In material science of elastomers the influence of nanoscale and nanostructured filler particles is of utmost significance for the performance of innovative rubber products, i.e., passenger car tires ...with ultralow rolling resistance but high wet-grip performance. A better understanding of the physical characteristics of the filler–rubber interface and the filler–rubber interphase as well is necessary to improve the overall macroscopic properties of these elastomeric nanocomposites. Therefore, the surface energies and polarities of filler particles with different modified surfaces were measured by a modified Wilhelmy technique. In all cases the rubber matrix consisted of a solution - styrene butadiene copolymers, filled with 20 or 40 phr pyrogenic or precipitated silica grades with different surface modifications by silanes, and a carbon black sample as reference. A moving die rheometer was employed to observe the filler flocculation at elevated temperatures (160 °C) in rubber mixtures containing no curatives. A significant influence of the surface energy of the filler was noticed: the flocculation tendency increased with increasing difference in work of adhesion between filler and rubber. In dynamic mechanical measurements the influence of the filler/filler and the filler/polymer interactions were studied in cured S-SBR samples. Amplitude sweep experiments were carried out to investigate the temperature dependent nonlinear characteristics of the elastic and viscous moduli, which is commonly associated with a progressive breakdown of the filler network at higher strain amplitudes (Payne effect). Static measurements and relaxations test were accomplished by large scale strain experiments. A structural–phenomenological modeling of the long strain mechanical properties of these rubber compounds was done: the “layered fiber model”. This new model is based on the hypothesis that during deformation of the composites the polymer chains slipped off from the polymer interphase around the filler particles into the gaps between aggregates, where high-strength polymer fibers in an uniaxially oriented state are formed. We find new interesting correlations between the physicochemical properties of the filler/polymer interface and the macroscopic mechanical properties of the elastomeric materials.
Previous studies of heat tolerance of tropical trees have focused on canopy leaves exposed to full sunlight and high temperatures. However, in lowland tropical forests with leaf area indices of 5–6, ...the vast majority of leaves experience varying degrees of shade and a reduced heat load compared to sun leaves. Here we tested whether heat tolerance is lower in shade than in sun leaves. For three tropical tree species,
Calophyllum inophyllum, Inga spectabilis
, and
Ormosia macrocalyx
, disks of fully developed shade and sun leaves were subjected to 15-min heat treatments, followed by measurement of chlorophyll
a
fluorescence after 48 h of recovery. In two of the three species, the temperature causing a 50% decrease of the fluorescence ratio
F
v
/
F
m
(
T
50
) was significantly lower (by ~ 1.0 °C) in shade than in sun leaves, indicating a moderately decreased heat tolerance of shade leaves. In shade leaves of these two species, the rise in initial fluorescence,
F
0
, also occurred at lower temperatures. In the third species, there was no shade-sun difference in
T
50
. In situ measurements of photosynthetic CO
2
assimilation showed that the optimum temperature for photosynthesis tended to be lower in shade leaves, although differences were not significant. At supra-optimal temperatures, photosynthesis was largely constrained by stomatal conductance, and the high-temperature CO
2
compensation point,
T
Max
, occurred at considerably lower temperatures than
T
50
. Our study demonstrates that the temperature response of shade leaves of tropical trees differs only marginally from that of sun leaves, both in terms of heat tolerance and photosynthetic performance.
SecDec is a program which can be used for the factorization of dimensionally regulated poles from parametric integrals, in particular multi-loop integrals, and the subsequent numerical evaluation of ...the finite coefficients. Here we present version 3.0 of the program, which has major improvements compared to version 2: it is faster, contains new decomposition strategies, an improved user interface and various other new features which extend the range of applicability.
Program title: SecDec 3.0
Catalogue identifier: AEIR_v3_0
Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEIR_v3_0.html
Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland
Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html
No. of lines in distributed program, including test data, etc.: 123828
No. of bytes in distributed program, including test data, etc.: 1651026
Distribution format: tar.gz
Programming language: Wolfram Mathematica, perl, Fortran/C++.
Computer: From a single PC to a cluster, depending on the problem.
Operating system: Unix, Linux.
RAM: Depending on the complexity of the problem
Classification: 4.4, 5, 11.1.
Catalogue identifier of previous version: AEIR_v2_1
Journal reference of previous version: Comput. Phys. Comm. 184(2013)2552
Does the new version supersede the previous version?: Yes
Nature of problem: Extraction of ultraviolet and infrared singularities from parametric integrals appearing in higher order perturbative calculations in gauge theories. Numerical integration in the presence of integrable singularities (e.g. kinematic thresholds).
Solution method: Algebraic extraction of singularities within dimensional regularization using iterated sector decomposition. This leads to a Laurent series in the dimensional regularization parameter, where the coefficients are finite integrals over the unit-hypercube. Those integrals are evaluated numerically by Monte Carlo integration. The integrable singularities are handled by choosing a suitable integration contour in the complex plane, in an automated way.
Reasons for new version:•Improved user interface.•Additional new decomposition strategies.•Usage on a cluster is much improved.•Speed-up in numerical evaluation times.•Various new features (please see below).Summary of revisions:•Implementation of two new decompositions strategies based on a geometric algorithm.•Scans over large ranges of parameters are facilitated.•Linear propagators can be treated.•Propagators with negative indices are possible.•Interface to reduction programs like Reduze, Fire, LiteRed facilitated.•Option to use numerical integrator from Mathematica.•Using CQUAD for 1-dimensional integrals to improve speed of numerical evaluations.•Option to include epsilon-dependent dummy functions.Restrictions: Depending on the complexity of the problem, limited by memory and CPU time.
Running time: Between a few seconds and several hours, depending on the complexity of the problem.
The purely numerical evaluation of multi-loop integrals and amplitudes can be a viable alternative to analytic approaches, in particular in the presence of several mass scales, provided sufficient ...accuracy can be achieved in an acceptable amount of time. For many multi-loop integrals, the fraction of time required to perform the numerical integration is significant and it is therefore beneficial to have efficient and well-implemented numerical integration methods. With this goal in mind, we present a new stand-alone integrator based on the use of (quasi-Monte Carlo) rank-1 shifted lattice rules. For integrals with high variance we also implement a variance reduction algorithm based on fitting a smooth function to the inverse cumulative distribution function of the integrand dimension-by-dimension. Additionally, the new integrator is interfaced to pySecDec to allow the straightforward evaluation of multi-loop integrals and dimensionally regulated parameter integrals. In order to make use of recent advances in parallel computing hardware, our integrator can be used both on CPUs and CUDA compatible GPUs where available.
Program Title: pySecDec, qmc
Program Files doi:http://dx.doi.org/10.17632/dnrkf5jxzh.2
Licensing provisions: GNU General Public License v3
Programming language: python, FORM, C++, CUDA
External routines/libraries: catch 1, gsl 2, numpy 3, sympy 4, Nauty 5, Cuba 6, FORM 7, Normaliz 8. The program can also be used in a mode which does not require Normaliz.
Journal reference of previous version: Comput. Phys. Commun. 222 (2018) 313–326.
Does the new version supersede the previous version?: Yes
Nature of problem: Extraction of ultraviolet and infrared singularities from parametric integrals appearing in higher order perturbative calculations in quantum field theory. Numerical integration in the presence of integrable singularities (e.g. kinematic thresholds).
Solution method: Algebraic extraction of singularities within dimensional regularization using iterated sector decomposition. This leads to a Laurent series in the dimensional regularization parameter ϵ (and optionally other regulators), where the coefficients are finite integrals over the unit-hypercube. Those integrals are evaluated numerically by Monte Carlo integration. The integrable singularities are handled by choosing a suitable integration contour in the complex plane, in an automated way. The parameter integrals forming the coefficients of the Laurent series in the regulator(s) are provided in the form of libraries which can be linked to the calculation of (multi-) loop amplitudes.
Restrictions: Depending on the complexity of the problem, limited by memory and CPU/GPU time.
References:
1 https://github.com/philsquared/Catch/.
2 http://www.gnu.org/software/gsl/.
3 http://www.numpy.org/.
4 http://www.sympy.org/.
5 http://pallini.di.uniroma1.it/.
6 T. Hahn, “CUBA: A Library for multidimensional numerical integration,” Comput. Phys. Commun. 168 (2005) 78 hep-ph/0404043, http://www.feynarts.de/cuba/.
7 J. Kuipers, T. Ueda and J. A. M. Vermaseren, “Code Optimization in FORM,” Comput. Phys. Commun. 189 (2015) 1 arXiv:1310.7007, http://www.nikhef.nl/ form/.
8 W. Bruns, B. Ichim, B. and T. Römer, C. Söger, “Normaliz. Algorithms for rational cones and affine monoids.” http://www.math.uos.de/normaliz/.
We present the calculation of the cross section and invariant mass distribution for Higgs boson pair production in gluon fusion at next-to-leading order (NLO) in QCD. Top-quark masses are fully taken ...into account throughout the calculation. The virtual two-loop amplitude has been generated using an extension of the program GoSam supplemented with an interface to Reduze for the integral reduction. The occurring integrals have been calculated numerically using the program SecDec. Our results, including the full top-quark mass dependence for the first time, allow us to assess the validity of various approximations proposed in the literature, which we also recalculate. We find substantial deviations between the NLO result and the different approximations, which emphasizes the importance of including the full top-quark mass dependence at NLO.
A
bstract
We present a calculation of the NNLO QCD corrections to Z-boson pair production at hadron colliders, based on the N-jettiness method for the real radiation parts. We discuss the size and ...shape of the perturbative corrections along with their associated scale uncertainties and compare our results to recent LHC data at
s
=
13
TeV.
We compute the full-color two-loop five-gluon amplitude for the all-plus helicity configuration. In order to achieve this, we calculate the required master integrals for all permutations of the ...external legs, in the physical scattering region. We verify the expected divergence structure of the amplitude and extract the finite hard function. We further validate our result by checking the factorization properties in the collinear limit. Our result is fully analytic and valid in the physical scattering region. We express it in a compact form containing logarithms, dilogarithms, and rational functions.
Adhesion between silica glass or acrylic balls and silicone elastomers and various industrial rubbers is investigated. The work of adhesion during pull-off is found to strongly vary depending on the ...system, which we attribute to the two opposite effects: (1) viscoelastic energy dissipation close to an opening crack tip and (2) surface roughness. Introducing surface roughness on the glass ball is found to increase the work of adhesion for soft elastomers, while for the stiffer elastomers it results in a strong reduction in the work of adhesion. For the soft silicone elastomers a strong increase in the work of adhesion with increasing pull-off velocity is observed, which may result from the non-adiabatic processes associated with molecular chain pull-out. In general, the work of adhesion is decreased after repeated contacts due to the transfer of molecules from the elastomers to the glass ball. Thus, extracting the free chains (oligomers) from the silicone elastomers is shown to make the work of adhesion independent of the number of contacts. The viscoelastic properties (linear and nonlinear) of all of the rubber compounds are measured, and the velocity dependent crack opening propagation energy at the interface is calculated. Silicone elastomers show a good agreement between the measured work of adhesion and the predicted results, but carbon black filled hydrogenated nitrile butadiene rubber compounds reveal that strain softening at the crack tip may play an important role in determining the work of adhesion. Additionally, adhesion measurement under submerged conditions in distilled water and water + soap solutions are also performed: a strong reduction in the work of adhesion is measured for the silicone elastomers submerged in water, and a complete elimination of adhesion is found for the water + soap solution attributed to an osmotic repulsion between the negatively charged surface of the glass and the elastomer.
The interplay of viscoelasticity, surface roughness and molecular mobility on rubber adhesion is investigated experimentally and supported by theoretical analysis.
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