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Motivated by the use of degenerate Jacobi metrics for the study of brake orbits and homoclinics, we develop a Morse theory for geodesics in conformal metrics having conformal factors vanishing on a regular hypersurface of a Riemannian…
The phenomenon of negative refraction generally requires negative refractive indices or phase discontinuities, which can be realized using metamaterials or metasurfaces. Recent theories have proposed a novel mechanism for negative…
We present a simpler and more powerful version of the recently-discovered action principle for the motion of a spinless point particle in spacetimes with curvature and torsion. The surprising feature of the new principle is that an action…
We present a novel method of simulating wave effects in graphics using ray--based renderers with a new function: the Wave BSDF (Bidirectional Scattering Distribution Function). Reflections from neighboring surface patches represented by…
We prove that convex hypersurfaces in ${\mathbb R}^{n+1}$ contracting under the flow by any power $\alpha>\frac{1}{n+2}$ of the Gauss curvature converge (after rescaling to fixed volume) to a limit which is a smooth, uniformly convex…
This paper addresses an open problem recently posed by V. Kozlov: a rigorous proof of the non-integrability of the geodesic flow on the cubic surface $x y z=1$. We prove this is the case using the Morales-Ramis theorem and Kovacic…
We study geodesics flows on curved quantum Riemannian geometries using a recent formulation in terms of bimodule connections and completely positive maps. We complete this formalism with a canonical $*$ operation on noncommutative vector…
The method of Hamilton-Jacobi is used to obtain geodesics around non- Riemannian planar torsional defects.It is shown that by perturbation expansion in the Cartan torsion the geodesics obtained are parabolic curves along the plane x-z when…
We investigate equatorial geodesics in the gravitational field of a rotating and deformed source described by the approximate Hartle-Thorne metric. In the case of massive particles, we derive within the same approximation analytic…
We study numerical methods of tomography in domains with a reflecting obstacle. It will be shown that tomography with sets containing both broken rays, i.e. rays reflecting at the obstacle, as well as unbroken rays, has a smaller error…
We analyze the steady fluid flow in a porous medium containing a network of thin fissures i.e. width $\mathcal{O}(\epsilon)$, where all the cracks are generated by the rigid translation of a continuous piecewise $C^{1}$ functions in a fixed…
We consider the inverse source problem of a fixed wavenumber: study properties of an acoustic source based on a single far- or near-field measurement. We show that nonradiating sources having a convex or non-convex corner or edge on their…
We study interaction of inertial waves with geostrophic flow in a rapidly rotating fluid system. In accordance with experimental conditions in [1, 2], we consider inertial waves, which were excited by a source being near side boundary of…
The possibility of subcritical behaviour in the geostrophic turbulence regime of rapidly rotating thermally driven convection is explored. In this regime a non-local inverse energy transfer may compete with the more traditional and local…
This paper compares different pseudo-Anosov maps coming from different Birkhoff sections of a given flow. More precisely, given a hyperbolic surface and a collection of periodic geodesics on it, we study those Birkhoff sections for the…
It is pointed out that the current form of extrinsic equation of motion for a particle constrained to remain on a hypersurface is in fact a half-finished version for it is established without regard to the fact that the particle can never…
We investigate through numerical simulations of the Navier-Stokes equations the influence of the surface roughness on the fluid flow through fracture joints. Using the Hurst exponent $H$ to characterize the roughness of the self-affine…
Weak gravitational lensing is normally assumed to have only two principle effects: a magnification of a source and a distortion of the sources shape in the form of a shear. However, further distortions are actually present owing to changes…
We introduce an analytically solvable model for a fragmented object that, despite of a low degree of randomness and of the extreme simplicity of the breaking process, displays non self-averaging effects in its thermodynamic limit.
Let $M$ be a smooth closed oriented surface. Gaussian thermostats on $M$ correspond to the geodesic flows arising from metric connections, including those with non-zero torsion. These flows may not preserve any absolutely continuous…