitative by demonstrating that the model equations can be
approximately reduced to space independent model equations for the average
dislocation densities, which is known to be low-dimensionally chaotic. However,
the scaling regime for the correlation dimension shrinks with increasing
applied strain rate due to increasing propensity for propagation of the
dislocation bands.Comment: 9 pages, 19 figure
Multi-scale Modeling Approach to Acoustic Emission during Plastic Deformation
We address the long standing problem of the origin of acoustic emission
commonly observed during plastic deformation. We propose a frame-work to deal
with the widely separated time scales of collective dislocation dynamics and
elastic degrees of freedom to explain the nature of acoustic emission observed
during the Portevin-Le Chatelier effect. The Ananthakrishna model is used as it
explains most generic features of the phenomenon. Our results show that while
acoustic emission bursts correlated with stress drops are well separated for
the type C serrations, these bursts merge to form nearly continuous acoustic
signals with overriding bursts for the propagating type A bands.Comment: 4 pages, 6 figure
A unified model for the dynamics of driven ribbon with strain and magnetic order parameters
We develop a unified model to explain the dynamics of driven one dimensional
ribbon for materials with strain and magnetic order parameters. We show that
the model equations in their most general form explain several results on
driven magnetostrictive metallic glass ribbons such as the period doubling
route to chaos as a function of a dc magnetic field in the presence of a
sinusoidal field, the quasiperiodic route to chaos as a function of the
sinusoidal field for a fixed dc field, and induced and suppressed chaos in the
presence of an additional low amplitude near resonant sinusoidal field. We also
investigate the influence of a low amplitude near resonant field on the period
doubling route. The model equations also exhibit symmetry restoring crisis with
an exponent close to unity. The model can be adopted to explain certain results
on magnetoelastic beam and martensitic ribbon under sinusoidal driving
conditions. In the latter case, we find interesting dynamics of a periodic one
orbit switching between two equivalent wells as a function of an ac magnetic
field that eventually makes a direct transition to chaos under resonant driving
condition. The model is also applicable to magnetomartensites and materials
with two order parameters.Comment: 11 pages, 18 figure
Optimal barrier subdivision for Kramers' escape rate
We examine the effect of subdividing the potential barrier along the reaction
coordinate on Kramers' escape rate for a model potential. Using the known
supersymmetric potential approach, we show the existence of an optimal number
of subdivisions that maximises the rate.Comment: 8 pages, 3 figures, To appear in Pramana - J. Phys, Indi
Collective stochastic resonance in shear-induced melting of sliding bilayers
The far-from-equilibrium dynamics of two crystalline two-dimensional
monolayers driven past each other is studied using Brownian dynamics
simulations. While at very high and low driving rates the layers slide past one
another retaining their crystalline order, for intermediate range of drives the
system alternates irregularly between the crystalline and fluid-like phases. A
dynamical phase diagram in the space of interlayer coupling and drive is
obtained. A qualitative understanding of this stochastic alternation between
the liquid-like and crystalline phases is proposed in terms of a reduced model
within which it can be understood as a stochastic resonance for the dynamics of
collective order parameter variables. This remarkable example of stochastic
resonance in a spatially extended system should be seen in experiments which we
propose in the paper.Comment: 12 pages, 18 eps figures, minor changes in text and labelling of
figures, accepted for publication in Phys. Rev.
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.
Development of sustainable Aluminium alloy powders for metal additive manufacturing
Pòster amb el resum gràfic de la tesi doctoral en curs, que forma part de l'exposició "Doctorat en Recursos Naturals i Medi Ambient de la UPC Manresa. 30 anys formant en recerca a la Catalunya Central 1992-2022".This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 101034328.Postprint (published version
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