Relativistic Lagrangians for the Lorentz–Dirac equation

We present two types of relativistic Lagrangians for the Lorentz–Dirac equation written in terms of an arbitrary world-line parameter. One of the Lagrangians contains an exponential damping function of the proper time and explicitly depends on the world-line parameter. Another Lagrangian includes additional cross-terms consisting of auxiliary dynamical variables and does not depend explicitly on the world-line parameter. We demonstrate that both the Lagrangians actually yield the Lorentz–Dirac equation with a source-like term.     

Preparation of free‐standing silicone particles in aqueous heterogeneous system

To prepare cross‐linked silicone (silicone rubber) particles in an aqueous medium, we investigated two synthesis methods involving a miniemulsion system. The first method was based on cationic ring‐opening polymerization of cyclic siloxane, which is a common synthetic route for linear silicone oil and uses octamethylcyclotetrasiloxane (D₄) as the monomer and dimeric D₄ (bis‐D₄) as the cross‐linker. Although this method produces silicone particles, the particles do not remain in the particulate state after drying because of low cross‐linking density. The polymerization mechanism of this method was also investigated, which proceeds under the ring‐opening reaction of D₄ in monomer droplets and upon polycondensation of hydrolyzed D₄, which occurs in the water phase (ie, outside the monomer droplets). This mechanism implied that introducing the cross‐linking structure into particles is difficult because of the low solubility of bis‐D₄ in water. To overcome these difficulties, we demonstrated a second method of preparing silicone particles based on the thiol‐Michael addition reaction between thiol‐terminated silicone oil and triacrylate in miniemulsion systems. Transmission electron microscopy images indicated that the silicone particles obtained in the particulate state upon drying and the aggregates of these particles showed elasticity.     

Persistence of sums of correlated increments and clustering in cellular automata

Let $T$ be the first return time to $(?\infty ,0]$ of sums of increments given by a functional of a stationary Markov chain. We determine the asymptotic behavior of the survival probability, $\mathbb{P}(T\ge t)～C{t}^{?1∕2}$ for an explicit constant $C$. Our analysis is based on a connection between the survival probability and the running maximum of the time-reversed process, and relies on a functional central limit theorem for Markov chains. As applications, we recover known clustering results for the 3-color cyclic cellular automaton and the Greenberg–Hastings model, and we prove a new clustering result for the 3-color firefly cellular automaton.     

An improved particle shifting technique for incompressible smoothed particle hydrodynamics methods

The smoothed particle hydrodynamics (SPH) method is one of the powerful Lagrangian tools for modeling free surface flows. However, it suffers from particle disorder, which leads to interpolation and numerical errors. To overcome this problem, several techniques have been introduced until now, among which the particle shifting technique (PST) based on Fick's law is an efficient one. The current form of this method needs tuning parameters to fulfill numerical stability criteria. In this study, to eliminate calibration factors, a new shifting coefficient is derived theoretically based on particle positions before and after shifting, regardless of other parameters such as velocity, pressure, time step intervals, etc. The only required input is particle positions, and the main concern is conserving particle densities in their updated positions. In addition to the proposed PST, a new distribution index (DI) is introduced for measuring the spatial uniformity of particles. Furthering the research, some novel treatments are also studied to improve particle movements near free surface boundary. The proposed idea is only assessed for ISPH method in this study, and its performance in other SPH schemes needs more investigations. Following this innovative method, it is validated by modeling different cases including dam break flow, paddle movement, and elliptical water drop. In all cases, particle arrangements have been improved by means of the modified shifting method. In that sense, good agreements between simulation results with experimental data, analytical solutions, and other numerical methods approve the ability of the developed method in simulating free surface flows.     

Variable spaced particle in mesh-free method to handle wave-floating body interactions

In this work, the motion of a two-dimensional rectangular freely floating body under waves is simulated using Improved Meshless Local Petrov-Galerkin method with Rankine Source function (IMLPG_R) with variable spacing resolutions. The IMLPG_R method is a particle method that solves Navier–Stokes equations using the fractional step method to capture the wave properties. However, many existing particle methods are computationally intensive to model the wave-floating body due to the requirement of fine particles, needing uniform distribution throughout the domain. To improve the computational efficiency and capture the body response properly, variable spaced particle distribution with fine resolution near the floating body and coarse resolution far from the body is implemented. Numerical schemes to handle variable resolutions are reported. An iterative scheme to handle the wave-floating body is implemented in the particle method. Two test cases, one with small wave and another with steep waves, are simulated for uniform particle distribution and the result shows good agreement with literature. Based on this, the performance of the variable spaced particle distribution is tested in coupling with floating body solver. The application of the method for wave impact load from the green water loading of the floating structure is also simulated.     

基于非线性梁理论的有限质点法

有限质点法是以向量式力学为基础,用有限数量的质点来模拟结构的变形行为,质点的运动由牛顿运动定律来计算。在有限质点法中,质点通过构件相连,构件约束着质点的运动,并且其内力由质点的运动变量来描述。基于向量式力学的基本思想和非线性梁理论,提出了一种新的有限质点法,该方法在共旋单元坐标系中描述梁的非线性变形。以空间梁系结构为例,推导了计算构件内力的非线性公式,并考虑了弯扭耦合变形。通过两个连续欧拉角的变换公式得到共旋坐标系的旋转矩阵。与传统的有限质点法相比,本文提出的方法避免了刚体虚转动分析。通过四个结构的数值求解,验证了本文方法在计算结构大变形响应时具有较高的精度。     

A novel method for making ultra-fine metal fibers and particles

A novel method based on plastic processing and equipment for preparing ultra-fine metal fibers and particles is reported. With this new method, metal fibers and particles can both be produced on the same equipment and the surfaces of the fibers and particles can be protected from oxidation by the polymers or solvents during the preparation process. Metal-alloy powders with lower melt point were filled into polymer by an extruder, followed by a die-drawing process at a temperature lower than the melt temperature of the metal alloy. Metal fibers or particles were obtained after the polymer matrix was washed away. Metal alloy fibers can be obtained when a polymer that strongly interacts with metal alloy, such as a special polyvinyl alcohol with a low alcoholysis degree, is used as the polymer matrix. Metal-alloy particles can be obtained when a polymer with weak interaction with metal alloy, such as polyethylene (PE), is used as the polymer matrix. Based on the principle of this new method, it is possible to produce finer or even nano-sized metal fibers and particles with higher melting points.     

A stochastic approach for the simulation of collisions between colloidal particles at large time steps

This paper presents a new approach for the detection and treatment of colloidal particle collisions. It has been developed in the framework of Lagrangian approaches where a large number of particles is explicitly tracked. The key idea is to account for the continuous trajectories of both colliding partners during a time step that is not restricted. Unlike classical approaches which consider only the distances between a pair of particles at the beginning and at the end of each time step (or assume straight-line motion in between), we model the whole relative, and possibly diffusive, trajectory. The collision event is dealt with using the probability that the relative distance reaches a minimum threshold (equal to the sum of the two particle radii). In that sense, the present paper builds on the idea of a previous work. However, in this first work, the collision event was simulated with a simplified scheme where one of the collision partners was removed and re-inserted randomly within the simulation domain. Though usually applied, this treatment is limited to homogeneous situations. Here, an extension of the stochastic model is proposed to treat more rigorously the collision event via a suitable evaluation of the time and spatial location of the collision and an adequate calculation of subsequent particle motion. The resulting collision kernels are successfully compared to theoretical predictions in the case of particle diffusive motion. With these promising results, the feasibility of simulating the collisional regime over a whole range of particle sizes (even nanoscopic) and time steps (from a ballistic to a purely diffusive regime) with a numerical method of reasonable computational cost has been confirmed. The present approach thus appears as a good candidate for the simulation of the agglomeration phenomenon between particles also in complex non-homogeneous flows.     

Effects of graft length and density of well‐defined graft polymers on the thermoresponsive behavior and self‐assembly morphology

A series of well‐defined thermoresponsive graft polymers with different lengths and graft densities, poly(glycidyl methacrylate)‐graft‐poly(N‐isopropylacrylate) (PGMA‐g‐PNIPAM), were successfully prepared by combination of controlled/living free radical polymerization and click chemistry. Effects of grafting length and density on the thermoresponsive behavior, aggregating mean diameter, and self‐assembly morphology are systematically investigated. The thermosensitive characteristics of graft polymers in aqueous solution prove that the length and graft density had positive co‐relationship with the lower critical solution temperature value and mean diameter of micelles as well as the size distribution, while the effect of graft length of polymers is more significant than that of density. Transmission electron microscopy analysis shows that the conformations of PGMA₄₅‐g‐PNIPAM₂₀ and PGMA₄₅‐g‐PNIPAM₄₆ with longer length and bigger grafting density in aqueous solutions are spherical nanoparticles with the increasing trend of the diameters, while that of PGMA₄₅‐g‐PNIPAM_{(73, 50%)} shows a spherical‐like morphology, which indicates that the graft length and density have a significant effect on the mean diameter of micelle but not on the self‐assembly morphology. These results reveal that to obtain desired thermoresponsive behavior and self‐assembly morphology of functional polymers, it is essential to design and fabricate the structure of graft polymers with proper length and graft density. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2014 , 52, 2442–2453     

A note on random walks with absorbing barriers and sequential Monte Carlo methods

In this article, we consider importance sampling (IS) and sequential Monte Carlo (SMC) methods in the context of one-dimensional random walks with absorbing barriers. In particular, we develop a very precise variance analysis for several IS and SMC procedures. We take advantage of some explicit spectral formulae available for these models to derive sharp and explicit estimates; this provides stability properties of the associated normalized Feynman–Kac semigroups. Our analysis allows one to compare the variance of SMC and IS techniques for these models. The work in this article is one of the few to consider an in-depth analysis of an SMC method for a particular model-type as well as variance comparison of SMC algorithms.