Extracting Scattering Phase-Shifts in Higher Partial-Waves from Lattice QCD Calculations

L\"uscher's method is routinely used to determine meson-meson, meson-baryon and baryon-baryon s-wave scattering amplitudes below inelastic thresholds from Lattice QCD calculations - presently at unphysical light-quark masses. In this work we review the formalism and develop the requisite expressions to extract phase-shifts describing meson-meson scattering in partial-waves with angular-momentum l<=6 and l=9. The implications of the underlying cubic symmetry, and strategies for extracting the phase-shifts from Lattice QCD calculations, are presented, along with a discussion of the signal-to-noise problem that afflicts the higher partial-waves.Comment: 79 pages, 41 figure

Color dipole cross section and inelastic structure function

Instead of starting from a theoretically motivated form of the color dipole cross section in the dipole picture of deep inelastic scattering, we start with a parametrization of the deep inelastic structure function for electromagnetic scattering with protons, and then extract the color dipole cross section. Using the parametrizations of $F_2(\xi=x \ {\rm or}\ W^2,Q^2)$ by Donnachie-Landshoff and Block et al., we find the dipole cross section from an approximate form of the presumed dipole cross section convoluted with the perturbative photon wave function for virtual photon splitting into a color dipole with massless quarks. The color dipole cross section determined this way reproduces the original structure function within about 10\% for $0.1$ GeV$^2\leq Q^2\leq 10$ GeV$^2$. We discuss the large and small form of the dipole cross section and compare with other parameterizations.Comment: 11 pages, 12 figure

The turbomachine blading design using S2-S1 approach

The boundary conditions corresponding to the design problem when the blades being simulated by the bound vorticity distribution are presented. The 3D flow is analyzed by the two steps S2 - S1 approach. In the first step, the number of blades is supposed to be infinite, the vortex distribution is transformed into an axisymmetric one, so that the flow field can be analyzed in a meridional plane. The thickness distribution of the blade producing the flow channel striction is taken into account by the modification of metric tensor in the continuity equation. Using the meridional stream function to define the flow field, the mass conservation is satisfied automatically. The governing equation is deduced from the relation between the azimuthal component of the vorticity and the meridional velocity. The value of the azimuthal component of the vorticity is provided by the hub to shroud equilibrium condition. This step leads to the determination of the axisymmetric stream sheets as well as the approximate camber surface of the blade. In the second step, the finite number of blades is taken into account, the inverse problem corresponding to the blade to blade flow confined in each stream sheet is analyzed. The momentum equation implies that the free vortex of the absolute velocity must be tangential to the stream sheet. The governing equation for the blade to blade flow stream function is deduced from this condition. At the beginning, the upper and the lower surfaces of the blades are created from the camber surface obtained from the first step with the assigned thickness distribution. The bound vorticity distribution and the penetrating flux conservation applied on the presumed blade surface constitute the boundary conditions of the inverse problem. The detection of this flux leads to the rectification of the geometry of the blades

Nucleon-Nucleon Scattering in a Harmonic Potential

The discrete energy-eigenvalues of two nucleons interacting with a finite-range nuclear force and confined to a harmonic potential are used to numerically reconstruct the free-space scattering phase shifts. The extracted phase shifts are compared to those obtained from the exact continuum scattering solution and agree within the uncertainties of the calculations. Our results suggest that it might be possible to determine the amplitudes for the scattering of complex systems, such as n-d, n-t or n-alpha, from the energy-eigenvalues confined to finite volumes using ab-initio bound-state techniques.Comment: 19 pages, 13 figure

Cometary implications of the internal energy distributions of the C2 and C3 radicals produced in the photolysis of the C2H and C3H2

The C2 and C3 radicals are prominent emission in the visible region of cometary spectra. Observational evidence exists that suggests these radicals are formed as granddaughter fragments in the photolysis of more stable molecules. Likely candidates for these parent molecules ar C2H2, C3H4 (allene), and CH3C2H (propyne). Recent laboratory studies were performed on all of these parent molecules and they indicate that they can indeed produce the observed cometary radicals. In the case of C2H2, the laboratory evidence suggest that C2 is formed via the following mechanisms: (1) C2H2 + photon(193 nm) yields C2H + H; and (2) C2H + photon(193 nm) yields C2 + H. Evidence is presented to show that the C2 radical produced in the second reaction occurs in a variety of electronic, vibrational, and rotational states. It is argued that this is a result of conical intersections in the potential energy curves and the density of states associated with these curves. Since this is a property of the C2H radical similar initial product state distributions are expected to occur in comets. This means that any models of the C2 emission may have to start off with rotationally excited C2 radicals in both the singlet and the triplet manifolds. When C3H4 (allene) and CH3C2H (propyne) were photolyzed, the C3 radical is formed. In the allene case, laboratory evidence shows that the C3 radical is formed via the following mechanism: (1) C3H4 + photon(193 nm) yields C3H2 + H2; and (2) C3H2 + photon(193 nm) yields C3 + H2. More C3 is formed in the case of allene than in the propyne case, even though the absorption cross section for propyne is a factor of 2 larger. This suggests that competing dissociation pathways are present during the photolysis of propyne that are not available to allene. The observed quantum state distributions of the C3 product were the same for both parent molecules, indicating that the same intermediate state is involved. These observations can be understood if the excited propyne formed in the initial absorption step isomerizes to excited allene before it dissociates to the same daughter compound. This postulate was tested by comparing RRKM calculations of the isomerization rate of excited propyne versus the decomposition rate to other products

Formulation of gradient multiaxial fatigue criteria

International audienceA formulation of gradient fatigue criteria is proposed in the context of multiaxial high-cycle fatigue (HCF) of metallic materials. The notable dependence of fatigue limit on some common factors not taken into account in classical fatigue criteria, is analyzed and modeled. Three interconnected factors, the size, stress gradient and loading effects, are here investigated. A new class of fatigue criteria extended from classical ones with stress gradient terms introduced not only in the normal stress but also in the shear stress components, is formulated. Such a formulation allows to capture gradient effects and related “size” effects, as well as to cover a wide range of loading mode, then can model both phenomena “Smaller is Stronger” and “Higher Gradient is Stronger”. Gradient versions of some classical fatigue criteria such as Crossland and Dang Van are provided as illustrations