相关论文: A Classification Scheme for Toroidal Molecules

Multipolar order in bulk crystalline solids is characterized by multipole densities -- denoted as polarizations in this work -- that cannot be cleanly defined using the concepts of classical electromagnetism. Here we use group theory to…

A new class of random spatial tessellations is introduced -- the so-called column tessellations of three-dimensional space. The construction is based on a stationary planar tessellation. Each cell of the spatial tessellation is a prism…

This paper proposes a machine learning (ML) method to predict stable molecular geometries from their chemical composition. The method is useful for generating molecular conformations which may serve as initial geometries for saving time…

A method of defining the complex structure(moduli) for dynamically triangulated(DT) surfaces with torus topology is proposed. Distribution of the moduli parameter is measured numerically and compared with the Liouville theory for the…

We provide a physical interpretation of the Kirchhoff index of any molecules as well as of the Wiener index of acyclic ones. For the purpose, we use a local vertex invariant that is obtained from first principles and describes the atomic…

Membrane particles such as proteins and lipids organize into zones that perform unique functions. Here, I introduce a topological and category-theoretic framework to represent particle and zone intra-scale interactions and inter-scale…

Given a triangulation of a closed, oriented, irreducible, atoroidal 3-manifold every oriented, incompressible surface may be isotoped into normal position relative to the triangulation. Such a normal oriented surface is then encoded by…

It is commonly believed that electromagnetic spectra of atoms and molecules can be fully described by interactions of electric and magnetic multipoles. However, it has recently become clear that interactions between light and matter also…

Holographic microscopy combined with forward modeling and inference allows colloidal particles to be characterized and tracked in three dimensions with high precision. However, current models ignore the effects of optical aberrations on…

Chiral tetrahedral molecules can be dealt under the standard of quaternionic algebra. Specifically, non-commutativity of quaternions is a feature directly related to the chirality of molecules. It is shown that a quaternionic representation…

For a given many-electron molecule, it is possible to define a corresponding one-electron Schr\"odinger equation, using potentials derived from simple atomic densities, whose solution predicts fairly accurate molecular orbitals for single-…

Instant machine learning predictions of molecular properties are desirable for materials design, but the predictive power of the methodology is mainly tested on well-known benchmark datasets. Here, we investigate the performance of machine…

We introduce orthogonal ring patterns in the 2-sphere and in the hyperbolic plane, consisting of pairs of concentric circles, which generalize circle patterns. We show that their radii are described by a discrete integrable system. This is…

We compute the tensor triangular spectrum of perfect complexes of filtered modules over a commutative ring, and deduce a classification of the thick tensor ideals. We give two proofs: one by reducing to perfect complexes of graded modules…

The fundamental issues of symmetry related to chirality are discussed and applied to simple situations relevant to liquid crystals. We show that any chiral measure of a geometric object is a pseudoscalar (invariant under proper rotations…

It is common knowledge that atoms can form molecules if they attract each other. Here, we show that it is possible to create molecules where bound states of the atoms are not the result of attractive interactions but have the topological…

The chemical and physical properties of molecular clusters can heavily depend on their size, which makes them very attractive for the design of new materials with tailored properties. Deriving the structure and dynamics of clusters is…

The thermodynamical stability of a set of circular double helical molecules is analyzed by path integral techniques. The minicircles differ only in \textit{i)} the radius and \textit{ii)} the number of base pairs ($N$) arranged along the…

For any convex preorder on the set of positive roots of affine type A, we classify and construct all associated cuspidal and semicuspidal skew shapes. These combinatorial objects correspond to cuspidal and semicuspidal skew Specht modules…

We develop a model of molecular binding based on the Bohr-Sommerfeld description of atoms together with a constraint taken from conventional quantum mechanics. The model can describe the binding energy curves of H2, H3 and other molecules…