Related papers: Effective equidistribution of shears and applicati…
Fourier series solutions to the deflection and magnification by a family of three-dimensional cusped two power-law ellipsoidal mass distributions are presented. The cusped two power-law ellipsoidal mass distributions are characterized by…
The radial distribution function is a characteristic geometric quantity of a point set in Euclidean space that reflects itself in the corresponding diffraction spectrum and related objects of physical interest. The underlying combinatorial…
Existence of shear horizontal (SH) surface waves in 2D-periodic phononic crystals with an asymmetric depth-dependent profile is theoretically reported. Examples of dispersion spectra with band gaps for subsonic and supersonic SH surface…
In this paper we discuss the variety of planar spiral segments and their applications in objects in both the real and artificial world. The discussed curves with monotonic curvature function are well-known in geometric modelling and…
One can represent Schwartz distributions with values in a vector bundle $E$ by smooth sections of $E$ with distributional coefficients. Moreover, any linear continuous operator which maps $E$-valued distributions to smooth sections of…
Sparse autoencoders (SAEs) have become a central tool for interpreting language models. However, two key SAE analyses that remain difficult to scale are (1) matching semantically similar features across multi-layers and (2) compressing…
We use a custom shear cell coupled to an optical microscope to investigate at the particle level the yielding transition in concentrated emulsions subjected to an oscillatory shear deformation. By performing experiments lasting thousands of…
We prove effective equidistribution of non-closed horocycles in the unit tangent bundle of infinite-volume geometrically finite hyperbolic surfaces.
We study the problem of moving a vertex in an unstructured mesh of triangular, quadrilateral, or tetrahedral elements to optimize the shapes of adjacent elements. We show that many such problems can be solved in linear time using…
We introduce a process, that we call "shearing", which for any given normal Loewner chain produces a normal Loewner chain made of shears automorphisms. As an application, and in stringent contrast to the one-dimensional case, we prove the…
Presented is a novel way to combine snapshot compressive imaging and lateral shearing interferometry in order to capture the spatio-spectral phase of an ultrashort laser pulse in a single shot. A deep unrolling algorithm is utilised for the…
Edge-preserving smoothing (EPS) can be formulated as minimizing an objective function that consists of data and prior terms. This global EPS approach shows better smoothing performance than a local one that typically has a form of weighted…
We study the dynamics of $SL_{2}(\mathbb{R})$ on the stratum of translation surfaces $\mathcal{H}(2)$. Especially, we obtain effective density theorems on $\mathcal{H}(2)$ for orbits of the upper triangular subgroup $P$ of…
We derive effective, parsimonious models from a heterogeneous second-gradient nonlinear elastic material taking into account chiral scale-size effects. Our classification of the effective equations depends on the hierarchy of four…
Shear viscosity is a dynamical property of fluid systems close to equilibrium, describing resistance to sheared flow. After reviewing the physics of viscosity and the reason it is usually difficult to compute, I discuss its importance…
We study the small scale distribution of the $L^2$-mass of eigenfunctions of the Laplacian on the the two-dimensional flat torus. Given an orthonormal basis of eigenfunctions, Lester and Rudnick showed the existence of a density one…
The focus of this thesis is the construction and analysis of efficient representations in nonlinear signal processing, and the applications of these structures to inverse problems in a variety of fields. The work is composed of three major…
We use a statistical-mechanical identity closely related to the familiar virial theorem, to derive unbiased estimators for spatial distribution functions of classical fluids. In particular, we obtain estimators for both the fluid density…
We formulate and solve a model problem of dispersion of dense granular materials in rapid shear flow down an incline. The effective dispersivity of the depth-averaged concentration of the dispersing powder is shown to vary as the P\'eclet…
We present a unified approach to the problems of reconstruction of large-scale structure distribution in the universe and determination of the underlying power spectrum. These have often been treated as two separate problems and different…