68 citations · 519 across the 21 of their papers we have counts for
21 papers
Variational derivation of the Flamant solution for a nonlinear elastic wedge
Dominik Engl, Paul Plucinsky, Ian Tobasco
Concentrated forces acting at the tip of a two-dimensional wedge give rise to the classical Flamant solution to linear elasticity, whose displacement and strain are singular at the…
Derivation of an effective plate theory for parallelogram origami from bar and hinge elasticity
Hu Xu, Ian Tobasco, Paul Plucinsky
Periodic origami patterns made with repeating unit cells of creases and panels bend and twist in complex ways. In principle, such soft modes of deformation admit a simplified asymp…
Bounds on heat transfer by incompressible flows between balanced sources and sinks
Binglin Song, Giovanni Fantuzzi, Ian Tobasco
Internally heated convection involves the transfer of heat by fluid motion between a distribution of sources and sinks. Focusing on the balanced case where the total heat added by…
Sharpness and non-sharpness of occupation measure bounds for integral variational problems
Giovanni Fantuzzi, Ian Tobasco
We analyze two recently proposed methods to establish a priori lower bounds on the minimum of general integral variational problems. The methods, which involve either `occupation m…
Modelling planar kirigami metamaterials as generalized elastic continua
Yue Zheng, Imtiar Niloy, Ian Tobasco +2
Kirigami metamaterials dramatically change their shape through a coordinated motion of nearly rigid panels and flexible slits. Here, we study a model system for mechanism-based pla…
Optimal cooling of an internally heated disc
Ian Tobasco
Motivated by the search for sharp bounds on turbulent heat transfer as well as the design of optimal heat exchangers, we consider incompressible flows that most efficiently cool an…
Continuum field theory for the deformations of planar kirigami
Yue Zheng, Imtiar Niloy, Paolo Celli +2
Mechanical metamaterials exhibit exotic properties at the system level, that emerge from the interactions of many nearly rigid building blocks. Determining these emergent propertie…
Exact solutions for the wrinkle patterns of confined elastic shells
Ian Tobasco, Yousra Timounay, Desislava Todorova +3
Complex textured surfaces occur in nature and industry, from fingerprints to lithography-based micropatterns. Wrinkling by confinement to an incompatible substrate is an attractive…
Wall-to-wall optimal transport in two dimensions
Andre N. Souza, Ian Tobasco, Charles R. Doering
Gradient ascent methods are developed to compute incompressible flows that maximize heat transport between two isothermal no-slip parallel walls. Parameterizing the magnitude of ve…
Curvature-driven wrinkling of thin elastic shells
Ian Tobasco
How much energy does it take to stamp a thin elastic shell flat? Motivated by recent experiments on the wrinkling patterns of floating shells, we develop a rigorous method via -…
On the optimal design of wall-to-wall heat transport
Charles R. Doering, Ian Tobasco
We consider the problem of optimizing heat transport through an incompressible fluid layer. Modeling passive scalar transport by advection-diffusion, we maximize the mean rate of t…
Optimal bounds and extremal trajectories for time averages in nonlinear dynamical systems
Ian Tobasco, David Goluskin, Charles R. Doering
For any quantity of interest in a system governed by ordinary differential equations, it is natural to seek the largest (or smallest) long-time average among solution trajectories,…
Optimal wall-to-wall transport by incompressible flows
Ian Tobasco, Charles R. Doering
We consider wall-to-wall transport of a passive tracer by divergence-free velocity vector fields . Given an enstrophy budget $\langle |\nabla \mathbf{u}|^{2} \rangle \l…
Bounding the Complexity of Replica Symmetry Breaking for Spherical Spin Glasses
Aukosh Jagannath, Ian Tobasco
In this paper, we study the Crisanti-Sommers variational problem, which is a variational formula for the free energy of spherical mixed -spin glasses. We begin by computing the…
Axial compression of a thin elastic cylinder: bounds on the minimum energy scaling law
Ian Tobasco
We consider the axial compression of a thin elastic cylinder placed about a hard cylindrical core. Treating the core as an obstacle, we prove upper and lower bounds on the minimum…
Low Temperature Asymptotics in Spherical Mean Field Spin Glasses
Aukosh Jagannath, Ian Tobasco
In this paper, we study the low temperature limit of the spherical Crisanti-Sommers variational problem. We identify the -limit of the Crisanti-Sommers functionals, thereby esta…
Symmetry breaking in indented elastic cones
Sergio Conti, Heiner Olbermann, Ian Tobasco
Motivated by simulations of carbon nanocones (see Jordan and Crespi, Phys. Rev. Lett., 2004), we consider a variational plate model for an elastic cone under compression in the dir…
Some Properties of the Phase Diagram for Mixed -Spin Glasses
Aukosh Jagannath, Ian Tobasco
In this paper we study the Parisi variational problem for mixed -spin glasses with Ising spins. Our starting point is a characterization of Parisi measures whose origin lies in…
A Dynamic Programming Approach to the Parisi Functional
Aukosh Jagannath, Ian Tobasco
G.Parisi predicted an important variational formula for the thermodynamic limit of the intensive free energy for a class of mean field spin glasses. In this paper, we present an el…
Wall to Wall Optimal Transport
Pedram Hassanzadeh, Gregory P. Chini, Charles R. Doering
The calculus of variations is employed to find steady divergence-free velocity fields that maximize transport of a tracer between two parallel walls held at fixed concentration for…
Navier-Stokes solver using Green's functions I: channel flow and plane Couette flow
Divakar Viswanath, Ian Tobasco
Numerical solvers of the incompressible Navier-Stokes equations have reproduced turbulence phenomena such as the law of the wall, the dependence of turbulence intensities on the Re…