, University of British Columbia, Vancouver
Pages: pp. 8-9
Noisy phenomena appear in all areas of science, and whether noise is beneficial or detrimental, understanding its cause and effect is crucial. However, in complex systems, it's usually difficult to isolate the effects of noise or the randomness from variations in complex but deterministic "non-noisy" behavior. This combination of effects often results in unexpected or deceptive behavior, requiring new perspectives to define the various interactions that can occur.
It's difficult to find a scientist studying any complex phenomenon today who doesn't have a reasonably powerful computer close at hand. One advantage of the ongoing increase in computational power is that it lets researchers pursue increasingly realistic systems, which in turn give a more detailed perspective of randomness in a system. Consequently, several questions related to noise have evolved right along with our ability to explore systems closer to reality: What is the source of the noise? Does it play a positive or negative role? Is it valuable to introduce it into the system, or should it be removed? Is the noise naturally there, or is it introduced by a measurement process? There's an additional problem to consider as well: how to distinguish between the noise that "should" be there and that which is introduced via computational error.
This special issue of CiSE magazine is a follow-up to a symposium at the 2005 annual meeting of the American Association for the Advancement of Science. Like this issue, the symposium brought together research from diverse applications in which understanding the interplay between noise and dynamical complexity is of central importance. The goal was to provide a forum for discussing the models and analyses used in different areas as well as the mechanisms by which noise can significantly alter various phenomena. The topics included seismic imaging, biological networks, computational and dynamical stability, optics, and characterization of rough surfaces, all of which are affected by noise. Through comparison and contrast, these different perspectives provided new alternatives for understanding the effects of noise in a wide range of applications, prompting discussions among scientists and engineers seeking insight into the various manifestations of noise and the possible approaches for analysis.
The viewpoint that noise is an element we want to understand, rather than something to be avoided, eliminated, or "averaged out" in the modeling or computational analysis process, has opened up research areas that can be a great source of interesting problems, even in relatively simple systems. Young researchers in particular have found accessible new directions of exploration and computational methods that let them "see inside" select systems.
The involvement of young researchers is also present in this collection of articles: two involve graduate student research, and one is a follow-up on an undergraduate computational project. As you'll see, all the approaches involve interdisciplinary research that combines physical modeling and mathematical frameworks with computational expertise.
The article on kink stochastics, for example, demonstrates computations in a canonical model for coherent structures—localized structures in what seems like unstructured behavior in thermodynamic and reactive processes. Here, the issue is how to obtain numerical accuracy in difficult-to-maintain regimes. For instance, we want computational results in situations not limited to low temperatures, which means doing a full computation of the interactions, rather than using low-temperature approximations. To illustrate convergence of the appropriate physical quantities, the article's authors compare computations with exact solutions wherever possible, thus benchmarking the schemes and allowing further exploration of complex kink interaction.
The article on seismic imaging deals with issues of image reconstruction in which the data isn't given in an ideal format—specifically, in the images that represent the wave fronts used to sample the Earth's structure or seismic activity. Finding an effective representation of the data has all the classical difficulties of imaging, including how noise and large data sets can make processing expensive. In addition, data can be acquired via nonuniform sampling, which can introduce artifacts if not handled carefully. Here, a modified version of the curvelet transform helps sift out noise effects without sensitivity to the data's irregular sampling.
The article on ship dynamics overviews a combination of methods used to identify the factors that can lead to dangerous rolling motions at sea. The process involves identifying variable nonlinear interactions, extracting the type of noise in the system, and constructing an excitation process that includes the appropriate noise and spectrum relevant for marine applications. The authors built all these aspects into a reasonable model for predicting unwanted rolling motions in ships, particularly those that are indirectly excited. This prediction can help optimize hull geometry.
Finally, the article on machine tool dynamics provides a construction that illustrates how even small noise can cause large changes in a physical system. An averaged model, in which noise is neglected, suggests a stable, smooth behavior, and thus fails to capture noise-driven instability, whereas computational methods investigating the full system can be expensive and noise-insensitive. The author outlines a reduced approach to show how noise effects are amplified in this sensitive range and provides a computationally efficient approach for exploring the resulting behavior.
Although this issue can't cover all the possible ways in which noise appears in physical systems and the computational methods used to study them, it does give a taste of the different issues that appear and some of the new numerical approaches used to understand the interactions of noise with complexity. Hopefully, the articles will provide some insight into the noise challenges you deal with in your own work.