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Artículos de revistas sobre el tema "Limit equilibrium"

Autor: Grafiati

Publicado: 4 de junio de 2021

Última modificación: 25 de julio de 2025

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1

Krahn, John. "The 2001 R.M. Hardy Lecture: The limits of limit equilibrium analyses." Canadian Geotechnical Journal 40, no. 3 (2003): 643–60. http://dx.doi.org/10.1139/t03-024.

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Limit equilibrium types of analysis have been in use in geotechnical engineering for a long time and are now used routinely in geotechnical engineering practice. Modern graphical software tools have made it possible to gain a much better understanding of the inner numerical details of the method. A closer look at the details reveals that the limit equilibrium method of slices has some serious limitations. The fundamental shortcoming of limit equilibrium methods, which only satisfy equations of statics, is that they do not consider strain and displacement compatibility. This limitation can be o

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2

Myerson, Roger B., та Philip J. Reny. "Perfect Conditional ε‐Equilibria of Multi‐Stage Games With Infinite Sets of Signals and Actions". Econometrica 88, № 2 (2020): 495–531. http://dx.doi.org/10.3982/ecta13426.

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We extend Kreps and Wilson's concept of sequential equilibrium to games with infinite sets of signals and actions. A strategy profile is a conditional ε‐equilibrium if, for any of a player's positive probability signal events, his conditional expected utility is within ε of the best that he can achieve by deviating. With topologies on action sets, a conditional ε‐equilibrium is full if strategies give every open set of actions positive probability. Such full conditional ε‐equilibria need not be subgame perfect, so we consider a non‐topological approach. Perfect conditional ε‐equilibria are def

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3

Huang, Jicai, Xiaojing Xia, Xinan Zhang, and Shigui Ruan. "Bifurcation of Codimension 3 in a Predator–Prey System of Leslie Type with Simplified Holling Type IV Functional Response." International Journal of Bifurcation and Chaos 26, no. 02 (2016): 1650034. http://dx.doi.org/10.1142/s0218127416500346.

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It was shown in [Li & Xiao, 2007] that in a predator–prey model of Leslie type with simplified Holling type IV functional response some complex bifurcations can occur simultaneously for some values of parameters, such as codimension 1 subcritical Hopf bifurcation and codimension 2 Bogdanov–Takens bifurcation. In this paper, we show that for the same model there exists a unique degenerate positive equilibrium which is a degenerate Bogdanov–Takens singularity (focus case) of codimension 3 for other values of parameters. We prove that the model exhibits degenerate focus type Bogdanov–Takens b

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4

Yu, H. S., R. Salgado, S. W. Sloan, and J. M. Kim. "Limit Analysis versus Limit Equilibrium for Slope Stability." Journal of Geotechnical and Geoenvironmental Engineering 124, no. 1 (1998): 1–11. http://dx.doi.org/10.1061/(asce)1090-0241(1998)124:1(1).

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5

Leshchinsky, Dov, H. S. Yu, R. Salgado, S. W. Sloan, and J. M. Kim. "Limit Analysis versus Limit Equilibrium for Slope Stability." Journal of Geotechnical and Geoenvironmental Engineering 125, no. 10 (1999): 914–18. http://dx.doi.org/10.1061/(asce)1090-0241(1999)125:10(914).

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6

Michel, Bernard. "Limit equilibrium of ice jams." Cold Regions Science and Technology 20, no. 2 (1992): 107–17. http://dx.doi.org/10.1016/0165-232x(92)90011-i.

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7

Chowdhury, Prabal Roy. "Limit-pricing as Bertrand equilibrium." Economic Theory 19, no. 4 (2002): 811–22. http://dx.doi.org/10.1007/s001990100171.

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8

Dai, Yanfei, and Yulin Zhao. "Hopf Cyclicity and Global Dynamics for a Predator–Prey System of Leslie Type with Simplified Holling Type IV Functional Response." International Journal of Bifurcation and Chaos 28, no. 13 (2018): 1850166. http://dx.doi.org/10.1142/s0218127418501663.

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This paper is concerned with a predator–prey model of Leslie type with simplified Holling type IV functional response, provided that it has either a unique nondegenerate positive equilibrium or three distinct positive equilibria. The type and stability of each equilibrium, Hopf cyclicity of each weak focus, and the number and distribution of limit cycles in the first quadrant are studied. It is shown that every equilibrium is not a center. If the system has a unique positive equilibrium which is a weak focus, then its order is at most [Formula: see text] and it has Hopf cyclicity [Formula: see

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9

Jiang, Jiao, and Yongli Song. "Stability and Bifurcation Analysis of a Delayed Leslie-Gower Predator-Prey System with Nonmonotonic Functional Response." Abstract and Applied Analysis 2013 (2013): 1–19. http://dx.doi.org/10.1155/2013/152459.

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A delayed Leslie-Gower predator-prey model with nonmonotonic functional response is studied. The existence and local stability of the positive equilibrium of the system with or without delay are completely determined in the parameter plane. Using the method of upper and lower solutions and monotone iterative scheme, a sufficient condition independent of delay for the global stability of the positive equilibrium is obtained. Hopf bifurcations induced by the ratio of the intrinsic growth rates of the predator and prey and by delay, respectively, are found. Employing the normal form theory, the d

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10

Enoki, Meiketsu, Norio Yagi, Ryuichi Yatabe, and Elzaburo Ichimoto. "Relation of Limit Equilibrium Method to Limit Analysis Method." Soils and Foundations 31, no. 4 (1991): 37–47. http://dx.doi.org/10.3208/sandf1972.31.4_37.

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11

Florig, Michael, and Jorge Rivera. "Walrasian equilibrium as limit of competitive equilibria without divisible goods." Journal of Mathematical Economics 84 (October 2019): 1–8. http://dx.doi.org/10.1016/j.jmateco.2019.05.001.

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12

Fudenberg, Drew, Giacomo Lanzani, and Philipp Strack. "Limit Points of Endogenous Misspecified Learning." Econometrica 89, no. 3 (2021): 1065–98. http://dx.doi.org/10.3982/ecta18508.

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We study how an agent learns from endogenous data when their prior belief is misspecified. We show that only uniform Berk–Nash equilibria can be long‐run outcomes, and that all uniformly strict Berk–Nash equilibria have an arbitrarily high probability of being the long‐run outcome for some initial beliefs. When the agent believes the outcome distribution is exogenous, every uniformly strict Berk–Nash equilibrium has positive probability of being the long‐run outcome for any initial belief. We generalize these results to settings where the agent observes a signal before acting.

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13

Renault, Jérôme, and Bruno Ziliotto. "Limit Equilibrium Payoffs in Stochastic Games." Mathematics of Operations Research 45, no. 3 (2020): 889–95. http://dx.doi.org/10.1287/moor.2019.1015.

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We study the limit of equilibrium payoffs, as the discount factor goes to one, in non-zero-sum stochastic games. We first show that the set of stationary equilibrium payoffs always converges. We then provide two-player examples in which the whole set of equilibrium payoffs diverges. The construction is robust to perturbations of the payoffs and to the introduction of normal-form correlation.

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14

Morel, Jim E., and Jeffery D. Densmore. "A two-component equilibrium-diffusion limit." Annals of Nuclear Energy 31, no. 17 (2004): 2049–57. http://dx.doi.org/10.1016/j.anucene.2004.07.011.

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15

Morel, Jim E., and Jeffery D. Densmore. "A two-component equilibrium-diffusion limit." Annals of Nuclear Energy 32, no. 2 (2005): 233–40. http://dx.doi.org/10.1016/j.anucene.2004.08.010.

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16

Beghian, L. E. "Thermostatic equilibrium in the classical limit." Il Nuovo Cimento B Series 11 107, no. 12 (1992): 1437–44. http://dx.doi.org/10.1007/bf02722854.

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17

Alexakis, Haris, and Nicos Makris. "Limit equilibrium analysis of masonry arches." Archive of Applied Mechanics 85, no. 9-10 (2014): 1363–81. http://dx.doi.org/10.1007/s00419-014-0963-6.

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18

Makarenkov, Oleg, and Lakmi Niwanthi Wadippuli Achchige. "Bifurcations of Finite-Time Stable Limit Cycles from Focus Boundary Equilibria in Impacting Systems, Filippov Systems, and Sweeping Processes." International Journal of Bifurcation and Chaos 28, no. 10 (2018): 1850126. http://dx.doi.org/10.1142/s0218127418501262.

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We establish a theorem on bifurcation of limit cycles from a focus boundary equilibrium of an impacting system, which is universally applicable to prove the bifurcation of limit cycles from focus boundary equilibria in other types of piecewise-smooth systems, such as Filippov systems and sweeping processes. Specifically, we assume that one of the subsystems of the piecewise-smooth system under consideration admits a focus equilibrium that lie on the switching manifold at the bifurcation value of the parameter. In each of the three cases, we derive a linearized system which is capable of conclu

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19

Fang, Lidong, Apala Majumdar, and Lei Zhang. "Surface, size and topological effects for some nematic equilibria on rectangular domains." Mathematics and Mechanics of Solids 25, no. 5 (2020): 1101–23. http://dx.doi.org/10.1177/1081286520902507.

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We study nematic equilibria on rectangular domains, in a reduced two-dimensional Landau–de Gennes framework. These reduced equilibria carry over to the three-dimensional framework at a special temperature. There is one essential model variable, [Formula: see text], which is a geometry-dependent and material-dependent variable. We compute the limiting profiles exactly in two distinguished limits: the [Formula: see text] 0 limit relevant for macroscopic domains and the [Formula: see text] limit relevant for nanoscale domains. The limiting profile has line defects near the shorter edges in the [F

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20

Liu, Weiping, Lina Hu, Yongxuan Yang, and Mingfu Fu. "Limit Support Pressure of Tunnel Face in Multi-Layer Soils Below River Considering Water Pressure." Open Geosciences 10, no. 1 (2018): 932–39. http://dx.doi.org/10.1515/geo-2018-0074.

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AbstractThis paper presents a method to determine the limit support pressure of tunnel face in multi-layer soils below river considering the water pressure. The proposed method is based on the 3D Terzaghi earth pressure theory and the wedge theory considering the water pressure. The limit support pressures are investigated using the limit equilibrium method and compared to those calculated using a numerical method, such as FLAC3D. Four cases focusing different combinations of three layers are analyzed. The results obtained by the numerical method agree well with the predictions of the proposed

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21

Albouy, Alain, and Yanning Fu. "Relative equilibria of four identical satellites." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 465, no. 2109 (2009): 2633–45. http://dx.doi.org/10.1098/rspa.2009.0115.

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We consider the Newtonian 5-body problem in the plane, where four bodies have the same mass m , which is small compared with the mass M of the remaining body. We consider the (normalized) relative equilibria in this system and follow them to the limit when m / M →0. In some cases, two small bodies will coalesce at the limit. We call the other equilibria the relative equilibria of four separate identical satellites. We prove rigorously that there are only three such equilibria, all already known after the numerical researches by H. Salo and C. F. Yoder. Our main contribution is to prove that an

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22

Leshchinsky, Ben, and Spencer Ambauen. "Limit Equilibrium and Limit Analysis: Comparison of Benchmark Slope Stability Problems." Journal of Geotechnical and Geoenvironmental Engineering 141, no. 10 (2015): 04015043. http://dx.doi.org/10.1061/(asce)gt.1943-5606.0001347.

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23

SEKORA, MICHAEL D. "EXTENDING A HYBRID GODUNOV METHOD FOR RADIATION HYDRODYNAMICS TO MULTIPLE DIMENSIONS." International Journal of Modern Physics C 22, no. 05 (2011): 457–81. http://dx.doi.org/10.1142/s0129183111016373.

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This paper presents a hybrid Godunov method for three-dimensional radiation hydrodynamics. The multidimensional technique outlined in this paper is an extension of the one-dimensional method that was developed by Sekora and Stone 2009, 2010. The earlier one-dimensional technique was shown to preserve certain asymptotic limits and be uniformly well behaved from the photon free streaming (hyperbolic) limit through the weak equilibrium diffusion (parabolic) limit and to the strong equilibrium diffusion (hyperbolic) limit. This paper gives the algorithmic details for constructing a multidimensiona

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24

Lee, Joonkyum, and Bumsoo Kim. "Airline Booking Limit Competition Game Under Differentiated Fare Structure." Journal of Applied Business Research (JABR) 33, no. 3 (2017): 615–22. http://dx.doi.org/10.19030/jabr.v33i3.9950.

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We address a two-firm booking limit competition game in the airline industry. We assume aggregate common demand, and differentiated ticket fare and capacity, to make this study more realistic. A game theoretic approach is used to analyze the competition game. The optimal booking limits and the best response functions are derived. We show the existence of a pure Nash equilibrium and provide the closed-form equilibrium solution. The location of the Nash equilibrium depends on the relative magnitude of the ratios of the full and discount fares. We also show that the sum of the booking limits of t

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25

Kuehn, Christian, and Iacopo P. Longo. "Estimating rate-induced tipping via asymptotic series and a Melnikov-like method*." Nonlinearity 35, no. 5 (2022): 2559–87. http://dx.doi.org/10.1088/1361-6544/ac62dc.

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Abstract The paper deals with the study of rate-induced tipping in asymptotically autonomous scalar ordinary differential equations. We prove that, in such a tipping scenario, a solution which limits at a hyperbolic stable equilibrium of the past limit-problem loses uniform asymptotic stability and coincides with a solution which limits at a hyperbolic unstable equilibrium of the future limit-problem. We use asymptotic series to approximate such pairs of solutions and characterize the occurrence of a rate-induced tipping by using only solutions calculable on finite time intervals. Moreover, we

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26

Mundell, C., P. McCombie, C. Bailey, A. Heath, and P. Walker. "Limit-equilibrium assessment of drystone retaining structures." Proceedings of the Institution of Civil Engineers - Geotechnical Engineering 162, no. 4 (2009): 203–12. http://dx.doi.org/10.1680/geng.2009.162.4.203.

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27

Powrie, W. "Limit equilibrium analysis of embedded retaining walls." Géotechnique 46, no. 4 (1996): 709–23. http://dx.doi.org/10.1680/geot.1996.46.4.709.

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28

Bartoszek, K. "A Central Limit Theorem for punctuated equilibrium." Stochastic Models 36, no. 3 (2020): 473–517. http://dx.doi.org/10.1080/15326349.2020.1752242.

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29

GOETTLER, RONALD L., CHRISTINE A. PARLOUR, and UDAY RAJAN. "Equilibrium in a Dynamic Limit Order Market." Journal of Finance 60, no. 5 (2005): 2149–92. http://dx.doi.org/10.1111/j.1540-6261.2005.00795.x.

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30

Burakovsky, L., and L. P. Horwitz. "Galilean limit of equilibrium relativistic mass distribution." Journal of Physics A: Mathematical and General 27, no. 8 (1994): 2623–31. http://dx.doi.org/10.1088/0305-4470/27/8/003.

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31

Zhu, Jian-Zhou. "Continuum limit of electrostatic gyrokinetic absolute equilibrium." Physics of Plasmas 19, no. 6 (2012): 062304. http://dx.doi.org/10.1063/1.4725725.

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32

Lysova, S. S., T. A. Starikova, and Yu E. Zevatskii. "Limit of concentration constant of protolytic equilibrium." Russian Journal of General Chemistry 84, no. 8 (2014): 1634–35. http://dx.doi.org/10.1134/s1070363214080325.

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33

Ferguson, J. M., J. E. Morel, and R. Lowrie. "The equilibrium-diffusion limit for radiation hydrodynamics." Journal of Quantitative Spectroscopy and Radiative Transfer 202 (November 2017): 176–86. http://dx.doi.org/10.1016/j.jqsrt.2017.07.031.

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34

Hungr, O., and F. Amann. "Limit equilibrium of asymmetric laterally constrained rockslides." International Journal of Rock Mechanics and Mining Sciences 48, no. 5 (2011): 748–58. http://dx.doi.org/10.1016/j.ijrmms.2011.04.008.

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35

Renault, Jérôme, and Bruno Ziliotto. "Hidden stochastic games and limit equilibrium payoffs." Games and Economic Behavior 124 (November 2020): 122–39. http://dx.doi.org/10.1016/j.geb.2020.08.001.

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36

Zhu, D. Y., and C. F. Lee. "Explicit limit equilibrium solution for slope stability." International Journal for Numerical and Analytical Methods in Geomechanics 26, no. 15 (2002): 1573–90. http://dx.doi.org/10.1002/nag.260.

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37

LEE, SANG SOO. "Generalized critical-layer analysis of fully coupled resonant-triad interactions in boundary layers." Journal of Fluid Mechanics 347 (September 25, 1997): 71–103. http://dx.doi.org/10.1017/s0022112097006617.

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The critical-layer analysis of the nonlinear resonant-triad interaction by Goldstein & Lee (1992) is extended to include viscous effects. A generalized scaling which is valid both for the quasi-equilibrium and non-equilibrium critical-layer analyses in zero- or non-zero-pressure-gradient boundary layers is obtained. A system of partial differential equations which governs the fully coupled non-equilibrium critical-layer dynamics is obtained and it is solved by using a numerical method. Amplitude equations and their viscous limits are also presented. The parametric-resonance growth rate of

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38

Zhang, Chang Liang, Xiao Feng Lei, Tong Lu Li, and Ping Li. "Study of the General Form of 3D Limit Equilibrium." Advanced Materials Research 250-253 (May 2011): 1951–61. http://dx.doi.org/10.4028/www.scientific.net/amr.250-253.1951.

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On the base of the equilibrium of the whole force equilibrium, the whole moment equilibrium of the slope, and the force equilibrium of the differential column, this paper provides a general form of the 3D limit equilibrium which includes three equations. Through these equations and each assumption of the classical methods, their analytic forms can be gotten. Thus, not only the computation quantities of the classical method can be decreased greatly, but also the programming of them become very easy, and the computation efficiency also can be developed. At last, through the example in Zhang Xing

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39

Goncalves, Estefany, Ileana Herrera, Jake Alexander, et al. "The Upper Range Limit of Alien Plants Is Not in Equilibrium with Climate in the Andes of Central Chile." Plants 11, no. 18 (2022): 2345. http://dx.doi.org/10.3390/plants11182345.

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Alien plant species are colonizing high-elevation areas along roadsides. In this study, we evaluated whether the distributions of alien plants in the central Chilean mountains have reached climatic equilibrium (i.e., upper distribution limits consistent with their climatic requirements). First, we evaluated whether the upper elevational limits of alien plants changed between 2008 and 2018 based on the Mountain Invasion Research Network (MIREN) database. Second, we compared the observed upper elevational limits with the upper limits predicted by each species’ global climatic niche. On average a

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40

Wei, Bin. "Stability Analysis of Equilibrium Point and Limit Cycle of Two-Dimensional Nonlinear Dynamical Systems—A Tutorial." Applied Sciences 13, no. 2 (2023): 1136. http://dx.doi.org/10.3390/app13021136.

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The equilibrium state of a dynamical system can be divided into the equilibrium point and limit cycle. In this paper, the stability analysis of the equilibrium point and limit cycle of dynamical systems are presented through different and all possible approaches, and those approaches are compared as well. In particular, the author presented the stability analysis of the equilibrium point through phase plane approach, Lyapunov–LaSalle energy-based approach, and linearization approach, respectively, for two-dimensional nonlinear system, while the stability analysis of the limit cycle is analyzed

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41

Sengani, Fhatuwani, and Dhiren Allopi. "Accuracy of Two-Dimensional Limit Equilibrium Methods in Predicting Stability of Homogenous Road-Cut Slopes." Sustainability 14, no. 7 (2022): 3872. http://dx.doi.org/10.3390/su14073872.

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Although limit equilibrium methods are widely used by engineers and scientists in predicting the stability of homogenous slopes, their use has been demonstrated to present significant errors due to the violation of kinematic and static admissibility. The concern is often voiced regarding the accuracy of limit equilibrium methods (LEMs) solutions in predicting the stability of homogenous slopes. There are no exact limit equilibrium solutions or charts available that could be used to check the LEMs solutions. The present study has used the rigorous upper and lower bounds solutions of limit analy

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42

Kuang, Lin, Ai Zhong Lv, and Yu Zhou. "Slope Stability Analysis of Elastic Limit Equilibrium Method." Applied Mechanics and Materials 275-277 (January 2013): 1423–26. http://dx.doi.org/10.4028/www.scientific.net/amm.275-277.1423.

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Based on finite element analysis software ANSYS, slope stability analysis is carried out by Elastic limiting equilibrium method proposed in this paper. A series of sliding surface of the slope can be assumed firstly, and then stress field along the sliding surface is analyzed as the slope is in elastic state. The normal and tangential stresses along each sliding surface can be obtained, respectively. Then the safety factor for each slip surface can be calculated, the slip surface which the safety factor is smallest is the most dangerous sliding surface. This method is different from the previo

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43

Zhai, Yan, Wei Ya Xu, Chong Shi, Sheng Nian Wang, and Hai Long Zhang. "Application of Limit Equilibrium FEM Method to the Slope." Advanced Materials Research 926-930 (May 2014): 524–28. http://dx.doi.org/10.4028/www.scientific.net/amr.926-930.524.

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The limit equilibrium FEM method is a common method using the result of stresses fields obtained from numerical calculation to get resistant sliding force and driving sliding force on the dangerous sliding surface to analyze the stability of slope. The safety factor is the ratio of resistant sliding force to driving sliding force on the most dangerous sliding surface.When compares limit equilibrium FEM method with the rigid body limit equilibrium method, its applicability needs to be verified. Taking a project as an example, this work uses the two methods to analyze the stability of the slope.

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44

Alonso-Carrera, Jaime, and Timothy Kam. "ANATOMIZING INCOMPLETE-MARKETS SMALL OPEN ECONOMIES: POLICY TRADE-OFFS AND EQUILIBRIUM DETERMINACY." Macroeconomic Dynamics 20, no. 4 (2015): 1022–50. http://dx.doi.org/10.1017/s1365100514000728.

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We propose a simple incomplete-markets small-open-economy model that is amenable to analytical dissection of its policy-relevant mechanisms. In contrast to its complete-markets limit, the equilibrium real exchange rate is irreducible from the incomplete-markets equilibrium. Market incompleteness exacerbates the domestic-inflation and output-gap monetary-policy trade-off in two ways: its steepness and its resulting endogenous cost-push to the trade-off. The latter depends on an equilibrium combination of structural shocks and on agents' beliefs of future events. Thus, in comparison to its compl

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45

Qin, Wenjie, Xuewen Tan, Xiaotao Shi, Marco Tosato, and Xinzhi Liu. "Sliding Dynamics and Bifurcations in the Extended Nonsmooth Filippov Ecosystem." International Journal of Bifurcation and Chaos 31, no. 08 (2021): 2150119. http://dx.doi.org/10.1142/s0218127421501194.

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We propose a nonsmooth Filippov refuge ecosystem with a piecewise saturating response function and analyze its dynamics. We first investigate some key elements to our model which include the sliding segment, the sliding mode dynamics and the existence of equilibria which are classified into regular/virtual equilibrium, pseudo-equilibrium, boundary equilibrium and tangent point. In particular, we consider how the existence of the regular equilibrium and the pseudo-equilibrium are related. Then we study the stability of the standard periodic solution (limit cycle), the sliding periodic solutions

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46

Du, Chaoxiong, Yirong Liu, and Qi Zhang. "Limit Cycles in a Class of Quartic Kolmogorov Model with Three Positive Equilibrium Points." International Journal of Bifurcation and Chaos 25, no. 06 (2015): 1550080. http://dx.doi.org/10.1142/s0218127415500807.

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Limit cycle bifurcation problem of Kolmogorov model is interesting and significant both in theory and applications. In this paper, we will focus on investigating limit cycles for a class of quartic Kolmogorov model with three positive equilibrium points. Perturbed model can bifurcate three small limit cycles near (1, 2) or (2, 1) under a certain condition and can bifurcate one limit cycle near (1, 1). In addition, we have given some examples of simultaneous Hopf bifurcation and the structure of limit cycles bifurcated from three positive equilibrium points. The limit cycle bifurcation problem

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47

Huang, Chuan Zhi, Yong Hua Cao, and Wan He Sun. "Generalized Limit Equilibrium Method for Slope Stability Analysis." Applied Mechanics and Materials 170-173 (May 2012): 557–68. http://dx.doi.org/10.4028/www.scientific.net/amm.170-173.557.

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On the basis of the limit equilibrium method and the physical significance of Coulomb’s yield criteria, extremum conditions of yield functions is established, which will be the fundamental equations for the limit analysis of soil mass. Once the stress equation along a sliding surface is available, the normal stress on the sliding surface can be obtained, a new limit analysis method, generalized limit equilibrium method (GLEM), can be established. With the generalized limit equilibrium method, an analysis method to solve the problem of slope stability can be obtained without introducing any oth

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48

Pham, Ha T. V., and Delwyn G. Fredlund. "The application of dynamic programming to slope stability analysis." Canadian Geotechnical Journal 40, no. 4 (2003): 830–47. http://dx.doi.org/10.1139/t03-033.

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The applicability of the dynamic programming method to two-dimensional slope stability analyses is studied. The critical slip surface is defined as the slip surface that yields the minimum value of an optimal function. The only assumption regarding the shape of the critical slip surface is that the surface is an assemblage of linear segments. Stresses acting along the critical slip surface are computed using a finite element stress analysis. Assumptions associated with limit equilibrium methods of slices related to the shape of the critical slip surface and the relationship between interslice

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LI, CHUNBIAO, and J. C. SPROTT. "MULTISTABILITY IN A BUTTERFLY FLOW." International Journal of Bifurcation and Chaos 23, no. 12 (2013): 1350199. http://dx.doi.org/10.1142/s021812741350199x.

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A dynamical system with four quadratic nonlinearities is found to display a butterfly strange attractor. In a relatively large region of parameter space the system has coexisting point attractors and limit cycles. At some special parameter combinations, there are five coexisting attractors, where a limit cycle coexists with two equilibrium points and two strange attractors in different attractor basins. The basin boundaries have a symmetric fractal structure. In addition, the system has other multistable regimes where a pair of point attractors coexist with a single limit cycle or a symmetric

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50

GIRIMAJI, SHARATH S. "Pressure–strain correlation modelling of complex turbulent flows." Journal of Fluid Mechanics 422 (November 3, 2000): 91–123. http://dx.doi.org/10.1017/s0022112000001336.

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A methodology for deriving a pressure–strain correlation model with variable coefficients is developed. The methodology is based on two important premises: (i) the extreme states of turbulence – the rapid distortion and equilibrium limits – are more amenable to mathematically rigorous modelling because of significant simplifications not possible at other states; and (ii) the models of the extreme states collectively contain all of the relevant physics so that models for any intermediate state can be obtained by suitable interpolation. A pressure–strain model of the standard form is considered

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