Doubly periodic patterns of modulated hydrodynamic waves:exact solutions of the Davey-Stewartson system

Exact doubly periodic standing wave patterns of the Davey-Stewartson （DS） equations are derived in terms of rational expressions of elliptic functions.In fluid mechanics,DS equations govern the evolution of weakly nonlinear,free surface wave packets when long wavelength modulations in two mutually perpendicular,horizontal directions are incorporated.Elliptic functions with two different moduli （periods） are necessary in the two directions.The relation between the moduli and the wave numbers constitutes the dispersion relation of such waves.In the long wave limit,localized pulses are recovered.

High Utility Periodic Frequent Pattern Mining in Multiple Sequences

Periodic patternmining has become a popular research subject in recent years;this approach involves the discoveryof frequently recurring patterns in a transaction sequence. However, previous algorithms for periodic patternmining have ignored the utility (profit, value) of patterns. Additionally, these algorithms only identify periodicpatterns in a single sequence. However, identifying patterns of high utility that are common to a set of sequencesis more valuable. In several fields, identifying high-utility periodic frequent patterns in multiple sequences isimportant. In this study, an efficient algorithm called MHUPFPS was proposed to identify such patterns. To addressexisting problems, three new measures are defined: the utility, high support, and high-utility period sequenceratios. Further, a new upper bound, upSeqRa, and two new pruning properties were proposed. MHUPFPS usesa newly defined HUPFPS-list structure to significantly accelerate the reduction of the search space and improvethe overall performance of the algorithm. Furthermore, the proposed algorithmis evaluated using several datasets.The experimental results indicate that the algorithm is accurate and effective in filtering several non-high-utilityperiodic frequent patterns.

Bifurcation Points of Periodic Triangular Patterns Obtained in Reaction-Diffusion System with Anisotropic Diffusion

Turing demonstrated that spatially heterogeneous patterns can be self-organized, when the two substances interact locally and diffuse randomly. Turing systems have been applied not only to explain patterns observed within the biological and chemical fields, but also to develop image information processing tools. In a twin study, to evaluate the V-shaped bundle of the inner ear outer hair, we developed a method that utilizes a reaction-diffusion system with anisotropic diffusion that exhibited triangular patterns with the introduction of a certain anisotropy strength. In this study, we explored the parameter range over which these periodic triangular patterns were obtained. First, we defined an index for triangular clearness, TC. Triangular patterns can be obtained by introducing a large anisotropy δ, but the range of δ depends on the diffusion coefficient. We found an explanatory variable that can explain the change in TC based on a heuristic argument of the relative distance of the pitchfork bifurcation point between the maximum and minimum anisotropic diffusion function values. Clear periodic triangular patterns were obtained when the distance between the minimum anisotropic function value and pitchfork bifurcation point was over 2.5 times the distance to the anisotropic diffusion function maximum value. By changing the diffusion coefficients or the reaction terms, we further confirmed the accuracy of this condition using computer simulation. Its relevance to diffusion instability has also been discussed.

Characteristics of Temperature Change in China over the Last 2000 years and Spatial Patterns of Dryness/Wetness during Cold and Warm Periods

This paper presents new high-resolution proxies and paleoclimatic reconstructions for studying climate changes in China for the past 2000 years. Multi-proxy synthesized reconstructions show that temperature variation in China has exhibited significant 50–70-yr, 100–120-yr, and 200–250-yr cycles. Results also show that the amplitudes of decadal and centennial temperature variation were 1.3℃ and 0.7℃, respectively, with the latter significantly correlated with long-term changes in solar radiation, especially cold periods, which correspond approximately to sunspot minima. The most rapid warming in China occurred over AD 1870–2000, at a rate of 0.56°± 0.42℃（100 yr）^（-1）; however, temperatures recorded in the 20 th century may not be unprecedented for the last 2000 years, as data show records for the periods AD 981–1100 and AD1201–70 are comparable to the present. The ensemble means of dryness/wetness spatial patterns in eastern China across all centennial warm periods illustrate a tripole pattern： dry south of 25°N, wet from 25°–30°N, and dry to the north of 30°N. However, for all centennial cold periods, this spatial pattern also exhibits a meridional distribution. The increase in precipitation over the monsoonal regions of China associated with the 20 th century warming can primarily be attributed to a mega El Nino–Southern Oscillation and the Atlantic Multidecadal Oscillation. In addition, a significant association between increasing numbers of locusts and dry/cold conditions is found in eastern China. Plague intensity also generally increases in concert with wetness in northern China, while more precipitation is likely to have a negative effect in southern China.

Rhythmic precipitate patterns and fractal structure

Liesegang patterns of parallel precipitate bands are obtained when solutions containing co-precipitate ions interdiffuse in a 1D gel matrix.The sparingly soluble salt formed,displays a beautiful stratification of discs of precipitate perpendicular to the 1D tube axis.The Liesegang structures are analyzed from the viewpoint of their fractal nature.Geometric Liesegang patterns are constructed in conformity with the well-known empirical laws such as the time,band spacing and band width laws.The dependence of the band spacing on the initial concentrations of diffusing（outer）and immobile（inner）electrolytes（A0 and B0,respectively）is taken to follow the Matalon-Packter law.Both mathematical fractal dimensions and box-count dimensions are calculated.The fractal dimension is found to increase with increasing A0 and decreasing B0.We also analyze mosaic patterns with random distribution of crystallites,grown under different conditions than the classical Liesegang gel method,and report on their fractal properties.Finally,complex Liesegang patterns wherein the bands are grouped in multiplets are studied,and it is shown that the fractal nature increases with the multiplicity.

Periodic surface functional group density on graphene via laserinduced substrate patterning at Si/SiO2 interface

Controlling the spatial distribution of functional groups on two-dimensional(2D)materials on a micrometer scale and below represents a fascinating opportunity to achieve anisotropic(opto)electronic properties of these materials.Periodic patterns of covalent functionalization can lead to pericxJic potentials in the monolayer;however,creating such superstructures is very challenging.Here,we describe an original approach to the periodic functionalization of graphene induced by substrate patterning using a pulsed laser.Laser-induced periodic surface structures(LIPSS)are produced on silicon wafers with thermally-grown oxide layers.The irradiation conditions for the formation of UPSS confined at the SiO2/Si interface have been unravelled.LIPSS imprint their periodicity to the reactivity of the monolayer graphene placed on the substrate via modulation of its local doping level.This method is clean,straightforward and scalable with high spatial resolution.

A flexible ultra-broadband metamaterial absorber working on whole K-bands with polarization-insensitive and wide-angle stability

For potential military applications, a flexible metamaterial absorber(MMA) working on whole K-bands with totalthickness of 3.367 mm, ultra-broadband, polarization-insensitive, and wide-angle stability is presented based on frequencyselective surface(FSS). The absorber is composed of polyvinyl chloride(PVC) layer, polyimide(PI) layer, and poly tetra fluoro ethylene(PTFE) layer, with a sandwich structure of PVC–PI–PTFE–metal plate. Periodic conductive patterns play a crucial role in the absorber, and in traditional, it is designed on the upper surface of PI layer to form LC resonance. Different from commonly absorber, all the patterns are located on the lower surface of the PI layer in this work, and hence the impedance matching and absorptivity are improved in this purposed absorber. The flexible absorber with patterns on lower surface of the PI layer is compared with that on upper surface of the PI layer, the difference and the reasons are explained by absorption mechanism based on equivalent circuit model, and surface current density and electric field distribution are used to analyze resonance peaks. Absorptivity is greater than 90% in a frequency range of 10.47 GHz–45.44 GHz with relative bandwidth of 125.1%, covering the whole Ku, K, Ka, and some of X, U bands, especially containing the whole K bands from 12 GHz to 40 GHz. Radar cross section(RCS) is reduced at least 10 dB in 11.48 GHz–43.87 GHz frequency ranges,and absorption remained about 90% when the incident angle changed from 0°to 55°. The purposed absorber is fabricated,measured, and experiment results show good agreement with theoretical analysis and numerical simulation. After bonded on outer surface of different cylinders with diameters of 200 mm and 100 mm, the absorption of MMA is approximately reduced 10% and 20% respectively, which shows good conformal character with surface of various curvatures. Due to the attractive performance on strong absorption in the whole K-bands, flexible and easy conformal, our design exhibits broad potential application in radar stealth and sensors.

Complex bursting patterns in Van der Pol system with two slowly changing external forcings

This paper investigates the generation of complex bursting patterns in Van der Pol system with two slowly changing external forcings. Complex bursting patterns, including complex periodic bursting and chaotic bursting, are presented for the cases when the two frequencies are commensurate and incommensurate. These complex bursting patterns are novel and have not been reported in previous work. Based on the fast-slow dynamics, the evolution processes of the slow forcing are presented to reveal the dynamical mechanisms undedying the appearance of these complex bursting patterns. With the change of ampli- tudes and frequencies, the slow forcing may visit the spiking and rest areas in different ways, which leads to the generation of different complex bursting patterns.