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Composite Materials and Aerospace Construction
Published in Daniel Gay, Composite Materials, 2023
The front fuselage and the rear fuselage are obtained each from a framework formed by the fuselage frames and by transverse junctional beams (which stabilize the shape of the fuselage and support the floor). This framework is covered by four panels in the form of stiffened cylindrical carbon/epoxy shells. The surface area of these panels may exceed 90 m2. Their thickness varies (from less than 2 mm to more than 5 mm) in order to provide proper resistance to local loads in their relevant areas. Such a mechanical optimization leads to a reduced mass. In addition, in view of polymerization, this solution requires a smaller autoclave than for monolithic fuselage section. Furthermore, in case of fabrication defect or damage, the loss is limited to a single panel. These stiffened panels are fixed on carbon/epoxy common frames of varying thicknesses, by means of carbon/PEEK connecting parts or attachment fittings. Heavily loaded frames are made of titanium. The transverse junction beams are metallic (aluminum–lithium).
Mechanics of Rigid Bodies
Published in Osamu Morita, Classical Mechanics in Geophysical Fluid Dynamics, 2019
is called the reduced mass. Equation (7.15) is Newton’s second law for a particle of mass µ, and is solved if the forces F1, F2 and F21 were given. The position vectors of particle 1 and particle 2 are given by the solutions of (7.13) and (7.15), using the following equations, () r1=R−μm1r, () r2=R−μm2r.
Vibrational spectroscopy: infra-red and Raman spectroscopy
Published in D. Campbell, R.A. Pethrick, J.R. White, Polymer Characterization, 2017
D. Campbell, R.A. Pethrick, J.R. White
When molecular vibrations result in a change in the bond dipole moment, as a consequence of change in the electron distribution in the bond, it is possible to stimulate transitions between energy levels by interaction with EM radiation of an appropriate frequency. When the vibrating dipole is in phase with the electric vector of the incident radiation the vibrations are enhanced and there is transfer of energy from the incident radiation to the molecule. For a simple diatomic molecule the vibration can be modelled as two masses, m1 and m2, joined by a spring with the deformation obeying Hooke’s law. The vibration frequency (v) is then expressed by v = (k/μ)1/2/2π where k is the force constant and μ = m1m2/(m1 + m2) is the reduced mass. The detection of the energy absorption constitutes IR spectroscopy. In continuous recording spectrometers the spectral transitions are detected by scanning through the frequency whilst continuously monitoring the transmitted light intensity. The energies of molecular vibrations of interest for analytical work correspond to wavelengths in the range 2.5−25 pm or 4000−400 cm−1 (frequency in wavenumber (cm−1) = 104/wavelength in μm). Some spectrometers operate in the near-infrared region (NIR): 0.7−2.5 pm (4000−14 000 cm−1) and others in the far-infrared (FIR): 50−800 pm (200−12.5 cm−1) and some spectrometers are designed to operate over the whole frequency range.
Dynamical and interference effects in X-ray emission spectroscopy of H-bonded water – origin of the split lone-pair peaks
Published in Molecular Physics, 2023
Osamu Takahashi, Lars G. M. Pettersson
Including the low-frequency (translational and librational) modes in the sampling can clearly be replaced by additional sampling of situations of the underlying molecular dynamics trajectory. However, if one is anyway sampling a particular situation one might as well include all modes. We note that the internal modes show a very small spread in position while that in momentum is large making sampling the momenta of these modes more important than the positions [62]. For the modes involving motion of the whole molecule in the field from its neighbours, the zero-point energy and corresponding spread in momentum is quite small, while the spread in position is larger. We note that including the translational modes requires that the appropriate reduced mass be used as it differs significantly from that of a single proton.
Benchmark calculations of the 3 D Rydberg spectrum of beryllium
Published in Molecular Physics, 2022
Monika Stanke, Ludwik Adamowicz
The largest basis set of 15,300 ECGs for each state is used to calculate the total nonrelativistic energy for Be. The results are shown in Table 2. As expected, making the nuclear mass heavier lowers the total energy. The lowering is about 0.001 hartree and decreases slightly as the level of excitation decreases. This effect is due to an increase of the reduced mass of the electron caused by the increase of the nuclear mass. As a result, the electrons are slightly closer to the nucleus in Be than in Be. This makes the total energy of Be being lower than the energy of Be. However, the lowering of the energies of the four electrons due to the increasing nuclear mass is somewhat uneven. Particularly, the energy of the Rydberg d electron is lowered more for the lowest state, where it is located closer to the nucleus, than for the fourth state. The total energies calculated for Be and Be and shown in Table 2 may provide a reference for future nonrelativistic calculations performed by other researchers for an infinite nuclear mass (i.e. with assuming the Born–Oppenheimer approximation).
Deviation of the rate of the
Published in Molecular Physics, 2021
Katharina Höveler, Johannes Deiglmayr, Frédéric Merkt
For both reaction systems, we could detect a clear enhancement of the reaction rates below 1 K. Whereas the overall shape of the observed rate enhancements was very similar for both reactions, the amplitude of the enhancement was found to be a factor of 2.8(3) larger in the reaction than in the reaction. This factor could be attributed to (i) the different population of the J = 1 rotational state in the jet-cooled samples of pure and samples, and (ii) the scaling with the reduced mass of the deviation from Langevin-capture behaviour at low collision energies. Remarkable quantitative agreement was found between the experimental results and simulations based on the scaled reaction-rate coefficients at low collision energies reported by Dashevskaya, Litvin, Nikitin and Troe [26].