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

The emergence of order in natural systems is a constant source of inspiration for both physical and biological sciences. While the spatial order characterizing for example the crystals has been the basis of many advances in contemporary physics, most complex systems in nature do not offer such high degree of order. Many of these systems form complex networks whose nodes are the elements of the system and edges represent the interactions between them. 
Traditionally complex networks have been described by the random graph theory founded in 1959 by Paul Erdohs and Alfred Renyi. One of the defining features of random graphs is that they are statistically homogeneous, and their degree distribution (characterizing the spread in the number of edges starting from a node) is a Poisson distribution. In contrast, recent empirical studies, including the work of our group, indicate that the topology of real networks is much richer than that of random graphs. In particular, the degree distribution of real networks is a power-law, indicating a heterogeneous topology in which the majority of the nodes have a small degree, but there is a significant fraction of highly connected nodes that play an important role in the connectivity of the network. 
The scale-free topology of real networks has very important consequences on their functioning. For example, we have discovered that scale-free networks are extremely resilient to the random disruption of their nodes. On the other hand, the selective removal of the nodes with highest degree induces a rapid breakdown of the network to isolated subparts that cannot communicate with each other. 
The non-trivial scaling of the degree distribution of real networks is also an indication of their assembly and evolution. Indeed, our modeling studies have shown us that there are general principles governing the evolution of networks. Most networks start from a small seed and grow by the addition of new nodes which attach to the nodes already in the system. This process obeys preferential attachment: the new nodes are more likely to connect to nodes with already high degree. We have proposed a simple model based on these two principles wich was able to reproduce the power-law degree distribution of real networks. Perhaps even more importantly, this model paved the way to a new paradigm of network modeling, trying to capture the evolution of networks, not just their static topology.

/pdf/statistical-mechanics-of-complex-networks-1zfjpvxipu.pdf

Statistical mechanics of complex networks

http://www.maths.qmul.ac.uk/%7Elatora/report_06.pdf

Complex networks: Structure and dynamics

exactly solved models in statistical mechanics exactly solved models in statistical mechanics rodney j baxter exactly solved models in statistical mechanics exactly solved models in statistical mechanics flae exactly solved models in statistical mechanics dover books exactly solved models in statistical mechanics dover books exactly solved models in statistical mechanics dover books hatsutori in size 15 gvg7bzbookyo.qhigh literature cited r. j. baxter, exactly solved models in exactly solvable models in statistical mechanics exactly solved models in statistical mechanics dover books okazaki in size 24 vk19j3book.buncivy exactly solved models of statistical mechanics valerio nishizawa in size 11 b4zntdbookntey fukuda in size 13 33oloxbooknhuy yamada in size 19 x6g84ybook.zolay in honour of r j baxter’s 75th birthday arxiv:1608.04899v2 statistical mechanics, threedimensionality and np beautiful models: 70 years of exactly solved quantum many exactly solved models in statistical mechanics (dover solved lattice models: 1944 2010 university of melbourne exactly solved models and beyond: a special issue in the statistical mechanics of the classical two-dimensional faculty of science, p. j. saf ́arik university in ko?sice? a one-dimensional statistical mechanics model with exact statistical mechanics department of physics and astronomy statistical mechanics principles and selected applications graph theory and statistical physics yaroslavvb chapter 4 methods of statistical mechanics ijs thermodynamics and an introduction to thermostatistics potts models and related problems in statistical mechanics methods of quantum field theory in statistical physics statistical mechanics: theory and molecular simulation exactly solvable su(n) mixed spin ladders springer statistical field theory : an introduction to exactly

Exactly solved models in statistical mechanics

A simple model with a novel type of dynamics is introduced in order to investigate the emergence of self-ordered motion in systems of particles with biologically motivated interaction. In our model particles are driven with a constant absolute velocity and at each time step assume the average direction of motion of the particles in their neighborhood with some random perturbation $(\ensuremath{\eta})$ added. We present numerical evidence that this model results in a kinetic phase transition from no transport (zero average velocity, $|{\mathbf{v}}_{a}|\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0$) to finite net transport through spontaneous symmetry breaking of the rotational symmetry. The transition is continuous, since $|{\mathbf{v}}_{a}|$ is found to scale as $({\ensuremath{\eta}}_{c}\ensuremath{-}\ensuremath{\eta}{)}^{\ensuremath{\beta}}$ with $\ensuremath{\beta}\ensuremath{\simeq}0.45$.

https://arxiv.org/pdf/cond-mat/0611743.pdf

Novel Type of Phase Transition in a System of Self-Driven Particles

This is a paperback edition of a distinguished book, originally published by Clarendon Press in 1971. It was then the first text on critical phenomena, a field that has enjoyed great activity for the past twenty years and that still continues to attract much attention. The book is at the level at which a graduate student who has studied condensed matter physics can begin to comprehend the nature of phase transitions, which involve the transformation of one state of matter into another. (A simple example is the melting of a solid to become a liquid.) Such a transformation is termed 'critical' when, after a certain amount of the substance changes phase, the entire bulk virtually instantaneously also makes the transition. A second, updated edition is planned for future publication, but in the mean time this paperback reissue will be useful in teaching the fundamental principles of this extremely interesting subject.

Introduction to Phase Transitions and Critical Phenomena

The progress in our understanding of several aspects of turbulent Rayleigh-Benard convection is reviewed. The focus is on the question of how the Nusselt number and the Reynolds number depend on the Rayleigh number Ra and the Prandtl number Pr, and on how the thicknesses of the thermal and the kinetic boundary layers scale with Ra and Pr. Non-Oberbeck-Boussinesq effects and the dynamics of the large scale convection roll are addressed as well. The review ends with a list of challenges for future research on the turbulent Rayleigh-Benard system.

/pdf/heat-transfer-and-large-scale-dynamics-in-turbulent-rayleigh-39oz2czpiy.pdf

Heat transfer and large scale dynamics in turbulent Rayleigh-Bénard convection

▪ Abstract This review summarizes results for Rayleigh-Benard convection that have been obtained over the past decade or so. It concentrates on convection in compressed gases and gas mixtures with Prandtl numbers near one and smaller. In addition to the classical problem of a horizontal stationary fluid layer heated from below, it also briefly covers convection in such a layer with rotation about a vertical axis, with inclination, and with modulation of the vertical acceleration.

Recent Developments in Rayleigh-Bénard Convection

Measurements of the Nusselt number Nu and of a Reynolds number ${\mathrm{Re}}_{\mathrm{eff}}$ for Rayleigh-B\'enard convection (RBC) over the Rayleigh-number range ${10}^{12}\ensuremath{\lesssim}\mathrm{Ra}\ensuremath{\lesssim}{10}^{15}$ and for Prandtl numbers Pr near 0.8 are presented. The aspect ratio $\ensuremath{\Gamma}\ensuremath{\equiv}D/L$ of a cylindrical sample was 0.50. For $\mathrm{Ra}\ensuremath{\lesssim}{10}^{13}$ the data yielded $\mathrm{Nu}\ensuremath{\propto}{\mathrm{Ra}}^{{\ensuremath{\gamma}}_{\mathrm{eff}}}$ with ${\ensuremath{\gamma}}_{\mathrm{eff}}\ensuremath{\simeq}0.31$ and ${\mathrm{Re}}_{\mathrm{eff}}\ensuremath{\propto}{\mathrm{Ra}}^{{\ensuremath{\zeta}}_{\mathrm{eff}}}$ with ${\ensuremath{\zeta}}_{\mathrm{eff}}\ensuremath{\simeq}0.43$, consistent with classical turbulent RBC. After a transition region for ${10}^{13}\ensuremath{\lesssim}\mathrm{Ra}\ensuremath{\lesssim}5\ifmmode\times\else\texttimes\fi{}{10}^{14}$, where multistability occurred, we found ${\ensuremath{\gamma}}_{\mathrm{eff}}\ensuremath{\simeq}0.38$ and ${\ensuremath{\zeta}}_{\mathrm{eff}}=\ensuremath{\zeta}\ensuremath{\simeq}0.50$, in agreement with the results of Grossmann and Lohse for the large-Ra asymptotic state with turbulent boundary layers which was first predicted by Kraichnan.

https://physics.aps.org/featured-article-pdf/10.1103/PhysRevLett.108.024502

Transition to the Ultimate State of Turbulent Rayleigh-Bénard Convection

We report experiments on convection patterns in a cylindrical cell with a large aspect ratio. The fluid had a Prandtl number [sigma][approx]1. We observed a chaotic pattern consisting of many rotating spirals and other defects in the parameter range where theory predicts that steady straight rolls should be stable. The correlation length of the pattern decreased rapidly with increasing control parameter so that the size of a correlated area became much smaller than the area of the cell. This suggests that the chaotic behavior is intrinsic to large aspect ratio geometries.

Guenter Ahlers

Papers

Introduction to Phase Transitions and Critical Phenomena

Heat transfer and large scale dynamics in turbulent Rayleigh-Bénard convection

Recent Developments in Rayleigh-Bénard Convection

Transition to the Ultimate State of Turbulent Rayleigh-Bénard Convection

Spiral defect chaos in large aspect ratio Rayleigh-Bénard convection.