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In many virus families, tens to thousands of proteins assemble spontaneously into a capsid (protein shell) while packaging the genomic nucleic acid. This review summarizes recent advances in computational modeling of these dynamical…
Assembling clusters on surfaces has emerged as a novel way to grow thin films with targeted properties. In particular, it has been proposed from experimental findings that fullerenes deposited on surfaces could give rise to thin films…
Recently, a principle for state confinement has been proposed in a category theoretic framework and to accomodate this result the notion of a pre-monoidal category was developed. Here we describe an algebraic approach for the construction…
The influence of world-sheet boundary condensates on the toroidal compactification of bosonic string theories is considered. At the special points in the moduli space at which the closed-string theory possesses an enhanced unbroken $G\times…
Some time ago, conformal data with affine fusion rules were found. Our purpose here is to realize some of these conformal data, using systems of free bosons and parafermions. The so constructed theories have an extended $W$ algebras which…
In this paper we will first introduce the notion of affine structures on a ringed space and then obtain several properties. Affine structures on a ringed space, arising mainly from complex analytical spaces of algebraic schemes over number…
Molecular simulations of the self-assembly of cone-shaped particles with specific, attractive interactions are performed. Upon cooling from random initial conditions, we find that the cones self assemble into clusters and that clusters…
A symmetry is a `change without change'. As simple as it sounds, this concept is the fundamental cornerstone that unifies all branches of theoretical physics. Virtually all physical laws -- ranging from classical mechanics and…
Let $X$ be a scheme, proper over a commutative noetherian ring $A$. We introduce the concept of an ample filter of invertible sheaves on $X$ and generalize the most important equivalent criteria for ampleness of an invertible sheaf. We also…
The covering of the affine symmetry group, a semidirect product of translations and special linear transformations, in $D \geq 3$ dimensional spacetime is considered. Infinite dimensional spinorial representations on states and fields are…
Systematic efforts to synthesise fullerene containing LCs have produced a variety of successful model compounds. We present a simple molecular theory relating the self-organisation observed in these systems to their molecular structure. The…
The physics of complex systems stands to greatly benefit from the qualitative changes in data availability and advances in data-driven computational methods. Many of these systems can be represented by interacting degrees of freedom on…
The implications of large-scale coherence in biological systems and possible links to quantum theory are only beginning to be explored. Whether quantum-like coherent phenomena are relevant, or even possible at all, at the high temperatures…
Graphene has received a great deal of attention and this has more recently extended to boron nitride sheets (BNS) with a similar structure. Both have hexagonal lattices and it is only the alternation of atoms in boron nitride, which changes…
Symmetry packaging is the phenomenon whereby, upon particle creation, all the internal quantum numbers (IQNs) become locked into a single irreducible representation (irrep) block of the gauge group, as required by locality and gauge…
We study algebraic and geometric properties of metric spaces endowed with dilatation structures, which are emergent during the passage through smaller and smaller scales. In the limit we obtain a generalization of metric affine geometry,…
The paper introduces new sufficient conditions of strict positive definiteness for kernels on d-dimensional spheres which are not radially symmetric but possess specific coefficient structures. The results use the series expansion of the…
We use ab initio density functional calculations to study the formation and structural as well as thermal stability of cellular foam-like carbon nanostructures. These systems with a mixed $sp^2/sp^3$ bonding character may be viewed as…
The goal of this paper is to relate the quantum category $\mathcal{O}$ (known also as the category of modules over the mixed quantum group) at an odd root of unity to the affine Hecke category. Namely, we prove equivalences of highest…
Symmetries play an essential role in the construction and phenomenology of quantum field theories (QFTs). We discuss how to construct symmetries of QFTs by extending minimal "seed" symmetry groups to larger groups that contain the seed(s)…