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At least 109 records · Page 6

Higher-order symmetry plane correlations in Pb-Pb collisions at $\sqrt{s_{NN}}$ = 5.02 TeV

The correlations between event-by-event fluctuations of symmetry planes are measured in Pb-Pb collisions at a center-of-mass energy per nucleon pair $\sqrt{s_{NN}}$ = 5.02 TeV recorded by the ALICE detector at the Large Hadron Collider. This analysis is conducted using the Gaussian estimator technique, which is insensitive to biases from correlations between different flow amplitudes. The study presents, for the first time, the centrality dependence of correlations involving up to five different symmetry planes. The correlation strength varies depending on the harmonic order of the symmetry plane and the collision centrality. Comparisons with measurements from lower energies indicate no significant differences within uncertainties. Additionally, the results are compared with hydrodynamic model calculations. Although the model predictions provide a qualitative explanation of the experimental results, they overestimate the data for some observables. This is particularly true for correlators that are sensitive to the nonlinear response of the medium to initial-state anisotropies in the collision system. As these new correlators provide unique information—independent of flow amplitudes—their usage in future model developments can further constrain the properties of the strongly interacting matter created in ultrarelativistic heavy-ion collisions.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Two-photon excitation of atomic oxygen

A standard perturbation expansion in the atom-radiation-field interaction is used to calculate the two-photon excitation cross section for the 1s2 2s2 2p4 3p to 1s2 2s2 3(4S)3p 3P transition in atomic oxygen. The lowest-order summation over bound and continuum intermediate states is handled by solving the equivalent inhomogeneous differential equation. Higher-order electron-correlation effects are also examined.

Pindzola, M. S.↗

An extension of MacCormack's method for flows with higher-order equations and in different configurations

The numerical scheme for the computation of a shock discontinuity developed by MacCormack has been extended to solve a number of differential equations, including cases explicitly containing higher-order derivatives: (1) Korteweg-de Vries equation with a term of third-order derivative, (2) a system of nonlinear equations governing nonsteady one-dimensional plasma flow in cylindrical coordinate, (3) equations of solar wind. Comparisons with previous results are made, if available, to illustrate the advantages of the present method. The question of convergence of the numerical calculation is discussed.

Ying, S. J.↗

Higher-order skewness and excess coefficients of some probability distributions applicable to optical propagation phenomena

Expressions are derived for higher-order skewness and excess coefficients using central moments and cumulants up to 8th order. These coefficients are then calculated for three probability distributions: (1) Log-normal, (2) Rice-Nakagami, and (3) Gamma distributions. Curves are given to shown the variation of skewness with excess coefficients for these distributions. These curves are independent of the particular distribution parameters. This method is useful for studying fluctuating phenomena, which obey non-Gaussian statistics.

Majumdar, A. K.↗

On various treatments of potential equations at shocks

The potential equation that governs transonic inviscid flowfields is elliptic in subsonic regions and hyperbolic in supersonic regions. The transition from supersonic to subsonic flow may occur either continuously or across a surface of discontinuity known as a shock. Because of the changing type of governing equation and the presence of the surfaces of discontinuity, special treatments of the governing equations are needed at shocks to preserve mass conservation and to ensure satisfaction of the governing equation. In the so-called shock-capturing techniques, shocks are captured by smearing the discontinuity over several mesh cells in the computational domain. Most existing conservative schemes conserve mass flux throughout the flowfield, including shock boundaries; however, they also introduce zero-order errors in the approximation to the governing equation. It is shown that the zero-order errors, which do not diminish as the mesh spacing approaches zero, can cause discrepancies in the prediction of shock strength and location. These parameters are extremely sensitive features of transonic inviscid flowfield calculations. It is also shown that the zero-order errors can be avoided by developing higher-order schemes that properly model the governing equation at shocks.

Chen, L. T.↗

Higher-order derivative correlations and the alignment of small-scale structures in isotropic numerical turbulence

In a three dimensional simulation higher order derivative correlations, including skewness and flatness factors, are calculated for velocity and passive scalar fields and are compared with structures in the flow. The equations are forced to maintain steady state turbulence and collect statistics. It is found that the scalar derivative flatness increases much faster with Reynolds number than the velocity derivative flatness, and the velocity and mixed derivative skewness do not increase with Reynolds number. Separate exponents are found for the various fourth order velocity derivative correlations, with the vorticity flatness exponent the largest. Three dimensional graphics show strong alignment between the vorticity, rate of strain, and scalar-gradient fields. The vorticity is concentrated in tubes with the scalar gradient and the largest principal rate of strain aligned perpendicular to the tubes. Velocity spectra, in Kolmogorov variables, collapse to a single curve and a short minus 5/3 spectral regime is observed.

Kerr, R. A.↗

The application of a second generation low-order panel method - program 'Vsaero' - to powerplant installation studies

Results from the application of a second generation low-order panel method to a number of powerplant installations are presented. The method, which retains the advantages of ease of use and low operating cost of earlier panel methods while retaining the aerodynamic modelling rigor of higher-order methods was used to predict the flow in and around typical nacelles and aircraft for a wide range of conditions. The ability of the second generation low-order analysis to calculate internal flows without the leakage problems associated with earlier programs is demonstrated and correlation between calculated and measured surface pressures and flow behavior, including predicting streamlines and locating regions of separated flow, is presented.

Clark, D. R.↗

Group-kinetic theory of turbulence

The two phases are governed by two coupled systems of Navier-Stokes equations. The couplings are nonlinear. These equations describe the microdynamical state of turbulence, and are transformed into a master equation. By scaling, a kinetic hierarchy is generated in the form of groups, representing the spectral evolution, the diffusivity and the relaxation. The loss of memory in formulating the relaxation yields the closure. The network of sub-distributions that participates in the relaxation is simulated by a self-consistent porous medium, so that the average effect on the diffusivity is to make it approach equilibrium. The kinetic equation of turbulence is derived. The method of moments reverts it to the continuum. The equation of spectral evolution is obtained and the transport properties are calculated. In inertia turbulence, the Kolmogoroff law for weak coupling and the spectrum for the strong coupling are found. As the fluid analog, the nonlinear Schrodinger equation has a driving force in the form of emission of solitons by velocity fluctuations, and is used to describe the microdynamical state of turbulence. In order for the emission together with the modulation to participate in the transport processes, the non-homogeneous Schrodinger equation is transformed into a homogeneous master equation. By group-scaling, the master equation is decomposed into a system of transport equations, replacing the Bogoliubov system of equations of many-particle distributions. It is in the relaxation that the memory is lost when the ensemble of higher-order distributions is simulated by an effective porous medium. The closure is thus found. The kinetic equation is derived and transformed into the equation of spectral flow.

Tchen, C. M.↗

Numerical solution of the incompressible Navier-Stokes equations for steady-state and time-dependent problems

An algorithm for the solution of the incompressible Navier-Stokes equations in three-dimensional generalized curvilinear coordinates is presented. The algorithm can be used to compute both steady-state and time-dependent flow problems. The algorithm is based on the method of artificial compressibility and uses a higher-order flux-difference splitting technique for the convective terms and a second-order central difference for the viscous terms. The steady-state solution of flow through a square duct with a 90 deg bend is computed and the results are compared with experimental data. Good agreement is observed. A comparison with an analytically known exact solution is then performed to verify the time accuracy of the algorithm. Finally, the flow through an artificial heart configuration with moving boundaries is calculated and presented.

Rogers, Stuart E.↗

Postbuckling response of long thick plates loaded in compression including higher order transverse shearing effects

Buckling and postbuckling results are presented for compression-loaded simply-supported aluminum plates and composite plates with a symmetric lay-up of thin + or - 45 deg plies composed of many layers. Buckling results for aluminum plates of finite length are given for various length-to-width ratios. Asymptotes to the curves based on buckling results give N(sub xcr) for plates of infinite length. Postbuckling results for plates with transverse shearing flexibility are compared to results from classical theory for various width-to-thickness ratios. Characteristic curves indicating the average longitudinal direct stress resultant as a function of the applied displacements are calculated based on four different theories: Classical von Karman theory using the Kirchoff assumptions, first-order shear deformation theory, higher-order shear deformation theory, and 3-D flexibility theory. Present results indicate that the 3-D flexibility theory gives the lowest buckling loads. The higher-order shear deformation theory has fewer unknowns than the 3-D flexibility theory but does not take into account through-the-thickness effects. The figures presented show that small differences occur in the average longitudinal direct stress resultants from the four theories that are functions of applied end-shortening displacement.

Stein, Manuel↗

Postbuckling response of long thick plates loaded in compression including higher order transverse shearing effects

This paper presents buckling and postbuckling results for compression-loaded simply-supported aluminum plates and composite plates with a symmetric lay-up of thin +/-45-deg plies composed of many layers. Buckling results for aluminum plates of finite length are given for various length-to-width ratios. Asymptotes to the curves based on the buckling results give N(XCr) for plates of infinite length. Postbuckling results for plates with transverse shearing flexibility are compared to results from classical theory for various width-to-thickness ratios. Characteristic curves indicating the average longitudinal direct stress resultant as a function of the applied displacements are calculated based on four different theories: classical von Karman theory using the Kirchhoff assumptions, first-order shear deformation theory, higher-order shear deformation theory, and three-dimensional flexibility theory. Present results indicate that the three-dimensional flexibility theory gives the lowest buckling loads. The higher-order shear deformation theory has fewer unknowns than the three-dimensional flexibility theory but does not take into account through-the-thickness effects. The figures presented show that small differences occur in the average longitudinal direct stress resultants from the four theories that are functions of applied end-shortening displacement.

Stein, Manuel↗

An approximate viscous shock layer approach to calculating hypersonic flows about blunt-nosed bodies

An approximate axisymmetric method has been developed which can reliably calculate fully viscous hypersonic flows over blunt-nosed bodies. By substituting Maslen's second order pressure expression for the normal momentum equation, a simplified form of the viscous shock layer (VSL) equations is obtained. This approach can solve both the subsonic and supersonic regions of the shock layer without a starting solution for the shock shape. Since the method is fully viscous, the problems associated with coupling a boundary-layer solution with an inviscid-layer solution are avoided. This procedure is significantly faster than the parabolized Navier-Stokes (PNS) or VSL solvers and would be useful in a preliminary design environment. Problems associated with a previously developed approximate VSL technique are addressed. Surface heat transfer and pressure predictions are comparable to both VSL results and experimental data. The present technique generates its own shock shape as part of its solution, and therefore could be used to provide more accurate initial shock shapes for higher-order procedures which require starting solutions.

Cheatwood, F. MCN.↗

An approximate viscous shock layer technique for calculating nonequilibrium hypersonic flows about blunt-nosed bodies

An approximate axisymmetric method has been developed which can reliably calculate nonequilibrium fully viscous hypersonic flows over blunt-nosed bodies. By substituting Maslen's second-order pressure expression for the normal momentum equation, a simplified form of the viscous shock layer (VSL) equations is obtained. This approach can solve both the subsonic and supersonic regions of the shock layer without a starting solution for the shock shape. This procedure is significantly faster than the parabolized Navier-Stokes and VSL solvers and would be useful in a preliminary design environment. Solutions have been generated for air flows over several analytic body shapes. Surface heat transfer and pressure predictions are comparable to VSL results. Computed heating rates are in good agreement with experimental data. The present technique generates its own shock shape as part of its solution, and therefore could be used to provide more accurate initial shock shapes for higher-order procedures which require starting solutions.

Cheatwood, F. M.↗

Oligomeric baroeffect and gas aggregation states

The baroeffect is analyzed to include a gas that aggregates into higher-order polymers or oligomers. The resulting pressure change is found to vary independently of the molecular weight of the gas components and to depend only on the aggregation or oligomeric order of the gas. With increasing aggregation, diffusive slip velocities are found to increase. The calculations are extended to include general counterdiffusion of two distinct aggregation states (k-, j-mer) for the gas, and the pressure change is derived as a function that is independent of both molecular weight and the absolute aggregation. The only parameter that determines the baroeffect is the ratio of aggregated states, beta = k/j. For gases that reversibly aggregate, possible oscillatory behavior and complex dynamics for pressure are discussed. Gas aggregation may play a role for low-temperature crystal-growth conditions in which vapor concentrations of one (or more) species are high.

Noever, David A.↗

On the use of residue theory for treating the subsonic flow of a compressible fluid

A new mathematical technique, due to Milne-Thomson, is used to obtain an improved form of the method of Poggi for calculating the effect of compressibility on the subsonic flow past an obstacle. By means of this new method, the difficult surface integrals of the original Poggi method can be replaced by line integrals. These line integrals are then solved by the use of residue theory. In this way an equation is obtained giving the second-order effect of compressibility on the velocity of the fluid. The method is practicable for obtaining the higher-order effects of compressibility on the velocity field. As an illustration of the general result, the flow past an elliptic cylinder is discussed.

Kaplan, Carl↗

Alignment of dust grains in ionized regions

The rate at which charged dust grains in a plasma are torqued by passing ions and electrons is calculated. When photo-emission of electrons is not important, attraction of ions by the grain monopole potential increases the rate at which the grains' spins are dealigned by nearly an order of magnitude. Consequently, the energy density of the magnetic field required to align grains in an H II region may be increased by about an order of magnitude. In contrast, electric dipole and quadrupole moments are unlikely to produce large dealignment rates for grains of modest length-to-width ratio. Nonetheless, for positively charged grains these higher-order moments likely prevent monopole repulsion of ions from reducing the dealignment rate far below that for neutral grains. The presence of positive grain charge therefore does not greatly facilitate grain alignment in an H II region.

Anderson, Nels↗

A comparison of Lorentz, planetary gravitational, and satellite gravitational resonances

We consider a charged dust grain whose orbital motion is dominated by a planet's point-source gravity, but perturbed by higher-order terms in the planet's gravity field as well as by the Lorentz force arising from an asymmetric planetary magnetic field. Perturbations to Keplerian orbits due to a nonspherical gravity field are expressed in the traditional way: in terms of a disturbing function which can be expanded in a series of spherical harmonics (W. M. Kaula, 1966). In order to calculate the electromagnetic perturbation, we first write the Lorentz force in terms of the orbital elements and then substitute it into Gauss' perturbation equations. We use our result to derive strengths of Lorentz resonances and elucidate their properties. In particular, we compare Lorentz resonances to two types of gravitational resonances: those arising from periodic tugs of a satellite and those due to the attraction of an arbitrarily shaped planet. We find that Lorentz resonances share numerous properties with their gravitational counterparts and show, using simple physical arguments, that several of these patterns are fundamental, applying not only to our expansions, but to all quantities expressed in terms of orbital elements. Some of these patterns have been previously called 'd'Alembert rules' for satellite resonances. Other similarities arise because, to first-order in the perturbing force, the three problems share an integral of the motion. Yet there are also differences; for example, first-order inclination resonances exist for perturbations arising from planetary gravity and from the Lorentz force, but not for those due to an orbiting satellite. Finally, we provide a heuristic treatment of a particle's orbital evolution under the influence of drag and resonant forces. Particles brought into mean-motion resonances experience either trapping or resonant 'jumps,' depending on the direction from which the resonance is approached. We show that this behavior does not depend on the details of the perturbing force but rather is fundamental to all mean-motion resonances.

Hamilton, Douglas P.↗