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Vikash Pandey

Publications and source records attributed to Vikash Pandey.

At least 19 recordsLinked to original sources
arXiv2025

Scale-by-scale energy transfers in bubbly flows

Buoyancy-driven bubbly flows naturally have spatially-dependent density fields, which allow for multiple definitions of the scale-dependent (or filtered) energy. A priori, it is not obvious which of these provide the most physically apt scale-by-scale budget. In the present study, we compare two such definitions, based on (a) filtered momentum and filtered velocity (Pandey et al. 2020), and (b) Favre filtered energy (Aluie 2013; Pandey et al. 2023). We also derive a K\'arm\'an-Howarth-Monin (KHM) relation using the momentum-velocity correlation function and contrast it with the scale-by-scale energy budget obtained in (a). We find that for the volume fraction and Atwood number explored, irrespective of the definition, energy transfers due to the advective nonlinearity and surface tension are identical. However, discrepancies arise for the buoyancy and pressure contributions. We show that the Favre filtered definition is the more appropriate choice, within which buoyancy injects energy, pressure transfers energy to large scales, and both advective nonlinearity and surface tension transfer energy downscales where it is dissipated by viscosity.

physics.flu-dyn↗
arXiv2025

A Linear Time-Variant Rheological Model for Frictional Aging, Stress Relaxation, and Creep

Most materials undergo aging, leading to time-dependent evolution of their mechanical properties. This aging is reflected in their mechanical response to external strain and stress, which often exhibits logarithmic stress relaxation and power-law creep. Such responses are typically described using complex phenomenological models, including fractional viscoelastic formulations. While these approaches successfully reproduce experimental trends, they typically provide limited insight into the physical origin of aging and its connection to material parameters. We introduce jerk-elasticity, a linear time-variant rheological model in which the constitutive response incorporates the time evolution of stress-rate dynamics through time-dependent material parameters. The framework is motivated by the physics of interfacial stick-slip dynamics underlying frictional aging, together with thermodynamic considerations. An asymptotic correspondence is found between the jerk-elasticity model and the rate-and-state friction law, thereby linking rheological aging with interfacial frictional aging. The proposed model reproduces the Guiu-Pratt law of logarithmic stress relaxation and Andrade's power-law creep. It further provides a framework for interpreting different creep regimes through the evolution of material parameters, without invoking distributed relaxation spectra or nonlinear constitutive assumptions. The governing parameters admit interpretation in terms of thermodynamic quantities, including activation volume, whose evolution provides a physically interpretable measure of aging. In appropriate asymptotic limits, the model recovers behaviors analogous to classical viscous and fractional Maxwell models, while also approaching Mittag-Leffler-type relaxation and Lomnitz-type creep in a specific limit. Jerk-elasticity provides a LTV framework that links frictional aging to creep and relaxation.

cond-mat.soft↗
arXiv2024

Anomalous diffusion and effective shear modulus in a semi-solid membrane

From the perspective of physical properties, the cell membrane is an exotic two-dimensional material that has a dual nature: it exhibits characteristics of fluids, i.e., lipid molecules show lateral diffusion, while also demonstrating properties of solids, evidenced by a non-zero shear modulus. We construct a model for such a $\textit{semi-solid}$ $\textit{membrane}$. Our model is a fluctuating randomly triangulated mesh with two different kinds of nodes. The solid nodes never change their neighbors, while the fluid nodes do. As the area fraction occupied by the solid nodes ($\Phi$) is increased the motion of fluid nodes transition from diffusion to localization via subdiffusion. Next, the solid nodes are pinned to mimic the pinning of the plasma membrane to the cytoskeleton. For the pinned membrane, there exists a range of $\Phi$ over which the model has both a non-zero shear modulus and a non-zero lateral diffusivity. The bending modulus, measured through the spectrum of height fluctuations remains unchanged.

cond-mat.soft↗
arXiv2023

Kolmogorov Turbulence Coexists with Pseudo-Turbulence in Buoyancy-Driven Bubbly Flows

We investigate spectral properties of buoyancy driven bubbly flows. Using high-resolution numerical simulations and phenomenology of homogeneous turbulence, we identify the relevant energy transfer mechanisms. We find: (a) At high enough Galilei number (ratio of the buoyancy to viscous forces) the kinetic energy spectrum shows the Kolmogorov scaling with a power law exponent $-5/3$ for the range of scales between the bubble diameter and the dissipation scale ($η$). (b) For scales smaller than $η$, the physics of pseudo-turbulence is recovered.

physics.flu-dyn↗
arXiv2023

Hidden jerk in universal creep and aftershocks

Most materials exhibit creep memory under the action of a constant load. The memory behavior is governed by Andrade's creep law, which also has an inherent connection with the Omori-Utsu law of earthquake aftershocks. Both empirical laws lack a deterministic interpretation. Coincidentally, the Andrade law is similar to the time-varying part of the creep compliance of the fractional dashpot in anomalous viscoelastic modeling. Consequently, fractional derivatives are invoked, but since they lack a physical interpretation, the physical parameters of the two laws extracted from curve fit lack confidence. In this Letter, we establish an analogous linear physical mechanism that underlies both laws and relates its parameters with the material's macroscopic properties. Surprisingly, the explanation does not require the property of viscosity. Instead, it necessitates the existence of a rheological property that relates strain with the first order time derivative of stress, which involves jerk. Further, we justify the constant quality factor model of acoustic attenuation in complex media. The obtained results are validated in light of the established observations.

physics.geo-ph↗
arXiv2023

Active buckling of pressurized spherical shells : Monte Carlo Simulation

We study the buckling of pressurized spherical shells by Monte Carlo simulations in which the detailed balance is explicitly broken -- thereby driving the shell active, out of thermal equilibrium. Such a shell typically has either higher (active) or lower (quiescent) fluctuations compared to one in thermal equilibrium depending on how the detailed balance is broken. We show that for the same set of elastic parameters, a shell that is not buckled in thermal equilibrium can be buckled if turned active. Similarly, a shell that is buckled in thermal equilibrium can unbuckle if turned quiescent. Based on this result, we suggest that it is possible to experimentally design microscopic elastic shells whose buckling can be optically controlled.

cond-mat.soft↗
arXiv2022

Energy spectra of buoyancy-driven bubbly flow in a vertical Hele-Shaw cell

We present direct numerical simulations (DNS) study of confined buoyancy-driven bubbly flows in a Hele-Shaw setup. We investigate the spectral properties of the flow and make comparisons with experiments. The energy spectrum obtained from the gap-averaged velocity field shows $E(k) \sim k$ for $k < k_d$, $E(k) \sim k^{-5}$ for $k > k_d$, and an intermediate scaling range with $E(k) \sim k^{-3}$ around $k \sim k_d$. We perform an energy budget analysis to understand the dominant balances and explain the observed scaling behavior. We also show that the Navier-Stokes equation with a linear drag can be used to approximate large scale flow properties of bubbly Hele-Shaw flow.

physics.flu-dyn↗
arXiv2022

Response to "Comment on 'Origin of the Curie--von Schweidler law and the fractional capacitor from time-varying capacitance [J. Pow. Sources 532 (2022) 231309]' "

We welcome Allagui et al.'s discussions about our recent paper that has proposed revisions to the existing theory of capacitors. It gives us an opportunity to emphasize on the physical underpinnings of the mathematical expressions that are relevant for modeling using fractional derivatives. The concerns raised by Allagui et al. are found to be quite questionable when examined in light of the established standard results of fractional calculus. Consequently, the inferences that they have drawn are not true. Finally, we would like to thank Allagui et al. because this subsequent Response to their Comment has actually led to a further consolidation of our results that are supposed to be significant for materials science as well as for fractional control systems and engineering.

cond-mat.mtrl-sci↗
arXiv2022

MeMC: A package for monte-carlo simulations of spherical shells

The MeMC is an open-source software package for monte-carlo simulation of elastic shells. It is designed as a tool to interpret the force-distance data generated by indentation of biological nano-vesicles by atomic force microscopes. The code is written in c++ and python. The code is customizable -- new modules can be added in a straightforward manner.

physics.comp-ph↗
arXiv2022

Origin of the Curie-von Schweidler law and the fractional capacitor from time-varying capacitance

Most dielectrics of practical purpose exhibit memory and are described by the century-old Curie-von Schweidler law. Interestingly, the Curie-von Schweidler law is the motivation behind an unconventional circuit component called fractional capacitor which due to its power-law property is extensively used in the modeling of complex dielectric media. Unfortunately, the empirical nature of the Curie-von Schweidler law plagues the applications of the fractional capacitor. Here, we derive the Curie-von Schweidler law from a series combination of a resistor and a capacitor with a linear time-varying capacitance. This may possibly be its first derivation from physical principles. However, this required a modification of the classical charge--voltage relation of a capacitor to account for the time-varying capacitance. The limitation of the classical charge-voltage relation and its subsequent modification are justified using appropriate circuit modeling. Consequently, the parameters of the Curie-von Schweidler law and the fractional capacitor gain physical interpretation. The Debye response of dielectrics emerges naturally from the limiting case of the power-law response at short timescales. The obtained results are validated by matching them with the published experimental reports.

cond-mat.mtrl-sci↗
arXiv2021

Turbulence modulation in buoyancy-driven bubbly flows

We present a Direct Numerical Simulation (DNS) study of buoyancy-driven bubbly flows in the presence of large scale driving that generates turbulence. On increasing the turbulence intensity: (a) the bubble trajectories become more curved, and (b) the average rise velocity of the bubbles decreases. We find that the energy spectrum of the flow shows a pseudo-turbulence scaling for length scales smaller than the bubble diameter and a Kolmogorov scaling for scales larger than the bubble diameter. We conduct a scale-by-scale energy budget analysis to understand the scaling behaviour observed in the spectrum. Although our bubbles are weakly buoyant, the statistical properties of our DNS are consistent with the experiments that investigate turbulence modulation by air bubbles in water.

physics.flu-dyn↗
arXiv2021

Rate of formation of caustics in heavy particles advected by turbulence

The rate of collision and the relative velocities of the colliding particles in turbulent flows is a crucial part of several natural phenomena, e.g., rain formation in warm clouds and planetesimal formation in a protoplanetary disks. The particles are often modeled as passive, but heavy and inertial. Within this model, large relative velocities emerge due to formation of singularities (caustics) of in the gradient matrix of the velocities of the particles. Using extensive direct numerical simulations of heavy particles in both two (direct and inverse cascade) and three dimensional turbulent flows we calculate the rate of formation of caustics, $J$ as a function of the Stokes number (${\rm St}$).The best approximation to our data is $J \sim \exp(-C/{\rm St})$, in the limit ${\rm St} \to 0 $ where $C$ is a non-universal constant.

physics.flu-dyn↗
arXiv2021

Paths to caustic formation in turbulent aerosols

The dynamics of small, yet heavy, identical particles in turbulence exhibits singularities, called caustics, that lead to large fluctuations in the spatial particle-number density, and in collision velocities. For large particle, inertia the fluid velocity at the particle position is essentially a white-noise signal and caustic formation is analogous to Kramers escape. Here we show that caustic formation at small particle inertia is different. Caustics tend to form in the vicinity of particle trajectories that experience a specific history of fluid-velocity gradients, characterised by low vorticity and a violent strain exceeding a large threshold. We develop a theory that explains our findings in terms of an optimal path to caustic formation that is approached in the small inertia limit.

physics.flu-dyn↗
arXiv2020

Pseudo-turbulence in two-dimensional buoyancy driven bubbly flows: a DNS study

We present a direct numerical simulation (DNS) study of buoyancy driven bubbly flows in two-dimensions. We employ volume of fluid (VOF) method to track the bubble interface. To investigate spectral properties of the flow, we derive the scale-by-scale energy budget equation. We show that the Galilei number (Ga) controls different scaling regimes in the energy spectrum. For high Galilei numbers, we find the presence of an inverse energy cascade. Our study indicates that the density ratio of the bubble with the ambient fluid or the presence of coalescence between the bubbles does not alter the scaling behaviour.

physics.flu-dyn↗
arXiv2020

Charge-voltage relation for a universal capacitor

Most capacitors do not satisfy the conventional assumption of a constant capacitance. They exhibit memory which is often described by a time-varying capacitance. It is shown that the classical relation, $Q\left(t\right)=CV\left(t\right)$, that relates the charge, $Q$, with the capacitance, $C$, and the voltage, $V$, is not applicable for capacitors with a time-varying capacitance. The expression for the current, $dQ/dt$, that is subsequently obtained following the substitution of $C$ by $C\left(t\right)$ in the classical relation corresponds to an inconsistent circuit. In order to address the inconsistency, I propose a charge-voltage relation according to which the charge on a capacitor is expressed by the convolution of its time-varying capacitance with the first-order time-derivative of the applied voltage, i.e., $Q\left(t\right)=C\left(t\right)\ast dV/dt$. This relation corresponds to the universal capacitor which is also known as the fractional capacitor among the fractional calculus community. Since the fractional capacitor has an inherent connection with the universal dielectric response that is expressed by the century old Curie-von Schweidler law, the finding extends to the study of dielectrics as well.

physics.app-ph↗
arXiv2019

Liquid velocity fluctuations and energy spectra in three-dimensional buoyancy driven bubbly flows

We present a direct numerical simulation (DNS) study of pseudo-turbulence in buoyancy driven bubbly flows for a range of Reynolds ($\Rey$) and Atwood ($\At$) numbers. We study the probability distribution function of the horizontal and vertical liquid velocity fluctuations and find them to be in quantitative agreement with the experiments. The energy spectrum shows the $k^{-3}$ scaling at high $\Rey$ and becomes steeper on reducing the $\Rey$. To investigate the spectral transfers in the flow, we derive the scale-by-scale energy budget equation. Our analysis shows that, for scales smaller than the bubble diameter, the net production because of the surface tension and the kinetic energy flux balances viscous dissipation to give the $k^{-3}$ scaling of the energy spectrum for both low and high $\At$.

physics.flu-dyn↗
arXiv2019

Asymmetricity and sign reversal of secondary Bjerknes force from strong nonlinear coupling in cavitation bubble pairs

Most of the current applications of acoustic cavitation use bubble clusters that exhibit multibubble dynamics. This necessitates a complete understanding of the mutual nonlinear coupling between individual bubbles. In this study, strong nonlinear coupling is investigated in bubble pairs which is the simplest case of a bubble-cluster. This leads to the derivation of a more comprehensive set of coupled Keller-Miksis equations (KMEs) that contain nonlinear coupling terms of higher order. The governing KMEs take into account the convective contribution that stems from the Navier-Stokes equation. The system of KMEs is numerically solved for acoustically excited bubble pairs. It is shown that the higher order corrections are important in the estimation of secondary Bjerknes force for closely spaced bubbles. Further, asymmetricity is witnessed in both magnitude and sign reversal of the secondary Bjerknes force in weak, regular, and strong acoustic fields. The obtained results are examined in the light of published scientific literature. It is expected that the findings reported in this paper may have implications in industries where there is a requirement to have a control on cavitation and its effects.

physics.flu-dyn↗