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At least 1,009 records · Page 56

Magnetohydrodynamic Riemann problem and the structure of the magnetic reconnection layer

We present a complete solution for a set of magnetohydrodynamic (MHD) Riemann problems in which the upstream and downstream states have the same total pressure, and in which the normal component of the magnetic field is very small. These solutions are pertinent to subfast flows in the earth's magnetic tail and near the magnetopause. In a coplanar situation a family of solutions exists that depend on two parameters as well as on dissapation mechanisms. In the parallel case the transverse magnetic field either does not change direction or changes the direction twice by involving two intermediate shocks. In the antiparallel case an intermediate shock is always required, except when the solution consists of two switch-off shocks. In a noncoplanar case the solution is not self-similar as a function of x/t, but continues to evolve. At early times the evolution is similar to the coplanar case. In general two time-dependent intermediate shocks are required to rotate the magnetic fields. The velocity shear has a strong effect on the Riemann solution. In some cases no Riemann solution can exist because of the cavitation caused by the slow refraction waves. The calculated magnetopause structure resembles the observed structure for northward interplanetary magnetic field (IMF). However, for southward IMF, the MHD result shows the existence of a depletion layer, which is not supported by observations. We also show that on the magnetosheath side, the Walen relation, which is exact for a rotational discontinuity, can also be well satisfied by a slow shock, an intermediate shock, or the head of a slow rarefaction wave.

Wu, C. C.↗

A low-rank power iteration scheme for neutron transport criticality problems

Computing effective eigenvalues for neutron transport often requires a fine numerical resolution. Here, the main challenge of such computations is the high memory effort of classical solvers, which limits the accuracy of chosen discretizations. In this work, we derive a method for the computation of effective eigenvalues when the underlying solution has a low-rank structure. This is accomplished by utilizing dynamical low-rank approximation (DLRA), which is an efficient strategy to derive time evolution equations for low-rank solution representations. The main idea is to interpret the iterates of the classical inverse power iteration as pseudo-time steps and apply the DLRA concepts in this framework. In our numerical experiment, we demonstrate that our method significantly reduces memory requirements while achieving the desired accuracy. Analytic investigations show that the proposed iteration scheme inherits the convergence speed of the inverse power iteration, at least for a simplified setting.

97 MATHEMATICS AND COMPUTING↗

Resurgent trans-series for generalized Hastings–McLeod solutions

Here, we show that the physical Hastings–McLeod solution of the integrable Painlevé II equation generalizes in a natural way to a class of non-integrable equations, in a way that preserves many of the significant qualitative properties. The Hastings–McLeod solution of Painlevé II is an important and universal example of resurgent relations between perturbative and non-perturbative physics. We derive the trans-series structure of the generalized Hastings–McLeod solutions, demonstrating that integrability is not essential for the resurgent asymptotic properties of the solutions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

An adaptive implicit/explicit finite element scheme for compressible viscous high speed flow

An adaptive implicit/explicit finite element procedure for the solution of three-dimensional problems of steady compressible viscous high-speed flows is presented. In the vicinity of solid walls, a grid-exhibiting structure in the normal direction is employed, while away from this region the grid is totally unstructured. The implicit form of the algorithm is used near solid walls, with the grid structure being utilized in an equation solution approach based upon line relaxation. The explicit form of the algorithm is used elsewhere. Grid adaptation is achieved by means of adaptive remeshing. To illustrate the performance of the proposed method, solutions are obtained for the problems of shock-boundary layer interaction and shock-shock interaction on a swept cylindrical leading edge. Comparisons are made with experimental observations.

Hassan, O.↗

Experimental and numerical studies of seismic fluid-structure interaction in a base-supported cylindrical vessel

Seismic design and qualification of advanced reactors will rely heavily on the use of verified and validated numerical models capable of capturing the interaction of the vessel, its contained fluid, and the internal equipment: fluid-structure interaction (FSI) analysis. Analytical solutions can be used for preliminary sizing and design of such vessels but their application is limited to simple geometries and boundary conditions, and small amplitude, translational (and rotational) inputs. To validate numerical models for seismic FSI analysis in finite element codes, a comprehensive set of experiments was performed on a liquid-filled cylindrical vessel, using a 6 degree-of-freedom earthquake simulator. Results in terms of sloshing frequency, damping ratio in sloshing modes, and hydrodynamic responses (wave height, hydrodynamic pressure, base shear, and base moment) for multi-directional earthquake simulator inputs are reported and compared with analytical solutions for liquid-filled vessels. The impact of seismic (base) isolation on hydrodynamic responses was studied using earthquake simulator inputs generated using a virtual isolation system. Data from the experiments are used to validate a numerical model of the fluid-filled vessel using the Arbitrary Lagrangian Eulerian (ALE) solver in the commercial finite element program LS-DYNA. Validation studies are presented for multi-directional seismic inputs, including rocking motions. Lagrangian modeling approaches using an elastic material formulation for the fluid are also investigated and their limitations and possible applications are identified. Here, the results are broadly applicable to the seismic response of base supported, liquid-filled vessels.

58 GEOSCIENCES↗

The vertical filamentary structures of quiescent prominences

The thin vertical filaments making up the quiescent prominence plasma, as revealed by fine spatial resolution H-alpha photographs, are characterized by a magnetostatic theory in which a horizontal row of long vertical filaments whose weights are supported by bowed magnetic field lines is described by a class of exact equilibrium solutions. The Kippenhahn-Schlueter (1957) solution for a long sheet without filamentary structures is a member of this class of solutions. In illustrating the role of the magnetic field in supporting and thermally shielding the filament plasma, it is found that the filament can have a sharp transition perpendicular to the local field, while the transition in the direction of the local field is diffuse. A consequence of the filamentary structure is that its support by the Lorentz force requires the electric current to have a component along the magnetic field.

Low, B. C.↗

Microwave Scattering Model for Grass Blade Structures

In this paper, the electromagnetic scattering solution for a grass blade with complex cross-section geometry is considered. It is assumed that the blade cross section is electrically small, but its length is large compared to the incident wavelength. In a recent study it has been shown that the scattering solution for such problems, in the form of a polarizability tensor, can be obtained using the low-frequency approximation in conjunction with the method of moments. In addition, the study shows that the relationship between the polarizability tensor of a dielectric cylinder and its dielectric constant can be approximated by a simple algebraic expression. The results of this study are used to show that this algebraic approximation is valid also for cylinders with cross sections the shape of grass blades, providing that proper values am selected for each of three constants appearing in the expression. These constants are dependent on cylinder shape, and if the relationship between the constants and the three parameters describing a grass blade shape can be determined, an algebraic approximation relating polarizability tensor to blade shape, as well as dielectric constant, can be formed. Since the elements of the polarizability tensor are dependent on only these parameters, this algebraic approximation can replace the cumbersome method of moments model. A conjugate gradient method is then implemented to correctly determine the three constants of the algebraic approximation for each blade shape. A third-order polynomial fit to the data is then determined for each constant, thus providing a complete analytic replacement to the numerical (moment method) scattering model. Comparisons of this approximation to the numerical model show an average error of less than 3%.

Stiles, James M.↗

Recent advances in numerical analysis of structural eigenvalue problems

A wide range of eigenvalue problems encountered in practical structural engineering analyses is defined, in which the structures are assumed to be discretized by any suitable technique such as the finite-element method. A review of the usual numerical procedures for the solution of such eigenvalue problems is presented and is followed by an extensive account of recently developed eigenproblem solution procedures. Particular emphasis is placed on the new numerical algorithms and associated computer programs based on the Sturm sequence method. Eigenvalue algorithms developed for efficient solution of natural frequency and buckling problems of structures are presented, as well as some eigenvalue procedures formulated in connection with the solution of quadratic matrix equations associated with free vibration analysis of structures. A new algorithm is described for natural frequency analysis of damped structural systems.

Gupta, K. K.↗

Steady-State Solution of a Flexible Wing

A fluid-structure interaction code, ENSAERO, has been used to compute the aerodynamic loads on a swept-tapered wing. The code has the capability of using Euler or Navier-Stokes equations. Both options have been used and compared in the present paper. In the calculation of the steady-state solution, we are interested in knowing how the flexibility of the wing influences the lift coefficients. If the results of a flexible wing are not affected by the flexibility of the wing significantly, one could consider the wing to be rigid and reduce the problem from fluid-structure interaction to a fluid problem.

Karkehabadi, Reza↗

Evaluation of average leaf inclination angle quantified by indirect optical instruments in crop fields

Average leaf inclination angle ($\overline{θ}$ L ) is an important canopy structure variable that influences light regime, photosynthesis, and evapotranspiration of plants. $\overline{θ}$ L can be measured through direct methods (e.g., protractor), which are labor-intensive and time-consuming, or through indirect optical instruments, which are more efficient than the direct methods. However, uncertainties of different indirect optical instruments for quantifying $\overline{θ}$ L remain largely unquantified. In this study, we evaluated and compared the performances of three major indirect optical instruments: (1) LAI-2200, (2) 30°-tilted camera, and (3) digital hemispherical photography (DHP), in different crop fields over a growing season, benchmarked with direct measurements. LAI-2200 and 30°-tilted camera showed higher agreement with direct $\overline{θ}$ measurements (R 2 = 0.54, RMSE = 7.37°; R 2 = 0.58, RMSE = 8.08°) than DHP (R 2 = 0.14, RMSE = 13.96°). Different performances of indirect optical instruments could be attributed to the accuracy of gap fraction measurement and the performance of the $\overline{θ}$ L quantification algorithms. When using the LAI-2200 algorithm, larger gap fraction gradients over view zenith angles led to larger $\overline{θ}$ L values, and smaller gap fraction gradients led to smaller $\overline{θ}$ L values. Such error propagation was larger in sparse canopy than in dense canopy. The Wilson G function of the LAI-2200 algorithm performed better in estimating $\overline{θ}$ L than the G function based on the ellipsoidal LAD function used by the CAN_EYE algorithm. We also proposed a modification of the LAI-2200 algorithm, which further improved the performance of LAI-2200 and 30°-tilted cameras in estimating $\overline{θ}$ L . We envision that the low-cost 30°-tilted cameras provide a promising sensor solution to continuously monitor canopy structure for various ecosystems.

30°-tilted camera↗

Tuning Organic Semiconductor Packing and Morphology through Non-equilibrium Solution Processing (Final Report)

Organic semiconductors (OSCs) are a promising candidate to produce low-cost, large area, and flexible electronics. There has previously been successful development of organic field effect transistors (OFETs), photovoltaics (OPV), and bioelectronics using OSCs. Solution processing of these materials allows for the fabrication of large-area devices in the kinetic crystallization regime. The charge transport capabilities have been shown to depend on the morphology and molecular packing of the OSC within thin films. Our hypothesis is that solution processing conditions may significantly impact OSC morphology and as a result the charge transport. Therefore, this work has focused on obtaining a fundamental understanding of the morphology and molecular packing of OSCs for optimal device performance. Through our work, we have gained a better understanding of how these structural conditions were influenced by the solution processing conditions. Our studies have led to a more systematic understanding of the various parameters that impact OSC morphology. Solution processing leads to non-equilibrium films, thus allowing for the formation of diverse morphologies that are inaccessible by other fabrication methods. Previously, our group has focused on tuning the morphology of small-molecular OSCs [53, 55-57]. However, little work had been devoted to polymer OSCs. There was a lack of detailed studies characterizing the solution-state of polymer OSCs in terms of their conformation, degree of entanglement, polymer aggregation, and chain relaxation dynamics. The solution state properties are also likely to be influenced by the rigidity and molecular weight of the polymer OSCs investigated. Thus, we have focused our attention on gaining a better insight of polymer OSC films and solution processing methods. Through this proposal, our approach is to investigate the correlation between solution-state properties and the morphology of the resulting polymer OSC films. We worked three specific aims: investigate the effects of 1) polymer OSC solution-state properties on final film morphology; 2) molecular additives on the solution-state and final film properties; 3) controlled pre-aggregation in the solution-state in the final film morphology. More rigid and planar polymer backbones should promote interchain charge transport and more efficient interchain hopping between polymer chains. Through tailoring the polymer backbone, polymer sidechains, and molecular weight, we expected the altered solution-state properties to affect the final film morphology. In addition, reducing the entanglements and promoting chain alignment will likely prevent charge carrier trapping through conformation disorders. We thus studied different mechanisms, such as molecular additives, to reduce entanglements in solution. Devices fabricated from these solutions were expected to have improved charge transport abilities. In addition to tailoring the solution-state characteristics of the polymer OSCs, we investigated the effect of solution processing methods on the molecular packing and morphology of polymer OSC films. Two main solution processing techniques, e.g., spin-coating and solution shearing, were employed to fabricate OFETs. Spin coating was employed to prepare OSC films, which produce isotropic films. This technique creates several parameters to tune such as spin coating speed, acceleration, and time. Additionally, our research group developed the solution shearing method, which consists of the solution initially sandwiched between two plates. By sliding the top plate, the solution front is exposed and drying begins. This technique allows for the creation of aligned large crystalline domains. Solution shearing consists of different processing parameters which can affect the final morphology, such as shearing speed, substrate temperature and temperature gradient, distance between both plates, and the tilt angle of the top plate. Due to the complexity of the polymer systems investigated, numerous techniques were employed to characterize the polymer OSC solution state and films. All the materials were characterized using the DOE supported synchrotron X-ray scattering facilities at the Stanford Synchrotron Radiation Lightsource (SSRL). Using grazing incidence X-ray scattering (GIXS) and Near Edge X-ray Absorption Fine Structure (NEXAFS) techniques, the crystalline structure and molecular orientations of the thin films were measured. Optical absorption (UV-Vis) spectroscopy was employed to determine the aggregation state in solution and films of the polymer systems. Polarized UV-Vis also allowed for the determination of the relative degree of polymer chain alignment for solution sheared films. Additionally, various other techniques were used to investigate other properties within the film, such as atomic force microscopy (AFM) and solution rheology. Finally, the device performance is quantified through the fabrication and characterization of OFETs, which will highlight the effects of morphology on charge transport.

36 MATERIALS SCIENCE↗

Thermodynamic characterization of synthetic lead-arsenate apatites with different halogen substitutions

Abstract Thermodynamic parameters have been measured for synthetic analogs of the mimetite-group minerals Pb5(AsO4)3X (X = OH, Cl, Br, I) belonging to the apatite supergroup. Phases precipitated from aqueous solutions under ambient conditions with well characterized structures and compositions were studied. For each phase, dissolution enthalpy was experimentally determined by oxide melt drop solution calorimetry in a molten solvent of sodium molybdate (3Na2O·4MoO3) at 976 K. The enthalpy of formation from the elements ΔHf,elo was calculated using thermochemical cycles and was −3030.6 ± 11.5, −3026.6 ± 15.8, −2967.6 ± 25.0, and −2993.1 ± 12.2 kJ/mol for Pb5.00(AsO4)3.00OH0.86(CO3)0.07, Pb5.00(AsO4)3.00Cl0.80(CO3)0.10, Pb5.00(AsO4)3.00Br0.80(CO3)0.10, and Pb5.00(AsO4)3.00I0.45OH0.35(CO3)0.10, respectively. These ΔHf,elo values exhibit typical trends for apatites: they increased (were less negative) with the increasing molar mass and ionic radius of X and decreased with the electronegativity and ionization energy of X. The compilation and comparison of data for Ca-, Pb-, P-, and As-apatites revealed correlations indicating that thermodynamic enthalpic stability is largely influenced by chemical factors (e.g., differences in electronegativities of the elements, ionization energy, or ionic characteristics of the bonds) and to a lesser extent by physical and geometric parameters in the crystal structure related to the mass and size of the X anion. Using the correlations, it was possible to estimate the value of hitherto unknown ΔHf,elo for Pb5(AsO4)3F, −3144.3 ± 66.5 kJ/mol. The observed relationships apply to the entire apatite supergroup and can be used to predict the values of ΔHf,elo for phases that have not been studied experimentally. The new data on environmentally significant phases will contribute to the modeling of mineral-water interactions, particularly for potential use in the remediation of soils and wastes contaminated with Pb and As and in the immobilization of radioactive waste containing I-129.

Geochemistry & Geophysics↗

A 3-D hydroelastic analysis in NASTRAN with general fluid and structure geometry

The implementation of a general three dimensional hydroelastic mode analysis capability in NASTRAN is presented. Finite elements with polyhedral shapes define the fluid; existing NASTRAN plate elements define the fluid/structure interface. Efficient solution methods were implemented to allow a separate structural matrix reduction and to allow connection of the fluid mass directly to a small set of grid points or modal coordinates representing the structure. Test case results for the various solution options are presented.

Herting, D. N.↗

The simulation of 2D compressible viscous high speed flow by the finite element method

Am implicit/explicit procedure for the solution of problems of two-dimensional steady compressible viscous high-speed flows is presented. In the vicinity of solid walls, a grid which need only exhibit structure in the normal direction is employed while, away from this region, the grid is totally unstructured. The implicit form of the algorithm is used near solid walls, with the grid structure being utilized in an equation solution approach, based upon line relaxation. The explicit form of the algorithm is used elsewhere. Grid adaptation is achieved by means of adaptive remeshing. To illustrate the performance of the proposed method, problems of shock-boundary layer interaction and flow over a simulated forebody at high Mach number are included.

Hassan, O.↗

On the Minimum Induced Drag of Wings

Of all the types of drag, induced drag is associated with the creation and generation of lift over wings. Induced drag is directly driven by the span load that the aircraft is flying at. The tools by which to calculate and predict induced drag we use were created by Ludwig Prandtl in 1903. Within a decade after Prandtl created a tool for calculating induced drag, Prandtl and his students had optimized the problem to solve the minimum induced drag for a wing of a given span, formalized and written about in 1920. This solution is quoted in textbooks extensively today. Prandtl did not stop with this first solution, and came to a dramatically different solution in 1932. Subsequent development of this 1932 solution solves several aeronautics design difficulties simultaneously, including maximum performance, minimum structure, minimum drag loss due to control input, and solution to adverse yaw without a vertical tail. This presentation lists that solution by Prandtl, and the refinements by Horten, Jones, Kline, Viswanathan, and Whitcomb

Bowers, Albion H.↗

On the Minimum Induced Drag of Wings

Of all the types of drag, induced drag is associated with the creation and generation of lift over wings. Induced drag is directly driven by the span load that the aircraft is flying at. The tools by which to calculate and predict induced drag we use were created by Ludwig Prandtl in 1903. Within a decade after Prandtl created a tool for calculating induced drag, Prandtl and his students had optimized the problem to solve the minimum induced drag for a wing of a given span, formalized and written about in 1920. This solution is quoted in textbooks extensively today. Prandtl did not stop with this first solution, and came to a dramatically different solution in 1932. Subsequent development of this 1932 solution solves several aeronautics design difficulties simultaneously, including maximum performance, minimum structure, minimum drag loss due to control input, and solution to adverse yaw without a vertical tail. This presentation lists that solution by Prandtl, and the refinements by Horten, Jones, Kline, Viswanathan, and Whitcomb.

Bowers, Albion H.↗

On the Minimum Induced Drag of Wings -or- Thinking Outside the Box

Of all the types of drag, induced drag is associated with the creation and generation of lift over wings. Induced drag is directly driven by the span load that the aircraft is flying at. The tools by which to calculate and predict induced drag we use were created by Ludwig Prandtl in 1903. Within a decade after Prandtl created a tool for calculating induced drag, Prandtl and his students had optimized the problem to solve the minimum induced drag for a wing of a given span, formalized and written about in 1920. This solution is quoted in textbooks extensively today. Prandtl did not stop with this first solution, and came to a dramatically different solution in 1932. Subsequent development of this 1932 solution solves several aeronautics design difficulties simultaneously, including maximum performance, minimum structure, minimum drag loss due to control input, and solution to adverse yaw without a vertical tail. This presentation lists that solution by Prandtl, and the refinements by Horten, Jones, Kline, Viswanathan, and Whitcomb.

Bowers, Albion H.↗

Deconvoluting the impact of current collector structure and electrolyte selection on Coulombic efficiency of lithium metal anodes

Lithium metal batteries are regarded as a promising avenue for significantly boosting the gravimetric energy density of batteries, particularly for electric vehicles. However, the instability of the lithium metal anode continues to hinder performance. While 3D structured current collectors for lithium metal anodes have been frequently proposed as a solution, few studies explore the impact of these structures when combined with various electrolytes and the inclusion of a lithium reservoir within the structure. This study pairs four commercially available copper current collectors with four different electrolytes to assess how these factors influence cycling performance with a 4 mAh/cm2 lithium reservoir. Coulombic efficiency (CE) measurements revealed no statistically significant difference in CE across different current collectors within the same electrolyte. However, significant variations were noted when the current collector remained intact, and the electrolyte was changed. Although polarization, electrochemical impedance, and lithium morphology varied between structures and electrolytes, no consistent patterns emerged to suggest superior performance by any specific current collector structure. Therefore, the choice of structure appears inconsequential when a lithium reservoir is present, and efforts should focus on selecting and designing the electrolyte.

White, Julia↗