6,979 research outputs found
Brownian microhydrodynamics of active filaments
Slender bodies capable of spontaneous motion in the absence of external
actuation in an otherwise quiescent fluid are common in biological, physical
and technological contexts. The interplay between the spontaneous fluid flow,
Brownian motion, and the elasticity of the body presents a challenging
fluid-structure interaction problem. Here, we model this problem by
approximating the slender body as an elastic filament that can impose
non-equilibrium velocities or stresses at the fluid-structure interface. We
derive equations of motion for such an active filament by enforcing momentum
conservation in the fluid-structure interaction and assuming slow viscous flow
in the fluid. The fluid-structure interaction is obtained, to any desired
degree of accuracy, through the solution of an integral equation. A simplified
form of the equations of motion, that allows for efficient numerical solutions,
is obtained by applying the Kirkwood-Riseman superposition approximation to the
integral equation. We use this form of the equation of motion to study
dynamical steady states in free and hinged minimally active filaments. Our
model provides the foundation to study collective phenomena in
momentum-conserving, Brownian, active filament suspensions.Comment: 13 pages, 5 figure
Irreducible Representations Of Oscillatory And Swirling Flows In Active Soft Matter
Recent experiments imaging fluid flow around swimming microorganisms have
revealed complex time-dependent velocity fields that differ qualitatively from
the stresslet flow commonly employed in theoretical descriptions of active
matter. Here we obtain the most general flow around a finite sized active
particle by expanding the surface stress in irreducible Cartesian tensors. This
expansion, whose first term is the stresslet, must include, respectively,
third-rank polar and axial tensors to minimally capture crucial features of the
active oscillatory flow around translating Chlamydomonas and the active
swirling flow around rotating Volvox. The representation provides explicit
expressions for the irreducible symmetric, antisymmetric and isotropic parts of
the continuum active stress. Antisymmetric active stresses do not conserve
orbital angular momentum and our work thus shows that spin angular momentum is
necessary to restore angular momentum conservation in continuum hydrodynamic
descriptions of active soft matter.Comment: 9 pages, 5 figures, includes supplementary text; corrected link to
supplementary video at https://www.youtube.com/watch?v=tRO1nm_UQi
Anomalous magnetic moment of muon and L-violating Supersymmetric Models
We consider L-violating Supersymmetric Models to explain the recent muon
deviation from the Standard Model. The order of trilinear
L-violating couplings which we require also generate neutrino mass which is
somewhat higher than expected unless one considers highly suppressed
mixing of sfermions. However, without such fine tuning for sfermions it is
possible to get appropriate muon deviation as well as neutrino mass
if one considers some horizontal symmetry for the lepton doublet. Our studies
show that deviation may not imply upper bound of about 500 GeV on
masses of supersymmetric particles like chargino or neutralino as proposed by
other authors for R parity conserving supersymmetric models. However, in our
scenario sneutrino mass is expected to be light ( GeV) and
universality violation may be observed experimentally in near
future.Comment: 11 pages, latex, 2 figure
Left Translates of a Square Integrable Function on the Heisenberg group
The aim of this paper is to study some properties of left translates of a
square integrable function on the Heisenberg group. First, a necessary and
sufficient condition for the existence of the canonical dual to a function
is obtained in the case of twisted
shift-invariant spaces. Further, characterizations of -linear
independence and the Hilbertian property of the twisted translates of a
function are obtained. Later these results
are shown in the case of the Heisenberg group.Comment: 13 page
Shift-invariant Spaces with Countably Many Mutually Orthogonal Generators on the Heisenberg group
Let denote the shift-invariant space associated with a
countable family of functions in with
mutually orthogonal generators, where denotes the Heisenberg
group. The characterizations for the collection to be
orthonormal, Bessel sequence, Parseval frame and so on are obtained in terms of
the group Fourier transform of the Heisenberg group. These results are derived
using such type of results which were proved for twisted shift-invariant spaces
and characterized in terms of Weyl transform. In the last section of the paper,
some results on oblique dual of the left translates of a single function
is discussed in the context of principal shift-invariant space
.Comment: 15 pages, no figur
Generalized Stokes laws for active colloids and their applications
The force per unit area on the surface of a colloidal particle is a
fundamental dynamical quantity in the mechanics and statistical mechanics of
colloidal suspensions. Here we compute it in the limit of slow viscous flow for
a suspension of spherical active colloids in which activity is represented
by surface slip. Our result is best expressed as a set of linear relations, the
"generalized Stokes laws", between the coefficients of a tensorial spherical
harmonic expansion of the force per unit area and the surface slip. The
generalized friction tensors in these laws are many-body functions of the
colloidal configuration and can be obtained to any desired accuracy by solving
a system of linear equations. Quantities derived from the force per unit area -
forces, torques and stresslets on the colloids and flow, pressure and entropy
production in the fluid - have succinct expressions in terms of the generalized
Stokes laws. Most notably, the active forces and torques have a dissipative,
long-ranged, many-body character that can cause phase separation,
crystallization, synchronization and a variety of other effects observed in
active suspensions. We use the results above to derive the Langevin and
Smoluchowski equations for Brownian active suspensions, to compute active
contributions to the suspension stress and fluid pressure, and to relate the
synchrony in a lattice of harmonically trapped active colloids to entropy
production. Our results provide the basis for a microscopic theory of active
Brownian suspensions that consistently accounts for momentum conservation in
the bulk fluid and at fluid-solid boundariesComment: add published version; supplemental movies at
https://www.youtube.com/playlist?list=PLOKQ_pz8e2Vu0Pr0Fn2IpD2iIF1oj5G1
A Homogeneous Ensemble of Artificial Neural Networks for Time Series Forecasting
Enhancing the robustness and accuracy of time series forecasting models is an
active area of research. Recently, Artificial Neural Networks (ANNs) have found
extensive applications in many practical forecasting problems. However, the
standard backpropagation ANN training algorithm has some critical issues, e.g.
it has a slow convergence rate and often converges to a local minimum, the
complex pattern of error surfaces, lack of proper training parameters selection
methods, etc. To overcome these drawbacks, various improved training methods
have been developed in literature; but, still none of them can be guaranteed as
the best for all problems. In this paper, we propose a novel weighted ensemble
scheme which intelligently combines multiple training algorithms to increase
the ANN forecast accuracies. The weight for each training algorithm is
determined from the performance of the corresponding ANN model on the
validation dataset. Experimental results on four important time series depicts
that our proposed technique reduces the mentioned shortcomings of individual
ANN training algorithms to a great extent. Also it achieves significantly
better forecast accuracies than two other popular statistical models.Comment: 8 pages, 4 figures, 2 tables, 26 references, international journa
Combining Multiple Time Series Models Through A Robust Weighted Mechanism
Improvement of time series forecasting accuracy through combining multiple
models is an important as well as a dynamic area of research. As a result,
various forecasts combination methods have been developed in literature.
However, most of them are based on simple linear ensemble strategies and hence
ignore the possible relationships between two or more participating models. In
this paper, we propose a robust weighted nonlinear ensemble technique which
considers the individual forecasts from different models as well as the
correlations among them while combining. The proposed ensemble is constructed
using three well-known forecasting models and is tested for three real-world
time series. A comparison is made among the proposed scheme and three other
widely used linear combination methods, in terms of the obtained forecast
errors. This comparison shows that our ensemble scheme provides significantly
lower forecast errors than each individual model as well as each of the four
linear combination methods.Comment: 6 pages, 3 figures, 2 tables, conferenc
An Introductory Study on Time Series Modeling and Forecasting
Time series modeling and forecasting has fundamental importance to various
practical domains. Thus a lot of active research works is going on in this
subject during several years. Many important models have been proposed in
literature for improving the accuracy and effectiveness of time series
forecasting. The aim of this dissertation work is to present a concise
description of some popular time series forecasting models used in practice,
with their salient features. In this thesis, we have described three important
classes of time series models, viz. the stochastic, neural networks and SVM
based models, together with their inherent forecasting strengths and
weaknesses. We have also discussed about the basic issues related to time
series modeling, such as stationarity, parsimony, overfitting, etc. Our
discussion about different time series models is supported by giving the
experimental forecast results, performed on six real time series datasets.
While fitting a model to a dataset, special care is taken to select the most
parsimonious one. To evaluate forecast accuracy as well as to compare among
different models fitted to a time series, we have used the five performance
measures, viz. MSE, MAD, RMSE, MAPE and Theil's U-statistics. For each of the
six datasets, we have shown the obtained forecast diagram which graphically
depicts the closeness between the original and forecasted observations. To have
authenticity as well as clarity in our discussion about time series modeling
and forecasting, we have taken the help of various published research works
from reputed journals and some standard books.Comment: 67 pages, 29 figures, 33 references, boo
Fast Bayesian inference of the multivariate Ornstein-Uhlenbeck process
The multivariate Ornstein-Uhlenbeck process is used in many branches of
science and engineering to describe the regression of a system to its
stationary mean. Here we present an Bayesian method to estimate the
drift and diffusion matrices of the process from discrete observations of a
sample path. We use exact likelihoods, expressed in terms of four sufficient
statistic matrices, to derive explicit maximum a posteriori parameter estimates
and their standard errors. We apply the method to the Brownian harmonic
oscillator, a bivariate Ornstein-Uhlenbeck process, to jointly estimate its
mass, damping, and stiffness and to provide Bayesian estimates of the
correlation functions and power spectral densities. We present a Bayesian model
comparison procedure, embodying Ockham's razor, to guide a data-driven choice
between the Kramers and Smoluchowski limits of the oscillator. These provide
novel methods of analyzing the inertial motion of colloidal particles in
optical traps.Comment: add published versio
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