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Journal articles on the topic 'Vertex flow'

Author: Grafiati

Published: 10 March 2023

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1

Requerey, Iker S., Basilio Ruiz Cobo, Milan Gošić, and Luis R. Bellot Rubio. "Persistent magnetic vortex flow at a supergranular vertex." Astronomy & Astrophysics 610 (February 2018): A84. http://dx.doi.org/10.1051/0004-6361/201731842.

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Context. Photospheric vortex flows are thought to play a key role in the evolution of magnetic fields. Recent studies show that these swirling motions are ubiquitous in the solar surface convection and occur in a wide range of temporal and spatial scales. Their interplay with magnetic fields is poorly characterized, however. Aims. We study the relation between a persistent photospheric vortex flow and the evolution of a network magnetic element at a supergranular vertex. Methods. We used long-duration sequences of continuum intensity images acquired with Hinode and the local correlation-tracking method to derive the horizontal photospheric flows. Supergranular cells are detected as large-scale divergence structures in the flow maps. At their vertices, and cospatial with network magnetic elements, the velocity flows converge on a central point. Results. One of these converging flows is observed as a vortex during the whole 24 h time series. It consists of three consecutive vortices that appear nearly at the same location. At their core, a network magnetic element is also detected. Its evolution is strongly correlated to that of the vortices. The magnetic feature is concentrated and evacuated when it is caught by the vortices and is weakened and fragmented after the whirls disappear. Conclusions. This evolutionary behavior supports the picture presented previously, where a small flux tube becomes stable when it is surrounded by a vortex flow.

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2

Hassin, Refael, and Asaf Levin. "Flow trees for vertex-capacitated networks." Discrete Applied Mathematics 155, no. 4 (February 2007): 572–78. http://dx.doi.org/10.1016/j.dam.2006.08.012.

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3

Shahrokhi, Farhad, and László A. Székely. "On Canonical Concurrent Flows, Crossing Number and Graph Expansion." Combinatorics, Probability and Computing 3, no. 4 (December 1994): 523–43. http://dx.doi.org/10.1017/s0963548300001383.

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We define and efficiently compute the canonical flow on a graph, which is a certain feasible solution for the concurrent flow problem and exhibits invariance under the action of the automorphism group of the graph. Using estimates for the congestion of our canonical flow, we derive lower bounds on the crossing number, bisection width, and the edge and vertex expansion of a graph in terms of sizes of the edge and vertex orbits and the average distance in the graph. We further exhibit classes of graphs for which our lower bounds are tight within a multiplicative constant. Also, in cartesian product graphs a concurrent flow is constructed in terms of the concurrent flows in the factors, and in this way lower bounds for the edge and vertex expansion of the power graphs are derived in terms of that of the original graph.

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4

MASOUMI, M., A. M. MOBASSERI, and A. R. REZAEI. "MINIMUM FLOW VARIATION IN MAXIMUM FLOWS." Discrete Mathematics, Algorithms and Applications 02, no. 03 (September 2010): 389–93. http://dx.doi.org/10.1142/s1793830910000735.

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Network flows are of growing interest in both applications and theory. Given a network flow with costs and arc capacities, the classical max flow-min cost problem is to send a given amount of flow from the source vertex to the sink vertex at least cost. Among the predominant issues in this field are problems that result when the flow is going through one arc to another arc in the same direction, such as the role of compressors in gas pipeline networks or the role of transformers in electricity wide networks. Hence, in order to minimize the cost of these elements in the network, we perform applications of line-digraphs in the form of an optimization algorithm. This paper proposes a new variant of the max flow-min cost problem. Our objective is to find the smoothest max flow over a given network.

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5

Bhandari, Phanindra Prasad, Shree Ram Khadka, Stefan Ruzika, and Luca E. Schäfer. "Lexicographically Maximum Dynamic Flow with Vertex Capacities." Journal of Mathematics and Statistics 16, no. 1 (January 1, 2020): 142–47. http://dx.doi.org/10.3844/jmssp.2020.142.147.

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6

Laber, Rob, and Geoffrey Mason. "C-Graded vertex algebras and conformal flow." Journal of Mathematical Physics 55, no. 1 (January 2014): 011705. http://dx.doi.org/10.1063/1.4862194.

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7

Khuller, Samir, and Joseph (Seffi) Naor. "Flow in planar graphs with vertex capacities." Algorithmica 11, no. 3 (March 1994): 200–225. http://dx.doi.org/10.1007/bf01240733.

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8

Antipov, Y. A., and V. V. Silvestrov. "Double cavity flow past a wedge." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 464, no. 2099 (July 10, 2008): 3021–38. http://dx.doi.org/10.1098/rspa.2008.0136.

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A mathematical model of supercavitating flow past a wedge with sides of arbitrary length is proposed. The flow branches at a point on the lower side of the wedge. At the vertex of the wedge and at the ends of the wedge, the flow breaks away forming a nose bubble and a trailing cavity. The closure mechanism is described by the Tulin single-spiral-vortex model. The flow domain is mapped into a parametric plane cut along a unit segment. The conformal mapping function is reconstructed through the exact solution of two Riemann–Hilbert problems on a genus-zero Riemann surface. To complete the solution, one needs to determine five real parameters from a certain system of transcendental equations. Numerical results are presented for the case when a wedge can rotate about the vertex in the flow domain. In this case, the flow branches at the vertex and the number of the parameters to be determined is 3.

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Faria, Luerbio, André L. P. Guedes, and Lilian Markenzon. "On feedback vertex set in reducible flow hypergraphs." Procedia Computer Science 195 (2021): 212–20. http://dx.doi.org/10.1016/j.procs.2021.11.027.

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10

D'APICE, CIRO, and BENEDETTO PICCOLI. "VERTEX FLOW MODELS FOR VEHICULAR TRAFFIC ON NETWORKS." Mathematical Models and Methods in Applied Sciences 18, supp01 (August 2008): 1299–315. http://dx.doi.org/10.1142/s0218202508003042.

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Some models of flow on a network are discussed. Assuming a macroscopic approach on each arc of the network, we consider a system of conservation laws and various possible choices to describe the evolution at vertices are discussed. A general framework proposed in recent literature is presented, then some new solutions for the scalar case are proposed and analyzed.

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11

Ji, Zhongping, Ligang Liu, Bin Wang, and Wenping Wang. "Feature Enhancement by Vertex Flow for 3D Shapes." Computer-Aided Design and Applications 8, no. 5 (January 2011): 649–64. http://dx.doi.org/10.3722/cadaps.2011.649-664.

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12

Raghavan Unnithan, Sunil Kumar, Balakrishnan Kannan, and Madambi Jathavedan. "Betweenness Centrality in Some Classes of Graphs." International Journal of Combinatorics 2014 (December 25, 2014): 1–12. http://dx.doi.org/10.1155/2014/241723.

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There are several centrality measures that have been introduced and studied for real-world networks. They account for the different vertex characteristics that permit them to be ranked in order of importance in the network. Betweenness centrality is a measure of the influence of a vertex over the flow of information between every pair of vertices under the assumption that information primarily flows over the shortest paths between them. In this paper we present betweenness centrality of some important classes of graphs.

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13

Hinton, Edward M., Andrew J. Hogg, and Herbert E. Huppert. "Shallow free-surface Stokes flow around a corner." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 378, no. 2174 (June 8, 2020): 20190515. http://dx.doi.org/10.1098/rsta.2019.0515.

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The steady lateral spreading of a free-surface viscous flow down an inclined plane around a vertex from which the channel width increases linearly with downstream distance is investigated analytically, numerically and experimentally. From the vertex the channel wall opens by an angle α to the downslope direction and the viscous fluid spreads laterally along it before detaching. The motion is modelled using lubrication theory and the distance at which the flow detaches is computed as a function of α using analytical and numerical methods. Far downslope after detachment, it is shown that the motion is accurately modelled in terms of a similarity solution. Moreover, the detachment point is well approximated by a simple expression for a broad range of opening angles. The results are corroborated through a series of laboratory experiments and the implication for the design of barriers to divert lava flows are discussed. This article is part of the theme issue ‘Stokes at 200 (Part 1)’.

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14

Barron, Katrina, Karina Batistelli, Florencia Orosz Hunziker, Veronika Pedić Tomić, and Gaywalee Yamskulna. "On rationality of C-graded vertex algebras and applications to Weyl vertex algebras under conformal flow." Journal of Mathematical Physics 63, no. 9 (September 1, 2022): 091706. http://dx.doi.org/10.1063/5.0117895.

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Using the Zhu algebra for a certain category of [Formula: see text]-graded vertex algebras V, we prove that if V is finitely Ω-generated and satisfies suitable grading conditions, then V is rational, i.e., it has semi-simple representation theory, with a one-dimensional level zero Zhu algebra. Here, Ω denotes the vectors in V that are annihilated by lowering the real part of the grading. We apply our result to the family of rank one Weyl vertex algebras with conformal element ω μ parameterized by [Formula: see text] and prove that for certain non-integer values of μ, these vertex algebras, which are non-integer graded, are rational, with a one-dimensional level zero Zhu algebra. In addition, we generalize this result to appropriate [Formula: see text]-graded Weyl vertex algebras of arbitrary ranks.

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15

Singh, Jeeoot, Tripti Agrawal, and Shashi Yadav. "Study of Vertex Shedding Phenomenon in Vortex Flow Meter." Materials Today: Proceedings 18 (2019): 2977–83. http://dx.doi.org/10.1016/j.matpr.2019.07.168.

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16

Kaplan, Haim, and Yahav Nussbaum. "Maximum Flow in Directed Planar Graphs with Vertex Capacities." Algorithmica 61, no. 1 (August 3, 2010): 174–89. http://dx.doi.org/10.1007/s00453-010-9436-7.

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17

Petrichenko, Mihail R., and Ol’ga A. Solov’yova. "Merging and splitting flows in a tee: the Pavlovsky method." Vestnik MGSU, no. 11 (November 2020): 1546–55. http://dx.doi.org/10.22227/1997-0935.2020.11.1546-1555.

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Introduction. The Pavlovsky method is employed to consider the flows that merge and split inside a tee. Materials and methods. The problem of flows, merging and splitting inside a simple straight tee, is reduced to the problem of limits in a theory of functions applied to the characteristic function of a flow. The influence of the geometric parameter of a tee (a module), head losses and an external power source, produced on the flow rate coefficient in a tee, is identified in the work. Results. The co-authors identified a relation between the geometric parameters of a tee and its capacity in case of an isoenergetic flow and an external mechanical power supply. Conclusions. As for practical tasks, it is sufficient to reproduce a pentagon, stylizing a simple straight tee, on a strip having a ledge, while preserving the correspondence of points of polygons. The following conclusions are made: dissipation does not reduce the flow rate coefficient when flows merge, neither does it reduce the flow rate coefficient when flows split; minimum values of flow rate coefficient q = Q0/Q1 in case of merging flows are attained in the absence of dissipation, and they do not exceed the maximum value of the flow rate coefficient in case of splitting flows is attained in the absence of dissipation and it is not less than dissipation in a tee is explained by the flow separation from the vertex of angle B when flows merge and by the flow separation from the vertex of angle C when flows merge. Hydraulic losses do not reduce flow rate coefficient q = q+ when flows merge and do not increase flow rate coefficient q = q– when flows split. flow rate coefficient q+ goes down if a source of external mechanical power (a pump) is connected to a tee when flows merge; if flows split, the flow rate coefficient goes up and varies within the 1 < q– < 2 interval, and it doesn’t go up if q– > 2.

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18

Yu, K. M., and M. W. Nansteel. "Buoyancy-induced Stokes flow in a wedge-shaped enclosure." Journal of Fluid Mechanics 221 (December 1990): 437–51. http://dx.doi.org/10.1017/s0022112090003627.

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The problem of buoyancy-induced Stokes flow in a sectorial region is addressed. Skew-symmetric flows are considered for wedge or opening angles of the sector in the range 0 < α [les ] π. The basic structure and character of the motion are found to depend critically upon the relative dominance, near the sector vertex, of the particular solution of the system with respect to the leading eigenfunction. A simple criterion is developed for the appearance of eddies, such as those observed by Moffatt (1964), in the neighbourhood of the sector vertex. A calculation is carried out for the specific case of motion induced by different temperatures on the radial boundaries of the enclosure. It is found that corner eddies may be present in this circumstance for wedge angles in the range 126° [lsim ] α [lsim ] 146°. The eddying motion near the vertex is examined, in some detail, for the wedge angle α = 135°. In the limiting case of α = π, corresponding to a semicircular-shaped sector, the particular solution is found to exhibit singular behaviour. However, this singular nature is found to be spurious, as a bounded particular solution can be constructed with the aid of one of the eigensolutions. Results are given for no-slip and shear-free conditions on the circular boundary of the sector for the purpose of comparison.

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19

GOMILKO, A. M., V. S. MALYUGA, and V. V. MELESHKO. "On steady Stokes flow in a trihedral rectangular corner." Journal of Fluid Mechanics 476 (February 10, 2003): 159–77. http://dx.doi.org/10.1017/s0022112002003026.

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Motivated by the recent paper of Hills & Moffatt (2000), we investigate the Stokes flow in a trihedral corner formed by three mutually orthogonal planes, induced by a non-zero velocity distribution over one of the walls of the corner. It is shown that the local behaviour of the velocity field near the edges of the corner, where a discontinuity of the boundary velocity is assumed, coincides with the Goodier–Taylor solution for a two-dimensional wedge. Analysis of the streamline patterns confirms the existence of eddies near the stationary edge in the flow, induced either by uniform translation of one of the walls of the corner in the direction perpendicular to its bisectrix or by uniform rotation of a side about the vertex of the corner. These flows are shown to be quasi-two-dimensional. If the wall rotates about a centre displaced from the vertex, the induced flow is essentially three-dimensional. In the antisymmetric velocity field, a stagnation line appears composed of stagnation points of different types. Otherwise the three-dimensionality manifests itself in a non-closed spiral shape of the streamlines.

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20

Joshaghani, M. S., V. Girault, and B. Riviere. "A vertex scheme for two-phase flow in heterogeneous media." Journal of Computational Physics 449 (January 2022): 110778. http://dx.doi.org/10.1016/j.jcp.2021.110778.

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21

Brankov, J. G., and M. Schreckenberg. "A five-vertex model interpretation of one-dimensional traffic flow." Journal of Physics A: Mathematical and General 31, no. 9 (March 6, 1998): 2133–40. http://dx.doi.org/10.1088/0305-4470/31/9/005.

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22

Klein, Cerry M., and Sencer Yeralan. "Network flow models with fuzzy auxiliary edge and vertex attributes." International Journal of Approximate Reasoning 2, no. 2 (April 1988): 103. http://dx.doi.org/10.1016/0888-613x(88)90085-0.

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23

Nasiruddin, Sheikh, S. N. Singh, S. V. Veeravalli, and S. Hegde. "Effect of vertex angle and vertex tip radius on the performance of V-cone flow meter using CFD." Measurement 138 (May 2019): 536–44. http://dx.doi.org/10.1016/j.measurement.2019.02.039.

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24

Hussain, Ruqiya Abed, Sawsan Abdullah Hassan, and Asmaa Abdul Jabbar Jamel. "Experimental Study on Flow over Triangular Labyrinth Weirs." International Journal of Design & Nature and Ecodynamics 17, no. 2 (April 27, 2022): 249–55. http://dx.doi.org/10.18280/ijdne.170211.

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Recently, many research studies have focused on labyrinth weirs' hydraulic performance, especially as dependent on engineering features. In the current study, the hydraulic properties of flow over labyrinth triangular weirs models (from the upper perspective) with sharp crest have been experimentally studied and compare their efficiency with suppressed rectangular weirs (conventional weirs). Twelve fiberglass models are developed for this reason and tested in a 6m in length, 30cm in width, and 40cm height in laboratory flume, nine models were constructed for triangular labyrinth weirs and three models were constructed for suppressed rectangular weirs, Three alternative heights (p=15, 20, and 25cm) were employed in this research, for each height, the vertex angle (θ) changed three times (60օ, 90օ, 120օ), and for each one of these weirs was used, seven different discharge were approved. The overall tests in this study were 84. The dimensionless parameters on which the discharge coefficient (Cd) is dependent were obtained using dimensional analysis. parameters were plotted. According to this experimental present study, as compared to linear weirs, labyrinth triangular weirs shown to be more hydraulically efficient. Also, the height of the weir (P) has effects on the discharge coefficient, where (Cd) increased with decreasing (P). Also, the vertex angle of triangular labyrinth weirs(θ) has a major influence on discharge coefficient and on weir performance, where the discharge coefficient raises when decreases the value of angle(θ), in another means, when the angle decreases gave an increase in the path of the flow, where it gave the triangular labyrinth weir with an angle of 60o the discharge coefficient reached its greatest value (2.55), followed by the weir with an angle of 90o and 120o respectively. In other words (a small vertex angle gives more length effective (Le) to the weir) and this leads to an increase in flow capacity or performance for the weir.

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HAN, YICHEOL, STEPHAN J. GOETZ, JEONGJAE LEE, and SEONGSOO YOON. "SIMULATING NETWORK STRUCTURES USING BERNOULLI'S PRINCIPLE." Advances in Complex Systems 15, no. 05 (July 2012): 1250032. http://dx.doi.org/10.1142/s0219525912500324.

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Using the fact that connections between vertices of a network often represent directed and weighted flows, we apply hydraulic principles to develop novel insights into network structure and growth. We develop a network model based on Bernoulli's principle and use it to analyze changes in network properties. Simulation results show that velocity of flow, resistance, fitness and existing connections in a system determine network connections of a vertex as well as overall network structure. We demonstrate how network structure is affected by changes in velocity and resistance, and how one vertex can monopolize connections within a network. Using Bernoulli's principle, we are able to independently reproduce key results in the network literature.

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26

Jiang, Qingfang. "Precipitation over Concave Terrain." Journal of the Atmospheric Sciences 63, no. 9 (September 1, 2006): 2269–88. http://dx.doi.org/10.1175/jas3761.1.

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Abstract Many topographic barriers are comprised of a series of concave or convex ridges that modulate the intensity and distribution of precipitation over mountainous areas. In this model-based idealized study, stratiform precipitation associated with stratified moist airflow past idealized concave ridges is investigated with a focus on windward blocking, flow confluence, and the associated precipitation enhancement. It is found that flow confluence and precipitation enhancement by a concave ridge are controlled by the nondimensional ridge height M (M = Nmhm/U, where Nm is the moist buoyancy frequency, hm is the maximum ridge height, and U is the wind speed), based on which three dynamical regimes can be defined. In the linear regime (M < 0.4), a flow confluence zone is present over the upwind slope of the ridge vertex, where precipitation is significantly enhanced. The precipitation enhancement is due to the additional updraft driven by the horizontal flow convergence with a considerable contribution from lateral confluence. In the blocking regime (0.4 < M < Mc), the area and intensity of the flow confluence zone decrease with increasing mountain height due to low-level blocking. The critical nondimensional ridge height (Mc) for windward flow stagnation decreases with increasing concave angle. In the two regimes, flow confluence and precipitation enhancement are more pronounced for concave ridges with a longer cross-stream dimension or a larger concave angle. In the flow reversal regime (M > Mc), no steady state can be achieved and the precipitation enhancement at the vertex is absent. In addition, the flow confluence and precipitation enhancement upstream of a concave ridge are sensitive to the presence of a relative gap or peak at the vertex, the earth’s rotation, and the incident wind. The relevant dynamics has been examined.

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27

Manjula, V. "Graphs in Network Flows." Mapana - Journal of Sciences 11, no. 4 (September 4, 2012): 99–108. http://dx.doi.org/10.12723/mjs.23.8.

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This paper presents a collection of basics and application of Network flows in Graph theory which is an out- growth of set of lecture notes on Graph applications. It is not only a record of material from text books but also a reflection of precise graphical concept which will be useful for students where such facts are needed. There are many real life problems dealing with discrete objects and binary relations and graph is very convenient form of its representation. A network flow graph G=(V,E) is a directed graph with two special vertices: the source vertex s, and the sink vertex t. Many problems in the real world are to be solved using maximum flow. "Real" networks, like the Internet or electronic circuit boards, are good examples of flow networks. Generally graphs can be used in two situations. Firstly since graph is a very simple, convenient and natural way of representing the relationship between objects. Secondly we have graph as model solve the appropriate graph theoretic problem then interpret the solution in terms of original problem In the modern world, planning efficient routes is essential for business and industry, The flow of information or water or gas etc in a network are useful to find the max rate of flow that is possible from one station to another A Transport network represents a general model for transportation of material from origin of supply to destination through shipping routes. The objective of this paper is to discuss the concepts and terminology of Network flows with Graphical representations.

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28

Herrero, M. A., M. Ughi, and J. J. L. Vel�zquez. "Approaching a vertex in a shrinking domain under a nonlinear flow." NoDEA : Nonlinear Differential Equations and Applications 11, no. 1 (February 1, 2004): 1–28. http://dx.doi.org/10.1007/s00030-003-1033-x.

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29

Millington, Peter, and Paul M. Saffin. "Vertex functions and their flow equations from the 2PI effective action." Journal of Physics A: Mathematical and Theoretical 55, no. 43 (October 28, 2022): 435402. http://dx.doi.org/10.1088/1751-8121/ac99ae.

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Abstract By exploiting the convexity of the two-particle-irreducible effective action, we describe a procedure for extracting n-point vertex functions. This procedure is developed within the context of a zero-dimensional ‘quantum field theory’ and subsequently extended to higher dimensions. These results extend the practicability and utility of a recent, alternative approach to the functional renormalization group programme (see Alexander et al 2021 Phys. Rev. D 104 069906; Millington and Saffin 2021 J. Phys. A: Math. Theor. 54 465401), and clarify the relationship between the flow equations for coupling parameters and vertices.

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Bhandari, Phanindra Prasad, and Shree Ram Khadka. "Lexicographically Maximum Contraflow Problem with Vertex Capacities." International Journal of Mathematics and Mathematical Sciences 2021 (February 13, 2021): 1–7. http://dx.doi.org/10.1155/2021/6651135.

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The contraflow approach has been extensively considered in the literature for modeling evacuations and has been claimed, due to its lane-direction-reversal capability, as an efficient idea to speed up the evacuation process. This paper considers the contraflow evacuation model on network with prioritized capacitated vertices that allows evacuees to be held at intermediate spots too, respecting their capacities and priority order. In particular, it studies the maximum flow evacuation planning problem and proposes polynomial and pseudo-polynomial time solution algorithms for static network and dynamic multinetwork, respectively. A real dataset of Kathmandu road network with evacuation spaces is considered to implement the algorithm designed for dynamic multinetwork and to observe its computational performance.

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Needleman, A., and V. Tvergaard. "Analyses of Plastic Flow Localization in Metals." Applied Mechanics Reviews 45, no. 3S (March 1, 1992): S3—S18. http://dx.doi.org/10.1115/1.3121390.

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The continuum mechanics framework for analyzing plastic flow localization is reviewed. The prediction of the localization of deformation into shear bands is sensitive to the constitutive description. The classical isotropic hardening elastic-plastic solid with a smooth yield surface and normality is very resistant to localization, but deviations from these idealizations have a strong effect. Thus, a material that forms a sharp vertex on the yield surface, as predicted by crystal plasticity, shows flow localization at quite realistic levels of strain, and even the formation of a rounded vertex on the yield surface has an important influence. Also softening induced by material damage or by the heating due to plastic dissipation have significant influence in promoting the onset of flow localization. In a practical situation one effect, such as thermal softening under high deformation rates, may be the dominant cause of localization, but often the interaction of different effects appears to be the more realistic explanation of observed flow localization. Some relevant constitutive models are reviewed and the effect of the different material models on localization predictions is illustrated. Important information on localization behavior in uniformly strained solids is obtained by a relatively simple material stability analysis, but often failure by flow localization occurs in nonuniformly strained regions, where numerical solution procedures are necessary to obtain theoretical predictions. The numerical results reviewed cover localization under dynamic as well as quasi-static loading conditions.

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32

Endaylalu, Sintayehu Assefa, and Wei-Hsin Tien. "A Numerical Investigation of the Mixing Performance in a Y-Junction Microchannel Induced by Acoustic Streaming." Micromachines 13, no. 2 (February 21, 2022): 338. http://dx.doi.org/10.3390/mi13020338.

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In this study, the mixing performance in a Y-junction microchannel with acoustic streaming was investigated through numerical simulation. The acoustic streaming is created by inducing triangular structures at the junction and sidewalls regions. The numerical model utilizes Navier–Stokes equations in conjunction with the convection–diffusion equations. The parameters investigated were inlet velocities ranging from 4.46 to 55.6 µm/s, triangular structure’s vertex angles ranging from 22° to 90° oscillation amplitude ranging from 3 to 6 µm, and an oscillation frequency set to 13 kHz. The results show that at the junction region, a pair of counter-rotating streaming vortices were formed, and unsymmetrical or one-sided vortices were formed when additional triangles were added along the sidewalls. These streaming flows significantly increase the vorticity compared with the case without the acoustic stream. Mixing performances were found to have improved with the generation of the acoustic stream. The mixing performance was evaluated at various inlet velocities, the vertex angles of the triangular structure, and oscillation amplitudes. The numerical results show that adding the triangular structure at the junction region considerably improved the mixing efficiency due to the generation of acoustic streaming, and further improvements can be achieved at lower inlet velocity, sharper vertex angle, and higher oscillation amplitude. Integrating with more triangular structures at the sidewall regions also improves the mixing performance within the laminar flow regime in the Y-microchannel. At Y = 2.30 mm, oscillation amplitude of 6 µm, and flow inlet velocity of 55.6 µm/s, with all three triangles integrated and the triangles’ vertex angles fixed to 30°, the mixing index can achieve the best results of 0.9981, which is better than 0.8355 in the case of using only the triangle at the junction, and 0.6642 in the case without acoustic streaming. This is equal to an improvement of 50.27% in the case of using both the junction and the two sidewall triangles, and 25.79% in the case of simply using a junction triangle.

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33

XIN, ZHOUPING, and HUICHENG YIN. "GLOBAL MULTIDIMENSIONAL SHOCK WAVE FOR THE STEADY SUPERSONIC FLOW PAST A THREE-DIMENSIONAL CURVED CONE." Analysis and Applications 04, no. 02 (April 2006): 101–32. http://dx.doi.org/10.1142/s0219530506000747.

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In this paper, we establish the global existence and stability of a multidimensional conic shock wave for three-dimensional steady supersonic flow past an infinite cone. The flow is assumed to be hypersonic and described by a steady potential flow equation. Under an appropriate boundary condition on the curved cone, we show that a pointed shock attached at the vertex of the cone will exist globally in the whole space.

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Yi Sun, Xiaochen Chen, Matthew Rosato, and Lijun Yin. "Tracking Vertex Flow and Model Adaptation for Three-Dimensional Spatiotemporal Face Analysis." IEEE Transactions on Systems, Man, and Cybernetics - Part A: Systems and Humans 40, no. 3 (May 2010): 461–74. http://dx.doi.org/10.1109/tsmca.2010.2041659.

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35

Zhang, Yongqian. "Steady supersonic flow past an almost straight wedge with large vertex angle." Journal of Differential Equations 192, no. 1 (July 2003): 1–46. http://dx.doi.org/10.1016/s0022-0396(03)00037-8.

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36

Mo, Zeyao, Aiqing Zhang, and Zhang Yang. "A new parallel algorithm for vertex priorities of data flow acyclic digraphs." Journal of Supercomputing 68, no. 1 (September 26, 2013): 49–64. http://dx.doi.org/10.1007/s11227-013-1022-8.

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37

Takeuchi, Masashi, Wataru Kishimoto, and Genya Kishi. "Synthesis of a flow network with a given centrality on each vertex." Electronics and Communications in Japan (Part III: Fundamental Electronic Science) 72, no. 3 (1989): 73–87. http://dx.doi.org/10.1002/ecjc.4430720307.

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38

Brimkov, Boris, and Illya V. Hicks. "Chromatic and flow polynomials of generalized vertex join graphs and outerplanar graphs." Discrete Applied Mathematics 204 (May 2016): 13–21. http://dx.doi.org/10.1016/j.dam.2015.10.016.

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39

Jia, Jun, Xiao Yuan He, and Xiao Feng Hu. "Drawing Hypergraphs in Hyperedge’s Average Degree and Multi-Rules." Applied Mechanics and Materials 713-715 (January 2015): 1682–88. http://dx.doi.org/10.4028/www.scientific.net/amm.713-715.1682.

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By analysing the past algorithms of drawing hypergraphs, this paper gives the definition of hyper graphs’ vertex degree and hyperedge’s average degree at first. Then it introduces the flow of this algorithm and particularly describes the rule set in setting the position of the vertex and the principal of minimum envelop law in drawing the hyperedge, and the complexity of this algorithm is analyzed. At last it draws a hypergraphs of scientific collaboration network successfully based on this algorithm and the result proves that the drawing algorithm of hyper graphs based on hyper edge’s average degree and multi-rules is feasible.

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40

P., Arun Kumar, and E. Rathakrishnan. "Triangular tabs for supersonic jet mixing enhancement." Aeronautical Journal 118, no. 1209 (November 2014): 1245–78. http://dx.doi.org/10.1017/s0001924000009969.

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AbstractThe mixing promoting capability of right-angled triangular tab with sharp and truncated vertex has been investigated by placing two identical tabs at the exit of a Mach 2 axi-symmetric nozzle. The mixing promoting efficiency of these tabs have been quantified in the presence of adverse and marginally favourable pressure gradients at the nozzle exit. It was found that, at all levels of expansion of the present study though the core length reduction caused by both the tabs are appreciable, but the mixing caused by the truncated tab is superior. The mixing promoting efficiency of the truncated tab is found to increase with increase of nozzle pressure ratio (that is, decrease of adverse pressure gradient). For all the nozzle pressure ratios of the present study, the core length reduction caused by the truncated vertex tab is more than that of sharp vertex tab. As high as 84% reduction in core length is achieved with truncated vertex right-angled triangular tabs at moderately overexpanded level, corresponding to expansion levelpe/pa= 0·90. The corresponding core length reduction for right-angled triangular tabs with sharp vertex and rectangular tabs are 65% and 31%, respectively. The present results clearly show that the mixing promoting capability of the triangular tab is best than that of rectangular tabs at identical blockage and flow conditions.

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41

Xu, Gang, and Huicheng Yin. "Instability of one global transonic shock wave for the steady supersonic Euler flow past a sharp cone." Nagoya Mathematical Journal 199 (September 2010): 151–81. http://dx.doi.org/10.1215/00277630-2010-008.

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AbstractIn this paper, we are concerned with the instability problem of one global transonic conic shock wave for the supersonic Euler flow past an infinitely long conic body whose vertex angle is less than some critical value. This is motivated by the following descriptions in the book Supersonic Flow and Shock Waves by Courant and Friedrichs: if there is a supersonic steady flow which comes from minus infinity, and the flow hits a sharp cone along its axis direction, then it follows from the Rankine-Hugoniot conditions, the physical entropy condition, and the apple curve method that there will appear a weak shock or a strong shock attached at the vertex of the cone, which corresponds to the supersonic shock or the transonic shock, respectively. A long-standing open problem is that only the weak shock could occur, and the strong shock is unstable. However, a convincing proof of this instability has apparently never been given. The aim of this paper is to understand this. In particular, under some suitable assumptions, because of the essential influence of the rotation of Euler flow, we show that a global transonic conic shock solution is unstable as long as the related sharp circular cone is perturbed.

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42

Xu, Gang, and Huicheng Yin. "Instability of one global transonic shock wave for the steady supersonic Euler flow past a sharp cone." Nagoya Mathematical Journal 199 (September 2010): 151–81. http://dx.doi.org/10.1017/s0027763000022261.

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AbstractIn this paper, we are concerned with the instability problem of one global transonic conic shock wave for the supersonic Euler flow past an infinitely long conic body whose vertex angle is less than some critical value. This is motivated by the following descriptions in the bookSupersonic Flow and Shock Wavesby Courant and Friedrichs: if there is a supersonic steady flow which comes from minus infinity, and the flow hits a sharp cone along its axis direction, then it follows from the Rankine-Hugoniot conditions, the physical entropy condition, and the apple curve method that there will appear a weak shock or a strong shock attached at the vertex of the cone, which corresponds to the supersonic shock or the transonic shock, respectively. A long-standing open problem is that only the weak shock could occur, and the strong shock is unstable. However, a convincing proof of this instability has apparently never been given. The aim of this paper is to understand this. In particular, under some suitable assumptions, because of the essential influence of the rotation of Euler flow, we show that a global transonic conic shock solution is unstable as long as the related sharp circular cone is perturbed.

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43

VASIL'EV, ALEXANDER. "ISOPERIMETRIC INEQUALITY FOR A CORNER HELE–SHAW DYNAMICS." Analysis and Applications 03, no. 03 (July 2005): 285–91. http://dx.doi.org/10.1142/s0219530505000595.

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We consider a two-dimensional Hele–Shaw flow in a wedge under injection into wedge's vertex. An isoperimetric inequality is obtained. It shows that the rate of the area growth is controlled by a special conformal quantity-triangle conformal radius.

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44

Hiraiwa, Tetsuya, Fu-Lai Wen, Tatsuo Shibata, and Erina Kuranaga. "Mathematical Modeling of Tissue Folding and Asymmetric Tissue Flow during Epithelial Morphogenesis." Symmetry 11, no. 1 (January 19, 2019): 113. http://dx.doi.org/10.3390/sym11010113.

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Recent studies have revealed that intrinsic, individual cell behavior can provide the driving force for deforming a two-dimensional cell sheet to a three-dimensional tissue without the need for external regulatory elements. However, whether intrinsic, individual cell behavior could actually generate the force to induce tissue deformation was unclear, because there was no experimental method with which to verify it in vivo. In such cases, mathematical modeling can be effective for verifying whether a locally generated force can propagate through an entire tissue and induce deformation. Moreover, the mathematical model sometimes provides potential mechanistic insight beyond the information obtained from biological experimental results. Here, we present two examples of modeling tissue morphogenesis driven by cell deformation or cell interaction. In the first example, a mathematical study on tissue-autonomous folding based on a two-dimensional vertex model revealed that active modulations of cell mechanics along the basal–lateral surface, in addition to the apical side, can induce tissue-fold formation. In the second example, by applying a two-dimensional vertex model in an apical plane, a novel mechanism of tissue flow caused by asymmetric cell interactions was discovered, which explained the mechanics behind the collective cellular movement observed during epithelial morphogenesis.

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45

Franzblau, D. S., and A. Raychaudhuri. "Optimal Hamiltonian completions and path covers for trees, and a reduction to maximum flow." ANZIAM Journal 44, no. 2 (October 2002): 193–204. http://dx.doi.org/10.1017/s1446181100013894.

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A minimum Hamiltonian completion of a graph G is a minimum-size set of edges that, when added to G, guarantee a Hamiltonian path. Finding a Hamiltonian completion has applications to frequency assignment as well as distributed computing. If the new edges are deleted from the Hamiltonian path, one is left with a minimum path cover, a minimum-size set of vertex-disjoint paths that cover the vertices of G. For arbitrary graphs, constructing a minimum Hamiltonian completion or path cover is clearly NP-hard, but there exists a linear-time algorithm for trees. In this paper we first give a description and proof of correctness for this linear-time algorithm that is simpler and more intuitive than those given previously. We show that the algorithm extends also to unicyclic graphs. We then give a new method for finding an optimal path cover or Hamiltonian completion for a tree that uses a reduction to a maximum flow problem. In addition, we show how to extend the reduction to construct, if possible, a covering of the vertices of a bipartite graph with vertex-disjoint cycles, that is, a 2-factor.

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46

Nakayama, Akira. "NP-COMPLETENESS AND APPROXIMATION ALGORITHM FOR THE MAXIMUM INTEGRAL VERTEX-BALANCED FLOW PROBLEM." Journal of the Operations Research Society of Japan 34, no. 1 (1991): 13–27. http://dx.doi.org/10.15807/jorsj.34.13.

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47

YILMAZ, E., M. S. KAVSAOGLU, H. U. AKAY, and I. S. AKMANDOR. "Cell-vertex Based Parallel and Adaptive Explicit 3D Flow Solution on Unstructured Grids." International Journal of Computational Fluid Dynamics 14, no. 4 (January 2001): 271–86. http://dx.doi.org/10.1080/10618560108940729.

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48

Grassi, Rosanna. "Vertex centrality as a measure of information flow in Italian Corporate Board Networks." Physica A: Statistical Mechanics and its Applications 389, no. 12 (June 2010): 2455–64. http://dx.doi.org/10.1016/j.physa.2009.12.069.

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49

Shao, Xueming, Xiaolong Zhang, Zhaosheng Yu, and Jianzhong Lin. "Numerical studies on the dynamics of an open triangle in a vertically oscillatory flow." Journal of Fluid Mechanics 788 (January 5, 2016): 381–406. http://dx.doi.org/10.1017/jfm.2015.703.

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A direct-forcing fictitious domain method is employed to study the dynamics of an open triangle in a vertically oscillatory flow. The flow structures, the vertical force and the torque on the fixed body are analysed for the stable flow regime in which the flow structures form and evolve exactly in the same way in each period and the unstable regime, respectively. Our results indicate that in the stable flow regime for the body with upright orientation, the steady streaming structure mainly comprises two vortex pairs located respectively above and below the body. Due to up–down asymmetry of the body, the pair below the body produces a larger vertical force on the body than the upper pair, which is mainly responsible for the non-zero average force at relatively high Reynolds numbers. The average force increases with increasing Reynolds number or increasing dimensionless period for the parameter range studied, due to the vortex effects. In the unstable regime, a vortex pair is ejected downward from each body edge. The irregular motion of the emitted vortices below the body leads to the irregular fluctuation of the vertical force. Regarding the torque on a tilted body, in the stable regime, the body experiences a restoring torque when its vertex angle is larger than a critical value being close to (and smaller than) 60°, and otherwise a destructive torque, irrespective of the value of tilt angle. For a fixed vertex angle, the torque magnitude is largest when the tilt angle is around 45°. In the unstable regime, the persistent ejection of the vortex pair during upward flow and corresponding restoring torque are observed for a large tilt angle with one edge aligned close to the horizontal direction, as in the experiment of Liu et al. (Phys. Rev. Lett., vol. 108, 2012, 068103). For a relatively small tilt angle, the emission direction of the vortex pair has intermittency, leading to the intermittency in the direction of torque. The reasons for the above observations are discussed. The predictions on the stable orientation for a hovering body in the stable flow regime and the irregular orientation in the unstable regime are confirmed in the dynamic simulation of a freely moving body. The body with the stable horizontal orientation in case of small vertex angle migrates along the body-shape-diverging direction.

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50

RICHARDSON, S. "Hele-Shaw flows with free boundaries in a corner or around a wedge Part I: Liquid at the vertex." European Journal of Applied Mathematics 12, no. 6 (December 2001): 665–76. http://dx.doi.org/10.1017/s0956792501004594.

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Consider a Hele-Shaw cell with the fluid (liquid) confined to an angular region by a solid boundary in the form of two half-lines meeting at an angle απ; if 0 < α < 1 we have flow in a corner, while if 1 < α [les ] 2 we have flow around a wedge. We suppose contact between the fluid and each of the lines forming the solid boundary to be along a single segment emanating from the vertex, so we have liquid at the vertex, and contemplate such a situation that has been produced by injection at a number of points into an initially empty cell. We show that, if we assume the pressure to be constant along the free boundary, the region occupied by the fluid is the image of a semidisc (a domain bounded by a semicircle and its diameter) in the ζ-plane under a conformal map given by a function of the form ζα times a rational function of ζ. The form of this rational function can be written down, and the parameters appearing in it then determined as the solution to a set of algebraic equations. Examples of such flows are given (including one which shows that, in a certain sense, injection can produce a cusp), and the limiting situation in the wedge configuration as one injection point is moved to infinity is also considered.

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