A hybrid proper orthogonal decomposition and next generation reservoir computing approach for high-dimensional chaotic prediction: Application to flow-induced vibration of tube bundles.

Chaotic time series prediction is a central science problem in diverse areas, ranging from engineering, economy to nature. Classical chaotic prediction techniques are limited to short-term prediction of low- or moderate-dimensional systems. Chaotic prediction of high-dimensional engineering problems is notoriously challenging. Here, we report a hybrid approach by combining proper orthogonal decomposition (POD) with the recently developed next generation reservoir computing (NGRC) for the chaotic forecasting of high-dimensional systems. The hybrid approach integrates the synergistic features of the POD for model reduction and the high efficiency of NGRC for temporal data analysis, resulting in a new paradigm on data-driven chaotic prediction. We perform the first chaotic prediction of the nonlinear flow-induced vibration (FIV) of loosely supported tube bundles in crossflow. Reducing the FIV of a continuous beam into a 3-degree-of-freedom system using POD modes and training the three time coefficients via a NGRC network with three layers, the hybrid approach can predict time series of a weakly chaotic system with root mean square prediction error less than 1% to 19.3 Lyapunov time, while a three Lyapunov time prediction is still achieved for a highly chaotic system. A comparative study demonstrates that the POD-NGRC outperforms the other existing methods in terms of either predictability or efficiency. The efforts open a new avenue for the chaotic prediction of high-dimensional nonlinear dynamic systems.

Coupled controls of the infiltration of rivers, urban activities and carbonate on trace elements in a karst groundwater system from Guiyang, Southwest China.

Hydrogeochemical processes of trace elements (TEs) are of considerable significance to river water and groundwater resource assessment and utilization in the karst region. Therefore, seven TEs were analyzed to investigate their contents, spatial variations, sources, and controlling factors in Guiyang, a typical karst urban area in southwest China. The results showed that the average content of TEs in river water (e.g., As = 1.44 ± 0.47 µg/L andCo = 0.15 ± 0.06 µg/L) was higher than that of groundwater (e.g., As = 0.51 ± 0.42 µg/L andCo = 0.09 ± 0.05 µg/L). The types of groundwater samples were dominated by Ca/Mg-HCO3 and Ca/Mg-Cl types, while those of the river water samples were Ca-Cl and Ca/Mg-Cl types. Principal component analysis (PCA) and correlation analysis (CA) analyses indicated that As and Mn in the groundwater of the study area were related to river infiltration. The end-member analysis further revealed that river infiltration (As = 0.86-1.81 µg/L, Cl/SO42- = 0.62-0.89) and urban activities (As = 0.21-0.32 µg/L, Cl/SO42- = 0.51-0.89) were two main controlling factors of TEs (e.g., As, Co, and Mn) in the study area. In addition, the ion ratios in river and groundwater samples indicated that the weathering of carbonates was also an important control on the hydrogeochemistry of TEs (e.g., Fe and Mn) in Guiyang waters. This study showed that the trace element (TE) contents of groundwater in the Guiyang area were greatly associated with urban input and river recharge, and provided a new perspective for understanding the geochemical behavior of TEs in urban surface and groundwater bodies, which will help the protection of groundwater in the karst areas of southwest China.

Reaction-induced swelling of ionic gels.

A chemomechanical theory is proposed to describe the dynamic behavior and response time of ionic gels. The large deformation of these gels accompanied by the migration of mobile ions is driven by a common non-equilibrium chemical reaction. The theoretical model was validated using existing experimental data. Further investigations showed that the dynamic deformation and response time of an ionic gel are dependent on the concentration of reactive and non-reactive ions, the time of exposure to external stimuli, the initial state and the density of ionizable groups on the polymer chains.

Exceptionally tough and notch-insensitive magnetic hydrogels.

Most existing magnetic hydrogels are weak and brittle. The development of strong and tough magnetic hydrogels would extend their applications into uncultivated areas, such as in actuators for soft machines and guided catheters for magnetic navigation systems, which is still a big challenge. Here a facile and versatile approach to fabricating highly stretchable, exceptionally tough and notch-insensitive magnetic hydrogels, Fe(3)O(4)@Fe-alginate/polyacrylamide (PAAm), is developed, by dispersing alginate-coated Fe(3)O(4) nanoparticles into the interpenetrating polymer networks of alginate and PAAm, with hybrid physical and chemical crosslinks. A cantilever bending beam actuator as well as a proof-of-concept magnetically guided hydrogel catheter is demonstrated. The method proposed in this work can be integrated into other strong and tough magnetic hydrogels for the development of novel hydrogel nanocomposites with both desirable functionality and superior mechanical properties.

Photoactive Self-Shaping Hydrogels as Noncontact 3D Macro/Microscopic Photoprinting Platforms.

A photocleavable terpolymer hydrogel cross-linked with o-nitrobenzyl derivative cross-linker is shown to be capable of self-shaping without losing its physical integrity and robustness due to spontaneous asymmetric swelling of network caused by UV-light-induced gradient cleavage of chemical cross-linkages. The continuum model and finite element method are used to elucidate the curling mechanism underlying. Remarkably, based on the self-changing principle, the photosensitive hydrogels can be developed as photoprinting soft and wet platforms onto which specific 3D characters and images are faithfully duplicated in macro/microscale without contact by UV light irradiation under the cover of customized photomasks. Importantly, a quick response (QR) code is accurately printed on the photoactive hydrogel for the first time. Scanning QR code with a smartphone can quickly connect to a web page. This photoactive hydrogel is promising to be a new printing or recording material.

Tough photoluminescent hydrogels doped with lanthanide.

Photoluminescent hydrogels have emerged as novel soft materials with potential applications in many fields. Although many photoluminescent hydrogels have been fabricated, their scope of usage has been severely limited by their poor mechanical performance. Here, a facile strategy is reported for preparing lanthanide (Ln)-alginate/polyacrylamide (PAAm) hydrogels with both high toughness and photoluminescence, which has been achieved by doping Ln(3+) ions (Ln = Eu, Tb, Eu/Tb) into alginate/PAAm hydrogel networks, where Ln(3+) ions serve as both photoluminescent emitters and physical cross-linkers. The resulting hydrogels exhibit versatile advantages including excellent mechanical properties (∼ MPa strength, ≈ 20 tensile strains, ≈ 10(4) kJ m(-3) energy dissipation), good photoluminescent performance, tunable emission color, excellent processability, and cytocompatibility. The developed tough photoluminescent hydrogels hold great promises for expanding the usage scope of hydrogels.

Self-healing gels based on constitutional dynamic chemistry and their potential applications.

As representative soft materials with widespread applications, gels with various functions have been developed. However, traditional gels are vulnerable to stress-induced formation of cracks. The propagation of these cracks may affect the integrity of network structures of gels, resulting in the loss of functionality and limiting the service life of the gels. To address this challenge, self-healing gels that can restore their functionalities and structures after damage have been developed as "smart" soft materials. In this paper, we present an overview of the current strategies for synthesizing self-healing gels based on the concept of constitutional dynamic chemistry, which involves molecular structures capable of establishing dynamic networks based upon physical interactions or chemical reactions. The characterization methods of self-healing gels and the key factors that affect self-healing properties are analyzed. We also illustrate the emerging applications of self-healing gels, with emphasis on their usage in industry (coatings, sealants) and biomedicine (tissue adhesives, agents for drug or cell delivery). We conclude with a perspective on challenges facing the field, along with prospects for future development.

Kinetic modelling and bifurcation analysis of chemomechanically miniaturized gels under mechanical load.

Chemomechanically responsive gels, with great potential applications in the fields of smart structures and biomedicines, present autonomously oscillatory deformation driven by the Belousov-Zhabotinsky chemical reaction. The dynamic behavior of the responsive gels is obviously affected by the external mechanical load. This approach proposed a kinetic model with an ordinary differential equation to describe the oscillatory deformation of the gels under the mechanical load. Then the periodic solutions and phase diagrams of the oscillation are obtained using the improved Runge-Kutta and shooting methods. The results demonstrated that bifurcations are typically existent in the system and the characters of the oscillatory deformation regularly depend on the mechanical load as well as the concentration of reactants and the stoichiometric coefficient of chemical reaction. This development is supposed to promote the practical applications of the chemomechanically responsive gels.

Designing Soft Mobile Machines Enabled by Dielectric Elastomer Minimum Energy Structures.

Dielectric elastomers (DE) are ideal electro-active polymers with large voltage-induced deformation for the design and realization of soft machines. Among the diversity of configurations of DE-based soft machines, dielectric elastomer minimum energy structures (DEMES) are unique due to their ease of fabrication, readiness to extend into multiple segments, and versatility of design configurations. Despite many successful demonstrations of DEMES actuators, these DEMES devices are limited to immobile use. We report several possible implementations of soft mobile machines through the combination of DEMES design, finite element simulation, and experiment. Our designs mimic the biomimetic locomotion of inchworms and marry complex components such as ratchet wheels with soft DEMES actuators. We even elucidate that buckling of DE can be harnessed to achieve asymmetric feet, which is otherwise realized via more complicated means. The examples presented here enrich DE devices' design and provide valuable insights into the design and fabrication of soft machines that other soft-active materials enable. All the codes and files used in this paper can be downloaded from GitHub.

A Biomimetic 3D-Self-Forming Approach for Microvascular Scaffolds.

The development of science and technology often drew lessons from natural phenomena. Herein, inspired by drying-driven curling of apple peels, hydrogel-based micro-scaled hollow tubules (MHTs) are proposed for biomimicking microvessels, which promote microcirculation and improve the survival of random skin flaps. MHTs with various pipeline structures are fabricated using hydrogel in corresponding shapes, such as Y-branches, anastomosis rings, and triangle loops. Adjustable diameters can be achieved by altering the concentration and cross-linking time of the hydrogel. Based on this rationale, biomimetic microvessels with diameters of 50-500 µm are cultivated in vitro by coculture of MHTs and human umbilical vein endothelial cells. In vivo studies show their excellent performance to promote microcirculation and improve the survival of random skin flaps. In conclusion, the present work proposes and validifies a biomimetic 3D self-forming method for the fabrication of biomimetic vessels and microvascular scaffolds with high biocompatibility and stability based on hydrogel materials, such as gelatin and hyaluronic acid.

Engineering ellipsoidal cap-like hydrogel particles as building blocks or sacrificial templates for three-dimensional cell culture.

Hydrogel particles that can be engineered to compartmentally culture cells in a three-dimensional (3D) and high-throughput manner have attracted increasing interest in the biomedical area. However, the ability to generate hydrogel particles with specially designed structures and their potential biomedical applications need to be further explored. This work introduces a method for fabricating hydrogel particles in an ellipsoidal cap-like shape (i.e., ellipsoidal cap-like hydrogel particles) by employing an open-pore anodic aluminum oxide membrane. Hydrogel particles of different sizes are fabricated. The ability to produce ellipsoidal cap-like magnetic hydrogel particles with controlled distribution of magnetic nanoparticles is demonstrated. Encapsulated cells show high viability, indicating the potential for using these hydrogel particles as structure- and remote-controllable building blocks for tissue engineering application. Moreover, the hydrogel particles are also used as sacrificial templates for fabricating ellipsoidal cap-like concave wells, which are further applied for producing size controllable cell aggregates. The results are beneficial for the development of hydrogel particles and their applications in 3D cell culture.

Electroluminescence of Giant Stretchability.

A new type of electroluminescent device achieves giant stretchability by integrating electronic and ionic components. The device uses phosphor powders as electroluminescent materials, and hydrogels as stretchable and transparent ionic conductors. Subject to cyclic voltage, the phosphor powders luminesce, but the ionic conductors do not electrolyze. The device produces constant luminance when stretched up to an area strain of 1500%.

Tough Al-alginate/poly(N-isopropylacrylamide) hydrogel with tunable LCST for soft robotics.

Tough Al-alginate/poly(N-isopropylacrylamide) (PNIPAM) hydrogel has been synthesized by introducing an interpenetrating network with hybrid physically cross-linked alginate and chemically cross-linked PNIPAM. Varying the concentration of AlCl3 regulates the mechanical properties of the tough hydrogel and tunes its lower critical solution temperature (LCST) as well. The tough Al-alginate/PNIPAM exhibits 6.3 ± 0.3 MPa of compressive stress and 9.95 of uniaxial stretch. Tunability of LCST is also achieved in a wide range within 22.5-32 °C. A bending beam actuator and a four-arm gripper made of bilayer (Na-alginate/PNIPAM)/(Al-alginate/PNIPAM) hydrogel as prototype of all-hydrogel soft robotics are demonstrated. A finite element (FE) simulation model is developed to simulate the deformation of the soft robotics. The FE simulation not only reproduces the deformation process of performed experiments but also predicts more complicated devices that can be explored in the future. This work broadens the application of temperature-responsive PNIPAM-based hydrogels.

Highly stretchable and transparent ionogels as nonvolatile conductors for dielectric elastomer transducers.

Large deformation of soft materials is harnessed to provide functions in the nascent field of soft machines. This paper describes a new class of systems enabled by highly stretchable, transparent, stable ionogels. We synthesize an ionogel by polymerizing acrylic acid in ionic liquid 1-ethyl-3-methylimidazolium ethylsulfate ([C2mim][EtSO4]). The ionogel exhibits desired attributes of adequate conductivity (0.22 S m(-1)), low elastic modulus (∼3 kPa), large rupturing stretch (∼4.6), and negligible hysteresis and degradation after cyclic stretches of large amplitude. Using the ionogel and a dielectric elastomer, we fabricate electromechanical transducers that achieve a voltage-induced areal strain of 140%. The ionogel is somewhat hygroscopic, but the transducers remain stable after a million cycles of excitation in a dry oven and in air. The transparency of the ionogels enable the transducers with conductors placed in the path of light, and the nonvolatility of the ionogels enable the transducers to be used in open air.

Nano-optomechanical actuator and pull-back instability.

This paper studies the nonlinear behavior of a nano-optomechanical actuator, consisting of a free-standing arc in a ring resonator that is coupled to a bus waveguide through evanescent waves. The arc deflects when a control light of a fixed wavelength and optical power is pumped into the bus waveguide, while the amount of deflection is monitored by measuring the transmission spectrum of a broadband probe light. This nanoactuator achieves a maximal deflection of 43.1 nm, with a resolution of 0.28 nm. The optical force is a nonlinear function of the deflection of the arc, leading to pull-back instability when the control light is red-tuned. This instability is studied by a combination of experiment and modeling. Potential applications of the nanoactuator include bio-nanomotor, optical switches, and optomechanical memories.

Strengthening alginate/polyacrylamide hydrogels using various multivalent cations.

We successfully synthesized a family of alginate/polyacrylamide hydrogels using various multivalent cations. These hydrogels exhibit exceptional mechanical properties. In particular, we discovered that the hydrogels cross-linked by trivalent cations are much stronger than those cross-linked by divalent cations. We demonstrate stretchability and toughness of the hydrogels by inflating a hydrogel sheet into a large balloon, and the elasticity by using a hydrogel block as a vibration isolator in a forced vibration test. The excellent mechanical properties of these hydrogels may open up applications for hydrogels.