Investigation on the Concept of Limit Involving E by Exploring the Secret of Mr. Buffet

This article uses problem-driven teaching methods to explore a mathematical class of important limit in course design. We first start with the story of Buffett’s wealth to gain students’ interest in the concept. We establish mathematical models based on the financial management issues and guide students to explore them. Then, through the analysis of the compound interest problem, solution with limit expression of the problem and its relationship with the natural constant e are obtained. Finally, in response to Buffett’s sentiment, we use this limit to analyze and explain the mathematical principles of investment issues and to lead students to think about their views of life and values, resulting in a positive influence on their life planning

Coupled Interactions Analysis of a Floating Tidal Current Power Station in Uniform Flow

For a floating tidal current power station moored in the sea, the mutual interactions between the carrier and the turbine are pretty complex. Current simulation methods based on potential flow theory could not consider the complicated viscous effects between the carrier motion and rotor rotation. To accurately account for the viscous effect, developing a different numerical simulation method based on computational fluid dynamics is necessary. This paper deals with a moored FTCPS (floating tidal current power station) with 6-degree-of-freedom motion in uniform flow based on dynamic fluid body interactions (DFBI) method. Results showed that the blockage effect caused by the columns would increase the average power output of the turbine, while the power output fluctuation also increased. When the carrier is individually moored in the sea, the motion response of the carrier is pretty small, and the carrier is obviously trimming by the bow. However, when the turbine is mounted on the carrier, the carrier motion response is simple harmonic. The motion response frequency of the carrier is in relation to the rotation frequency of the turbine

Interaction of the Hydrophobic Tip of an Atomic Force Microscope with Oligopeptides Immobilized Using Short and Long Tethers

We report an investigation of the adhesive force generated between the hydrophobic tip of an atomic force microscope (AFM) and surfaces presenting oligopeptides immobilized using either short (∼1 nm) or long (∼60 nm) tethers. Specifically, we used either sulfosuccinimidyl-4-(<i>N</i>-maleimidomethyl)­cyclohexane-1-carboxylate (SSMCC) or 10 kDa polyethylene glycol (PEG) end-functionalized with maleimide and <i>N</i>-hydroxysuccinimide groups to immobilize helical oligomers of β-amino acids (β-peptides) to mixed monolayers presenting tetraethylene glycol (EG4) and amine-terminated EG4 (EG4N) groups. When SSMCC was used to immobilize the β-peptides, we measured the adhesive interaction between the AFM tip and surface to rupture through a single event with magnitude consistent with the interaction of a single β-peptide with the AFM tip. Surprisingly, this occurred even when, on average, multiple β-peptides were located within the interaction area between the AFM tip and surface. In contrast, when using the long 10 kDa PEG tether, we observed the magnitude of the adhesive interaction as well as the dynamics of the rupture events to unmask the presence of the multiple β-peptides within the interaction area. To provide insight into these observations, we formulated a simple mechanical model of the interaction of the AFM tip with the immobilized β-peptides and used the model to demonstrate that adhesion measurements performed using short tethers (but not long tethers) are dominated by the interaction of single β-peptides because (i) the mechanical properties of the short tether are highly nonlinear, thus causing one β-peptide to dominate the adhesion force at the point of rupture, and (ii) the AFM cantilever is mechanically unstable following the rupture of the adhesive interaction with a single β-peptide. Overall, our study reveals that short tethers offer the basis of an approach that facilitates measurement of adhesive interactions with single molecules presented at surfaces

Large-Area Electronics-Enabled High-Resolution Digital Microfluidics for Parallel Single-Cell Manipulation

Large-area electronics as switching elements are an ideal option for electrode-array-based digital microfluidics. With support of highly scalable thin-film semiconductor technology, high-resolution digital droplets (diameter around 100 μm) containing single-cell samples can be manipulated freely on a two-dimensional plane with programmable addressing logic. In addition, single-cell generation and manipulation as foundations for single-cell research demand ease of operation, multifunctionality, and accurate tools. In this work, we reported an active-matrix digital microfluidic platform for single-cell generation and manipulation. The active device contained 26,368 electrodes that could be independently addressed to perform parallel and simultaneous droplet generation and achieved single-cell manipulation. We demonstrate a high-resolution digital droplet generation with a droplet volume limit of 500 pL and show the continuous and stable movement of droplet-contained cells for over 1 h. Furthermore, the success rate of single droplet formation was higher than 98%, generating tens of single cells within 10 s. In addition, a pristine single-cell generation rate of 29% was achieved without further selection procedures, and the droplets containing single cells could then be tested for on-chip cell culturing. After 20 h of culturing, about 12.5% of the single cells showed cell proliferation

Active-matrix digital microfluidics design for field programmable high-throughput digitalized liquid handling

Summary: Digital liquid sample handling is an enabling tool for cutting-edge life-sciences research. We present here an active-matrix thin-film transistor (TFT) based digital microfluidics system, referred to as Field Programmable Droplet Array (FPDA). The system contains 256 × 256 pixels in an active area of 10.65 cm2, which can manipulate thousands of addressable liquid droplets simultaneously. By leveraging a novel TFT device and circuits design solution, we manage to programmatically manipulate droplets at single-pixel level. The minimum achievable droplet volume is around 0.5 nL, which is two orders of magnitude smaller than the smallest droplet ever reported on active-matrix digital microfluidics. The movement of droplets can be either pre-programmed or controlled in real-time. The FPDA system shows great potential of the ubiquitous thin-film electronics technology in digital liquid handling. These efforts will make it possible to create a true programmable lab-on-a-chip device to enable great advances in life science research

Large-Area Electronics-Enabled High-Resolution Digital Microfluidics for Parallel Single-Cell Manipulation

Large-area electronics as switching elements are an ideal option for electrode-array-based digital microfluidics. With support of highly scalable thin-film semiconductor technology, high-resolution digital droplets (diameter around 100 μm) containing single-cell samples can be manipulated freely on a two-dimensional plane with programmable addressing logic. In addition, single-cell generation and manipulation as foundations for single-cell research demand ease of operation, multifunctionality, and accurate tools. In this work, we reported an active-matrix digital microfluidic platform for single-cell generation and manipulation. The active device contained 26,368 electrodes that could be independently addressed to perform parallel and simultaneous droplet generation and achieved single-cell manipulation. We demonstrate a high-resolution digital droplet generation with a droplet volume limit of 500 pL and show the continuous and stable movement of droplet-contained cells for over 1 h. Furthermore, the success rate of single droplet formation was higher than 98%, generating tens of single cells within 10 s. In addition, a pristine single-cell generation rate of 29% was achieved without further selection procedures, and the droplets containing single cells could then be tested for on-chip cell culturing. After 20 h of culturing, about 12.5% of the single cells showed cell proliferation

2020 Roadmap on Zinc Metal Batteries

Metallic zinc (Zn) is considered to be a safe and low-cost anode for rechargeable batteries. Thus, several zinc metal batteries (ZMBs) have been well developed, i. e., zinc silver batteries, Zn−MnO batteries, nickel-zinc batteries, zinc-air batteries and other kinds of zinc ion batteries. ZMBs are strongly correlated with electrochemistry, electrodes, electrolytes and battery structures. To support the development of this field, we herein invite some famous research experts to write this roadmap for giving some guidance in future research. The roadmap will include their research status, challenge, opportunities, and the technology advance in their fields. We expect this roadmap will produce active influence in developing green, low-cost, safe ZMBs for our bright life in future

Large-Area Electronics-Enabled High-Resolution Digital Microfluidics for Parallel Single-Cell Manipulation

Large-area electronics as switching elements are an ideal option for electrode-array-based digital microfluidics. With support of highly scalable thin-film semiconductor technology, high-resolution digital droplets (diameter around 100 μm) containing single-cell samples can be manipulated freely on a two-dimensional plane with programmable addressing logic. In addition, single-cell generation and manipulation as foundations for single-cell research demand ease of operation, multifunctionality, and accurate tools. In this work, we reported an active-matrix digital microfluidic platform for single-cell generation and manipulation. The active device contained 26,368 electrodes that could be independently addressed to perform parallel and simultaneous droplet generation and achieved single-cell manipulation. We demonstrate a high-resolution digital droplet generation with a droplet volume limit of 500 pL and show the continuous and stable movement of droplet-contained cells for over 1 h. Furthermore, the success rate of single droplet formation was higher than 98%, generating tens of single cells within 10 s. In addition, a pristine single-cell generation rate of 29% was achieved without further selection procedures, and the droplets containing single cells could then be tested for on-chip cell culturing. After 20 h of culturing, about 12.5% of the single cells showed cell proliferation

Roadmap on Ionic Liquid Electrolytes for Energy Storage Devices

Ionic liquids are considered to be promising electrolyte solvents or additives for rechargeable batteries (i. e., lithium-ion batteries, sodium-ion batteries, lithium-sulfur batteries, aluminum-ion batteries, etc.) and supercapacitors. This is related with the superior physical and electrochemical properties of ionic liquids, which can influence the performance of rechargeable batteries. Therefore, it is necessary to write a roadmap on ionic liquids for rechargeable batteries. In this roadmap, some progress, critical techniques, opportunities and challenges of ionic liquid electrolytes for various batteries and supercapacitors are pointed out. Especially, properties and roles of ionic liquids should be considered in energy storage. Ionic liquids can be used as electrolyte salts, electrolyte additives, and solvents. For optimizing ionic liquid-based electrolytes for energy storage, their applications in various energy storage devices should be considered by combing native chemical/physical properties and their roles. We expect that this roadmap will give a useful guidance in directing future research in ionic liquid electrolytes for rechargeable batteries and supercapacitors