Related papers: Point Charges and Polygonal Linkages
Given a set $P$ of $n$ points in the plane, its unit-disk graph $G(P)$ is a graph with $P$ as its vertex set such that two points of $P$ are connected by an edge if their (Euclidean) distance is at most $1$. We consider several classical…
This paper considers a class of thrust vectoring systems, which are nonlinear, overactuated, and time-invariant. We assume that the system is composed of two subsystems and there exist singular points around which the linearized system is…
The grand potential of a classical Coulomb system has universal finite-size corrections similar to the ones which occur in the free energy of a simple critical system : the massless Gaussian field. Here, the Coulomb system is assumed to be…
We study equilibrium configurations of infinitely many identical particles on the real line or finitely many particles on the circle, such that the (repelling) force they exert on each other depends only on their distance. The main question…
It is shown that an ensemble of particles with tripolar (colour) charges will necessarily cohere in a hierarchy of structures, from simple clusters and strings to complex aggregates and cyclic molecule-like structures. The basic…
We present a theory of Coulomb blockade oscillations in tunneling through a pair of quantum dots connected by a tunable tunneling junction. The positions and amplitudes of peaks in the linear conductance are directly related, respectively,…
A pentagonal geometry PENT($k$, $r$) is a partial linear space, where every line, or block, is incident with $k$ points, every point is incident with $r$ lines, and for each point $x$, there is a line incident with precisely those points…
We show that the effect of finite acceptance drastically influences the net-baryon and net-charge cumulants, which are believed to be sensitive probes of the QCD phase diagram. We derive the general formulae that relate the true cumulants…
Recent experiments performed on weakly pinched quantum point contacts, have shown a resistance that tend to decrease at low source drain voltage. We show that enhanced Coulomb interactions, prompt by the presence of the point contact, may…
2-point topological charge correlation functions of several types of geometric singularity in gaussian random fields are calculated explicitly, using a general scheme: zeros of $n$-dimensional random vectors, signed by the sign of their…
The structure of atomic levels originating from the lowest Landau level in a superstrong magnetic field is analyzed. The influence of the screening of the Coulomb potential on the values of critical nuclear charge is studied.
We establish a class of area-angular momentum-charge inequalities satisfied by stable marginally outer trapped surfaces in 5-dimensional minimal supergravity which admit a $U(1)^2$ symmetry. A novel feature is the fact that such surfaces…
The critical point between varieties A and B of algebras is defined as the least cardinality of the semilattice of compact congruences of a member of A but of no member of B, if it exists. The study of critical points gives rise to a whole…
This paper considers critical points of the length-penalized elastic bending energy among planar curves whose endpoints are fixed. We classify all critical points with an explicit parametrization. The classification strongly depends on a…
We provide a complete classification, in the language of weak-combinatorics, of minimal plus-one generated line arrangements in the complex projective plane with double and triple intersection points.
Weak optimal transport generalizes the classical theory of optimal transportation to nonlinear cost functions and covers a range of problems that lie beyond the traditional theory - including entropic transport, martingale transport, and…
We study electric transport near the Mott metal-insulator transition. Optical conductivity of the half-filled Hubbard model on a triangular lattice is calculated based on a cellular dynamical mean field theory including vertex corrections…
A systematic study of the properties of particle and charge correlation functions in the two-dimensional Coulomb gas confined to a one-dimensional domain is undertaken. Two versions of this system are considered: one in which the positive…
We consider independent long-range percolation models on locally finite vertex-transitive graphs. Using coupling ideas we prove strict monotonicity of the critical points with respect to local perturbations in the connection function,…
In this paper, we study the existence of fixed points for mappings defined on complete, (sequentially compact) cone metric spaces, satisfying a general contractive inequality depending of two additional mappings.