Rolling friction of a viscous sphere on a hard plane

A first-principle continuum-mechanics expression for the rolling friction coefficient is obtained for the rolling motion of a viscoelastic sphere on a hard plane. It relates the friction coefficient to the viscous and elastic constants of the sphere material. The relation obtained refers to the case when the deformation of the sphere $\xi$ is small, the velocity of the sphere $V$ is much less than the speed of sound in the material and when the characteristic time $\xi/V$ is much larger than the dissipative relaxation times of the viscoelastic material. To our knowledge this is the first ``first-principle'' expression of the rolling friction coefficient which does not contain empirical parameters.Comment: 6 pages, 2 figure

How large are the level sets of the Takagi function?

Let T be Takagi's continuous but nowhere-differentiable function. This paper considers the size of the level sets of T both from a probabilistic point of view and from the perspective of Baire category. We first give more elementary proofs of three recently published results. The first, due to Z. Buczolich, states that almost all level sets (with respect to Lebesgue measure on the range of T) are finite. The second, due to J. Lagarias and Z. Maddock, states that the average number of points in a level set is infinite. The third result, also due to Lagarias and Maddock, states that the average number of local level sets contained in a level set is 3/2. In the second part of the paper it is shown that, in contrast to the above results, the set of ordinates y with uncountably infinite level sets is residual, and a fairly explicit description of this set is given. The paper also gives a negative answer to a question of Lagarias and Maddock by showing that most level sets (in the sense of Baire category) contain infinitely many local level sets, and that a continuum of level sets even contain uncountably many local level sets. Finally, several of the main results are extended to a version of T with arbitrary signs in the summands.Comment: Added a new Section 5 with generalization of the main results; some new and corrected proofs of the old material; 29 pages, 3 figure

Geometric Mixing, Peristalsis, and the Geometric Phase of the Stomach

Mixing fluid in a container at low Reynolds number - in an inertialess environment - is not a trivial task. Reciprocating motions merely lead to cycles of mixing and unmixing, so continuous rotation, as used in many technological applications, would appear to be necessary. However, there is another solution: movement of the walls in a cyclical fashion to introduce a geometric phase. We show using journal-bearing flow as a model that such geometric mixing is a general tool for using deformable boundaries that return to the same position to mix fluid at low Reynolds number. We then simulate a biological example: we show that mixing in the stomach functions because of the "belly phase": peristaltic movement of the walls in a cyclical fashion introduces a geometric phase that avoids unmixing.Comment: Revised, published versio

Complex and unexpected dynamics in simple genetic regulatory networks

Peer reviewedPublisher PD

Psi-Series Solution of Fractional Ginzburg-Landau Equation

One-dimensional Ginzburg-Landau equations with derivatives of noninteger order are considered. Using psi-series with fractional powers, the solution of the fractional Ginzburg-Landau (FGL) equation is derived. The leading-order behaviours of solutions about an arbitrary singularity, as well as their resonance structures, have been obtained. It was proved that fractional equations of order $alpha$ with polynomial nonlinearity of order $s$ have the noninteger power-like behavior of order $\alpha/(1-s)$ near the singularity.Comment: LaTeX, 19 pages, 2 figure

Synthetic Biology Open Language Visual (SBOL Visual) Version 2.0

People who are engineering biological organisms often find it useful to communicate in diagrams, both about the structure of the nucleic acid sequences that they are engineering and about the functional relationships between sequence features and other molecular species. Some typical practices and conventions have begun to emerge for such diagrams. The Synthetic Biology Open Language Visual (SBOL Visual) has been developed as a standard for organizing and systematizing such conventions in order to produce a coherent language for expressing the structure and function of genetic designs. This document details version 2.0 of SBOL Visual, which builds on the prior SBOL Visual 1.0 standard by expanding diagram syntax to include functional interactions and molecular species, making the relationship between diagrams and the SBOL data model explicit, supporting families of symbol variants, clarifying a number of requirements and best practices, and significantly expanding the collection of diagram glyphs

280 one-opposition near-Earth asteroids recovered by the EURONEAR with the <i>Isaac Newton</i> Telescope

Context. One-opposition near-Earth asteroids (NEAs) are growing in number, and they must be recovered to prevent loss and mismatch risk, and to improve their orbits, as they are likely to be too faint for detection in shallow surveys at future apparitions. Aims. We aimed to recover more than half of the one-opposition NEAs recommended for observations by the Minor Planet Center (MPC) using the Isaac Newton Telescope (INT) in soft-override mode and some fractions of available D-nights. During about 130 h in total between 2013 and 2016, we targeted 368 NEAs, among which 56 potentially hazardous asteroids (PHAs), observing 437 INT Wide Field Camera (WFC) fields and recovering 280 NEAs (76% of all targets). Methods. Engaging a core team of about ten students and amateurs, we used the THELI, Astrometrica, and the Find_Orb software to identify all moving objects using the blink and track-and-stack method for the faintest targets and plotting the positional uncertainty ellipse from NEODyS. Results. Most targets and recovered objects had apparent magnitudes centered around V ~ 22.8 mag, with some becoming as faint as V ~ 24 mag. One hundred and three objects (representing 28% of all targets) were recovered by EURONEAR alone by Aug. 2017. Orbital arcs were prolonged typically from a few weeks to a few years; our oldest recoveries reach 16 years. The O−C residuals for our 1854 NEA astrometric positions show that most measurements cluster closely around the origin. In addition to the recovered NEAs, 22 000 positions of about 3500 known minor planets and another 10 000 observations of about 1500 unknown objects (mostly main-belt objects) were promptly reported to the MPC by our team. Four new NEAs were discovered serendipitously in the analyzed fields and were promptly secured with the INT and other telescopes, while two more NEAs were lost due to extremely fast motion and lack of rapid follow-up time. They increase the counting to nine NEAs discovered by the EURONEAR in 2014 and 2015. Conclusions. Targeted projects to recover one-opposition NEAs are efficient in override access, especially using at least two-meter class and preferably larger field telescopes located in good sites, which appear even more efficient than the existing surveys

Synthetic biology open language visual (SBOL Visual) version 2.3

People who are engineering biological organisms often find it useful to communicate in diagrams, both about the structure of the nucleic acid sequences that they are engineering and about the functional relationships between sequence features and other molecular species. Some typical practices and conventions have begun to emerge for such diagrams. The Synthetic Biology Open Language Visual (SBOL Visual) has been developed as a standard for organizing and systematizing such conventions in order to produce a coherent language for expressing the structure and function of genetic designs. This document details version 2.3 of SBOL Visual, which builds on the prior SBOL Visual 2.2 in several ways. First, the specification now includes higher-level "interactions with interactions," such as an inducer molecule stimulating a repression interaction. Second, binding with a nucleic acid backbone can be shown by overlapping glyphs, as with other molecular complexes. Finally, a new "unspecified interaction" glyph is added for visualizing interactions whose nature is unknown, the "insulator" glyph is deprecated in favor of a new "inert DNA spacer" glyph, and the polypeptide region glyph is recommended for showing 2A sequences

OAZ-t/OAZ3 Is Essential for Rigid Connection of Sperm Tails to Heads in Mouse

Polyamines are known to play important roles in the proliferation and differentiation of many types of cells. Although considerable amounts of polyamines are synthesized and stored in the testes, their roles remain unknown. Ornithine decarboxylase antizymes (OAZs) control the intracellular concentration of polyamines in a feedback manner. OAZ1 and OAZ2 are expressed ubiquitously, whereas OAZ-t/OAZ3 is expressed specifically in germline cells during spermiogenesis. OAZ-t reportedly binds to ornithine decarboxylase (ODC) and inactivates ODC activity. In a prior study, polyamines were capable of inducing a frameshift at the frameshift sequence of OAZ-t mRNA, resulting in the translation of OAZ-t. To investigate the physiological role of OAZ-t, we generated OAZ-t–disrupted mutant mice. Homozygous OAZ-t mutant males were infertile, although the polyamine concentrations of epididymides and testes were normal in these mice, and females were fertile. Sperm were successfully recovered from the epididymides of the mutant mice, but the heads and tails of the sperm cells were easily separated in culture medium during incubation. Results indicated that OAZ-t is essential for the formation of a rigid junction between the head and tail during spermatogenesis. The detached tails and heads were alive, and most of the headless tails showed straight forward movement. Although the tailless sperm failed to acrosome-react, the heads were capable of fertilizing eggs via intracytoplasmic sperm injection. OAZ-t likely plays a key role in haploid germ cell differentiation via the local concentration of polyamines