相关论文: Variational models for prestrained plates with Mon…

In this paper, we consider the Monge-Amp\`{e}re type equations on compact almost Hermitian manifolds. We derive $C^{\infty}$ a priori estimates under the existence of an admissible $\mathcal{C}$-subsolution. Finally, we obtain an existence…

This work builds the connection between the regularity theory of optimal transportation map, Monge-Amp\`{e}re equation and GANs, which gives a theoretic understanding of the major drawbacks of GANs: convergence difficulty and mode collapse.…

There has been remarkable recent progress in the formation of nano-resonators that support ultra-low-loss, compact dielectric photonic crystals with exceptional high-Q modes that operate at visible or telecom wavelengths. New insights into…

In moir\'e crystals formed by stacking van der Waals (vdW) materials, surprisingly diverse correlated electronic phases and optical properties can be realized by a subtle change in the twist angle. Here, we discover that phonon spectra are…

We investigate energetically optimal configurations of thin structures with a pre-strain. Depending on the strength of the pre-strain we consider a whole hierarchy of effective plate theories with a spontaneous curvature term, ranging from…

We study the problem of the existence and the holomorphicity of the Monge-Amp\`ere foliation associated to a plurisubharmonic solutions of the complex homogeneous Monge-Amp\`ere equation even at points of arbitrary degeneracy. We obtain…

Elaborating reliable and versatile strategies for efficient light coupling between free space and thin films is of crucial importance for new technologies in energy efficiency. Nanostructured materials have opened unprecedented…

We investigate minimizers defined on a bounded domain $\Omega$ in $\mathbb{R}^2$ for singular constrained energy functionals that include Ball and Majumdar's modification of the Landau-de Gennes Q-tensor model for nematic liquid crystals.…

In order to investigate the optical properties of rubrene we study the vibronic progression of the first absorption band (lowest \pi -> \pi^* transition). We analyze the dielectric function of rubrene in solution and thin films using the…

On a compact K\"ahler manifold $(X,\omega)$, we study the strong continuity of solutions with prescribed singularities of complex Monge-Amp\`ere equations with integrable Lebesgue densities. Moreover, we give sufficient conditions for the…

Asymptotic homogenisation is considered for problems with integral constraints imposed on a slowly-varying microstructure; an insulator with an array of perfectly dielectric inclusions of slowly varying size serves as a paradigm. Although…

We investigate stationary solutions of a thin-film model for liquid two-layer flows in an energetic formulation that is motivated by its gradient flow structure. The goal is to achieve a rigorous understanding of the contact-angle…

We present a universal nanomechanical sensing platform for the investigation of magnetostriction in thin films. It is based on a doubly-clamped silicon nitride nanobeam resonator covered with a thin magnetostrictive film. Changing the…

The convexity of solutions to boundary value problems for fully nonlinear elliptic partial differential equations (such as real or complex $k$-Hessian equations) is a challenging topic. In this paper, we establish the power convexity of…

A computationally efficient method is presented for approximate optimization of cutting pattern of frame-supported and pneumatic membrane structures. The plane cutting sheet is generated by minimizing the error from the shape obtained by…

We investigate a variational theory for magnetoelastic solids under the incompressibility constraint. The state of the system is described by deformation and magnetization. While the former is classically related to the reference…

Let $(X,\omega)$ be a compact Hermitian manifold of complex dimension $n$, equipped with a Hermitian metric $\omega$. Let $\beta$ be a possibly non-closed smooth $(1,1)$-form on $X$ such that $\int_X\beta^n>0$. Assume that there is a…

Birefringent materials or nanostructures that introduce phase differences between two linear polarizations underpin the operation of wave plates for polarization control of light. Here we develop metasurfaces realizing a distinct class of…

We introduce a monotone (degenerate elliptic) discretization of the Monge-Ampere operator, on domains discretized on cartesian grids. The scheme is consistent provided the solution hessian condition number is uniformly bounded. Our approach…

Given a compact complex manifold $X$, we study the existence and the uniqueness of weak solutions to degenerate Monge-Amp\`ere equations on $X$ with prescribed singularities when the reference form is semipositive and big, while the right…