Effective dynamicsof a coupled microscopic-macroscopic stochastic system

A conceptual model for microscopic-macroscopic slow-fast stochastic systems is considered. A dynamical reduction procedure is presented in order to extract effective dynamics for this kind of systems. Under appropriate assumptions, the effective system is shown to approximate the original system, in the sense of a probabilistic convergence.Comment: 14 page

The impact of multiplicative noise in SPDEs close to bifurcation via amplitude equations

This article deals with the approximation of a stochastic partial differential equation (SPDE) via amplitude equations. We consider an SPDE with a cubic nonlinearity perturbed by a general multiplicative noise that preserves the constant trivial solution and we study the dynamics around it for the deterministic equation being close to a bifurcation. Based on the separation of time-scales close to a change of stability, we rigorously derive an amplitude equation describing the dynamics of the bifurcating pattern. This allows us to approximate the original infinite dimensional dynamics by a simpler effective dynamics associated with the solution of the amplitude equation. To illustrate the abstract result we apply it to a simple one-dimensional stochastic Ginzburg-Landau equation

Observation of Exciton-Phonon Sideband in Individual Metallic Single-Walled Carbon Nanotubes

Single-walled carbon nanotubes (SWCNTs) are quasi-one-dimensional systems with poor Coulomb screening and enhanced electron-phonon interaction, and are good candidates for excitons and exciton-phonon couplings in metallic state. Here we report back scattering reflection experiments on individual metallic SWCNTs. An exciton-phonon sideband separated by 0.19 eV from the first optical transition peak is observed in a metallic SWCNT of chiral index (13,10), which provides clear evidences of excitons in metallic SWCNTs. A static dielectric constant of 10 is estimated from the reflectance spectrum.Comment: 5 pages, 3 figures; typos corrected, references updated, text re-arrange

Slow Manifolds for Multi-Time-Scale Stochastic Evolutionary Systems

This article deals with invariant manifolds for infinite dimensional random dynamical systems with different time scales. Such a random system is generated by a coupled system of fast-slow stochastic evolutionary equations. Under suitable conditions, it is proved that an exponentially tracking random invariant manifold exists, eliminating the fast motion for this coupled system. It is further shown that if the scaling parameter tends to zero, the invariant manifold tends to a slow manifold which captures long time dynamics. As examples the results are applied to a few systems of coupled parabolic-hyperbolic partial differential equations, coupled parabolic partial differential-ordinary differential equations, and coupled hyperbolic-hyperbolic partial differential equations

Sketch2Stress: Sketching with Structural Stress Awareness

In the process of product design and digital fabrication, the structural analysis of a designed prototype is a fundamental and essential step. However, such a step is usually invisible or inaccessible to designers at the early sketching phase. This limits the user's ability to consider a shape's physical properties and structural soundness. To bridge this gap, we introduce a novel approach Sketch2Stress that allows users to perform structural analysis of desired objects at the sketching stage. This method takes as input a 2D freehand sketch and one or multiple locations of user-assigned external forces. With the specially-designed two-branch generative-adversarial framework, it automatically predicts a normal map and a corresponding structural stress map distributed over the user-sketched underlying object. In this way, our method empowers designers to easily examine the stress sustained everywhere and identify potential problematic regions of their sketched object. Furthermore, combined with the predicted normal map, users are able to conduct a region-wise structural analysis efficiently by aggregating the stress effects of multiple forces in the same direction. Finally, we demonstrate the effectiveness and practicality of our system with extensive experiments and user studies.Comment: 16 figure

View suggestion for interactive segmentation of indoor scenes

Point cloud segmentation is a fundamental problem. Due to the complexity of real-world scenes and the limitations of 3D scanners, interactive segmentation is currently the only way to cope with all kinds of point clouds. However, interactively segmenting complex and large-scale scenes is very time-consuming. In this paper, we present a novel interactive system for segmenting point cloud scenes. Our system automatically suggests a series of camera views, in which users can conveniently specify segmentation guidance. In this way, users may focus on specifying segmentation hints instead of manually searching for desirable views of unsegmented objects, thus significantly reducing user effort. To achieve this, we introduce a novel view preference model, which is based on a set of dedicated view attributes, with weights learned from a user study. We also introduce support relations for both graph-cut-based segmentation and finding similar objects. Our experiments show that our segmentation technique helps users quickly segment various types of scenes, outperforming alternative methods