Structural stability

In mathematics, structural stability is a fundamental property of a dynamical system which means that the qualitative behavior of the trajectories is unaffected by small perturbations (to be exact C1-small perturbations). Examples of such qualitative properties are numbers of fixed points and periodic orbits (but not their periods). Unlike Lyapunov stability, which considers perturbations of initial conditions for a fixed system, structural stability deals with perturbations of the system itself. Variants of this notion apply to systems of ordinary differential equations, vector fields on smooth manifolds and flows generated by them, and diffeomorphisms. Structurally stable systems were introduced by Aleksandr Andronov and Lev Pontryagin in 1937 under the name "systèmes grossiers", or rough systems. They announced a characterization of rough systems in the plane, the Andronov–Pontryagin criterion. In this case, structurally stable systems are typical, they form an open dense set in

Computational Analysis and Design of Structurally Stable Assemblies with Rigid Parts

Ziqi Wang

An assembly refers to a collection of parts joined together to achieve a specific form and/or functionality. Assemblies make it possible to fabricate large and complex objects with several small and simple parts. Such parts can be assembled and disassembled repeatedly, benefiting the transportation and maintenance of the assembly. Due to these advantages, assemblies are ubiquitous in our daily lives, including most furniture, household appliances, and architecture. The recent advancement in digital fabrication lowers the hurdles for fabricating objects with complex shapes. However, designing physically plausible assemblies is still a non-trivial task as a slight local modification on a part's geometry could have a global impact on the structural and/or functional performance of the whole assembly. New computational tools are developed to enable general users involved in the design process exploiting their imagination. This thesis focuses on static assemblies with rigid parts. We develop computational methods for analyzing and designing assemblies that are structurally stable and assemblable. To address this problem, we use integral joints i.e., tenon and mortise, that are historically used because of their reversibility which simplifies the disassembly process significantly. Properly arranged integral joints can restrict parts' relative movement for improved structural stability. However, manually finding the right joints' geometry is a tedious and error-prone task. Inspired by the kinematic-static duality, we first propose a new kinematic-based method for analyzing the structural stability of assemblies. We then develop a two-stage computational design framework based on this new analyzing method. The kinematic design stage determines the amount of motion restrictions imposed by joints to make a given assembly stable in the motion space. The geometric design stage searches for proper shapes of the joints to satisfy the motion restriction requirements computed from the previous stage. To solve the problem numerically, we propose the joint motion cones to measure the motion restriction capacity of given joints. Compared with previous works, our framework can efficiently handle inputs with complex geometry. Besides, our design framework is very flexible and can easily be adapted to various applications:First, we focus on designing globally interlocking assemblies that can withstand arbitrary external forces and torques. Second, we are interested in designing assemblies of rigid convex blocks to approximate freeform surfaces. Our design framework can optimize the blocks' shape to generate assemblies with good resistance against lateral forces, and in some cases, globally interlocking assemblies.Lastly, we present a method for designing complex assemblies with cone joints. By optimizing the shapes of cone joints, our design framework can find the best trade-off between structural stability and assemblability.We validate our computational tools by fabricating a series of physical prototypes. Our algorithms have great potential to be applied for solving various assembly design problems ranging from small-scale such as toys and furniture to large-scale such as art installation and architecture. For example, the proposed techniques could be applied for designing discrete architecture that can be automatically constructed with robots.

EPFL2021

Etude par STM de la déposition d'agrégats d'or sur TiO2 et mesure de l'émission électronique secondaire induite par l'impact d'agrégats sur une surface

Pierre Convers

This thesis work focuses on impact and diffusion processes as well as equilibrium positions of a metal deposited on a surface. The metal is deposited in the form of clusters containing n atoms in a controlled way. Gold or silver clusters cations (Au+n and Ag+n ) are used. Their size (n ∈ [1, 9]), charge state and deposition energy (E = 10 - 4500 eV) are well defined. The surface being at room temperature during the deposition, can be annealed and transferred in a scanning tunnelling microscope (STM) after deposition. The variable temperature microscope was developed during this thesis. The approach of the tip is carried out by an axial motor, which renders the microscope very stable. The first part of this work treats of the evolution of gold deposited on a TiO2(110) surface. Position and size of gold islands created by cluster or atomic depositions are determined by STM. Compared to atomic deposition at the same energy (10 < E < 100 eV), the cluster deposition produces smaller islands with a large islands density after annealing at 800 K. Regardless the deposition conditions, gold atoms diffuse on the surface already at 300 K. The impact energy is the key parameter to reduce the diffusion by cluster or atomic implantation or defect creation. Upon a high energy deposition, part of the deposited gold is invisible to the STM. The fate of these gold atoms is unclear : they are either buried under the surface or ejected in vacuum at the impact. The control of the islands size should permit the creation of a stable system with an optimum catalytic activity (i. e. CO combustion). Research groups have shown that this activity is strongly influenced by the islands size. It is equal to zero if the diameter is greater than 5 nm. The second part of this work is devoted to the electron emission γ induced by the impact of silver clusters Ag+n on a Pt and HOPG surface. Measurements are made by varying the impact energy (and so the speed v) of size-selected clusters on a defined surface. Impact velocity ranges from 104 to 105 m/s, which is lower than the classical threshold. Nevertheless every cluster size produces an electron emission. A potential emission (γ(v=0) ≠ 0) is observed for the monomer on both surfaces, which is caused by excited ions in a metastable state. The γ(v) curves are increasing, and no mesurable oscillation are observed. This does not confirm earlier work by Meiwes-Broer et al. These authors found oscillations in γ on similar systems relating them to the electronic structure of the clusters and the surface. A model based on heating of the electron gas is developed. This model gives good agreements with the γ(v) curves. The electronic temperature is estimated to 3000-8000 K. Similar behavior on both surfaces (Pt and HOPG) depending of the cluster size is shown. This behavior is probably related to the geometrical structure of the clusters. Finally, a more pronounced molecular effect is observed for the HOPG : the number of electrons emitted by the impact of a Ag+n is up to 7 times higher than the number of electrons emitted by impacts of n independent atoms. This value is smaller than 2 for the Pt surface.

EPFL2005

Etude par STM de la déposition d'agrégats d'or sur TiO2 et mesure de l'émission électronique secondaire induite par l'impact d'agrégats sur une surface

Pierre Convers

EPFL2005

Computational Analysis and Design of Structurally Stable Assemblies with Rigid Parts

Ziqi Wang

EPFL2021

Computational Analysis and Design of Structurally Stable Assemblies with Rigid Parts

Etude par STM de la déposition d'agrégats d'or sur TiO2 et mesure de l'émission électronique secondaire induite par l'impact d'agrégats sur une surface

On the H-stability property and energy of Wigner Lattices in the one component classical plasma : a numerical analysis

Etude par STM de la déposition d'agrégats d'or sur TiO2 et mesure de l'émission électronique secondaire induite par l'impact d'agrégats sur une surface

On the H-stability property and energy of Wigner Lattices in the one component classical plasma : a numerical analysis

Computational Analysis and Design of Structurally Stable Assemblies with Rigid Parts