de Amorim Filho, Edgar C Moreira, Rodrigo A N Santos, Fernando A
Published in
Journal of Physics: Complexity

In this work, we use methods and concepts of applied algebraic topology to comprehensively explore the recent idea of topological phase transitions (TPTs) in complex systems. TPTs are characterized by the emergence of nontrivial homology groups as a function of a threshold parameter. Under certain conditions, one can identify TPTs via the zeros of ...

jingyi zhang, junlan xian;

In this work, we study the Hawking temperature of the global monopole spacetime (non-spherical symmetrical black hole) based on the topological method proposed by Robson, Villari, and Biancalana (RVB). By connecting the Hawking temperature with the topological properties of black holes, the Hawking temperature of the global monopole spacetime can b...

Gagneux, Gérard Millet, Olivier

The didactic object of these developments on differential geometry of curves and surfaces is to present fine and convenient mathematical strategies, adapted to the study of capillary bridges from experimental data and relatively simple to use in practice. The common thread is to be able to calculate accurately in any situation the bending stress ov...

Pevec, Tjaša

Definicija simplicialnih kompleksov in mnogoterosti nam omogoči razumevanje dveh osnovnih lastnosti ploskev, ki sta Eulerjeva karakteristika in orientabilnost. S pomočjo Dehn-Sommervillovih enačb zapisanih s f- in h-vektorjem definiramo Eulerjevo karakteristiko. Vidimo, da ta, poleg orientabilnosti, natanko določa vse sklenjene ploskve. Do homeomor...

farooq;, omer

We show that there is a relationship between the generalized Euler characteristic Eo(|VDo|) of the original graph that was split at vertices into two disconnected subgraphs i=1,2 and their generalized Euler characteristics Ei(|VDi|). Here, |VDo| and |VDi| denote the numbers of vertices with the Dirichlet boundary conditions in the graphs. The theor...

McClure, James E. Abaid, Nicole
Published in
Frontiers in Applied Mathematics and Statistics

In this work, we explore how the emergence of collective motion in a system of particles is influenced by the structure of their domain. Using the Vicsek model to generate flocking, we simulate two-dimensional systems that are confined based on varying obstacle arrangements. The presence of obstacles alters the topological structure of the domain w...

frolkova, anastasia v.

The study of topological invariants of phase diagrams allows for the development of a qualitative theory of the processes being researched. Studies of the properties of objects in the same equivalence class may be carried out with the aim of predicting the properties of unexplored objects from this class, or predicting the behavior of a whole syste...

Naskręcki, Bartosz Dauter, Zbigniew Jaskolski, Mariusz
Published in
Acta Crystallographica. Section A, Foundations and Advances

The notion of the Euler characteristic of a polyhedron or tessellation has been the subject of in-depth investigations by many authors. Two previous papers worked to explain the phenomenon of the vanishing (or zeroing) of the modified Euler characteristic of a polyhedron that underlies a periodic tessellation of a space under a crystallographic spa...

Déglise, Frédéric Jin, Fangzhou Khan, Adeel A.

We develop the theory of fundamental classes in the setting of motivic homotopy theory. Using this we construct, for any motivic spectrum, an associated bivariant theory in the sense of Fulton-MacPherson. We import the tools of Fulton's intersection theory into this setting: (refined) Gysin maps, specialization maps, and formulas for excess interse...

Jakimowicz, Aleksander Rzeczkowski, Daniel
Published in
Entropy

The location quotient is one of the basic quantitative tools for identifying the regional poles and the turnpikes of economic growth in spatial economy. The disadvantage of this traditional measure is the limited scope of economic information contained in it. The new measure of economic development proposed in the article encompasses a complex spec...