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We solve for waves in a polytropic, stratified medium with a spatially varying background magnetic field that points along a horizontal $x$-direction, and with gravity that is directed along the vertical $z$-direction. Force balance determines the magnitude of the background magnetic field, $B_0^2 \sim z^{n+1}$, where $n$ is the polytropic index. Using numerical and asymptotic methods, we deduce an accurate and explicit dispersion relation for fast pressure-driven waves: $\Omega^2 \sim K\left(2m+n\right) \left[1 + (1/M_\mathrm{A})^2 (4-2\gamma+\cos^2\theta-3\cos^4\theta)/4 \right]$. Here, $\Omega$ is the frequency, $K$ the wavenumber, $\theta$ the angle the wave-vector makes with the background magnetic field, $M_\mathrm{A}$ the Alfv\'enic Mach number, and $m$ an integer representing the eigen state. Applications of our result are in magnetoseismology and nonlinear asteroseismology., Comment: 11 pages, 5 figures

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.

Lagrangian pair dispersion provides insights into mixing in turbulent flows. By direct numerical simulations (DNS) we show that the statistics of pair dispersion in the randomly forced two-dimensional Burgers equation, which is a typical model of shock-dominated turbulence, is very different from its incompressible counterpart because Lagrangian particles get trapped in shocks. We develop a heuristic theoretical framework that accounts for this -- a generalization of the multifractal model -- whose prediction of the scaling of Lagrangian exit times agrees well with our DNS.

Elastic turbulence is the chaotic fluid motion resulting from elastic instabilities due to the addition of polymers in small concentrations at very small Reynolds ($\mbox{Re}$) numbers. Our direct numerical simulations show that elastic turbulence, though a low $\mbox{Re}$ phenomenon, has more in common with classical, Newtonian turbulence than previously thought. In particular, we find power-law spectra for kinetic energy $E(k) \sim k^{-4}$ and polymeric energy $E_{\rm p}(k) \sim k^{-3/2}$, independent of the Deborah ($\mbox{De}$) number. This is further supported by calculation of scale-by-scale energy budget which shows a balance between the viscous term and the polymeric term in the momentum equation. In real space, as expected, the velocity field is smooth, i.e., the velocity difference across a length scale $r$, $\delta u \sim r$ but, crucially, with a non-trivial sub-leading contribution $r^{3/2}$ which we extract by using the second difference of velocity. The structure functions of second difference of velocity up to order $6$ show clear evidence of intermittency/multifractality. We provide additional evidence in support of this intermittent nature by calculating moments of rate of dissipation of kinetic energy averaged over a ball of radius $r$, $\varepsilon_{r}$, from which we compute the multifractal spectrum.

Motivated by wind blowing over water, we use asymptotic methods to study the evolution of short wavelength interfacial waves driven by the combined action of these flows. We solve the Rayleigh equation for the stability of the shear flow, and construct a uniformly valid approximation for the perturbed streamfunction, or eigenfunction. We then expand the real part of the eigenvalue, the phase speed, in a power series of the inverse wavenumber and show that the imaginary part is exponentially small. We give expressions for the growth rates of the Miles (1957) and rippling (e.g., Young & Wolfe 2013) instabilities that are valid for an arbitrary shear flow. The accuracy of the results is demonstrated by a comparison with the exact solution of the eigenvalue problem in the case when both the wind and the current have an exponential profile.

We study a single, freely--floating, inextensible, elastic filament in a linear shear flow: $\mathbf{U}_{0}(x,y) = \dot{\gamma} y \hat{x}$. In our model: the elastic energy depends only on bending; the rate-of-strain, $\dot{\gamma} = S \sin(\omega t)$ is a periodic function of time, $t$; and the interaction between the filament and the flow is approximated by a local isotropic drag force. Based on the shape of the filament we find five different dynamical phases: straight, buckled, periodic (with period two, period three, period four, etc), chaotic, and one with chaotic transients. In the chaotic phase, we show that the iterative map for the angle, which the end-to-end vector of the filament makes with the tangent its one end, has period three solutions; hence it is chaotic. Furthermore, in the chaotic phase the flow is an efficient mixer., Comment: 7 pages, 5 figures, 2 tables

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., Comment: 10 pages, 8 figures, 2 table

We use the short-time inference scheme (Manikandan, Gupta and Krishnamurthy, Phys. Rev. Lett. 124, 120603, 2020), obtained within the framework of stochastic thermodynamics, to infer a lower-bound to entropy generation rate from flickering data generated by Interference Reflection Microscopy of HeLA cells. We can clearly distinguish active cell membranes from their ATP depleted selves and even spatio-temporally resolve activity down to the scale of about one $\mu$m. Our estimate of activity is model--independent., Comment: Published version

We carry out a detailed study of dynamic multiscaling in the turbulent nonequilibrium, but statistically steady, state of the stochastically forced one-dimensional Burgers equation. We introduce the concept of $\textit{interval collapse times}$ $\tau_{\rm col}$, the time taken for an interval of length $\ell$, demarcated by a pair of Lagrangian tracers, to collapse at a shock. By calculating the dynamic scaling exponent of the order-$p$ moment of $\tau_{\rm col}$, we show that (a) there is $\textit{not one but an infinity of characteristic time scales}$ and (b) the probability distribution function of $\tau_{\rm col}$ is non-Gaussian and has a power-law tail. Our study is based on (a) a theoretical framework that allows us to obtain dynamic-multiscaling exponents analytically, (b) extensive direct numerical simulations, and (c) a careful comparison of the results of (a) and (b). We discuss possible generalizations of our work to dimensions $d >1 $, for the stochastically forced Burgers equation, and to other compressible flows that exhibit turbulence with shocks.

Solar flares create adverse space weather impacting space and Earth-based technologies. However, the difficulty of forecasting flares, and by extension severe space weather, is accentuated by the lack of any unique flare trigger or a single physical pathway. Studies indicate that multiple physical properties contribute to active region flare potential, compounding the challenge. Recent developments in machine learning (ML) have enabled analysis of higher-dimensional data leading to increasingly better flare forecasting techniques. However, consensus on high-performing flare predictors remains elusive. In the most comprehensive study to date, we conduct a comparative analysis of four popular ML techniques (k-nearest neighbor, logistic regression, random forest classifier, and support vector machine) by training these on magnetic parameters obtained from the Helioseismic and Magnetic Imager (HMI) on board the Solar Dynamics Observatory (SDO) for the entirety of solar cycle 24. We demonstrate that the logistic regression and support vector machine algorithms perform extremely well in forecasting active region flaring potential. The logistic regression algorithm returns the highest true skill score of $0.967 \pm 0.018$, possibly the highest classification performance achieved with any strictly parametric study. From a comparative assessment, we establish that the magnetic properties like total current helicity, total vertical current density, total unsigned flux, R_VALUE, and total absolute twist are the top-performing flare indicators. We also introduce and analyze two new performance metrics, namely, severe and clear space weather indicators. Our analysis constrains the most successful ML algorithms and identifies physical parameters that contribute most to active region flare productivity.

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 ($\eta$). (b) For scales smaller than $\eta$, the physics of pseudo-turbulence is recovered.

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., Comment: 6 pages,4 figures

The flow of Newtonian fluid at low Reynolds number is, in general, regular and time-reversible due to absence of nonlinear effects. For example, if the fluid is sheared by its boundary motion that is subsequently reversed, then all the fluid elements return to their initial positions. Consequently, mixing in microchannels happens solely due to molecular diffusion and is very slow. Here, we show, numerically, that the introduction of a single, freely-floating, flexible filament in a time-periodic linear shear flow can break reversibility and give rise to chaos due to elastic nonlinearities, if the bending rigidity of the filament is within a carefully chosen range. Within this range, not only the shape of the filament is spatiotemporally chaotic, but also the flow is an efficient mixer. Overall, we find five dynamical phases: the shape of a stiff filament is time-invariant -- either straight or buckled; it undergoes a period-two bifurcation as the filament is made softer; becomes spatiotemporally chaotic for even softer filaments but, surprisingly, the chaos is suppressed if bending rigidity is decreased further., Comment: 18 pages, 13 figures

We use direct numerical simulations to study homogeneous, and isotropic turbulent flows of dilute polymer solutions at high Reynolds and Deborah numbers. We find that for small wavenumbers $k$, the kinetic energy spectrum shows Kolmogorov--like behavior which crosses over at a larger $k$ to a novel, elastic scaling regime, $E(k) \sim k^{-\xi}$, with $\xi \approx 2.3$. We study the contribution of the polymers to the flux of kinetic energy through scales, and find that it can be decomposed into two parts: one increase in effective viscous dissipation, and a purely elastic contribution that dominates over the nonlinear flux in the range of $k$ over which the elastic scaling is observed. The multiscale balance between the two fluxes determines the crossover wavenumber which depends non-monotically on the Deborah number. Consistently, structure functions also show two scaling ranges, with intermittency present in both of them in equal measure.

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., Comment: Consistent with the version accepted for publication in Philosophical Transactions of the Royal Society A

We use direct numerical simulations and scaling arguments to study coarsening in binary fluid mixtures with a conserved order parameter in the droplet-spinodal regime -- the volume fraction of the droplets is neither too small nor symmetric -- for small diffusivity and viscosity. Coagulation of droplets drives a turbulent flow that eventually decays. We uncover a novel coarsening mechanism, driven by turbulence where the characteristic length scale of the flow is different from the characteristic length scale of droplets, giving rise to a domain growth law of $t^{1/2}$, where $t$ is time. At intermediate times, both the flow and the droplets form self-similar structures: the structure factor $S(q) \sim q^{-2}$ and the kinetic energy spectra $E(q) \sim q^{-5/3}$ for an intermediate range of $q$, the wavenumber., Comment: 10 pages 7 figures