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"Resistentiam, quae oritur ex defectu lubricitatis partium fluidi, caeteris paribus, proportionalem esse velocitati, qua partes fluidi separantur ab invicem." - and then we start!

My work comprises of a balance between analytic calculations and numerical computation to understand different material properties that can be accessed via experiments as well as theoretic challenges. Within the classical physics domain, my scientific interest is distributed into studying, a) multispecies diffusion in a miscible non-ideal liquid mixture, b) statics and kinetics of liquid crystals and c) Shear response of dense colloidal melt. They are briefly described below. Here is a comprehensive list of developed computational benchmarks:

Nematic disclinations under non-uniform electric forces and thermal inhibitors

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Manipulating topological disclination networks that arise in a symmetry-breaking phase transformation of anisotropic materials can potentially lead to the design of nove materials like conductive microwires, self-assembled resonators, and active anisotropic matter. However, progress in this direction is hindered by a lack of control of the kinetics and microstructure due to inherent complexity arising from competing energy and topology [Figure 1]. Here we have studied thermal and electrokinetic effects on disclinations in a three-dimensional nonabsorbing nematic material with both signs of the dielectric anisotropy. The electric flux lines are found to be highly nonuniform in uniaxial media [Figure 2] after an electric field below the Fréedericksz threshold is switched on, and the kinetics of the disclination lines is slowed down as seen experimentally. In biaxial media, depending on the sign of the dielectric anisotropy, apart from the slowing down of the disclination kinetics, a nonuniform electric field filters out disclinations of different topology by inducing a kinetic asymmetry [Figure 3]. These results enhance the current understanding of forced disclination networks and establish the presented method (fluctuating electronematics) as a potentially useful tool for designing materials with novel properties in silico.

Hyperbolic-hedgehog encapsulated anisotropic microdroplets in metastable nematic film

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In this work, we utilize our constructed Langevin equations describing the fluctuations of the orientational tensor that preserves the symmetry and tracelessness of the tensor order, and satisfy Einstein's fluctuation-dissipation relation at thermal equilibrium, to study nucleation kinetics in quasi two-dimensional nematic film above supercooling and below superheating limit [Figure 1]. Droplets of nematic (isotropic) order are spontaneous generated in the thermally fluctuating isotropic (nematic) bath [Figure 4: 3D nematic droplet (vide PhD-Thesis)]. Hyperbolic-hedgehog defect encapsulated elliptic microdroplets with outer Biaxial rings are formed [Figure 2]. A polynomial dependence on time of the growth kinetics with drastic violation of the Classical Nucleation Theory (CNT) - as realized through breakdwon of Johnson-Mehl-Avirami-Kolmogorov equation, as well the nucleation rate kinetics - is observed. Spatially distant events are temporally correlated due to long-ranged elastic interactions [Figure 3]. Two-stage growth process is observed in isotropic droplets in super-heated nematic film. Details of the numerical formulation, benchmarks and results can be read in the two articles below & The animations can be viewed here ,

Dimerization reaction in chemically reactive multicomponent gas under low-Mach number flow

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We have formulated a coupling between compressible fluctuating hydrodynamics equations for multispecies gas to the Law of mass action to study dimerization reaction, e.g. two H-atoms forming a Hydrogen molecule, in a chemically reactive ideal gas. We show that a large scale non-equilibrium fluctuation in the presence of concentration gradients is suppressed due to the chemical reactions. This is shown in Figure(12) which can be compared to the response in non-reactive mixtures fig(6). We also have compared different existing numerical methodology (e.g. GENERIC formalism, chemical Master equation, chemical Langevin equation etc) to predict accurate chemical kinetics for systems with small number of atoms/molecules. Finally we also compare the pattern formation, a high noise late time snapshot for one species in Baras-Pearson-Mansour model is shown in Figure(13). More details are published here:

Multispecies non-ideal liquid mixtures under low-Mach flow, microgravity and thermal gradient

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We have formulated a low-Mach number fluctuating hydrodynamics equation for multispecies nonideal liquid, where fast isentropic fluctuations in pressure are eliminated by replacing the equation of state with a local thermodynamic constraint. We demonstate of large scale non-equilibrium fluctuation [Figure 1] in the presence of concentration gradients, reported in light-scattering experiments and shadowgraphy techniques. We had studied mixed-mode instability occuring on the miscible interface between sugarwater and saltwater in the presence of gravity. The buoyancy driven instability like double-diffusive effects and Rayleigh-Taylor instability with the mixed-mode instability triggers a fingering instability of the interface in a Hele-Shaw cell geometry as shown in [Figure 2]. Figure 3 shows the development of Diffusive Layer Convection (DLC) instability in our computation, when a layer of less-dense salty water is placed on top of a horizontal layer of denser sweet water. Our findings with detailed numerical methodology is referenced here:

Bauschinger effect in supercooled melts under instantaneous shear reversal

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We have studied the nonlinear rheology of a glass-forming binary mixture under the reversal of shear flow using dissipative particle dynamics simulations that validates Einstein's fluctuation dissipation relation in quiescent state. Planar Couette flow is established via Lees-Edwards boundary between particles interacting through a Weeks-Chandler-Andersen potential. Memory effects lead to a history-dependent response of the melt, as exemplified by the vanishing of a stress overshoot phenomenon in the stress–strain curves of the sheared liquid, and a change in the apparent elastic coefficients around states with zero stress. The connection of this macroscopic response to single particle motion is demonstrated via particle mean squared displacement as well as the self-intermediate scattering function. The results are compared to the schematic mode coupling theory model of sheared glassy liquid where we find excellent agreement with the simulation. Figure(6) shows the overshoot of shear and normal stress in forward shear and no overshoot at instantaneous shear reversal. Figure(7) depicts of the local stress on individual particle at a stage where elasto-plastic rearrangements occur in forward shear while in figure(8), induced anisotropy due to shear is shown in shear-gradient plane, where particles are squeezed along the compressional axis and extended along the extensional axis. Figure (9) shows the coarse grained elastic map in forward shear at 1-percent strain, having different regions with higher and lower elastic constant. The references are inscribed below:

Topological point and line defects in spinodal kinetics of uniaxial and biaxial nematics

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In this work using MOL method, we have performed spinodal kinetics of coarsening following a quench from isotropic to deep into the nematic phase. We study the scaling behaviour and defect morphology and validate the dynamical scaling with a clear separation of time scales from diffusive to Porod's law at late stage of the kinetics [Figure 5]. Details of the numerical study, benchmarks and results are highlighted here:

We also have developed new visualization techniques as well as easy defect-finding algorithm, that classifies point and line defects in quasi-two and three dimensions [Figure 1], not only via the Schlieren texture [Figure 2] but also by the scalar order [Figure 3-4]. Both integer, half-integer defects of respective topological class are recognized. These are animated here ,

de Gennes ansatz: nature of liquid-nematic interface

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The work describes of statics and kinetics of liquid crystal phase change from liquid to uniaxial/biaxial nematic phase within the framework of Ginzburg-Landau-deGennes (GLdG) approach. A new deterministic method of lines (MOL) solution to the dynamic equations of the Q-tensor is presented. We benchmark through the study of the classic tanh isotropic-nematic interface at zero temperature [Figure 1]. We perform a stringent test of the de Gennes ansatz , proposed back in '70s era, and find the condition when the interface remains strictly uniaxial or partially Biaxial. Benchmarks are reported underneath,

We next develop an extremely accurate collocation scheme for the solution of the GLdG equations to comment about the nature of the interface as well as the role of anisotropic elastic constants to the nematic director (planar, homeotropic and oblique) anchoring along the interface [Figure 2]. These are compared with an approximate analytic exposition and reported in the following articles, We also perform the stochastic generalization of MOL to examine capillary waves in a thermally fluctuating interface reported here,