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

Biological flows over surfaces and interfaces can result in accumulation hotspots or depleted voids of microorganisms in natural environments. Apprehending the mechanisms that lead to such distributions is essential for understanding biofilm initiation. Using a systematic framework, we resolve the dynamics and statistics of swimming microbes within flowing films, considering the impact of confinement through steric and hydrodynamic interactions, flow and motility, along with Brownian and run-tumble fluctuations. Micro-swimmers can be peeled off the solid wall above a critical flow strength. However, the interplay of flow and fluctuations causes organisms to migrate back towards the wall above a secondary critical value. Hence, faster flows may not always be the most efficacious strategy to discourage biofilm initiation. Moreover, we find run-tumble dynamics commonly used by flagellated microbes to be an intrinsically more successful strategy to escape from boundaries than equivalent levels of enhanced Brownian noise in ciliated organisms.

https://royalsocietypublishing.org/doi/pdf/10.1098/rsif.2015.0936

Hotspots of boundary accumulation: dynamics and statistics of micro-swimmers in flowing films.

We study the nematic phase of rodlike f d-virus particles confined to channels with wedge-structured walls. Using laser scanning confocal microscopy we observe a splay-to-bend transition at the single particle level as a function of the wedge opening angle. Lattice Boltzmann simulations reveal the underlying origin of the transition and its dependence on nematic elasticity and wedge geometry. Our combined work provides a simple method to estimate the splay-to-bend elasticity ratios of the virus and offers a way to control the position of defects through the confining boundary conditions.

/pdf/confinement-induced-splay-to-bend-transition-of-colloidal-1kkobvhk57.pdf

Confinement induced splay-to-bend transition of colloidal rods.

The authors study the interface behaviour of the two-dimensional Blume-Emery-Griffiths model (1971) which is described by the Hamiltonian H=-J Sigma (ij)SiSj=K Sigma (ij)Si2Sj 2+D Sigma iSi2 Si=1, 0, -1. An interface is introduced into the system by fixing the spins on opposite boundaries in two different states, +1 and -1. They pay particular attention to the appearance of an excess of the third state, 0, in the vicinity of the interface. The net adsorption of the non-boundary state is studied near critical, first-order and tricritical transitions. Two methods have been used to attack this problem, the Monte Carlo technique and a modified version of the interface free energy approximation of Muller-Hartmann and Zittartz (1977) which is seen to give a surprisingly good description of interface properties in three-state systems.

Interface properties of the two-dimensional Blume-Emery-Griffiths model

We investigate the dynamics of capillary filling using two lattice Boltzmann schemes: a liquid-gas model and a binary model. The simulation results are compared to the well-known Washburn's law, which predicts that the filled length of the capillary scales with time as l ∝ t 1/2 . We find that the liquid-gas model does not reproduce Washburn's law due to condensation of the gas phase at the interface, which causes the asymptotic behaviour of the capillary penetration to be faster than t 1/2 . The binary model, on the other hand, captures the correct scaling behaviour when the viscosity ratio between the two phases is sufficiently high.

Modelling capillary filling dynamics using lattice Boltzmann simulations

We present a generic framework for modeling three-dimensional deformable shells of active matter that captures the orientational dynamics of the active particles and hydrodynamic interactions on the shell and with the surrounding environment. We find that the cross talk between the self-induced flows of active particles and dynamic reshaping of the shell can result in conformations that are tunable by varying the form and magnitude of active stresses. We further demonstrate and explain how self-induced topological defects in the active layer can direct the morphodynamics of the shell. These findings are relevant to understanding morphological changes during organ development and the design of bioinspired materials that are capable of self-organization.

/pdf/topology-and-morphology-of-self-deforming-active-shells-5jl187bytw.pdf

Julia M. Yeomans

Papers

Hotspots of boundary accumulation: dynamics and statistics of micro-swimmers in flowing films.

Confinement induced splay-to-bend transition of colloidal rods.

Interface properties of the two-dimensional Blume-Emery-Griffiths model

Modelling capillary filling dynamics using lattice Boltzmann simulations

Topology and Morphology of Self-Deforming Active Shells.