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Journal articles on the topic 'Flow hierarchy'

Author: Grafiati

Published: 13 April 2024

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1

Huang, Yehui, Yuqin Yao, and Yunbo Zeng. "Links between(γn,σk)-KP Hierarchy,(γn,σk)-mKP Hierarchy, and (2+1)-(γn,σk)-Harry Dym Hierarchy." Advances in Mathematical Physics 2015 (2015): 1–11. http://dx.doi.org/10.1155/2015/392723.

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The new (2+1)-(γn,σk)-Harry Dym hierarchy and(γn,σk)-mKP hierarchy with two new time seriesγnandσk, which consist ofγn-flow,σk-flow, and mixedγnandσkevolution equations of eigenfunctions, are proposed. Gauge transformations and reciprocal transformations between(γn,σk)-KP hierarchy,(γn,σk)-mKP hierarchy, and (2+1)-(γn,σk)-Harry Dym hierarchy are studied. Their soliton solutions are presented.

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2

Yoshida, Z., S. M. Mahajan, and S. Ohsaki. "Scale hierarchy created in plasma flow." Physics of Plasmas 11, no. 7 (July 2004): 3660–64. http://dx.doi.org/10.1063/1.1762877.

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3

Thunis, P., and R. Bornstein. "Hierarchy of Mesoscale Flow Assumptions and Equations." Journal of the Atmospheric Sciences 53, no. 3 (February 1996): 380–97. http://dx.doi.org/10.1175/1520-0469(1996)053<0380:homfaa>2.0.co;2.

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4

Aghaeepour, Nima, Adrin Jalali, Kieran O'Neill, Pratip K. Chattopadhyay, Mario Roederer, Holger H. Hoos, and Ryan R. Brinkman. "RchyOptimyx: Cellular hierarchy optimization for flow cytometry." Cytometry Part A 81A, no. 12 (October 8, 2012): 1022–30. http://dx.doi.org/10.1002/cyto.a.22209.

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5

Usami, S., H. Ohtani, R. Horiuchi, and M. Den. "Simulation of Plasma Flow Injection with Multi-Hierarchy Model Aiming Magnetic Reconnection Studies." Communications in Computational Physics 11, no. 3 (March 2012): 1006–10210. http://dx.doi.org/10.4208/cicp.181010.090611a.

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AbstractA multi-hierarchy simulation model aiming magnetic reconnection studies is developed and improved in which macroscopic and microscopic physics are computed consistently and simultaneously. Macroscopic physics is solved by mag-netohydrodynamics (MHD) algorithm, while microscopic dynamics is expressed by particle-in-cell (PIC) algorithm. The multi-hierarchy model relies on the domain decomposition method, and macro- and micro-hierarchies are interlocked smoothly by hand-shake scheme. As examination, plasma flow injection is simulated in the multi-hierarchy model. It is observed that plasmas flow from a macro-hierarchy to a micro-hierarchy across the magnetic field smoothly and continuously.

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6

Gao, Binfang, Kai Tian, and Qing Ping Liu. "A super Degasperis–Procesi equation and related integrable systems." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 477, no. 2245 (January 2021): 20200780. http://dx.doi.org/10.1098/rspa.2020.0780.

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Based on a 4 × 4 matrix spectral problem, a super Degasperis–Procesi (DP) equation is proposed. We show that under a reciprocal transformation, the super DP equation is related to the first negative flow of a super Kaup–Kupershmidt (KK) hierarchy, which turns out to be a particular reduction of a super Boussinesq hierarchy. The bi-Hamiltonian structure of the super Boussinesq hierarchy is established and subsequently produces a Hamiltonian structure, as well as a conjectured symplectic formulation of the super KK hierarchy via suitable reductions. With the help of the reciprocal transformation, the bi-Hamiltonian representation of the super DP equation is constructed from that of the super KK hierarchy. We also calculate a positive flow of the super DP hierarchy and explain its relations with the super KK equation. Infinitely many conservation laws are derived for the super DP equation, as well as its positive flow.

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7

Motoori, Yutaro, and Susumu Goto. "Hierarchy of coherent structures in turbulent channel flow." Journal of Physics: Conference Series 1522 (April 2020): 012004. http://dx.doi.org/10.1088/1742-6596/1522/1/012004.

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8

Jiun-Liang, Chen, and Feng-Jian Wang. "An inheritance flow model for class hierarchy analysis." Information Processing Letters 66, no. 6 (June 1998): 309–15. http://dx.doi.org/10.1016/s0020-0190(98)00072-6.

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9

Ning, Wang. "Rescaling Symmetry Flow of the Kadomtsev–Petviashvili Hierarchy." Chinese Physics Letters 21, no. 12 (December 2004): 2327–29. http://dx.doi.org/10.1088/0256-307x/21/12/002.

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10

Wang, Lian, and Tzui Raz. "Analytic hierarchy process based on data flow diagram." Computers & Industrial Engineering 20, no. 3 (January 1991): 355–65. http://dx.doi.org/10.1016/0360-8352(91)90007-s.

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11

Linga, Gaute, and Tore Flåtten. "A hierarchy of non-equilibrium two-phase flow models." ESAIM: Proceedings and Surveys 66 (2019): 109–43. http://dx.doi.org/10.1051/proc/201966006.

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We review and extend a hierarchy of relaxation models for two-phase flow. The models are derived from the non-equilibrium Baer–Nunziato model, which is endowed with relaxation source terms to drive it towards equilibrium. The source terms cause transfer of volume, heat, mass and momentum due to differences between the phases in pressure, temperature, chemical potential and velocity, respectively. In the context of two-phase flow models, the subcharacteristic condition implies that the sound speed of an equilibrium system can never exceed that of the relaxation system. Here, previous work by Flåtten and Lund [Math. Models Methods Appl. Sci., 21 (12), 2011, 2379–2407] and Lund [SIAM J. Appl. Math. 72, 2012, 1713–1741] is extended to encompass two-fluid models, i.e. models with separately governed velocities for the two phases. Each remaining model in the hierarchy is derived, and analytical expressions for the sound speeds are presented. Given only physically fundamental assumptions, the subcharacteristic condition is shown to be satisfied in the entire hierarchy, either in a weak or in a strong sense.

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12

Lund, Halvor. "A Hierarchy of Relaxation Models for Two-Phase Flow." SIAM Journal on Applied Mathematics 72, no. 6 (January 2012): 1713–41. http://dx.doi.org/10.1137/12086368x.

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13

HANAJIMA, Keita, and Susumu GOTO. "Hierarchy of the Vortical Structures in Turbulent Channel Flow." Proceedings of Conference of Kansai Branch 2018.93 (2018): 702. http://dx.doi.org/10.1299/jsmekansai.2018.93.702.

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14

Flores, Oscar, and Javier Jiménez. "Hierarchy of minimal flow units in the logarithmic layer." Physics of Fluids 22, no. 7 (July 2010): 071704. http://dx.doi.org/10.1063/1.3464157.

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15

Fateev, Vladimir A., and Sergei L. Lukyanov. "Boundary RG flow associated with the AKNS soliton hierarchy." Journal of Physics A: Mathematical and General 39, no. 41 (September 27, 2006): 12889–925. http://dx.doi.org/10.1088/0305-4470/39/41/s10.

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16

BRUNELLI, J. C., and A. DAS. "A NONSTANDARD SUPERSYMMETRIC KP HIERARCHY." Reviews in Mathematical Physics 07, no. 08 (November 1995): 1181–94. http://dx.doi.org/10.1142/s0129055x95000438.

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We show that the supersymmetric nonlinear Schrödinger equation can be written as a constrained super KP flow in a nonstandard representation of the Lax equation. We construct the conserved charges and show that this system reduces to the super mKdV equation with appropriate identifications. We construct various flows generated by the general nonstandard super Lax equation and show that they contain both the KP and mKP flows in the bosonic limits. This nonstandard supersymmetric KP hierarchy allows us to construct a new super KP equation which is nonlocal.

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17

GONG, DONG, and XIANGUO GENG. "QUASI-PERIODIC SOLUTIONS OF THE RELATIVISTIC TODA HIERARCHY." Journal of Nonlinear Mathematical Physics 19, no. 04 (December 2012): 1250030. http://dx.doi.org/10.1142/s1402925112500301.

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On the basis of the theory of algebraic curves, the continuous flow and discrete flow related to the relativistic Toda hierarchy are straightened out using the Abel–Jacobi coordinates. The meromorphic function and the Baker–Akhiezer function are introduced on the hyperelliptic curve. Quasi-periodic solutions of the relativistic Toda hierarchy are constructed with the help of the asymptotic properties and the algebro-geometric characters of the meromorphic function and the hyperelliptic curve.

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18

FENG, YU-LEI, LI-XIN XU, and YU-TING WANG. "HIERARCHY IN HOŘAVA-LIKE GRAVITY." International Journal of Modern Physics A 26, no. 16 (June 30, 2011): 2795–805. http://dx.doi.org/10.1142/s0217751x11053602.

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We investigate a Hořava-like gravity model in (4+1)-dimensional space–time. Differing from the original one, we put a critical exponent z to the extra space dimension, which preserves the 4-dimensional diffeomorphism. Surprisingly, we obtain a mass hierarchy [Formula: see text] in a way completely different from the Randall–Sundrum model, we also obtain an exponential factor solution with the use of Ricci-like flow. More interesting relations with AdS5/CFT4 are further demonstrated. Since AdS/CFT is a realization of holography, we conclude that the Hořava-like gravity may be also a realization of holography.

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19

Herty, Michael, and Elisa Iacomini. "Uncertainty quantification in hierarchical vehicular flow models." Kinetic and Related Models 15, no. 2 (2022): 239. http://dx.doi.org/10.3934/krm.2022006.

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<p style='text-indent:20px;'>We consider kinetic vehicular traffic flow models of BGK type [<xref ref-type="bibr" rid="b24">24</xref>]. Considering different spatial and temporal scales, those models allow to derive a hierarchy of traffic models including a hydrodynamic description. In this paper, the kinetic BGK–model is extended by introducing a parametric stochastic variable to describe possible uncertainty in traffic. The interplay of uncertainty with the given model hierarchy is studied in detail. Theoretical results on consistent formulations of the stochastic differential equations on the hydrodynamic level are given. The effect of the possibly negative diffusion in the stochastic hydrodynamic model is studied and numerical simulations of uncertain traffic situations are presented.</p>

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20

Etikyala, R., S. Göttlich, A. Klar, and S. Tiwari. "Particle methods for pedestrian flow models: From microscopic to nonlocal continuum models." Mathematical Models and Methods in Applied Sciences 24, no. 12 (August 15, 2014): 2503–23. http://dx.doi.org/10.1142/s0218202514500274.

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A hierarchy of models for pedestrian flow is numerically investigated using particle methods. It includes microscopic models based on interacting particle system coupled to an eikonal equation, hydrodynamic models using equations for density and mean velocity, nonlocal continuum equations for the density and diffusive Hughes equations. Particle methods are used on all levels of the hierarchy. Numerical test cases are investigated by comparing the above models.

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21

GENG, XIANGUO, and BO XUE. "SOME NEW INTEGRABLE NONLINEAR EVOLUTION EQUATIONS AND THEIR INFINITELY MANY CONSERVATION LAWS." Modern Physics Letters B 24, no. 19 (July 30, 2010): 2077–90. http://dx.doi.org/10.1142/s021798491002447x.

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A hierarchy of new nonlinear evolution equations associated with a 3×3 matrix spectral problem with two potentials is derived and its Hamiltonian structures are established with the aid of trace identity. The negative flow of the hierarchy is then discussed. A reduction of this hierarchy and its Hamiltonian structures are constructed. An infinite sequence of conserved quantities of several new soliton equations is obtained.

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22

Suchecki, Krzysztof, and Janusz A. Hołyst. "Hierarchy Depth in Directed Networks." Entropy 24, no. 2 (February 8, 2022): 252. http://dx.doi.org/10.3390/e24020252.

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In this study, we explore the depth measures for flow hierarchy in directed networks. Two simple measures are defined—rooted depth and relative depth—and their properties are discussed. The method of loop collapse is introduced, allowing investigation of networks containing directed cycles. The behavior of the two depth measures is investigated in Erdös-Rényi random graphs, directed Barabási-Albert networks, and in Gnutella p2p share network. A clear distinction in the behavior between non-hierarchical and hierarchical networks is found, with random graphs featuring unimodal distribution of depths dependent on arc density, while for hierarchical systems the distributions are similar for different network densities. Relative depth shows the same behavior as existing trophic level measure for tree-like networks, but is only statistically correlated for more complex topologies, including acyclic directed graphs.

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23

Ball, Peter. "Low energy production impact on lean flow." Journal of Manufacturing Technology Management 26, no. 3 (April 7, 2015): 412–28. http://dx.doi.org/10.1108/jmtm-12-2012-0120.

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Purpose – Rising energy costs and potential scarcity are driving energy reduction initiatives in manufacturing companies. The reduction in energy use is complementary to the classic lean production philosophy and the lean and green literature implies that reducing energy waste supports lean objectives. The purpose of this paper is to examine this perceived positive correlation and identify the impact level of energy reduction of lean product flow. Design/methodology/approach – To achieve this, published case studies and practices from interview were gathered and categorised against a waste management hierarchy. Findings – Energy reduction activities implicitly reduce waste which is compatible with the lean waste objective, however, when applying the waste hierarchy principle to energy efficiency practice, lean product flow is progressively constrained or compromised towards the lower levels of the hierarchy. Research limitations/implications – The hierarchical classification seeks to communicate how reported energy efficiency improvements will/will not impact on flow. The research focuses on the modification of existing discrete part production facilities towards greater energy efficiency and neglects alternative production technologies and new build. The results suggest that as manufacturers seeking to be more energy efficient move away from preventative actions to more reduce and reuse actions then production flexibility could become restricted and the design of production facilities make re-think the fast, linear and short flow of product. Practical implications – Examples of industrial practices are provided to show the implications of energy reduction practice on production flow. Originality/value – Categorises the relationship between classic lean and industrial low-energy initiatives to provide insight to how higher energy cost could impact on production.

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24

Kramar, Mirna, and Karen Alim. "Encoding memory in tube diameter hierarchy of living flow network." Proceedings of the National Academy of Sciences 118, no. 10 (February 22, 2021): e2007815118. http://dx.doi.org/10.1073/pnas.2007815118.

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The concept of memory is traditionally associated with organisms possessing a nervous system. However, even very simple organisms store information about past experiences to thrive in a complex environment—successfully exploiting nutrient sources, avoiding danger, and warding off predators. How can simple organisms encode information about their environment? We here follow how the giant unicellular slime mold Physarum polycephalum responds to a nutrient source. We find that the network-like body plan of the organism itself serves to encode the location of a nutrient source. The organism entirely consists of interlaced tubes of varying diameters. Now, we observe that these tubes grow and shrink in diameter in response to a nutrient source, thereby imprinting the nutrient’s location in the tube diameter hierarchy. Combining theoretical model and experimental data, we reveal how memory is encoded: a nutrient source locally releases a softening agent that gets transported by the cytoplasmic flows within the tubular network. Tubes receiving a lot of softening agent grow in diameter at the expense of other tubes shrinking. Thereby, the tubes’ capacities for flow-based transport get permanently upgraded toward the nutrient location, redirecting future decisions and migration. This demonstrates that nutrient location is stored in and retrieved from the networks’ tube diameter hierarchy. Our findings explain how network-forming organisms like slime molds and fungi thrive in complex environments. We here identify a flow networks’ version of associative memory—very likely of relevance for the plethora of living flow networks as well as for bioinspired design.

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25

OHNARI, Hirofumi, Takanori SAGA, and Takashi SAITOU. "The hierarchy of the coherent structures in turbulent channel flow." JOURNAL OF THE FLOW VISUALIZATION SOCIETY OF JAPAN 6, no. 22 (1986): 411–14. http://dx.doi.org/10.3154/jvs1981.6.411.

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26

Chaudhari, Nikhil P., P. M. Ravanan, and Asghar Shaikh. "Optimal Selection of Gas Flow Meter using Analytical Hierarchy Process." International Journal of Engineering Research 6, no. 6 (2017): 300. http://dx.doi.org/10.5958/2319-6890.2017.00023.x.

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27

He, Jingsong, Junyi Tu, Xiaodong Li, and Lihong Wang. "Explicit flow equations and recursion operator of the ncKP hierarchy." Nonlinearity 24, no. 10 (September 7, 2011): 2875–90. http://dx.doi.org/10.1088/0951-7715/24/10/011.

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28

Cheng, Ji-Peng, Jing-Song He, and Li-Hong Wang. "A General Formula of Flow Equations for Harry—Dym Hierarchy." Communications in Theoretical Physics 55, no. 2 (February 2011): 193–98. http://dx.doi.org/10.1088/0253-6102/55/2/01.

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29

Li, Jian, and Chuanzhong Li. "Additional symmetries for the supersymmetric Gelfand–Dickey hierarchy." International Journal of Geometric Methods in Modern Physics 17, no. 11 (September 2020): 2050164. http://dx.doi.org/10.1142/s0219887820501649.

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In this paper, we first define a supersymmetric Gelfand–Dickey hierarchy using the Sato equation. Then we introduce some time variables and derivations involving those that from a non-abelian Lie superalgebra. Next, we construct additional symmetries for the supersymmetric Gelfand–Dickey hierarchy with the aid of the Orlov–Schulman operators which involve the above time variables and dressing operators. We give the additional flow equations of the supersymmetric Gelfand–Dickey hierarchy, and prove that the additional flows are symmetries of the supersymmetric Gelfand–Dickey hierarchy. In this way, an isomorphism between the additional symmetries of the supersymmetric Gelfand–Dickey hierarchy and the super [Formula: see text] algebra is constructed. Finally, the [Formula: see text] type supersymmetric Gelfand–Dickey hierarchy is constructed and we consider the additional symmetries for the supersymmetric Gelfand–Dickey hierarchy with the [Formula: see text] type condition which is compatible with the flows of the [Formula: see text] type supersymmetric Gelfand–Dickey hierarchy.

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30

YAO, YUQIN, YEHUI HUANG, and YUNBO ZENG. "A NEW (γn, σk)-KP HIERARCHY AND GENERALIZED DRESSING METHOD." Journal of Nonlinear Mathematical Physics 19, no. 04 (December 2012): 1250027. http://dx.doi.org/10.1142/s1402925112500271.

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A new (γn, σk)-KP hierarchy (KPH) with two new time series γn and σk, which consists of γn-flow, σk-flow and mixed γn and σk evolution equations of eigenfunctions, is proposed. Two reductions and constrained flows of (γn, σk)-KPH are studied. The dressing method is generalized to the (γn, σk)-KPH and some solutions are presented.

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31

DAS, ASHOK, and SHIBAJI ROY. "INTEGRABLE MODELS AND SPIN ALGEBRAS." International Journal of Modern Physics A 06, no. 08 (March 30, 1991): 1429–45. http://dx.doi.org/10.1142/s0217751x91000757.

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We show how the entire KdV hierarchy as well as the recursion relation between the conserved quantities can be obtained from a spin-2 flow. The relationship between this approach and the zero curvature formulation of the KdV system based on the group SL(2, R) is clarified. We show that the Boussinesq equation can be derived as a flow of the spin-3 transformations. The Boussinesq hierarchy, as well as the relevant Lenard relation, is derived from a combined flow of the spin-2 and spin-3 transformations. We have also given an independent derivation of the Lenard relation for the Boussinesq equation starting from the third order Schrödinger equation.

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32

FLÅTTEN, TORE, and HALVOR LUND. "RELAXATION TWO-PHASE FLOW MODELS AND THE SUBCHARACTERISTIC CONDITION." Mathematical Models and Methods in Applied Sciences 21, no. 12 (December 2011): 2379–407. http://dx.doi.org/10.1142/s0218202511005775.

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The subcharacteristic condition for hyperbolic relaxation systems states that wave velocities of an equilibrium system cannot exceed the corresponding wave velocities of its relaxation system. This condition is central to the stability of hyperbolic relaxation systems, and is expected to hold for most such models describing natural phenomena. In this paper, we study a hierarchy of two-phase flow models. We consider relaxation with respect to volume transfer, heat transfer and mass transfer. We formally verify that our relaxation processes are consistent with the first and second laws of thermodynamics, and present analytical expressions for the wave velocities for each model in the hierarchy. Through an appropriate choice of variables, we prove directly by sums-of-squares that for all relaxation processes considered, the subcharacteristic condition holds for any thermodynamically stable equation of state.

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33

White, C. M., Y. Dubief, and J. Klewicki. "Properties of the mean momentum balance in polymer drag-reduced channel flow." Journal of Fluid Mechanics 834 (November 17, 2017): 409–33. http://dx.doi.org/10.1017/jfm.2017.721.

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Mean momentum equation based analysis of polymer drag-reduced channel flow is performed to evaluate the redistribution of mean momentum and the mechanisms underlying the redistribution processes. Similar to channel flow of Newtonian fluids, polymer drag-reduced channel flow is shown to exhibit a four layer structure in the mean balance of forces that also connects, via the mean momentum equation, to an underlying scaling layer hierarchy. The self-similar properties of the flow related to the layer hierarchy appear to persist, but in an altered form (different from the Newtonian fluid flow), and dependent on the level of drag reduction. With increasing drag reduction, polymer stress usurps the role of the inertial mechanism, and because of this the wall-normal position where inertially dominated mean dynamics occurs moves outward, and viscous effects become increasingly important farther from the wall. For the high drag reduction flows of the present study, viscous effects become non-negligible across the entire hierarchy and an inertially dominated logarithmic scaling region ceases to exist. It follows that the state of maximum drag reduction is attained only after the inertial sublayer is eradicated. According to the present mean equation theory, this coincides with the loss of a region of logarithmic dependence in the mean profile.

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34

Geng, Xianguo, and Xin Zeng. "Quasi-periodic solutions of the Belov–Chaltikian lattice hierarchy." Reviews in Mathematical Physics 29, no. 08 (August 20, 2017): 1750025. http://dx.doi.org/10.1142/s0129055x17500258.

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Utilizing the characteristic polynomial of Lax matrix for the Belov–Chaltikian (BC) lattice hierarchy associated with a [Formula: see text] discrete matrix spectral problem, we introduce a trigonal curve with three infinite points, from which we establish the associated Dubrovin-type equations. The essential properties of the Baker–Akhiezer function and the meromorphic function are discussed, that include their asymptotic behavior near three infinite points on the trigonal curve and the divisor of the meromorphic function. The Abel map is introduced to straighten out the continuous flow and the discrete flow in the Jacobian variety, from which the quasi-periodic solutions of the entire BC lattice hierarchy are obtained in terms of the Riemann theta function.

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35

Barnes, Richard, Kerry L. Callaghan, and Andrew D. Wickert. "Computing water flow through complex landscapes – Part 3: Fill–Spill–Merge: flow routing in depression hierarchies." Earth Surface Dynamics 9, no. 1 (March 2, 2021): 105–21. http://dx.doi.org/10.5194/esurf-9-105-2021.

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Abstract. Depressions – inwardly draining regions – are common to many landscapes. When there is sufficient moisture, depressions take the form of lakes and wetlands; otherwise, they may be dry. Hydrological flow models used in geomorphology, hydrology, planetary science, soil and water conservation, and other fields often eliminate depressions through filling or breaching; however, this can produce unrealistic results. Models that retain depressions, on the other hand, are often undesirably expensive to run. In previous work we began to address this by developing a depression hierarchy data structure to capture the full topographic complexity of depressions in a region. Here, we extend this work by presenting the Fill–Spill–Merge algorithm that utilizes our depression hierarchy data structure to rapidly process and distribute runoff. Runoff fills depressions, which then overflow and spill into their neighbors. If both a depression and its neighbor fill, they merge. We provide a detailed explanation of the algorithm and results from two sample study areas. In these case studies, the algorithm runs 90–2600 times faster (with a reduction in compute time of 2000–63 000 times) than the commonly used Jacobi iteration and produces a more accurate output. Complete, well-commented, open-source code with 97 % test coverage is available on GitHub and Zenodo.

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36

Hu, Fei Hu, Jie Jiang, Wei Yang Qin, and Yi Li. "Generating Document Tree of Workflow with Synchronization Process." Applied Mechanics and Materials 182-183 (June 2012): 1766–70. http://dx.doi.org/10.4028/www.scientific.net/amm.182-183.1766.

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In this paper, we introduce the concept of data model, and design an algorithm to generate a tree-like structure that describes the hierarchy of nested synchronizations. A data model and document tree example based on the RTWD net is studided. The resulting document tree shares information with control flow, and displays its hierarchy structure.

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37

Vidal, Jean-Philippe, Benoît Hingray, Claire Magand, Eric Sauquet, and Agnès Ducharne. "Hierarchy of climate and hydrological uncertainties in transient low-flow projections." Hydrology and Earth System Sciences 20, no. 9 (September 8, 2016): 3651–72. http://dx.doi.org/10.5194/hess-20-3651-2016.

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Abstract. This paper proposes a methodology for estimating the transient probability distribution of yearly hydrological variables conditional to an ensemble of projections built from multiple general circulation models (GCMs), multiple statistical downscaling methods (SDMs), and multiple hydrological models (HMs). The methodology is based on the quasi-ergodic analysis of variance (QE-ANOVA) framework that allows quantifying the contributions of the different sources of total uncertainty, by critically taking account of large-scale internal variability stemming from the transient evolution of multiple GCM runs, and of small-scale internal variability derived from multiple realizations of stochastic SDMs. This framework thus allows deriving a hierarchy of climate and hydrological uncertainties, which depends on the time horizon considered. It was initially developed for long-term climate averages and is here extended jointly to (1) yearly anomalies and (2) low-flow variables. It is applied to better understand possible transient futures of both winter and summer low flows for two snow-influenced catchments in the southern French Alps. The analysis takes advantage of a very large data set of transient hydrological projections that combines in a comprehensive way 11 runs from four different GCMs, three SDMs with 10 stochastic realizations each, as well as six diverse HMs. The change signal is a decrease in yearly low flows of around −20 % in 2065, except for the more elevated catchment in winter where low flows barely decrease. This signal is largely masked by both large- and small-scale internal variability, even in 2065. The time of emergence of the change signal is however detected for low-flow averages over 30-year time slices starting as early as 2020. The most striking result is that a large part of the total uncertainty – and a higher one than that due to the GCMs – stems from the difference in HM responses. An analysis of the origin of this substantial divergence in HM responses for both catchments and in both seasons suggests that both evapotranspiration and snowpack components of HMs should be carefully checked for their robustness in a changed climate in order to provide reliable outputs for informing water resource adaptation strategies.

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Vidal, J. P., B. Hingray, C. Magand, E. Sauquet, and A. Ducharne. "Hierarchy of climate and hydrological uncertainties in transient low flow projections." Hydrology and Earth System Sciences Discussions 12, no. 12 (December 4, 2015): 12649–701. http://dx.doi.org/10.5194/hessd-12-12649-2015.

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Abstract. This paper proposes a methodology for estimating the transient probability distribution of yearly hydrological variables conditional to an ensemble of projections built from multiple general circulation models (GCMs), multiple statistical downscaling methods (SDMs) and multiple hydrological models (HMs). The methodology is based on the quasi-ergodic analysis of variance (QE-ANOVA) framework that allows quantifying the contributions of the different sources of total uncertainty, by critically taking account of large-scale internal variability stemming from the transient evolution of multiple GCM runs, and of small-scale internal variability derived from multiple realizations of stochastic SDMs. The QE-ANOVA framework was initially developed for long-term climate averages and is here extended jointly to (1) yearly anomalies and (2) low flow variables. It is applied to better understand possible transient futures of both winter and summer low flows for two snow-influenced catchments in the southern French Alps. The analysis takes advantage of a very large dataset of transient hydrological projections that combines in a comprehensive way 11 runs from 4 different GCMs, 3 SDMs with 10 stochastic realizations each, as well as 6 diverse HMs. The change signal is a decrease in yearly low flows of around −20 % in 2065, except for the most elevated catchment in winter where low flows barely decrease. This signal is largely masked by both large- and small-scale internal variability, even in 2065. The time of emergence of the change signal on 30 year low-flow averages is however around 2035, i.e. for time slices starting in 2020. The most striking result is that a large part of the total uncertainty – and a higher one than that due to the GCMs – stems from the difference in HM responses. An analysis of the origin of this substantial divergence in HM responses for both catchments and in both seasons suggests that both evapotranspiration and snowpack components of HMs should be carefully checked for their robustness in a changed climate in order to provide reliable outputs for informing water resource adaptation strategies.

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Prough, D. S., A. T. Rogers, S. A. Mills, A. R. Cordell, D. A. Stump, and C. Taylor. "HIERARCHY OF FACTORS DETERMINING CEREBRAL BLOOD FLOW DURING HYPOTHERMIC CARDIOPULMONARY BYPASS." Anesthesiology 71, Supplement (September 1989): A39. http://dx.doi.org/10.1097/00000542-198909001-00039.

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Lévesque, Jean-Pierre, and Ingrid G. Winkler. "Hierarchy of immature hematopoietic cells related to blood flow and niche." Current Opinion in Hematology 18, no. 4 (July 2011): 220–25. http://dx.doi.org/10.1097/moh.0b013e3283475fe7.

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Kim, Kyung-Man. "Hierarchy of Scientific Consensus and the Flow of Dissensus Over Time." Philosophy of the Social Sciences 26, no. 1 (March 1996): 3–25. http://dx.doi.org/10.1177/004839319602600101.

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Slater, Jared M., Thomas A. Orszulak, and David J. Cook. "Distribution and hierarchy of regional blood flow during hypothermic cardiopulmonary bypass." Annals of Thoracic Surgery 72, no. 2 (August 2001): 542–47. http://dx.doi.org/10.1016/s0003-4975(01)02778-3.

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Luo, Jianxi, and Christopher L. Magee. "Detecting evolving patterns of self-organizing networks by flow hierarchy measurement." Complexity 16, no. 6 (January 25, 2011): 53–61. http://dx.doi.org/10.1002/cplx.20368.

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GENG, XIANGUO, and DONG GONG. "QUASI-PERIODIC SOLUTIONS OF THE DISCRETE mKdV HIERARCHY." International Journal of Geometric Methods in Modern Physics 10, no. 03 (January 10, 2013): 1250094. http://dx.doi.org/10.1142/s0219887812500946.

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On the basis of the theory of algebraic curves, the continuous flow related to the discrete mKdV hierarchy is straightened using the Abel–Jacobi coordinates. The meromorphic function and the Baker–Akhiezer function are introduced on the hyperelliptic curve. Quasi-periodic solutions of the discrete mKdV hierarchy are constructed with the help of the asymptotic properties and the algebro-geometric characters of the meromorphic function and the hyperelliptic curve.

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Blaizot, Jean-Paul. "Renormalization group flow equations with full momentum dependence." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 369, no. 1946 (July 13, 2011): 2735–58. http://dx.doi.org/10.1098/rsta.2011.0071.

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After a short elementary introduction to the exact renormalization group for the effective action, I discuss a particular truncation of the hierarchy of flow equations that allows for the determination of the full momentum of the n -point functions. Applications are then briefly presented, to critical O ( N ) models, to Bose–Einstein condensation and to finite-temperature field theory.

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Pursley, W. C. "The Calibration of Flowmeters." Measurement and Control 19, no. 5 (June 1986): 37–45. http://dx.doi.org/10.1177/002029408601900504.

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The paper presents an account of all the main methods in current use for the calibration of liquid and gas flowmeters both in the laboratory and in the field. Also included is a description of the traceability hierarchy for flow measurement in the United Kingdom and the paper ends with an estimation of the calibration accuracies which might be expected at various levels in the traceability hierarchy.

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McManamay, Ryan A., Brandon K. Peoples, Donald J. Orth, Charles A. Dolloff, and David C. Matthews. "Isolating causal pathways between flow and fish in the regulated river hierarchy." Canadian Journal of Fisheries and Aquatic Sciences 72, no. 11 (November 2015): 1731–48. http://dx.doi.org/10.1139/cjfas-2015-0227.

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Unregulated river systems are organized in a hierarchy in which large-scale factors (i.e., landscape and segment scales) influence local habitats (i.e., reach, meso-, and microhabitat scales), and both differentially exert selective pressures on biota. Dams, however, create discontinua in these processes and change the hierarchical structure. We examined the relative roles of hydrology and other instream factors, within a hierarchical landscape context, in organizing fish communities in regulated and unregulated tributaries to the Upper Tennessee River, USA. We used multivariate regression trees to identify factors that partition fish assemblages based on trait similarities, irrespective of spatial scale. We then used classical path analysis and structural equation modeling to evaluate the most plausible hierarchical causal structure of specific trait-based community components, given the data. Both statistical approaches suggested that river regulation affects stream fishes through a variety of reach-scale variables, not always through hydrology itself. Although we observed different changes in flow, temperature, and biotic responses according to regulation types, the most predominant path in which dam regulation affected biota was via temperature alterations. Diversion dams had the strongest effects on fish assemblages. Diversion dams reduced flow magnitudes, leading to declines in fish richness but increased temperatures, leading to lower abundances in equilibrium species and nest guarders. Peaking and run-of-river dams increased flow variability, leading to lower abundances in nest-guarding fishes. Flow displayed direct relationships with biotic responses; however, results indicated that changes in temperature and substrate had equal, if not stronger, effects on fish assemblage composition. The strength and nature of relationships depended on whether flow metrics were standardized for river size. We suggest that restoration efforts in regulated rivers focus on improving flow conditions in conjunction with temperature and substrate restoration.

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Wang, Zhangjun, Xiaoman Zhou, and Zhongquan Fang. "Assessment of the resilience of urban tourism flow network structure based on the impact of COVID-19: A case of Chongqing." Smart Tourism 3, no. 2 (September 17, 2022): 14. http://dx.doi.org/10.54517/st.v3i2.2142.

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<p>Based on the change data of network comments of tourist attractions in the central urban area of Chongqing from 2019 to 2021, the urban tourism flow network of Chongqing before and after the epidemic was constructed in stages based on the gravity model. And from the three dimensions of resistance, resilience and adaptability, the six measurement indicators of network load, stability, growth, hierarchy, matching and transmission are evaluated. The results show that: 1) Although the comprehensive indicator of network load of urban tourism flow in Chongqing is seriously impacted by the COVID-19 pandemic, the network structure of tourism flow has obvious resilience in the indicators of stability and growth. 2) COVID-19 helps to force the optimization of tourism flow network structure. The hierarchy of the urban tourism flow network structure in Chongqing tends to be flat, and the indicator of assortative shows obvious heterogeneity characteristics. 3) Transmission is a weak link in the network structure of urban tourism flow in Chongqing, which needs to be further optimized.</p><div><p> </p></div>

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Pau, George S. H., Ann S. Almgren, John B. Bell, and Michael J. Lijewski. "A parallel second-order adaptive mesh algorithm for incompressible flow in porous media." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 367, no. 1907 (November 28, 2009): 4633–54. http://dx.doi.org/10.1098/rsta.2009.0160.

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In this paper, we present a second-order accurate adaptive algorithm for solving multi-phase, incompressible flow in porous media. We assume a multi-phase form of Darcy’s law with relative permeabilities given as a function of the phase saturation. The remaining equations express conservation of mass for the fluid constituents. In this setting, the total velocity, defined to be the sum of the phase velocities, is divergence free. The basic integration method is based on a total-velocity splitting approach in which we solve a second-order elliptic pressure equation to obtain a total velocity. This total velocity is then used to recast component conservation equations as nonlinear hyperbolic equations. Our approach to adaptive refinement uses a nested hierarchy of logically rectangular grids with simultaneous refinement of the grids in both space and time. The integration algorithm on the grid hierarchy is a recursive procedure in which coarse grids are advanced in time, fine grids are advanced multiple steps to reach the same time as the coarse grids and the data at different levels are then synchronized. The single-grid algorithm is described briefly, but the emphasis here is on the time-stepping procedure for the adaptive hierarchy. Numerical examples are presented to demonstrate the algorithm’s accuracy and convergence properties and to illustrate the behaviour of the method.

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SHIN, D. G., and J. LEONE. "AM/AG MODEL: A HIERARCHICAL SOCIAL SYSTEM METAPHOR FOR DISTRIBUTED PROBLEM SOLVING." International Journal of Pattern Recognition and Artificial Intelligence 04, no. 03 (September 1990): 473–87. http://dx.doi.org/10.1142/s0218001490000289.

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This work explores a distributed problem solving (DPS) approach, namely the AM/AG (Amplification/Aggregation) model. The AM/AG model is a hierarchic social system metaphor for DPS based on Mintzberg’s model of organizations. At the core of the model are information flow mechanisms, namely, amplification and aggregation. Amplification is a process of decomposing a given task, called an agenda, into a set of subtasks with magnified degree of specificity and distributing them to multiple processing units downward in the hierarchy. Aggregation is a process of combining the results reported from multiple processing units into a unified view, called a resolution, and promoting the conclusion upward in the hierarchy. Amplification is discussed in detail. A set of generative rules is introduced. Each rule specifies a set of actions for transforming an input agenda into other forms with higher specificity. The proposed model can be used to account for the memory recall process which makes associations between vast amounts of related concepts, sorts out the combined results, and promotes the most plausible ones. An example of memory recall is used to illustrate the model.

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