Related papers: Point Charges and Polygonal Linkages
We consider again stationary solutions to the spherically symmetric Einstein--Maxwell--Klein--Gordon system, commonly known as ``charged boson stars'', originally studied by Jetzer and Van Der Bij. We construct families of charged boson…
We prove up-to-constants bounds on the two-point function (i.e., point-to-point connection probabilities) for critical long-range percolation on the $d$-dimensional hierarchical lattice. More precisely, we prove that if we connect each pair…
We study the possibility of getting infinite energy in the center of mass frame of colliding charged particles in a general stationary charged black hole. For black holes with two-fold degenerate horizon, it is found that arbitrary high…
Coherent electronic transport in single-molecule junctions is investigated in the Coulomb blockade regime. Both the transmission phase and probability are calculated for junctions with various contact symmetries. A dramatic suppression of…
Given a smoothly bounded non-contractible domain $\Omega\subset \mathbb{R}^2$, we prove the existence of positive critical points of the Trudinger-Moser embedding for arbitrary Dirichlet energies. This is done via degree theory, sharp…
In the packing-constrained point covering problem, PC^2, one seeks configurations of points in the plane that cannot all be covered by a packing arrangement of unit disks. We consider in particular the problem of finding the minimum number…
In 1982, Ungar proved that the connecting lines of a set of $n$ noncollinear points in the plane determine at least $2\lfloor n/2 \rfloor$ directions (slopes). Sets achieving this minimum for $n$ odd (even) are called…
Fixed points for scalar theories in $4-\varepsilon$, $6-\varepsilon$ and $3-\varepsilon$ dimensions are discussed. It is shown how a large range of known fixed points for the four dimensional case can be obtained by using a general…
Coulomb charges confined by a harmonic potential display a rich structure at strong coupling, both classical and quantum. A simple density functional theory is reviewed showing the essential role of correlations in forming shell structure…
We show a surprising connexion between a property of the inf convolution of a family of convex lower semicontinuous functions and the fact that the intersection of maximal cyclically monotone graphs is the critical set of a bipotential. We…
The model under consideration is an asymmetric two-dimensional Coulomb gas of positively (q_1=+1) and negatively (q_2=-1/2) charged pointlike particles, interacting via a logarithmic potential. This continuous system is stable against…
The tensorial equations for non trivial fully interacting fixed points at lowest order in the $\varepsilon$ expansion in $4-\varepsilon$ and $3-\varepsilon$ dimensions are analysed for $N$-component fields and corresponding multi-index…
We consider an exit-time minimum problem with a running cost, $l\geq 0$ and unbounded controls. The occurrence of points where $l=0$ can be regarded as a transversality loss. Furthermore, since controls range over unbounded sets, the family…
We show how to couple two critical Q-state Potts models to yield a new self-dual critical point. We also present strong evidence of a dense critical phase near this critical point when the Potts models are defined in their completely packed…
Constructing charges in the covariant phase space formalism often leads to formally divergent expressions, even when the fields satisfy physically acceptable fall-off conditions. These expressions can be rendered finite by corner…
A general relativistic, stationary and axisymmetric black hole in a four-dimensional asymptotically-flat spacetime is fully determined by its mass, angular momentum and electric charge. The expectation that astrophysically relevant black…
Relative equilibria of Lagrangian and Hamiltonian systems with symmetry are critical points of appropriate scalar functions parametrized by the Lie algebra (or its dual) of the symmetry group. Setting aside the structures - symplectic,…
Utilizing a new variational principle that allows dealing with problems beyond the usual locally compactness structure, we study problems with a supercritical nonlinearity of the type $ -\Delta u + u= a(x) f(u)$ in $ \Omega$ with…
We study the effect of positive correlations on the critical threshold of site and bond percolation in a square lattice with d = 2. We propose two algorithms for generating dependent lattices with minimal correlation length and non-negative…
We derive a sufficient condition for the existence of a subcritical percolation phase for a wide range of continuum percolation models where each vertex is embedded into Euclidean space according to an iid-marked stationary Poisson point…