Search results for "Topological complexity"
showing 6 items of 6 documents
Dynamics and topological mass of skyrmionic spin structures (presentation video)
2014
Skyrmions are topologically protected particle-like configurations, with a topological complexity described by their Skyrmion number. In magnetic systems, they have been numerically predicted to exhibit rich dynamics, such as the gyrotropic and breathing modes, dominated by their topology. Recent experimental advances brought their static manipulation well under control. However, their dynamical behaviour is largely unexplored experimentally. In this work, we provide with the first direct observation of eigenmode skyrmion dynamics. In particular, we present dynamical imaging data with high temporal and spatial resolution to demonstrate the GHz gyrotropic mode of a single skyrmion bubble, as…
Minimal Morse flows on compact manifolds
2006
Abstract In this paper we prove, using the Poincare–Hopf inequalities, that a minimal number of non-degenerate singularities can be computed in terms only of abstract homological boundary information. Furthermore, this minimal number can be realized on some manifold with non-empty boundary satisfying the abstract homological boundary information. In fact, we present all possible indices and types (connecting or disconnecting) of singularities realizing this minimal number. The Euler characteristics of all manifolds realizing this minimal number are obtained and the associated Lyapunov graphs of Morse type are described and shown to have the lowest topological complexity.
Comparison between Entropy and Resilience as Indirect Measures of Reliability in the Framework of Water Distribution Network Design
2014
Abstract The aim of this paper is to investigate which between the entropy and resilience indices represents a better indirect measure of reliability in the framework of water distribution network design. The methodology adopted consisted of (a) multi-objective optimizations performed in order to minimize costs and maximize reliability, expressed by means of one of the indirect indices at time; (b) retrospective performance assessment of the solutions of Pareto fronts obtained. Two case studies of different topological complexity were considered. Results showed that indices based on energetic concepts (resilience and modified resilience) represent a better compact estimate of reliability th…
A Stevedore's protein knot.
2009
Protein knots, mostly regarded as intriguing oddities, are gradually being recognized as significant structural motifs. Seven distinctly knotted folds have already been identified. It is by and large unclear how these exceptional structures actually fold, and only recently, experiments and simulations have begun to shed some light on this issue. In checking the new protein structures submitted to the Protein Data Bank, we encountered the most complex and the smallest knots to date: A recently uncovered α-haloacid dehalogenase structure contains a knot with six crossings, a so-called Stevedore knot, in a projection onto a plane. The smallest protein knot is present in an as yet unclassified …
Lévy flights in confining potentials.
2009
We analyze confining mechanisms for L\'{e}vy flights. When they evolve in suitable external potentials their variance may exist and show signatures of a superdiffusive transport. Two classes of stochastic jump - type processes are considered: those driven by Langevin equation with L\'{e}vy noise and those, named by us topological L\'{e}vy processes (occurring in systems with topological complexity like folded polymers or complex networks and generically in inhomogeneous media), whose Langevin representation is unknown and possibly nonexistent. Our major finding is that both above classes of processes stay in affinity and may share common stationary (eventually asymptotic) probability densit…
Water distribution network robust design based on energy surplus index maximization
2015
The aim of this paper is to show that energy surplus indices, such as resilience index, besides providing a very good indirect measure of water distribution network reliability to be adopted during the design phase, represent also a valuable and effective indicator of the robustness of the network in alternative network scenarios, and can thus be profitably used in condition of future demands uncertainty. The methodology adopted consisted of (I) multi-objective design optimization performed in order to minimize construction costs while maximizing the resilience index; (II) retrospective performance assessment of the alternative solutions of the Pareto front obtained, under demand conditions…