arXiv subjects

Saikat Roy

Publications and source records attributed to Saikat Roy.

At least 55 records · Page 3Linked to original sources

arXiv2022

Spatial stress correlations in strong colloidal gel

In this work, we systematically investigate for the first time the nature of stress correlations in soft colloidal gel materials which support tensile and compressive forces as well as finite rolling torque, as a function of system pressure. Similar to previous studies on frictional granular matter with only compressive forces and without any rolling torque, the full stress autocorrelation matrix is dictated by the pressure and torque autocorrelations due to mechanical balance and material isotropy constraints. Surprisingly, it is observed that the gel materials do not behave as a normal elastic solid close to the gel point as assumed loosely in the literature because the real space pressure fluctuations decay slower than the normal. We also demonstrate that at low pressure the fractal like structural correlation determines the pressure fluctuations and this is manifested in the real space in terms of inhomogeneous and anisotropic force networks formed due to large voids. Far away from the gel point, as the voids collapse under compression, the force chain network becomes homogeneous and isotropic and the pressure fluctuations become normal leading to normal elastic decay at long range, behaving similar to frictionless granular matter and glass. We also observe that the torque autocorrelation is not hyperuniform in the presence of rolling resistance close to the gel point. Furthermore, we link the abnormal pressure fluctuations to the non-hyperuniform behaviour of the system with respect to the local packing fraction fluctuations, thus relating the deviations from the normal elastic behaviour across various non-equilibrium systems under a common framework.

cond-mat.soft↗

arXiv2021

Birkhoff-James orthogonality in complex Banach spaces and Bhatia-Šemrl Theorem revisited

We explore Birkhoff-James orthogonality of two elements in a complex Banach space by using the directional approach. Our investigation illustrates the geometric distinctions between a smooth point and a non-smooth point in a complex Banach space. As a concrete outcome of our study, we obtain a new proof of the Bhatia-Šemrl Theorem on orthogonality of linear operators.

math.FA↗

arXiv2021

Numerical radius and a notion of smoothness in the space of bounded linear operators

We observe that the classical notion of numerical radius gives rise to a notion of smoothness in the space of bounded linear operators on certain Banach spaces, whenever the numerical radius is a norm. We demonstrate an important class of \emph{real} Banach space $ \mathbb{X} $ for which the numerical radius defines a norm on $ \mathbb{L}(\mathbb{X}), $ the space of all bounded linear operators on $ \mathbb{X} $. We characterize Birkhoff-James orthogonality in the space of bounded linear operators on a finite-dimensional Banach space, endowed with the numerical radius norm. Some examples are also discussed to illustrate the geometric differences between the numerical radius norm and the usual operator norm, from the viewpoint of operator smoothness.

math.FA↗

arXiv2021

Anomalous Elasticity and Screening in Amorphous Solids

Amorphous solids appear to react elastically to small external strains, but in contrast to ideal elastic media, plastic responses abound immediately, at any value of the strain. Such plastic responses are quasi-localized in nature, with the ``cheapest" one being a quadrupolar source. The existence of such plastic responses results in {\em screened elasticity} in which strains and stresses can either quantitatively or qualitatively differ from the un-screened theory, depending on the specific screening mechanism. Here we offer a theory of such screening effects by plastic quadrupoles, dipoles and monopoles, explain their natural appearance, and point out the analogy to electrostatic screening by electric charges and dipoles. For low density of quadrupoles the effect is to normalize the elastic moduli without a qualitative change compared to pure elasticity theory; for higher density of quadrupoles the screening effects result in qualitative changes. Predictions for the spatial dependence of displacement fields caused by local sources of strains are provided and compared to numerical simulations. We find that anomalous elasticity is richer than electrostatics in having a screening mode that does not appear in the electrostatic analog

cond-mat.dis-nn↗

arXiv2021

On best approximations in Banach spaces from the perspective of orthogonality

We study best approximations in Banach spaces via Birkhoff-James orthogonality of functionals. To exhibit the usefulness of Birkhoff-James orthogonality techniques in the study of best approximation problems, some algorithms and distance formulae are presented. As an application of our study, we obtain some crucial inequalities, which also strengthen the classical Hölder's inequality. The relevance of the algorithms and the inequalities are discussed through concrete examples.

math.FA↗

arXiv2020

Frictional Granular Matter: Protocol Dependence of Mechanical Properties

Theoretical treatments of frictional granular matter often assume that it is legitimate to invoke classical elastic theory to describe its coarse-grained mechanical properties. Here we show, based on experiments and numerical simulations, that this is generically not the case since stress auto-correlation functions decay more slowly than the elastic Green's function. It was shown theoretically that standard elastic decay demands pressure and torque density fluctuations to be normal, with possibly one of them being hyperuniform. Generic compressed frictional assemblies exhibit however abnormal pressure fluctuations, failing to conform with the central limit theorem. The physics of this failure is linked to correlations built in the material during compression from a dilute configuration prior to jamming. By changing the protocol of compression one can observe different pressure fluctuations and stress auto-correlations decay at large scales.

cond-mat.soft↗

arXiv2020

Stress Correlations in Frictional Granular Media

This paper investigates whether in frictional granular packings, like in Hamiltonian amorphous elastic solids, the stress autocorrelation matrix presents long range anisotropic contributions just as elastic Green's functions. We find that in a standard model of frictional granular packing this is not the case. We prove quite generally that mechanical balance and material isotropy constrain the stress auto-correlation matrix to be fully determined by two spatially isotropic functions: the pressure and torque auto-correlations. The pressure and torque fluctuations being respectively normal and hyperuniform force the stress autocorrelation to decay as the elastic Green's function. Since we find the torque fluctuations to be hyper-uniform, the culprit is the pressure whose fluctuations decay slower than normally as a function of the system's size. Investigating the reason for these abnormal pressure fluctuations we discover that anomalous correlations build up already during the compression of the dilute system before jamming. Once jammed these correlations remain frozen. Whether this is true for frictional matter in general or is it the consequence of the model properties is a question that must await experimental scrutiny and possible alternative models.

cond-mat.soft↗

arXiv2019

Orthogonality in a vector space with a topology And a generalization of Bhatia-Semrl Theorem

We introduce the notion of orthogonality in a vector space with a topology on it. To serve our purpose, we define orthogonality space for a given vector space X, using the topology on it. We show that for a suitable choice of orthogonality space, Birkhoff-James orthogonality in a Banach space is a particular case of the orthogonality introduced by us. We characterize the right additivity of orthogonality in our setting and obtain a necessary and sufficient condition for a Banach space to be smooth as a corollary to our characterization. Finally, using our notion of orthogonality, we obtain a topological generalization of the Bhatia-Semrl Theorem.

math.FA↗

arXiv2019

A study of symmetric points in Banach spaces

We completely characterize the left-symmetric points, the right-symmetric points, and, the symmetric points in the sense of Birkhoff-James, in a Banach space. We obtain a complete characterization of the left-symmetric (right-symmetric) points in the infinity sum of two Banach spaces, in terms of the left-symmetric (right-symmetric) points of the constituent spaces. As an application of this characterization, we explicitly identify the left-symmetric (right-symmetric) points of some well-known three-dimensional polyhedral Banach spaces.

math.FA↗

arXiv2019

Modeling the Generic Breakthrough Curve for Adsorption Process

This work is aimed at understanding the basic principles of adsorption process in great details as adsorptive separation process has broad applications in the industry. To this end, a simple mathematical model has been used to describe transient fixed bed physical adsorption process. Governing equations are solved numerically to obtain breakthrough curves for single component and multi-component monolayer adsorption. Desorption of a saturated bed by an inert fluid is also considered. A full parametric study is performed to analyze the effects of different parameters such as bed length, velocity, diffusivity, particle radius and isotherm properties on the nature of the breakthrough curve. Analysis of these results led to the development of the generic breakthrough curve for a single component monolayer adsorption which will enable us to tell the nature of breakthrough curve for different process parameters without recourse to the numerical simulation or experiment. Thus this study will be of great interest in the industrial separation process.

physics.app-ph↗

arXiv2019

Diffusion in Agitated Frictional Granular Matter Near the Jamming Transition

We study agitated frictional disks in two dimensions with the aim of developing a scaling theory for their diffusion over time. As a function of the area fraction $ϕ$ and mean-square velocity fluctuations $\langle v^2\rangle$ the mean-square displacement of the disks $\langle d^2\rangle$ spans 4-5 orders of magnitude. The motion evolves from a subdiffusive form to a complex diffusive behabvior at long times. The statistics of $\langle d^n\rangle$ at all times are multiscaling, since the probability distribution function (pdf) of displacements has very broad wings. Even where a diffusion constant can be identified it is a complex function of $ϕ$ and $\langle v^2\rangle$. By identifying the relevant length and time scales and their interdependence one can rescale the data for the mean square displacement and the pdf of displacements into collapsed scaling functions for all $ϕ$ and $\langle v^2\rangle$. These scaling functions provide a predictive tool, allowing to infer from one set of measurements (at a given $ϕ$ and $\langle v^2\rangle$) what are the expected results at any value of $ϕ$ and $\langle v^2\rangle$.

cond-mat.soft↗

arXiv2019

Extreme contractions on finite-dimensional polygonal Banach spaces-II

We introduce the concept of weak L-P property for a pair of Banach spaces, in the study of extreme contractions. We give examples of pairs of Banach spaces (not) satisfying weak L-P property and apply the concept to compute the exact number of extreme contractions between a particular pair of polygonal Banach spaces. We also study the optimality of our results on the newly introduced weak L-P property for a pair of Banach spaces, by considering appropriate examples.

math.FA↗

arXiv2018

Document Image Classification with Intra-Domain Transfer Learning and Stacked Generalization of Deep Convolutional Neural Networks

In this work, a region-based Deep Convolutional Neural Network framework is proposed for document structure learning. The contribution of this work involves efficient training of region based classifiers and effective ensembling for document image classification. A primary level of `inter-domain' transfer learning is used by exporting weights from a pre-trained VGG16 architecture on the ImageNet dataset to train a document classifier on whole document images. Exploiting the nature of region based influence modelling, a secondary level of `intra-domain' transfer learning is used for rapid training of deep learning models for image segments. Finally, stacked generalization based ensembling is utilized for combining the predictions of the base deep neural network models. The proposed method achieves state-of-the-art accuracy of 92.2% on the popular RVL-CDIP document image dataset, exceeding benchmarks set by existing algorithms.

cs.CV↗

arXiv2018

Scaling Theory of Giant Frictional Slips in Decompressed Granular Media

When compressed frictional granular media are decompressed, generically a fragile configuration is created at low pressures. Typically this is accompanied by a giant frictional slippage as the fragile state collapses. We show that this instability is understood in terms of a scaling theory with theoretically computable amplitudes and exponents. The amplitude diverges in the thermodynamic limit hinting to the possibility of huge frictional slip events in decompressed granular media. The physics of this slippage is discussed in terms of the probability distribution functions of the tangential and normal forces on the grains which are highly correlated due to the Coulomb condition.

cond-mat.soft↗

arXiv2018

Force Distributions in Frictional Granular Media

We report a joint experimental and theoretical investigation of the probability distribution functions (pdf's) of the normal and tangential (frictional) forces in amorphous frictional media. We consider both the joint pdf of normal and tangential forces together, and the marginal pdf's of normal forces separately and tangential forces separately. A maximum entropy formalism is utilized for all these cases after identifying the appropriate constraints. Excellent agreements with both experimental and simulational data are reported. The proposed joint pdf (which appears new to the literature) predicts giant slip events at low pressures, again in agreement with observations.

cond-mat.soft↗

arXiv2018

Handwritten Isolated Bangla Compound Character Recognition: a new benchmark using a novel deep learning approach

In this work, a novel deep learning technique for the recognition of handwritten Bangla isolated compound character is presented and a new benchmark of recognition accuracy on the CMATERdb 3.1.3.3 dataset is reported. Greedy layer wise training of Deep Neural Network has helped to make significant strides in various pattern recognition problems. We employ layerwise training to Deep Convolutional Neural Networks (DCNN) in a supervised fashion and augment the training process with the RMSProp algorithm to achieve faster convergence. We compare results with those obtained from standard shallow learning methods with predefined features, as well as standard DCNNs. Supervised layerwise trained DCNNs are found to outperform standard shallow learning models such as Support Vector Machines as well as regular DCNNs of similar architecture by achieving error rate of 9.67% thereby setting a new benchmark on the CMATERdb 3.1.3.3 with recognition accuracy of 90.33%, representing an improvement of nearly 10%.

cs.CV↗

arXiv2018

On maximum distance separable group codes with complementary duals

Given an LCD group code $C$ in a group algebra $KG$, we inspect kinship between $C$ and $G$, more precisely between the subgroup structures of $G$ and $C$. Under some special circumstances our inspection provides an estimation for various parameters of a group code $C$. When $C$ is MDS, the inter relation between $K$ and $G$ becomes more impressive. Application of Sylow theorem facilitated us to explore the inter relation between $G$ and $K$ (when $C$ is LCD and MDS) in more general way and finally we get the result of Cruz and Willems (Lemma $4.4$) as a simple sequel.

math.RA↗

arXiv2018

Training, Memory and Universal Scaling in Amorphous Frictional Granular Matter

We report a joint experimental and theoretical investigation of cyclic training of amorphous frictional granular assemblies, with special attention to memory formation and retention. Measures of dissipation and compactification are introduced, culminating with a proposed scaling law for the reducing dissipation and increasing memory. This scaling law is expected to be universal, insensitive to the details of the elastic and frictional interactions between the granules.

cond-mat.soft↗