Related papers: Rigidity and functional properties of $\mathrm{BD}…
We investigate the existence of minimizers of variational models with Eulerian-Lagrangian formulations. We consider energy functionals depending on the deformation of a body, defined on its reference configuration, and an Eulerian map…
In this research oriented manuscript, foundational aspects of rigid geometry are discussed, putting emphasis on birational side of formal schemes and topological feature of rigid spaces. Besides the rigid geometry itself, topics include the…
Thin beams made of magnetorheological elastomers embedded with hard magnetic particles (hard-MREs) are capable of large deflections under an applied magnetic field. We propose a comprehensive framework, comprising a beam model and 3D finite…
We investigate the deformation of a longitudinally stretched rectangular sheet which is clamped at two opposite boundaries and free otherwise with experiments, numerical analysis and asymptotic analysis of the biharmonic elastic equation…
We study, both theoretically and numerically, the equilibrium of a hinged rigid leaflet with an attached rotational spring, immersed in a stationary incompressible fluid within a rigid channel. Through a careful investigation of the…
The spectral theory for operator pencils and operator differential-algebraic equations is studied. Special focus is laid on singular operator pencils and three different concepts of singularity of operator pencils are introduced. The…
We study a decomposition problem for a class of unitary representations associated with wavelet analysis, wavelet representations, but our framework is wider and has applications to multi-scale expansions arising in dynamical systems theory…
The space of abelian functions of a principally polarized abelian variety J is studied as a module over the ring D of global holomorphic differential operators on J. We construct a D-free resolution in case the theta divisor is…
We propose a novel projection-based approach to derive structure-preserving Finite Element Exterior Calculus (FEEC) discretizations using standard tensor-product splines on domains with a polar singularity. This approach follows the main…
We consider a dilute system of small hard beads or hard fibers immersed in a very soft gel able to withstand large elastic deformations. Because of its low to very low shear modulus, this system is very sensitive to small forces. We…
We introduce Besov spaces with variable smoothness and integrability by using the continuous version of Calder\`on reproducing formula. We show that our space is well-defined, i.e., independent of the choice of basis functions. We…
A new deformed canonical commutation relation, generalizing various known deformations, is defined together with its structure function of deformation. Then, the related irreducible representations are characterized and classified. Finally,…
One studies a system of differential equations defined by Abel integrals associated to a real cycle defined for the versal deformation of an isolated simple singularity. As application, one obtains an estimation on the multiplicity of zeros…
Optical periodic structures exhibiting a degenerate band edge (DBE) are of significant interest for various applications such as switching, sensing, high-power amplification, and lasing. At the edge of the bandgap in such structures, a…
Plastic deformation is widely regarded as an intrinsically dissipative phenomenon and its theoretical description is largely phenomenological. We argue instead that plasticity possesses a non-dissipative, symmetry determined backbone:…
This paper establishes a functorial framework for convergence of Drinfeld's Universal Deformation Formula (UDF) on spaces of analytic vectors. This is accomplished by matching the order of the latter with an equicontinuity condition on the…
Two finite element approximations of the Oldroyd-B model for dilute polymeric fluids are considered, in bounded 2- and 3-dimensional domains, under no flow boundary conditions. The pressure and the symmetric conformation tensor are…
We present an accurate and efficient framework for real-space Hubbard-corrected density functional theory. In particular, we obtain expressions for the energy, atomic forces, and stress tensor suitable for real-space finite-difference…
This work is devoted to the variational derivation of a reduced model for brittle membranes in finite elasticity. The main mathematical tools we develop for our analysis are: (i) a new density result in $GSBV^{p}$ of functions satisfying a…
We introduce extremal affine surface areas in a functional setting. We show their main properties. Among them are linear invariance, isoperimetric inequalities and monotonicity properties. We establish a new duality formula, which shows…