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

The phase diagram of the uniaxial three-state chiral Potts or asymmetric clock model at low temperatures is calculated for dimensions d>2, using systematic series expansions carried to indefinitely high order. The model exhibits two arbitrarily long sequences of distinct commensurate phases with (mean) wavevectors q= pi /3a and q=2 pi j/3(2j+or-1)a for j=1,2,3,...,jmax with jmax approximately= square root 2 ln(1+ square root 2) exp(3J/2kBT) to infinity as T to 0.

Many commensurate phases in the chiral Potts or asymmetric clock models

We use a free energy lattice Boltzmann approach to investigate numerically the dynamics of drops moving across superhydrophobic surfaces. The surfaces comprise a regular array of posts small compared to the drop size. For drops suspended on the posts the velocity increases as the number of posts decreases. We show that this is because the velocity is primarily determined by the contact angle which, in turn, depends on the area covered by posts. Collapsed drops, which fill the interstices between the posts, behave in a very different way. The posts now impede the drop behaviour and the velocity falls as their density increases.

http://iopscience.iop.org/article/10.1209/epl/i2005-10597-8/pdf

Dynamics of sliding drops on superhydrophobic surfaces

The authors use a finite-size renormalisation group to study the phase diagram of a spin model which exhibits modulated order, the two-dimensional three-state chiral clock model. In addition to the usual scaling of the correlation length, wavevector scaling is shown to provide useful information about the position of the Lifshitz point, and about the position and nature of the commensurate to incommensurate and commensurate to paramagnetic phase transitions.

https://iopscience.iop.org/article/10.1088/0305-4470/17/4/005/pdf

Wavevector scaling and the phase diagram of the chiral clock model

The authors use an interface potential approach to consider the adsorption of a fluid with long-range interactions onto a substrate of two adjacent spheres. The interplay between prewetting-like thin-thick transitions and capillary condensation is discussed.

Capillary condensation and prewetting between spheres

We experimentally study the viscous fingering instability in a fluid–fluid phase separated colloid–polymer mixture by means of laser scanning confocal microscopy and microfluidics. We focus on three aspects of the instability. (i) The interface between the two demixed phases has an ultralow surface tension, such that we can address the role of thermal interface fluctuations. (ii) We image the interface in three dimensions allowing us to study the interplay between interface curvature and flow. (iii) The displacing fluid wets all walls completely, in contrast to traditional viscous fingering experiments, in which the displaced fluid wets the walls. We also perform lattice Boltzmann simulations, which help to interpret the experimental observations.

Julia M. Yeomans

Papers

Many commensurate phases in the chiral Potts or asymmetric clock models

Dynamics of sliding drops on superhydrophobic surfaces

Wavevector scaling and the phase diagram of the chiral clock model

Capillary condensation and prewetting between spheres

Viscous fingering at ultralow interfacial tension