Prediction of gas leakage of environmental control systems

Mathematical models of leakage configurations and various flow theories are presented with the substantive experimental test data to provide background material for future design and failure analysis. Normal-rate leakage and emergency, high-rate leakage are considered

The total nucleon-nucleon cross section at large N_c

It is shown that at sufficiently large $N_c$ for incident momenta which are much larger than the QCD, the total nucleon-nucleon cross section is independent of incident momentum and given by $\sigma^{\rm total}=2 \pi \log^2(N_c) / (m^2_{\pi})$. This result is valid in the extreme large $N_c$ regime of $\log(N_c) \gg 1$ and has corrections of relative order $\log (\log(N_c))/\log(N_c)$. A possible connection of this result to the Froissart-Martin bound is discussed.Comment: 4 page

The Indians and the Agriculture of Crow Creek Indian Reservation

The Crow Creek Indian Reservation is located in South Dakota, bordering the east side of the Missouri River, about forty miles below Pierre, the Capital. In fact, a part of Hughes county lies in the Big Bend District of the reservation, and the south end of Hyde County and the west end of Buffalo County make up the rest of it - in all 313,304,23 acres or 489.5 square miles - about 13.5 townships. Parallel 44° North Latitude cuts the southern part of the Reservation, while meridian 99° West Longitude is just east of it. The nearest rail road point is Chamberlain on the Chicago, Milwaukee and St. Paul R.R., which is about twenty five miles down the river, same being about one hundred and eighty miles north west of Sioux City

General Thomas J. Stonewall Jackson to William Cook Lewis

In this letter, General Jackson submits payment of $150 to William Cook Lewis for the lease of slave, Jim. Jim Lewis served as Stonewall Jackson\u27s cook and servant throughout the war, cared for Jackson while he was dying, and led Jackson\u27s horse during his funeral

Shock wave compression of single-crystal forsterite

Hugoniot equation of state measurements have been performed on pure synthetic single-crystal forsterite (Mg_2SiO_4) in the pressure range 70–160 GPa (0.7–1.6 Mbar). These and earlier data for polycrystalline forsterite are compared with theoretical Hugoniots for the assemblages 2MgO (rocksalt) + SiO_2 (stishovite) and MgO (rocksalt) + MgSiO_3 (perovskite). The densities attained by single-crystal forsterite at pressures in excess of 120 GPa are greater than those expected in the event of shock-induced transformation to the isochemical oxide mixture. A similar test of the hypothesis of shock-induced transformation to the perovskite-bearing assemblage is sensitive to the choice of MgSiO_3 (perovskite) bulk modulus. Recent static compression measurements of Yagi et al. (1978) yield a K_(0T) of 286 GPa (for K_(0T)′ = 5), which, along with other elastic and thermodynamic parameters, suggests that shocked forsterite may be more dense than the perovskite-bearing assemblage. Crystalline phases of up to 5% greater zeropressure density or equally dense short-range-order-only phases may well be involved. Alternatively, the use of an isentropic bulk modulus of 250 GPa (estimated by Liebermann et al., 1977) for MgSiO_3 (perovskite) allows consistency between the data and the calculated MgO + MgSiO_3 (perovskite) Hugoniot for a reasonable choice (∼3.8) of K_(0s)′ for the latter phase. The new forsterite data along with high-pressure Hugoniot data for other olivines and olivinitic rocks define a smooth isobaric variation of Hugoniot density with composition. It is shown that an estimated pyrolite (Ringwood, 1975) Hugoniot density of 5.31 g/cm^3 at 120 GPa is ∼2% less dense than inferred from typical lower mantle density profiles

Foldy-Wouthuysen transformation for a Dirac-Pauli dyon and the Thomas-Bargmann-Michel-Telegdi equation

The classical dynamics for a charged point particle with intrinsic spin is governed by a relativistic Hamiltonian for the orbital motion and by the Thomas-Bargmann-Michel-Telegdi equation for the precession of the spin. It is natural to ask whether the classical Hamiltonian (with both the orbital and spin parts) is consistent with that in the relativistic quantum theory for a spin-1/2 charged particle, which is described by the Dirac equation. In the low-energy limit, up to terms of the 7th order in $1/E_g$ ($E_g=2mc^2$ and $m$ is the particle mass), we investigate the Foldy-Wouthuysen (FW) transformation of the Dirac Hamiltonian in the presence of homogeneous and static electromagnetic fields and show that it is indeed in agreement with the classical Hamiltonian with the gyromagnetic ratio being equal to 2. Through electromagnetic duality, this result can be generalized for a spin-1/2 dyon, which has both electric and magnetic charges and thus possesses both intrinsic electric and magnetic dipole moments. Furthermore, the relativistic quantum theory for a spin-1/2 dyon with arbitrary values of the gyromagnetic and gyroelectric ratios can be described by the Dirac-Pauli equation, which is the Dirac equation with augmentation for the anomalous electric and anomalous magnetic dipole moments. The FW transformation of the Dirac-Pauli Hamiltonian is shown, up to the 7th order again, to be also in accord with the classical Hamiltonian.Comment: 18 page

Validity of effective material parameters for optical fishnet metamaterials

Although optical metamaterials that show artificial magnetism are mesoscopic systems, they are frequently described in terms of effective material parameters. But due to intrinsic nonlocal (or spatially dispersive) effects it may be anticipated that this approach is usually only a crude approximation and is physically meaningless. In order to study the limitations regarding the assignment of effective material parameters, we present a technique to retrieve the frequency-dependent elements of the effective permittivity and permeability tensors for arbitrary angles of incidence and apply the method exemplarily to the fishnet metamaterial. It turns out that for the fishnet metamaterial, genuine effective material parameters can only be introduced if quite stringent constraints are imposed on the wavelength/unit cell size ratio. Unfortunately they are only met far away from the resonances that induce a magnetic response required for many envisioned applications of such a fishnet metamaterial. Our work clearly indicates that the mesoscopic nature and the related spatial dispersion of contemporary optical metamaterials that show artificial magnetism prohibits the meaningful introduction of conventional effective material parameters

Representing Structural Information of Helical Charge Distributions in Cylindrical Coordinates

Structural information in the local electric field produced by helical charge distributions, such as dissolved DNA, is revealed in a straightforward manner employing cylindrical coordinates. Comparison of structure factors derived in terms of cylindrical and helical coordinates is made. A simple coordinate transformation serves to relate the Green function in cylindrical and helical coordinates. We also compare the electric field on the central axis of a single helix as calculated in both systems.Comment: 11 pages in plain LaTex, no figures. Accepted for publication in PRE March, 199

Negative refractive index due to chirality

We demonstrate experimentally and numerically that metamaterials based on bilayer cross wires give giant optical activity, circular dichroism, and negative refractive index. The presented chiral design offers a much simpler geometry and more efficient way to realize negative refractive index at any frequency. We also developed a retrieval procedure for chiral materials which works successfully for circularly polarized waves

Singular electrostatic energy of nanoparticle clusters

The binding of clusters of metal nanoparticles is partly electrostatic. We address difficulties in calculating the electrostatic energy when high charging energies limit the total charge to a single quantum, entailing unequal potentials on the particles. We show that the energy at small separation $h$ has a strong logarithmic dependence on $h$. We give a general law for the strength of this logarithmic correction in terms of a) the energy at contact ignoring the charge quantization effects and b) an adjacency matrix specifying which spheres of the cluster are in contact and which is charged. We verify the theory by comparing the predicted energies for a tetrahedral cluster with an explicit numerical calculation.Comment: 17 pages, 3 figures. Submitted to Phys Rev