Complex Dynamical Behavior of Holling–Tanner Predator-Prey Model with Cross-Diffusion

Spatial predator-prey models have been studied by researchers for many years, because the exact distributions of the population can be well illustrated via pattern formation. In this paper, amplitude equations of a spatial Holling–Tanner predator-prey model are studied via multiple scale analysis. First, by amplitude equations, we obtain the corresponding intervals in which different kinds of patterns will be onset. Additionally, we get the conclusion that pattern transitions of the predator are induced by the increasing rate of conversion into predator biomass. Specifically, pattern transitions of the predator between distinct Turing pattern structures vary in an orderly manner: from spotted patterns to stripe patterns, and finally to black-eye patterns. Moreover, it is discovered that pattern transitions of prey can be induced by cross-diffusion; that is, patterns of prey transmit from spotted patterns to stripe patterns and finally to a mixture of spot and stripe patterns. Meanwhile, it is found that both effects of cross-diffusion and interaction between the prey and predator can lead to the complicated phenomenon of dynamics in the system of biology.

Turing Patterns for a Nonlocal Lotka–Volterra Cooperative System

This paper is devoted to investigating the pattern dynamics of Lotka–Volterra cooperative system with nonlocal effect and finding some new phenomena. Firstly, by discussing the Turing bifurcation, we build the conditions of Turing instability, which indicates the emergence of Turing patterns in this system. Then, by using multiple scale analysis, we obtain the amplitude equations about different Turing patterns. Furthermore, all possible pattern structures of the model are obtained through some transformation and stability analysis. Finally, two new patterns of the system are given by numerical simulation.

The rise in maximum determinant matrix complexity

Introduction: In spite of the apparent relation between maximum determinant matrices of even (Hadamard matrices) and odd orders, the latter have particularly complex patterns of repetitive elements. This is what makes them unique and attractive for various applications in visual data processing, coding and masking. Purpose: Developing the theory of maximum determinant matrices, with the focus on using computer-aided analysis, and calculating unique matrices with unique pattern structures in their portraits. Results: We have found some peculiarities of maximum determinant matrices, outlined their families related to Fermat numbers, demonstrated the complication of patterns in other matrices as their orders grow. The presumption about the increasing complexity of structures as the matrix orders grow is confirmed by a chain of matrix portraits we demonstrate. As applied to orthogonal Belevitch matrices, it follows that they cannot be found even in small orders such as 66 or 86.

Experiment and Simulation Research on the Fatigue Wear of Aircraft Tire Tread Rubber

The road surface and the tread pattern structures directly affect the wear performance of aircraft tire, especially for lateral sliding conditions. In this paper, wear tests of tread block with different draft angles and root radiuses, different interfaces, and different slip angles were carried out, and combined with the simulation, the effects of tread groove structure and slip angle on the wear mechanism were analyzed. Results indicated that the influences of draft angle were greater than the root radius; the wear geometry of the tread block decreased when the draft angle increased in the range of 0° to 15°, but for the root radius, the wear geometry of each sample was similar to a strip shape. A considerable material loss occurred at the front edge when the slip angle increased, and the slip angle was larger in the range of 0° to 45°. Combined with the simulation and wear test, fatigue wear and abrasive wear of the slide surface are dominant factors when considering the effects of tread groove structure and slip angle, and both front edges of the tread blocks roll up repeatedly; the coefficient decreases with the increase in load when the cement concrete pavement interface is dry, but for a wet interface, the coefficient decreases softly.

Laser Interference Lithography for Fabrication of Planar Scale Gratings for Optical Metrology

Laser interference lithography is an attractive method for the fabrication of a large-area two-dimensional planar scale grating, which can be employed as a scale for multi-axis optical encoders or a diffractive optical element in many types of optical sensors. Especially, optical configurations such as Lloyd’s mirror interferometer based on the division of wavefront method can generate interference fringe fields for the patterning of grating pattern structures at a single exposure in a stable manner. For the fabrication of a two-dimensional scale grating to be used in a planar/surface encoder, an orthogonal two-axis Lloyd’s mirror interferometer, which has been realized through innovation to Lloyd’s mirror interferometer, has been developed. In addition, the concept of the patterning of the two-dimensional orthogonal pattern structure at a single exposure has been extended to the non-orthogonal two-axis Lloyd’s mirror interferometer. Furthermore, the optical setup for the non-orthogonal two-axis Lloyd’s mirror interferometer has been optimized for the fabrication of a large-area scale grating. In this review article, principles of generating interference fringe fields for the fabrication of a scale grating based on the interference lithography are reviewed, while focusing on the fabrication of a two-dimensional scale grating for planar/surface encoders. Verification of the pitch of the fabricated pattern structures, whose accuracy strongly affects the performance of planar/surface encoders, is also an important task to be addressed. In this paper, major methods for the evaluation of a grating pitch are also reviewed.

Microsteganography on All Inorganic Perovskite Micro-Platelets by Direct Laser Writing

Direct laser writing (DLW) is a mask-free and cost-efficient micro-fabrication technology, which has been explored to pattern structures on perovskites. However, there is still a lack of research on DLW...