Related papers: Geometry of interactions in complex bodies
An ensemble with random n-body interactions is investigated in the presence of symmetries. A striking emergence of regularities in spectra, ground state spins and isospins is discovered in both odd and even-particle systems. Various types…
The bulk-boundary correspondence is an integral feature of topological analysis and the existence of boundary or interface modes offers direct insight into the topological structure of the Bloch wave function. While only the topology of the…
When two surfaces are brought into contact and slide against each other, junctions are formed at the interface. The dynamics of formation, rupture and evolution of these junctions governs the tribological response of the macro-contact.…
We study various manifestations of structural crossover in the properties of a binary mixture of hard-spheres. For homogeneous mixtures that are sufficiently asymmetric, there is a crossover line in the phase diagram such that for…
We analyze the surface tension exerted at the interface between an active fluid and a solid boundary in terms of tangential forces. Focusing on active systems known to possess an equation of state for the pressure, we show that interfacial…
Dynamical symmetries are of considerable importance in elucidating the complex behaviour of strongly interacting systems with many degrees of freedom. Paradigmatic examples are cooperative phenomena as they arise in phase transitions, where…
Many turbulent flows encountered in nature -- seas, oceans and rivers -- are bounded by a deformable free surface. A question that remained to be fully explored is to what extent the underlying turbulent flow field can be revealed solely by…
I study the effect of length polydispersity in the surface phase diagram of hard rods interacting with a hard wall. The properly extended interface Gibbs-Duhem equation for a polydisperse system allows us to predict the behaviour of the…
Long-range interacting systems exhibit unusual physical properties not shared by systems with short-range interactions. Understanding the dynamical and statistical effects of long-range interactions yields insights into a host of physical…
The structural properties of packed soft-core particles provide a platform to understand the cross-pollinated physical concepts in solid-state- and soft-matter physics. Confined on spherical surface, the traditional differential geometry…
This dissertation explores various nonlinear responses that arise from the rich interplay between quantum geometry, disorder, magnetism and topology in quantum materials. In addition to presenting generalizations of quantum kinetic theory,…
We study differential geometric properties of cuspidal edges with boundary. There are several differential geometric invariants which are related with the behavior of the boundary in addition to usual differential geometric invariants of…
This note is a survey on the topology of hyperplane arrangements. We mainly focus on the relationship between topology and the real structure, such as adjacent relations of chambers and stratifications related to real structures.
The study of networks plays a crucial role in investigating the structure, dynamics, and function of a wide variety of complex systems in myriad disciplines. Despite the success of traditional network analysis, standard networks provide a…
In forced wetting, a rapidly moving surface drags with it a thin layer of trailing fluid as it is plunged into a second fluid bath. Using high-speed interferometry, we find characteristic structure in the thickness of this layer with…
We study the geometry of surfaces in $\mathbb{R}^{4}$ with corank $1$ singularities. For such surfaces the singularities are isolated and at each point we define the curvature parabola in the normal space. This curve codifies all the second…
Topological phases of matter are one of the hallmarks of quantum condensed matter physics. One of their striking features is a bulk-boundary correspondence wherein the topological nature of the bulk manifests itself on boundaries via exotic…
In this paper, we consider holomorphic mappings between real hypersurfaces in different dimensional complex spaces. We give a number of conditions that imply that such mappings are transversal to the target hypersurface at most points.
Interfaces such as grain boundaries in polycrystalline as well as heterointerfaces in multiphase solids are ubiquitous in materials science and engineering. Far from being featureless dividing surfaces between neighboring crystals,…
Given a distribution of defects on a structured surface, such as those represented by 2-dimensional crystalline materials, liquid crystalline surfaces, and thin sandwiched shells, what is the resulting stress field and the deformed shape?…