DSpace Collection:
https://dspace.lboro.ac.uk/2134/90
20170121T13:22:02Z

Complete commutative subalgebras in polynomial poisson algebras: a proof of the MischenkoFomenko conjecture
https://dspace.lboro.ac.uk/2134/23653
Title: Complete commutative subalgebras in polynomial poisson algebras: a proof of the MischenkoFomenko conjecture
Authors: Bolsinov, Alexey V.
Abstract: The Mishchenko–Fomenko conjecture says that for each real or
complex finitedimensional Lie algebra g there exists a complete set of commuting
polynomials on its dual space g*. In terms of the theory of integrable
Hamiltonian systems this means that the dual space g* endowed with the standard
Lie–Poisson bracket admits polynomial integrable Hamiltonian systems.
This conjecture was proved by S. T. Sadetov in 2003. Following his idea, we
give an explicit geometric construction for commuting polynomials on g* and
consider some examples.
Description: This paper is a revised version of: BOLSINOV, A.V., 2006. Complete commutative families of polynomials in PoissonLie algebras: a proof of the MischenkoFomenko conjecture. Trudy seminara po vektornomu i tenzornomu analizu (ISSN: 03734870), 26, pp.87109.
20160101T00:00:00Z

Dynamics of a thin film flowing down a heated wall with finite thermal diffusivity
https://dspace.lboro.ac.uk/2134/23495
Title: Dynamics of a thin film flowing down a heated wall with finite thermal diffusivity
Authors: Dallaston, Michael C.; Tseluiko, Dmitri; Kalliadasis, Serafim
Abstract: Consider the dynamics of a thin film flowing down a heated substrate. The substrate
heating generates a temperature distribution on the free surface, which in turn induces
surfacetension gradients and corresponding thermocapillary stresses that affect the free
surface and therefore the fluid flow. We study here the effect of finite substrate thermal
diffusivity on the film dynamics. Linear stability analysis of the full NavierStokes and
heat transport equations indicates if the substrate diffusivity is sufficiently small, the film
becomes unstable at a finite wavelength and at a Reynolds number smaller than that
predicted in the longwavelength limit. This property is captured in a reducedorder system
of equations derived using a weightedresidual integralboundarylayer method. This
reducedorder model is also used to compute the bifurcation diagrams of solution branches
connecting the trivial flat film to travelingwaves including solitary pulses. The effect of finite
diffusivity is to separate a simultaneous Hopftranscritical bifurcation into its individual
component bifurcations. The appropriate Hopf bifurcation then connects only to the solution
branch of negativehump pulses, with wave speed less than the linear wave speed, while
the branch of positivesinglehump pulses merges with the branch of positivetwohump
pulses at a supercritical Reynolds number. In the regime where finitewavelength instability
occurs, there exists a Hopfbifurcation pair connected by a branch of periodic solutions,
whose period cannot be increased indefinitely. Numerical simulation of the reducedorder
system shows the development of a train of coherent structures, each of which resembles
a stationary positivehump pulse, and, in the regime of finitewavelength instability,
wavelength selection and saturation to periodic traveling waves.
20160101T00:00:00Z

Estimates of local biodiversity change over time stand up to scrutiny
https://dspace.lboro.ac.uk/2134/23313
Title: Estimates of local biodiversity change over time stand up to scrutiny
Authors: Vellend, Mark; Dornelas, Maria; Baeten, Lander; Beausejour, Robin; Brown, Carissa D.; De Frenne, Pieter; Elmendorf, Sarah C.; Gotelli, Nicholas J.; Moyes, Faye; MyersSmith, Isla H.; Magurran, Anne E.; McGill, Brian; Shimadzu, Hideyasu; Sievers, Caya
Abstract: We present new data and analyses revealing fundamental flaws in a critique of two
recent metaanalyses of localscale temporal biodiversity change. First, the conclusion that shortterm time series lead to biased estimates of longterm change was based on two errors in the simulations used to support it. Second, the conclusion of negative relationships between temporal biodiversity change and study duration was entirely dependent on unrealistic model
assumptions, the use of a subset of data, and inclusion of one outlier data point in one study. Third, the finding of a decline in local biodiversity, after eliminating postdisturbance studies, is not robust to alternative analyses on the original dataset, and is absent in a larger, updated
dataset. Finally, the undebatable point – noted in both original papers – that studies in the ecological literature are geographically biased, was used to cast doubt on the conclusion that, outside of areas converted to croplands or asphalt, the distribution of biodiversity trends is
centered approximately on zero. Future studies may modify conclusions, but at present, alternative conclusions based on the geographicbias argument rely on speculation. In sum, the critique raises points of uncertainty typical of all ecological studies, but does not provide an
evidencebased alternative interpretation.
Description: This paper was accepted for publication in the journal Ecology and the definitive published version is available at http://dx.doi.org/10.1002/ecy.1660
20170101T00:00:00Z

Decay of correlation for random intermittent maps
https://dspace.lboro.ac.uk/2134/23279
Title: Decay of correlation for random intermittent maps
Authors: Bahsoun, Wael; Bose, Christopher; Duan, Yuejiao
Abstract: We study a class of random transformations built over finitely many intermittent maps sharing a common indifferent fixed point. Using a Youngtower technique, we show that the map with the fastest relaxation rate dominates the asymptotics. In particular, we prove that the rate of correlation decay for the annealed dynamics of the random map is the same as the sharp rate of correlation decay for the map with the fastest relaxation rate.
Description: This article was published in the journal Nonlinearity [© IOP Publishing Ltd & London Mathematical Society ] and the definitive version is available at: http:dx.doi.org/10.1088/09517715/27/7/1543
20140101T00:00:00Z