Search results for "geometry."
showing 10 items of 4386 documents
On the limit velocity and buckling phenomena of axially moving orthotropic membranes and plates
2011
In this paper, we consider the static stability problems of axially moving orthotropic membranes and plates. The study is motivated by paper production processes, as paper has a fiber structure which can be described as orthotropic on the macroscopic level. The moving web is modeled as an axially moving orthotropic plate. The original dynamic plate problem is reduced to a two-dimensional spectral problem for static stability analysis, and solved using analytical techniques. As a result, the minimal eigenvalue and the corresponding buckling mode are found. It is observed that the buckling mode has a shape localized in the regions close to the free boundaries. The localization effect is demon…
Voisinages tubulaires épointés et homotopie stable à l'infini
2022
We initiate a study of punctured tubular neighborhoods and homotopy theory at infinity in motivic settings. We use the six functors formalism to give an intrinsic definition of the stable motivic homotopy type at infinity of an algebraic variety. Our main computational tools include cdh-descent for normal crossing divisors, Euler classes, Gysin maps, and homotopy purity. Under-adic realization, the motive at infinity recovers a formula for vanishing cycles due to Rapoport-Zink; similar results hold for Steenbrink's limiting Hodge structures and Wildeshaus' boundary motives. Under the topological Betti realization, the stable motivic homotopy type at infinity of an algebraic variety recovers…
Ledrappier-Young formula and exact dimensionality of self-affine measures
2017
In this paper, we solve the long standing open problem on exact dimensionality of self-affine measures on the plane. We show that every self-affine measure on the plane is exact dimensional regardless of the choice of the defining iterated function system. In higher dimensions, under certain assumptions, we prove that self-affine and quasi self-affine measures are exact dimensional. In both cases, the measures satisfy the Ledrappier-Young formula. peerReviewed
Aménités urbaines et périurbaines dans une aire métropolitaine de forme fractale
2002
In the THÜNEN tradition, Urban Economy is a striking abstraction, giving models that keep the main features of the wide diversity of real word cities. Nevertheless, this paradigm less suits the modern urban spatial structures (polycentrism, weak centripetal forces, etc.), particularly the peri-urban form of metropolitan areas, which are an urban/rural integrated space. In this paper, we propose a classical micro-economic urban model combined with a " SIERPINSKI's carpet " geometry, a fractal form which suits for fit together urban and rural areas in a hierarchical structure. Subject to a budget constraint, a household maximises a Cobb-Douglas/CES function, where household's taste for divers…
Neuromuscular function and bone geometry and strength in aging
2010
Domain wall motion in a diffusive weak ferromagnet
2019
We study the domain wall motion in a disordered weak ferromagnet, induced by injecting a spin current from a strong ferromagnet. Starting from the spin diffusion equation describing the spin accumulation in the weak ferromagnet, we calculate the force and torque acting on the domain wall. We also study the ensuing domain wall dynamics, and suggest a possible measurement method for detecting the domain wall motion via measuring the additional resistance.
Thermodiffusion motion of electrically charged nanoparticles
2012
AbstractThe present work deals with experimental studies to examine the theoretical model of thermodiffusion of electrically charged nanoparticles. Three different ionic magnetic colloid samples have been synthesized and profoundly analyzed. The theoretical model is a classical one, based on the calculation of the temperature and the electric potential distribution around nanoparticles. The discrepancy between experimental data and theory turns out not to exceed 20%. We focus on applying different approximations between calculated electrical double layer in the theoretical model and experimental determination of the surface charge density of colloidal particles. We assume this is the main r…
Analysis of the effects of magnetic field on the induced stress in drilled plates
2013
Abstract A drilled plate of ferromagnetic material suitably coupled by coils of enameled copper wire fed by a DC power supply to 30 V is considered in this paper. It is analyzed with finite element and later experiments are performed to validate the obtained results. After polishing the plate, two strain gauges for measuring the deformation along the x axis and along the z axis are installed. The values of strain are 5 μm/m in z direction and −2 μm/m in x direction. The experimental–numerical comparison shows that the laboratory results are lower than numerical, while signs and orders of magnitude are the same. It is concluded that the results of the FEM analysis can be considered acceptabl…
An Inverse Problem for the Relativistic Boltzmann Equation
2020
We consider an inverse problem for the Boltzmann equation on a globally hyperbolic Lorentzian spacetime $(M,g)$ with an unknown metric $g$. We consider measurements done in a neighbourhood $V\subset M$ of a timelike path $\mu$ that connects a point $x^-$ to a point $x^+$. The measurements are modelled by a source-to-solution map, which maps a source supported in $V$ to the restriction of the solution to the Boltzmann equation to the set $V$. We show that the source-to-solution map uniquely determines the Lorentzian spacetime, up to an isometry, in the set $I^+(x^-)\cap I^-(x^+)\subset M$. The set $I^+(x^-)\cap I^-(x^+)$ is the intersection of the future of the point $x^-$ and the past of th…
A blow-up result for a nonlinear wave equation on manifolds: the critical case
2021
We consider a inhomogeneous semilinear wave equation on a noncompact complete Riemannian manifold (Formula presented.) of dimension (Formula presented.), without boundary. The reaction exhibits the combined effects of a critical term and of a forcing term. Using a rescaled test function argument together with appropriate estimates, we show that the equation admits no global solution. Moreover, in the special case when (Formula presented.), our result improves the existing literature. Namely, our main result is valid without assuming that the initial values are compactly supported.