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We consider the problem of estimating the $2D$ vector displacement field in a heterogeneous elastic solid deforming under plane stress conditions. The problem is motivated by applications in quasistatic elastography. From precise and…
The elastic moduli of four numerical random isotropic packings of Hertzian spheres are studied. The four samples are assembled with different preparation procedures, two of which aim to reproduce experimental compaction by vibration and…
This paper concerns the inverse source problems for the time-harmonic elastic and electromagnetic wave equations. The goal is to determine the external force and the electric current density from boundary measurements of the radiated wave…
This paper provides a new unified framework for second-moment stability of discrete-time linear systems with stochastic dynamics. Relations of notions of second-moment stability are studied for the systems with general stochastic dynamics,…
Spatially localized deformation components are very useful for shape analysis and synthesis in 3D geometry processing. Several methods have recently been developed, with an aim to extract intuitive and interpretable deformation components.…
We give computational results to study the accuracy of several quasicontinuum methods for two benchmark problems - the stability of a Lomer dislocation pair under shear and the stability of a lattice to plastic slip under tensile loading.…
Assessing the vulnerability of atherosclerotic plaques requires an accurate knowledge of the mechanical properties of the plaque constituents. It is possible to measure displacements in vivo inside a plaque using magnetic resonance imaging.…
We consider the problem of learning linear prediction models with model misspecification bias. In such case, the collinearity among input variables may inflate the error of parameter estimation, resulting in instability of prediction…
In amorphous materials, plasticity is localized and occurs as shear transformations. It was recently shown by Wu et al. that these shear transformations can be predicted by applying topological defect concepts developed for liquid crystals…
In the present paper, the simplest model of strain-gradient elasticity will be considered, that is the isotropy in a bidimensional space. Paralleling the definition of the classic elastic moduli, our aim is to introduce second-order…
This paper is concerned with the analysis of the inf-sup condition arising in the stationary Stokes problem in exterior domains. We deduce values of the constant in the stability lemma, which yields fully computable estimates of the…
I shortly describe the main results on elastically driven instabilities and elastic turbulence in viscoelastic inertia-less flows with curved streamlines. Then I describe a theory of elastic turbulence and prediction of elastic waves at…
We derive the equations of motion for relativistic elastic membranes, that is, two-dimensional elastic bodies whose internal energy depends only on their stretching, starting from a variational principle. We show how to obtain conserved…
In this paper, we address stability of parabolic linear Partial Differential Equations (PDEs). We consider PDEs with two spatial variables and spatially dependent polynomial coefficients. We parameterize a class of Lyapunov functionals and…
We study the modulational stability problem for the traveling periodic waves (called Stokes waves) in an infinitely deep fluid by using pseudo-differential operators in conformal variables. We derive the criteria and the normal forms for…
Occurring in protoplanetary discs composed of dust and gas, streaming instabilities are a favoured mechanism to drive the formation of planetesimals. The Polydispserse Streaming Instability is a generalisation of the Streaming Instability…
Solving the linear elasticity and Stokes equations by an optimal domain decomposition method derived algebraically involves the use of non standard interface conditions. The one-level domain decomposition preconditioners are based on the…
We present a computational framework to investigate steady state distributions and perform stability analysis for random ordinary differential equations driven by parameter uncertainty. Using the nonlinear Rosenzweig McArthur predator prey…
In this paper, the stabilized finite element approximation of the Stokes eigenvalue problems is considered for both the two-field (displacement-pressure) and the three-field (stress-displacement-pressure) formulations. The method presented…
We present a general framework to study uniqueness, stability and reconstruction for infinite-dimensional inverse problems when only a finite-dimensional approximation of the measurements is available. For a large class of inverse problems…