Browsing by Subject "BOUNDARY"

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  • Gyllenberg, Mats; Jiang, Jifa; Niu, Lei (2019)
    In the recent paper [E. C. Balreira, S. Elaydi, and R. Luis, J. Differ. Equ. Appl. 23 (2017), pp. 2037-2071], Balreira, Elaydi and Luis established a good criterion for competitive mappings to have a globally asymptotically stable interior fixed point by a geometric approach. This criterion can be applied to three dimensional Kolmogorov competitive mappings on a monotone region with a carrying simplex whose planar fixed points are saddles but globally asymptotically stable on their positive coordinate planes. For three dimensional Ricker models, they found mild conditions on parameters such that the criterion can be applied to. Observing that Balreira, Elaydi and Luis' discussion is still valid for the monotone region with piecewise smooth boundary, we prove in this note that the interior fixed point of three dimensional Kolmogorov competitive mappings is globally asymptotically stable if they admit a carrying simplex and three planar fixed points which are saddles but globally asymptotically stable on their positive coordinate planes. This result is much easier to apply in the application.
  • Casteras, Jean-Baptiste; Holopainen, Ilkka; Ripoll, Jaime B. (2020)
    We prove the existence of solutions to the asymptotic Plateau problem for hypersurfaces of prescribed mean curvature in Cartan-Hadamard manifolds N. More precisely, given a suitable subset L of the asymptotic boundary of N and a suitable function H on N, we are able to construct a set of locally finite perimeter whose boundary has generalized mean curvature H provided that N satisfies the so-called strict convexity condition and that its sectional curvatures are bounded from above by a negative constant. We also obtain a multiplicity result in low dimensions.
  • Bakharev, F. L.; Taskinen, J. (2017)
    We study the spectral linear elasticity problem in an unbounded periodic waveguide, which consists of a sequence of identical bounded cells connected by thin ligaments of diameter of order h > 0. The essential spectrum of the problem is known to have band-gap structure. We derive asymptotic formulas for the position of the spectral bands and gaps, as h -> 0.
  • Strganac, Christopher; Salminen, Johanna; Jacobs, Louis L.; Polcyn, Michael J.; Ferguson, Kurt M.; Mateus, Octavio; Schulp, Anne S.; Morais, Maria Luisa; Tavares, Tatiana da Silva; Goncalves, Antonio Olimpio (2014)
  • Gyllenberg, Mats; Jiang, Jifa; Niu, Lei (2020)
    We study the occurrence of chaos in the Atkinson-Allen model of four competing species, which plays the role as a discrete-time Lotka-Volterra-type model. We show that in this model chaos can be generated by a cascade of quasiperiod-doubling bifurcations starting from a supercritical Neimark-Sacker bifurcation of the unique positive fixed point. The chaotic attractor is contained in a globally attracting invariant manifold of codimension one, known as the carrying simplex. Biologically, our study implies that the invasion attempts by an invader into a trimorphic population under Atkinson-Allen dynamics can lead to chaos.
  • Aikio, A. T.; Pitkanen, T.; Honkonen, I.; Palmroth, M.; Amm, O. (2013)
  • Plado, Juri; Ainsaar, Leho; Dmitrijeva, Marija; Poldsaar, Kairi; Ots, Siim; Pesonen, Lauri J.; Preeden, Ulla (2016)
    Magnetic susceptibility (MS), its frequency-dependence and anisotropy of the Middle Ordovician Dapingian and Darriwilian sedimentary sequence from three sites (Uuga, Testepere and Leetse) in the Pakri Peninsula, NW Estonia are analysed in combination with the mineralogical composition. The study is based on 463 cores drilled at intervals of a few centimetres to a maximum of about 1 m. All the samples show low and positive MS, which suggests the presence of small quantities of paraand/or ferromagnetic minerals. The stratigraphic units of the three studied sites have a similar along-section appearance, which provides a base for a composite curve. The relatively higher susceptibilities are carried by secondary Fe-Ti oxides (Toila Formation), goethite ooids (Kandle Formation) and ferrous dolomite (Pae Member), whereas paramagnetic minerals are mostly responsible for the rest of the sequence. Considering the dependence of MS on regressive transgressive cycles (high/low MS within deposits of regressive/transgressive parts of the cycles, respectively), the MS data do not agree with sedimentologically derived sea-level compilations. The measured changes in MS in the Pakri Peninsula outcrops correlate at certain characteristic levels with those deposited in the deeper part of the palaeobasin (Viki core), indicating that the post-depositional iron mobilization within the sediments took place at least at a regional level. Because of post-depositional reorganization of ferromagnetic carrier minerals, the MS values may, however, not be used as a detrital proxy.
  • Lumme, E.; Kazachenko, M. D.; Fisher, G. H.; Welsch, B. T.; Pomoell, J.; Kilpua, E.K.J. (2019)
    We study how the input-data cadence affects the photospheric energy and helicity injection estimates in eruptive NOAA Active Region 11158. We sample the novel 2.25-minute vector magnetogram and Dopplergram data from the Helioseismic and Magnetic Imager (HMI) instrument onboard the Solar Dynamics Observatory (SDO) spacecraft to create input datasets of variable cadences ranging from 2.25 minutes to 24 hours. We employ state-of-the-art data processing, velocity, and electric-field inversion methods for deriving estimates of the energy and helicity injections from these datasets. We find that the electric-field inversion methods that reproduce the observed magnetic-field evolution through the use of Faraday's law are more stable against variable cadence: the PDFI (PTD-Doppler-FLCT-Ideal, where PTD refers to Poloidal-Toroidal Decomposition, and FLCT to Fourier Local Correlation Tracking) electric-field inversion method produces consistent injection estimates for cadences from 2.25 minutes up to two hours, implying that the photospheric processes acting on time scales below two hours contribute little to the injections, or that they are below the sensitivity of the input data and the PDFI method. On other hand, the electric-field estimate derived from the output of DAVE4VM (Differential Affine Velocity Estimator for Vector Magnetograms), which does not fulfill Faraday's law exactly, produces significant variations in the energy and helicity injection estimates in the 2.25 minutes - two hours cadence range. We also present a third, novel DAVE4VM-based electric-field estimate, which corrects the poor inductivity of the raw DAVE4VM estimate. This method is less sensitive to the changes of cadence, but it still faces significant issues for the lowest of considered cadences (two hours). We find several potential problems in both PDFI- and DAVE4VM-based injection estimates and conclude that the quality of both should be surveyed further in controlled environments.
  • Fefferman, Charles; Ivanov, Sergei; Kurylev, Yaroslav; Lassas, Matti; Narayanan, Hariharan (2020)
    We study the geometric Whitney problem on how a Riemannian manifold (M, g) can be constructed to approximate a metric space (X, d(X)). This problem is closely related to manifold interpolation (or manifold reconstruction) where a smooth n-dimensional submanifold S subset of R-m, m > n needs to be constructed to approximate a point cloud in Rm. These questions are encountered in differential geometry, machine learning, and in many inverse problems encountered in applications. The determination of a Riemannian manifold includes the construction of its topology, differentiable structure, and metric. We give constructive solutions to the above problems. Moreover, we characterize the metric spaces that can be approximated, by Riemannian manifolds with bounded geometry: We give sufficient conditions to ensure that a metric space can be approximated, in the Gromov-Hausdorff or quasi-isometric sense, by a Riemannian manifold of a fixed dimension and with bounded diameter, sectional curvature, and injectivity radius. Also, we show that similar conditions, with modified values of parameters, are necessary. As an application of the main results, we give a new characterization of Alexandrov spaces with two-sided curvature bounds. Moreover, we characterize the subsets of Euclidean spaces that can be approximated in the Hausdorff metric by submanifolds of a fixed dimension and with bounded principal curvatures and normal injectivity radius. We develop algorithmic procedures that solve the geometric Whitney problem for a metric space and the manifold reconstruction problem in Euclidean space, and estimate the computational complexity of these procedures. The above interpolation problems are also studied for unbounded metric sets and manifolds. The results for Riemannian manifolds are based on a generalization of the Whitney embedding construction where approximative coordinate charts are embedded in R-m and interpolated to a smooth submanifold.
  • Rajala, Antti; Akkerman, Sanne (2019)
    In this paper, we have conducted a detailed analysis of video-records of a class fieldtrip to an outdoor environmental education center to examine how the activity and its material context were interpreted, negotiated and sometimes contested in dialogic interactions between the students, teacher and two environmental educators. The findings shed light into the varied ways in which the different interpretations during the fieldtrip produced the forest and its surroundings as the material context of the activity. The findings also show how hybrid forms of activity were produced when the different interpretations collided and merged in the dialogic interactions among the actors. The study challenges existing ways of conceptualizing and researching school fieldtrips which to date have often disregarded the negotiation of diverse interpretations that participants make of the ongoing activity and its contexts. More generally, the study opens new ground for dialogical research approaches on learning and education by showing how an explicit focus on disjunctures between different interpretations of activity can shed light into the dynamics of the moment-to-moment production of emergent material contexts of activity.
  • Niu, Lei; Ruiz-Herrera, Alfonso (2018)
    In this paper we show that the dynamical behavior in R-+(3) (first octant) of the classical Kolmogorov systems T(x(1), x(2), x(3)) = (x(1)F(1)(x), x(2)F(2)(x), x(3)F(3)(x)) of competitive type admitting a carrying simplex can be sometimes determined completely by the number of fixed points on the boundary and the local behavior around them. Roughly speaking, T has trivial dynamics (i.e. the omega limit set of any orbit is a connected set contained in the set of fixed points) provided T has exactly four hyperbolic nontrivial fixed points {p(1), p(2), p(3), p(4)} in partial derivative R-+(3) with {p(1), p(3)} local attractors on the carrying simplex and {p(2), p(4)} local repellers on the carrying simplex; and there exists a unique hyperbolic fixed point in IntR(+)(3). Our results are applied to some classical models including the Leslie-Gower models, Atkinson-Allen systems and Ricker maps.
  • Leugering, Günter; Nazarov, Sergei A.; Taskinen, Jari (2019)
    We develop and investigate radiation conditions at infinity for composite piezo-elastic waveguides. The approach is based on the Mandelstam radiation principle according to which the energy flux at infinity is directed away from the source and which implies constraints on the (sign of the) group velocities. On the other side, the Sommerfeld radiation condition implies limitations on the wave phase velocity and is, in fact, not applicable in the context of piezo-elastic wave guides. We analyze the passage to the limit when the piezo-electric moduli tend to zero in certain regions yielding purely elastic inclusions there. We provide a number of examples, e.g. elastic and acoustic waveguides as well as purely elastic insulating and conducting inclusions.