Controlled surface patterns are useful in a wide range of applications including flexible electronics, elastomeric optics, fluidic channels, surface engineering, measurement technique, biological templates, stamps, and sensors. In this work, we report on the controlled formation of surface patterns in metal films deposited on elasticity-gradient polydimethylsiloxane (PDMS) substrates. Because of the temperature gradient during the curing process, the PDMS substrate in each sample successively changes from a purely liquid state at one side to a purely elastic state at the opposite side. It is found that surface folds appear in the liquid or viscous PDMS region while wrinkles form in the elastic region. In the transition region from the liquid to elastic PDMS, a nested pattern (i.e., the coexisting of folds and wrinkles) can be observed. The folding wave is triggered by the intrinsic stress during the film deposition and its wavelength is independent of the film thickness. The wrinkling wave is induced by the thermal compression after deposition and its wavelength is proportional to the film thickness. The report in this work could promote better understanding of the effect of substrate elasticity on the surface patterns and fabrication of such patterns (folds and wrinkles) by tuning the substrate property.

Strain-induced complex surface patterns such as wrinkles, folds and hierarchical structures are quite useful in a wide range of practical applications. Although various surface patterns have been extensively investigated, precisely controlling the coexistence and transition of multimodal structures is still a challenge. In this work, we report on a facile technique to harness fold-to-wrinkle transition and hierarchical wrinkling on soft material surfaces by regulating substrate stiffness and sputtering flux. It is found that as the substrate stiffness or sputtering flux increases, the surface patterns successively evolve from networked folds to isolated folds (coexistence of folds and wrinkles) and finally to labyrinth-like wrinkles. For larger sputtering flux, two distinct wrinkling patterns (i.e., G1 wrinkling due to surface instability during sputtering and G2 wrinkling due to thermal compression after deposition) can coexist on the sample surfaces, resulting in the spontaneous formation of hierarchical wrinkles. The report in this work could promote better understanding of the sputtering effect on the spontaneous pattern formation for soft materials and controllable fabrication of multiple complex patterns by simply regulating substrate stiffness and sputtering flux.

Surface wrinkles in homogeneous and heterogeneous film-substrate systems have received intense attention in both science and engineering. Understanding the wrinkling phenomena of heterogeneous systems with continuously variable features is still a challenge. In this work, we propose an unconventional strategy to prepare periodic thickness-gradient metal films on polydimethylsiloxane (PDMS) substrates by masking of copper grids which are weaved by orthometric copper wires. It is found that a periodic thickness-gradient film spontaneously forms during the sputtering process because of the specific structures of the copper grids. Surface wrinkles are strongly modulated by the copper grid structures and are position-dependent within a period. A phase diagram has been established to correlate the wrinkle morphology with the mesh size and film thickness. The film surfaces at mesh centers are evolved from labyrinth wrinkling to herringbone wrinkling and then to stripe wrinkling and finally to wrinkling-free state when the mesh size decreases and/or the film thickness increases. The morphological characteristics, evolutional behaviors, and underlying mechanisms of such wrinkling are discussed in detail based on the stress theory and numerical simulation.

Biofuel production in China suffers from many uncertainties due to concerns about the government's support policy and supply of biofuel raw material. Predicting biofuel production is critical to the development of this energy industry. Depending on the biofuel's characteristics, we improve the prediction precision of the conventional prediction method by creating a dynamic fuzzy grey-Markov prediction model. Our model divides random time series decomposition into a change trend sequence and a fluctuation sequence. It comprises two improvements. We overcome the problem of considering the status of future time from a static angle in the traditional grey model by using the grey equal dimension new information and equal dimension increasing models to create a dynamic grey prediction model. To resolve the influence of random fluctuation data and weak anti-interference ability in the Markov chain model, we improve the traditional grey-Markov model with classification of states using the fuzzy set theory. Finally, we use real data to test the dynamic fuzzy prediction model. The results prove that the model can effectively improve the accuracy of forecast data and can be applied to predict biofuel production. However, there are still some defects in our model. The modeling approach used here predicts biofuel production levels based upon past production levels dictated by economics, governmental policies, and technological developments but none of which can be forecast accurately based upon past events.

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In this paper, a Hirota method is developed for applying to the nonlinear Schrö dinger equation with an arbitrary time-dependent linear potential which denotes the dynamics of soliton solutions in quasi-one-dimensional Bose-Einstein condensation. The nonlinear Schrö dinger equation is decoupled to two equations carefully. With a reasonable assumption the one-and two-soliton solutions are constructed analytically in the presence of an arbitrary time-dependent linear potential.

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We investigated random lasing from a fluid self-assembly sphere-phase liquid crystal, which was composed of three-dimensional twist sphere structures with disclinations among them. The threshold energy of the random lasing from sphere-phase liquid crystal was 32% of that from the chiral nematic phase because of the interference associated with multiple scattering by randomly distributed sphere-phase platelets. Such random lasers composed of self-assembly soft organic materials may be useful for holographic displays, point-of-care biomedical analysis, and optical security coatings.