Search results for " relativity"
showing 10 items of 1158 documents
The effect of body posture on long range time-to-contact estimation
2011
On Earth, gravity accelerates freely moving objects downward, whereas upward-moving objects are being decelerated. Do humans take internalised knowledge of gravity into account when estimating time-to-contact (TTC, the time remaining before the moving object reaches the observer)? To answer this question, we created a motion-prediction task in which participants saw the initial part of an object's trajectory moving on a collision course prior to an occlusion. Observers had to judge when the object would make contact with them. The visual scene was presented with a head-mounted display. Participants lay either supine (looking up) or prone (looking down), suggestive of the ball either rising…
The next-to-ladder approximation for linear Dyson–Schwinger equations
2007
We solve the linear Dyson Schwinger equation for a massless vertex in Yukawa theory, iterating the first two primitive graphs.
Why the Cosmological Constant Seems to Hardly Care About Quantum Vacuum Fluctuations: Surprises From Background Independent Coarse Graining
2020
International audience; Background Independence is a sine qua non for every satisfactory theory of Quantum Gravity. In particular if one tries to establish a corresponding notion of Wilsonian renormalization, or coarse graining, it presents a major conceptual and technical difficulty usually. In this paper we adopt the approach of the gravitational Effective Average Action and demonstrate that generically coarse graining in Quantum Gravity and in standard field theories on a non-dynamical spacetime are profoundly different. By means of a concrete example, which in connection with the cosmological constant problem is also interesting in its own right, we show that the surprising and sometime…
Exact solution of ‘‘hot dimer’’ adsorption in one-dimensional lattices
1993
An analytical solution for the kinetics of the ``hot-dimer'' adsorption in a one-dimensional lattice is reported. Hot dimers are molecules that dissociate after deposition, and each of the remaining monomers fly apart up to a maximum distance R from the original adsorption sites. The kinetics of this process is strongly dependent on the flying distance R. We find a particular behavior of the jamming coverage as a function of R. Monte Carlo simulation results are in agreement with such a calculation.
Two multilayered plate models with transverse shear warping functions issued from three dimensional elasticity equations
2014
Abstract A multilayered plate theory which uses transverse shear warping functions is presented. Two methods to obtain the transverse shear warping functions from three-dimensional elasticity equations are proposed. The warping functions are issued from the variations of transverse shear stresses computed at specific points of a simply supported plate. The first method considers an exact 3D solution of the problem. The second method uses the solution provided by the model itself: the transverse shear stresses are computed integrating equilibrium equations. Hence, an iterative process is applied, the model is updated with the new warping functions, and so on. Once the sets of warping functio…
Error Estimates for a Class of Elliptic Optimal Control Problems
2016
In this article, functional type a posteriori error estimates are presented for a certain class of optimal control problems with elliptic partial differential equation constraints. It is assumed that in the cost functional the state is measured in terms of the energy norm generated by the state equation. The functional a posteriori error estimates developed by Repin in the late 1990s are applied to estimate the cost function value from both sides without requiring the exact solution of the state equation. Moreover, a lower bound for the minimal cost functional value is derived. A meaningful error quantity coinciding with the gap between the cost functional values of an arbitrary admissible …
Sub-Finsler Geodesics on the Cartan Group
2018
This paper is a continuation of the work by the same authors on the Cartan group equipped with the sub-Finsler $\ell_\infty$ norm. We start by giving a detailed presentation of the structure of bang-bang extremal trajectories. Then we prove upper bounds on the number of switchings on bang-bang minimizers. We prove that any normal extremal is either bang-bang, or singular, or mixed. Consequently, we study mixed extremals. In particular, we prove that every two points can be connected by a piecewise smooth minimizer, and we give a uniform bound on the number of such pieces.
Supermanifolds, symplectic geometry and curvature
2015
We present a survey of some results and questions related to the notion of scalar curvature in the setting of symplectic supermanifolds.
Numerical study of the transverse stability of the Peregrine solution
2020
We generalise a previously published approach based on a multi-domain spectral method on the whole real line in two ways: firstly, a fully explicit 4th order method for the time integration, based on a splitting scheme and an implicit Runge--Kutta method for the linear part, is presented. Secondly, the 1D code is combined with a Fourier spectral method in the transverse variable both for elliptic and hyperbolic NLS equations. As an example we study the transverse stability of the Peregrine solution, an exact solution to the one dimensional nonlinear Schr\"odinger (NLS) equation and thus a $y$-independent solution to the 2D NLS. It is shown that the Peregrine solution is unstable against all…
Complex Potential Function in Elasticity Theory: shear and torsion solution through line integrals
2012
Aim of this paper is to introduce a basis formulation framed into complex analysis valid to solve shear and torsion problems. Solution, in terms of a complex function related to the complete tangential stress field, may be evaluated performing line integrals only. This basis formulation framed into elasticity problems may be a useful support for a boundary method to verify the accuracy of an approximation of function solution. The numerical applications stress the latter point and show the validity of these formulas since exact solutions may be reached for sections where the exact solution is known.