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

A comprehensive review of spatiotemporal pattern formation in systems driven away from equilibrium is presented, with emphasis on comparisons between theory and quantitative experiments. Examples include patterns in hydrodynamic systems such as thermal convection in pure fluids and binary mixtures, Taylor-Couette flow, parametric-wave instabilities, as well as patterns in solidification fronts, nonlinear optics, oscillatory chemical reactions and excitable biological media. The theoretical starting point is usually a set of deterministic equations of motion, typically in the form of nonlinear partial differential equations. These are sometimes supplemented by stochastic terms representing thermal or instrumental noise, but for macroscopic systems and carefully designed experiments the stochastic forces are often negligible. An aim of theory is to describe solutions of the deterministic equations that are likely to be reached starting from typical initial conditions and to persist at long times. A unified description is developed, based on the linear instabilities of a homogeneous state, which leads naturally to a classification of patterns in terms of the characteristic wave vector q0 and frequency ω0 of the instability. Type Is systems (ω0=0, q0≠0) are stationary in time and periodic in space; type IIIo systems (ω0≠0, q0=0) are periodic in time and uniform in space; and type Io systems (ω0≠0, q0≠0) are periodic in both space and time. Near a continuous (or supercritical) instability, the dynamics may be accurately described via "amplitude equations," whose form is universal for each type of instability. The specifics of each system enter only through the nonuniversal coefficients. Far from the instability threshold a different universal description known as the "phase equation" may be derived, but it is restricted to slow distortions of an ideal pattern. For many systems appropriate starting equations are either not known or too complicated to analyze conveniently. It is thus useful to introduce phenomenological order-parameter models, which lead to the correct amplitude equations near threshold, and which may be solved analytically or numerically in the nonlinear regime away from the instability. The above theoretical methods are useful in analyzing "real pattern effects" such as the influence of external boundaries, or the formation and dynamics of defects in ideal structures. An important element in nonequilibrium systems is the appearance of deterministic chaos. A greal deal is known about systems with a small number of degrees of freedom displaying "temporal chaos," where the structure of the phase space can be analyzed in detail. For spatially extended systems with many degrees of freedom, on the other hand, one is dealing with spatiotemporal chaos and appropriate methods of analysis need to be developed. In addition to the general features of nonequilibrium pattern formation discussed above, detailed reviews of theoretical and experimental work on many specific systems are presented. These include Rayleigh-Benard convection in a pure fluid, convection in binary-fluid mixtures, electrohydrodynamic convection in nematic liquid crystals, Taylor-Couette flow between rotating cylinders, parametric surface waves, patterns in certain open flow systems, oscillatory chemical reactions, static and dynamic patterns in biological media, crystallization fronts, and patterns in nonlinear optics. A concluding section summarizes what has and has not been accomplished, and attempts to assess the prospects for the future.

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Pattern formation outside of equilibrium

Couplings and changes of variables.- Three examples of coupling techniques.- The founding fathers of optimal transport.- Qualitative description of optimal transport.- Basic properties.- Cyclical monotonicity and Kantorovich duality.- The Wasserstein distances.- Displacement interpolation.- The Monge-Mather shortening principle.- Solution of the Monge problem I: global approach.- Solution of the Monge problem II: Local approach.- The Jacobian equation.- Smoothness.- Qualitative picture.- Optimal transport and Riemannian geometry.- Ricci curvature.- Otto calculus.- Displacement convexity I.- Displacement convexity II.- Volume control.- Density control and local regularity.- Infinitesimal displacement convexity.- Isoperimetric-type inequalities.- Concentration inequalities.- Gradient flows I.- Gradient flows II: Qualitative properties.- Gradient flows III: Functional inequalities.- Synthetic treatment of Ricci curvature.- Analytic and synthetic points of view.- Convergence of metric-measure spaces.- Stability of optimal transport.- Weak Ricci curvature bounds I: Definition and Stability.- Weak Ricci curvature bounds II: Geometric and analytic properties.

Optimal Transport: Old and New

Physical and numerical experiments show that deterministic noise, or chaos, is ubiquitous. While a good understanding of the onset of chaos has been achieved, using as a mathematical tool the geometric theory of differentiable dynamical systems, moderately excited chaotic systems require new tools, which are provided by the ergodic theory of dynamical systems. This theory has reached a stage where fruitful contact and exchange with physical experiments has become widespread. The present review is an account of the main mathematical ideas and their concrete implementation in analyzing experiments. The main subjects are the theory of dimensions (number of excited degrees of freedom), entropy (production of information), and characteristic exponents (describing sensitivity to initial conditions). The relations between these quantities, as well as their experimental determination, are discussed. The systematic investigation of these quantities provides us for the first time with a reasonable understanding of dynamical systems, excited well beyond the quasiperiodic regimes. This is another step towards understanding highly turbulent fluids.

Ergodic theory of chaos and strange attractors

This textbook presents a modern account of turbulence, one of the greatest challenges in physics. The state-of-the-art is put into historical perspective five centuries after the first studies of Leonardo and half a century after the first attempt by A. N. Kolmogorov to predict the properties of flow at very high Reynolds numbers. Such 'fully developed turbulence' is ubiquitous in both cosmical and natural environments, in engineering applications and in everyday life. The intended readership for the book ranges from first-year graduate students in mathematics, physics, astrophysics, geosciences and engineering, to professional scientists and engineers. Elementary presentations of dynamical systems ideas, of probabilistic methods (including the theory of large deviations) and of fractal geometry make this a self-contained textbook.

Turbulence: The Legacy of A. N. Kolmogorov

We show that a class of deterministic lattice gases with discrete Boolean elements simulates the Navier-Stokes equation, anc can be used to design simple, massively parallel computing machines.

Lattice-Gas Automata for the Navier-Stokes Equation

Hydrodynamical phenomena can be simulated by discrete lattice gas models obeing cellular automata rules (U. Frisch, B. Hasslacher, and Y. Pomeau, Phys. Rev. Lett. 56, 1505, (1986); D. d'Humieres, P. Lallemand, and U. Frisch, Europhys. Lett. 2, 291, (1986)). It is here shown for a class of D-dimensional lattice gas models how the macrodynamical (large-scale) equations for the densities of microscopically conserved quantities can be systematically derived from the underlying exact ''microdynamical'' Boolean equations. With suitable restrictions on the crystallographic symmetries of the lattice and after proper limits are taken, various standard fluid dynamical equations are obtained, including the incompressible Navier-Stokes equations in two and three dimensions. The transport coefficients appearing in the macrodynamical equations are obtained using variants of fluctuation-dissipation and Boltzmann formalisms adapted to fully discrete situations.

Lattice gas hydrodynamics in two and three dimensions

To understand the turbulent generation of large-scale magnetic fields and to advance beyond purely kinematic approaches to the dynamo effect like that introduced by Steenbeck, Krause & Radler (1966)’ a new nonlinear theory is developed for three-dimensional, homogeneous, isotropic, incompressible MHD turbulence with helicity, i.e. not statistically invariant under plane reflexions. For this, techniques introduced for ordinary turbulence in recent years by Kraichnan (1971~~)’ Orszag (1970, 1976) and others are generalized to MHD; in particular we make use of the eddy-damped quasi-normal Markovian approximation. The resulting closed equations for the evolution of the kinetic and magnetic energy and helicity spectra are studied both theoretically and numerically in situations with high Reynolds number and unit magnetic Prandtl number. Interactions between widely separated scales are much more important than for non-magnetic turbulence. Large-scale magnetic energy brings to equipartition small-scale kinetic and magnetic excitation (energy or helicity) by the ‘AlfvBn effect ’; the small-scale ‘residual’ helicity, which is the difference between a purely kinetic and a purely magnetic helical term, induces growth of largescale magnetic energy and helicity by the ‘helicity effect’. In the absence of helicity an inertial range occurs with a cascade of energy to small scales; to lowest order it is a - power law with equipartition of kinetic and magnetic energy spectra as in Kraichnan (1965) but there are - 2 corrections (and possibly higher ones) leading to a slight excess of magnetic energy. When kinetic energy is continuously injected, an initial seed of magnetic field willgrow to approximate equipartition, at least in the small scales. If in addition kinetic helicity is injected, an inverse cascade of magnetic helicity is obtained leading to the appearance of magnetic energy and helicity in ever-increasing scales (in fact, limited by the size of the system). This inverse cascade, predicted by Frisch et aZ. (1975), results from a competition between the helicity and Alfvh effects and yields an inertial range with approximately - 1 and - 2 power laws for magnetic energy and helicity. When kinetic helicity is injected at the scale Zinj and the rate k (per unit mass), the time of build-up of magnetic energy with scale L 9 Zinl is t % L( prp;nj)-k 21 FLM 77

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Strong MHD helical turbulence and the nonlinear dynamo effect

We present a phenomenological model of intermittency called the P-model and related to the Novikov-Stewart (1964) model. The key assumption is that in scales N &2-” only a fraction /3n of the total space has an appreciable excitation. The model, the idea of which owes much to Kraichnan (1972, 1974)’ is dynamical in the sense that we work entirely with inertial-range quantities such as velocity amplitudes, eddy turnover times and energy transfer. This gives more physical insight than the traditional approach based on probabilistic models of the dissipation. The P-model leads in an elementary way to the concept of the self-similarity dimension D, a special case of Mandelbrot’s (1974, 1976) ‘fractal dimension’. For threedimensional turbulence, the correction B to the Q exponent of the energy spectrum is equal to +( 3 - D) and is related to the exponent p of the dissipation correlation function by B = Qp (0.17 for the currently accepted value). This is a borderline case of the Mandelbrot inequality B < Qp. It is shown in the appendix that this inequality may be derived from the Navier-Stokes equation under the strong, but plausible, assumption that the inertial-range scaling laws for second- and fourth-order moments have the same viscous cut-off. The predictions of the P-model for the spectrum and for higher-order statistics are in agreement with recent conjectures based on analogies with critical phenomena (Nelkin 1975) but generally diasgree with the 1962 Kolmogorov lognormal model. However, the sixth-order structure function (8v6(Z)) and the dissipation correlation function (e(r) e(r + 1)) are related by

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Uriel Frisch

Papers

Turbulence: The Legacy of A. N. Kolmogorov

Lattice-Gas Automata for the Navier-Stokes Equation

Lattice gas hydrodynamics in two and three dimensions

Strong MHD helical turbulence and the nonlinear dynamo effect

A simple dynamical model of intermittent fully developed turbulence