Related papers: Kinetic Transition Networks for the Thomson Proble…
We have studied the configurations of minimal energy of $N$ charges on a curve on the plane, interacting with a repulsive potential $V_{ij} = 1/r_{ij}^s$, with $s \geq 1$ and $i,j=1,\dots, N$. Among the examples considered are ellipses of…
The classical Thomson problem of $n$ charged particles confined to the surface of a sphere of radius $a$ is analyzed within the Darwin approximation of electrodynamics. For $n<n_c(a)$ the ground state corresponds to a hexagonal Wigner…
We report on parallel observations in two seemingly unrelated areas of dynamical network research. The one is the so-called small world phenomenon and/or the observation of scale freeness in certain types of large (empirical) networks and…
One of the challenging problems in the condensed matter physics is to understand the quantum many-body systems, especially, their physical mechanisms behind. Since there are only a few complete analytical solutions of these systems, several…
We present new lower bounds that show that a polynomial number of passes are necessary for solving some fundamental graph problems in the streaming model of computation. For instance, we show that any streaming algorithm that finds a…
Here we analyze the topology of the network formed by the minima and transition states on the potential energy landscape of small clusters. We find that this network has both a small-world and scale-free character. In contrast to other…
We use moment techniques to construct a converging hierarchy of optimization problems to lower bound the ground state energy of interacting particle systems. We approximate (from below) the infinite dimensional optimization problems in this…
The folding pathway and rate coefficients of the folding of a knotted protein are calculated for a potential energy function with minimal energetic frustration. A kinetic transition network is constructed using the discrete path sampling…
We consider a wireless network with a set of transmitter-receiver pairs, or links, that share a common channel, and address the problem of emptying finite traffic volume from the transmitters in minimum time. This, so called, minimum-time…
Correspondences between the Thomson Problem and atomic electron shell-filling patterns are observed as systematic non-uniformities in the distribution of potential energy necessary to change configurations of $N\le 100$ electrons into…
To provide a phenomenological theory for the various interesting transitions in restructuring networks we employ a statistical mechanical approach with detailed balance satisfied for the transitions between topological states. This enables…
The quantum statistics mechanism is very powerful for investigating the equilibrium states and the phase transitions in complex spin disorder systems. The spin disorder systems act as an interdisciplinary platform for solving the optimum…
We give a description of numerical Newton algorithm on a constraint manifold using only the ambient coordinates (usually Euclidean coordinates) and the geometry of the constraint manifold. We apply the numerical Newton algorithm on a sphere…
Systems of identical particles with equal charge are studied under a special type of confinement. These classical particles are free to move inside some convex region S and on the boundary of it $\Omega$ (the $S^{d-1}-$ sphere, in our…
We consider the minimizing problem for energy functionals with two types of competing particles and completely monotone potential on a lattice. We prove that the minima of sum of two completely monotone functions among lattices is located…
The outbreak of epidemics, the emergence of the financial crisis, the collapse of ecosystem, and the explosive spreading of rumors, we face many challenges in today's world. These real-world problems can be abstracted into a sequential…
Consider a knot $K$ in $S^3$ with uniformly distributed electric charge. Whilst solutions to the Laplace equation in terms of Dirichlet integrals are readily available, it is still of theoretical and physical interest to understand the…
The transition to turbulence via spatiotemporal intermittency is investigated in the context of coupled maps defined on small-world networks. The local dynamics is given by the Chat\'e-Manneville minimal map previously used in studies of…
In this survey paper, we will present a number of core algorithmic questions concerning several transitive reduction problems on network that have applications in network synthesis and analysis involving cellular processes. Our starting…
In the quantum repeater networks of the quantum Internet, the varying stability of entangled quantum links makes dynamic topology adaption an emerging issue. Here we define an efficient topology adaption method for quantum repeater…