Related papers: Universal building block for (1 1 0)-family silico…
Quantum access to arbitrary classical data encoded in unitary black-box oracles underlies interesting data-intensive quantum algorithms, such as machine learning or electronic structure simulation. The feasibility of these applications…
The ground state structures of small silicon clusters are determined through exhaustive tight-binding molecular dynamics simulation studies. These simulations revealed that \Si{11} is an icosahedron with one missing cap, \Si{12} is a…
We construct an $SO(10)$ grand unified theory in the formulation of non-com-\break mutative geometry. The geometry of space-time is that of a product of a continuos four dimensional manifold times a discrete set of points. The properties of…
This short survey of recent work in tile self-assembly discusses the use of simulation to classify and separate the computational and expressive power of self-assembly models. The journey begins with the result that there is a single…
Grand unification of gauge couplings and fermionic representations remains an appealing proposal to explain the seemingly coincidental structure of the Standard Model. However, to realise the Standard Model at low energies, the unified…
The 7x7 reconstruction of Si(111) surface is widely understood by the dimer-adatom-stacking-fault model (DAS), but the predicted metallicity of DAS contradicts experimental signs of insulation. It is still challenge to predict DAS-like…
There are three complete plane geometries of constant curvature: spherical, Euclidean and hyperbolic geometry. We explain how a closed oriented surface can carry a geometry which locally looks like one of these. Focussing on the hyperbolic…
In this paper, we show the fundamental theorems for rotationally symmetric hypersurfaces, and thus, together with the earlier results in [3] and [4], provide a complete classification of umbilic hypersurfaces in the Heisenberg groups…
A new SO(10) unified model is proposed based on a one step breaking of SO(10) to the Standard Model gauge group $SU(3)\times SU(2)\times U(1)_Y$ using a single 144 of Higgs. The symmetry breaking occurs when the SU(5) 24-plet component of…
We offer a systematic account of decomposition of quantum systems into parts. Different decompositions (structures) are mutually linked via the proper linear canonical transformations. Different kinds of structures, as well as their…
We show that the self-assembly of a diverse collection of building blocks can be understood within a common physical framework. These building blocks, which form periodic honeycomb networks and nonperiodic variants thereof, range in size…
This paper views the honeycomb conjecture and the Kepler problem essentially as extreme value problems and solves them by partitioning 2-space and 3-space into building blocks and determining those blocks that have the universal extreme…
In considering the nature of the basic mathematical structures appropriate for describing the fundamental elements of particle physics a significant role for the octonions, as an extension from the complex numbers and uniquely the largest…
We construct triangular hyperbolic polyhedra whose links are generalized 4-gons. The universal cover of those polyhedra are hyperbolic buildings, which appartments are hyperbolic planes tesselated by regular triangles with angles $\pi/4$.…
The local structure of terminal Brauer classes on arithmetic surfaces were classified in [CI21] generalising the classification on geometric surfaces carried out in [CI05]. Part of the interest in these classifications is that it enables…
In this paper we construct a new family of simply connected minimal complex surfaces of general type with $p_g=1$, $q=0$, and $K^2=3, 4, 5, 6, 8$ using a $\mathbb{Q}$-Gorenstein smoothing theory. We also reconstruct minimal complex surfaces…
We simulate the liquid silicon surface with first-principles molecular dynamics in a slab geometry. We find that the atom-density profile presents a pronounced layering, similar to those observed in low-temperature liquid metals like Ga and…
The main respiratory muscle, the diaphragm, is an example of a thin structure. We aim to perform detailed numerical simulations of the muscle mechanics based on individual patient data. This requires a representation of the diaphragm…
The structural, electronic and dynamical properties of a group of 2D germanium-based compounds, including GeC, GeN, GeO, GeSi, GeS, GeSe, and germanene, are investigated by employing first-principles calculations. The most stable structure…
A general method for constructing essential uniform algebras with prescribed properties is presented. Using the method, the following examples are constructed: an essential, natural, regular uniform algebra on the closed unit disc; an…