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

Shift-invariant Spaces with Countably Many Mutually Orthogonal Generators on the Heisenberg group

Let $E(\mathscr{A})$ denote the shift-invariant space associated with a countable family $\mathscr{A}$ of functions in $L^{2}(\mathbb{H}^{n})$ with mutually orthogonal generators, where $\mathbb{H}^{n}$ denotes the Heisenberg group. The characterizations for the collection $E(\mathscr{A})$ 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 $\varphi$ is discussed in the context of principal shift-invariant space $V(\varphi)$.Comment: 15 pages, no figur

Anomalous magnetic moment of muon and L-violating Supersymmetric Models

We consider L-violating Supersymmetric Models to explain the recent muon $g_{\mu} -2$ 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 $L-R$ mixing of sfermions. However, without such fine tuning for sfermions it is possible to get appropriate muon $g_{\mu}-2$ deviation as well as neutrino mass if one considers some horizontal symmetry for the lepton doublet. Our studies show that $g_{\mu} -2$ 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 ($\sim 100$ GeV) and $e-\mu-\tau$ 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 $\varphi\in L^{2}(\mathbb{R}^{2n})$ is obtained in the case of twisted shift-invariant spaces. Further, characterizations of $\ell^{2}$-linear independence and the Hilbertian property of the twisted translates of a function $\varphi\in L^{2}(\mathbb{R}^{2n})$ are obtained. Later these results are shown in the case of the Heisenberg group.Comment: 13 page

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 $N$ 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 $O(N)$ Bayesian method to estimate the drift and diffusion matrices of the process from $N$ 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