R. Venkatraman

activity

20112025

most citedEvolution of Weak Shocks in One Dimensional Planar and Non-planar Gasdynamic Flows

17 citations · 37 across the 13 of their papers we have counts for

collaborators

17 papers

math.AP2025

Interaction energies in nematic liquid crystal suspensions

Lia Bronsard, Xavier Lamy, Dominik Stantejsky +1

We establish, as $ρ \to 0$ , an asymptotic expansion for the minimal Dirichlet energy of $S^{2}$ -valued maps outside a finite number of three-dimensional particles of size $ρ$ …

math.AP2023

Interaction energies in paranematic colloids

Dmitry Golovaty, Jamie Taylor, Raghavendra Venkatraman +1

We consider a system of colloidal particles embedded in a paranematic -- an isotropic phase of a nematogenic medium above the temperature of the nematic-to-isotropic transition. In…

math.NT2023

A Note on Quartic Diophantine equation $X^{4} - Y^{4} = R^{2} - S^{2}$

S. Muthuvel, R. Venkatraman

In this paper, we deal with the quartic Diophantine equation $X^{4} - Y^{4} = R^{2} - S^{2}$ to present its infinitely many integer solutions.

math.AP2022

Asymptotic expansion of the spectrum for periodic Schrödinger operators

Scott Armstrong, Raghavendra Venkatraman

We prove an asymptotic expansion for the eigenvalues and eigenfunctions of Schrödinger-type operator with a confining potential and with principle part a periodic elliptic operator…

math.AP2022

Complex Analytic Dependence on the Dielectric Permittivity in ENZ Materials: The Photonic Doping Example

Robert V. Kohn, Raghavendra Venkatraman

Motivated by the physics literature on "photonic doping" of scatterers made from "epsilon-near-zero" (ENZ) matrials, we consider how the scattering of time-harmonic TM electromagne…

math.AP2022★ 5 cited

Far-Field Expansions for Harmonic Maps and the Electrostatics Analogy in Nematic Suspensions

Stan Alama, Lia Bronsard, Xavier Lamy +1

For a smooth bounded domain $G \subset R^{3}$ we consider maps $n : R^{3} ∖ G \to S^{2}$ minimizing the energy $E(n)=\int_{\mathbb R^3\setminus G}|\nabla n…

math.AP2021

Least Wasserstein distance between disjoint shapes with perimeter regularization

Michael Novack, Ihsan Topaloglu, Raghavendra Venkatraman

We prove the existence of global minimizers to the double minimization problem \[ \inf\Big\{ P(E) + λW_p(\mathcal{L}^n \lfloor \, E,\mathcal{L}^n \lfloor\, F) \colon |E \cap F| = 0…

math.AP2020

Anisotropic Surface Tensions for Phase Transitions in Periodic Media

Rustum Choksi, Irene Fonseca, Jessica Lin +1

This paper establishes bounds on the homogenized surface tension for a heterogeneous Allen-Cahn energy functional in a periodic medium. The approach is based on relating the homoge…

math.CA2020

Quantitative Stability for the Heisenberg-Pauli-Weyl inequality

Sean McCurdy, Raghavendra Venkatraman

We prove a quantitative stability result for the Heisenberg-Pauli-Weyl inequality. This yields next and next-to-next order correction terms, sharpening the inequality in all dimens…

math.AP2020

Homogenization of quasi-crystalline functionals via two-scale-cut-and-project convergence

Rita Ferreira, Irene Fonseca, Raghavendra Venkatraman

We consider a homogenization problem associated with quasi-crystalline multiple integrals of the form \begin{equation*} \begin{aligned} u_\varepsilon\in L^p(Ω;\mathbb{R}^d) \mapsto…

math.AP2019★ 5 cited

Bounds on the energy of a soft cubic ferromagnet with large magnetostriction

Raghavendra Venkatraman, Vivekanand Dabade, Richard D. James

We complete the analysis initiated in [5] on the micromagnetics of cubic ferromagnets in which the role of magnetostriction is significant. We prove ansatz-free lower bounds for th…

math.AP2018

A Model Problem for Nematic-Isotropic Transitions with Highly Disparate Elastic Constants

Dmitry Golovaty, Michael Novack, Peter Sternberg +1

We analyze a model problem based on highly disparate elastic constants that we propose in order to understand corners and cusps that form on the boundary between the nematic and is…

math.AP2017

A Ginzburg-Landau type problem for highly anisotropic nematic liquid crystals

Dmitry Golovaty, Peter Sternberg, Raghavendra Venkatraman

We carry out an asymptotic analysis of a thin nematic liquid crystal in which one elastic constant dominates over the others, namely \begin{align} \label{energyab} \inf E_\varepsil…

math.AP2016★ 10 cited

Diffusive stability of spatially periodic solutions of the Brusselator model

Alim Sukhtayev, Kevin Zumbrun, Soyeun Jung +1

Applying the Lyapunov-Schmidt reduction approach introduced by Mielke and Schneider in their analysis of the fourth-order scalar Swift-Hohenberg equation, we carry out a rigorous s…

math.AP2016

Periodic Orbits of Gross Pitaevskii in the Disc with Vortices Following Point Vortex Flow

Raghavendra Venkatraman

We prove the existence of non-constant time periodic vortex solutions to the Gross-Pitaevskii equations for small but \textit{fixed} $ε > 0.$ The vortices of these soluti…

math.AP2011

Lecture Notes: The Galerkin Method