Symmetry as a sufficient condition for a finite flex

We show that if the joints of a bar and joint framework $(G,p)$ are positioned as `generically' as possible subject to given symmetry constraints and $(G,p)$ possesses a `fully-symmetric' infinitesimal flex (i.e., the velocity vectors of the infinitesimal flex remain unaltered under all symmetry operations of $(G,p)$), then $(G,p)$ also possesses a finite flex which preserves the symmetry of $(G,p)$ throughout the path. This and other related results are obtained by symmetrizing techniques described by L. Asimov and B. Roth in their paper `The Rigidity Of Graphs' from 1978 and by using the fact that the rigidity matrix of a symmetric framework can be transformed into a block-diagonalized form by means of group representation theory. The finite flexes that can be detected with these symmetry-based methods can in general not be found with the analogous non-symmetric methods.Comment: 26 pages, 10 figure

Ionization by bulk heating of electrons in capacitive radio frequency atmospheric pressure microplasmas

Electron heating and ionization dynamics in capacitively coupled radio frequency (RF) atmospheric pressure microplasmas operated in helium are investigated by Particle in Cell simulations and semi-analytical modeling. A strong heating of electrons and ionization in the plasma bulk due to high bulk electric fields are observed at distinct times within the RF period. Based on the model the electric field is identified to be a drift field caused by a low electrical conductivity due to the high electron-neutral collision frequency at atmospheric pressure. Thus, the ionization is mainly caused by ohmic heating in this "Omega-mode". The phase of strongest bulk electric field and ionization is affected by the driving voltage amplitude. At high amplitudes, the plasma density is high, so that the sheath impedance is comparable to the bulk resistance. Thus, voltage and current are about 45{\deg} out of phase and maximum ionization is observed during sheath expansion with local maxima at the sheath edges. At low driving voltages, the plasma density is low and the discharge becomes more resistive resulting in a smaller phase shift of about 4{\deg}. Thus, maximum ionization occurs later within the RF period with a maximum in the discharge center. Significant analogies to electronegative low pressure macroscopic discharges operated in the Drift-Ambipolar mode are found, where similar mechanisms induced by a high electronegativity instead of a high collision frequency have been identified

Material matters: predicting the core hardness variance in industrialized case hardening of 18CrNi8 [Vorhersage der Kernhärtenvarianz von industriell einsatzgehärtetem 18CrNi8]

To explain the variance in core hardness of 18CrNi8 nozzle bodies after industrial heat treatment, several data sources, including steel melt composition, sensor process data, and measurement errors, of five years are aggregated. In order to predict hardness variations caused by alloy composition, traditional physical models by Maynier are compared with data-driven machine learning models, which show no advantage due to low data variability. Neither method can fully explain the visible drifts, which are better tracked by an alternative (i. e., filter model) that uses past measurements. Machine learning on features from heat treatment is not successful in predicting hardness change, presumably because the process is too stable. Finally, a large part of the variance is caused by the HV 1 measurement error

Nuclear effects in g1A(x,Q2)g_{1A}(x,Q^2) at small xx in deep inelastic scattering on 7^7Li and 3^3He

We suggest to use polarized nuclear targets of $^7$Li and $^3$He to study nuclear effects in the spin dependent structure functions $g_{1A}(x,Q^2)$. These effects are expected to be enhanced by a factor of two as compared to the unpolarized targets. We predict a significant $x$ dependence at $10^{-4} \div 10^{-3} \leq x \leq 0.2$ of $g_{1A}(x,Q^2)/g_{1N}(x,Q^2)$ due to nuclear shadowing and nuclear enhancement. The effect of nuclear shadowing at $x \approx 10^{-3}$ is of an order of 16% for $g_{1A=7}^{n.s. 3/2}(x,Q^2)/g_{1N}^{n.s.}(x,Q^2)$ and 10% for $g_{1A=3}^{n.s}(x,Q^2)/g_{1N}^{n.s.}(x,Q^2)$. By imposing the requirement that the Bjorken sum rule is satisfied we model the effect of enhancement. We find the effect of enhancement at $x \approx 0.125 (0.15)$ to be of an order of $20 (55)$ for $g_{1A=7}^{n.s. 3/2}(x,Q^2)/g_{1N}^{n.s.}(x,Q^2)$ and $14 (40)$ for $g_{1A=3}^{n.s}(x,Q^2)/g_{1N}^{n.s.}(x,Q^2)$, if enhancement occupies the region $0.05 \leq x \leq 0.2$ ($0.1 \leq x \leq 0.2$). We predict a 2% effect in the difference of the scattering cross sections of deep inelastic scattering of an unpolarized projectile off $^7$Li with $M_{J}$=3/2 and $M_{J}$=1/2. We also show explicitly that the many-nucleon description of deep inelastic scattering off $^7$Li becomes invalid in the enhancement region $0.05 < x \leq 0.2$.Comment: 29 pages, 5 figures, RevTe

Universal amplitude ratios from numerical studies of the three-dimensional O(2) model

We investigate the three-dimensional O(2) model near the critical point by Monte Carlo simulations and calculate the major universal amplitude ratios of the model. The ratio U_0=A+/A- is determined directly from the specific heat data at zero magnetic field. The data do not, however, allow to extract an accurate estimate for alpha. Instead, we establish a strong correlation of U_0 with the value of alpha used in the fit. This numerical alpha-dependence is given by A+/A- = 1 -4.20(5) alpha + O(alpha^2). For the special alpha-values used in other calculations we find full agreement with the corresponding ratio values, e. g. that of the shuttle experiment with liquid helium. On the critical isochore we obtain the ratio xi+/xi-_T=0.293(9), and on the critical line the ratio xi_T^c/xi_L^c=1.957(10) for the amplitudes of the transverse and longitudinal correlation lengths. These two ratios are independent of the used alpha or nu-values.Comment: 34 pages, 19 Ps-figures, Latex2e, revised version, to be published in J. Phys.

The orbit rigidity matrix of a symmetric framework

A number of recent papers have studied when symmetry causes frameworks on a graph to become infinitesimally flexible, or stressed, and when it has no impact. A number of other recent papers have studied special classes of frameworks on generically rigid graphs which are finite mechanisms. Here we introduce a new tool, the orbit matrix, which connects these two areas and provides a matrix representation for fully symmetric infinitesimal flexes, and fully symmetric stresses of symmetric frameworks. The orbit matrix is a true analog of the standard rigidity matrix for general frameworks, and its analysis gives important insights into questions about the flexibility and rigidity of classes of symmetric frameworks, in all dimensions. With this narrower focus on fully symmetric infinitesimal motions, comes the power to predict symmetry-preserving finite mechanisms - giving a simplified analysis which covers a wide range of the known mechanisms, and generalizes the classes of known mechanisms. This initial exploration of the properties of the orbit matrix also opens up a number of new questions and possible extensions of the previous results, including transfer of symmetry based results from Euclidean space to spherical, hyperbolic, and some other metrics with shared symmetry groups and underlying projective geometry.Comment: 41 pages, 12 figure

Valence band offset in heterojunctions between crystalline silicon and amorphous silicon (sub)oxides (a-SiOx:H, 0 < x < 2)

The heterojunction between amorphous silicon (sub)oxides (a-SiOx:H, 0 < x < 2) and crystalline silicon (c-Si) is investigated. We combine chemical vapor deposition with in-system photoelectron spectroscopy in order to determine the valence band offset ΔEV and the interface defect density, being technologically important junction parameters. ΔEV increases from ≈0.3 eV for the a-Si:H/c-Si interface to >4 eV for the a-SiO2/c-Si interface, while the electronic quality of the heterointerface deteriorates. High-bandgap a-SiOx:H is therefore unsuitable for the hole contact in heterojunction solar cells, due to electronic transport hindrance resulting from the large ΔEV. Our method is readily applicable to other heterojunctions