A general strategy for designing seamless multiscale methods

We present a new general framework for designing multiscale methods. Compared with previous work such as Brandt’s systematic up-scaling, the heterogeneous multiscale method (HMM) and the “equation-free” approach, this new framework has the distinct feature that it does not require reinitializing the microscale model at each macro time step or each macro iteration step. In the new strategy, the macro- and micro-models evolve simultaneously using different time steps (and therefore different clocks), and they exchange data at every step. The micro-model uses its own appropriate time step. The macro-model runs at a slower pace than required by accuracy and stability considerations for the macroscale dynamics, in order for the micro-model to relax. Examples are discussed and application to modeling complex fluids is presented.     

On the Crystallization of 2D Hexagonal Lattices

It is a fundamental problem to understand why solids form crystals at zero temperature and how atomic interaction determines the particular crystal structure that a material selects. In this paper we focus on the zero temperature case and consider a class of atomic potentials V = V ₂ + V ₃, where V ₂ is a pair potential of Lennard-Jones type and V ₃ is a three-body potential of Stillinger-Weber type. For this class of potentials we prove that the ground state energy per particle converges to a finite value as the number of particles tends to infinity. This value is given by the corresponding value for a optimal hexagonal lattice, optimized with respect to the lattice spacing. Furthermore, under suitable periodic or Dirichlet boundary condition, we show that the minimizers do form a hexagonal lattice. Dedicated with admiration to Professor Tom Spencer on occasion of his 60th birthday     

A numerical method for the study of nucleation of ordered phases

A numerical approach based on the string method is developed to study nucleation of ordered phases in first-order phase transitions. Among other things, this method allows an efficient computation of the minimum energy path (MEP) during the nucleation process. The MEP provides information about the size, shape and free energy barrier of the critical nucleus. To improve the efficiency of the string method, a special initialization process is proposed. Constraints from physical models are treated using two methods, a generalized coordinates method and a projection method. Strategies for choosing the computational domain and defining the nucleus boundary are also introduced. The validity of our approach is illustrated by two nontrivial examples from soft condensed matter physics, namely the nematic–isotropic transition of liquid crystals and the ordered-to-ordered phase transition of diblock copolymers.     

All-optical broadband phase modulation of a subcarrier in a radio over fiber system

An optical modulator that provides broadband phase modulation of microwave subcarriers directly in the photonic domain has been proposed. This modulator, which involves no millimeter-wave device, can provide a dispersion-tolerant output signal with arbitrary phase shift. Therefore it has wide applications in high-frequency radio over fiber systems employing complex constellation modulation. Simulations and a proof-of-concept experiment demonstrate the feasibility of the modulator.     

Efficient Preparation of Large‐Sized Rings of Single‐Stranded DNA through One‐Pot Ligation of Multiple Fragments

Circular single‐stranded DNA (c‐ssDNA) has significant applications in DNA detection, the development of nucleic acid medicine, and DNA nanotechnology because it shows highly unique features in mobility, dynamics, and topology. However, in most cases, the efficiency of c‐ssDNA preparation is very low because polymeric byproducts are easily formed due to intermolecular reaction. Herein, we report a one‐pot ligation method to efficiently prepare large c‐ssDNA. By ligating several short fragments of linear single‐stranded DNA (l‐ssDNA) in one‐pot by using T4 DNA ligase, longer l‐ssDNAs intermediates are formed and then rapidly consumed by the cyclization. Since the intramolecular cyclization reaction is much faster than intermolecular polymerization, the formation of polymeric products is suppressed and the dominance of intramolecular cyclization is promoted. With this simple approach, large‐sized single‐stranded c‐ssDNAs (e.g., 200‐nt) were successfully synthesized in high selectivity and yield.     

Noisy Hegselmann-Krause Systems: Phase Transition and the 2<Emphasis Type="Italic">R</Emphasis>-Conjecture

The classic Hegselmann-Krause (HK) model for opinion dynamics consists of a set of agents on the real line, each one instructed to move, at every time step, to the mass center of the agents within a fixed distance R. In this work, we investigate the effects of noise in the continuous-time version of the model as described by its mean-field Fokker-Planck equation. In the presence of a finite number of agents, the system exhibits a phase transition from order to disorder as the noise increases. We introduce an order parameter to track the phase transition and resolve the corresponding phase diagram. The system undergoes a phase transition for small R but none for larger R. Based on the stability analysis of the mean-field equation, we derive the existence of a forbidden zone for the disordered phase to emerge. We also provide a theoretical explanation for the well-known 2R conjecture, which states that, for a random initial distribution in a fixed interval, the final configuration consists of clusters separated by a distance of roughly 2R. Our theoretical analysis confirms previous simulations and predicts properties of the noisy HK model in higher dimension.     

An Improved Residual Network for Pork Freshness Detection Using Near-Infrared Spectroscopy

Effective and rapid assessment of pork freshness is significant for monitoring pork quality. However, a traditional sensory evaluation method is subjective and physicochemical analysis is time-consuming. In this study, the near-infrared spectroscopy (NIRS) technique, a fast and non-destructive analysis method, is employed to determine pork freshness. Considering that commonly used statistical modeling methods require preprocessing data for satisfactory performance, this paper presents a one-dimensional squeeze-and-excitation residual network (1D-SE-ResNet) to construct the complex relationship between pork freshness and NIRS. The developed model enhances the one-dimensional residual network (1D-ResNet) with squeeze-and-excitation (SE) blocks. As a deep learning model, the proposed method is capable of extracting features from the input spectra automatically and can be used as an end-to-end model to simplify the modeling process. A comparison between the proposed method and five popular classification models indicates that the 1D-SE-ResNet achieves the best performance, with a classification accuracy of 93.72%. The research demonstrates that the NIRS analysis technique based on deep learning provides a promising tool for pork freshness detection and therefore is helpful for ensuring food safety.     

Effect of energy density on the machining character of C/SiC composites by picosecond laser

The effect of laser energy density on the machining character of C/SiC composites by picosecond laser was investigated using two machining modes: single ring line and helical lines scanning. For single ring line scanning mode, the width and depth of machining grooves increased nonlinearly with the increase of laser energy density. Moreover, periodic surface structures (ripples) were generated at relative low laser energy density and disappeared at high energy density. With the increasing energy density, the oxygen content of machining debris increased dramatically. For helical lines scanning mode, the depth of machining grooves increased nonlinearly with the increasing laser energy density. With the increasing energy density, the oxygen content of machining debris also increased dramatically. The machining character showed as nano-scale laser-induced ripples, pores, strip structures and bubble pits. Finally, micro-holes of high aspect ratio were obtained in the mode of helical lines scanning by removing multiple layers.     

Nested stochastic simulation algorithm for chemical kinetic systems with disparate rates

An efficient simulation algorithm for chemical kinetic systems with disparate rates is proposed. This new algorithm is quite general, and it amounts to a simple and seamless modification of the classical stochastic simulation algorithm (SSA), also known as the Gillespie [J. Comput. Phys. 22, 403 (1976); J. Phys. Chem. 81, 2340 (1977)] algorithm. The basic idea is to use an outer SSA to simulate the slow processes with rates computed from an inner SSA which simulates the fast reactions. Averaging theorems for Markov processes can be used to identify the fast and slow variables in the system as well as the effective dynamics over the slow time scale, even though the algorithm itself does not rely on such information. This nested SSA can be easily generalized to systems with more than two separated time scales. Convergence and efficiency of the algorithm are discussed using the established error estimates and illustrated through examples.     

Exponential convergence of the deep neural network approximation for analytic functions Dedicated to Professor Ta Tsien Li on the Occasion of His 80th Birthday

We prove that for analytic functions in low dimension, the convergence rate of the deep neural network approximation is exponential.