Related papers: Regular Polygonal Vortex Filament Evolution and Ex…
In 1959 Fejes T\'oth posed a conjecture that the sum of pairwise non-obtuse angles between $N$ unit vectors in $\mathbb S^d$ is maximized by periodically repeated elements of the standard orthonormal basis. We obtain new improved upper…
We study the long-time dynamics of hexagonal directional-solidification patterns in bulk samples of a transparent eutectic alloy using an optical method which permits real-time observation of the growth front. A slow dilatation of the…
In this paper we consider planar polygons with parallel opposite sides. This type of polygons can be regarded as discretizations of closed convex planar curves by taking tangent lines at samples with pairwise parallel tangents. For this…
We prove an elementary but somewhat unexpected result about projective embeddings of smooth varieties X whose cotangent bundles are numerically effective. Specifically, we show that the degree of X in any projective embedding must grow…
It is shown that, under some natural assumptions, the tensor product of differentially smooth algebras and the skew-polynomial rings over differentially smooth algebras are differentially smooth.
We show that the periodic orbit sums for 2-dimensional billiards satisfy an infinity of exact sum rules. We test such sum rules and demonstrate that they can be used to accelerate the convergence of cycle expansions for averages such as…
We estimate whether there is an embedding from one n-dimensional rectangle into another which expands every k-dimensional area. Our estimate is sharp up to a constant factor in each dimension.
In a wide variety of natural and laboratory magnetized plasmas, filaments appear as a result of interchange instability. These convective structures substantially enhance transport in the direction perpendicular to the magnetic field.…
We examine exponential sums of the form $\sum_{n \le X} w(n) e^{2\pi i\alpha n^k}$, for $k=1,2$, where $\alpha$ satisfies a generalized Diophantine approximation and where $w$ are different arithmetic functions that might be multiplicative,…
Despite decades of research, the question of whether solutions and melts of highly entangled polymers exhibit shear banding as their steady state response to a steadily imposed shear flow remains controversial. From a theoretical viewpoint,…
Using a simple model, we study the fluctuating dynamics of inextensible, semiflexible polar filaments interacting with active and directed force generating centres such as molecular motors. Taking into account the fact that the activity…
Using the theory of metaplectic forms,we study the asymptotic behavior of cubic exponential sums over the ring of Eisenstein integers. In the first part of the paper, some non-trivial estimates on average over arithmetic progressions are…
We discuss the expansions used in spin foam cosmology. We point out that already at the one vertex level arbitrarily complicated amplitudes contribute, and discuss the geometric asymptotics of the five simplest ones. We discuss what type of…
The propagation of electron beams carrying angular momentum in crystals is studied using a multislice approach for the model system Fe. It is found that the vortex beam is distorted strongly due to elastic scattering. Consequently, the…
We consider a viscous fluid with kinematic viscosity $\nu $ and initial data consisting of a smooth closed vortex filament with circulation $\Gamma $. We show that, for short enough time, the solution consists of a deformed Lamb-Oseen…
Based on a modified Anderson-Weiss approximation (N. Fatkullin, A. Gubaidullin, C. Mattea, S.Stapf, J. Chem. Phys. 137 (2012), 224907) an improved theory of proton spin solid echo in polymer melts is formulated, taking into account…
In this paper, we show that equiangular spirals (also known as logarithmic spirals) appear naturally in fluids going through sinks. We provide a simple mathematical model that explains the spiral forms in some natural formations. For this…
The square of the horizontal projected (rms) beam emittance is expressed as the sum of four nonnegative contributions, each described using the slice moments of the beam and possessing a natural interpretation in terms of the geometrical…
We have theoretically studied how the azimuthal phase structure of an electron vortex beam excites surface plasmons on metal particles of different geometries as observed in electron energy loss spectroscopy. To do so, we have developed a…
Vogt's theorem, concerning boundary angles of a convex arc with monotonic curvature (spiral arc), is taken as a starting point to establish basic properties of spirals. The theorem is expanded by removing requirements of convexity and…