Related papers: Following Knots Down Their Energy Gradients
Electron energy loss spectroscopy is consolidating as a powerful tool to explore electronic (as well as vibrational) excitations of matter, including molecules. Performed in a scanning transmission electron microscope, this technique is…
Knot theory is the Mathematical study of knots. In this paper we have studied the Composition of two knots. Knot theory belongs to Mathematical field of Topology, where the topological concepts such as topological spaces, homeomorphisms,…
Knots have a twisted history in quantum physics. They were abandoned as failed models of atoms. Only much later was the connection between knot invariants and Wilson loops in topological quantum field theory discovered. Here we show that…
We study numerically the energetics and atomic mechanisms of misfit dislocation nucleation and stress relaxation in a two-dimensional atomistic model of strained epitaxial layers on a substrate with lattice misfit. Relaxation processes from…
Jet substructure provides one of the most exciting new approaches for searching for physics in and beyond the Standard Model at the Large Hadron Collider. Modern jet substructure searches are often performed with Neural Network (NN) taggers…
Indentation is a common experimental technique to study the mechanics of polymeric materials. The main advantage of using indentation is because this provides a direct correlation between the microstructure and the small-scale mechanical…
A construction of polytopes is given based on integers. These geometries are constructed through a mapping to pure numbers and have multiple applications, including statistical mechanics and computer science. The number form is useful in…
Motivated by recent advances in single molecule manipulation techniques that enabled several groups to tie knots in individual polymer strands and to monitor their dynamics, we have used computer simulations to study "friction knots"…
The freely jointed chain is often applied to model the thermodynamics of single polymer chains, but the traditional formulation of the model lacks internal energy changes due to bond stretching. For this reason, the extensible freely…
Among the several topological properties of complex networks, the shortest path represents a particularly important characteristic because of its potential impact not only on other topological properties, but mainly for its influence on…
Link equivalence up to isotopy in a 3-space is the problem that lies at the root of knot theory, and is important in 3-dimensional topology and geometry. We consider its restriction to alternating links, given by two alternating diagrams…
This paper addresses the regulation and trajectory-tracking problems for two classes of weakly coupled electromechanical systems. To this end, we formulate an energy-based model for these systems within the port-Hamiltonian framework. Then,…
The aim of this paper is to shed light on the problem of controlling a complex network with minimal control energy. We show first that the control energy depends on the time constant of the modes of the network, and that the closer the…
This paper gives new and elementary combinatorial topological proofs of the classification of unoriented and oriented rational knots and links. These proofs are based on the known classification of alternating knots through flyping, and the…
We propose a protocol that, given a communication network, computes a subnetwork such that, for every pair $(u,v)$ of nodes connected in the original network, there is a minimum-energy path between $u$ and $v$ in the subnetwork (where a…
Knots are commonly represented and manipulated via diagrams, which are decorated planar graphs. When such a knot diagram has low treewidth, parameterized graph algorithms can be leveraged to ensure the fast computation of many invariants…
Vortex stretching is a common feature of many complex flows, including turbulence. Experiments and simulations of isolated vortex knots demonstrate that this behavior can also be seen in relatively simple systems, and appears to be…
2-dimensional knots and links are studied in the article. The notion of parity is introduced via techniques similar to the ones used by the second named author in 1-dimensional case. By using parity new invariants are constructed and known…
We develop a variational formalism in order to study the structure of low energy spectra of frustrated quantum spin systems. It is first applied to trial wavefunctions of ladders with one spin-1/2 on each site. We determine energy minima of…
Using dimensionally reduced models for the numerical simulation of thin objects is highly attractive as this reduces the computational work substantially. The case of narrow thin elastic bands is considered and a convergent finite element…