scholarly journals Transition to Measure Synchronization in Coupled Hamiltonian Systems

2003 ◽  
Vol 17 (22n24) ◽  
pp. 4349-4354
Author(s):  
Xingang Wang ◽  
Gang Hu ◽  
Kai Hu ◽  
C.-H. Lai
Keyword(s):  
Random Walk ◽  
Hamiltonian Systems ◽  
Phase Difference ◽  
Phase Distribution ◽  
Phase Locking ◽  
Scaling Relationship ◽  
Measure Synchronization ◽  
Relationship Of ◽  
Synchronized Region

The transition to measure synchronization in two coupled φ4 equations are investigated numerically both for quasiperiodic and chaotic cases. Quantities like the bare energy and phase difference are employed to study the underlying behaviors during this process. For transition between quasiperiodic states, the distribution of phase difference tends to concentrate at large angles before measure synchronization, and is confined to within a certain range after measure synchronization. For transition between quasiperiodicity and chaos, phase locking is not achieved and a random-walk-like behavior of the phase difference is found in the measure synchronized region. The scaling relationship of the phase distribution and the behavior of the bare energy are also discussed.

scholarly journals Shifting the scaling relations of single-atom catalysts for facile methane activation by tuning the coordination number

2021 ◽  
Author(s):  
Changhyeok Choi ◽  
Sungho Yoon ◽  
Yousung Jung
Keyword(s):  
Transition State ◽  
Coordination Number ◽  
Active Sites ◽  
Methane Activation ◽  
Single Atom ◽  
Scaling Relations ◽  
Scaling Relationship ◽  
Relationship Of

The scaling relationship of methane activation via a radical-like transition state shifts toward a more reactive region with decreasing coordination number of the active sites.

scholarly journals Study on the measure synchronization in coupled Hamiltonian systems*

2004 ◽  
Vol 53 (12) ◽  
pp. 4098
Author(s):  
Chen Shao－Ying ◽  
Xu Hai－Bo ◽  
Wang Guang－Rui ◽  
Chen Shi－Ga ng
Keyword(s):  
Hamiltonian Systems ◽  
Measure Synchronization

scholarly journals Anomalous diffusion of random walk on random planar maps

2020 ◽  
Vol 178 (1-2) ◽  
pp. 567-611
Author(s):  
Ewain Gwynne ◽  
Tom Hutchcroft
Keyword(s):  
Random Walk ◽  
Universality Class ◽  
Simple Random Walk ◽  
Growth Exponent ◽  
Graph Distance ◽  
Link Type ◽  
Random Planar Map ◽  
Planar Maps ◽  
Relationship Of ◽  
The Given

Abstract We prove that the simple random walk on the uniform infinite planar triangulation (UIPT) typically travels graph distance at most $$n^{1/4 + o_n(1)}$$ n 1 / 4 + o n ( 1 ) in n units of time. Together with the complementary lower bound proven by Gwynne and Miller (2017) this shows that the typical graph distance displacement of the walk after n steps is $$n^{1/4 + o_n(1)}$$ n 1 / 4 + o n ( 1 ) , as conjectured by Benjamini and Curien (Geom Funct Anal 2(2):501–531, 2013. arXiv:1202.5454). More generally, we show that the simple random walks on a certain family of random planar maps in the $$\gamma $$ γ -Liouville quantum gravity (LQG) universality class for $$\gamma \in (0,2)$$ γ ∈ ( 0 , 2 ) —including spanning tree-weighted maps, bipolar-oriented maps, and mated-CRT maps—typically travels graph distance $$n^{1/d_\gamma + o_n(1)}$$ n 1 / d γ + o n ( 1 ) in n units of time, where $$d_\gamma $$ d γ is the growth exponent for the volume of a metric ball on the map, which was shown to exist and depend only on $$\gamma $$ γ by Ding and Gwynne (Commun Math Phys 374:1877–1934, 2018. arXiv:1807.01072). Since $$d_\gamma > 2$$ d γ > 2 , this shows that the simple random walk on each of these maps is subdiffusive. Our proofs are based on an embedding of the random planar maps under consideration into $${\mathbb {C}}$$ C wherein graph distance balls can be compared to Euclidean balls modulo subpolynomial errors. This embedding arises from a coupling of the given random planar map with a mated-CRT map together with the relationship of the latter map to SLE-decorated LQG.

Controlling Hamiltonian systems by using measure synchronization

2002 ◽  
Vol 298 (5-6) ◽  
pp. 383-387 ◽  
Author(s):  
Xingang Wang ◽  
Zhang Ying ◽  
Gang Hu
Keyword(s):  
Hamiltonian Systems ◽  
Measure Synchronization

The scale of it all: postcanine tooth size, the taxon-level effect, and the universality of Gould's scaling law

Paleobiology ◽  
2010 ◽  
Vol 36 (2) ◽  
pp. 188-203 ◽  
Author(s):  
Lynn E. Copes ◽  
Gary T. Schwartz
Keyword(s):  
Body Mass ◽  
Scaling Law ◽  
Small Sample ◽  
Tooth Size ◽  
Mathematical Methods ◽  
Scaling Relationship ◽  
Small Sample Sizes ◽  
Relationship Of ◽  
The Impact ◽  
Level Effect

In a seminal paper in 1975, Gould proposed that postcanine occlusal area (PCOA) should scale metabolically (0.75) with body mass across mammals. By regressing PCOA against skull length in a small sample of large-bodied herbivorous mammals, Gould provided some marginal support for this hypothesis, which he then extrapolated as a universal scaling law for Mammalia. Since then, many studies have sought to confirm this scaling relationship within a single order and have found equivocal support for Gould's assertion. In part, this may be related to the use of proxies for both PCOA and body mass, small sample sizes, or the influence of a “taxon-level effect,” rendering Gould's scaling “universal” problematic.Our goal was to test the universality of Gould's prediction and the impact of the taxon-level effect on regressions of tooth size on body mass in a large extant mammalian sample (683 species spanning 14 orders). We tested for the presence of two types of taxon-level effect that may influence the acceptance or rejection of hypothesized scaling coefficients. The hypotheses of both metabolic and isometric scaling can be rejected in Mammalia, but not in all sub-groups therein. The level of data aggregation also influences the interpretation of the scaling relationship. Because the scaling relationship of tooth size to body mass is highly dependent on both the taxonomic level of analysis and the mathematical methods used to organize the data, paleontologists attempting to retrodict body mass from fossilized dental remains must be aware of the effect that sample composition may have on their results.

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