6 citations · 9 across the 9 of their papers we have counts for
8 papers · 1 filter
Regularity for Minimizers of a Planar Partitioning Problem with Cusps
Michael Novack
We study the regularity of minimizers for a variant of the soap bubble cluster problem: \begin{align*} \min \sum_{\ell=0}^N c_{\ell} P( S_\ell)\,, \end{align*} where , am…
A smectic liquid crystal model in the periodic setting
Michael Novack, Xiaodong Yan
We consider the asymptotic behavior as goes to zero of the 2D smectics model in the periodic setting given by \begin{equation*} \mathcal{E}_{\varepsilon }( w) =\frac…
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…
Nonlinear approximation of 3D smectic liquid crystals: sharp lower bound and compactness
Michael Novack, Xiaodong Yan
We consider the 3D smectic energy $$\mathcal{E}_{ε}\left( u\right) =\frac{1}{2}\int_{Ω}\frac{1}{\varepsilon } \left( u_z-\frac{( u_x)^{2}+( u_y)^{2}}{2}\right) ^{2}+\varepsilon \le…
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…
Compactness and sharp lower bound for a 2D smectics model
Michael Novack, Xiaodong Yan
We consider a 2D smectics model \begin{equation*} E_{ε}\left( u\right) =\frac{1}{2}\int_Ω\frac{1}{\varepsilon }\left( u_{z}-\frac{1% }{2}u_{x}^{2}\right) ^{2}+\varepsilon \left( u_…
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…
Dimension Reduction for the Landau-de Gennes Model: The Vanishing Nematic Correlation Length Limit
Michael R. Novack
We study nematic liquid crystalline films within the framework of the Landau-de Gennes theory in the limit when both the thickness of the film and the nematic correlation length ar…