Drift without flux: Brownian walker with a space dependent diffusion coefficient

Space dependent diffusion of micrometer sized particles has been directly observed using digital video microscopy. The particles were trapped between two nearly parallel walls making their confinement position dependent. Consequently, not only did we measure a diffusion coefficient which depended on the particles' position, but also report and explain a new effect: a drift of the particles' individual positions in the direction of the diffusion coefficient gradient, in the absence of any external force or concentration gradient.Comment: 4 pages, 4 ps figures, include

The Mystery of Two Straight Lines in Bacterial Genome Statistics. Release 2007

In special coordinates (codon position--specific nucleotide frequencies) bacterial genomes form two straight lines in 9-dimensional space: one line for eubacterial genomes, another for archaeal genomes. All the 348 distinct bacterial genomes available in Genbank in April 2007, belong to these lines with high accuracy. The main challenge now is to explain the observed high accuracy. The new phenomenon of complementary symmetry for codon position--specific nucleotide frequencies is observed. The results of analysis of several codon usage models are presented. We demonstrate that the mean--field approximation, which is also known as context--free, or complete independence model, or Segre variety, can serve as a reasonable approximation to the real codon usage. The first two principal components of codon usage correlate strongly with genomic G+C content and the optimal growth temperature respectively. The variation of codon usage along the third component is related to the curvature of the mean-field approximation. First three eigenvalues in codon usage PCA explain 59.1%, 7.8% and 4.7% of variation. The eubacterial and archaeal genomes codon usage is clearly distributed along two third order curves with genomic G+C content as a parameter.Comment: Significantly extended version with new data for all the 348 distinct bacterial genomes available in Genbank in April 200

Conspiracy in bacterial genomes

The rank ordered distribution of the codon usage frequencies for 123 bacteriae is best fitted by a three parameters function that is the sum of a constant, an exponential and a linear term in the rank n. The parameters depend (two parabolically) from the total GC content. The rank ordered distribution of the amino acids is fitted by a straight line. The Shannon entropy computed over all the codons is well fitted by a parabola in the GC content, while the partial entropies computed over subsets of the codons show peculiar different behavior, exhibiting therefore a first conspiracy effect. Moreover the sum of the codon usage frequencies over particular sets, e.g. with C and A (respectively G and U) as i-th nucleotide, shows a clear linear dependence from the GC content, exhibiting another conspiracy effect.Comment: revised version: introduction and conclusion enhanced, references added, figures added, some tables remove

DC-conductivity of a suspension of insulating particles with internal rotation

We analyse the consequences of Quincke rotation on the conductivity of a suspension. Quincke rotation refers to the spontaneous rotation of insulating particles dispersed in a slightly conducting liquid and subject to a high DC electric field: above a critical field, each particle rotates continuously around itself with an axis pointing in any direction perpendicular to the DC field. When the suspension is subject to an electric field lower than the threshold one, the presence of insulating particles in the host liquid decreases the bulk conductivity since the particles form obstacles to ion migration. But for electric fields higher than the critical one, the particles rotate and facilitate ion migration: the effective conductivity of the suspension is increased. We provide a theoretical analysis of the impact of Quincke rotation on the apparent conductivity of a suspension and we present experimental results obtained with a suspension of PMMA particles dispersed in weakly conducting liquids

Relaxation of surface charge on rotating dielectric spheres: Implications on dynamic electrorheological effects

We have examined the effect of an oscillatory rotation of a polarized dielectric particle. The rotational motion leads to a re-distribution of the polarization charge on the surface of the particle. We show that the time averaged steady-state dipole moment is along the field direction, but its magnitude is reduced by a factor which depends on the angular velocity of rotation. As a result, the rotational motion of the particle reduces the electrorheological effect. We further assume that the relaxation of polarized charge is arised from a finite conductivity of the particle or host medium. We calculate the relaxation time based on the Maxwell-Wagner theory, suitably generalized to include the rotational motion. Analytic expressions for the reduction factor and the relaxation time are given and their dependence on the angular velocity of rotation will be discussed.Comment: Accepted for publications by Phys. Rev.

On local linearization of control systems

We consider the problem of topological linearization of smooth (C infinity or real analytic) control systems, i.e. of their local equivalence to a linear controllable system via point-wise transformations on the state and the control (static feedback transformations) that are topological but not necessarily differentiable. We prove that local topological linearization implies local smooth linearization, at generic points. At arbitrary points, it implies local conjugation to a linear system via a homeomorphism that induces a smooth diffeomorphism on the state variables, and, except at "strongly" singular points, this homeomorphism can be chosen to be a smooth mapping (the inverse map needs not be smooth). Deciding whether the same is true at "strongly" singular points is tantamount to solve an intriguing open question in differential topology

Hydrodynamic Coupling of Two Brownian Spheres to a Planar Surface

We describe direct imaging measurements of the collective and relative diffusion of two colloidal spheres near a flat plate. The bounding surface modifies the spheres' dynamics, even at separations of tens of radii. This behavior is captured by a stokeslet analysis of fluid flow driven by the spheres' and wall's no-slip boundary conditions. In particular, this analysis reveals surprising asymmetry in the normal modes for pair diffusion near a flat surface.Comment: 4 pages, 4 figure

Controllability on infinite-dimensional manifolds

Following the unified approach of A. Kriegl and P.W. Michor (1997) for a treatment of global analysis on a class of locally convex spaces known as convenient, we give a generalization of Rashevsky-Chow's theorem for control systems in regular connected manifolds modelled on convenient (infinite-dimensional) locally convex spaces which are not necessarily normable.Comment: 19 pages, 1 figur

Higher order glass-transition singularities in colloidal systems with attractive interactions

The transition from a liquid to a glass in colloidal suspensions of particles interacting through a hard core plus an attractive square-well potential is studied within the mode-coupling-theory framework. When the width of the attractive potential is much shorter than the hard-core diameter, a reentrant behavior of the liquid-glass line, and a glass-glass-transition line are found in the temperature-density plane of the model. For small well-width values, the glass-glass-transition line terminates in a third order bifurcation point, i.e. in a A_3 (cusp) singularity. On increasing the square-well width, the glass-glass line disappears, giving rise to a fourth order A_4 (swallow-tail) singularity at a critical well width. Close to the A_3 and A_4 singularities the decay of the density correlators shows stretching of huge dynamical windows, in particular logarithmic time dependence.Comment: 19 pages, 12 figures, Phys. Rev. E, in prin

Conflict between Translation Initiation and Elongation in Vertebrate Mitochondrial Genomes

The strand-biased mutation spectrum in vertebrate mitochondrial genomes results in an AC-rich L-strand and a GT-rich H-strand. Because the L-strand is the sense strand of 12 protein-coding genes out of the 13, the third codon position is overall strongly AC-biased. The wobble site of the anticodon of the 22 mitochondrial tRNAs is either U or G to pair with the most abundant synonymous codon, with only one exception. The wobble site of Met-tRNA is C instead of U, forming the Watson-Crick match with AUG instead of AUA, the latter being much more frequent than the former. This has been attributed to a compromise between translation initiation and elongation; i.e., AUG is not only a methionine codon, but also an initiation codon, and an anticodon matching AUG will increase the initiation rate. However, such an anticodon would impose selection against the use of AUA codons because AUA needs to be wobble-translated. According to this translation conflict hypothesis, AUA should be used relatively less frequently compared to UUA in the UUR codon family. A comprehensive analysis of mitochondrial genomes from a variety of vertebrate species revealed a general deficiency of AUA codons relative to UUA codons. In contrast, urochordate mitochondrial genomes with two tRNA(Met) genes with CAU and UAU anticodons exhibit increased AUA codon usage. Furthermore, six bivalve mitochondrial genomes with both of their tRNA-Met genes with a CAU anticodon have reduced AUA usage relative to three other bivalve mitochondrial genomes with one of their two tRNA-Met genes having a CAU anticodon and the other having a UAU anticodon. We conclude that the translation conflict hypothesis is empirically supported, and our results highlight the fine details of selection in shaping molecular evolution