There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

다중혈관 관상동맥 환자에서 y-문합을 이용하여 양쪽 내흉동맥만을 사용한 우회술의 조기 성적

抗原变异可使得多种致病微生物易于逃避宿主免疫应答。表达在感染红细胞表面的恶性疟原虫红细胞表面蛋白1（PfPMP1）与感染红细胞、内皮细胞、树突状细胞以及胎盘的单个或多个受体作用，在黏附及免疫逃避中起关键的作用。每个单倍体基因组var基因家族编码约60种成员，通过启动转录不同的var基因变异体为抗原变异提供了分子基础。

疟原虫var基因转换速率变化导致抗原变异[英]／Paul H, Robert P, Christodoulou Z, et al//Proc Natl Acad Sci U S A

We present an overview of the lattice Boltzmann method (LBM), a parallel and efficient algorithm for simulating single-phase and multiphase fluid flows and for incorporating additional physical complexities. The LBM is especially useful for modeling complicated boundary conditions and multiphase interfaces. Recent extensions of this method are described, including simulations of fluid turbulence, suspension flows, and reaction diffusion systems.

Lattice boltzmann method for fluid flows

We critically review dissipative particle dynamics (DPD) as a mesoscopic simulation method. We have established useful parameter ranges for simulations, and have made a link between these parameters and χ-parameters in Flory-Huggins-type models. This is possible because the equation of state of the DPD fluid is essentially quadratic in density. This link opens the way to do large scale simulations, effectively describing millions of atoms, by firstly performing simulations of molecular fragments retaining all atomistic details to derive χ-parameters, then secondly using these results as input to a DPD simulation to study the formation of micelles, networks, mesophases and so forth. As an example application, we have calculated the interfacial tension σ between homopolymer melts as a function of χ and N and have found a universal scaling collapse when σ/ρkBTχ0.4 is plotted against χN for N>1. We also discuss the use of DPD to simulate the dynamics of mesoscopic systems, and indicate a possible problem with...

https://www.physics.iitm.ac.in/~iol/lecture_notes/groot-warren.pdf

Dissipative particle dynamics : bridging the gap between atomistic and mesoscopic simulation

We investigate the applicability of a mesoscale modeling approach, lattice Boltzmann simulations, to the problem of contact line motion in one- and two-component two phase fluids. In this, the second of two papers, we consider binary systems. We show that the contact line singularity is overcome by diffusion which is effective over a length scale L about the contact line and derive a scaling form for the dependence of L on system parameters.

Lattice Boltzmann simulations of contact line motion. II. Binary fluids.

We describe a lattice Boltzmann algorithm to simulate liquid crystal hydrodynamics The equations of motion are written in terms of a tensor order parameter This allows both the isotropic and the nematic phases to be considered Backflow effects and the hydrodynamics of topological defects are naturally included in the simulations, as are non-Newtonian flow properties such as shear thinning and shear banding

https://arxiv.org/pdf/cond-mat/0010320.pdf

Lattice Boltzmann Simulations of Liquid Crystal Hydrodynamics

We investigate the properties of stochastic rotation dynamics, a mesoscopic model used for simulating fluctuating hydrodynamics. Analytical results are given for the shear viscosity and the friction exerted on a massive solute particle moving within the fluid. We discuss an efficient way of measuring the shear viscosity and viscous friction, and obtain excellent agreement between the theoretical and numerical calculations.

Transport coefficients of a mesoscopic fluid dynamics model

We present numerical and analytical results describing the effect of hydrodynamic interactions on the dynamics of a short polymer chain in solution. A molecular dynamics algorithm for the polymer is coupled to a direct simulation Monte Carlo algorithm for the solvent. We give an explicit expression for the velocity autocorrelation function of the centre of mass of the polymer which agrees well with numerical results if Brownian dynamics, hydrodynamic correlations and sound wave scattering are included.

https://iopscience.iop.org/article/10.1209/epl/i2000-00428-0/pdf

Dynamics of short polymer chains in solution

After a long gap following the classic work of Taylor, there have recently been several studies dealing with hydrodynamic synchronization. It is now apparent that synchronization driven by hydrodynamic interactions is not only possible, but relevant to the efficiency of pumping by arrays of cilia and to bacterial swimming. Recent work has included experiments demonstrating synchronization, both in model systems and between bacterial flagella. The effect has been demonstrated in model swimmers and pumps, and large scale simulations have been used to investigate synchronization of cilia and of sperm cells. In this review article, we summarize the various experimental and theoretical studies of hydrodynamic synchronization, and put them in a framework which draws parallels between the different systems and suggests useful directions for further research.

Julia M. Yeomans

Papers

Lattice Boltzmann simulations of contact line motion. II. Binary fluids.

Lattice Boltzmann Simulations of Liquid Crystal Hydrodynamics

Transport coefficients of a mesoscopic fluid dynamics model

Dynamics of short polymer chains in solution

Hydrodynamic synchronization at low Reynolds number