Related papers: Slope Gap Distributions of Veech Surfaces
The slope variety of a graph is an algebraic set whose points correspond to drawings of a graph. A complement-reducible graph (or cograph) is a graph without an induced four-vertex path. We construct a bijection between the zeroes of the…
Surface roughness becomes relevant if typical length scales of the system are comparable to the scale of the variations as it is the case in microfluidic setups. Here, an apparent boundary slip is often detected which can have its origin in…
Network theory and inverse modeling are two standard tools of applied physics, whose combination is needed when studying the dynamical organization of spatially distributed systems from indirect measurements. However, the associated…
While the zero-drift first arrival position (FAP) channel exhibits a Cauchy-distributed lateral displacement, nonzero drift in practical systems introduces advective transport that regularizes this singular limit. This letter characterizes…
This paper provides a prescription for the turbulent viscosity in rotating shear flows for use e.g. in geophysical and astrophysical contexts. This prescription is the result of the detailed analysis of the experimental data obtained in…
We study dispersion properties of linear surface gravity waves propagating in an arbitrary direction atop a current profile of depth-varying magnitude using a piecewise linear approximation, and develop a robust numerical framework for…
The primary data which determine the evolution of glaciation are the bedrock elevation and the surface mass balance. From this data, which we assume is defined over a fixed land region, the glacier's geometry solves a free boundary problem…
Snow slab avalanches are among the most dangerous natural hazards in mountain areas. Recent progress in numerical modelling, field measurements, and large-scale fracture experiments has renewed interest in shear-failure interpretations of…
In this work we study the degree distribution, the maximum vertex and edge flow in non-uniform random Delaunay triangulations when geodesic routing is used. We also investigate the vertex and edge flow in Erd\"os-Renyi random graphs,…
The original investigation of Lamb (1932, {\S}349) for the effect of viscosity on monochromatic surface waves is extended to account for second-order Stokes surface waves on deep water in the presence of surface tension. This extension is…
This paper consists in discussing some issues on generic local classification of typical singularities of $2D$ piecewise smooth vector fields when the switching set is an algebraic variety. The main focus is to obtain classification results…
We consider a square expanding with constant speed seen from an observer moving away with constant acceleration and study the distribution of angles between rays from the observer towards the lattice points in the square. We prove the…
We extend the statistical field-theoretical framework of rough surface contact mechanics to characterize the interfacial gap between an elastic half-space and a randomly rough surface incorporating exponential repulsion. Building upon a…
A translation surface in the Heisenberg group is constructed as the product of two planar curves. We classify a type of such surfaces with vanishing intrinsic curvature by analyzing the determinant of their Gauss map
Statistical mechanics of infinite avalanches is studied in the framework of nonequilibrium random-field Ising model. Critical behavior of the model on a random graph (dilute Bethe lattice) is analyzed in detail. We show that sites with a…
We study the spectral statistics for quantized skew translations on the torus, which are ergodic but not mixing for irrational parameters. It is shown explicitly that in this case the level--spacing distribution and other common spectral…
Complex analytical structure of Stokes wave for two-dimensional potential flow of the ideal incompressible fluid with free surface and infinite depth is analyzed. Stokes wave is the fully nonlinear periodic gravity wave propagating with the…
Equilibrium and non-equilibrium growth phenomena, e.g., surface growth, generically yields self-affine distributions. Analysis of statistical properties of these distributions appears essential in understanding statistical mechanics of…
Superhydrophobic surfaces demonstrate promising potential for skin friction reduction in naval and hydrodynamic applications. Recent developments of superhydrophobic surfaces aiming for scalable applications use random distribution of…
We consider flow directions on the translation surfaces formed from double $(2n+1)$-gons, and give a sufficient condition in terms of a natural gcd algorithm for a direction to be hyperbolic in the sense that it is the fixed direction for…