Related papers: Second-order structured deformations: relaxation, …
An analytical solution of the perturbed equations is obtained, which exists in all ergodic models of collisionless spherical stellar systems with a single length parameter. This solution corresponds to variations of this parameter, i.e.,…
We prove results on the relaxation and weak* lower semicontinuity of integral functionals of the form \[ \mathcal{F}[u] := \int_{\Omega} f \bigg( \frac{1}{2} \bigl( \nabla u(x) + \nabla u(x)^T \bigr) \bigg)\,\mathrm{d} x, \qquad u : \Omega…
In this Thesis we develop the geometric formulations for higher-order autonomous and non-autonomous dynamical systems, and second-order field theories. In all cases, the physical information of the system is given in terms of a Lagrangian…
We introduce bendlets, a shearlet-like system that is based on anisotropic scaling, translation, shearing, and bending of a compactly supported generator. With shearing being linear and bending quadratic in spatial coordinates, bendlets…
We consider shape optimization problems subject to elliptic partial differential equations. In the context of the finite element method, the geometry to be optimized is represented by the computational mesh, and the optimization proceeds by…
Open-system approaches are gaining traction in the simulation of charge transport in nanoscale and molecular electronic devices. In particular, "extended reservoir" simulations, where explicit reservoir degrees of freedom are present, allow…
We present a new and simple bound for the exponential decay of second order systems using the spectral shift. This result is applied to finite matrices as well as to partial differential equations of Mathematical Physics. The type of the…
We consider the problem of deforming simultaneously a pair of given structures. We show that such deformations are governed by an L-infinity algebra, which we construct explicitly. Our machinery is based on Th. Voronov's derived bracket…
We simulate a two dimensional model of self-propelled particles confined by a deformable boundary. The particles tend to accumulate near the boundary and the shape of the boundary deforms upon the collisions. We find that there are two…
We present a new first-principle theory for the calculation of the macroscopic second-order susceptibility chi^(2), based on the Time-Dependent Density-Functional Theory approach. Our method allows to include straightforwardly the many-body…
We study no-gap second-order optimality conditions for a non-uniformly convex and non-smooth integral functional. The integral functional is extended to the space of measures. The obtained second-order derivatives contain integrals on…
In this paper, we model, classify and investigate the solutions of (normalized) second order ode's with \emph{nonconstant continuous coefficients}. We introduce a generalized \emph{frequency function} as the solution of a \emph{nonlinear…
High resolution numerical simulations of stationary inverse energy cascade in two-dimensional turbulence are presented. Deviations from Gaussianity of velocity differences statistics are quantitatively investigated. The level of statistical…
We discuss the physics of RNA as described by its secondary structure. We examine the static properties of a homogeneous RNA-model that includes pairing and base stacking energies as well as entropic costs for internal loops. For large…
The Green's function method which has been originally proposed for linear systems has several extensions to the case of nonlinear equations. A recent extension has been proposed to deal with certain applications in quantum field theory. The…
This study explores the role that the microstructure plays in determining the macroscopic static response of porous elastic continua and exposes the occurrence of position-dependent nonlocal effects that are strictly correlated to the…
We associate bicomplexes with several integrable models in such a way that conserved currents are obtained by a simple iterative construction. Gauge transformations and dressings are discussed in this framework and several examples are…
The discovery of configurational forces acting on elastic structures and its initial applications are reviewed. Configurational forces are related to the possibility that an elastic structure can change its configuration, thus inducing a…
Continuum equations are ubiquitous in physical modelling of elastic, viscous, and viscoelastic systems. The equations of continuum mechanics take nontrivial forms on curved surfaces. Although the curved surface formulation of the continuum…
We present the growing mode solutions of cosmological perturbations to the second order in the matter dominated era. We also present several gauge-invariant combinations of perturbation variables to the second order in most general fluid…