In a Material World. Hyperbolische Geometrie in biologischen Materialien

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Orientation fluctuation-induced spinodal decomposition in polymer–liquid-crystal mixtures

We study the early stages of spinodal decomposition (SD) in polymer–liquid-crystal mixtures by solving linearized time-dependent Landau-Ginzburg equations for concentration (conserved order parameter) and orientation (nonconserved order parameter). The theory takes into account a cross term between concentration and orientation gradients, which becomes an important factor for phase separation kinetics. We calculate structure factors for concentration and for orientation, depending on a quench temperature and concentration. We find a new SD process driven by instability of the orientational order parameter. In this case, the average domain size initially grows as a nontrivial and evolving power of time, which starts as t1/3 in our minimal model. The domain growth is advanced by the coupling between the two order parameters

Negative s and Light New Physics

Motivated by the difference between SLD's recent measurement of ALR and the corresponding LEP results, we explore which kinds of new particles can (1) contribute dominantly to new physics through oblique corrections, (2) produce negative values for S and T, and (3) not be in conflict with any other experiments, on or off the Z resonance. We are typically led to models which involve new particles which are not much heavier than MZ/2, and so which may also have implications for other experiments in the near future. For such light particles, we show how the oblique-parameter analysis of purely Z-pole data requires the interpretation of the data in terms of modified parameters, S' and T', whose difference from S and T improves the available parameter space of the models.Comment: plain TeX, 16 pages, 6 figures attached as a uuencoded file, McGill-94/27, NEIP-94-00

Phase Transition in the ABC Model

Recent studies have shown that one-dimensional driven systems can exhibit phase separation even if the dynamics is governed by local rules. The ABC model, which comprises three particle species that diffuse asymmetrically around a ring, shows anomalous coarsening into a phase separated steady state. In the limiting case in which the dynamics is symmetric and the parameter $q$ describing the asymmetry tends to one, no phase separation occurs and the steady state of the system is disordered. In the present work we consider the weak asymmetry regime $q=\exp{(-\beta/N)}$ where $N$ is the system size and study how the disordered state is approached. In the case of equal densities, we find that the system exhibits a second order phase transition at some nonzero $\beta_c$. The value of $\beta_c = 2 \pi \sqrt{3}$ and the optimal profiles can be obtained by writing the exact large deviation functional. For nonequal densities, we write down mean field equations and analyze some of their predictions.Comment: 18 pages, 3 figure

Emergence and function of complex form in self-assembly and biological cells

This year, 2017, marks the centenary of the first publication of 'On Growth and Form', by the extraordinary Scottish classicist, biologist and part-time mathematician, D'Arcy Wentworth Thompson [1]..

Strichartz estimates for the water-wave problem with surface tension

Strichartz-type estimates for one-dimensional surface water-waves under surface tension are studied, based on the formulation of the problem as a nonlinear dispersive equation. We establish a family of dispersion estimates on time scales depending on the size of the frequencies. We infer that a solution $u$ of the dispersive equation we introduce satisfies local-in-time Strichartz estimates with loss in derivative: $$\| u \|_{L^p([0,T]) W^{s-1/p,q}(\mathbb{R})} \leq C, \qquad \frac{2}{p} + \frac{1}{q} = {1/2},$$ where $C$ depends on $T$ and on the norms of the initial data in $H^s \times H^{s-3/2}$. The proof uses the frequency analysis and semiclassical Strichartz estimates for the linealized water-wave operator.Comment: Fixed typos and mistakes. Merged with arXiv:0809.451

Pathogenic Potential to Humans of Bovine Escherichia coli O26, Scotland

Escherichia coli O26 and O157 have similar overall prevalences in cattle in Scotland, but in humans, Shiga toxin–producing E. coli O26 infections are fewer and clinically less severe than E. coli O157 infections. To investigate this discrepancy, we genotyped E. coli O26 isolates from cattle and humans in Scotland and continental Europe. The genetic background of some strains from Scotland was closely related to that of strains causing severe infections in Europe. Nonmetric multidimensional scaling found an association between hemolytic uremic syndrome (HUS) and multilocus sequence type 21 strains and confirmed the role of stx<sub>2</sub> in severe human disease. Although the prevalences of E. coli O26 and O157 on cattle farms in Scotland are equivalent, prevalence of more virulent strains is low, reducing human infection risk. However, new data on E. coli O26–associated HUS in humans highlight the need for surveillance of non-O157 enterohemorrhagic E. coli and for understanding stx<sub>2</sub> phage acquisition

The liquid-vapor interface of an ionic fluid

We investigate the liquid-vapor interface of the restricted primitive model (RPM) for an ionic fluid using a density-functional approximation based on correlation functions of the homogeneous fluid as obtained from the mean-spherical approximation (MSA). In the limit of a homogeneous fluid our approach yields the well-known MSA (energy) equation of state. The ionic interfacial density profiles, which for the RPM are identical for both species, have a shape similar to those of simple atomic fluids in that the decay towards the bulk values is more rapid on the vapor side than on the liquid side. This is the opposite asymmetry of the decay to that found in earlier calculations for the RPM based on a square-gradient theory. The width of the interface is, for a wide range of temperatures, approximately four times the second moment correlation length of the liquid phase. We discuss the magnitude and temperature dependence of the surface tension, and argue that for temperatures near the triple point the ratio of the dimensionless surface tension and critical temperature is much smaller for the RPM than for simple atomic fluids.Comment: 6 postscript figures, submitted to Phys. Rev.

Deformation of Platonic foam cells: Effect on growth rate

The diffusive growth rate of a polyhedral cell in dry three-dimensional foams depends on details of shape beyond cell topology, in contrast to the situation in two dimensions, where, by von Neumann's law, the growth rate depends only on the number of cell edges. We analyze the dependence of the instantaneous growth rate on the shape of single foam cells surrounded by uniform pressure; this is accomplished by supporting the cell with films connected to a wire frame and inducing cell distortions by deforming the wire frame. We consider three foam cells with a very simple topology; these are the Platonic foam cells, which satisfy Plateau's laws and are based on the trivalent Platonic solids (tetrahedron, cube, and dodecahedron). The Surface Evolver is used to model cell deformations induced through extension, compression, shear, and torsion of the wire frames. The growth rate depends on the deformation mode and frame size and can increase or decrease with increasing cell distortion. The cells have negative growth rates, in general, but dodecahedral cells subjected to torsion in small wire frames can have positive growth rates. The deformation of cubic cells is demonstrated experimentally

A lock-in model for the complex Matuyama-Brunhes boundary record of the loess/palaeosol sequence at Lingtai (Central Chinese Loess Plateau)

ISSN:0956-540XISSN:1365-246