A Topological Evolution Model Based on the Attraction of the Motif Vertex

As a fundamental problem in the field of the network science,the study of topological evolution model is of great significance for revealing the inherent dynamics and mechanisms of complex network evolution.In order to study the influence of different scales of preferential attachment on topological evolution,a topological evolution model based on the attraction of the motif vertex is proposed.From the perspective of network motif,this model proposes the concept of attraction of the motif vertex based on the degree of the motif,quantifies the influence of local structure on the node preferential attachment,and performs the preferential selection of the new link based on the Local World model.The simulation experiments show that the model has the small world characteristic apparently,and the clustering coefficient varies with the scale of the local world.The degree distribution of the model changes from power-law distribution to exponential distribution with the change of parameters.In some cases,the piecewise power-law distribution is presented.In addition,the proposed model can present a network with different matching patterns as the parameters change.

Fractal growth kinematics abstracted from snowflakes:topological evolution

Based on the kinematic viewpoint, the concept of proportional movement is abstracted to explain the strange behaviors of fractal snowflakes. A transformation group for proportional movement is defined. Under the proportional movement transformation groups, necessary and sufficient conditions for self-similarity of multilevel structures are presented. The characteristic topology of snowflake-like fractal patterns, identical to the topology of ternary-segment fractal line, is proved. Moreover, the topological evolution of N-segment line is explored. The concepts of limit growth and infinite growth are clarified,and the corresponding growth conditions are derived. The topological invariant properties of N-segment line are exposed. In addition, the proposition that the topological evolution of the N-segment line is mainly controlled by the topological invariant N is verified.

Topological evolution of laminar juncture flows under different critical parameters

Horseshoe vortex topological structure has been studied extensively in the past,traditional"saddle of separation"and new"attachment saddle point"topologies found in literature both have theoretical basis and experimental and computational evidences for support.The laminar incompressible juncture flows at low Reynolds numbers especially are observed to have new topology.Studies concerning the existence of the new topology though found in literature,the topological evolution and its dependency on various critical flow parameters require further investigation.A Particle Image Velocimetry based analysis is carried out to observe the effect of aspect ratio,?*/D and shape of the obstacle on laminar horseshoe vortex topology for small obstacles.Rise in aspect ratio evolves the topology from the traditional to new for all the cases observed.The circular cross section obstacles are found more apt to having the new topology compared to square cross sections.It is noted that the sweeping effect of the fluid above the vortex system in which horseshoe vortex is immersed plays a critical role in this evolution.Topological evolution is observed not only in the most upstream singular point region of horseshoe vortex system but also in the corner region.The corner vortex topology evolves from the traditional type to new one before the topological evolution of the most upstream singular point,resulting in a new topological pattern of the laminar juncture flows"separation-attachment combination".The study may help extend the understanding of the three-dimensional boundary layer separation phenomenon.

Polygonal Shape Blending with Topological Evolutions

This paper presents a new general approach to blend 2D shapes with differenttopologies. All possible topolog-ical evolutions are classified into three types by attaching threedifferent topological cells. This formalism is resulted from Morse theory on the behavior of the 3Dsurface around a non-degenerate critical point. Also we incorporate degenerate topologicalevolutions into our framework which produce more attractive morphing effects. The user controls themorph by specifying the types of topological evolutions as well as the feature correspondencesbetween the source and target shapes. Some techniques are also provided to control the vertex pathduring the morphing process. The amount of user input required to produce a morph is directlyproportional to the amount of control the user wishes to impose on the process. The user may allowthe system to automatically generate the morph as well. Our approaches are totally geometric basedand are easy and fast enough in fully interactive time. Many experimental results show theapplicability and flexibility of our approaches.

Evolution of IPv6 Internet topology with unusual sudden changes

The evolution of Internet topology is not always smooth but sometimes with unusual sudden changes. Consequently, identifying patterns of unusual topology evolution is critical for Internet topology modeling and simulation. We analyze IPv6 Internet topology evolution in IP-level graph to demonstrate how it changes in uncommon ways to restructure the Internet. After evaluating the changes of average degree, average path length, and some other metrics over time, we find that in the case of a large-scale growing the Internet becomes more robust; whereas in a top–bottom connection enhancement the Internet maintains its efficiency with links largely decreased.

Topological quantum catalyst: Dirac nodal line states and a potential electrocatalyst of hydrogen evolution in the TiSi family

Topological nodal line（DNL） semimetals, a closed loop of the inverted bands in its bulk phases, result in the almost flat drumhead-like non-trivial surface states（DNSSs） with an unusually high electronic density near the Fermi level. High catalytic active sites generally associated with high electronic densities around the Fermi level, high carrier mobility and a close-to-zero free energy of the adsorbed state of hydrogen（？G_（H＊）≈0） are prerequisite to design alternative of precious platinum for catalyzing electrochemical hydrogen production from water. By combining these two aspects, it is natural to consider if the DNLs are a good candidate for the hydrogen evolution reaction（HER） or not because its DNSSs provide a robust platform to activate chemical reactions. Here, through first-principles calculations we reported a new DNL TiSi-type family, exhibiting a closed Dirac nodal line due to the linear band crossings in k_y=0 plane.The hydrogen adsorbed state on the surface yields ？G_（H＊） to be almost zero and the topological charge carries participate in HER. The results highlight a new routine to design topological quantum catalyst utilizing the topological DNL-induced surface bands as active sites, rather than edge sites-, vacancy-,dopant-, strain-, or heterostructure-created active sites.

Comparison between the eruptive X2.2 flare on 2011 February15 and confined X3.1 flare on 2014 October 24

We compare two contrasting X-class flares in terms of magnetic free energy, relative magnetic helicity and decay index of the active regions （ARs） in which they occurred. The events in question are the eruptive X2.2 flare from AR 11158 accompanied by a halo coronal mass ejection （CME） and the confined X3.1 flare from AR 12192 with no associated CME. These two flares exhibit similar behavior of free magnetic energy and helicity buildup for a few days preceding them. A major difference between the two flares is found to lie in the time-dependent change of magnetic helicity of the ARs that hosted them. AR 11158 shows a significant decrease in magnetic helicity starting -4 hours prior to the flare, but no apparent decrease in helicity is observed in AR 12192. By examining the magnetic helicity injection rates in terms of sign, we confirmed that the drastic decrease in magnetic helicity before the eruptive X2.2 flare was not caused by the injection of reversed helicity through the photosphere but rather the CME-related change in the coronal magnetic field. Another major difference we find is that AR 11158 had a significantly larger decay index and therefore weaker overlying field than AR 12192. These results suggest that the coronal magnetic helicity and the decay index of the overlying field can provide a clue about the occurrence of CMEs.

Connectivity in finite ad-hoc networks

Research on ad-hoc network connectivity has mainly focused on asymptotic results in the number of nodes in the network. For a one-dimensional ad-hoc network G1, assuming all the nodes are independently uniform distributed in a closed interval [0, Z]（z ∈ R^＋）, we derive a generic formula for the probability that the network is connected. The finite connected ad-hoc networks is analyzed. And we separately suggest necessary conditions to make the ad-hoc network to be connected in one and two dimensional cases, facing possible failed nodes （f-nodes）. Based on the necessary condition and unit-disk assumption for the node transmission, we prove that the nodes of the connected two-dimensional ad-hoc networks （G2） can be divided into at most five different groups. For an f-node no in either of the five groups, we derive a close formula for the probability that there is at least one route between a pair of nodes in G2 -- {no}.