arXiv subjects

Yubin Gao

Publications and source records attributed to Yubin Gao.

5 recordsLinked to original sources

arXiv2025

Disordered Continuity: Programming Resolution-Independent Stochastic Metamaterials with Differentiable Anisotropic Property Distribution

Nature-inspired stochastic metamaterials with disordered and multiscale architectures have shown great promise towards extraordinary functionalities, including high mechanical resilience, stress modulation and biased stiffness reinforcement. As a special type of functionally graded metamaterial, programming multiscale stochastic metamaterial to achieve required functional property is computationally demanding due to the iterative simulation process, and thereby often intuitively implemented by filling a predefined subset of functional units into rasterized design space of fixed resolution, which restricts the flexibility and effectiveness of the designed functionality. To mitigate the computational complexity introduced by the multiscale architecture, we proposed a two-stage approach to programming stochastic metamaterials towards customized mechanical response. Instead of directly optimizing stochastic microstructures, the proposed approach first optimizes a differentiable physical property distribution, e.g. stiffness that targets desired functionality, and then generates spinodal architected microstructures to realize such property distribution under resolution-independent rasterization. The key enabler is the incorporation of spherical harmonics to represent, modulate and interpolate anisotropic stiffness distribution, which then serves as a non-uniform distribution function for the generation of anisotropic spinodal infills with high continuity. The test results demonstrated effective design of stochastic metamaterials with programmed functionalities to enable stress modulation, texture encoding and mechanical cloaking.

physics.app-ph↗

arXiv2025

Geometric phase metasurfaces for linearly polarized light

The geometric phase is a universal concept in modern physics and has enabled the development of metasurfaces for versatile wavefront shaping. However, its realization in metasurfaces has been restricted to circularly polarized light, confining geometric phase metasurfaces to helicity-dependent operation and excluding them from the linear-polarization domain that dominates modern optics. In this work, we overcome this limitation by harnessing exceptional points of non-Hermitian physics. We introduce and experimentally realize quasi-exceptional-point metasurfaces that exploit engineered singularities to directly impart a geometric phase onto linearly polarized light. Proof-of-principle demonstrations with gratings and holograms confirm broadband and high-fidelity wavefront shaping across arbitrary linear polarizations, which has not been achieved with previous phase modulation approaches. By revealing an intrinsic connection between geometric phase and non-Hermitian photonics, our work resolves a long-standing theoretical impasse and establishes a new framework for high-dimensional light control, opening opportunities for scalable polarization optics, advanced imaging, holography, optical communications, and integrated photonics.

physics.optics↗

arXiv2018

On the regularity of product of pure power complete intersections

Let I be a complete intersection in a polynomial ring over a field, the Castelnuovo-Mumford regularity of I^n is given by using an induction method. When I, J and K are three pure power complete intersections, it is proved that reg(IJK) is not more than reg(I)+reg(J)+reg(K).

math.AC↗

arXiv2013

Sign patterns with minimum rank 3 and point-line configurations

A \emph{sign pattern (matrix)} is a matrix whose entries are from the set $\{+, -, 0\}$. The \emph{minimum rank} (respectively, \emph{rational minimum rank}) of a sign pattern matrix $\cal A$ is the minimum of the ranks of the real (respectively, rational) matrices whose entries have signs equal to the corresponding entries of $\cal A$. A sign pattern $\cal A$ is said to be \emph{condensed} if $\cal A$ has no zero row or column and no two rows or columns are identical or negatives of each other. In this paper, a new direct connection between condensed $m \times n $ sign patterns with minimum rank $r$ and $m$ point--$n$ hyperplane configurations in ${\mathbb R}^{r-1}$ is established. In particular, condensed sign patterns with minimum rank 3 are closed related to point--line configurations on the plane. It is proved that for any sign pattern $\cal A$ with minimum rank $r\geq 3$, if the number of zero entries on each column of $\cal A$ is at most $r-1$, then the rational minimum rank of $\cal A$ is also $r$. Furthermore, we construct the smallest known sign pattern whose minimum rank is 3 but whose rational minimum rank is greater than 3.

math.CO↗

arXiv2009

The kth Upper Bases of Primitive Non-powerful Signed Digraphs

In this paper, we study the kth upper bases of primitive non-powerful signed digraphs. A bound on the kth upper bases of all primitive non-powerful signed digraphs is obtained, and the equality case of the bound is characterized. We also show that there exists "gap" in the kth upper base set of primitive non-powerful signed digraphs.

math.CO↗