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Orthonormal bases serve as a powerful mathematical tool in theoretical and experimental optics. However, producing arbitrary optical fields in real-world experiments is limited by the hardware, which in many cases involves a phase-only…
We consider an $\varepsilon$-periodic ($\varepsilon\to 0$) tubular structure, modelled as a magnetic Laplacian on a metric graph, which is periodic along a single axis. We show that the corresponding Hamiltonian admits norm-resolvent…
We claim that $M$(atroid) theory may provide a mathematical framework for an underlying description of $M$-theory. Duality is the key symmetry which motivates our proposal. The definition of an oriented matroid in terms of the Farkas…
Colloidal systems offer unique opportunities for the study of phase formation and structure since their characteristic length scales are accessible to visible light. As a model system the two dimensional assembly of colloidal magnetic and…
The realization and detection of topological phases with ultracold atomic gases is at the frontier of current theoretical and experimental research. Here, we identify cold atoms in optical ladders subjected to synthetic magnetic fields as…
We analyze phase matching with reference to frequency doubling in nanosized quadratic waveguides encompassing form birefringence and supporting cross-polarized fundamental and second-harmonic modes. In an AlGaAs rod with an air void, we…
We describe many different realizations with integer coordinates for the associahedron (i.e. the Stasheff polytope) and for the cyclohedron (i.e. the Bott-Taubes polytope) and compare them to the permutahedron of type A_n and B_n…
We present a study of the structure of phase diagrams for matter-radiation systems, based on the use of coherent states and the catastrophe formalism, that compares very well with the exact quantum solutions as well as providing analytical…
If S is a set of matroids, then the matroid M is S-fragile if, for every element e in E(M), either M\e or M/e has no minor isomorphic to a member of S. Excluded-minor characterizations often depend, implicitly or explicitly, on…
We introduce the notion of a Lie algebroid structure on an affine bundle whose base manifold is fibred over the real numbers. It is argued that this is the framework which one needs for coming to a time-dependent generalization of the…
A theoretical study of toroidal membranes with various degrees of intrinsic orientational order is presented at mean-field level. The study uses a simple Ginzburg-Landau style free energy functional, which gives rise to a rich variety of…
We show that, given a rank 3 affine root system $\Phi$ with Weyl group $W$, there is a unique oriented matroid structure on $\Phi$ which is $W$-equivariant and restricts to the usual matroid structure on rank 2 subsystems. Such oriented…
We study second-order topological insulators and semimetals characterized by chiral symmetry. We investigate topological phase transitions of a model for construction of the two-dimensional second-order topological insulators protected only…
The windowed quadratic phase Fourier transform (WQPFT) combines the localization capabilities of windowed transforms with the phase modulation structure of the quadratic phase Fourier transform (QPFT). This paper investigates fundamental…
Phase-shifting structured illumination is a powerful technique used across diverse imaging modalities, including 3D surface measurement, quantitative phase imaging, and super-resolution microscopy. However, conventional implementations…
We study the Bergman complex B(M) of a matroid M: a polyhedral complex which arises in algebraic geometry, but which we describe purely combinatorially. We prove that a natural subdivision of the Bergman complex of M is a geometric…
We show that oxidation of phosphorene can lead to the formation of a new family of planar (2D) and tubular (1D) oxides and sub-oxides, most of them insulating. This confers to black phosphorus a native oxide that can be used as barrier…
We investigate the properties of oxygen-functionalized carbides of lanthanide elements with the composition M2CO2 (M=Gd, Tb,Dy) that form two-dimensional (2D) structures. Our ab initio calculations reveal that oxygen termination turns M2C…
Quantum field theories with identical local dynamics can admit different choices of global structure, leading to different partition functions and spectra of extended operators. Such choices can be reformulated in terms of a topological…
Classical designs and their (projective) q-analogs can both be viewed as designs in matroids, using the matroid of all subsets of a set and the matroid of linearly independent subsets of a vector space, respectively. Another natural matroid…