146 citations · 281 across the 17 of their papers we have counts for
22 papers
Allen-Cahn Solutions with Triple Junction Structure at Infinity
Étienne Sandier, Peter Sternberg
We construct an entire solution to the elliptic system \[ ΔU=\nabla_uW(U), \] where is a `triple-well' potential. Thi…
Solutions of the Ginzburg-Landau equations with vorticity concentrating near a nondegenerate geodesic
Andrew Colinet, Robert Jerrard, Peter Sternberg
It is well-known that under suitable hypotheses, for a sequence of solutions of the (simplified) Ginzburg-Landau equations $-Δu_\varepsilon +\varepsilon^{-2}(|u_\varepsilon|^2-1)u_…
A One-Dimensional Variational Problem for Cholesteric Liquid Crystals with Disparate Elastic Constants
Dmitry Golovaty, Michael Novack, Peter Sternberg
We consider a one-dimensional variational problem arising in connection with a model for cholesteric liquid crystals. The principal feature of our study is the assumption that the…
Reduced equations for an active model of the hydroelastic waves in the cochlea
Jacob Rubinstein, Peter Sternberg
Building upon our earlier passive models for the cochlea, here we enhance the model with an active mechanism. Starting with a one-chamber simplification leading to a system of a ti…
A Novel Landau-de Gennes Model with Quartic Elastic Terms
Dmitry Golovaty, Michael Novack, Peter Sternberg
Within the framework of the generalized Landau-de Gennes theory, we identify a -tensor-based energy that reduces to the four-constant Oseen-Frank energy when it is considered ov…
Phase Transitions in Nematics: Textures with Tactoids and Disclinations
Dmitry Golovaty, Young-Ki Kim, Oleg D. Lavrentovich +2
We demonstrate that a first order isotropic-to-nematic phase transition in liquid crystals can be succesfully modeled within the generalized Landau-de Gennes theory by selecting an…
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…
Asymptotic Behavior of Allen-Cahn Type Energies and Neumann Eigenvalues via Inner Variations
Nam Q. Le, Peter Sternberg
We use the notion of first and second inner variations as a bridge allowing one to pass to the limit of first and second Gateaux variations for the Allen-Cahn, Cahn-Hilliard and Oh…
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…
A singular local minimizer for the volume constrained minimal surface problem in a nonconvex domain
Peter Sternberg, Kevin Zumbrun
It has recently been established byWang and Xia [WX] that local minimizers of perimeter within a ball subject to a volume constraint must be spherical caps or planes through the or…
Dimension reduction for the Landau-de Gennes model on curved nematic thin films
Dmitry Golovaty, Alberto Montero, Peter Sternberg
We use the method of -convergence to study the behavior of the Landau-de Gennes model for a nematic liquid crystalline film attached to a general fixed surface in the limit of v…
A Degenerate Isoperimetric Problem in the Plane
Jiri Dadok, Peter Sternberg
We establish sufficient conditions for existence of curves minimizing length as measured with respect to a degenerate metric on the plane while enclosing a specified amount of Eucl…
Convergence of a particle method for diffusive gradient flows in one dimension
J. A. Carrillo, F. S. Patacchini, P. Sternberg +1
We prove the convergence of a particle method for the approximation of diffusive gradient flows in one dimension. This method relies on the discretisation of the energy via non-ove…
On the heteroclinic connection problem for multi-well gradient systems
Andres Zuniga, Peter Sternberg
We revisit the existence problem of heteroclinic connections in associated with Hamiltonian systems involving potentials having severa…
A Degenerate Isoperimetric Problem and Traveling Waves to a Bi-stable Hamiltonian System
Stan Alama, Lia Bronsard, Andres Contreras +2
We analyze a non-standard isoperimetric problem in the plane associated with a metric having degenerate conformal factor at two points. Under certain assumptions on the conformal f…
Dimension reduction for the Landau-de Gennes model in planar nematic thin films
Dmitry Golovaty, José Alberto Montero, Peter Sternberg
We use the method of -convergence to study the behavior of the Landau-de Gennes model for a nematic liquid crystalline film in the limit of vanishing thickness. In this asymptot…
Cascade of minimizers for a nonlocal isoperimetric problem in thin domains
Massimiliano Morini, Peter Sternberg
For $Ω_\e=(0,\e)\times (0,1)$ a thin rectangle, we consider minimization of the two-dimensional nonlocal isoperimetric problem given by \[ \inf_u E^γ_{Ω_\e}(u)\] where \[ E^γ_{Ω_\e…
Kinematic and dynamic vortices in a thin film driven by an applied current and magnetic field
Lydia Peres Hari, Jacob Rubinstein, Peter Sternberg
Using a Ginzburg-Landau model, we study the vortex behavior of a rectangular thin film superconductor subjected to an applied current fed into a portion of the sides and an applied…
Dynamics Of Ginzburg-Landau And Gross-Pitaevskii Vortices On Manifolds
Ko-Shin Chen, Peter Sternberg
We consider the dissipative heat flow and conservative Gross-Pitaevskii dynamics associated with the Ginzburg-Landau energy posed on a Riemannian 2-manifold M. We show the limiting…
The resistive state in a superconducting wire: Bifurcation from the normal state
Jacob Rubinstein, Peter Sternberg, Kevin Zumbrun
We study formally and rigorously the bifurcation to steady and time-periodic states in a model for a thin superconducting wire in the presence of an imposed current. Exploiting the…
Bifurcation diagram and pattern formation in superconducting wires with electric currents
J. rubinstein, P. Sternberg, Q. Ma
We examine the behavior of a one-dimensional superconducting wire exposed to an applied electric current. We use the time-dependent Ginzburg-Landau model to describe the system and…
Phase transition curves for mesoscopic superconducting samples
H. T. Jadallah, J. Rubinstein, P. Sternberg
We compute the phase transition curves for mesoscopic superconductors. Special emphasis is given to the limiting shape of the curve when the magnetic flux is large. We derive an as…