Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userDistance to plane elasticity orthotropy by Euler-Lagrange method
86
0
0.0
(
0
)
Authors
Adrien Antonelli
Ask ChatGPT about the research
No Arabic abstract
Constitutive tensors are of common use in mechanics of materials. To determine the relevant symmetry class of an experimental tensor is still a tedious problem. For instance, it requires numerical methods in three-dimensional elasticity. We address here the more affordable case of plane (bi-dimensional) elasticity, which has not been fully solved yet. We recall first Vianellos orthogonal projection method, valid for both the isotropic and the square symmetric (tetragonal) symmetry classes. We then solve in a closed-form the problem of the distance to plane elasticity orthotropy, thanks to the Euler-Lagrange method.
rate research
Read More
Model-based paradigms for decision-making and control are becoming ubiquitous in robotics. They rely on the ability to efficiently learn a model of the system from data. Structured Mechanical Models (SMMs) are a data-efficient black-box parameterization of mechanical systems, typically fit to data by minimizing the error between predicted and observed accelerations or next states. In this work, we propose a methodology for fitting SMMs to data by minimizing the discrete Euler-Lagrange residual. To study our methodology, we fit models to joint-angle time-series from undamped and damped double-pendulums, studying the quality of learned models fit to data with and without observation noise. Experiments show that our methodology learns models that are better in accuracy to those of the conventional schemes for fitting SMMs. We identify use cases in which our method is a more appropriate methodology. Source code for reproducing the experiments is available at https://github.com/sisl/delsmm.
The classical models of Hertz, Sneddon and Boussinesq provide solutions for problems of indentation of a semi-infinite elastic massif by a sphere, a sphere or a cone and a flat punch. Although these models have been widely tested, it appears that at small scales and for flexible materials, surface tension can contribute to considerably to the mechanical response to indentation. The scales are typically those of the less than one micron for an elastomer and less than one millimetre for a gel. The exploitation of certain experimental results of microscopy or nanoindentation remain approximate due to the absence of models incorporating the effect of surface tension.
Classical reversible circuits, acting on $w$~bits, are represented by permutation matrices of size $2^w times 2^w$. Those matrices form the group P($2^w$), isomorphic to the symmetric group {bf S}$_{2^w}$. The permutation group P($n$), isomorphic to {bf S}$_n$, contains cycles with length~$p$, ranging from~1 to $L(n)$, where $L(n)$ is the so-called Landau function. By Lagrange interpolation between the $p$~matrices of the cycle, we step from a finite cyclic group of order~$p$ to a 1-dimensional Lie group, subgroup of the unitary group U($n$). As U($2^w$) is the group of all possible quantum circuits, acting on $w$~qubits, such interpolation is a natural way to step from classical computation to quantum computation.
Relativistic dipolar to hexadecapolar polarizabilities of the ground state and some excited states of hydrogenic atoms are calculated by using numerically exact energies and wave functions obtained from the Dirac equation with the Lagrange-mesh method. This approach is an approximate variational method taking the form of equations on a grid because of the use of a Gauss quadrature approximation. The partial polarizabilities conserving the absolute value of the quantum number $kappa$ are also numerically exact with small numbers of mesh points. The ones where $|kappa|$ changes are very accurate when using three different meshes for the initial and final wave functions and for the calculation of matrix elements. The polarizabilities of the $n=2$ excited states of hydrogenic atoms are also studied with a separate treatment of the final states that are degenerate at the nonrelativistic approximation. The method provides high accuracies for polarizabilities of a particle in a Yukawa potential and is applied to a hydrogen atom embedded in a Debye plasma.
Using SDSS DR15 to its full extent, we derived fundamental plane distances to over 317 000 early-type galaxies up to a redshift of 0.4. In addition to providing the largest sample of fundamental plane distances ever calculated, as well as a well calibrated group catalogue covering the entire SDSS spectroscopic footprint as far a redshift of 0.5, we present several improvements reaching beyond the traditional definition of the fundamental plane. In one approach, we adjusted the distances by removing systematic biases and selection effects in redshift-magnitude space, thereby greatly improving the quality of measurements. Alternatively, by expanding the traditional fundamental plane by additional terms, we managed to remove systematic biases caused by the selection of our SDSS spectroscopic galaxy sample as well as notably reducing its scatter. We discuss the advantages and caveats of these various methods and calibrations in detail. We found that improving the fundamental plane distance estimates beyond the established methods requires a delicate balancing act between various systematic biases and gains, but managed to reduce the uncertainty of our distance measurements by about a factor of two compared to the traditional fundamental plane.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
