In this work, we show that the eigenvalues of the problem  (∆2 + V (x) + λ)u(x) = 0 x ∈ Ω u(x) = ∆u(x) = 0 x ∈ ∂Ω are generically simple in the set of C4 regular regions of Rn, n ≥ 2. In fact, we prove that there exists a residual set of regions C4 diffeomorphic to a given Ω such that all the eigenvalues for a supported plate equation are simple.

With the increasing complexity of photo-realistic scenes, the question of building and placing objects in three-dimensional scenes is becoming ever more di cult. While the question of placement of rigid objects has captured the attention of researchers in the past, this work presents an intuitive and interactive scheme to properly place deformable objects with the aid of free-form deformation t...

We study numerically localised short circuits in Li||Bi liquid metal batteries. In the prototype of a classical, three liquid-layer system, we assume perceptible local deformation Li-salt interface. find that there always exists critical current at which Li-droplet is cut off from this hump, and transferred to Bi-phase. second case, molten Li contained foam, small emerges below foam due insuffi...

Shear-induced migration is ubiquitous in a suspension of solid and soft particles. The contribution to particle deformability frictional contacts between particles needs be clarified. By measuring normal forces with viscous resuspension experiments frictionless droplets, we show droplet deformation does not play significant role, contrary contacts, as the force much weaker for droplets than at ...

In this research, the results of comparative analysis of a single fuel droplet evaporation models are presented. Three well-known evaporation models including Spalding, Borman-Johnson and Abramzon-Sirignano models are analyzed using Computational Fluid Dynamic (CFD). The original Spalding model is extended to consider the effects of the Stefan flow, unsteady vaporization, and variable propertie...

This paper investigates the rim fragmentation of a millimeter-sized methyl-ethyl-ketone droplet imposed by impact different millijoule nanosecond laser beams. The physical mechanisms that determine deformation, expansion, and evolution detached fragments from are demonstrated, considering influence beam energy. key finding our numerical study is quantification during process using physically co...

– A weakly deformable droplet impinging on a rigid surface rebounds if the surface is intrinsically hydrophobic or if the gas film trapped underneath the droplet is able to keep the interfaces from touching. A simple, physically motivated model inspired by analysis of droplets colliding with deformable interfaces is proposed in order to investigate the dynamics of the rebound process and the ef...