Related papers: Topological theory of physical fields

We study the evolution of homogeneous and isotropic, flat cosmological models within the general scalar-tensor theory of gravity with arbitrary coupling function and potential. After introducing the limit of general relativity we describe…

The elsewhere surmised topological origin of phase transitions is given here new important evidence through the analytic study of an exactly solvable model for which both topology and thermodynamics are worked out. The model is a mean-field…

Motivated by the goal to give the simplest possible microscopic foundation for a broad class of topological phases, we study quantum mechanical lattice models where the topology of the lattice is one of the dynamical variables. However, a…

Identifying the regions responsible for plastic flow in amorphous solids remains an open problem, since structural disorder seems to prevent the direct application of concepts such as dislocations, topological defects that successfully…

The proposition that photon is a topological object (J. Math. Phys. 49, 032303, 2008) is given rigorous foundation based on pure vector field theory independent of the electromagnetic fields. Holomorphy of 4-dimensional space-time and the…

Topology optimization is a powerful tool utilized in various fields for structural design. However, its application has primarily been restricted to static or passively moving objects, mainly focusing on hard materials with limited…

We study a model for dynamical localization of topology using ideas from non-commutative geometry and topology in quantum mechanics. We consider a collection $X$ of $N$ one-dimensional manifolds and the corresponding set of boundary…

Topological phases are characterised by a topological invariant that remains unchanged by deformations in the Hamiltonian. Materials exhibiting topological phases include topological insulators, superconductors exhibiting strong spin-orbit…

Topology transcends boundaries that conventionally delineate physical, biological and engineering sciences. Our ability to mathematically describe topology, combined with our access to precision tracking and manipulation approaches, has…

Any two infinite-dimensional (separable) Hilbert spaces are unitarily isomorphic. The sets of all their self-adjoint operators are also therefore unitarily equivalent. Thus if all self-adjoint operators can be observed, and if there is no…

In the $\phi $-mapping theory, the topological current constructed by the order parameters can possess different inner structure. The difference in topology must correspond to the difference in physical structure. The transition between…

We construct algorithms and topological invariants that allow us to distinguish the topological type of a surface, as well as functions and vector fields for their topological equivalence. In the first part (arXiv:2501.15657), we discused…

Topological defects (TDs) are crucial for understanding important physical properties of crystalline materials including mechanical failure, ion transport, and two-dimensional melting. This concept has not translated to disordered materials…

For studying the local topology of maps, one uses deformations which split the singularities into simpler ones while preserving the general fibres. We give conditions under which such conservation holds.

We apply the Bogomol'nyi technique, which is usually invoked in the study of solitons or models with topological invariants, to the case of elastic energy of vesicles. We show that spontaneous bending contribution caused by any deformation…

We construct some extension ({\it Stable Field Theory}) of Cohomological Field Theory. The Stable Field Theory is a system of homomorphisms to some vector spaces generated by spheres and disks with punctures. It is described by a formal…

Computing a morph between two drawings of a graph is a classical problem in computational geometry and graph drawing. While this problem has been widely studied in the context of planar graphs, very little is known about the existence of…

The requirement of diffeomorphism symmetry for the target space can lead to anomalous commutators for the energy-momentum tensor for sigma models and for fluid dynamics, if certain topological terms are added to the action. We analyze…

The topological mechanics is a perfect tool that can bridge the gap between the quantum and Newtonian physics and mechanics of materials. It requires discrete models of the material with analogies with the topological characteristics of…

Over a given regular domain of independent variables {x,y,z,t}, every covariant vector field of flow can be constructed in terms a differential 1-form of Action. The associated Cartan topology permits the definition of four basic…