Related papers: On instability mechanisms for inverse problems
It is known that a finite-size homogeneous granular fluid develops an hydrodynamic-like instability when dissipation crosses a threshold value. This instability is analyzed in terms of modified hydrodynamic equations: first, a source term…
Soft machines typically exhibit slow locomotion speed and low manipulation strength because of intrinsic limitations of soft materials. Here, we present a generic design principle that harnesses mechanical instability for a variety of…
We derive an efficient stochastic algorithm for inverse problems that present an unknown linear forcing term and a set of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of the problem is…
Here the buckling of inextensible rods due to axial body forces is mapped to 1d, nonrelativistic, time-independent quantum mechanics. Focusing on the pedagogical case of rods confined to 2d, three simple and physically realizable…
Computational formulations for large strain, polyconvex, nearly incompressible elasticity have been extensively studied, but research on enhancing solution schemes that offer better tradeoffs between accuracy, robustness, and computational…
The paper presents a new control algorithm for unstable linear systems with input delay. In comparison with known analogues, the control law has been designed, which is a modification of the Smith predictor, and is the simplest one to…
We present an algorithm for robust model predictive control with consideration of uncertainty and safety constraints. Our framework considers a nonlinear dynamical system subject to disturbances from an unknown but bounded uncertainty set.…
This article establishes the foundation for a new theory of invariant/integral manifolds for non-autonomous dynamical systems. Current rigorous support for dimensional reduction modelling of slow-fast systems is limited by the rare events…
We propose a systematic methodology to derive the regularized thirteen-moment equations in the rarefied gas dynamics for a general class of linearized collision models. Detailed expressions of the moment equations are written down for all…
In this paper, using 1+1D models as examples, we study symmetries and anomalous symmetries via multi-component partition functions obtained through symmetry twists, and their transformations under the mapping class group of spacetime. This…
The aim of this paper is to present and analyze a new direct method for solving the linear elasticity inverse problem. Given measurements of some displacement fields inside a medium, we show that a stable reconstruction of elastic…
Following Smale, we study simple symmetric mechanical systems of $n$ point particles in the plane. In particular, we address the question of the linear and spectral stability properties of relative equilibria, which are special solutions of…
In this paper, we consider inverse scattering and inverse boundary value problems at sufficiently large and fixed energy for the multidimensional relativistic and nonrelativistic Newton equations in a static external electromagnetic field…
This paper concerns models and convergence principles for dealing with stochasticity in a wide range of algorithms arising in nonlinear analysis and optimization in Hilbert spaces. It proposes a flexible geometric framework within which…
We study the inverse electrostatic and elasticity problems associated with Poisson and Navier equations. The uniqueness of solutions of these problems is proved for piecewise constant electric charge and internal stress distributions having…
Monitoring the dynamics processes in combustors is crucial for safe and efficient operations. However, in practice, only limited data can be obtained due to limitations in the measurable quantities, visualization window, and temporal…
High-order accurate, $\textit{entropy stable}$ numerical methods for hyperbolic conservation laws have attracted much interest over the last decade, but only a few rigorous convergence results are available, particularly in multiple space…
The use of available disturbance predictions within a nominal model predictive control formulation is studied. The main challenge that arises is the loss of recursive feasibility and stability guarantees when a persistent disturbance is…
This work belongs to the framework of inverse problems with linear model. The resolution of this type of problem consists in minimizing (possibly under constraints) a function of discrepancy between the measurements and a physical model of…
The paper considers the general case of incompressible non-classical elasticity with small deformations and rotations. The thermodynamic stability is analysed for free energy density with three rotational degrees of freedom. Although the…