289 research outputs found
The role of pinning and instability in a class of non-equilibrium growth models
We study the dynamics of a growing crystalline facet where the growth
mechanism is controlled by the geometry of the local curvature. A continuum
model, in (2+1) dimensions, is developed in analogy with the
Kardar-Parisi-Zhang (KPZ) model is considered for the purpose. Following
standard coarse graining procedures, it is shown that in the large time, long
distance limit, the continuum model predicts a curvature independent KPZ phase,
thereby suppressing all explicit effects of curvature and local pinning in the
system, in the "perturbative" limit. A direct numerical integration of this
growth equation, in 1+1 dimensions, supports this observation below a critical
parametric range, above which generic instabilities, in the form of isolated
pillared structures lead to deviations from standard scaling behavior.
Possibilities of controlling this instability by introducing statistically
"irrelevant" (in the sense of renormalization groups) higher ordered
nonlinearities have also been discussed.Comment: 10 pages, 4 figures, references updated and minor changes in the
text, to appear in Euro. Phys. J.
Dynamics of Pulsed Flow in an Elastic Tube
Internal haemorrhage, often leading to cardio-vascular arrest happens to be
one of the prime sources of high fatality rates in mammals. We propose a
simplistic model of fluid flow to specify the location of the haemorrhagic
spots, which, if located accurately, could be operated upon leading to a
possible cure. The model we employ for the purpose is inspired by fluid
mechanics and consists of a viscous fluid, pumped by a periodic force and
flowing through an elastic tube. The analogy is with that of blood, pumped from
the heart and flowing through an arte ry or vein. Our results, aided by
graphical illustrations, match reasonably well with experimental observations.Comment: 6 pages and 4 figure
Memory effects in a non-equilibrium growth model
We study memory effects in a kinetic roughening model. For d=1, a different dynamic scaling is uncovered in the memory dominated phases; the Kardar-Parisi-Zhang scaling is restored in the absence of noise. dc=2 represents the critical dimension where memory is shown to smoothen the roughening front (a=0). Studies on a discrete atomistic model in the same universality class reconfirm the analytical results in the large time limit, while a different scaling behavior shows up for t<t, with t being the memory characteristic of the atomistic model. Results can be generalized for other nonconservative systems
A Topological Distance between Multi-fields based on Multi-Dimensional Persistence Diagrams
The problem of computing topological distance between two scalar fields based
on Reeb graphs or contour trees has been studied and applied successfully to
various problems in topological shape matching, data analysis, and
visualization. However, generalizing such results for computing distance
measures between two multi-fields based on their Reeb spaces is still in its
infancy. Towards this, in the current paper we propose a technique to compute
an effective distance measure between two multi-fields by computing a novel
\emph{multi-dimensional persistence diagram} (MDPD) corresponding to each of
the (quantized) Reeb spaces. First, we construct a multi-dimensional Reeb graph
(MDRG), which is a hierarchical decomposition of the Reeb space into a
collection of Reeb graphs. The MDPD corresponding to each MDRG is then computed
based on the persistence diagrams of the component Reeb graphs of the MDRG. Our
distance measure extends the Wasserstein distance between two persistence
diagrams of Reeb graphs to MDPDs of MDRGs. We prove that the proposed measure
is a pseudo-metric and satisfies a stability property. Effectiveness of the
proposed distance measure has been demonstrated in (i) shape retrieval contest
data - SHREC and (ii) Pt-CO bond detection data from computational
chemistry. Experimental results show that the proposed distance measure based
on the Reeb spaces has more discriminating power in clustering the shapes and
detecting the formation of a stable Pt-CO bond as compared to the similar
measures between Reeb graphs.Comment: Acepted in the IEEE Transactions on Visualization and Computer
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