Laws of 4D printing

The main difference between 3D and 4D printed structures is one extra dimension that is smart evolution over time. However, currently, there is no general formula to model and predict this extra dimension. Here, by starting from fundamental concepts, we derive and validate a universal bi-exponential formula that is required to model and predict the fourth D of 4D printed multi-material structures. 4D printing is a new manufacturing paradigm to elaborate stimuli-responsive materials in multi-material structures for advanced manufacturing (and construction) of advanced products (and structures). It conserves the general attributes of 3D printing (such as the elimination of molds, dies, and machining) and further enables the fourth dimension of products and structures to provide intelligent behavior over time. This intelligent behavior is encoded (usually by an inverse mathematical problem) into stimuli-responsive multi-materials during printing and is enabled by stimuli after printing. Here, we delve into the fourth dimension and reveal three general laws that govern the time-dependent shape-shifting behaviors of almost all (photochemical-, photothermal-, solvent-, pH-, moisture-, electrochemical-, electrothermal-, ultrasound-, enzyme-, etc.-responsive) multi-material 4D structures. We demonstrate that two different types of time-constants govern the shape-shifting behavior of almost all the multi-material 4D printed structures over time. Our results starting from the most fundamental concepts and ending with governing equations can serve as general design principles for future research in the 4D printing field, where the time-dependent behaviors should be understood, modeled, and predicted, correctly. Future software and hardware developments in 4D printing can also benefit from these results.Comment: This manuscript is currently under review in a journa

Invited Article: 4D Printing as a New Paradigm for Manufacturing with Minimum Energy Consumption

4D printing is a new manufacturing paradigm that combines stimuli-responsive materials, mathematics, and multi-material additive manufacturing to yield encoded multi-material structures with intelligent behavior over time. This emerging field has received growing interests from various disciplines such as space exploration, renewable energy, bioengineering, textile industry, infrastructures, soft robotics, and so on. Here, as a first attempt, we consider the energy aspect of 4D printing. By a thermodynamic analysis, we obtain the theoretical limit of energy consumption in 4D printing and prove that 4D printing can be the most energy-efficient manufacturing process. Before that, we clearly underpin 4D printing as a new manufacturing process and identify its unique attributes.Comment: Under Revisio

Lamb shift calculated by simple noncovariant method

The Lamb Shift (LS) of Hydrogenlike atom is evaluated by a simple method of quantum electrodynamics in noncovariant form, based on the relativistic stationary Schr\"odinger equation. An induced term proportional to $\overrightarrow{p}^4$ in the effective Hamiltonian is emphasized. Perturbative calculation of second order leads to the LS of $1S_{1/2}$ state and that of $2S_{1/2}-2P_{1/2}$ states in H atom with the high accuracy within 0.1%Comment: 9 pages, Revtex, 1 Postscript figur

Autonomous Driving System Design for Formula Student Driverless Racecar

This paper summarizes the work of building the autonomous system including detection system and path tracking controller for a formula student autonomous racecar. A LIDAR-vision cooperating method of detecting traffic cone which is used as track mark is proposed. Detection algorithm of the racecar also implements a precise and high rate localization method which combines the GPS-INS data and LIDAR odometry. Besides, a track map including the location and color information of the cones is built simultaneously. Finally, the system and vehicle performance on a closed loop track is tested. This paper also briefly introduces the Formula Student Autonomous Competition (FSAC) in 2017.Comment: The 2018 IEEE Intelligent Vehicles Symposiu

Half-CNN: A General Framework for Whole-Image Regression

The Convolutional Neural Network (CNN) has achieved great success in image classification. The classification model can also be utilized at image or patch level for many other applications, such as object detection and segmentation. In this paper, we propose a whole-image CNN regression model, by removing the full connection layer and training the network with continuous feature maps. This is a generic regression framework that fits many applications. We demonstrate this method through two tasks: simultaneous face detection & segmentation, and scene saliency prediction. The result is comparable with other models in the respective fields, using only a small scale network. Since the regression model is trained on corresponding image / feature map pairs, there are no requirements on uniform input size as opposed to the classification model. Our framework avoids classifier design, a process that may introduce too much manual intervention in model development. Yet, it is highly correlated to the classification network and offers some in-deep review of CNN structures

Comparison among Klein-Gordon equation, Dirac equation and Relativistic Stationary Schrodinger equation

A particle is always not pure. It always contains hiding antiparticle ingredient which is the essence of special relativity. Accordingly, the Klein-Gordon (KG) equation and Dirac equation are restudied and compared with the Relativistic Stationary Schr\"odinger Equation (RSSE). When an electron is bound in a Hydrogenlike atom with pointlike nucleus having charge number $Z$, the critical value of $Z, Z_c$, equals to 137 in Dirac equation whereas $Z_c=\sqrt{M/\mu} (137)$ in RSSE with $M$ and $\mu$ being the total mass of atom and the reduced mass of the electron.Comment: 10 pages, Revtex, 10 Postscript figure

Why can an electron mass vary from zero to infinity?

When a particle is in high speed or bound in the Coulomb potential of point nucleus, the variation of its mass can be ascribed to the variation of relative ratio of hiding antimatter to matter in the particle. At two limiting cases, the ratio approaches to 1.Comment: 8 pages, Latex, No Figur

Effects of the non-uniform initial environment and the guide field on the plasmoid instability

Effects of non-uniform initial mass density and temperature on the plasmoid instability are studied via 2.5-dimensional resistive magnetohydrodynamic(MHD) simulations. Our results indicate that the development of the plasmoid instability is apparently prevented when the initial plasma density at the center of the current sheet is higher than that in the upstream region. As a result, the higher the plasma density at the center and the lower the plasma $\beta$ in the upstream region, the higher the critical Lundquist number needed for triggering secondary instabilities. When $\beta =0.2$, the critical Lundquist number is higher than $10^4$. For the same Lundquist number, the magnetic reconnection rate is lower for the lower plasma $\beta$ case. Oppositely, when the initial mass density is uniform and the Lundquist number is low, the magnetic reconnection rate turns out to be higher for the lower plasma $\beta$ case. For the high Lundquist number case ($>10^4$) with uniform initial mass density, the magnetic reconnection is not affected by the initial plasma $\beta$ and the temperature distribution. Our results indicate that the guide field has a limited impact on the plasmoid instability in resistive MHD

Klein paradox and antiparticle

The Klein paradox of Klein-Gordon (KG) equation is discussed to show that KG equation is self-consistent even at one-particle level and the wave function for antiparticle is uniquely determined by the reasonable explanation of Klein paradox. No concept of ``hole'' is needed.Comment: 4 pages, no figures, revte

Numerical experiments on the detailed energy conversion and spectrum studies in a corona current sheet

In this paper, we study the energy conversion and spectra in a corona current sheet by 2.5-dimensional MHD numerical simulations. Numerical results show that many Petschek-like fine structures with slow-mode shocks mediated by plasmoid instabilities develop during the magnetic reconnection process. The termination shocks can also be formed above the primary magnetic island and at the head of secondary islands. These shocks play important roles in generating thermal energy in a corona current sheet. For a numerical simulation with initial conditions close to the solar corona environment, the ratio of the generated thermal energy to the total dissipated magnetic energy is around $1/5$ before secondary islands appear. After secondary islands appear, the generated thermal energy starts to increase sharply and this ratio can reach a value about $3/5$. In an environment with a relatively lower plasma density and plasma $\beta$, the plasma can be heated to a much higher temperature. After secondary islands appear, the one dimensional energy spectra along the current sheet do not behave as a simple power law and the spectrum index increases with the wave number. The average spectrum index for the magnetic energy spectrum along the current sheet is about $1.8$. The two dimensional spectra intuitively show that part of the high energy is cascaded to large $kx$ and $ky$ space after secondary islands appear. The plasmoid distribution function calculated from numerical simulations behaves as a power law closer to $f(\psi) \sim \psi^{-1}$ in the intermediate $\psi$ regime. By using $\eta_{eff} = v_{inflow}\cdot L$, the effective magnetic diffusivity is estimated about $10^{11}\sim10^{12}$~m$^2$\,s$^{-1}$.Comment: arXiv admin note: text overlap with arXiv:1011.4035 by other author