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 wetting properties of surfaces patterned with fine elastic hairs, with an emphasis on identifying superhydrophobic states on hydrophilic hairs. We formulate a two dimensional model of a large drop in contact with a row of equispaced elastic hairs and, by minimising the free energy of the model, identify the stable and metastable states. In particular we concentrate on "partially suspended" states, where the hairs bend to support the drop -- singlet states where all hairs bend in the same direction, and doublet states where neighbouring hairs bend in opposite directions -- and find the limits of stability of these configurations in terms of material contact angle, hair flexibility, and system geometry. The drop can remain suspended in a singlet state at hydrophilic contact angles, but doublets exist only when the hairs are hydrophobic. The system is more likely to evolve into a singlet state if the hairs are inclined at the root. We discuss how, under limited circumstances, the results can be modified to describe an array of hairs in three dimensions. We find that now both singlets and doublets can exhibit superhydrophobic behaviour on hydrophilic hairs. We discuss the limitations of our approach and the directions for future work.

Superhydrophobicity on hairy surfaces

We study the zero-temperature behavior of several simple models for randomly self-interacting polymers in one and 1+1 dimensions. Results are based on exact enumeration and closed-form expressions.

Zero-temperature properties of randomly self-interacting polymers

Crystal structures can be analysed at many levels. At the most fundamental level, they are described in terms of the relative distribution of their constituent atoms, or of the coordination polyhedra of the component cations and anions. It is becoming increasingly apparent, however, that many families of structures can be usefully described in terms of larger basic structural units or modules. If such an approach to the description of crystal structures is adopted, many complex solids may be systematised in terms of series of stacking variants of the simple subunits; these phases are known as polytypes. This relatively broad definition of polytypism closely follows that of THOMPSON [1] and is discussed at length by ANGEL [2]. The definition removes any chemical constraints upon stacking variants, and allows more than one type of module to be present in a given polytype family. Polytypism is however a special form of polymorphism, and although there is no constraint upon the chemistry or structure of the modules involved, to be considered polymorphic the various modes of module stacking should not affect the composition of the phase as a whole. It should also be noted that this definition of polytypism allows for the existence of 2- and 3-dimensional polytypic structures, comprised of prismatic (rod-like) and block modules respectively, as well as the classically more familiar layer modules of the 1-dimensional polytypes.

Competing Interactions and the Origins of Polytypism

Interaction between active materials and the boundaries of geometrical confinement is key to many emergent phenomena in active systems. For living active matter consisting of animal cells or motile bacteria, the confinement boundary is often a deformable interface, and it has been unclear how activity-induced interface dynamics might lead to morphogenesis and pattern formation. Here, we studied the evolution of bacterial active matter confined by a deformable boundary. We found that an ordered morphological pattern emerged at the interface characterized by periodically spaced interfacial protrusions; behind the interfacial protrusions, bacterial swimmers self-organized into multicellular clusters displaying +1/2 nematic defects. Subsequently, a hierarchical sequence of transitions from interfacial protrusions to creeping branches allowed the bacterial active drop to rapidly invade surrounding space with a striking self-similar branch pattern. We found that this interface patterning is geometrically controlled by the local curvature of the interface, a phenomenon we denote as collective curvature sensing. Using a continuum active model, we revealed that the collective curvature sensing arises from enhanced active stresses near high-curvature regions, with the active length scale setting the characteristic distance between the interfacial protrusions. Our findings reveal a protrusion-to-branch transition as a unique mode of active matter invasion and suggest a strategy to engineer pattern formation of active materials.

Geometrical control of interface patterning underlies active matter invasion.

We show that the injection of polymer chains into nanochannels becomes easier as the channel becomes narrower. This counter intuitive result arises because of a decrease in the diffusive time scale of the chains with increasing confinement. The results are obtained by extending the de Gennes blob model of confined polymers, and confirmed by hybrid molecular dynamics - lattice-Boltzmann simulations.

Julia M. Yeomans

Papers

Superhydrophobicity on hairy surfaces

Zero-temperature properties of randomly self-interacting polymers

Competing Interactions and the Origins of Polytypism

Geometrical control of interface patterning underlies active matter invasion.

Easier sieving through narrower pores: fluctuations and barrier crossing in flow-driven polymer translocation