Related papers: Tailoring a pair of pants: the phase tropical vers…

We prove the existence and uniqueness of solutions for a family of nonlinear parabolic systems related to phase field models taking in account variations of temperature and the possibility of a general class of nonlinearities. The present…

As a means of realizing oscillatory pairing between fermions, we study superfluid pairing between two fermion "spin" species that are confined to adjustable spin-dependent trapping potentials. Focusing on the one-dimensional limit, we find…

We investigate reinforced non-linear urns with interacting types, and show that where there are three interacting types there are phenomena which do not occur with two types. In a model with three types where the interactions between the…

Let X and X' be closed subschemes of an algebraic torus T over a non-archimedean field. We prove the rational equivalence as tropical cycles, in the sense of Henning Meyer's graduate thesis, between the tropicalization of the intersection…

We introduce tropically unirational varieties, which are subvarieties of tori that admit dominant rational maps whose tropicalisation is surjective. The central (and unresolved) question is whether all unirational varieties are tropically…

Hot giant exoplanets are very exotic objects with no equivalent in the Solar System that allow us to study the behavior of atmospheres under extreme conditions. Their thermal and chemical day--night dichotomies associated with extreme wind…

The preservation of ambient isotopic equivalence under piecewise linear (PL) approximation for smooth knots are prominent in molecular modeling and simulation. Sufficient conditions are given regarding: (1) Hausdorff distance, and (2) a sum…

Colloidal particles are not simple rigid particles, in general an isolated particle is a system with many degrees of freedom in its own right, e.g., the counterions around a charged colloidal particle.The behaviour of model colloidal…

Tropical ideals, introduced in arXiv:1609.03838, define subschemes of tropical toric varieties. We prove that the top-dimensional parts of their varieties are balanced polyhedral complexes of the same dimension as the ideal. This means that…

We address the question of the quantitative relationship between thermodynamic phase transitions and topological changes in the potential energy manifold analyzing two classes of one dimensional models, the Burkhardt solid-on-solid model…

In this article, we study the knots realized by periodic orbits of R-covered Anosov flows in compact 3-manifolds. We show that if two orbits are freely homotopic then in fact they are isotopic. We show that lifts of periodic orbits to the…

We determine the exact complex-temperature (CT) phase diagram of the 1D $Z_6$ clock model. This is of interest because it is the first exactly solved system with a CT phase boundary exhibiting a finite-$K$ intersection point where an odd…

This work studies the heat equation in a two-phase material with spherical inclusions. Under some appropriate scaling on the size, volume fraction and heat capacity of the inclusions, we derive a coupled system of partial differential…

We consider planar maps with three boundaries, colloquially called pairs of pants. In the case of bipartite maps with controlled face degrees, a simple expression for their generating function was found by Eynard and proved bijectively by…

Tropical algebraic geometry is the geometry of the tropical semiring (R, min, +). The theory of total positivity is a natural generalization of the study of matrices with all minors positive. In this paper we introduce the totally positive…

In frameworks of the phenomenological approach we analyze of the phase diagram of mixed compounds. We obtain space groups of symmetry of the real structures as result of phase transition from close-packed degenerate structure. The theory of…

In a recent paper we introduced two Potts-like models in three dimensions, which share the following properties: (A) One of the ice rules is always fulfilled (in particular also at infinite temperature). (B) Both ice rules hold for…

We propose a new method to compute asymptotics of periods using tropical geometry, in which the Riemann zeta values appear naturally as error terms in tropicalization. Our method suggests how the Gamma class should arise from the…

This is the less official, English version of the proof of the fact that every closed atoroidal 3-manifold carries finitely many isotopy classes of tight contact structures.

We give an alternative argument for the classification of real bundle pairs over smooth symmetric surfaces and extend this classification to nodal symmetric surfaces. We also classify the homotopy classes of automorphisms of real bundle…