Detailed numerical simulation and experimental investigation on micromixers with serpentine Koch fractal microchannels

Micromixer is a kind of microfluidic chip for fast mixing and analysis. Mixing in a micromixer is usually a micron scale. At low Reynolds number, the fluid in the channel is laminar flow, which mainly depends on molecular diffusion as the main mixing mode. Fluid mixing in microchannels is very difficult, especially when the viscosity of the fluid is high. In this paper, we design a novel passive micromixer. The effects of fractal number, Koch fractal channel spacing, microchannel depth and cross-section shape on mixing efficiency were studied. Through a large number of numerical simulations, we continue to optimize the structure of the micromixer and improve the mixing efficiency. Finally, through the continuous optimization of the structure of the micromixer, the mixing efficiency of the micromixer can reach more than 95%.

Chaotic model for COVID-19 growth-factor

The new COVID-19 Pandemic caused by SARS-CoV-2 initiated in the world a largest quarantine, due to is exponential capacity of the virus in spreading from human contact. In the present work, it was evaluated the dynamics of such spreading by the indicator of growth-factor, and applied to it the space phase of the time series, the detrended fluctuation analysis (DFA) of the series, and the fractal dimension of the space phase. It was possible to notice a strange attractor in the space phase of the growth-factor, indicating that the process is chaotic deterministic. The value of the alpha coefficient by DFA showed to be less than 0.5, characteristic of long-range memory of the series, in which large events precedes small events. The fractal dimension of the phase space was a fractal number, between 1 and 2, another indicator that the exponential growth-rate of the virus spreading among humans is fractal. These results, even with small number of data, is pointing that the spread of COVID-19 is fractal.

AUTOMATIC DETECTION OF HANDWRITING FORGERY USING A FRACTAL NUMBER ESTIMATE OF WRINKLINESS

We investigate the detection of handwriting forged by novices. To facilitate document examination it is important to develop an automated system to identify forgeries, or at least to identify those handwritings that are likely to be forged. Because forgers often carefully copy or trace genuine handwriting, we hypothesize that good forgeries — those that retain the shape and size of genuine writing — are usually written more slowly and are therefore wrinklier (less smooth) than genuine writing. From online handwriting samples we find that the writing speed of the good forgeries is significantly slower than that of the genuine writings. From corresponding offline samples we find that the wrinkliness of the good forgeries is significantly greater than that of the genuine writings, showing that this feature can help identify candidate forgeries from scanned documents. Using a total of eight handwriting distance features, including the wrinkliness feature, we train a neural network to achieved 89% accuracy on detecting forged handwriting on test samples from ten writers.

Fractal Dimensions in Elastic-Plastic Beam Dynamics

Calculations of two types of fractal dimension are reported, regarding the elastic-plastic response of a two-degree-of-freedom beam model to short pulse loading. The first is Mandelbrot’s (1982) self-similarity dimension, expressing independence of scale of a figure showing the final displacement as function of the force in the pulse loading; these calculations were made with light damping. These results are equivalent to a microscopic examination in which the magnification is increased by factors of 102; 104; and 106. It is found that the proportion and distribution of negative final displacements remain nearly constant, independent of magnification. This illustrates the essentially unlimited sensitivity to the load parameter, and implies that the final displacement in this range of parameters is unpredictable. The second fractal number is the correlation dimension of Grassberger and Procaccia (1983), derived from plots of Poincare intersection points of solution trajectories computed for the undamped model. This fractional number for strongly chaotic cases underlies the random and discontinuous selection by the solution trajectory of the potential well leading to the final rest state, in the case of the lightly damped model.

Stereological Estimation of Fractal Number of Fracture Planes in Concrete

ABSTRACTConcrete is a man-made material containing a particulate filler designed on the basis of a sieve curve. In case of river aggregate, the particles are approximately spherical and smoothtextured. The particle-matrix interface is mostly the weakest chain link in the mechanical system. This implies damage evolution to start at particle-matrix interfaces. In case of direct tension, these interface cracks will be on average perpendicular to the loading direction. In case of direct compression, they will be parallel to the loading direction. A single fracture surface is formed in tension and a series of fracture surfaces in compression. They are the result of crack concentration within a process zone, in which the engineering crack closely meanders around a dividing plane. This allows to model these fracture surfaces on different resolution levels. It is shown, using stereological notions, that the very phenomenon is of a non-ideal fractal nature. Estimates for fractal dimension of fracture surfaces in concretes based on sieve curves at the border of the practical range are found to closely match experimental data reported in the literature.