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

When a drop of liquid dries on a solid surface, its suspended particulate matter is deposited in ring-like fashion. This phenomenon, known as the coffee-ring effect, is familiar to anyone who has observed a drop of coffee dry. During the drying process, drop edges become pinned to the substrate, and capillary flow outward from the centre of the drop brings suspended particles to the edge as evaporation proceeds. After evaporation, suspended particles are left highly concentrated along the original drop edge. The coffee-ring effect is manifested in systems with diverse constituents, ranging from large colloids to nanoparticles and individual molecules. In fact--despite the many practical applications for uniform coatings in printing, biology and complex assembly-the ubiquitous nature of the effect has made it difficult to avoid. Here we show experimentally that the shape of the suspended particles is important and can be used to eliminate the coffee-ring effect: ellipsoidal particles are deposited uniformly during evaporation. The anisotropic shape of the particles significantly deforms interfaces, producing strong interparticle capillary interactions. Thus, after the ellipsoids are carried to the air-water interface by the same outward flow that causes the coffee-ring effect for spheres, strong long-ranged interparticle attractions between ellipsoids lead to the formation of loosely packed or arrested structures on the air-water interface. These structures prevent the suspended particles from reaching the drop edge and ensure uniform deposition. Interestingly, under appropriate conditions, suspensions of spheres mixed with a small number of ellipsoids also produce uniform deposition. Thus, particle shape provides a convenient parameter to control the deposition of particles, without modification of particle or solvent chemistry.

/pdf/suppression-of-the-coffee-ring-effect-by-shape-dependent-3uzao8r2nz.pdf

Suppression of the coffee-ring effect by shape-dependent capillary interactions

流体力学杂志“Journal of Fluid Mechanics”由剑桥大学教授George Batchelor在1956年5月创办，在国际流体力学界享有很高的学术声望，被公认为是流体力学最著名的学术刊物之一，2005年的影响因子为2．061，雄居同类期刊之首．在它创刊50周年之际，2006年5月JFM出版了第554卷的纪念特刊，其中刊登了现任主编（美国西北大学S．H．Davis教授和英国剑桥大学T．J．Pedley教授）合写的述评：“Editorial：JFM at50”，以JFM为背景，从独特的视角对近50年来流体力学的发展进行了简明的回顾和展望，并归纳了一系列非常有启发性的有趣统计数字．2006年7月21日在剑桥大学应用数学和理论物理研究所（DAMTP）举行了创刊50周年的庆祝会．下午2点，JFM的新老编辑和来宾会聚一堂，Pedley教授致开幕词，其后是5个精彩的报告：The mysterious rattleback and its fluid counterpart（Keith Moffatt），Developments in shear instabilities（Patrick Huerre），Falling clouds（Elisabeth Guazzelli），Ecotectural fluid mechanics（Paul Linden），The success of JFM（Herbert Huppert），最后由Davis教授致闭幕词．

Journal of Fluid Mechanics创刊50周年

As their name indicates, liquid crystals simultaneously exhibit some characteristics common to both ordinary isotropic liquids and solid crystals. This ambivalence is also found in the effects of surfaces on these systems which lead to a great diversity of phenomena. These phenomena are reviewed focusing on nematic liquid crystals which have the simplest structure among the many existing types and which have been the most extensively studied. Three main kinds of effects can be distinguished. The first concerns the perturbation of the liquid crystalline structure close to the surface. Beyond this transition region, the bulk liquid crystalline structure is recovered with an orientation which is fixed by the surface: this phenomenon of orientation of liquid crystals by surfaces is the so-called anchoring. Finally, close to bulk phase transitions, critical adsorption or wetting can occur at surfaces as is also seen in isotropic systems.

https://iopscience.iop.org/article/10.1088/0034-4885/54/3/002/pdf

Surface effects and anchoring in liquid crystals

http://www.msc.univ-paris-diderot.fr/~jbfournier/publi/64.pdf

Membrane deformation under local pH gradient: mimicking mitochondrial cristae dynamics.

We propose a simple surface potential favoring the planar degenerate anchoring of nematic liquid crystals, i.e., the tendency of the molecules to align parallel to one another along any direction parallel to the surface. We show that, at lowest order in the tensorial Landau-de Gennes order-parameter, fourth-order terms must be included. We analyze the anchoring and wetting properties of this surface potential. In the nematic phase, we find the desired degenerate planar anchoring, with positive scalar order-parameter and some surface biaxiality. In the isotropic phase, we find, in agreement with experiments, that the wetting layer may exhibit a uniaxial ordering with negative scalar order-parameter. For large enough anchoring strength, this negative ordering transits towards the planar degenerate state.

/pdf/modeling-planar-degenerate-wetting-and-anchoring-in-nematic-5f2yly1ood.pdf

Modeling planar degenerate wetting and anchoring in nematic liquid crystals

Anisotropic inclusions are shown to induce spontaneous deviatoric bendings in lipidic membranes, by orienting at right angles across the bilayer. In the limit of strong membrane curvatures, a nonanalytical bending energy term is generated that favors saddlelike and cylindrical shapes, without penalizing spherical ones. An “egg-carton” instability results in flat membranes as well as a wormlike shape instability for vesicles. [S0031-9007(96)00321-3]

/pdf/nontopological-saddle-splay-and-curvature-instabilities-from-e7xtdjcuur.pdf

Nontopological saddle-splay and curvature instabilities from anisotropic membrane inclusions.

The spectroscopy and the dynamics of ${\mathrm{CO}}^{2+}$ and ${\mathrm{CO}}^{3+}$ in the 35--150-eV energy range have been studied using various complementary experiments, such as photoionization with synchrotron radiation, ion-ion coincidence technique, and ${\mathrm{H}}^{+}$ double-charge-transfer spectroscopy. In addition, ab initio calculations have been performed in order to obtain the potential-energy curves of the ${\mathrm{CO}}^{2+}$ electronic states lying between 35 and 60 eV. The lowest-energy state of ${\mathrm{CO}}^{2+}$ is shown to be predissociated. The metastable molecular doubly charged ions that appear at 40.75 eV energy correspond to transition(s) to the lowest-energy singlet state(s) of ${\mathrm{CO}}^{2+}$ $^{1}\mathrm{\ensuremath{\Pi}}$ and/or $^{1}\mathrm{\ensuremath{\Sigma}}^{+}$. The formation of the ${\mathrm{C}}^{+}$${(}^{2}$${\mathrm{P}}_{\mathrm{u}}$)+${\mathrm{O}}^{+}$ ${(}^{4}$${S}_{u}$) ion pair is shown to have a threshold energy of 38.4\ifmmode\pm\else\textpm\fi{}0.5 eV and is ascribed to highly excited (${\mathrm{CO}}^{\mathrm{*}}$${)}^{+}$ states, which autoionize into the double-ionization continuum. For most of the observed states, the partial cross section is reported from threshold up to 130 eV. No metastable ${\mathrm{CO}}^{3+}$ can be observed. The dominating dissociative path of triply charged molecular ions is the formation of the ${\mathrm{C}}^{2+}$+${\mathrm{O}}^{+}$ ion pair, for which we report the cross section up to 140 eV. The appearance energy is 81\ifmmode\pm\else\textpm\fi{}2 eV. The comparison of the double-photoionization cross section for the gas-phase molecule with previous photodesorption results is discussed.

Experimental and theoretical investigation of the spectroscopy and dynamics of multiply charged CO cations.

We study the collective behavior of inclusions inducing local anisotropic curvatures in a flexible fluid membrane. The N-body interaction energy for general anisotropic inclusions is calculated explicitly, including multi-body interactions. Long-range attractive interactions between inclusions are found to be sufficiently strong to induce aggregation. Monte Carlo simulations show a transition from compact clusters to aggregation on lines or circles. These results might be relevant to proteins in biological membranes or colloidal particles bound to surfactant membranes.

/pdf/n-body-study-of-anisotropic-membrane-inclusions-membrane-3twaqdkurg.pdf

Jean-Baptiste Fournier

Papers

Membrane deformation under local pH gradient: mimicking mitochondrial cristae dynamics.

Modeling planar degenerate wetting and anchoring in nematic liquid crystals

Nontopological saddle-splay and curvature instabilities from anisotropic membrane inclusions.

Experimental and theoretical investigation of the spectroscopy and dynamics of multiply charged CO cations.

N-body study of anisotropic membrane inclusions: Membrane mediated interactions and ordered aggregation