The shape of a figure-eight under the curve shortening flow.
Matthew A. Grayson (1989)
Inventiones mathematicae
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Matthew A. Grayson (1989)
Inventiones mathematicae
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P. Gordon, M. Frankel, G. Sivashinsky (2010)
Mathematical Modelling of Natural Phenomena
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The paper is concerned with an extension of the classical relation between the flame speed and the curvature-flow stretch, valid only for high Lewis numbers (diffusively stable flames). At low Lewis numbers the corresponding flame-flow system suffers short-wavelength instability, making the associated initial value problem ill-posed. In this study the difficulty is resolved by incorporation of higher-order effects. As a result one ends up with a reduced model based on a coupled system...
Ekhaus, Michael, Seppäläinen, Timo (1996)
Annales Academiae Scientiarum Fennicae. Mathematica
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A.I. Lobanov, A.V. Nikolaev, T.K. Starozhilova (2011)
Mathematical Modelling of Natural Phenomena
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Blood clotting system (BCS) modelling is an important issue with a plenty of applications in medicine and biophysics. The BCS main function is to form a localized clot at the site of injury preventing blood loss. Mutual influence of fibrin clot consisting mainly of fibrin polymer gel and blood flow is an important factor for BCS to function properly. The process of fibrin polymer mesh formation has not adequately been described by current mathematical models. That is why it is not possible...
Mayer, Uwe F. (1997)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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Horňák, Ivan, Přikryl, Jan
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Despite their deficiencies, continuous second-order traffic flow models are still commonly used to derive discrete-time models that help traffic engineers to model and predict traffic oflow behaviour on highways. We brie fly overview the development of traffic flow theory based on continuous flow-density models of Lighthill-Whitham-Richards (LWR) type, that lead to the second-order model of Aw-Rascle. We will then concentrate on widely-adopted discrete approximation to the LWR model...
Fredrik Johansson Viklund, Alan Sola, Amanda Turner (2012)
Annales de l'I.H.P. Probabilités et statistiques
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We consider a variation of the standard Hastings–Levitov model HL(0), in which growth is anisotropic. Two natural scaling limits are established and we give precise descriptions of the effects of the anisotropy. We show that the limit shapes can be realised as Loewner hulls and that the evolution of harmonic measure on the cluster boundary can be described by the solution to a deterministic ordinary differential equation related to the Loewner equation. We also characterise the stochastic...
Neustupa, Tomáš
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The paper deals with analysis of mathematical model of incompressible viscous nonstationary flow through a plane cascade of profiles. We formulate the nonstationary problem and construct a solution by means of semidiscretization in time (Rothe's method).
Mohamed Kayid, Salman Izadkhah, Dalal ALmufarrej (2016)
Applications of Mathematics
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By considering a covariate random variable in the ordinary proportional mean residual life (PMRL) model, we introduce and study a general model, taking more situations into account with respect to the ordinary PMRL model. We investigate how stochastic structures of the proposed model are affected by the stochastic properties of the baseline and the mixing variables in the model. Several characterizations and preservation properties of the new model under different stochastic orders and...
Nick Verheul, Jan Viebahn, Daan Crommelin (2017)
Mathematics of Climate and Weather Forecasting
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In this study we investigate a covariate-based stochastic approach to parameterize unresolved turbulent processes within a standard model of the idealised, wind-driven ocean circulation. We focus on vertical instead of horizontal coarse-graining, such that we avoid the subtle difficulties of horizontal coarsegraining. The corresponding eddy forcing is uniquely defined and has a clear physical interpretation related to baroclinic instability.We propose to emulate the baroclinic eddy forcing...
Peter Knabner, Jean E. Roberts (2014)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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We consider a model for flow in a porous medium with a fracture in which the flow in the fracture is governed by the Darcy−Forchheimerlaw while that in the surrounding matrix is governed by Darcy’s law. We give an appropriate mixed, variational formulation and show existence and uniqueness of the solution. To show existence we give an analogous formulation for the model in which the Darcy−Forchheimerlaw is the governing equation throughout the domain. We show existence and uniqueness...