Effect of Marangoni stress on the bulk rheology of a dilute emulsion of surfactant-laden deformable droplets in linear flows

In the present study we analytically investigate the deformation and bulk rheology of a dilute emulsion of surfactant-laden droplets suspended in a linear flow. We use an asymptotic approach to predict the effect of surfactant distribution on the deformation of a single droplet as well as the effective shear and extensional viscosity for the dilute emulsion. The non-uniform distribution of surfactants due to the bulk flow results in the generation of a Marangoni stress which affects both the deformation as well as the bulk rheology of the suspension. The present analysis is done for the limiting case when the surfactant transport is dominated by the surface diffusion relative to surface convection. As an example, we have used two commonly encountered bulk flows, namely, uniaxial extensional flow and simple shear flow. With the assumption of negligible inertial forces present in either of the phases, we are able to show that both the surfactant concentration on the droplet surface as well as the ratio of viscosity of the droplet phase with respect to the suspending fluid has a significant effect on the droplet deformation as well as the bulk rheology. It is seen that increase in the non-uniformity in surfactant distribution on the droplet surface results in a higher droplet deformation and a higher effective viscosity for either of linear flows considered. For the case of simple shear flow, surfactant distribution is found to have no effect on the inclination angle, however, a higher viscosity ratio predicts the droplet to be more aligned towards the direction of flow

Complex Fluid-Fluid Interface may Non Trivially Dictate Droplet Deformation in an Incipient Flow

The present study theoretically predicts the effect of interfacial viscosity on the deformation of a compound drop as well as on the bulk rheology. The system at hand comprises of a dilute emulsion of concentric compound drops, laden with surfactants and suspended in a linear flow. Two types of linear flows are considered in this study, namely, a uniaxial extensional flow and a simple shear flow. Presence of surfactants along the drop surface leads to the generation of an interfacial viscosity, which is different from the bulk. This interfacial viscosity generates a viscous drag that along with bulk flow-induced nonuniform surfactant distribution on the drop surface significantly alters drop dynamics. For the present study an asymptotic approach is used to solve the flow field under the limiting case of diffusion-dominated-surfactant transport. Assuming the surfactants to be bulk-insoluble and negligible inertia to be present in fluid flow, it is shown that presence of interfacial viscosity reduces the deformation of a compound drop and enhances the stability of a dilute double emulsion. At the same time the effective viscosity of the emulsion also increases with rise in interfacial viscosity. For large values of interfacial dilatational viscosity the drop deformation is seen to increase and hence the stability of the double emulsion is questionable

Cross-stream migration of a surfactant-laden deformable droplet in a Poiseuille flow

The motion of a viscous deformable droplet suspended in an unbounded Poiseuille flow in the presence of bulk-insoluble surfactants is studied analytically. Assuming the convective transport of fluid and heat to be negligible, we perform a small-deformation perturbation analysis to obtain the droplet migration velocity. The droplet dynamics strongly depends on the distribution of surfactants along the droplet interface, which is governed by the relative strength of convective transport of surfactants as compared with the diffusive transport of surfactants. The present study is focused on the following two limits: (i) when the surfactant transport is dominated by surface diffusion, and (ii) when the surfactant transport is dominated by surface convection. In the first limiting case, it is seen that the axial velocity of the droplet decreases with increase in the advection of the surfactants along the surface. The variation of cross-stream migration velocity, on the other hand, is analyzed over three different regimes based on the ratio of the viscosity of the droplet phase to that of the carrier phase. In the first regime the migration velocity decreases with increase in surface advection of the surfactants although there is no change in direction of droplet migration. For the second regime, the direction of the cross-stream migration of the droplet changes depending on different parameters. In the third regime, the migration velocity is merely affected by any change in the surfactant distribution. For the other limit of higher surface advection in comparison to surface diffusion of the surfactants, the axial velocity of the droplet is found to be independent of the surfactant distribution. However, the cross-stream velocity is found to decrease with increase in non-uniformity in surfactant distribution

Persistent 1-Cycles: Definition, Computation, and Its Application

Persistence diagrams, which summarize the birth and death of homological features extracted from data, are employed as stable signatures for applications in image analysis and other areas. Besides simply considering the multiset of intervals included in a persistence diagram, some applications need to find representative cycles for the intervals. In this paper, we address the problem of computing these representative cycles, termed as persistent 1-cycles, for $\text{H}_1$-persistent homology with $\mathbb{Z}_2$ coefficients. The definition of persistent cycles is based on the interval module decomposition of persistence modules, which reveals the structure of persistent homology. After showing that the computation of the optimal persistent 1-cycles is NP-hard, we propose an alternative set of meaningful persistent 1-cycles that can be computed with an efficient polynomial time algorithm. We also inspect the stability issues of the optimal persistent 1-cycles and the persistent 1-cycles computed by our algorithm with the observation that the perturbations of both cannot be properly bounded. We design a software which applies our algorithm to various datasets. Experiments on 3D point clouds, mineral structures, and images show the effectiveness of our algorithm in practice.Comment: Correct the algorithm numbering issu

Magnetism in the Early Universe

Blazar observations point toward the possible presence of magnetic fields over intergalactic scales of the order of up to $\sim1\,$Mpc, with strengths of at least $\sim10^{-16}\,$G. Understanding the origin of these large-scale magnetic fields is a challenge for modern astrophysics. Here we discuss the cosmological scenario, focussing on the following questions: (i) How and when was this magnetic field generated? (ii) How does it evolve during the expansion of the universe? (iii) Are the amplitude and statistical properties of this field such that they can explain the strengths and correlation lengths of observed magnetic fields? We also discuss the possibility of observing primordial turbulence through direct detection of stochastic gravitational waves in the mHz range accessible to LISA.Comment: Invited talk given at FM8 "New Insights in Extragalactic Magnetic Fields", XXX IAU GA, Vienna, Austria, August 29, 2018; 4 pages; 2 figures; accepted for publicatio

Statistical Properties of Scale-Invariant Helical Magnetic Fields and Applications to Cosmology

We investigate the statistical properties of isotropic, stochastic, Gaussian distributed, helical magnetic fields characterized by different shapes of the energy spectra at large length scales and study the associated realizability condition. We discuss smoothed magnetic fields that are commonly used when the primordial magnetic field is constrained by observational data. We are particularly interested in scale-invariant magnetic fields that can be generated during the inflationary stage by quantum fluctuations. We determine the correlation length of such magnetic fields and relate it to the infrared cutoff of perturbations produced during inflation. We show that this scale determines the observational signatures of the inflationary magnetic fields on the cosmic microwave background. At smaller scales, the scale-invariant spectrum changes with time. It becomes a steeper weak-turbulence spectrum at progressively larger scales. We show numerically that the critical length scale where this happens is the turbulent-diffusive scale, which increases with the square root of time.Comment: 24 pages, 9 figures. Discussion expanded, references added, results unchanged. Accepted for publication in JCA

Cross-stream migration characteristics of a deformable droplet in a non-isothermal Poiseuille Flow through Microfluidic Channel

The migration characteristics of a suspended deformable droplet in a parallel plate microchannel is studied, both analytically and numerically, under the combined influence of a constant temperature gradient in the transverse direction and an imposed pressure driven flow. Any predefined transverse position in the micro channel can be attained by the droplet depending on the applied temperature gradient in the cross-stream direction or how small the droplet is with respect to the channel width. For the analytical solution, an asymptotic approach is used, where we neglect any effect of inertia or thermal convection of the fluid in either of the phases. To obtain a numerical solution, we use the conservative level set method. Variation of temperature in the flow field causes a jump in the tangential component of stress at the droplet interface. This jump in stress component, which is the thermal Marangoni stress, is an important factor that controls the trajectory of the droplet. The direction of cross-stream migration of the droplet is decided by the magnitude of the critical Marangoni stress, corresponding to which the droplet remains stationary. In order to analyze practical microfluidic setup, we do numerical simulations where we consider wall effects as well as the effect of thermal convection and finite shape deformation on the cross-stream migration of the droplet

End-to-End Bengali Speech Recognition

Bengali is a prominent language of the Indian subcontinent. However, while many state-of-the-art acoustic models exist for prominent languages spoken in the region, research and resources for Bengali are few and far between. In this work, we apply CTC based CNN-RNN networks, a prominent deep learning based end-to-end automatic speech recognition technique, to the Bengali ASR task. We also propose and evaluate the applicability and efficacy of small 7x3 and 3x3 convolution kernels which are prominently used in the computer vision domain primarily because of their FLOPs and parameter efficient nature. We propose two CNN blocks, 2-layer Block A and 4-layer Block B, with the first layer comprising of 7x3 kernel and the subsequent layers comprising solely of 3x3 kernels. Using the publicly available Large Bengali ASR Training data set, we benchmark and evaluate the performance of seven deep neural network configurations of varying complexities and depth on the Bengali ASR task. Our best model, with Block B, has a WER of 13.67, having an absolute reduction of 1.39% over comparable model with larger convolution kernels of size 41x11 and 21x11.Comment: 4 pages, 2 figures, 3 table

Primordial magnetic helicity evolution with a homogeneous magnetic field from inflation

Motivated by a scenario of magnetogenesis in which a homogeneous magnetic field is generated during inflation, we study the magnetohydrodynamic evolution of the primordial plasma motions for two kinds of initial conditions -- (i) a spatially homogeneous field with an unlimited correlation length, and (ii) a zero flux scale-invariant statistically homogeneous magnetic field. In both cases, we apply, for a short initial time interval, monochromatic forcing at a certain wave number so that the correlation length is finite, but much smaller than the typical length scale of turbulence. In particular, we investigate the decay of nonhelical and helical hydromagnetic turbulence. We show that, in the presence of a homogeneous magnetic field, the decay of helical and nonhelical small-scale fields can occur rapidly. This is a special property of a system with a perfectly homogeneous magnetic field, which is sometimes considered as a local approximation to a slowly varying background field. It can never change and acts as an imposed magnetic field. This is in a sharp contrast to the case of a statistically homogeneous magnetic field, where we recover familiar decay properties: a much slower decay of magnetic energy and a faster growth of the correlation length, especially in the case with magnetic felicity. The result suggests that a homogeneous magnetic field, if generated during inflation, should persist under the influence of small-scale fields and could be the origin of the large-scale magnetic field in the Universe.Comment: 16 pages, 7 figures, 1 table. Journal versio

Computing Minimal Persistent Cycles: Polynomial and Hard Cases

Persistent cycles, especially the minimal ones, are useful geometric features functioning as augmentations for the intervals in a purely topological persistence diagram (also termed as barcode). In our earlier work, we showed that computing minimal 1-dimensional persistent cycles (persistent 1-cycles) for finite intervals is NP-hard while the same for infinite intervals is polynomially tractable. In this paper, we address this problem for general dimensions with $\mathbb{Z}_2$ coefficients. In addition to proving that it is NP-hard to compute minimal persistent d-cycles (d>1) for both types of intervals given arbitrary simplicial complexes, we identify two interesting cases which are polynomially tractable. These two cases assume the complex to be a certain generalization of manifolds which we term as weak pseudomanifolds. For finite intervals from the d-th persistence diagram of a weak (d+1)-pseudomanifold, we utilize the fact that persistent cycles of such intervals are null-homologous and reduce the problem to a minimal cut problem. Since the same problem for infinite intervals is NP-hard, we further assume the weak (d+1)-pseudomanifold to be embedded in $\mathbb{R}^{d+1}$ so that the complex has a natural dual graph structure and the problem reduces to a minimal cut problem. Experiments with both algorithms on scientific data indicate that the minimal persistent cycles capture various significant features of the data.Comment: Content same as appeared in the proceeding of SODA20