42 research outputs found
Linear chaos for the Quick-Thinking-Driver model
The final publication is available at Springer via http://dx.doi.org/10.1007/s00233-015-9704-6In recent years, the topic of car-following has experimented an increased importance in traffic engineering and safety research. This has become a very interesting topic because of the development of driverless cars (Google driverless cars, http://en.wikipedia.org/wiki/Google_driverless_car).Driving models which describe the interaction between adjacent vehicles in the same lane have a big interest in simulation modeling, such as the Quick-Thinking-Driver model. A non-linear version of it can be given using the logistic map, and then chaos appears. We show that an infinite-dimensional version of the linear model presents a chaotic behaviour using the same approach as for studying chaos of death models of cell growth.The authors were supported by a grant from the FPU program of MEC and MEC Project MTM2013-47093-P.Conejero, JA.; Murillo Arcila, M.; Seoane-SepĂșlveda, JB. (2016). Linear chaos for the Quick-Thinking-Driver model. Semigroup Forum. 92(2):486-493. https://doi.org/10.1007/s00233-015-9704-6S486493922Aroza, J., Peris, A.: Chaotic behaviour of birth-and-death models with proliferation. J. Differ. Equ. Appl. 18(4), 647â655 (2012)Banasiak, J., Lachowicz, M.: Chaos for a class of linear kinetic models. C. R. Acad. Sci. Paris SĂ©rie II 329, 439â444 (2001)Banasiak, J., Lachowicz, M.: Topological chaos for birth-and-death-type models with proliferation. Math. Models Methods Appl. Sci. 12(6), 755â775 (2002)Banasiak, J., Lachowicz, M., MoszyĆski, M.: Topological chaos: when topology meets medicine. Appl. Math. Lett. 16(3), 303â308 (2003)Banasiak, J., MoszyĆski, M.: A generalization of DeschâSchappacherâWebb criteria for chaos. Discret. Contin. Dyn. Syst. 12(5), 959â972 (2005)Banasiak, J., MoszyĆski, M.: Dynamics of birth-and-death processes with proliferationâstability and chaos. Discret. Contin. Dyn. 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Massachusetts Institute of Technology. Cambridge (1973)CNN (2014) Driverless car tech gets serious at CES. http://edition.cnn.com/2014/01/09/tech/innovation/self-driving-cars-ces/ . Accessed 7 Apr 2014Conejero, J.A., Rodenas, F., Trujillo, M.: Chaos for the hyperbolic bioheat equation. Discret. Contin. Dyn. Syst. 35(2), 653â668 (2015)DARPA Grand Challenge. http://en.wikipedia.org/wiki/2005_DARPA_Grand_Challenge#2005_Grand_Challengede Laubenfels, R., Emamirad, H., Protopopescu, V.: Linear chaos and approximation. J. Approx. Theory 105(1), 176â187 (2000)Desch, W., Schappacher, W., Webb, G.F.: Hypercyclic and chaotic semigroups of linear operators. Ergod. Theory Dyn. Syst. 17(4), 793â819 (1997)El Mourchid, S.: The imaginary point spectrum and hypercyclicity. Semigroup Forum 73(2), 313â316 (2006)El Mourchid, S., Metafune, G., Rhandi, A., Voigt, J.: On the chaotic behaviour of size structured cell populations. J. Math. Anal. 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Universitext. Springer, London (2011)Herman, R., Montroll, E.W., Potts, R.B., Rothery, R.W.: Traffic dynamics: analysis of stability in car following. Op. Res. 7, 86â106 (1959)Helly, W.: Simulation of Bottleneckes in Single-Lane Traffic Flow. Research Laboratories, General Motors. Elsevier, New York (1953)Li, T.: Nonlinear dynamics of traffic jams. Phys. D 207(1â2), 41â51 (2005)Lo, S.C., Cho, H.J.: Chaos and control of discrete dynamic traffic model. J. Franklin Inst. 342(7), 839â851 (2005)MartĂnez-GimĂ©nez, F., Oprocha, P., Peris, A.: Distributional chaos for backward shifts. J. Math. Anal. Appl. 351(2), 607â615 (2009)Pipes, L.A.: An operational analysis of traffic dynamics. J. Appl. Phys. 24, 274â281 (1953
Galaxy Formation Theory
We review the current theory of how galaxies form within the cosmological
framework provided by the cold dark matter paradigm for structure formation.
Beginning with the pre-galactic evolution of baryonic material we describe the
analytical and numerical understanding of how baryons condense into galaxies,
what determines the structure of those galaxies and how internal and external
processes (including star formation, merging, active galactic nuclei etc.)
determine their gross properties and evolution. Throughout, we highlight
successes and failings of current galaxy formation theory. We include a review
of computational implementations of galaxy formation theory and assess their
ability to provide reliable modelling of this complex phenomenon. We finish
with a discussion of several "hot topics" in contemporary galaxy formation
theory and assess future directions for this field.Comment: 58 pages, to appear in Physics Reports. This version includes minor
corrections and a handful of additional reference
Coastal Upwelling Supplies Oxygen-Depleted Water to the Columbia River Estuary
Low dissolved oxygen (DO) is a common feature of many estuarine and shallow-water
environments, and is often attributed to anthropogenic nutrient enrichment from
terrestrial-fluvial pathways. However, recent events in the U.S. Pacific
Northwest have highlighted that wind-forced upwelling can cause naturally
occurring low DO water to move onto the continental shelf, leading to
mortalities of benthic fish and invertebrates. Coastal estuaries in the Pacific
Northwest are strongly linked to ocean forcings, and here we report observations
on the spatial and temporal patterns of oxygen concentration in the Columbia
River estuary. Hydrographic measurements were made from transect (spatial
survey) or anchor station (temporal survey) deployments over a variety of wind
stresses and tidal states during the upwelling seasons of 2006 through 2008.
During this period, biologically stressful levels of dissolved oxygen were
observed to enter the Columbia River estuary from oceanic sources, with minimum
values close to the hypoxic threshold of 2.0 mg Lâ1. Riverine
water was consistently normoxic. Upwelling wind stress controlled the timing and
magnitude of low DO events, while tidal-modulated estuarine circulation patterns
influenced the spatial extent and duration of exposure to low DO water. Strong
upwelling during neap tides produced the largest impact on the estuary. The
observed oxygen concentrations likely had deleterious behavioral and
physiological consequences for migrating juvenile salmon and benthic crabs.
Based on a wind-forced supply mechanism, low DO events are probably common to
the Columbia River and other regional estuaries and if conditions on the shelf
deteriorate further, as observations and models predict, Pacific Northwest
estuarine habitats could experience a decrease in environmental quality