Related papers: Symmetry in Sphere-based Assembly Configuration Sp…
Entropic self-assembly is governed by the shape of the constituent particles, yet a priori prediction of crystal structures from particle shape alone is non-trivial for anything but the simplest of space-filling shapes. At the same time,…
The self-assembly of hard polyhedral particles confined to a flat interface is studied using Monte Carlo simulations. The particles are pinned to the interface by restricting their movement in the direction perpendicular to it while…
A series of simulations aimed at elucidating the self-assembly dynamics of spherical virus capsids is described. This little-understood phenomenon is a fascinating example of the complex processes that occur in the simplest of organisms.…
Symmetries and isomorphisms play similar conceptual roles when we consider how models represent physical situations, but they are formally distinct, as two models related by symmetries are not typically isomorphic. I offer a rigorous…
Symmetry topological field theory (SymTFT) is a convenient tool for studying finite generalized symmetries of a given quantum field theory (QFT). In particular, SymTFTs encode all the symmetry structures and properties, including anomalies.…
Knowing which parts of a complex system have identical roles simplifies computations and reveals patterns in its network structure. Group theory has been applied to study symmetries in unweighted networks. However, in real-world weighted…
Outer automorphisms of symmetries ("symmetries of symmetries") in relativistic quantum field theories are studied, including charge conjugation (C), space-reflection (P) , and time-reversal (T) transformations. The group theory of outer…
Symmetry is one of the most general and useful concepts in physics. A theory or a system that has a symmetry is fundamentally constrained by it. The same constraints do not apply when the symmetry is broken. The quantitative determination…
Hard spheres are ubiquitous in condensed matter: they have been used as models for liquids, crystals, colloidal systems, granular systems, and powders. Packings of hard spheres are of even wider interest, as they are related to important…
Cluster synchronization is a phenomenon in which a network self-organizes into a pattern of synchronized sets. It has been shown that diverse patterns of stable cluster synchronization can be captured by symmetries of the network. Here we…
In this paper, we study the relation between entanglement and global internal symmetries on de Sitter space. We consider two symmetric causally disconnected regions in the hyperbolic chart on de Sitter space. Since entanglement measures…
We survey the role of symmetry in diffeomorphic registration of landmarks, curves, surfaces, images and higher-order data. The infinite dimensional problem of finding correspondences between objects can for a range of concrete data types be…
In this work, we analyse static spherically symmetric solutions in the framework of mimetic gravity, an extension of general relativity where the conformal degree of freedom of gravity is isolated in a covariant fashion. Here we extend…
The program of understanding Shape Theory layer by layer topologically and geometrically -- proposed in Part I -- is now addressed for 4 points in 1-$d$. Topological shape space graphs are far more complex here, whereas metric shape spaces…
Experiments have reached a monumental capacity for designing and synthesizing microscopic particles for self-assembly, making it possible to precisely control particle concentrations, shapes, and interactions. However, more physical insight…
A comprehensive framework of characterizing complex self-assembled structures with a set of orientational order parameters is presented. It is especially relevant in the context of using anisotropic building blocks with various symmetries.…
We study how the spin-statistics theorem relates to the geometric structures on phase space that are introduced in quantisation procedures (namely a U(1) bundle and connection). The relation can be proved in both the relativistic and the…
A theory of structure is formulated for systems of many structureless classical particles with stable local interactions in Euclidean space. Such systems are shown to have their structure in thermodynamic equilibrium determined exactly by a…
This manuscript presents a novel framework that integrates higher-order symmetries and category theory into machine learning. We introduce new mathematical constructs, including hyper-symmetry categories and functorial representations, to…
We discuss the relation between the emergence of new phases with broken symmetry within the framework of simple models of biopolymers. We start with a classic model for a chain molecule of spherical beads tethered together, with the steric…