Related papers: On Tropical Intersection Theory
In this paper, a thermodynamically consistent phase-field model is proposed to describe the mass transport and reaction processes of multiple species in a fluid. A key feature of this model is that reactions between different species occur…
For nonlinear hyperbolic systems of conservation laws in one space variable, we establish the existence of nonclassical entropy solutions exhibiting nonlinear interactions between shock waves with strong strength. The proposed theory is…
We propose a definition of tropical linear series that isolates some of the essential combinatorial properties of tropicalizations of not-necessarily-complete linear series on algebraic curves. The definition combines the Baker-Norine…
We develop a formalism for particle production in a field theory coupled to a strong time-dependent external source. An example of such a theory is the Color Glass Condensate. We derive a formula, in terms of cut vacuum-vacuum Feynman…
Starting from certain rational varieties blown-up from (P^1)^N, we construct a tropical, i.e., subtraction-free birational, representation of Weyl groups as a group of pseudo isomorphisms of the varieties. Furthermore, we develop an…
It is shown how to extend the formal variational calculus in order to incorporate integrals of divergences into it. Such a generalization permits to study nontrivial boundary problems in field theory on the base of canonical formalism.
Polytropes are both ordinary and tropical polytopes. We show that tropical types of polytropes in $\mathbb{TP}^{n-1}$ are in bijection with cones of a certain Gr\"{o}bner fan $\mathcal{GF}_n$ in $\mathbb{R}^{n^2 - n}$ restricted to a small…
In this paper, we study the deformation theory of degenerate algebraic curves on singular varieties which appear as the degenerate limit of families of varieties. For this purpose, we systematically develop a new method to calculate the…
We introduce a notion of density which extends both the notion of Lelong number and the theory of intersection for positive closed currents on Kaehler manifolds. For arbitrary finite family of positive closed currents on a compact Kaehler…
In theoretical physics, we sometimes have two perturbative expansions of physical quantity around different two points in parameter space. In terms of the two perturbative expansions, we introduce a new type of smooth interpolating function…
In this continuum theory, we propose a mathematical framework to study the mechanical interplay of bulk-surfaces materials undergoing deformation and phase segregation. To this end, we devise a principle of virtual powers with a…
The present work discusses about a possible physical interpretation of the occurrence of turbulence in a dynamic fluid with mathematical modeling and computer simulation. Here turbulence is defined to be a phenomenon of random velocity…
The Frenkel line, a crossover line between rigid and nonrigid dynamics of fluid particles, has recently been the subject of intense debate regarding its relevance as a partitioning line of supercritical phase, where the main criticism comes…
We define tropical rational function semifields $\overline{\boldsymbol{T}(X_1, \ldots, X_n)}$ and prove that a tropical curve $\varGamma$ is realized (except for points at infinity) as the congruence variety $V \subset \boldsymbol{R}^n$…
A novel description of kinetic theory dynamics is proposed in terms of resummed moments that embed information of both hydrodynamic and non-hydrodynamic modes. The resulting expansion can be used to extend hydrodynamics to higher orders in…
In a previous paper the authors develop an intersection theory for subspaces of rational functions on an algebraic variety X over complex numbers. In this note, we first extend this intersection theory to an arbitrary algebraically closed…
We extend the statistical field-theoretical framework of rough surface contact mechanics to characterize the interfacial gap between an elastic half-space and a randomly rough surface incorporating exponential repulsion. Building upon a…
We give a classification of generic bifurcations of intersections of wavefronts generated by different points of a hypersurface with or without boundaries.
It has long been known that weakly nonlinear field theories can have a late-time stationary state that is not the thermal state, but a wave turbulent state with a far-from-equilibrium cascade of energy. We go beyond the existence of the…
A novel flow state consisting of two oppositely travelling waves (TWs) with oscillating amplitudes has been found in the counterrotating Taylor-Couette system by full numerical simulations. This structure bifurcates out of axially standing…