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- Disc-stacking model (2)
- Irregular pattern (2)
- Quasi-symmetry (2)
- Asymptotic analysis (1)
- Bio-inspired micro-swimming devices (1)
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- Combinatorial optimization (1)
- Convergence (1)
- Extensional flow (1)
- Fibonacci (1)
- Genus 2 (1)
- Grid unfolding (1)
- Heat kernels (1)
- Hydrodynamics (1)
- Linear refinement (1)
- Network seeding (1)
- Nonstationary 3-D Stokes equation (1)
- Orthogonal polyhedron (1)
- Phyllotaxis (1)
- Phyllotaxis; Fibonacci (1)
- Riemannian approximation (1)
- Spreading phenomenon (1)
- Stress diffusion (1)
- SubRiemannian geometry (1)
- Subelliptic PDE (1)
- Swimming models (1)
- Viscoelastic creeping flow (1)
Articles 1 - 12 of 12
Full-Text Articles in Physical Sciences and Mathematics
Fibonacci Or Quasi-Symmetric Phyllotaxis. Part Ii: Botanical Observations, Stéphane Douady, Christophe Golé
Fibonacci Or Quasi-Symmetric Phyllotaxis. Part Ii: Botanical Observations, Stéphane Douady, Christophe Golé
Mathematics Sciences: Faculty Publications
Historically, the study of phyllotaxis was greatly helped by the simple description of botanical patterns by only two integer numbers, namely the number of helices (parastichies) in each direction tiling the plant stem. The use of parastichy num- bers reduced the complexity of the study and created a proliferation of generaliza- tions, among others the simple geometric model of lattices. Unfortunately, these simple descriptive method runs into difficulties when dealing with patterns pre- senting transitions or irregularities. Here, we propose several ways of addressing the imperfections of botanical reality. Using ontogenetic analysis, which follows the step-by-step genesis of the pattern, …
Fibonacci Or Quasi-Symmetric Phyllotaxis. Part I: Why?, Christophe Golé, Jacques Dumais, Stéphane Douady
Fibonacci Or Quasi-Symmetric Phyllotaxis. Part I: Why?, Christophe Golé, Jacques Dumais, Stéphane Douady
Mathematics Sciences: Faculty Publications
The study of phyllotaxis has focused on seeking explanations for the occurrence of consecutive Fibonacci numbers in the number of helices paving the stems of plants in the two opposite directions. Using the disk-accretion model, first introduced by Schwendener and justified by modern biological studies, we observe two dis- tinct types of solutions: the classical Fibonacci-like ones, and also more irregular configurations exhibiting nearly equal number of helices in a quasi-square pack- ing, the quasi-symmetric ones, which are a generalization of the whorled patterns. Defining new geometric tools allowing to work with irregular patterns and local transitions, we provide simple …
Unfolding Genus-2 Orthogonal Polyhedra With Linear Refinement, Mirela Damian, Erik Demaine, Robin Flatland, Joseph O'Rourke
Unfolding Genus-2 Orthogonal Polyhedra With Linear Refinement, Mirela Damian, Erik Demaine, Robin Flatland, Joseph O'Rourke
Mathematics Sciences: Faculty Publications
We show that every orthogonal polyhedron of genus g ≤ 2 can be unfolded without overlap while using only a linear number of orthogonal cuts (parallel to the polyhedron edges). This is the first result on unfolding general orthogonal polyhedra beyond genus- 0. Our unfolding algorithm relies on the existence of at most 2 special leaves in what we call the “unfolding tree” (which ties back to the genus), so unfolding polyhedra of genus 3 and beyond requires new techniques.
Smoothness Of Subriemannian Isometries, Luca Capogna, Enrico Le Donne
Smoothness Of Subriemannian Isometries, Luca Capogna, Enrico Le Donne
Mathematics Sciences: Faculty Publications
We show that the group of isometries (i.e., distance-preserving homeomorphisms) of an equiregular subRiemannian manifold is a finite-dimensional Lie group of smooth transformations. The proof is based on a new PDE argument, in the spirit of harmonic coordinates, establishing that in an arbitrary subRiemannian manifold there exists an open dense subset where all isometries are smooth.
Splines In Geometry And Topology, Julianna Tymoczko
Splines In Geometry And Topology, Julianna Tymoczko
Mathematics Sciences: Faculty Publications
This survey paper describes the role of splines in geometry and topology, emphasizing both similarities and differences from the classical treatment of splines. The exposition is non-technical and contains many examples, with references to more thorough treatments of the subject.
Regularity For Subelliptic Pde Through Uniform Estimates In Multi-Scale Geometries, Luca Capogna, Giovanna Citti
Regularity For Subelliptic Pde Through Uniform Estimates In Multi-Scale Geometries, Luca Capogna, Giovanna Citti
Mathematics Sciences: Faculty Publications
We aim at reviewing and extending a number of recent results addressing stability of certain geometric and analytic estimates in the Riemannian approximation of subRiemannian structures. In particular we extend the recent work of the the authors with Rea (Math Ann 357(3):1175–1198, 2013) and Manfredini (Anal Geom Metric Spaces 1:255–275, 2013) concerning stability of doubling properties, Poincare’ inequalities, Gaussian estimates on heat kernels and Schauder estimates from the Carnot group setting to the general case of Hörmander vector fields.
A Bayesian Method For Cluster Detection With Application To Five Cancer Sites In Puget Sound, Albert Y. Kim, Jon Wakefield
A Bayesian Method For Cluster Detection With Application To Five Cancer Sites In Puget Sound, Albert Y. Kim, Jon Wakefield
Mathematics Sciences: Faculty Publications
Cluster detection is an important public health endeavor and in this paper we describe and apply a recently developed Bayesian method. Commonly-used approaches are based on so-called scan statistics and suffer from a number of difficulties including how to choose a level of significance and how to deal with the possibility of multiple clusters. The basis of our model is to partition the study region into a set of areas which are either “null” or “non-null”, the latter corresponding to clusters (excess risk) or anti-clusters (reduced risk). We demonstrate the Bayesian method and compare with a popular existing approach, using …
Generalized Splines On Arbitrary Graphs, Simcha Gilbert, Julianna Tymoczko, Shira Viel
Generalized Splines On Arbitrary Graphs, Simcha Gilbert, Julianna Tymoczko, Shira Viel
Mathematics Sciences: Faculty Publications
Let G be a graph whose edges are labeled by ideals of a commutative ring. We introduce a generalized spline, which is a vertex labeling of G by elements of the ring so that the difference between the labels of any two adjacent vertices lies in the corresponding edge ideal. Generalized splines arise naturally in combinatorics (algebraic splines of Billera and others) and in algebraic topology (certain equivariant cohomology rings, described by Goresky, Kottwitz, and MacPherson, among others). The central question of this paper asks when an arbitrary edge-labeled graph has nontrivial generalized splines. The answer is “always”, and we …
Sticky Seeding In Discrete-Time Reversible-Threshold Networks, Gwen Spencer
Sticky Seeding In Discrete-Time Reversible-Threshold Networks, Gwen Spencer
Mathematics Sciences: Faculty Publications
When nodes can repeatedly update their behavior (as in agent-based models from computational social science or repeated-game play settings) the problem of optimal network seeding becomes very complex. For a popular spreading-phenomena model of binary-behavior updating based on thresholds of adoption among neighbors, we consider several planning problems in the design of Sticky Interventions: when adoption decisions are reversible, the planner aims to find a Seed Set where temporary intervention leads to long-term behavior change. We prove that completely converting a network at minimum cost is Ω(ln(OP T ))-hard to approximate and that maximizing conversion subject to a budget is …
Equilibrium Circulation And Stress Distribution In Viscoelastic Creeping Flow, Joseph A. Biello, Becca Thomases
Equilibrium Circulation And Stress Distribution In Viscoelastic Creeping Flow, Joseph A. Biello, Becca Thomases
Mathematics Sciences: Faculty Publications
An analytic, asymptotic approximation of the nonlinear steady-state equations for viscoelastic creeping flow, modeled by the Oldroyd-B equations with polymer stress diffusion, is derived. Near the extensional stagnation point the flow stretches and aligns polymers along the outgoing streamlines of the stagnation point resulting in a stress-island, or birefringent strand. The polymer stress diffusion coefficient is used, both as an asymptotic parameter and a regularization parameter. The structure of the singular part of the polymer stress tensor is a Gaussian aligned with the incoming streamline of the stagnation point a smoothed δ-distribution whose width is proportional to the square-root of …
A Coin Vibrational Motor Swimming At Low Reynolds Number, Alice C. Quillen, Hesam Askari, Douglas H. Kelley, Tamar Friedmann, Patrick W. Oakes
A Coin Vibrational Motor Swimming At Low Reynolds Number, Alice C. Quillen, Hesam Askari, Douglas H. Kelley, Tamar Friedmann, Patrick W. Oakes
Mathematics Sciences: Faculty Publications
Low-cost coin vibrational motors, used in haptic feedback, exhibit rotational internal motion inside a rigid case. Because the motor case motion exhibits rotational symmetry, when placed into a fluid such as glycerin, the motor does not swim even though its oscillatory motions induce steady streaming in the fluid. However, a piece of rubber foam stuck to the curved case and giving the motor neutral buoyancy also breaks the rotational symmetry allowing it to swim. We measured a 1 cm diameter coin vibrational motor swimming in glycerin at a speed of a body length in 3 seconds or at 3 mm/s. …
A Generalization Of Turaev’S Virtual String Cobracket And Self-Intersections Of Virtual Strings, Patricia Cahn
A Generalization Of Turaev’S Virtual String Cobracket And Self-Intersections Of Virtual Strings, Patricia Cahn
Mathematics Sciences: Faculty Publications
Previously we defined an operation µ that generalizes Turaev’s cobracket for loops on a surface. We showed that, in contrast to the cobracket, this operation gives a formula for the minimum number of self-intersections of a loop in a given free homotopy class. In this paper we consider the corresponding question for virtual strings, and conjecture that µ gives a formula for the minimum number of self-intersection points of a virtual string in a given virtual homotopy class. To support the conjecture, we show that µ gives a bound on the minimal self-intersection number of a virtual string which is …