arXiv subjects

Kaushik Bhattacharya

Publications and source records attributed to Kaushik Bhattacharya.

At least 55 records · Page 3Linked to original sources

arXiv2023

Accelerated Computational Micromechanics for Reactive Flow in Porous Media

Reactive transport in permeable porous media is relevant for a variety of applications, but poses a significant challenge due to the range of length and time scales. Multiscale methods that aim to link microstructure with the macroscopic response of geo-materials have been developed, but require the repeated solution of the small-scale problem and provide the motivation for this work. We present an efficient computational method to study fluid flow and solute transport problems in periodic porous media. Fluid flow is governed by the Stokes equation, and the solute transport is governed by the advection-diffusion equation. We follow the accelerated computational micromechanics approach that leads to an iterative computational method where each step is either local or the solution of a Poisson's equation. This enables us to implement these methods on accelerators like graphics processing units (GPUs) and exploit their massively parallel architecture. We verify the approach by comparing the results against established computational methods and then demonstrate the accuracy, efficacy, and performance by studying various examples. This method efficiently calculates the effective transport properties for complex pore geometries.

math.NA↗

arXiv2023

Embedding Ultra slow-roll inflaton dynamics in Warm Inflation

Slow-roll of the inflaton field defines the standard dynamics of the inflationary epoch. However, the inflationary system deviates from slow-roll when it encounters an extremely flat region of the inflaton potential, and enters a phase dubbed Ultra slow roll. In this article, we explore the possibility of realizing an Ultra slow-roll phase in a particularly interesting inflationary scenario, called Warm Inflation. In the Warm inflationary scenario a thermalized, sub-dominant radiation bath coexists with the inflaton energy density as an effect of dissipative dynamics. We show in this article that though the background dynamics indicate Ultra slow-roll when the potential becomes extremely flat, in Warm Inflation models, where the dissipation coefficient is a sole function of the temperature of the radiation bath, the system fails to maintain the thermal equilibrium as soon as it enters the Ultra slow-roll phase. As thermal equilibrium is a key feature of Warm Inflation, and as it is not yet known how to deal with Warm Inflation without thermal equilibrium, we could not analyze such systems any further in this article. However, we demonstrate that brief periods of Ultra slow-roll phase, which smoothly ends into standard slow-roll, can be accommodated in WI models where the dissipation coefficient is not only a function of the temperature of the radiation bath but also depends on the amplitude of the inflaton field. We theoretically determine the criteria of successfully embedding Ultra slow-roll in WI while the system remain in thermal equilibrium, and also demonstrate numerically that such short Ultra slow-roll phases can indeed be embedded in specific Warm Inflation models which comply with the theoretically determined criteria.

astro-ph.CO↗

arXiv2023

Optical penetration depth and periodic motion of a photomechanical strip

Liquid crystal elastomers (LCEs) containing light-sensitive molecules exhibit large reversible deformation when subjected to illumination. Here, we investigate the role of optical penetration depth on this photomechanical response. We present a model of the photomechanical behavior of photoactive LCE strips under illumination that goes beyond the common assumption of shallow penetration. This model reveals how the optical penetration depth and the consequent photomechanically induced deformation can depend on the concentration of photoactive molecules, their absorption cross-sections, and the intensity of illumination. Through a series of examples, we show that the penetration depth can quantitatively and qualitatively affect the photomechanical response of a strip. Shallow illumination leads to monotone curvature change while deep penetration can lead to non-monotone response with illumination duration. Further, the flapping behavior (a cyclic wave-like motion) of doubly clamped and buckled strips that has been proposed for locomotion can reverse direction with sufficiently large penetration depth. This opens the possibility of creating wireless light-driven photomechanical actuators and swimmers whose direction of motion can be controlled by light intensity and frequency.

cond-mat.soft↗

arXiv2023

Dynamical stability in models where dark matter and dark energy are non-minimally coupled to curvature

This work explores the dynamical stability of cosmological models where dark matter and dark energy can non-minimally couple to spacetime (scalar) curvature. Two different scenarios are presented here. In the initial case, only dark matter sector is coupled to curvature in the presence of a quintessence scalar field. In the second case both dark matter and the quintessence field are coupled to curvature. It is shown that one can get an accelerating expansion phase of the universe in both the cases. The nature of the fixed points show that there can be stable or unstable phases where the curvature coupling vanishes and dark energy and dark matter evolve independently. On the other hand there can be stable accelerating expansion phases where both the components are coupled to curvature.

gr-qc↗

arXiv2023

A learning-based multiscale model for reactive flow in porous media

We study solute-laden flow through permeable geological formations with a focus on advection-dominated transport and volume reactions. As the fluid flows through the permeable medium, it reacts with the medium, thereby changing the morphology and properties of the medium; this in turn, affects the flow conditions and chemistry. These phenomena occur at various lengths and time scales, and makes the problem extremely complex. Multiscale modeling addresses this complexity by dividing the problem into those at individual scales, and systematically passing information from one scale to another. However, accurate implementation of these multiscale methods are still prohibitively expensive. We present a methodology to overcome this challenge that is computationally efficient and quantitatively accurate. We introduce a surrogate for the solution operator of the lower scale problem in the form of a recurrent neural operator, train it using one-time off-line data generated by repeated solutions of the lower scale problem, and then use this surrogate in application-scale calculations. The result is the accuracy of concurrent multiscale methods, at a cost comparable to those of classical models. We study various examples, and show the efficacy of this method in understanding the evolution of the morphology, properties and flow conditions over time in geological formations.

math.NA↗

arXiv2023

Learning the Effective Adhesive Properties of Heterogeneous Substrates

Adhesion is a fundamental phenomenon that plays a role in many engineering and biological applications. This paper concerns the use of machine learning to characterize the effective adhesive properties when a thin film is peeled from a heterogeneous substrate. There has been recent interest in the use of machine learning in multiscale modeling where macroscale constitutive relations are learnt from data gathered from repeated solution of the microscale problem. We extend this approach to peeling; this is challenging because peeling from heterogenous substrates is characterized by pinning where the peel front gets stuck at a heterogeneity followed by an abrupt depinning. This results in a heterogeneity dependent critical force and a singular peel force vs. overall peel rate relationship. We propose a neural architecture that is able to accurately predict both the critical peel force and the singular nature of the peel force vs. overall peel rate relationship from the heterogeneous adhesive pattern. Similar issues arise in other free boundary and free discontinuity problems, and the methods we develop are applicable in those contexts.

physics.app-ph↗

arXiv2023

Realizing late-time cosmology in the context of Dynamical Stability Approach

We examine the scenario of non-minimally coupled relativistic fluid and $k$-essence scalar field in a flat Friedmann-Lemaitre-Robertson-Walker universe. By adding a non-minimal coupling term in the Lagrangian level, we study the variation of Lagrangian with respect to independent variables, which produces modified scalar field and Friedmann equations. Using dynamical stability approach in different types of interaction models with two types of scalar field potential, we explore this coupled framework. Implementing detailed analysis, we can conclude our models can able to produce stable late-time cosmic acceleration.

gr-qc↗

arXiv2023

Dynamical Analysis of the Dirac-Born-Infeld type of Tachyon field minimally coupled with barotropic fluid using EOS parametrization of a field

In this paper, we present a dynamical system analysis of the tachyon dark energy model by parametrization of the equation of state (EoS) of the dark energy. The choice of parametrization can constrain the form of the field potential, and as a result, the theory can be directly constrained from the observation without assuming a particular form of the potential.

gr-qc↗

arXiv2023

Gravitational collapse of matter in the presence of Quintessence and Phantom-like scalar fields

In this work, we propose a model of the gravitational collapse of dark matter in the presence of quintessence or phantom-like scalar fields. Our treatment is based on the principles of general relativity up to virialization. We have chosen a spherical patch that starts to collapse gravitationally as it happens in top-hat collapse. It is seen that although the dark matter sector collapses the dark energy sector does keep a profile that is almost similar to the dark energy profile for the background expanding Friedmann-Lemaitre-Robertson-Walker (FLRW) universe for suitable model parameters. It is observed that in order to formulate the problem in the general relativistic setting one has to abandon the idea of a closed FLRW isolated collapsing patch. General relativity requires an external generalized Vaidya spacetime to be matched with the internal spherical patch whose dynamics is guided by the FLRW metric. It is shown that almost all collapses are accompanied by some flux of matter and radiation in the generalized Vaidya spacetime. Some of the spherical regions of the universe are seen not to collapse but expand eternally, producing void-like structures. Whether a spherical region will collapse or expand depends upon the initial values of the system and other model parameters. As this work shows that collapsing structures must emit some form of radiation, this may be taken as an observational signature of our proposal.

gr-qc↗

arXiv2023

Dynamical Stability in presence of non-minimal derivative dependent coupling of $k$-essence field with a relativistic fluid

In this paper we investigate a non-minimal, space-time derivative dependent, coupling between the $k$-essence field and a relativistic fluid using a variational approach. The derivative coupling term couples the space-time derivative of the $k$-essence field with the fluid 4-velocity via an inner product. The inner product has a coefficient whose form specifies the various models of interaction. By introducing a coupling term at the Lagrangian level and using the variational technique we obtain the $k$-essence field equation and the Friedmann equations in the background of a spatially flat Friedmann-Lemaitre-Robertson-Walker (FLRW) metric. Explicitly using the dynamical analysis approach we analyze the dynamics of this coupled scenario in the context of two kinds of interaction models. The models are distinguished by the form of the coefficient multiplying the derivative coupling term. In the simplest approach we work with an inverse square law potential of the $k$-essence field. Both of the models are not only capable of producing a stable accelerating solution, they can also explain different phases of the evolutionary universe.

gr-qc↗

arXiv2023

Learning macroscopic internal variables and history dependence from microscopic models

This paper concerns the study of history dependent phenomena in heterogeneous materials in a two-scale setting where the material is specified at a fine microscopic scale of heterogeneities that is much smaller than the coarse macroscopic scale of application. We specifically study a polycrystalline medium where each grain is governed by crystal plasticity while the solid is subjected to macroscopic dynamic loads. The theory of homogenization allows us to solve the macroscale problem directly with a constitutive relation that is defined implicitly by the solution of the microscale problem. However, the homogenization leads to a highly complex history dependence at the macroscale, one that can be quite different from that at the microscale. In this paper, we examine the use of machine-learning, and especially deep neural networks, to harness data generated by repeatedly solving the finer scale model to: (i) gain insights into the history dependence and the macroscopic internal variables that govern the overall response; and (ii) to create a computationally efficient surrogate of its solution operator, that can directly be used at the coarser scale with no further modeling. We do so by introducing a recurrent neural operator (RNO), and show that: (i) the architecture and the learned internal variables can provide insight into the physics of the macroscopic problem; and (ii) that the RNO can provide multiscale, specifically FE2, accuracy at a cost comparable to a conventional empirical constitutive relation.

cond-mat.mtrl-sci↗

arXiv2023

Softening of the Hertz indentation contact in nematic elastomers

Polydomain liquid crystalline (nematic) elastomers have highly unusual mechanical properties, dominated by the dramatically non-linear stress-strain response that reflects stress-induced evolution of domain patterns. Here, we study the classical Hertz indentation problem in such a material. Experimentally, we find that polydomain nematic elastomers display a smaller exponent than the classical 3/2 in the load vs. indentation depth response. This is puzzling: asymptotically a softer stress-strain response requires a larger exponent at small loads. We resolve this by theory where three regimes are identified -- an initial elastic regime for shallow indentation that is obscured in experiment, an intermediate regime where local domain pattern evolution leads to a smaller scaling in agreement with experiments, and a final stiffening regime where the completion of local domain evolution returns the response to elastic. This three-regime structure is universal, but the intermediate exponent is not. We discuss how our work reveals a new mechanism of enhanced adhesion for pressure-sensitive adhesion of nematic elastomers.

cond-mat.soft↗

arXiv2023

A macroscopic constitutive relation for isotropic-genesis, polydomain liquid crystal elastomers

Liquid crystal elastomers (LCEs) are rubber-like solids that incorporate nematic mesogens (stiff rod-like molecules) as a part of their polymer chains. In recent years, isotropic-genesis, polydomain liquid crystal elastomers (I-PLCEs) has been a topic of both scientific and technological interest due to their intriguing properties such as soft behavior, ability to dissipate energy and stimuli response, as well as the ease with which they can be synthesized. We present a macroscopic or engineering scale constitutive model of the behavior of I-PLCEs. The model implicitly accounts for the complex evolution of the domain patterns and is able to faithfully capture the experimentally observed complex response to multi-axial loading. We describe a multiscale framework that motivates the model, explore various aspects of the model, validate it against experiments, and finally verify and demonstrate a numerical implementation.

cond-mat.soft↗

arXiv2023

Dynamical systems analysis of tachyon dark energy model from a new perspective

In this work we present a new scheme to study the tachyon dark energy model using dynamical systems analysis by considering parametrization of the equation of state(EoS) of the dark energy. Both the canonical and phantom field dynamics are investigated. In our method we do not require any explicit form of the tachyon potential. Instead of the potential we start with an approximate form of the EoS of the tachyon field. This EoS is phenomenologically motivated and contains some dimensionless parameters. Using our method we can construct the dynamical system which gives rise to the time evolution of the universe. We have considered two different parametrizations of the EoS and studied the phase space dynamics in details. Our analysis shows Taylor series parametrization of the EoS has serious cosmological limitations. Our proposal is generic in nature and can be applied to other scalar field dark energy models.

gr-qc↗

arXiv2023

Ghost condensates and pure kinetic $k$-essence condensates in presence of field-fluid non-minimal coupling in the dark sector

In this article we try to find out the conditions when a ghost field in conjunction with a barotropic fluid produces a stable accelerating expansion phase of the universe. It is seen that in many cases the ghost field produces a condensate and drives the fluid energy density to zero in the final accelerating phase, but there can be other possibilities. We have shown that a pure kinetic $k$-essence field (which is not a ghost field) interacting with a fluid can also form an interaction induced condensate and produce a stable accelerating phase of the universe. In the latter case the fluid energy density does not vanish in the stable phase.

gr-qc↗

arXiv2022

Universal deformations of ideal liquid crystal elastomers

Liquid crystal elastomers are rubber-like solids with liquid crystalline mesogens (stiff, rod-like molecules) incorporated either into the main chain or as a side chain of the polymer. These solids display a range of unusual thermo-mechanical properties as a result of the coupling between the entropic elasticity of rubber and the orientational phase transitions of liquid crystals. One of these intriguing properties is the soft behavior, where it is able to undergo significant deformations with almost no stress. While the phenomenon is well-known, it has largely been examined in the context of homogenous deformations. This paper investigates soft behavior in complex inhomogeneous deformations. We model these materials as hyperelastic, isotropic, incompressible solids and exploit the seminal work of Ericksen, who established the existence of non-trivial universal deformations, those that satisfy the equations of equilibrium in every hyperelastic, isotropic, incompressible solid. We study the inflation of spherical and cylindrical balloons, cavitation and bending.

cond-mat.soft↗

arXiv2022

Learning Dissipative Dynamics in Chaotic Systems

Chaotic systems are notoriously challenging to predict because of their sensitivity to perturbations and errors due to time stepping. Despite this unpredictable behavior, for many dissipative systems the statistics of the long term trajectories are governed by an invariant measure supported on a set, known as the global attractor; for many problems this set is finite dimensional, even if the state space is infinite dimensional. For Markovian systems, the statistical properties of long-term trajectories are uniquely determined by the solution operator that maps the evolution of the system over arbitrary positive time increments. In this work, we propose a machine learning framework to learn the underlying solution operator for dissipative chaotic systems, showing that the resulting learned operator accurately captures short-time trajectories and long-time statistical behavior. Using this framework, we are able to predict various statistics of the invariant measure for the turbulent Kolmogorov Flow dynamics with Reynolds numbers up to 5000.

cs.LG↗

arXiv2022

The nature of cosmological metric perturbations in presence of gravitational particle production

The present paper tries to answer the question: Can a de Sitter phase in presence of radiation be a competitor of the standard inflationary paradigm for the early universe? This kind of a de Sitter phase can exist in cosmological models where gravitational particle production takes place. To address the issue the metric perturbations in the de Sitter phase in presence of radiation must be known. The evolution of metric perturbations are explicitly calculated in the paper. It is seen that the evolution of scalar and vector perturbations are considerably different from standard inflationary models. These differences arise due to the particle production mechanism. The scalar perturbation power spectrum grows exponentially at small length scales. However, one cannot uniquely specify the scale at which this exponential growth starts because of the dependence of the power spectrum on the initial perturbation value. The time slice on which the initial perturbation starts is arbitrary. The arbitrariness of the initial time slice is related to the problem of setting the initial condition on the perturbations in the present model. The paper briefly opines on vector and tensor perturbations in the de Sitter space filled with radiation. It is seen that quantization of the perturbation modes in the present model is considerably difficult. One has to modify the present model to provide a consistent scheme of quantization of the perturbation modes.

gr-qc↗