Related papers: Real phase structures on matroid fans and matroid …
A matroid is a machine capturing linearity of mathematical objects and producing combinatorial structures. Matroid structure arises everywhere since linearity is a ubiquitous concept. One natural way to obtain matroids is by considering…
This paper studies rings of integral piecewise-exponential functions on rational fans. Motivated by lattice-point counting in polytopes, we introduce a special class of unimodular fans called Ehrhart fans, whose rings of integral…
A fully implicit phase field model has been implemented in Fortran for 1-3D simulations. It is intended for simulations of diffusion and diffusion controlled transformations. Gibbs energy contributions from both gradients in concentration…
In this paper we construct a family of complex structures on a complex flag manifold that converge to the real polarization coming from the Gelfand-Cetlin integrable system, in the sense that holomorphic sections of a prequantum line bundle…
The monograph contains a systematic treatment of a circle of problems in analysis and integral geometry related to inversion of the Radon transform on the space of real rectangular matrices. This transform assigns to a function $f$ on the…
Colloidal crystals are used to understand fundamentals of atomic rearrangements in condensed matter and build complex metamaterials with unique functionalities. Simulations predict a multitude of self-assembled crystal structures from…
We show the existence of families of periodic polyhedra in spaces of constant curvature whose fundamental domains can be obtained by attaching prisms and antiprisms to Archimedean solids. These polyhedra have constant discrete curvature and…
Artificial magnetic fields break time-reversal symmetry in engineered materials--also known as metamaterials, enabling robust, topological transport of neutral excitations, much like electronic conduction edge channels in the integer…
In this paper we present a definition of oriented Lagrangian symplectic matroids and their representations. Classical concepts of orientation and this extension may both be thought of as stratifications of thin Schubert cells into unions of…
The remarkable advances achieved in two-dimensional materials are now being directly transposed to low-dimensional oxides. Here we show using first-principles-based atomistic simulations that ultrathin freestanding ferroelectric layers host…
Parametrized field theories, which are generally covariant versions of ordinary field theories, are studied from the point of view of the covariant phase space: the space of solutions of the field equations equipped with a canonical…
We construct moduli spaces of rational covers of an arbitrary smooth tropical curve in R^r as tropical varieties. They are contained in the balanced fan parametrizing tropical stable maps of the appropriate degree to R^r. The weights of the…
In recent experiments bosonic [Atala et al., Nat. Phys. 10, 588 (2014), B. K. Stuhl et al., Science 349, 1514 (2015)] as well as fermionic ladders [M. Mancini et al., Science 349, 1510 (2015)] with a uniform flux were studied and different…
The phase structure of four-fermion theories is thoroughly investigated with varying temperature and chemical potential for arbitrary space-time dimensions $(2 \leq D < 4)$ by using the 1/N expansion method. It is shown that the chiral…
A lattice path matroid is a transversal matroid corresponding to a pair of lattice paths on the plane. A matroid base polytope is the polytope whose vertices are the incidence vectors of the bases of the given matroid. In this paper, we…
We consider a mixture of one neutral and two oppositely charged types of molecules confined to a surface. Using analytical techniques and molecular dynamics simulations, we construct the phase diagram of the system and exhibit the…
Oriented matroids can serve as a tool of modeling of collective decision-making processes in contradictory problems of pattern recognition. We present a generalization of the committee techniques of pattern recognition to oriented matroids.…
We present a paradigm in constructing very stable, faceted nanotube and fullerene structures by laterally joining nanoribbons or patches of different planar phosphorene phases. Our ab initio density functional calculations indicate that…
The ground state of colloidal magnetic particles in a modulated channel are investigated as function of the tilt angle of an applied magnetic field. The particles are confined by a parabolic potential in the transversal direction while in…
Optical approaches for wavefront shaping traditionally rely on phase modulation through holographic techniques. Shaping the phase determines a wave's diffraction and hence its intensity distribution in space. We instead show that shaping…