Related papers: Point Charges and Polygonal Linkages
A line g is a transversal to a family F of convex polytopes in 3-dimensional space if it intersects every member of F. If, in addition, g is an isolated point of the space of line transversals to F, we say that F is a pinning of g. We show…
We present the structures of putative global potential energy minima for clusters bound by the Stockmayer (Lennard-Jones plus point dipole) potential. A rich variety of structures is revealed as the cluster size and dipole strength are…
We study the lowest energy configurations of an equimolar binary mixture of classical pointlike particles with charges $Q_1$ and $Q_2$, such that $q=Q_2/Q_1\in [0,1]$. The particles interact pairwisely via 3D Coulomb potential and are…
A cubical polytope is a polytope with all its facets being combinatorially equivalent to cubes. We deal with the connectivity of the graphs of cubical polytopes. We first establish that, for any $d\ge 3$, the graph of a cubical $d$-polytope…
We study theoretically a quantum dot in the quantum Hall regime that is strongly coupled to a single lead via a point contact. We find that even when the transmission through the point contact is perfect, important features of the Coulomb…
We constrain $C\!P$-violating charged and neutral anomalous triple gauge couplings using LHC measurements and projections of diboson and VBF $Vjj$ production, both with subsequent leptonic decays. For triple gauge couplings involving $W$…
Quantum point contacts (QPC) are fundamental building blocks of nanoelectronic circuits. For their emission dynamics as well as for interaction effects such as the 0.7-anomaly the details of the electrostatic potential are important, but…
Connections are found between the two-component percolation problem and the conductor/insulator percolation problem. These produce relations between critical exponents, and suggest formulae connecting the conductivity exponents in different…
The critical charge $Z_c$ is estimated for elementary particles using a Newton-Wigner position operator inspired model. Particles with $Z \sim Z_c$ (maxicharged particles), if they exist at all, can have unusual properties which turn them…
We show that the maximum cardinality of an anti-chain composed of intersections of a given set of n points in the plane with half-planes is close to quadratic in n. We approach this problem by establishing the equivalence with the problem…
Here we prove critical exponents for Random Connections Models (RCMs) with random marks. The vertices are given by a marked Poisson point process on $\mathbb{R}^d$ and an edge exists between any pair of vertices independently with a…
A general scenario that leads to Coulomb quantum criticality with the dynamical critical exponent z=1 is proposed. I point out that the long-range Coulomb interaction and quenched disorder have competing effects on z, and that the balance…
A convergence theorem for martingales with c\`adl\`ag trajectories (right continuous with left limits everywhere) is obtained in the sense of the weak dual topology on Hilbert space, under conditions that are much weaker than those required…
A lower bound on the grand partition function of a classical charge-symmetric system is adapted to the neutral grand canonical ensemble, in which the system is constrained to have zero total charge. This constraint permits us to consider…
The sign structure of correlations of conserved charges are investigated in a QCD like model: the (2+1) flavor Polyakov Quark Meson model. We compute all susceptibilities of the conserved charges on the $(\mu_{B}-T)$ plane up to fourth…
A detailed combinatorial analysis of planar lattice convex polygonal lines is presented. This makes it possible to answer an open question of Vershik regarding the existence of a limit shape when the number of vertices is constrained. The…
This article explores additive codes with one-rank hull, offering key insights and constructions. The article introduces a novel approach to finding one-rank hull codes over finite fields by establishing a connection between self-orthogonal…
We study the static potential between electric charges in the finite temperature three dimensional compact gauge theory on the lattice. We show that in the deconfinement phase at small separations between the charges the potential contains…
The purpose of this article is to study a stochastic control problem on a junction, with control at the junction point. The problem of control is formulated in the weak sense, using a relaxed control, namely a control which takes values in…
By a length scale analysis, we study the equilibrium interactions between two like-charge planes confining neutralising counter-ions. At large Coulombic couplings, approaching the two charged bodies leads to an unbinding of counter-ions, a…