Related papers: The cat's cradle, stirring, and topological comple…
This paper considers the interaction between two droplets placed on a substrate in immediate vicinity. We show here that when the two droplets are of different fluids and especially when one of the droplet is highly volatile, a wealth of…
Stochastic processes are commonly used models to describe dynamics of a wide variety of nonequilibrium phenomena ranging from electrical transport to biological motion. The transition matrix describing a stochastic process can be regarded…
The ``crumpling" transition, between rigid and crumpled surfaces, has been object of much discussion over the past years. The common lore is that such transition should be of second order. However, some lattice versions of the rigidity term…
Topology is a powerful tool for categorizing magnetization textures by defining a topological index in both two-dimensional (2D) systems, such as thin films or curved surfaces, and in 3D bulk systems. In the emerging field of 3D…
Chirality, handedness, is one of the most fundamental intriguing asymmetries in nature. By definition, chiral objects cannot be superimposed onto each other after mirror reflection operation. Numerous examples of chiral structures can be…
Biological filaments such as DNA or bacterial flagella are typically curved in their natural states. To elucidate the interplay of viscous drag, twisting, and bending in the overdamped dynamics of such filaments, we compute the steady-state…
We consider collective dynamics of self-propelling particles in two dimensions. They can align themselves according to the direction of propulsion of their neighbours, together with a random perturbation (i.e. rotational fluctuation). They…
Motivated by the centering of biological objects in large cells, we study the generic properties of centering forces inside a ball (or a volume of spherical topology) in $n$ dimensions. We consider two scenarios : autonomous centering (in…
A particle jumps between the nodes of a graph interacting with local spins. We show that the entanglement entropy of the particle with the spin network is related to the length of the minimum cycle basis. The structure of the thermal state…
In this paper we consider the effects of the interaction between droplets or other deformable objects in an emulsion under random stirring of the host fluid. Our main interest is to obtain autocorrelation functions of the shape fluctuations…
Classically, a spin structure on the loop space of a manifold is a lift of the structure group of the looped frame bundle from the loop group to its universal central extension. Heuristically, the loop space of a manifold is spin if and…
We prove a necessary and sufficient condition for the occurrence of entanglement in two two-level systems, simple enough to be of experimental interest. Our results are illustrated in the context of a spin star system analyzing the exact…
Envelopes of parameterized families of plane curves is an important topic, both for the mathematics involved and for its applications. Nowadays, it is generally studied in a technology-rich environment, and automated methods are developed…
We investigate the interplay between substrate roughness and surrounding gas pressure in controlling the dynamics of splashing when a liquid drop hits a dry solid surface. We associate two distinct forms of splashing with each of these…
We give a topological classification of the evolution of entanglement, particularly the different ways the entanglement can disappear. Four categories exhaust all possibilities given the initial quantum state is entangled and the final one…
We investigate the interaction of magnetic vortices and skyrmions with a spin-polarized current. In a square lattice, fixed classical spins and quantum itinerant electrons, evolve according to the coupled Landau-Lifshitz and Schr\"odinger…
Topological dynamics constitutes the study of asymptotic properties of orbits under flows or maps on the Hausdorff phase space. Hyperbolic dynamics is the study of differentiable flows or maps that are usually characterized by the presence…
We study the entanglement entropy of theories that are derived from relevant perturbation of given CFTs for regions with a singular boundary by using the AdS/CFT correspondence. In the smooth case, it is well known that a relevant…
We discuss some applications of an intrinsic multipication in the space of simple loops in a surface.
We investigate the topological structure of entangled qudits under unitary local operations. Different sectors are identified in the evolution, and their geometrical and topological aspects are analyzed. The geometric phase is explicitly…