Related papers: Real phase structures on matroid fans and matroid …
The basis of the identity representation of a polyhedral group is able to describe functions with symmetries of a platonic solid, i.e., 3-D objects which geometrically obey the cubic symmetries. However, to describe the dynamic of assembles…
In this sequel to "Foundations of matroids - Part 1", we establish several presentations of the foundation of a matroid in terms of small building blocks. For example, we show that the foundation of a matroid M is the colimit of the…
The theory of matroids or combinatorial geometries originated in linear algebra and graph theory, and has deep connections with many other areas, including field theory, matching theory, submodular optimization, Lie combinatorics, and total…
The phase-field method has become in recent years the method of choice for simulating microstructural pattern formation during solidification. One of its main advantages is that time-dependent three-dimensional simulations become feasible.…
Metasurfaces in metal/insulator/metal configuration have recently been widely used in photonics research, with applications ranging from perfect absorption to phase modulation, but why and when such structures can realize what kind of…
Phase reconstruction is important in transmission electron microscopy for structural studies. We describe electron Fourier ptychography and its application to phase reconstruction of both radiation-resistant and beam-sensitive materials. We…
Material surfaces encompass structural and chemical discontinuities that often lead to the loss of the property of interest in the so-called dead layers. It is notably problematic in nanoscale oxide electronics, where the integration of…
We apply convex geometry (cones, fans) to homological input (abelian categories, hearts of bounded t-structures) to construct a new invariant of an abelian category, its heart fan. This can be viewed as a `universal phase diagram' for…
In response to recent chemical attempts to construct higher-spin ladder materials from organic polyradicals, we study the ground-state properties of a wide class of antiferromagnetic spin-1 ladders. Employing various numerical tools, we…
On-demand, switchable phase transitions between topologically non-trivial and trivial photonic states are demonstrated. Specifically, it is shown that integration of a 2D array of coupled ring resonators within a thermal heater array…
We study the positive Bergman complex B+(M) of an oriented matroid M, which is a certain subcomplex of the Bergman complex B(M) of the underlying unoriented matroid. The positive Bergman complex is defined so that given a linear ideal I…
Classical toric varieties are among the simplest objects in algebraic geometry. They arise in an elementary fashion as varieties parametrized by monomials whose exponents are a finite subset $\mathcal{A}$ of $\mathbb{Z}^n$. They may also be…
The main result of this paper is that every (separated) toric variety which has a semigroup structure compatible with multiplication on the underlying torus is necessarily affine. In the course of proving this statement, we also give a…
Freezing of charged colloids on square or triangular two-dimensional periodic substrates has been recently shown to realize a rich variety of orientational orders. We propose a theoretical framework to analyze the corresponding structures.…
We discuss the appearance of fractional topological phases on cyclic evolutions of entangled qudits. The original result reported in Phys. Rev. Lett. \textbf{106}, 240503 (2011) is detailed and extended to qudits of different dimensions.…
Perhaps the simplest approach to constructing models with sub-dimensional particles or fractons is to require the conservation of dipole or higher multipole moments. We generalize this approach to allow for moments in phase space and…
We revisit the question of whether a two-dimensional topological insulator may arise in a commensurate N\'eel antiferromagnet, where staggered magnetization breaks both the elementary translation and time reversal, but retains their product…
A phase diagram, defined by the amplitude square and phase of scattering coefficients for absorption cross-section in each individual channel, is introduced as a universal map on the electromagnetic properties for passive scatterers.…
The phase structure of QCD remains an open fundamental problem of standard model physics. In particular at finite density, our knowledge is limited. Yet, numerous model studies point towards a rich and complex phase diagram at large…
The moduli space of spatial polygons is known as a symplectic manifold equipped with both K\"ahler and real polarizations. In this paper, associated to the K\"ahler and real polarizations, morphisms of operads…