49 citations · 80 across the 17 of their papers we have counts for
20 papers
Elastic BB knots are multifold circles
Philipp Reiter, Heiko von der Mosel
We study elastic knots obtained by minimizing the bending energy of a unit loop together with a small multiple of ropelength. We assume a generalized Fáry-Milnor inequality on the…
Nonlinear elasticity with vanishing nonlocal self-repulsion
Stefan Krömer, Philipp Reiter
We prove that that for nonlinear elastic energies with strong enough energetic control of the outer distortion of admissible deformations, almost everywhere global invertibility as…
Flow states and heat transport in Rayleigh--Bénard convection with different sidewall boundary conditions
Philipp Reiter, Xuan Zhang, Olga Shiskina
This work addresses the effects of different thermal sidewall boundary conditions on the formation of flow states and heat transport in two- and three-dimensional Rayleigh--Bénard…
Knots with equal bridge index and braid index
Yuanan Diao, Claus Ernst, Philipp Reiter
In this paper we are interested in BB knots, namely knots and links where the bridge index equals the braid index. Supported by observations from experiments, it is conjectured tha…
Symmetric elastic knots
Alexandra Gilsbach, Philipp Reiter, Heiko von der Mosel
Minimizing the bending energy within knot classes leads to the concept of elastic knots which has been initiated in [von der Mosel, Asymptot. Anal. 1998]. Motivated by numerical ex…
Scale-invariant tangent-point energies for knots
Simon Blatt, Philipp Reiter, Armin Schikorra +1
We investigate minimizers and critical points for scale-invariant tangent-point energies of closed curves. We show that a) minimizing sequences in ambient isotopy…
Crossover of the relative heat transport contributions of plume ejecting and impacting zones in turbulent Rayleigh-Bénard convection
Philipp Reiter, Olga Shishkina, Detlef Lohse +1
Turbulent thermal convection is characterized by the formation of large-scale structures and strong spatial inhomogeneity. This work addresses the relative heat transport contribut…
Universal properties of penetrative turbulent Rayleigh--Bénard convection in cold water near
Qi Wang, Philipp Reiter, Detlef Lohse +1
Penetrative turbulence, which occurs in a convectively unstable fluid layer and penetrates into an adjacent, originally stably stratified layer, is numerically and theoretically an…
Generation of zonal flows in convective systems by travelling thermal waves
Philipp Reiter, Xuan Zhang, Rodion Stepanov +1
This work addresses the effect of travelling thermal waves applied at the fluid layer surface, on the formation of global flow structures in 2D and 3D convective systems. For a bro…
Data-driven identification of the spatio-temporal structure of turbulent flows by streaming Dynamic Mode Decomposition
Rui Yang, Xuan Zhang, Philipp Reiter +3
Streaming Dynamic Mode Decomposition (sDMD) (Hemati et al., Phys. Fluids 26(2014)) is a low-storage version of Dynamic Mode Decomposition (DMD) (Schmid, J. Fluid Mech. 656 (2010)),…
Sobolev Gradients for the Möbius Energy
Philipp Reiter, Henrik Schumacher
Aiming at optimizing the shape of closed embedded curves within prescribed isotopy classes, we use a gradient-based approach to approximate stationary points of the Möbius energy.…
Numerical solution of a bending-torsion model for elastic rods
Sören Bartels, Philipp Reiter
Aiming at simulating elastic rods, we discretize a rod model based on a general theory of hyperelasticity for inextensible and unshearable rods. After reviewing this model and disc…
On O'hara knot energies I: Regularity for critical knots
Simon Blatt, Philipp Reiter, Armin Schikorra
We develop a regularity theory for extremal knots of scale invariant knot energies defined by J. O'hara in 1991. This class contains as a special case the Möbius energy. For the Mö…
Open and closed random walks with fixed edgelengths in
Jason Cantarella, Kyle Chapman, Philipp Reiter +1
In this paper, we consider fixed edgelength -step random walks in . We give an explicit construction for the closest closed equilateral random walk to almost any o…
Stability of a simple scheme for the approximation of elastic knots and self-avoiding inextensible curves
Sören Bartels, Philipp Reiter
We discuss a semi-implicit numerical scheme that allows for minimizing the bending energy of curves within certain isotopy classes. To this end we consider a weighted sum of the be…
The elastic trefoil is the twice covered circle
Henryk Gerlach, Philipp Reiter, Heiko von der Mosel
We investigate the elastic behavior of knotted loops of springy wire. To this end we minimize the classic bending energy together with a small multiple of…
Towards a regularity theory for integral Menger curvature
Simon Blatt, Philipp Reiter
We generalize the notion of integral Menger curvature introduced by Gonzalez and Maddocks by decoupling the powers in the integrand. This leads to a new two-parameter family of kno…
Regularity theory for tangent-point energies: The non-degenerate sub-critical case
Simon Blatt, Philipp Reiter
In this article we introduce and investigate a new two-parameter family of knot energies that contains the tangent-point energies. These energies are obtained by decou…
Hard analysis meets critical knots (Stationary points of the Moebius energy are smooth)
Simon Blatt, Philipp Reiter, Armin Schikorra
We prove that if a curve parametrized by arc length is a stationary point of the Moebius energy introduced by Jun O'Hara, then it is smooth whenever the Moebius energy is finite. O…
Stationary Points of O'Hara's Knot Energies
Simon Blatt, Philipp Reiter
In this article we study the regularity of stationary points of the knot energies introduced by O'Hara in the range . In a first step we prove that is …