Related papers: Variational analysis of inextensible elastic curve…
The limits of linear electrodynamics are reviewed, and possible directions of nonlinear extension are explored. The central theme is that the qualitative character of the empirical successes of quantum electrodynamics must be used as a…
We consider the edge-triangle model, a two-parameter family of exponential random graphs in which dependence between edges is introduced through triangles. In the so-called replica symmetric regime, the limiting free energy exists together…
The purpose of this paper is twofold. Firstly, we conduct an in-depth analysis of mathematical modeling concerning thermal-mechanical curved beams, by taking into consideration three primary forces widely accepted in the literature: axial…
We introduce a model of infinite horizon linear dynamic optimization with linear constraints and obtain results concerning feasibility of trajectories and optimal solutions necessarily satisfying conditions that resemble the Euler condition…
We solve several problems that involve imposing metrics on surfaces. The problem of a strip with a linear metric gradient is formulated in terms of a Lagrangean similar to those used for spin systems. We are able to show that the low energy…
We introduce a modified Kirchhoff-Plateau problem adding an energy term to penalize shape modifications of the cross-sections appended to the elastic midline. In a specific setting, we characterize quantitatively some properties of…
We derive a model for the optimization of the bending and torsional rigidities of non-homogeneous elastic rods. This is achieved by studying a sharp interface shape optimization problem with perimeter penalization, that treats both…
Quadratic Unconstrained Binary Optimization models are useful for solving a diverse range of optimization problems. Constraints can be added by incorporating quadratic penalty terms into the objective, often with the introduction of slack…
In this work, we focus on separable convex optimization problems with box constraints and a set of triangular linear constraints. The solution is given in closed-form as a function of some Lagrange multipliers that can be computed through…
We introduce a variational approach for extracting curves between a list of possible endpoints, based on the discretization of an energy and Smirnov's decomposition theorem for vector fields. It is used to design a bi-level minimization…
The main contribution of this thesis is the development of a new algorithm for solving convex quadratic programs. It consists in combining the method of multipliers with an infeasible active-set method. Our approach is iterative. In each…
Almost all available results in elasticity on curved topographies are obtained within either a small curvature expansion or an empirical covariant generalization that accounts for screening between Gaussian curvature and disclinations. In…
We consider the cylindrical bending problem for an infinite plate as modelled with a family of generalized continuum models, including the micromorphic approach. The models allow to describe length scale effects in the sense that thinner…
We demonstrate a possibility of computation of inelastic scattering cross-section in a multi-peripheral model by application of the Laplace method to multidimensional integral over the domain of physical process. The constrained maximum…
A new class of exclusion type processes acting in continuum with synchronous updating is introduced and studied. Ergodic averages of particle velocities are obtained and their connections to other statistical quantities, in particular to…
Existence and regularity of minimizers for a geometric variational problem is shown. The variational integral models an energy contribution of the interface between two immiscible fluids in the presence of surfactants and includes a…
Applications of variational methods are typically restricted to conservative systems. Some extensions to dissipative systems have been reported too but require ad hoc techniques such as the artificial doubling of the dynamical variables.…
Inverse design of morphing slender structures with programmable curvature has significant applications in various engineering fields. Most existing studies formulate it as an optimization problem, which requires repeatedly solving the…
Exterior calculus and moving frames are used to describe curved elastic shells. The kinematics follow from the Lie-derivative on forms whereas the dynamics via stress-forms.
The use of trigonometric polynomials as Lagrange multipliers in the harmonic mortar method enables an efficient and elegant treatment of relative motion in the stator-rotor coupling of electric machine simulation. Explicit formulas for the…