Academic literature on the topic 'Crystalline Curvature Flows'
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Journal articles on the topic "Crystalline Curvature Flows"
Andrews, Ben. "Singularities in crystalline curvature flows." Asian Journal of Mathematics 6, no. 1 (2002): 101–22. http://dx.doi.org/10.4310/ajm.2002.v6.n1.a6.
Full textChambolle, Antonin, Massimiliano Morini, Matteo Novaga, and Marcello Ponsiglione. "Existence and uniqueness for anisotropic and crystalline mean curvature flows." Journal of the American Mathematical Society 32, no. 3 (April 11, 2019): 779–824. http://dx.doi.org/10.1090/jams/919.
Full textBELLETTINI, G., and M. NOVAGA. "APPROXIMATION AND COMPARISON FOR NONSMOOTH ANISOTROPIC MOTION BY MEAN CURVATURE IN ℝN." Mathematical Models and Methods in Applied Sciences 10, no. 01 (February 2000): 1–10. http://dx.doi.org/10.1142/s0218202500000021.
Full textNarumi, Takatsune, Jun Fukada, Satoru Kiryu, Shinji Toga, and Tomiichi Hasegawa. "Flow Induced Unstable Structure of Liquid Crystalline Polymer Solution in L-Shaped Slit Channels." Journal of Fluids Engineering 130, no. 8 (July 24, 2008). http://dx.doi.org/10.1115/1.2956604.
Full textDas, Rishita, Sean D. Peterson, and Maurizio Porfiri. "Stability of schooling patterns of a fish pair swimming against a flow." Flow 3 (2023). http://dx.doi.org/10.1017/flo.2023.25.
Full textDissertations / Theses on the topic "Crystalline Curvature Flows"
De, gennaro Daniele. "Flots de courbure cristalline et anisotrope, non linéaire et non local." Electronic Thesis or Diss., Université Paris sciences et lettres, 2024. http://www.theses.fr/2024UPSLD020.
Full textThis thesis is devoted to the study of geometric flows, with particular focus on the mean curvature flow. It is divided in two thematic parts. The first part, Part I, contains Chapters 2,3 and 4, and concerns convergence results for the minimizing movements scheme, which is a variational procedure extending Euler's implicit scheme to evolutions having a gradient flow-like structure. We implement this scheme for anisotropic or crystalline, nonlocal or inhomogeneous curvature flows, in linear and nonlinear instances, and study its convergence towards weak solutions to the flows. In Chapter 4 we also pair this study with a discrete-to-continuum limit. The second part, Part II, is devoted to the study of asymptotic behaviour of volume-preserving curvature flows both in the discrete- and continuus-in-time instances. The main technical tool employed is a new {L}ojasiewicz-Simon inequality suited to the study of these kind of evolutions
CHERMISI, MILENA. "Crystalline flow of planar partitions and a geometric approach for systems of PDEs." Doctoral thesis, Università degli Studi di Roma "Tor Vergata", 2006. http://hdl.handle.net/2108/202647.
Full textThe present thesis deals with two different subjects. Chapter 1 and Chapter 2 concern interfaces evolution problems in the plane. In Chapter 1 I consider the evolution of a polycrystalline material with three (or more) phases, in presence of for an even crystalline anisotropy ϕo whose one-sublevel set Fϕ := {ϕo ≤ 1} (the Frank diagram) is a regular polygon of n sides. The dual function ϕ : R2 → R defined by ϕ(ξ) := sup{ξ ·η : ϕo(η) ≤ 1} is crystalline too and Wϕ := {ϕ ≤ 1} is called the Wulff shape. I am particularly interested in the motion by crystalline curvature of special planar networks called elementary triods, namely a regular three-phase boundary given by the union of three Lipschitz curves, the interfaces, intersecting at a point called triple junction. Each interface is the union of a segment of finite length and a half-line, reproducing two consecutive sides of Wϕ. I analyze local and global existence and stability of the flow. I prove that there exists, locally in time, a unique stable regular flow starting from a stable regular initial datum. I show that if n, the number of sides of Wϕ, is a multiple of 6 then the flow is global and converge to a homothetic flow as t → +∞. The analysis of the long time behavior requires the study of the stability. Stability is the ingredient that ensures that no additional segments develop at the triple junction during the flow. In general, the flow may become unstable at a finite time: if this occurs and none of the segments desappears, it is possible to construct a regular flow at subsequent times by adding an infinitesimal segment (or even an arc with zero crystalline curvature) at the triple junction. I also show that a segment may desappear. In such a case, the Cahn-Hoffman vector field Nmin has a jump discontinuity and the triple junction translates along the remaining adjacent half-line at subsequent times. Each of these flows has the property that all crystalline curvatures remain bounded (even if a segment appears or disappears). I want to stress that Taylor already predicted the appearance of new edges from a triple junction. I also consider the crystalline curvature flow starting from a stable ϕ-regular partition formed by two adjacent elementary triods. I discuss some examples of collapsing situations that lead to changes of topology, such as for instance the collision of two triple junctions. These examples (as well as the local in time existence result) show one of the advantages of crystalline flows with respect, for instance, to the usual mean curvature flow: explicit computations can be performed to some extent, and in case of nonuniqueness, a comparison between the energies of different evolutions (difficult in the euclidean case) can be made. In Chapter 2 we introduce, using the theory of S1-valued functions of bounded variations, a class of energy functionals defined on partitions and we produce, through the first variation, a new model for the evolution of interfaces which partially extends the one in Chapter 1 and which consists of a free boundary problem defined on S1-valued functions of bounded variation. This model is related to the evolution of polycrystals where the Wulff shape is allowed to rotate. Assuming the local existence of the flow, we show convexity preserving and embeddedness preserving properties. The second subject of the thesis is considered in Chapter 3 where we aim to extend the level set method to systems of PDEs. The method we propose is consistent with the previous research pursued by Evans for the heat equation and by Giga and Sato for Hamilton-Jacobi equations. Our approach follows a geometric construction related to the notion of barriers introduced by De Giorgi. The main idea is to force a comparison principle between manifolds of different codimension and require each sub-level of a solution of the level set equation to be a barrier for the graph of a solution of the corresponding system. We apply the method for a class of systems of first order quasi-linear equations. We compute the level set equation associated with suitable first order systems of conservation laws, with the mean curvature flow of a manifold of arbitrary codimension and with systems of reaction-diffusion equations. Finally, we provide a level set equation associated with the parametric curvature flow of planar curves.
Book chapters on the topic "Crystalline Curvature Flows"
Arous, Gerard Ben, Allen Tannenbaum, and Ofer Zeitouni. "Crystalline Stochastic Systems and Curvature Driven Flows." In Mathematical Systems Theory in Biology, Communications, Computation, and Finance, 41–61. New York, NY: Springer New York, 2003. http://dx.doi.org/10.1007/978-0-387-21696-6_2.
Full textIshiwata, Tetsuya, and Shigetoshi Yazaki. "Convexity Phenomena Arising in an Area-Preserving Crystalline Curvature Flow." In Springer Proceedings in Mathematics & Statistics, 35–62. Singapore: Springer Nature Singapore, 2024. http://dx.doi.org/10.1007/978-981-97-0364-7_2.
Full textConference papers on the topic "Crystalline Curvature Flows"
Narumi, Takatsune, Jun Fukada, and Tomiichi Hasegawa. "Flow Induced Unstable Structure of Liquid Crystalline Polymer Solution in L-Shaped Slit Channels." In ASME/JSME 2007 5th Joint Fluids Engineering Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/fedsm2007-37169.
Full textISHIWATA, TETSUYA. "MOTION OF NON-CONVEX POLYGON BY CRYSTALLINE CURVATURE FLOW AND ITS GENERALIZATION." In Proceedings of the International Conference on Nonlinear Analysis. WORLD SCIENTIFIC, 2008. http://dx.doi.org/10.1142/9789812709257_0008.
Full textHIROTA, CHIAKI, ISHIWATA TETSUYA, and YAZAKI SHIGETOSHI. "NOTE ON THE ASYMPTOTIC BEHAVIOR OF SOLUTIONS TO AN ANISOTROPIC CRYSTALLINE CURVATURE FLOW." In Proceedings of the 2004 Swiss-Japanese Seminar. WORLD SCIENTIFIC, 2006. http://dx.doi.org/10.1142/9789812774170_0006.
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