Related papers: Mean Area of Self-Avoiding Loops
We study the averaged mean curvature flow, also called the volume preserving mean curvature flow, in the particular setting of axisymmetric surfaces embedded in R^3 satisfying periodic boundary conditions. We establish analytic…
Evaluating the propagator by the usual time-sliced manner, we use it to compute the second virial coefficient of an anyon gas interacting through the repulsive potential of the form $g/r^2 (g > 0)$. All the cusps for the unpolarized…
We present the synchronized unsteady wall pressure measurements performed at the circumference of a full scale 35 m circular chimney submitted to natural wind. The atmospheric turbulent boundary layer generates a turbulence intensity of 15…
In this work, we consider the area non-increasing map between manifolds with positive curvature. By exploring the strong maximum principle along the graphical mean curvature flow, we show that an area non-increasing map between certain…
At low densities, when radiation of an accreting gas is dynamically unimportant, quasi-spherical non-radiative accretion flow is formed around a compact object. We show that the density of the flow is n\propto r^{-1/2}. The gas compression…
Assuming self-similarity of the first kind, we get three possible values p=1/2, 1, 3/2 for the exponent describing the density profile, rho r^{-p}, of a non-radiative (and hence quasi-spherical) accretion flow. The high and low p cases are…
We perform Monte Carlo simulations to determine the average excluded area $<A_{ex}>$ of randomly oriented squares, randomly oriented widthless sticks and aligned squares in two dimensions. We find significant differences between our results…
The self-gravitating instability of a compressible-inviscid fluid cylinder immersed into a self-gravitating tenuous medium of negligible motion is developed. The stability criterion is derived based on the linear perturbation technique.…
This paper studies the 1-loop approximation for a massless spin-1/2 field on a flat four-dimensional Euclidean background bounded by two concentric 3-spheres, when non-local boundary conditions of the spectral type are imposed. The use of…
See http://www.youtube.com/watch?v=izbGXdjvK_I for a YouTube video showing part of the results in this paper.We will consider surfaces whose mean curvature at a point is a linear function of the square of the distance from that point to the…
In this paper, we investigate the volume-prserving mean curvature flow starting from a tube (of nonconstant radius) over a compact closed domain of a reflective submanifold in a symmetric space. We prove that the tubeness is preserved along…
Anomalously strong finite-size effects have been observed for the mean square radius of gyration $R^2_K$ of Gaussian random polygons with a fixed knot $K$ as a function of the number $N$ of polygonal nodes. Through computer simulations with…
The universal asymptotic amplitude ratio between the gyration radius and the hydrodynamic radius of self-avoiding walks is estimated by high-resolution Monte Carlo simulations. By studying chains of length of up to $N = 2^{25} \approx 34…
The linear response of two-dimensional amorphous elastic bodies to an external delta force is determined in analogy with recent experiments on granular aggregates. For the generated forces, stress and displacement fields, we find strong…
We calculate various Wilson loop averages in a pure $SU(N)$-gauge theory on a two-dimensional sphere, in the large $N$ limit. The results can be expressed through the density of rows in the most probable Young tableau. They are valid in…
We report on an observation of propagating compression waves in a quasi-two-dimensional monolayer of apolar granular rods fluidized by an upflow of air. The collective wave speed is an order of magnitude faster than the speed of the…
Werner's conformally invariant family of measures on self-avoiding loops on Riemann surfaces is determined by a single measure $\mu_0$ on self-avoiding loops in ${\mathbb C} \setminus\{0\}$ which surround $0$. Our first major objective is…
We consider the inverse mean curvature flow in smooth Riemannian manifolds of the form $([R_{0},\infty)\times S^n,\bar{g})$ with metric $\bar{g}=dr^2+{\vartheta}^2(r){\sigma}$ and non-positive radial sectional curvature. We prove, that for…
In this article, we examine complete, mean-convex self-expanders for the mean curvature flow whose ends have decaying principal curvatures. We prove a Liouville-type theorem associated to this class of self-expanders. As an application, we…
We study the asymptotic behavior of the motion of an ideal incompressible fluid in a perforated domain. The porous medium is composed of inclusions of size $\varepsilon$ separated by distances $d_\varepsilon$ and the fluid fills the…