Pressurized Ring-Stiffened Shells: A Model Study

The complex problem of interaction between general buckling and interframe buckling in ring-stiffened shells under external pressure is studied in a simple way by use of a rigid link model. The model incorporates linear and bilinear compressive springs with special properties to represent the circumferential stiffness and the buckling characteristics of a long shell and its ring stiffeners. The model allows the possibility of a shift of stiffness (material, weight) from the shell to the stiffeners. The optimum weight distribution may therefore be found in a relatively simple manner. It is found that interactive effects in the presence of geometrical imperfections have a considerable influence on the buckling strength of such structures.     

Multiscale Modeling of Colloid and Fluid Dynamics in Porous Media Including an Evolving Microstructure

We consider colloidal dynamics and single-phase fluid flow within a saturated porous medium in two space dimensions. A new approach in modeling pore clogging and porosity changes on the macroscopic scale is presented. Starting from the pore scale, transport of colloids is modeled by the Nernst?CPlanck equations. Here, interaction with the porous matrix due to (non-)DLVO forces is included as an additional transport mechanism. Fluid flow is described by incompressible Stokes equations with interaction energy as forcing term. Attachment and detachment processes are modeled by a surface reaction rate. The evolution of the underlying microstructure is captured by a level set function. The crucial point in completing this model is to set up appropriate boundary conditions on the evolving solid?Cliquid interface. Their derivation is based on mass conservation. As a result of an averaging procedure by periodic homogenization in a level set framework, on the macroscale we obtain Darcy??s law and a modified averaged convection?Cdiffusion equation with effective coefficients due to the evolving microstructure. These equations are supplemented by microscopic cell problems. Time- and space-dependent averaged coefficient functions explicitly contain information of the underlying geometry and also information of the interaction potential. The theoretical results are complemented by numerical computations of the averaged coefficients and simulations of a heterogeneous multiscale scenario. Here, we consider a radially symmetric setting, i.e., in particular we assume a locally periodic geometry consisting of circular grains. We focus on the interplay between attachment and detachment reaction, colloidal interaction forces, and the evolving microstructure. Our model contributes to the understanding of the effects and processes leading to porosity changes and pore clogging from a theoretical point of view.     

An algorithm for sequential tail value at risk for path-independent payoffs in a binomial tree

We present an algorithm that determines Sequential Tail Value at Risk (STVaR) for path-independent payoffs in a binomial tree. STVaR is a dynamic version of Tail-Value-at-Risk (TVaR) characterized by the property that risk levels at any moment must be in the range of risk levels later on. The algorithm consists of a finite sequence of backward recursions that is guaranteed to arrive at the solution of the corresponding dynamic optimization problem. The algorithm makes concrete how STVaR differs from TVaR over the remaining horizon, and from recursive TVaR, which amounts to Dynamic Programming. Algorithmic aspects are compared with the cutting-plane method. Time consistency and comonotonicity properties are illustrated by applying the algorithm on elementary examples.     

Scaling Platinum-Catalyzed Hydrogen Dissociation on Corrugated Surfaces

We determine absolute reactivities for dissociation at low coordinated Pt sites. Two curved Pt(111) single-crystal surfaces allow us to probe either straight or highly kinked step edges with molecules impinging at a low impact energy. A model extracts the average reactivity of inner and outer kink atoms, which is compared to the reactivity of straight A- and B-type steps. Local surface coordination numbers do not adequately capture reactivity trends for H₂ dissociation. We utilize the increase of reactivity with step density to determine the area over which a step causes increased dissociation. This step-type specific reactive area extends beyond the step edge onto the (111) terrace. It defines the reaction cross-section for H₂ dissociation at the step, bypassing assumptions about contributions of individual types of surface atoms. Our results stress the non-local nature of H₂ interaction with a surface and provide insight into reactivity differences for nearly identical step sites.     

Theoretical and Experimental Results on the Post-Buckling of Ring-Stiffened Cylinders

ABSTRACT

The post-buckling behavior of ring-stiffened cylinders subjected to lateral pressure is studied theoretically and experimentally. The theoretical analysis uses the energy method and terms of up to and including fourth order of the buckling displacements are considered. The results of experiments on ten machined ring-stiffened cylinders subjected to lateral pressure and used to verify the theoretical analysis. The theory shows the post-buckling behavior to be stable-symmetric for both the shell and general instability modes. The experimental results are in reasonable agreement with the theory, although they indicate, in general, a lower post-buckling stiffness. For the range of parameters considered, no instability or imperfection sensitivity is found in either the theoretical or the experimental studies.     

On evolutionary ray-projection dynamics

We introduce the ray-projection dynamics in evolutionary game theory by employing a ray projection of the relative fitness (vector) function, i.e., a projection unto the unit simplex along a ray through the origin. Ray-projection dynamics are weakly compatible in the terminology of Friedman (Econometrica 59:637–666, 1991), each of their interior fixed points is an equilibrium and each interior equilibrium is one of its fixed points. Furthermore, every interior evolutionarily stable strategy is an asymptotically stable fixed point, and every strict equilibrium is an evolutionarily stable state and an evolutionarily stable equilibrium. We also employ the ray-projection on a set of functions related to the relative fitness function and show that several well-known evolutionary dynamics can be obtained in this manner.     

A numerical study of energy transfer mechanisms in materials following irradiation by swift heavy ions

Swift heavy ions interact with electrons in materials and this may yield permanent atomic displacements; the energy transfer mechanisms that bring electronic excitations into atomic motion are not fully understood, and are generally discussed in terms of two theories, viz. Coulomb explosion and heat exchange between excited electrons and atoms, which is limited by electron-phonon coupling. We address this problem for a “generic” material using a semi-classical numerical approach where the dynamics of the evolving electron density is calculated by using molecular dynamics simulations applied to pseudo-electrons. The forces exerted on the nuclei are then used to calculated the trajectories of the nuclei. From the temporal evolution of the atomic kinetic energy, we find that the energy transfer between the electrons and the nuclei can be divided in two parts. First, a Coulomb heating starts the motion of the atoms by giving them a radial speed; this process differs from Coulomb explosion because the atoms are not displaced over interatomic distances. Second, a thermal energy transfer, as described in linear transport theory, takes place. Our study thus confirms the domination of thermal energy exchange mechanisms over Coulomb explosion models.     

MEMS-based adaptive optics scanning laser ophthalmoscopy

We have developed a compact, robust adaptive optics (AO) scanning laser ophthalmoscope using a microelectromechanical (MEMS) deformable mirror (DM). Facilitated with a Shack-Hartmann wavefront sensor, the MEMS-DM-based AO operates a closed-loop modal wave aberration correction for the human eye and reduces wave aberrations in most eyes to below 0.1 microm rms. Lateral resolution is enhanced, and images reveal a clear cone mosaic near the foveal center. The significant increase in throughput allows for a confocal pinhole whose diameter is less than the Airy disc of the collection lens, thereby fully exploiting the axial resolution capabilities of the system.