Hard-sphere limit of soft-sphere model for granular materials: Stiffness dependence of steady granular flow

Dynamical behavior of steady granular flow is investigated numerically in the inelastic hard sphere limit of the soft sphere model. We find distinctively different limiting behaviors for the two flow regimes, i.e., the collisional flow and the frictional flow. In the collisional flow, the hard sphere limit is straightforward; the number of collisions per particle per unit time converges to a finite value and the total contact time fraction with other particles goes to zero. For the frictional flow, however, we demonstrate that the collision rate diverges as the power of the particle stiffness so that the time fraction of the multiple contacts remains finite even in the hard sphere limit although the contact time fraction for the binary collisions tends to zero.Comment: 10 figures. Typos removed. to appear in Phys. Rev.

Linear stability analysis of rapid granular flow on a slope and density wave formation

The linear stability of rapid granular flow on a slope under gravity against the longitudinal perturbation is analyzed using hydrodynamic equations. It is demonstrated that the steady flow uniform along the flow direction becomes unstable against the long-wavelength perturbations longitudinal to the flow direction for certain parameter ranges to form the density wave, in contrast with the finite wavelength instability against the transverse perturbation (Forterre & Pouliquen 2002). It is shown that the instability can be understood as the the long-wave instability of the kinematic waves in a quasi-one dimensional system. The results are compared with our previous molecular dynamics simulations (Mitarai & Nakanishi 2001), where the spontaneous density wave formation has been found.Comment: 25 pages, 15 figures, submitted to J. Fluid Mech.; larger parameter range investigated, discussions revise

Spatio-temporal structure of traffic flow in a system with an open boundary

The spatio-temporal structure of traffic flow pattern is investigated under the open boundary condition using the optimal velocity (OV) model. The parameter region where the uniform solution is convectively unstable is determined. It is found that a localized perturbation triggers a linearly unstable oscillatory solution out of the linearly unstable uniform state, and it is shown that the oscillatory solution is also convectively stabilized. It is demonstrated that the observed traffic pattern near an on-ramp can be interpreted as the noise sustained structure in the open flow system.Comment: 5 pages (RevTex), 3 figures (EPS). Submitted to Physical Review Letter

Control of ribosome traffic by position-dependent choice of synonymous codons

Messenger RNA encodes a sequence of amino acids by using codons. For most amino acids there are multiple synonymous codons that can encode the amino acid. The translation speed can vary from one codon to another, thus there is room for changing the ribosome speed while keeping the amino acid sequence and hence the resulting protein. Recently, it has been noticed that the choice of the synonymous codon, via the resulting distribution of slow- and fast-translated codons, affects not only on the average speed of one ribosome translating the messenger RNA (mRNA) but also might have an effect on nearby ribosomes by affecting the appearance of "traffic jams" where multiple ribosomes collide and form queues. To test this "context effect" further, we here investigate the effect of the sequence of synonymous codons on the ribosome traffic by using a ribosome traffic model with codon-dependent rates, estimated from experiments. We compare the ribosome traffic on wild type sequences and sequences where the synonymous codons were swapped randomly. By simulating translation of 87 genes, we demonstrate that the wild type sequences, especially those with a high bias in codon usage, tend to have the ability to reduce ribosome collisions, hence optimizing the cellular investment in the translation apparatus. The magnitude of such reduction of the translation time might have a significant impact on the cellular growth rate and thereby have importance for the survival of the species.Comment: 12 pages, 6 Figures. This is an author-created, un-copyedited version of an article accepted for publication in Physical Biology. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from i

Disturbance accelerates the transition from low- to high- diversity state in a model ecosystem

The effect of disturbance on a model ecosystem of sessile and mutually competitive species [Mathiesen et al. Phys. Rev. Lett. 107, 188101 (2011); Mitarai et al. Phys. Rev. E 86, 011929 (2012) ] is studied. The disturbance stochastically removes individuals from the system, and the created empty sites are re-colonized by neighbouring species. We show that the stable high-diversity state, maintained by occasional cyclic species interactions that create isolated patches of meta-populations, is robust against small disturbance. We further demonstrate that finite disturbance can accelerate the transition from the low- to high-diversity state by helping creation of small patches through diffusion of boundaries between species with stand-off relation.Comment: 8 pages, 8 figures. Typos correcte

A scaling law of multilevel evolution: how the balance between within- and among-collective evolution is determined

Numerous living systems are hierarchically organised, whereby replicating components are grouped into reproducing collectives -- e.g., organelles are grouped into cells, and cells are grouped into multicellular organisms. In such systems, evolution can operate at two levels: evolution among collectives, which tends to promote selfless cooperation among components within collectives (called altruism), and evolution within collectives, which tends to promote cheating among components within collectives. The balance between within- and among-collective evolution thus exerts profound impacts on the fitness of these systems. Here, we investigate how this balance depends on the size of a collective (denoted by $N$) and the mutation rate of components ($m$) through mathematical analyses and computer simulations of multiple population genetics models. We first confirm a previous result that increasing $N$ or $m$ accelerates within-collective evolution relative to among-collective evolution, thus promoting the evolution of cheating. Moreover, we show that when within- and among-collective evolution exactly balance each other out, the following scaling relation generally holds: $Nm^{\alpha}$ is a constant, where scaling exponent $\alpha$ depends on multiple parameters, such as the strength of selection and whether altruism is a binary or quantitative trait. This relation indicates that although $N$ and $m$ have quantitatively distinct impacts on the balance between within- and among-collective evolution, their impacts become identical if $m$ is scaled with a proper exponent. Our results thus provide a novel insight into conditions under which cheating or altruism evolves in hierarchically-organised replicating systems.Comment: Accepted in Genetics after a minor revision. Revised based on referee reports. Added results on a binary-trait model. Conclusions do not chang

Ribosome collisions and Translation efficiency: Optimization by codon usage and mRNA destabilization

Individual mRNAs are translated by multiple ribosomes that initiate translation with a few seconds interval. The ribosome speed is codon dependant, and ribosome queuing has been suggested to explain specific data for translation of some mRNAs in vivo. By modelling the stochastic translation process as a traffic problem, we here analyze conditions and consequences of collisions and queuing. The model allowed us to determine the on-rate (0.8 to 1.1 initiations per sec) and the time (1 sec) the preceding ribosome occludes initiation for Escherichia coli lacZ mRNA in vivo. We find that ribosome collisions and queues are inevitable consequences of a stochastic translation mechanism that reduce the translation efficiency substantially on natural mRNAs. The cells minimize collisions by having its mRNAs being unstable and by a highly selected codon usage in the start of the mRNA. The cost of mRNA breakdown is offset by the concomitant increase in translational efficiency.Comment: 5 figures, 3 table