Whither tube theory: From believing to measuring

This short contribution examines the difficulties that have not yet been fully overcome in the many developments made from the simplest (and original) tube model for entangled polymers. It is concluded that many more length scales have to be considered sequentially when deriving a continuum rheological model from molecular considerations than have been considered in the past. In particular, most unresolved issues of the tube theory are related to the length scales of tube diameter, and molecular dynamics simulations is the perfect route to resolve them. The power of molecular simulations is illustrated by two examples: stress contributions from bonded and non-bonded interaction, and the inter-chain coupling, which is usually neglected in the tube theory.

Comparing tube models for predicting the linear rheology of branched polymer melts

The hierarchical and "bob" (or branch-on-branch) models are tube-based computational models recently developed for predicting the linear rheology of general mixtures of polydisperse branched polymers. These two models are based on a similar tube-theory framework but differ in their numerical implementation and details of relaxation mechanisms. We present a detailed overview of the similarities and differences of these models and examine the effects of these differences on the predictions of the linear viscoelastic properties of a set of representative branched polymer samples in order to give a general picture of the performance of these models. Our analysis confirms that the hierarchical and bob models quantitatively predict the linear rheology of a wide range of branched polymer melts but also indicate that there is still no unique solution to cover all types of branched polymers without case-by-case adjustment of parameters such as the dilution exponent alpha and the factor p(2) which defines the hopping distance of a branch point relative to the tube diameter. An updated version of the hierarchical model, which shows improved computational efficiency and refined relaxation mechanisms, is introduced and used in these analyses.

Constraint release in entangled binary blends of linear polymers: a molecular dynamics study

We present extensive molecular dynamics simulations of the dynamics of diluted long probe chains entangled with a matrix of shorter chains. The chain lengths of both components are above the entanglement strand length, and the ratio of their lengths is varied over a wide range to cover the crossover from the chain reptation regime to tube Rouse motion regime of the long probe chains. Reducing the matrix chain length results in a faster decay of the dynamic structure factor of the probe chains, in good agreement with recent neutron spin echo experiments. The diffusion of the long chains, measured by the mean square displacements of the monomers and the centers of mass of the chains, demonstrates a systematic speed-up relative to the pure reptation behavior expected for monodisperse melts of sufficiently long polymers. On the other hand, the diffusion of the matrix chains is only weakly perturbed by the diluted long probe chains. The simulation results are qualitatively consistent with the theoretical predictions based on constraint release Rouse model, but a detailed comparison reveals the existence of a broad distribution of the disentanglement rates, which is partly confirmed by an analysis of the packing and diffusion of the matrix chains in the tube region of the probe chains. A coarse-grained simulation model based on the tube Rouse motion model with incorporation of the probability distribution of the tube segment jump rates is developed and shows results qualitatively consistent with the fine scale molecular dynamics simulations. However, we observe a breakdown in the tube Rouse model when the short chain length is decreased to around N-S = 80, which is roughly 3.5 times the entanglement spacing N-e(P) = 23. The location of this transition may be sensitive to the chain bending potential used in our simulations.

Measurements and modelling of airflows in houses using passive sampling and HAM software

Passive samplers have been predominantly used to monitor environmental conditions in single volumes. However, measurements using a calibrated passive sampler- Solid Phase Microextraction (SPME) fibre, in three houses with cold pitched roof, successfully demonstrated the potential of the SPME fibre as a device for monitoring air movement in two volumes. The roofs monitored were pitched at 15° - 30° with insulation thickness varying between 200-300 mm on the ceiling. For effective analysis, two constant sources of volatile organic compounds were diffused steadily in the house. Emission rates and air movement from the house to the roof was predicted using developed algorithms. The airflow rates which were calibrated against conventional tracer gas techniques were introduced into a HAM software package to predict the effects of air movement on other varying parameters. On average it was shown from the in situ measurements that about 20-30% of air entering the three houses left through gaps and cracks in the ceiling into the roof. Although these field measurements focus on the airflows, it is associated with energy benefits such that; if these flows are reduced then significantly energy losses would also be reduced (as modelled) consequently improving the energy efficiency of the house. Other results illustrated that condensation formation risks were dependent on the airtightness of the building envelopes including configurations of their roof constructions.

Segmental dynamics in entangled linear polymer melts

We present molecular dynamics (MD) and slip-springs model simulations of the chain segmental dynamics in entangled linear polymer melts. The time-dependent behavior of the segmental orientation autocorrelation functions and mean-square segmental displacements are analyzed for both flexible and semiflexible chains, with particular attention paid to the scaling relations among these dynamic quantities. Effective combination of the two simulation methods at different coarse-graining levels allows us to explore the chain dynamics for chain lengths ranging from Z ≈ 2 to 90 entanglements. For a given chain length of Z ≈ 15, the time scales accessed span for more than 10 decades, covering all of the interesting relaxation regimes. The obtained time dependence of the monomer mean square displacements, g1(t), is in good agreement with the tube theory predictions. Results on the first- and second-order segmental orientation autocorrelation functions, C1(t) and C2(t), demonstrate a clear power law relationship of C2(t) C1(t)m with m = 3, 2, and 1 in the initial, free Rouse, and entangled (constrained Rouse) regimes, respectively. The return-to-origin hypothesis, which leads to inverse proportionality between the segmental orientation autocorrelation functions and g1(t) in the entangled regime, is convincingly verified by the simulation result of C1(t) g1(t)−1 t–1/4 in the constrained Rouse regime, where for well-entangled chains both C1(t) and g1(t) are rather insensitive to the constraint release effects. However, the second-order correlation function, C2(t), shows much stronger sensitivity to the constraint release effects and experiences a protracted crossover from the free Rouse to entangled regime. This crossover region extends for at least one decade in time longer than that of C1(t). The predicted time scaling behavior of C2(t) t–1/4 is observed in slip-springs simulations only at chain length of 90 entanglements, whereas shorter chains show higher scaling exponents. The reported simulation work can be applied to understand the observations of the NMR experiments.

Determination of tube theory parameters using a simple grid model as an example

Although the tube theory is successful in describing entangled polymers qualitatively, a more quantitative description requires precise and consistent definitions of its parameters. Here we investigate the simplest model of entangled polymers, namely a single Rouse chain in a cubic lattice of line obstacles, and illustrate the typical problems and uncertainties of the tube theory. In particular we show that in general one needs 3 entanglement related parameters, but only 2 combinations of them are relevant for the long-time dynamics. Conversely, the plateau modulus can not be determined from these two parameters and requires a more detailed model of entanglements with explicit entanglement forces, such as the slipsprings model. It is shown that for the grid model the Rouse time within the tube is larger than the Rouse time of the free chain, in contrast to what the standard tube theory assumes.

Analysis of DNA polymorphism in ancient barley herbarium material: validation of the KASP SNP genotyping platform

The availability of crop specimens archived in herbaria and old seed collections represent valuable resources for the analysis of plant genetic diversity and crop domestication. The ability to extract ancient DNA (aDNA) from such samples has recently allowed molecular genetic investigations to be undertaken in ancient materials. While analyses of aDNA initially focused on the use of markers which occur in multiple copies such as the internal transcribed spacer region (ITS) within ribosomal DNA and those requiring amplification of short DNA regions of variable length such as simple sequence repeats (SSRs), emphasis is now moving towards the genotyping of single nucleotide polymorphisms (SNPs), traditionally undertaken in aDNA by Sanger sequencing. Here, using a panel of barley aDNA samples previously surveyed by Sanger sequencing for putative causative SNPs within the flowering-time gene PPD-H1, we assess the utility of the Kompetitive Allele Specific PCR (KASP) genotyping platform for aDNA analysis. We find KASP to out-perform Sanger sequencing in the genotyping of aDNA samples (78% versus 61% success, respectively), as well as being robust to contamination. The small template size (≥46 bp) and one-step, closed-tube amplification/genotyping process make this platform ideally suited to the genotypic analysis of aDNA, a process which is often hampered by template DNA degradation and sample cross-contamination. Such attributes, as well as its flexibility of use and relatively low cost, make KASP particularly relevant to the genetic analysis of aDNA samples. Furthermore, KASP provides a common platform for the genotyping and analysis of corresponding SNPs in ancient, landrace and modern plant materials. The extended haplotype analysis of PPD-H1 undertaken here (allelic variation at which is thought to be important for the spread of domestication and local adaptation) provides further resolution to the previously identified geographic cline of flowering-time allele distribution, illustrating how KASP can be used to aid genetic analyses of aDNA from plant species. We further demonstrate the utility of KASP by genotyping ten additional genetic markers diagnostic for morphological traits in barley, shedding light on the phenotypic traits, alleles and allele combinations present in these unviable ancient specimens, as well as their geographic distributions.

Resilience of rice (Oryzaspp.) pollen germination and tube growth to temperature stress

Resilience of rice cropping systems to potential global climate change will partly depend on temperature tolerance of pollen germination (PG) and tube growth (PTG). Germination of pollen of high temperature susceptible Oryza glaberrima Steud. (cv. CG14) and O. sativa L. ssp. indica (cv. IR64) and high temperature tolerant O. sativa ssp. aus (cv. N22), was assessed on a 5.6-45.4°C temperature gradient system. Mean maximum PG was 85% at 27°C with 1488 μm PTG at 25°C. The hypothesis that in each pollen grain, minimum temperature requirements (Tn) and maximum temperature limits (Tx) for germination operate independently was accepted by comparing multiplicative and subtractive probability models. The maximum temperature limit for PG in 50% of grains (Tx(50)) was lowest (29.8°C) in IR64 compared with CG14 (34.3°C) and N22 (35.6°C). Standard deviation (sx) of Tx was also low in IR64 (2.3°C) suggesting that the mechanism of IR64's susceptibility to high temperatures may relate to PG. Optimum germination temperatures and thermal times for 1mm PTG were not linked to tolerating high temperatures at anthesis. However, the parameters Tx(50) and sx in the germination model define new pragmatic criteria for successful and resilient PG, preferable to the more traditional cardinal (maximum and minimum) temperatures.

Ionospheric ion upwelling in the wake of flux transfer events at the dayside magnetopause

The effects of flux transfer events (FTE) on the dayside auroral ionosphere are studied, using a simple twin-vortex model of induced ionospheric plasma flow. It is shown that the predicted and observed velocities of these flows are sufficient to drive nonthermal plasma in the F region, not only within the newly opened flux tube of the FTE, but also on the closed, or "old" open, field lines around it. In fact, with the expected poleward neutral wind, the plasma is more highly nonthermal on the flanks of, but outside, the open flux tube: EISCAT observations indicate that plasma is indeed driven into nonthermal distributions in these regions. The nonthermal plasma is thereby subject to additional upforce due to the resulting ion temperature anisotropy and transient expansion due to Joule heating and also to ion accelerations associated with the FTE field aligned current system. Any upflows produced on closed field lines in the vicinity of the FTE are effectively bunched-up in the "wake" of the FTE. Observations from the AMPTE-UKS satellite at the magnetopause reveal ion upflows of energy ∼100 eV flowing out from the ionosphere on closed field lines which are only found in the wake of the FTE. Such flows are also only found shortly after two, out of all the FTEs observed by AMPTE-UKS. The outflow from the ionosphere is two orders of magnitude greater than predicted for the "classical" polar wind. It is shown that such ionospheric ion flows are only expected in association with FTEs on the magnetopause which are well removed from the sub-solar point-either towards dusk or, as in the UKS example discussed here, towards dawn. It is suggested that such ionospheric ions will only be observed if the center of the FTE open flux tube passes very close to the satellite. Consequently, we conclude the ion upflows presented here are probably driven by the second of two possible source FTEs and are observed at the satellite with a lag after the FTE which is less than their time-of-flight.

Field-aligned plasma flow in the quiet, mid-latitude ionosphere deduced from topside soundings

A method for quantifying diffusive flows of O+ ions in the topside ionosphere from satellite soundings is described. A departure from diffusive equilibrium alters the shape of the plasma scale-height profile near the F2-peak where ion-neutral frictional drag is large. The effect enables the evaluation of , the field-aligned flux of O+ ions relative to the neutral oxygen atom gas, using MSIS model values for the neutral thermospheric densities and temperature. Upward flow values are accurate to within about 10%, the largest sources of error being the MSIS prediction for the concentration of oxygen atoms and the plasma temperature gradient deduced from the sounding. Downward flux values are only determined to within 20%. From 60,000 topside soundings, taken at the minimum and rising phase of the solar cycle, a total of 1098 mean scale-height profiles are identified for which no storm sudden commencement had occurred in the previous 12 days and for which Kp was less than 2o, each mean profile being an average of about six soundings. A statistical study ofdeduced from these profiles shows the diurnal cycle of O+ flow in the quiet, topside ionosphere at mid-latitudes and its seasonal variations. The differences betweenand ion flux observations from incoherent scatter radars are considered using the meridional thermospheric winds predicted by a global, three-dimensional model. The mean interhemispheric flow from summer to winter is compared with predictions by a numerical model of the protonospheric coupling of conjugate ionospheres for up to 6 days following a geomagnetic storm. The observed mean (of order 3 × 1016 ions day−1 along a flux tube of area 1 m2 at 1000 km) is larger than predicted for day 6 and the suggested explanation is a decrease in upward flows from the winter, daytime ionosphere between the sixth and twelfth days.

Commensalism in an agroecosystem: hydraulic redistribution by deep-rooted legumes improves survival of a droughted shallow-rooted legume companion

We investigated commensalism of water use among annual shallow-rooted and perennial deep-rooted pasture legumes by examining the effect of hydraulic lift by Cullen pallidum (N.T.Burb.) J.W.Grimes and Medicago sativa on growth, survival and nutrient uptake of Trifolium subterraneum L. A vertically split-root design allowed separate control of soil water in top and bottom soil. Thirty-five days after watering ceased in the top tube, but soil remained at field capacity in the bottom tube, an increase in shallow soil water content by hydraulic lift was 5.6 and 5.9 g kg−1 soil overnight for C. pallidum and M. sativa, respectively. Trifolium subterraneum in this treatment maintained higher leaf water potentials (with M. sativa) or exhibited a slower decline (with C. pallidum) than without companion perennial plants; and shoot biomass of T. subterraneum was 56% (with C. pallidum) and 67% (with M. sativa) of that when both top and bottom tubes were at field capacity. Uptake of rubidium (a potassium analog) and phosphorus by T. subterraneum was not facilitated by hydraulic lift. Interestingly, phosphorus content was threefold greater, and shoot biomass 1.5–3.3-fold greater when T. subterraneum was interplanted with C. pallidum compared with M. sativa, although dry weight of C. pallidum was much greater than that of M. sativa. This study showed that interplanting with deep-rooted perennial legumes has benefited the survival of T. subterraneum.

Recurrence and higher ergodic properties for quenched random Lorentz tubes in dimension bigger than two

We consider the billiard dynamics in a non-compact set of ℝ d that is constructed as a bi-infinite chain of translated copies of the same d-dimensional polytope. A random configuration of semi-dispersing scatterers is placed in each copy. The ensemble of dynamical systems thus defined, one for each global realization of the scatterers, is called quenched random Lorentz tube. Under some fairly general conditions, we prove that every system in the ensemble is hyperbolic and almost every system is recurrent, ergodic, and enjoys some higher chaotic properties.