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

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

Stochastic thermodynamics as reviewed here systematically provides a framework for extending the notions of classical thermodynamics such as work, heat and entropy production to the level of individual trajectories of well-defined non-equilibrium ensembles. It applies whenever a non-equilibrium process is still coupled to one (or several) heat bath(s) of constant temperature. Paradigmatic systems are single colloidal particles in time-dependent laser traps, polymers in external flow, enzymes and molecular motors in single molecule assays, small biochemical networks and thermoelectric devices involving single electron transport. For such systems, a first-law like energy balance can be identified along fluctuating trajectories. For a basic Markovian dynamics implemented either on the continuum level with Langevin equations or on a discrete set of states as a master equation, thermodynamic consistency imposes a local-detailed balance constraint on noise and rates, respectively. Various integral and detailed fluctuation theorems, which are derived here in a unifying approach from one master theorem, constrain the probability distributions for work, heat and entropy production depending on the nature of the system and the choice of non-equilibrium conditions. For non-equilibrium steady states, particularly strong results hold like a generalized fluctuation–dissipation theorem involving entropy production. Ramifications and applications of these concepts include optimal driving between specified states in finite time, the role of measurement-based feedback processes and the relation between dissipation and irreversibility. Efficiency and, in particular, efficiency at maximum power can be discussed systematically beyond the linear response regime for two classes of molecular machines, isothermal ones such as molecular motors, and heat engines such as thermoelectric devices, using a common framework based on a cycle decomposition of entropy production. (Some figures may appear in colour only in the online journal) This article was invited by Erwin Frey.

/pdf/stochastic-thermodynamics-fluctuation-theorems-and-molecular-2epwyvmpf0.pdf

Stochastic thermodynamics, fluctuation theorems and molecular machines

基礎講座 電気泳動(Electrophoresis)

Unlike the well-defined long-range order that characterizes crystalline metals, the atomic arrangements in amorphous alloys remain mysterious at present. Despite intense research activity on metallic glasses and relentless pursuit of their structural description, the details of how the atoms are packed in amorphous metals are generally far less understood than for the case of network-forming glasses. Here we use a combination of state-of-the-art experimental and computational techniques to resolve the atomic-level structure of amorphous alloys. By analysing a range of model binary systems that involve different chemistry and atomic size ratios, we elucidate the different types of short-range order as well as the nature of the medium-range order. Our findings provide a reality check for the atomic structural models proposed over the years, and have implications for understanding the nature, forming ability and properties of metallic glasses.

http://slapper.apam.columbia.edu/bib/papers/sheng_n06.pdf

Atomic packing and short-to-medium-range order in metallic glasses

We use the mesoscopic nonequilibrium thermodynamics theory to derive the general kinetic equation of a system in the presence of potential barriers. The result is applied to a description of the evolution of systems whose dynamics is influenced by entropic barriers. We analyze in detail the case of diffusion in a domain of irregular geometry in which the presence of the boundaries induces an entropy barrier when approaching the exact dynamics by a coarsening of the description. The corresponding kinetic equation, named the Fick-Jacobs equation, is obtained, and its validity is generalized through the formulation of a scaling law for the diffusion coefficient which depends on the shape of the boundaries. The method we propose can be useful to analyze the dynamics of systems at the nanoscale where the presence of entropy barriers is a common feature.

/pdf/kinetic-equations-for-diffusion-in-the-presence-of-entropic-2tadtg2k8x.pdf

Kinetic equations for diffusion in the presence of entropic barriers.

With few exceptions, the shells (capsids) of sphere-like viruses have the symmetry of an icosahedron and are composed of coat proteins (subunits) assembled in special motifs, the T-number structures. Although the synthesis of artificial protein cages is a rapidly developing area of materials science, the design criteria for self-assembled shells that can reproduce the remarkable properties of viral capsids are only beginning to be understood. We present here a minimal model for equilibrium capsid structure, introducing an explicit interaction between protein multimers (capsomers). Using Monte Carlo simulation we show that the model reproduces the main structures of viruses in vivo (T-number icosahedra) and important nonicosahedral structures (with octahedral and cubic symmetry) observed in vitro. Our model can also predict capsid strength and shed light on genome release mechanisms.

https://www.pnas.org/content/pnas/101/44/15556.full.pdf

Origin of icosahedral symmetry in viruses

We show that transport in the presence of entropic barriers exhibits peculiar characteristics which makes it distinctly different from that occurring through energy barriers. The constrained dynamics yields a scaling regime for the particle current and the diffusion coefficient in terms of the ratio between the work done to the particles and available thermal energy. This interesting property, genuine to the entropic nature of the barriers, can be utilized to effectively control transport through quasi-one-dimensional structures in which irregularities or tortuosity of the boundaries cause entropic effects. The accuracy of the kinetic description has been corroborated by simulations. Applications to different dynamic situations involving entropic barriers are outlined.

/pdf/entropic-transport-kinetics-scaling-and-control-mechanisms-42qarvop7w.pdf

Entropic transport: kinetics, scaling, and control mechanisms.

Concepts of everyday use such as energy, heat, and temperature have acquired a precise meaning after the development of thermodynamics. Thermodynamics provides the basis for understanding how heat ...

The mesoscopic dynamics of thermodynamic systems.

We present a new method to analyze molecular and Brownian dynamics simulations of activated processes based on the concept of mean first-passage times. The new method provides a simple and efficient strategy to evaluate reaction rates and it facilitates the localization of the transition state directly from the kinetics of the system without the need of thermodynamical considerations. It also provides a more rigorous value of the steady-state transition rate and gives valuable information about many important characteristics of the process. We illustrate the power of this new technique by its application to the study of nucleation in rare gases.

/pdf/new-method-to-analyze-simulations-of-activated-processes-1n146m87tr.pdf

David Reguera

Papers

Kinetic equations for diffusion in the presence of entropic barriers.

Origin of icosahedral symmetry in viruses

Entropic transport: kinetics, scaling, and control mechanisms.

The mesoscopic dynamics of thermodynamic systems.

New method to analyze simulations of activated processes