Coherent patterns and self-induced diffraction of electrons on a thin nonlinear layer

Electron scattering on a thin layer where the potential depends self-consistently on the wave function has been studied. When the amplitude of the incident wave exceeds a certain threshold, a soliton-shaped brightening (darkening) appears on the layer causing diffraction of the wave. Thus the spontaneously formed transverse pattern can be viewed as a self-induced nonlinear quantum screen. Attractive or repulsive nonlinearities result in different phase shifts of the wave function on the screen, which give rise to quite different diffraction patterns. Among others, the nonlinearity can cause self-focusing of the incident wave into a beam, splitting in two "beams," single or double traces with suppressed reflection or transmission, etc.

Swarm Intelligent Selection and Optimization of Machining System Parameters for Microchannel Fabrication in Medical Devices

Current technology trends in medical device industry calls for fabrication of massive arrays of microfeatures such as microchannels on to nonsilicon material substrates with high accuracy, superior precision, and high throughput. Microchannels are typical features used in medical devices for medication dosing into the human body, analyzing DNA arrays or cell cultures. In this study, the capabilities of machining systems for micro-end milling have been evaluated by conducting experiments, regression modeling, and response surface methodology. In machining experiments by using micromilling, arrays of microchannels are fabricated on aluminium and titanium plates, and the feature size and accuracy (width and depth) and surface roughness are measured. Multicriteria decision making for material and process parameters selection for desired accuracy is investigated by using particle swarm optimization (PSO) method, which is an evolutionary computation method inspired by genetic algorithms (GA). Appropriate regression models are utilized within the PSO and optimum selection of micromilling parameters; microchannel feature accuracy and surface roughness are performed. An analysis for optimal micromachining parameters in decision variable space is also conducted. This study demonstrates the advantages of evolutionary computing algorithms in micromilling decision making and process optimization investigations and can be expanded to other applications

Nonlinear principal and canonical directions from continuous extensions of multidimensional scaling

A continuous random variable is expanded as a sum of a sequence of uncorrelated random variables. These variables are principal dimensions in continuous scaling on a distance function, as an extension of classic scaling on a distance matrix. For a particular distance, these dimensions are principal components. Then some properties are studied and an inequality is obtained. Diagonal expansions are considered from the same continuous scaling point of view, by means of the chi-square distance. The geometric dimension of a bivariate distribution is defined and illustrated with copulas. It is shown that the dimension can have the power of continuum.

Full instability behavior of N-dimensional dynamical systems with a one-directional nonlinear vector field

We show how certain N-dimensional dynamical systems are able to exploit the full instability capabilities of their fixed points to do Hopf bifurcations and how such a behavior produces complex time evolutions based on the nonlinear combination of the oscillation modes that emerged from these bifurcations. For really different oscillation frequencies, the evolutions describe robust wave form structures, usually periodic, in which selfsimilarity with respect to both the time scale and system dimension is clearly appreciated. For closer frequencies, the evolution signals usually appear irregular but are still based on the repetition of complex wave form structures. The study is developed by considering vector fields with a scalar-valued nonlinear function of a single variable that is a linear combination of the N dynamical variables. In this case, the linear stability analysis can be used to design N-dimensional systems in which the fixed points of a saddle-node pair experience up to N21 Hopf bifurcations with preselected oscillation frequencies. The secondary processes occurring in the phase region where the variety of limit cycles appear may be rather complex and difficult to characterize, but they produce the nonlinear mixing of oscillation modes with relatively generic features

Experimental analysis of optimization techniques on the road passenger transportation problem

Analyzing the state of the art in a given field in order to tackle a new problem is always a mandatory task. Literature provides surveys based on summaries of previous studies, which are often based on theoretical descriptions of the methods. An engineer, however, requires some evidence from experimental evaluations in order to make the appropriate decision when selecting a technique for a problem. This is what we have done in this paper: experimentally analyzed a set of representative state-of-the-art techniques in the problem we are dealing with, namely, the road passenger transportation problem. This is an optimization problem in which drivers should be assigned to transport services, fulfilling some constraints and minimizing some function cost. The experimental results have provided us with good knowledge of the properties of several methods, such as modeling expressiveness, anytime behavior, computational time, memory requirements, parameters, and free downloadable tools. Based on our experience, we are able to choose a technique to solve our problem. We hope that this analysis is also helpful for other engineers facing a similar problem