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 Hamiltonian H specifies the energy levels and time evolution of a quantum theory. A standard axiom of quantum mechanics requires that H be Hermitian because Hermiticity guarantees that the energy spectrum is real and that time evolution is unitary (probability-preserving). This paper describes an alternative formulation of quantum mechanics in which the mathematical axiom of Hermiticity (transpose +complex conjugate) is replaced by the physically transparent condition of space?time reflection ( ) symmetry. If H has an unbroken symmetry, then the spectrum is real. Examples of -symmetric non-Hermitian quantum-mechanical Hamiltonians are and . Amazingly, the energy levels of these Hamiltonians are all real and positive!Does a -symmetric Hamiltonian H specify a physical quantum theory in which the norms of states are positive and time evolution is unitary? The answer is that if H has an unbroken symmetry, then it has another symmetry represented by a linear operator . In terms of , one can construct a time-independent inner product with a positive-definite norm. Thus, -symmetric Hamiltonians describe a new class of complex quantum theories having positive probabilities and unitary time evolution.The Lee model provides an excellent example of a -symmetric Hamiltonian. The renormalized Lee-model Hamiltonian has a negative-norm 'ghost' state because renormalization causes the Hamiltonian to become non-Hermitian. For the past 50 years there have been many attempts to find a physical interpretation for the ghost, but all such attempts failed. The correct interpretation of the ghost is simply that the non-Hermitian Lee-model Hamiltonian is -symmetric. The operator for the Lee model is calculated exactly and in closed form and the ghost is shown to be a physical state having a positive norm. The ideas of symmetry are illustrated by using many quantum-mechanical and quantum-field-theoretic models.

https://iopscience.iop.org/article/10.1088/0034-4885/70/6/R03/pdf

Making sense of non-Hermitian Hamiltonians

Intermolecular And Surface Forces

Advanced Mathematical Methods for Scientists and Engineers

Magnetic fields influence many natural and man-made flows. They are routinely used in industry to heat, pump, stir and levitate liquid metals. There is the terrestrial magnetic field which is maintained by fluid motion in the earth's core, the solar magnetic field, which generates sunspots and solar flares, and the galactic field which influences the formation of stars. This is an introductory text on magnetohydrodynamics (MHD) - the study of the interaction of magnetic fields and conducting fluids. This book is intended to serve as an introductory text for advanced undergraduates and postgraduate students in physics, applied mathematics and engineering. The material in the text is heavily weighted towards incompressible flows and to terrestrial (as distinct from astrophysical) applications. The final sections of the text also contain an outline of the latest advances in the metallurgical applications of MHD and so are relevant to professional researchers in applied mathematics, engineering and metallurgy.

An Introduction to Magnetohydrodynamics

We consider the interaction of differential rotation and toroidal fields that are current-free in the gap between two corotating axially unbounded cylinders. It is shown that nonaxisymmetric perturbations are unstable if the rotation rate and Alfven frequency of the field are of the same order almost independent of the magnetic Prandtl number Pm. For the very steep rotation law \Omega\propto R^{-2} (the Rayleigh limit) this Azimuthal MagnetoRotational Instability (AMRI) scales with the ordinary Reynolds number and the Hartmann number, which allows a laboratory experiment with liquid metals like sodium or gallium in a Taylor-Couette container. The growth rate of AMRI scales with \Omega^2 in the low-conductivity limit and with \Omega in the high-conductivity limit. For the weakly nonlinear system the numerical values of the kinetic energy and the magnetic energy are derived for magnetic Prandtl numbers between 0.05 and unity. We find that the magnetic energy scales with the magnetic Reynolds number Rm, while the kinetic energy scales with Rm/\sqrt{Pm}. The resulting turbulent Schmidt number as the ratio of the diffusion coefficients of angular momentum and a passive scalar (such as lithium) is of order 20 for Pm=1, but for small Pm drops to order unity. Hence, in a stellar core with fossil fields and steep rotation law the transport of angular momentum by AMRI is always accompanied by an intense mixing of the plasma, until the rotation becomes rigid.

The azimuthal magnetorotational instability (AMRI)

Magnetorotational instability (MRI) is one of the fundamental processes in astrophysics, driving angular momentum transport and mass accretion in a wide variety of cosmic objects. Despite much theoretical/numerical and experimental efforts over the last decades, its saturation mechanism and amplitude, which sets the angular momentum transport rate, remains not well understood, especially in the limit of high resistivity, or small magnetic Prandtl numbers typical to interiors (dead zones) of protoplanetary disks, liquid cores of planets and liquid metals in laboratory. Using direct numerical simulations, in this paper we investigate the nonlinear development and saturation properties of the helical magnetorotational instability (HMRI)—a relative of the standard MRI—in a magnetized Taylor–Couette flow at very low magnetic Prandtl number (correspondingly at low magnetic Reynolds number) relevant to liquid metals. For simplicity, the ratio of azimuthal field to axial field is kept fixed. From the linear theory of HMRI, it is known that the Elsasser number, or interaction parameter determines its growth rate and plays a special role in the dynamics. We show that this parameter is also important in the nonlinear problem. By increasing its value, a sudden transition from weakly nonlinear, where the system is slightly above the linear stability threshold, to strongly nonlinear, or turbulent regime occurs. We calculate the azimuthal and axial energy spectra corresponding to these two regimes and show that they differ qualitatively. Remarkably, the nonlinear state remains in all cases nearly axisymmetric suggesting that this HMRI-driven turbulence is quasi two-dimensional in nature. Although the contribution of non-axisymmetric modes increases moderately with the Elsasser number, their total energy remains much smaller than that of the axisymmetric ones.

/pdf/quasi-two-dimensional-nonlinear-evolution-of-helical-2m98d1b0vs.pdf

Quasi-two-dimensional nonlinear evolution of helical magnetorotational instability in a magnetized Taylor-Couette flow

The aim of the invention is to provide a method and a system for determining the spatial speed distributions in electrically conductive fluids, which guarantee replicable results for all speed components and avoid all contact with the fluid, or with the walls encompassing the latter. To achieve this, two different primary magnetic fields, which have a different direction in the total volume of fluid, are successively applied and the two induced magnetic fields, measured respectively at the detection points, are considered equally as necessary information for determining the spatial speed distribution. The system consists of conventional means comprising a pair of coils (1) which create a magnetic field for generating a primary magnetic field that penetrates the volume of fluid, a large number of magnetic field sensors (5) which are arranged outside the fluid for measuring the magnetic field induced by the interaction of the fluid motion and the generated primary field, a signal processor (6) placed downstream for receiving the measured values of the magnetic field sensors, an evaluation and memory unit (7) positioned downstream and an output device (8). According to the system, the pair of coils (1) is connected to a measuring and control unit (3) for measuring and temporally controlling the coil current in the pair of coils (1).

Verfahren und anordnung zur kontaktlosen bestimmung von räumlichen geschwindigkeitsverteilungen in elektrisch leitfähigen flüssigkeiten

We examine kinematic dynamo action driven by an axisymmetric large-scale flow that is superimposed with an azimuthally propagating non-axisymmetric perturbation with a frequency ω. Although we apply a rather simple large-scale velocity field, our simulations exhibit a complex behavior with oscillating and azimuthally drifting eigenmodes as well as stationary regimes. Within these non-oscillating regimes we find parametric resonances characterized by a considerable enhancement of dynamo action and by a locking of the phase of the magnetic field to the pattern of the perturbation. We find an approximate fulfillment of the relationship between the resonant frequency ω res of the excitation and the eigenfrequency ω 0 of the undisturbed system given by ω res = 2ω 0 , which is known from paradigmatic rotating mechanical systems and our prior study [Giesecke et al., Phys. Rev. E, 86, 066303 (2012)]. We find further, broader, regimes with weaker enhancement of the growth rates but without phase locking. However, this amplification regime arises only in case of a basic (i.e., unperturbed) state consisting of several different eigenmodes with rather close growth rates. Qualitatively, these observations can be explained in terms of a simple low-dimensional model for the magnetic field amplitude that is derived using Floquet theory. The observed phenomena may be of fundamental importance in planetary dynamo models with the base flow being disturbed by periodic external forces like precession or tides and for the realization of dynamo action under laboratory conditions where imposed perturbations with the appropriate frequency might facilitate the occurrence of dynamo action.

https://hal.archives-ouvertes.fr/hal-01816928/document

Frank Stefani

Papers

The azimuthal magnetorotational instability (AMRI)

Quasi-two-dimensional nonlinear evolution of helical magnetorotational instability in a magnetized Taylor-Couette flow

Verfahren und anordnung zur kontaktlosen bestimmung von räumlichen geschwindigkeitsverteilungen in elektrisch leitfähigen flüssigkeiten

Parametric instability in periodically perturbed dynamos

Long term time dependent frequency analysis of chaotic waves in the weakly magnetized spherical Couette system