The Complexity of Finding Small Triangulations of Convex 3-Polytopes

The problem of finding a triangulation of a convex three-dimensional polytope with few tetrahedra is proved to be NP-hard. We discuss other related complexity results.Comment: 37 pages. An earlier version containing the sketch of the proof appeared at the proceedings of SODA 200

Hybrid CO₂-Ti:sapphire laser with tunable pulse duration for mid-infrared-pump terahertz-probe spectroscopy

We describe a mid-infrared pump – terahertz-probe setup based on a CO2 laser seeded with 10.6 μm wavelength pulses from an optical parametric amplifier, itself pumped by a Ti:Al2O3 laser. The output of the seeded CO2 laser produces high power pulses of nanosecond duration, which are synchronized to the femtosecond laser. These pulses can be tuned in pulse duration by slicing their front and back edges with semiconductor-plasma mirrors irradiated by replicas of the femtosecond seed laser pulses. Variable pulse lengths from 5 ps to 1.3 ns are achieved, and used in mid-infrared pump, terahertz-probe experiments with probe pulses generated and electro-optically sampled by the femtosecond laser

Corrosion-protective coatings from electrically conducting polymers

In a joint effort between NASA Kennedy and LANL, electrically conductive polymer coatings were developed as corrosion protective coatings for metal surfaces. At NASA Kennedy, the launch environment consist of marine, severe solar, and intermittent high acid and/or elevated temperature conditions. Electrically conductive polymer coatings were developed which impart corrosion resistance to mild steel when exposed to saline and acidic environments. Such coatings also seem to promote corrosion resistance in areas of mild steel where scratches exist in the protective coating. Such coatings appear promising for many commercial applications

Catastrophic stress corrosion failure of Zr-base bulk metallic glass through hydrogen embrittlement

Zr-base bulk metallic glasses (BMG) are prone to pitting corrosion in halide containing solutions and also stress corrosion cracking (SCC) is often interpreted in this context. This work presents in situ SCC experiments on notched Zr52.5Cu17.9Ni14.6Al10Ti5 (at.%) BMG bars under 3-point bending in dilute NaCl solution. They show that pitting corrosion is only the initiating process. The pitted areas have a lower local corrosion potential and the reaction of Zr4+ to zirconyl ions in solution produces H+ that can be reduced and absorbed in the local acidic environment. So, hydrogen embrittlement causes the observed catastrophic failure and peculiar fracture surface characteristics. © 2019 The Author

BPS Saturation from Null Reduction

We show that any $d$-dimensional strictly stationary, asymptotically Minkowskian solution $(d\ge 4)$ of a null reduction of $d+1$-dimensional pure gravity must saturate the BPS bound provided that the KK vector field can be identified appropriately. We also argue that it is consistent with the field equations.Comment: 10 page

The supersymmetric Ward identities on the lattice

Supersymmetric (SUSY) Ward identities are considered for the N=1 SU(2) SUSY Yang Mills theory discretized on the lattice with Wilson fermions (gluinos). They are used in order to compute non-perturbatively a subtracted gluino mass and the mixing coefficient of the SUSY current. The computations were performed at gauge coupling $\beta$=2.3 and hopping parameter $\kappa$=0.1925, 0.194, 0.1955 using the two-step multi-bosonic dynamical-fermion algorithm. Our results are consistent with a scenario where the Ward identities are satisfied up to O(a) effects. The vanishing of the gluino mass occurs at a value of the hopping parameter which is not fully consistent with the estimate based on the chiral phase transition. This suggests that, although SUSY restoration appears to occur close to the continuum limit of the lattice theory, the results are still affected by significant systematic effects.Comment: 34 pages, 7 figures. Typo corrected, last sentence reformulated, reference added. To appear in Eur. Phys. J.

Extremal properties for dissections of convex 3-polytopes

A dissection of a convex d-polytope is a partition of the polytope into d-simplices whose vertices are among the vertices of the polytope. Triangulations are dissections that have the additional property that the set of all its simplices forms a simplicial complex. The size of a dissection is the number of d-simplices it contains. This paper compares triangulations of maximal size with dissections of maximal size. We also exhibit lower and upper bounds for the size of dissections of a 3-polytope and analyze extremal size triangulations for specific non-simplicial polytopes: prisms, antiprisms, Archimedean solids, and combinatorial d-cubes.Comment: 19 page

Influence of isothermal omega precipitation aging on deformation mechanisms and mechanical properties of a β-type Ti-Nb alloy

In this study, the influence of ωiso precipitates on the active deformation mechanisms and the mechanical properties of the biomedical β-type Ti-40Nb alloy are revealed. Low temperature heat treatments (aging) at 573 K for durations up to 108.0 ks were carried out for a cold-rolled and recrystallized sample state. After an aging time of 3.6 ks the ωiso phase was determined by means of synchrotron XRD and the fraction and the crystallite size of ωiso increased progressively with increasing aging time. Due to the high intrinsic Young's modulus of the ωiso phase, the Young's modulus increased gradually with the aging time from 63 GPa, for the recrystallized reference condition, to values of 70 GPa (3.6 ks), 73 GPa (14.4 ks), 81 GPa (28.8 ks) and 96 GPa (108.0 ks). Depending on the aging time, also a change of the active deformation mechanisms occurred, resulting in significantly altered mechanical properties. For the single β-phase reference microstructure, stress-induced martensite (SIM) formation, {332} twinning and dislocation slip were observed under tensile loading, resulting in a low 0.2% proof stress of around 315 MPa but a high elongation at fracture of 26.2%. With increasing aging time, SIM formation and mechanical twinning are progressively hindered under tensile loading. SIM formation could not be detected for samples aged longer than 3.6 ks. The amount and thickness of deformation twins is clearly reduced with increasing aging time and for samples aged longer than 14.4 ks deformation twinning is completely suppressed. As a result of the changed deformation mechanisms and the increase of the critical stress for slip caused by ωiso, the 0.2% proof stress of the aged samples increased gradually from 410 MPa (3.6 ks) to around 910 MPa (108.0 ks). With regard to application as new bone implant material, a balanced ratio of a low Young's modulus of E = 73 GPa and higher 0.2% proof stress of 640 MPa was achieved after an aging time of 14.4 ks

Damage-free single-mode transmission of deep-UV light in hollow-core PCF

Transmission of UV light with high beam quality and pointing stability is desirable for many experiments in atomic, molecular and optical physics. In particular, laser cooling and coherent manipulation of trapped ions with transitions in the UV require stable, single-mode light delivery. Transmitting even ~2 mW CW light at 280 nm through silica solid-core fibers has previously been found to cause transmission degradation after just a few hours due to optical damage. We show that photonic crystal fiber of the kagom\'e type can be used for effectively single-mode transmission with acceptable loss and bending sensitivity. No transmission degradation was observed even after >100 hours of operation with 15 mW CW input power. In addition it is shown that implementation of the fiber in a trapped ion experiment significantly increases the coherence times of the internal state transfer due to an increase in beam pointing stability