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

Magnetorotational instability (MRI) triggers turbulence and enables outward transport of angular momentum in hydrodynamically stable accretion discs By using the WKB approximation and methods of singular function theory, we resolve two different paradoxes of MRI that appear in the limits of infinite and vanishing magnetic Prandtl number For the latter case, we derive a strict limit of the critical Rossby number This limit of ${\mathrm{Ro}}_{\mathrm{c}}=\ensuremath{-}0802$, which appears for a finite Lundquist number of $\mathit{S}=0618$, extends the formerly known inductionless Liu limit of ${\mathrm{Ro}}_{\mathrm{c}}=\ensuremath{-}0828$ valid at $\mathit{S}=0$

/pdf/paradoxes-of-magnetorotational-instability-and-their-262dwoqr6m.pdf

Paradoxes of magnetorotational instability and their geometrical resolution.

Using a homotopic family of boundary eigenvalue problems for the mean-field ${\ensuremath{\alpha}}^{2}$ dynamo with helical turbulence parameter $\ensuremath{\alpha}(r)={\ensuremath{\alpha}}_{0}+\ensuremath{\gamma}\ensuremath{\Delta}\ensuremath{\alpha}(r)$ and homotopy parameter $\ensuremath{\beta}∊[0,1]$, we show that the underlying network of diabolical points for Dirichlet (idealized, $\ensuremath{\beta}=0$) boundary conditions substantially determines the choreography of eigenvalues and thus the character of the dynamo instability for Robin (physically realistic, $\ensuremath{\beta}=1$) boundary conditions. In the $({\ensuremath{\alpha}}_{0},\ensuremath{\beta},\ensuremath{\gamma})$ space the Arnold tongues of oscillatory solutions at $\ensuremath{\beta}=1$ end up at the diabolical points for $\ensuremath{\beta}=0$. In the vicinity of the diabolical points the space orientation of the three-dimensional tongues, which are cones in first-order approximation, is determined by the Krein signature of the modes involved in the diabolical crossings at the apexes of the cones. The Krein space-induced geometry of the resonance zones explains the subtleties in finding $\ensuremath{\alpha}$ profiles leading to spectral exceptional points, which are important ingredients in recent theories of polarity reversals of the geomagnetic field.

/pdf/determining-role-of-krein-signature-for-three-dimensional-4k5nh9a0rn.pdf

Determining role of Krein signature for three-dimensional Arnold tongues of oscillatory dynamos

The transition to turbulence in a precessing cylindrical vessel is experimentally investigated. Our measurements are performed for a { nearly-resonant} configuration with an initially laminar flow dominated by an inertial mode with azimuthal wave number $m=1$ superimposed on a solid body rotation. By increasing the precession ratio, we observe a transition from the laminar to a non-linear regime, which then breakdowns to turbulence for larger precession ratio. Our measurements show that the transition to turbulence is subcritical, with a discontinuity of the wall-pressure and the power consumption at the threshold $\epsilon_{LT}$. The turbulence is self-sustained below this threshold, describing a bifurcation diagram with a hysteresis. In this range of the control parameters, the turbulent flows can suddenly collapse after a finite duration, leading to a definitive relaminarization of the flow. The average lifetime $\langle \tau \rangle$ of the turbulence increases rapidly when $\epsilon$ tends to $\epsilon_{LT}$.

Subcritical transition to turbulence of a precessing flow in a cylindrical vessel

Kinematic simulations of the induction equation are carried out for different setups suitable for the von-Karman-Sodium (VKS) dynamo experiment. Material properties of the flow driving impellers are considered by means of high conducting and high permeability disks that are present in a cylindrical volume filled with a conducting fluid. Two entirely different numerical codes are mutually validated by showing quantitative agreement on Ohmic decay and kinematic dynamo problems using various configurations and physical parameters. Field geometry and growth rates are strongly modified by the material properties of the disks even if the high permeability/high conductivity material is localized within a quite thin region. In contrast the influence of external boundary conditions remains small. Utilizing a VKS like mean fluid flow and high permeability disks yields a reduction of the critical magnetic Reynolds number for the onset of dynamo action of the simplest non-axisymmetric field mode. However this decrease is not sufficient to become relevant in the VKS experiment. Furthermore, the reduction of Rm_c is essentially influenced by tiny changes in the flow configuration so that the result is not very robust against small modifications of setup and properties of turbulence.

Electromagnetic induction in non-uniform domains

We present results from three-dimensional nonlinear hydrodynamic simulations of a precession driven flow in cylindrical geometry. The simulations are motivated by a dynamo experiment currently under development at Helmholtz-Zentrum Dresden-Rossendorf in which the possibility of generating a magnetohydrodynamic dynamo will be investigated in a cylinder filled with liquid sodium and simultaneously rotating around two axes. In this study, we focus on the emergence of non-axisymmetric time-dependent flow structures in terms of inertial waves which—in cylindrical geometry—form so-called Kelvin modes. For a precession ratio (Poincare number) considered by us, the amplitude of the forced Kelvin mode reaches up to one fourth of the rotation velocity of the cylindrical container confirming that precession provides a rather efficient flow driving mechanism even at moderate values of Po. More relevant for dynamo action might be free Kelvin modes with higher azimuthal wave number. These free Kelvin modes are triggered by nonlinear interactions and may constitute a triadic resonance with the fundamental forced mode when the height of the container matches their axial wave lengths. Our simulations reveal triadic resonances at aspect ratios close to those predicted by the linear theory except around the primary resonance of the forced mode. In that regime we still identify various free Kelvin modes, however, all of them exhibit a retrograde drift around the symmetry axis of the cylinder and none of them can be assigned to a triadic resonance. The amplitudes of the free Kelvin modes always remain below the forced mode but may reach up to 6% of the of the container's angular velocity. The properties of the free Kelvin modes, namely their amplitude and their frequency, will be used in future simulations of the magnetic induction equation to investigate their ability to provide for dynamo action.

https://iopscience.iop.org/article/10.1088/1367-2630/17/11/113044/pdf

Frank Stefani

Papers

Paradoxes of magnetorotational instability and their geometrical resolution.

Determining role of Krein signature for three-dimensional Arnold tongues of oscillatory dynamos

Subcritical transition to turbulence of a precessing flow in a cylindrical vessel

Electromagnetic induction in non-uniform domains

Triadic resonances in nonlinear simulations of a fluid flow in a precessing cylinder