Infinitesimals without Logic

We introduce the ring of Fermat reals, an extension of the real field containing nilpotent infinitesimals. The construction takes inspiration from Smooth Infinitesimal Analysis (SIA), but provides a powerful theory of actual infinitesimals without any need of a background in mathematical logic. In particular, on the contrary with respect to SIA, which admits models only in intuitionistic logic, the theory of Fermat reals is consistent with classical logic. We face the problem to decide if the product of powers of nilpotent infinitesimals is zero or not, the identity principle for polynomials, the definition and properties of the total order relation. The construction is highly constructive, and every Fermat real admits a clear and order preserving geometrical representation. Using nilpotent infinitesimals, every smooth functions becomes a polynomial because in Taylor's formulas the rest is now zero. Finally, we present several applications to informal classical calculations used in Physics: now all these calculations become rigorous and, at the same time, formally equal to the informal ones. In particular, an interesting rigorous deduction of the wave equation is given, that clarifies how to formalize the approximations tied with Hook's law using this language of nilpotent infinitesimals.Comment: The first part of the preprint is taken directly form arXiv:0907.1872 The second part is new and contains a list of example

On topological charge carried by nexuses and center vortices

In this paper we further explore the question of topological charge in the center vortex-nexus picture of gauge theories. Generally, this charge is locally fractionalized in units of 1/N for gauge group SU(N), but globally quantized in integral units. We show explicitly that in d=4 global topological charge is a linkage number of the closed two-surface of a center vortex with a nexus world line, and relate this linkage to the Hopf fibration, with homotopy $\Pi_3(S^3)\simeq Z$; this homotopy insures integrality of the global topological charge. We show that a standard nexus form used earlier, when linked to a center vortex, gives rise naturally to a homotopy $\Pi_2(S^2)\simeq Z$, a homotopy usually associated with 't Hooft-Polyakov monopoles and similar objects which exist by virtue of the presence of an adjoint scalar field which gives rise to spontaneous symmetry breaking. We show that certain integrals related to monopole or topological charge in gauge theories with adjoint scalars also appear in the center vortex-nexus picture, but with a different physical interpretation. We find a new type of nexus which can carry topological charge by linking to vortices or carry d=3 Chern-Simons number without center vortices present; the Chern-Simons number is connected with twisting and writhing of field lines, as the author had suggested earlier. In general, no topological charge in d=4 arises from these specific static configurations, since the charge is the difference of two (equal) Chern-Simons number, but it can arise through dynamic reconnection processes. We complete earlier vortex-nexus work to show explicitly how to express globally-integral topological charge as composed of essentially independent units of charge 1/N.Comment: Revtex4; 3 .eps figures; 18 page

A new constitutive model for prediction of impact rates response of polypropylene

This paper proposes a new constitutive model for predicting the impact rates response of polypropylene. Impact rates, as used here, refer to strain rates greater than 1000 1/s. The model is a physically based, three-dimensional constitutive model which incorporates the contributions of the amorphous, crystalline, pseudo-amorphous and entanglement networks to the constitutive response of polypropylene. The model mathematics is based on the well-known Glass-Rubber model originally developed for glassy polymers but the arguments have herein been extended to semi-crystalline polymers. In order to predict the impact rates behaviour of polypropylene, the model exploits the well-known framework of multiple processes yielding of polymers. This work argues that two dominant viscoelastic relaxation processes – the alpha- and beta-processes – can be associated with the yield responses of polypropylene observed at low-rate-dominant and impact-rates dominant loading regimes. Compression test data on polypropylene have been used to validate the model. The study has found that the model predicts quite well the experimentally observed nonlinear rate-dependent impact response of polypropylene

Shifting sows: longitudinal changes in the periparturient faecal microbiota of primiparous and multiparous sows

Knowledge of periparturient longitudinal changes in sow microbiota composition is necessary to fully understand her role in the development of the piglet microbiota, but also to improve gut health and performance of the sow in lactation. Primiparous sows face the challenge of partitioning nutrients to support maternal growth in addition to supporting foetal growth and the demands of lactation. Additional metabolic stress present during the periparturient period may induce changes in the microbiota profile between primiparous and multiparous sows. Using 16S rRNA gene sequencing, the study aimed to characterise the longitudinal changes in the periparturient microbiota and identify differences within the sow microbiota profile associated with parity. Faecal samples from primiparous (n = 13) and multiparous (n = 16) sows were collected at four different time points (day - 6, - 1, 3 and 8) in relation to farrowing (day 0). Microbiota richness was lowest on day 3 and - 1 of the periparturient period (P < 0.05). Microbiota community composition, assessed by weighted and unweighted UniFrac distances, demonstrated longitudinal changes, with day 3 samples clustering away from all other sampling time points (P < 0.05). The relative abundance of several genera segregated gestation from lactation samples including Roseburia, Prevotella 1, Prevotella 2, Christensenellaceae R-7 group, Ruminococcaceae UCG-002 and Ruminococcaceae UCG-010 (P < 0.01). Furthermore, day 3 was characterised by a significant increase in the relative abundance of Escherichia/Shigella, Fusobacterium and Bacteroides, and a decrease in Alloprevotella, Prevotellaceae UCG-003 and Ruminococcus 1 (P < 0.001). Primiparous sows had overall lower periparturient microbiota diversity (P < 0.01) and there was a significant interaction between parity and sampling time point, with primiparous sows having lower microbiota richness on day - 6 (P < 0.001). There was a significant interaction between sow parity and sampling time point on microbiota composition on day - 6 and - 1 (unweighted UniFrac distances;  ≤ 0.01) and day 8 (weighted and unweighted UniFrac distances; P < 0.05). Whilst no significant interactions between sow parity and sampling day were observed for genera relative abundances, multiparous sows had a significantly higher relative abundance of Bacteroidetes dgA-11 gut group and Prevotellaceae UCG-004 (P < 0.01). This study demonstrates that the sow microbiota undergoes longitudinal changes, which are collectively related to periparturient changes in the sow environment, diet and physiological changes to support foetal growth, delivery and the onset of lactation, but also sow parity

Resistance to three thrips species in <i>Capsicum</i> spp. depends on site conditions and geographic regions

Capsicum species are commercially grown for pepper production. This crop suffers severely from thrips damage and the identification of natural sources of thrips resistance is essential for the development of resistant cultivars. It is unclear whether resistance to Frankliniella occidentalis as assessed in a specific environment holds under different conditions. Additionally, other thrips species may respond differently to the plant genotypes. Screening for robust and general resistance to thrips encompasses testing different Capsicum accessions under various conditions and with different thrips species. We screened 11 Capsicum accessions (C. annuum and C. chinense) for resistance to F. occidentalis at three different locations in the Netherlands. Next, the same 11 accessions were screened for resistance to Thrips palmi and Scirtothrips dorsalis at two locations in Asia. This resulted in a unique analysis of thrips resistance in Capsicum at five different locations around the world. Finally, all accessions were also screened for resistance to F. occidentalis in the Netherlands using a leaf disc choice assay, allowing direct comparison of whole plant and leaf disc assays. Resistance to F. occidentalis was only partially consistent among the three sites in the Netherlands. The most susceptible accessions were consistently susceptible, but which accession was the most resistant differed among sites. In Asia, one C. chinense accession was particularly resistant to S. dorsalis and T. palmi, but this was not the most resistant accession to F. occidentalis. Overall, resistance to F. occidentalis correlated with S. dorsalis but not with T. palmi resistance in the C. annuum accessions. Damage inflicted on leaf discs reflected damage on the whole plant level. Our study showed that identifying broad spectrum resistance to thrips in Capsicum may prove to be challenging. Breeding programmes should focus on developing cultivars suitable for growing in defined geographic regions with specific thrips species and abiotic conditions

Mechanisms for slow strengthening in granular materials

Several mechanisms cause a granular material to strengthen over time at low applied stress. The strength is determined from the maximum frictional force F_max experienced by a shearing plate in contact with wet or dry granular material after the layer has been at rest for a waiting time \tau. The layer strength increases roughly logarithmically with \tau -only- if a shear stress is applied during the waiting time. The mechanisms of strengthening are investigated by sensitive displacement measurements and by imaging of particle motion in the shear zone. Granular matter can strengthen due to a slow shift in the particle arrangement under shear stress. Humidity also leads to strengthening, but is found not to be its sole cause. In addition to these time dependent effects, the static friction coefficient can also be increased by compaction of the granular material under some circumstances, and by cycling of the applied shear stress.Comment: 21 pages, 11 figures, submitted to Phys. Rev.

A two-species model of a two-dimensional sandpile surface: a case of asymptotic roughening

We present and analyze a model of an evolving sandpile surface in (2 + 1) dimensions where the dynamics of mobile grains ({\rho}(x, t)) and immobile clusters (h(x, t)) are coupled. Our coupling models the situation where the sandpile is flat on average, so that there is no bias due to gravity. We find anomalous scaling: the expected logarithmic smoothing at short length and time scales gives way to roughening in the asymptotic limit, where novel and non-trivial exponents are found.Comment: 7 Pages, 6 Figures; Granular Matter, 2012 (Online

Statistics of the contact network in frictional and frictionless granular packings

Simulated granular packings with different particle friction coefficient mu are examined. The distribution of the particle-particle and particle-wall normal and tangential contact forces P(f) are computed and compared with existing experimental data. Here f equivalent to F/F-bar is the contact force F normalized by the average value F-bar. P(f) exhibits exponential-like decay at large forces, a plateau/peak near f = 1, with additional features at forces smaller than the average that depend on mu. Computations of the force-force spatial distribution function and the contact point radial distribution function indicate that correlations between forces are only weakly dependent on friction and decay rapidly beyond approximately three particle diameters. Distributions of the particle-particle contact angles show that the contact network is not isotropic and only weakly dependent on friction. High force-bearing structures, or force chains, do not play a dominant role in these three dimensional, unloaded packings.Comment: 11 pages, 13 figures, submitted to PR

Scalar mesons moving in a finite volume and the role of partial wave mixing

Phase shifts and resonance parameters can be obtained from finite-volume lattice spectra for interacting pairs of particles, moving with nonzero total momentum. We present a simple derivation of the method that is subsequently applied to obtain the pi pi and pi K phase shifts in the sectors with total isospin I=0 and I=1/2, respectively. Considering different total momenta, one obtains extra data points for a given volume that allow for a very efficient extraction of the resonance parameters in the infinite-volume limit. Corrections due to the mixing of partial waves are provided. We expect that our results will help to optimize the strategies in lattice simulations, which aim at an accurate determination of the scattering and resonance properties.Comment: 19 pages, 12 figure