Searcharxiv⌕ Search

arXiv subjects

Varghese Mathai

Publications and source records attributed to Varghese Mathai.

At least 19 recordsLinked to original sources
arXiv2026

Turbulence Decay Intensifies Clustering of Bubbles and Particles

Our understanding of inertial particle dynamics in turbulence is mostly based on flows held in a statistically stationary state, a particular regime that differs from many natural flows where energy input can often be intermittent or cyclic, or may abruptly cease. Here we investigate inertial particle and bubble dynamics in freely decaying turbulence through complementary experiments and direct numerical simulations. While particle accelerations decay monotonically in time, we find evidence that the clustering can exhibit a non-monotonic evolution, intensifying sharply before subsequently weakening. We demonstrate that both the acceleration and clustering behaviors can be mapped onto their counterparts in stationary turbulence using a dynamic rescaling of the evolving length and time scales of the turbulence. Validity conditions for the dynamic rescaling, satisfied by both the experimental and numerical datasets, are derived. The proposed mappings remain applicable across a broad range of density ratios, from light to heavy particles, and particle sizes spanning two orders of magnitude in Stokes number.

physics.flu-dyn↗
arXiv2026

Hydrodynamic Brachistochrone: Conflicting Paths of Time and Energy Minima within Viscous Media

We experimentally and theoretically study the hydrodynamic analog of the classical brachistochrone problem: the {\it time-} and {\it energy-minimizing} paths for a spherical particle rolling down an incline within a viscous fluid. We show that in the presence of viscous dissipation, the paths of minima diverge from the classical cycloid, into curves of opposing curvature for time and energy, and are characterized by an effective dimensionless parameter, $St_p$, representing the ratio of the particle's viscous response time scale to its gravitational time scale. Using a generalized variational framework, we show that the fastest path reduces to {nearly straight ramps}, however, beginning and terminating in localized cycloids of curvature, $\kappa_c \sim St_p^{-2}$. Remarkably, the path of fastest descent on a given energy budget requires navigating a non-monotonic path ({\it``S-shaped''}) with an interior point of inflection. Our findings reveal a unification of temporal and energetic optimality for transport through dissipative media, and expand the celebrated brachistochrone solutions to the hydrodynamic regime.

physics.flu-dyn↗
arXiv2026

Moduli Spaces of Connections and B-fields from T-duality with H-flux

We study the geometry of mixed fields, consisting of a connection and a $B$-field on a principal circle bundle over a Riemann surface, from the perspective of gauge theory and T-duality. Motivated by the foundational work of Atiyah--Bott and Segal, we introduce a twisted Yang--Mills functional whose critical locus, in the flat case, is governed by the simultaneous vanishing of the curvature and the $H$-flux. We show that the gauge group is a semi-direct product of abelian groups parametrised by an integer $\lambda$. The moduli spaces are constructed by presymplectic reduction and shown to be Heisenberg contact manifolds for $\lambda \neq 0$, whose topology we characterise completely. We show that T-duality preserves the twisted Yang--Mills functional and acts on the configuration space of flat mixed fields. We identify the subgroups of gauge transformations that are compatible with the T-duality map and describe the induced action on the singular quotient of T-dualizable flat mixed fields. Precisely at $\lambda =1$ does T-duality descend to an involutive contactomorphism of the moduli space.

hep-th↗
arXiv2025

Latitudinal dependence of heat transport in turbulent geostrophic convection

Latitudinal variations in turbulent heat flux play a key role in the thermal and magnetic evolution of rapidly rotating planets and stars. Although global spherical-shell simulations have documented such variations, explicit latitude-dependent scaling relations for heat transport have remained elusive. Here we employ the rotating Rayleigh-B\'enard convection (RRBC) framework with tilted rotation and gravity axes to model convection at different latitudes $\varphi$ in the geostrophic regime. We derive scaling relations for the latitude dependence of convective length scales $\ell(\varphi)$ and the Nusselt number $Nu(\varphi)$. At high latitudes, the scalings $Nu \sim \sin^{-4/3}\varphi$ (near onset) and $Nu \sim \sin^{-4}\varphi$ (above onset) emerge, while at low latitudes $Nu \sim \cos^{4}\varphi$. These predictions are validated against direct numerical simulations of convection in a spherical shell. The results provide a quantitative framework for regional thermal transport in planetary and stellar interiors and establish a unified interpretation of spherical convection that connects naturally with planar RRBC turbulence.

astro-ph.EP↗
arXiv2025

Active biphasic heat transfer enhancement in vertical natural convection

Vertical natural convection (VC), often cannot meet the high heat transfer demands due to the inherent misalignment of the direction of buoyancy (vertical) with the direction of the heat transfer (horizontal). Here we applied a novel strategy on a water based VC system to enhance the heat transfer. By adding 2% of the total volume with a low-boiling-temperature liquid (HFE-7000) and introducing a gas-liquid layer on top of the VC cell, we create a self-sustained state of pseudo-turbulence with evaporating, circulating and condensing biphasic bubbles. The system achieves 246% heat transfer enhancement at constant superheat $T_{sup}\approx6.4 \text{K}$ when the liquid in the full nucleate boiling state. Using shadowgraphy and Laser Doppler Anemometry (LDA) methods, we validate that the bubbles and biphasic particles induced agitation enhances the heat flux and modifies the temperature field of the heat transfer.

physics.flu-dyn↗
arXiv2025

A three-dimensional scanning stereoscopic particle image velocimetry for large-volume liquid flows

We introduce a Scanning Stereoscopic Particle Image velocimetry~(SSPIV) system which incorporates a thin rotating prism to obtain three-dimensional velocity fields in a large cubical measurement volume. The system makes use of an arrangement where a laser beam is first laterally deflected using an even-faced prism, and then passed through a cylindrical lens rod to obtain light sheets for illumination. This eliminates the need for large rotating mirrors or heavy prisms and facilitates relatively fast rotation speeds of up to 4800 rpm for the prism, yielding three-dimensional, three-component velocity field over a large depth at relatively high particle seeding density. About $10^6$ velocity vectors (3D-3C) are obtained in a single volumetric-scan of $100 \times 100 \times 100$ mm$^3$. The method is demonstrated using two independent experiments, (1) a round jet at Reynolds number Re = 1000, and (2) the flow field around a freely rising sphere at a Reynolds number Re$_p$ $\approx$ 260, and the wake flow is compared with direct numerical simulations of a falling viscous droplet. The scanning gives time-resolved evolution of the large-scale vortical structures of the Re = 1000 jet, with spatial gradients captured fairly well. The three-dimensional flow field surrounding the refractive-index-matched rising sphere is shown to be steady and non-axisymmetric. The flow field and separation bubble are seen to be similar, but slightly shorter than that of the falling droplet case and the uniform flow past a fixed sphere case at a comparable Reynolds number.

physics.flu-dyn↗
arXiv2025

Fluid Dynamical Pathways of Airborne Transmission while Waiting in a Line

Waiting in a line (or a queue) is an important, often unavoidable social interaction that occurs frequently in public spaces. Despite its wide prevalence and rich parametric variability, few studies have addressed the risks of airborne transmission while waiting in a line. Here we use a combination of scaled down laboratory experiments and direct numerical simulations (DNS) to assess the flow patterns and infection risks in a simplified waiting line setting. We observed the presence of fluid dynamical countercurrents, due to the competing effects of line kinematics and thermal gradients, which can either heighten or suppress the risks of transmission. Depending on the walking speed, an intermediate ambient temperature range can potentially heighten the infection risks by allowing the breath plume to linger in the air for extended durations; however, colder and warmer ambients both suppress the spread. The current guideline of increasing physical separation has limited impact on reducing transmission in the waiting line setting. The present work highlights the need for updated transmission mitigation guidelines that go beyond the simplicity of the six feet rule in social interactions where physical separation, duration of interaction, and periodicity of movements are factors.

physics.flu-dyn↗
arXiv2025

Loop Hori Formulae for T-duality and Twisted Bismut-Chern Character

The main purpose of this paper is to establish the loop space formulation of T-duality in the presence of background flux. In particular, we construct a loop space analogue of the Hori formula, termed \textbf{the loop Hori map}, and demonstrate that it induces a quasi-isomorphism between the exotic twisted equivariant cohomologies on the free loop spaces of the T-dual sides. Spacetime, when viewed as the constant loops, is a submanifold of loop space. The duality that we prove on loop space restricts to the T-duality with $H$-flux on spacetime. This significantly refines the earlier work of the authors in 2015 where T-duality was established after localisation to the base space. The construction of the loop Hori map is an application of our generalization of the Bismut--Chern character in 2015, originally introduced in the loop space interpretation of the Atiyah--Singer index theorem by Atiyah--Witten and Bismut.

hep-th↗
arXiv2023

Shape-Morphing Dynamics of Soft Compliant Membranes for Drag and Turbulence Modulation

We study the kinematics and dynamics of a highly compliant membrane disk placed head-on in a uniform flow. With increasing flow velocity, the membrane deforms nonlinearly into increasingly parachute-like shapes. These aerodynamically elongated materials exhibit a modified drag law, which is linked to the elastohydrodynamic interactions. We predict the unsteady structural response of the membranes using a nonlinear, aeroelastic model -- in excellent agreement with experimental measurements of deformations and force fluctuations. With simultaneous membrane interface tracking, force measurements and flow tracing, we reveal that a peculiar skewness in the membrane's oscillations triggers turbulence production in the wake, thereby modulating the drag. The present work provides a demonstration of the complex interplay between soft materials and fluid turbulence, leading to new, emergent system properties.

physics.flu-dyn↗
arXiv2023

Index and small bundle gerbes

By a small bundle gerbe we mean a bundle gerbe in the sense of Murray defined on a smooth, finite-dimensional, fibre bundle over a manifold. We construct such gerbes over compact oriented aspherical 3-manifolds, as well as in higher dimensions, generalizing the construction of decomposable bundle gerbes in earlier work with Singer. For these small bundle gerbes there is a direct index map given in terms of either fibrewise pseudodifferential operators, or more conveniently fibrewise semiclassical smoothing operators, twisted by the simplicial line bundle. We prove the Atiyah-Singer type theorem that this realizes the push-forward into twisted K-theory. We also give an application via the index of projective families of Spin_c Dirac operators, to show the existence of obstructions to metrics with large positive scalar curvature.

math.DG↗
arXiv2022

T-duality with $H$-flux for $2d$ $\sigma$-models

In this paper, we establish graded T-duality for $2d$ $\sigma$-models with $H$-flux after localization. This establishes the most general version of T-duality for Type II String Theory. The graded T-duality map, which we call {\bf graded Hori morphism}, is compatible with the Jacobi property of the graded fields, that was earlier studied in \cite{HM21}. Also included are some open problems/conjectures.

hep-th↗
arXiv2022

Fractional structures on bundle gerbe modules and fractional classifying spaces

We study the homotopy aspects of the twisted Chern classes of torsion bundle gerbe modules. Using Sullivan's rational homotopy theory, we realize the twisted Chern classes at the level of classifying spaces. The construction suggests a notion, which we call fractional U-structure serving as a universal framework to study the twisted Chern classes of torsion bundle gerbe modules from the perspective of classifying spaces. Based on this, we introduce and study higher fractional structures on torsion bundle gerbe modules parallel to the higher structures on ordinary vector bundles.

math.AT↗
arXiv2021

Higher localised $\hat{A}$-genera for proper actions and applications

For a finitely generated discrete group $\Gamma$ acting properly on a spin manifold $M$, we formulate new topological obstructions to $\Gamma$-invariant metrics of positive scalar curvature on $M$ that take into account the cohomology of the classifying space $\underline{B}\Gamma$ for proper actions. In the cocompact case, this leads to a natural generalisation of Gromov-Lawson's notion of higher $\hat{A}$-genera to the setting of proper actions by groups with torsion. It is conjectured that these invariants obstruct the existence of $\Gamma$-invariant positive scalar curvature on $M$. For classes arising from the subring of $H^*(\underline{B}\Gamma,\mathbb{R})$ generated by elements of degree at most $2$, we are able to prove this, under suitable assumptions, using index-theoretic methods for projectively invariant Dirac operators and a twisted $L^2$-Lefschetz fixed-point theorem involving a weighted trace on conjugacy classes. The latter generalises a result of Wang-Wang to the projective setting. In the special case of free actions and the trivial conjugacy class, this reduces to a theorem of Mathai, which provided a partial answer to a conjecture of Gromov-Lawson on higher $\hat{A}$-genera. If $M$ is non-cocompact, we obtain obstructions to $M$ being a partitioning hypersurface inside a non-cocompact $\Gamma$-manifold with non-negative scalar curvature that is positive in a neighbourhood of the hypersurface. Finally, we define a quantitative version of the twisted higher index and use it to prove a parameterised vanishing theorem in terms of the lower bound of the total curvature term in the square of the twisted Dirac operator.

math.DG↗
arXiv2021

Nonlinear fluid damping of elastically mounted pitching wings in quiescent water

We experimentally study the nonlinear fluid damping of a rigid but elastically mounted pitching wing in the absence of a freestream flow. The dynamics of the elastic mount are simulated using a cyber-physical system. We perturb the wing and measure the fluid damping coefficient from damped oscillations over a large range of pitching frequencies, pitching amplitudes, pivot locations and sweep angles. A universal fluid damping scaling is proposed to incorporate all these parameters. Flow fields obtained using particle image velocimetry are analyzed to explain the nonlinear behaviors of the fluid damping.

physics.flu-dyn↗
arXiv2020

Water entry of spheres into a rotating liquid

The transient cavity dynamics during water entry of a heavy, non-rotating sphere impacting a rotating pool of liquid is studied experimentally, numerically, and theoretically. We show that the pool rotation advances the transition of the cavity type - from deep seal to surface seal - marked by a reduction in the transitional Froude number. The role of the dimensionless rotational number $\mathcal{S} \equiv \omega R_0/U_0$ on the transient cavity dynamics is unveiled, where $R_0$ is the sphere radius, $\omega$ the angular speed of the liquid, and $U_0$ the impact velocity. The rotating background liquid has two discernible effects on the cavity evolution. Firstly, an increase in the underwater pressure field due to centripetal effects, and secondly a reduction in the pressure of airflow in the cavity neck near the water surface. The non-dimensional pinch-off time of the deep seal shows a robust 1/2 power-law dependence on the Froude number, but with a reducing prefactor for increasing $\omega$. Our findings reveal that the effects of a rotating background liquid on the water entry can be traced back to the subtle differences in the initial stage splash and the near-surface cavity dynamics.

physics.flu-dyn↗
arXiv2020

An equivariant Poincar\'e duality for proper cocompact actions by matrix groups

Let $G$ be a linear Lie group acting properly and isometrically on a $G$-spin$^c$ manifold $M$ with compact quotient. We show that Poincar\'e duality holds between $G$-equivariant $K$-theory of $M$, defined using finite-dimensional $G$-vector bundles, and $G$-equivariant $K$-homology of $M$, defined through the geometric model of Baum and Douglas.

math.KT↗
arXiv2020

T-duality and the exotic chiral de Rham complex

Let $Z$ be a principal circle bundle over a base manifold $M$ equipped with an integral closed $3$-form $H$ called the flux. Let $\widehat{Z}$ be the T-dual circle bundle over $M$ with flux $\widehat{H}$. Han and Mathai recently constructed the $\mathbb{Z}_2$-graded space of exotic differential forms $\mathcal{A}^{\bar{k}}(\widehat{Z})$. It has an additional $\mathbb{Z}$-grading such that the degree zero component coincides with the space of invariant twisted differential forms $\Omega^{\bar{k}}(\widehat{Z}, \widehat{H})^{\widehat{\mathbb{T}}}$, and it admits a differential that extends the twisted differential $d_{\widehat{H}} = d + \widehat{H}$. The T-duality isomorphism $\Omega^{\bar{k}}(Z,H)^{\mathbb{T}} \rightarrow \Omega^{\overline{k+1}}(\widehat{Z}, \widehat{H})^{\widehat{\mathbb{T}}}$ of Bouwknegt, Evslin and Mathai extends to an isomorphism $\Omega^{\bar{k}}(Z,H) \rightarrow \mathcal{A}^{\overline{k+1}}(\widehat{Z})$. In this paper, we introduce the exotic chiral de Rham complex $\mathcal{A}^{\text{ch},\widehat{H},\bar{k}}(\widehat{Z})$ which contains $\mathcal{A}^{\bar{k}}(\widehat{Z})$ as the weight zero subcomplex. We give an isomorphism $\Omega^{\text{ch},H,\bar{k}}(Z) \rightarrow \mathcal{A}^{\text{ch},\widehat{H},\overline{k+1}}(\widehat{Z})$ where $\Omega^{\text{ch},H,\bar{k}}(Z)$ denotes the twisted chiral de Rham complex of $Z$, which chiralizes the above T-duality map.

math.DG↗