Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “INTERFACES”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 145 records · Page 8

Concomitant appearance of conductivity and superconductivity in (111) LaAlO 3 /SrTiO 3 interface with metal capping

In epitaxial polar-oxide interfaces, conductivity sets in beyond a finite number of monolayers (ML). This threshold for conductivity is explained by accumulating sufficient electric potential to initiate charge transfer to the interface. Here we experimentally and theoretically study the LaAlO 3 /SrTiO 3 (111) interface where a critical thickness $t_c$ of nine epitaxial LaAlO 3 ML is required to turn the interface from insulating to conducting and even superconducting. In this work, we show that $t_c$ decreases to 3 ML when depositing a cobalt overlayer (capping) and 6 ML for platinum capping. The latter result contrasts with the (001) interface, where platinum capping increases $t_c$ beyond the bare interface. Our density functional theory calculations with a Hubbard U term confirm the observed threshold for conductivity for the bare and the metal-capped interfaces. Interestingly, conductivity appears concomitantly with superconductivity for metal/LaAlO 3 /SrTiO 3 (111) interfaces, in contrast with the metal/LaAlO 3 /SrTiO 3 (001) interfaces where conductivity appears without superconductivity. We attribute this dissimilarity to the different orbital polarization of eg for the (111) versus dxy for the (001) interface.

36 MATERIALS SCIENCE↗

A Comparison of Interface Growth Models Applied to Rayleigh–Taylor and Richtmyer–Meshkov Instabilities

Sophisticated numerical models that contain fluid interfaces rely upon interface evolution models to approximate the transition to turbulence near interfaces, in the presence of Rayleigh–Taylor (RTI) or Richtmyer–Meshkov (RMI) instability. Semi-analytical models have been developed in recent decades to predict the interface growth from an initial state into the nonlinear regime. Two of these models are considered in this study. They are the Goncharov and the z-models. Both of these interface models have strengths and weaknesses, which are examined here. Both of them have been implemented in the xRAGE compressible flow solver, which models fluid interfaces. The flow solver provides the fluids acceleration as a body force to the interface model. The purpose of such interface model is to evolve the early times of interface position as a subgrid model within a compressible flow simulation in order to then initialize a turbulence model. In this work, the interface models are assessed and compared for their evolution of RTI and RMI. The z-model performed better than the Goncharov model for all cases that were explored.

42 ENGINEERING↗

MPI-IO: A Parallel File I/O Interface for MPI Version 0.3

Thanks to MPI [9], writing portable message passing parallel programs is almost a reality. One of the remaining problems is file I/0. Although parallel file systems support similar interfaces, the lack of a standard makes developing a truly portable program impossible. Further, the closest thing to a standard, the UNIX file interface, is ill-suited to parallel computing. Working together, IBM Research and NASA Ames have drafted MPI-I0, a proposal to address the portable parallel I/0 problem. In a nutshell, this proposal is based on the idea that I/0 can be modeled as message passing: writing to a file is like sending a message, and reading from a file is like receiving a message. MPI-IO intends to leverage the relatively wide acceptance of the MPI interface in order to create a similar I/0 interface. The above approach can be materialized in different ways. The current proposal represents the result of extensive discussions (and arguments), but is by no means finished. Many changes can be expected as additional participants join the effort to define an interface for portable I/0. This document is organized as follows. The remainder of this section includes a discussion of some issues that have shaped the style of the interface. Section 2 presents an overview of MPI-IO as it is currently defined. It specifies what the interface currently supports and states what would need to be added to the current proposal to make the interface more complete and robust. The next seven sections contain the interface definition itself. Section 3 presents definitions and conventions. Section 4 contains functions for file control, most notably open. Section 5 includes functions for independent I/O, both blocking and nonblocking. Section 6 includes functions for collective I/O, both blocking and nonblocking. Section 7 presents functions to support system-maintained file pointers, and shared file pointers. Section 8 presents constructors that can be used to define useful filetypes (the role of filetypes is explained in Section 2 below). Section 9 presents how the error handling mechanism of MPI is supported by the MPI-IO interface. All this is followed by a set of appendices, which contain information about issues that have not been totally resolved yet, and about design considerations. The reader can find there the motivation behind some of our design choices. More information on this would definitely be welcome and will be included in a further release of this document. The first appendix contains a description of MPI-I0's 'hints' structure which is used when opening a file. Appendix B is a discussion of various issues in the support for file pointers. Appendix C explains what we mean in talking about atomic access. Appendix D provides detailed examples of filetype constructors, and Appendix E contains a collection of arguments for and against various design decisions.

Corbett, Peter↗

A 2-D Interface Element for Coupled Analysis of Independently Modeled 3-D Finite Element Subdomains

Over the past few years, the development of the interface technology has provided an analysis framework for embedding detailed finite element models within finite element models which are less refined. This development has enabled the use of cascading substructure domains without the constraint of coincident nodes along substructure boundaries. The approach used for the interface element is based on an alternate variational principle often used in deriving hybrid finite elements. The resulting system of equations exhibits a high degree of sparsity but gives rise to a non-positive definite system which causes difficulties with many of the equation solvers in general-purpose finite element codes. Hence the global system of equations is generally solved using, a decomposition procedure with pivoting. The research reported to-date for the interface element includes the one-dimensional line interface element and two-dimensional surface interface element. Several large-scale simulations, including geometrically nonlinear problems, have been reported using the one-dimensional interface element technology; however, only limited applications are available for the surface interface element. In the applications reported to-date, the geometry of the interfaced domains exactly match each other even though the spatial discretization within each domain may be different. As such, the spatial modeling of each domain, the interface elements and the assembled system is still laborious. The present research is focused on developing a rapid modeling procedure based on a parametric interface representation of independently defined subdomains which are also independently discretized.

Kandil, Osama A.↗

The Turbulent/Non-Turbulent Interface Bounding a Far-Wake

The velocity fields of a turbulent wake behind a flat plate obtained from the direct numerical simulations of Moser et al. are used to study the structure of the flow in the intermittent zone where there are, alternately, regions of fully turbulent flow and non-turbulent velocity fluctuations either side of a thin randomly moving interface. Comparisons are made with a wake that is 'forced' by amplifying initial velocity fluctuations. There is also a random temperature field T in the flow; T varies between constant values of 0.0 and 1.0 on the sides of the wake. The value of the Reynolds number based on the centreplane mean velocity defect and halfwidth b of the wake is Re approx. = 2000. It is found that the thickness of the continuous interface is about equal to 0.07b, whereas the amplitude of fluctuations of the instantaneous interface displacement y(sub I)(t) is an order of magnitude larger, being about 0.5b. This explains why the mean statistics of vorticity in the intermittent zone can be calculated in terms of the probability distribution of y(sub I) and the instantaneous discontinuity in vorticity across the interface. When plotted as functions of y - y(sub I), the conditional mean velocity (U) and temperature (T) profiles show sharp jumps Delta(U) and Delta(T) at the interface adjacent to a thick zone where (U) and (T) vary much more slowly. Statistics for the vorticity and velocity variances, available in such detail only from DNS data, show how streamwise and spanwise components of vorticity are generated by vortex stretching in the bulges of the interface. Flow fields around the interface, analyzed in terms of the local streamline pattern, confirm previous results that the advancement of the vortical interface into the irrotational flow is driven by large-scale eddy motion. It is argued that because this is an inviscid mechanism the entrainment process is not sensitive to the value of Re, and that small-scale nibbling only plays a subsidiary role. While mean Reynolds stresses decrease gradually in the intermittent zone, conditional stresses are found to decrease sharply towards zero at the interface. Using one-point turbulence models applied to either unconditional or conditional statistics for the turbulent region and then averaged, the entrainment rate E(sub b) would, if calculated exactly, be zero. But if computed with standard computational methods, E(sub b) would be non-zero because of numerical diffusion. It is concluded that the current practice in statistical models of approximating entrainment by a diffusion process is computationally arbitrary and physically incorrect. An analysis shows how E(sub b) is related to Delta(U) and the jump in shear stress at the interface, and correspondingly to Delta(T) and the heat flux.

Bisset, David K.↗

Viewpoint 9--molecular structure of aqueous interfaces

In this review we summarize recent progress in our understanding of the structure of aqueous interfaces emerging from molecular level computer simulations. It is emphasized that the presence of the interface induces specific structural effects which, in turn, influence a wide variety of phenomena occurring near the phase boundaries. At the liquid-vapor interface, the most probable orientations of a water molecule is such that its dipole moment lies parallel to the interface, one O-H bond points toward the vapor and the other O-H bond is directed toward the liquid. The orientational distributions are broad and slightly asymmetric, resulting in an excess dipole moment pointing toward the liquid. These structural preferences persist at interfaces between water and nonpolar liquids, indicating that the interactions between the two liquids in contact are weak. It was found that liquid-liquid interfaces are locally sharp but broadened by capillary waves. One consequence of anisotropic orientations of interfacial water molecules is asymmetric interactions, with respect to the sign of the charge, of ions with the water surface. It was found that even very close to the surface ions retain their hydration shells. New features of aqueous interfaces have been revealed in studies of water-membrane and water-monolayer systems. In particular, water molecules are strongly oriented by the polar head groups of the amphiphilic phase, and they penetrate the hydrophilic head-group region, but not the hydrophobic core. At infinite dilution near interfaces, amphiphilic molecules exhibit behavior different from that in the gas phase or in bulk water. This result sheds new light on the nature of hydrophobic effect in the interfacial regions. The presence of interfaces was also shown to affect both equilibrium and dynamic components of rates of chemical reactions. Applications of continuum models to interfacial problems have been, so far, unsuccessful. This, again, underscores the importance of molecular-level information about interfaces.

Review, Tutorial↗

A Moving Discontinuous Galerkin Method with Interface Condition Enforcement for Reacting Hypersonic Flows

The necessity of enforcing conservation in computational elements or cells (element conservation) for discontinuous solutions is well understood and respected for solving conservation laws in computational fluid dynamics (CFD). In contrast, interface conservation, where the conservation across cell interfaces is enforced, is long ignored, and yet is also ruled and required by the underlying physics just like element conservation. Violation of the interface conservation across discontinuities is the root cause why an exact discontinuous solution can never be achieved in shock capturing methods. The interface conservation is examined and explored in this talk. Moving discontinuous Galerkin (MDG) finite element method with interface conservation enforcement (MDG-ICE) [1],[2] are then presented for solving compressible flow problems with discontinuities based on the observation that the interface conservation can only be satisfied, only when mesh interfaces are aligned with discontinuities. In the MDG-ICE formulation, both conservative quantities and grid geometry are considered as independent variables. A space-time DG formulation is used to solve the multi-material compressible Euler equations in the standard discontinuous solution space and the discrete grid geometry is solved using a variational formulation in a continuous space. A self-adaptive Levenberg-Marquardt method is utilized to solve the resulting over-determined system of nonlinear equations arising from the MDG-ICE formulation. A number of numerical experiments for a variety of flow problems are conducted to assess the accuracy and performance of the MDG-ICE method. Numerical results obtained indicate that the MDG-ICE method is able to deliver the designed order of both h- and p-convergence even for discontinuous solutions, and detect all types of interfaces, via interface condition enforcement and satisfy, via grid movement, the compressible Euler equations and the associated interface condition.

Discontinuous Galekin↗

A sharp interface Lagrangian-Eulerian method for flexible-body fluid-structure interaction

This paper introduces a sharp-interface approach to simulating fluid-structure interaction (FSI) involving flexible bodies described by general nonlinear material models and across a broad range of mass density ratios. This new flexible-body immersed Lagrangian-Eulerian (ILE) scheme extends our prior work on integrating partitioned and immersed approaches to rigid-body FSI. Our numerical approach incorporates the geometrical and domain solution flexibility of the immersed boundary (IB) method with an accuracy comparable to body-fitted approaches that sharply resolve flows and stresses up to the fluid-structure interface. Unlike many IB methods, our ILE formulation uses distinct momentum equations for the fluid and solid subregions with a Dirichlet-Neumann coupling strategy that connects fluid and solid subproblems through simple interface conditions. As in earlier work, we use approximate Lagrange multiplier forces to treat the kinematic interface conditions along the fluid-structure interface. This penalty approach simplifies the linear solvers needed by our formulation by introducing two representations of the fluid-structure interface, one that moves with the fluid and another that moves with the structure, that are connected by stiff springs. This approach also enables the use of multi-rate time stepping, which allows us to use different time step sizes for the fluid and structure subproblems. Our fluid solver relies on an immersed interface method (IIM) for discrete surfaces to impose stress jump conditions along complex interfaces while enabling the use of fast structured-grid solvers for the incompressible Navier-Stokes equations. The dynamics of the volumetric structural mesh are determined using a standard finite element approach to large-deformation nonlinear elasticity via a nearly incompressible solid mechanics formulation. This formulation also readily accommodates compressible structures with a constant total volume, and it can handle fully compressible solid structures for cases in which at least part of the solid boundary does not contact the incompressible fluid. Selected grid convergence studies demonstrate second-order convergence in volume conservation and in the pointwise discrepancies between corresponding positions of the two interface representations as well as between first and second-order convergence in the structural displacements. The time stepping scheme is also demonstrated to yield second-order convergence. To assess and validate the robustness and accuracy of the new algorithm, comparisons are made with computational and experimental FSI benchmarks. Test cases include both smooth and sharp geometries in various flow conditions. Furthermore, we also demonstrate the capabilities of this methodology by applying it to model the transport and capture of a geometrically realistic, deformable blood clot in an inferior vena cava filter.

97 MATHEMATICS AND COMPUTING↗

A high-order Shifted Interface Method for Lagrangian shock hydrodynamics

Here, we present a new method for two-material Lagrangian hydrodynamics, which combines the Shifted Interface Method (SIM) with a high-order Finite Element Method. Our approach relies on an exact (or sharp) material interface representation, that is, it uses the precise location of the material interface. The interface is represented by the zero level-set of a continuous high-order finite element function that moves with the material velocity. This strategy allows to evolve curved material interfaces inside curved elements. By reformulating the original interface problem over a surrogate (approximate) interface, located in proximity of the true interface, the SIM avoids cut cells and the associated problematic issues regarding implementation, numerical stability, and matrix conditioning. Accuracy is maintained by modifying the original interface conditions using Taylor expansions. We demonstrate the performance of the proposed algorithms on established numerical benchmarks in one, two and three dimensions.

97 MATHEMATICS AND COMPUTING↗

Three-dimensional microstructure of a friction stir welded magnesium/steel interface characterized via high-energy synchrotron X-rays

Here, the three-dimensional (3D) microstructure of a friction stir assisted scribe technique (FaST) weld interface consisting of AZ31 magnesium (Mg) alloy and zinc (Zn)-coated DP590 steel was analyzed via synchrotron micro-computed tomography (μ-CT), correlated to synchrotron x-ray diffraction, and electron microscopy. Diffraction assessment of the AZ31/Zn-coated DP590 steel interface revealed the presence of several complex Mg–Zn intermetallic phases and differences in crystalline orientation of the Mg phase at the weld interface. The 3D characterization of the synchrotron μ-CT images of the weld interface revealed: (1) the presence of AZ31 weld nugget material with iron (Fe)-rich particles; (2) the presence of a weld layer at the joining interface with Fe-rich particles; (3) the formation of a thin non-uniform layer between the weld layer and the interface of the scribed DP590 material; and (4) the presence of an Fe–Al-rich intermetallic layer and Fe-rich particles at the interface of the scribed DP590 material. This study also performed a detailed analysis of lump-like features seen in the Zn coating layer at the weld interface. A detailed 3D particle analysis of the Fe-rich particles in the AZ31 weld nugget and the weld layer at the weld interface revealed the presence of several types of particle morphologies (i.e., spherical and irregular).

36 MATERIALS SCIENCE↗

Direct Optoelectronic Imaging of 2D Semiconductor–3D Metal Buried Interfaces

The semiconductor-metal junction is one of the most critical factors for high performance electronic devices. In two-dimensional (2D) semiconductor devices, minimizing voltage drop at this junction is of particularly challenging and important. Despite numerous studies on contact resistance in 2D semiconductors, the exact nature of the buried interface under a 3D metal remains elusive and unclear. Herein, we report the direct observation of 2D semiconductor-metal buried interface using recently developed metal-assisted transfer technique to expose the buried interface which is then directly investigated using scanning probe techniques. We characterize the spatially varying electronic and optical properties of this buried interface with < 20 nm resolution. To be specific, potential, conductance and photoluminescence at the buried metal/MoS 2 interface are correlated under variety of metal deposition conditions as well as type of metal contacts. We observe that direct evaporation of Au on MoS 2 induces large strain of ~5% in the MoS 2 which coupled with charge transfer leads to degenerate doping of the MoS 2 underneath the contact. These factors lead to improvement of contact resistance to record values of 138 kΩ μm measured using local conductance probes. This approach was adopted to investigate MoS 2 -In/Au alloy interface, which records lowest contact resistance of 63 kΩ μm. Overall, our results highlight that the MoS 2 /Metal interface is very sensitive to method of contact making and provides a universal strategy to characterize buried contact interfaces involving 2D semiconductors.

77 NANOSCIENCE AND NANOTECHNOLOGY↗

First-principles study of interfaces in Al/SiC metal-matrix composite system

In this work, first-principles calculations were performed on the interfaces between Al and SiC, which is a widely used strengthening agent in aluminum metal-matrix-composites (Al/MMC). C-terminated interfaces have much larger work of adhesion than Si-terminated interfaces, indicating that the former has much stronger interfacial bonding. The electron localization function shows that the chemical bonding between Al and C has a strong covalent character, while the bonding between Al and Si is largely metallic. As a result of the vastly different chemical bonding, the work of adhesion for C-terminated interfaces increases with the number of dangling bonds at the interface, while the opposite trend was observed for Si-terminated interfaces. Additionally, the interface energy for Si-terminated interfaces is comparable to that for C-terminated interfaces, suggesting both types of terminations can coexist in the Al/SiC system.

36 MATERIALS SCIENCE↗

Interface microstructure effects on dynamic failure behavior of layered Cu/Ta microstructures

Abstract Structural metallic materials with interfaces of immiscible materials provide opportunities to design and tailor the microstructures for desired mechanical behavior. Metallic microstructures with plasticity contributors of the FCC and BCC phases show significant promise for damage-tolerant applications due to their enhanced strengths and thermal stability. A fundamental understanding of the dynamic failure behavior is needed to design and tailor these microstructures with desired mechanical responses under extreme environments. This study uses molecular dynamics (MD) simulations to characterize plasticity contributors for various interface microstructures and the damage evolution behavior of FCC/BCC laminate microstructures. This study uses six model Cu/Ta interface systems with different orientation relationships that are as- created, and pre-deformed to understand the modifications in the plasticity contributions and the void nucleation/evolution behavior. The results suggest that pre-existing misfit dislocations and loading orientations (perpendicular to and parallel to the interface) affect the activation of primary and secondary slip systems. The dynamic strengths are observed to correlate with the energy of the interfaces, with the strengths being highest for low-energy interfaces and lowest for high-energy interfaces. However, the presence of pre-deformation of these interface microstructures affects not only the dynamic strength of the microstructures but also the correlation with interface energy.

42 ENGINEERING↗

Directing the adsorption and assembly of laponite nano-discs at oil–water interfaces

Achieving tunable controls on the adsorption and self-assembly of nanoscale building blocks at immiscible fluid interfaces is essential for synthesizing advanced materials, stabilizing emulsions, and the sustainable storage and recovery of fluids. Although extensive efforts have been directed toward resolving the assembly of spherical nanoparticles at water–hydrocarbon interfaces, 2D nanoparticles have received far less attention. In this study, we developed novel controls to direct the adsorption and assembly of 2D laponite nano-discs (diameter = ∼30 nm and thickness = ∼1 nm) at water–heptane interfaces using traces of sodium dodecyl sulfate (SDS) surfactant, demonstrated by advanced in situ small-angle X-ray scattering, atomic force microscopy, spinning drop tensiometer measurements and molecular dynamics simulations. The results show that SDS surfactant displaces the adsorbed laponite nano-discs from the interface toward the aqueous phase. The extent of this displacement increases with SDS concentration such that high SDS concentrations convert laponite-rich interfaces to SDS-rich interfaces free of laponite nano-discs. This transformation is associated with significant alterations in the rheological and nanomechanical properties of the host interface. In this context, reduction in interfacial tension and interfacial stiffness and an increase in the interfacial deformation is observed on increasing the SDS concentration from 0 to 0.1 wt%. The displacement of laponite nano-discs from the interface is driven by strong electrostatic interactions between the hydrophilic SDS group and interfacial water molecules. These studies unlock new insights into the adsorption and assembly of 2D nanoscale particles at water–hydrocarbons interfaces that are relevant for various applications related to energy and environmental science and engineering.

interfacial tension↗

Parallel Runtime Interface for Fortran (PRIF) Specification (Rev. 0.3)

This document specifies an interface to support the parallel features of Fortran, named the Parallel Runtime Interface for Fortran (PRIF). PRIF is a proposed solution in which the runtime library is responsible for coarray allocation, deallocation and accesses, image synchronization, atomic operations, events, and teams. In this interface, the compiler is responsible for transforming the invocation of Fortran-level parallel features into procedure calls to the necessary PRIF procedures. The interface is designed for portability across shared- and distributed-memory machines, different operating systems, and multiple architectures. Implementations of this interface are intended as an augmentation for the compiler's own runtime library. With an implementation-agnostic interface, alternative parallel runtime libraries may be developed that support the same interface. One benefit of this approach is the ability to vary the communication substrate. A central aim of this document is to define a parallel runtime interface in standard Fortran syntax, which enables us to leverage Fortran to succinctly express various properties of the procedure interfaces, including argument attributes.

97 MATHEMATICS AND COMPUTING↗

Parallel Runtime Interface for Fortran (PRIF) Specification (Rev. 0.5)

This document specifies an interface to support the parallel features of Fortran, named the Parallel Runtime Interface for Fortran (PRIF). PRIF is a proposed solution in which the runtime library is primarily responsible for implementing coarray allocation, deallocation and accesses, image synchronization, atomic operations, events, teams and collective subroutines. In this interface, the compiler is responsible for transforming the invocation of Fortran-level parallel features into procedure calls to the necessary PRIF subroutines. The interface is designed for portability across shared- and distributed-memory machines, different operating systems, and multiple architectures. Implementations of this interface are intended as an augmentation for the compiler's own runtime library. With an implementation-agnostic interface, alternative parallel runtime libraries may be developed that support the same interface. One benefit of this approach is the ability to vary the communication substrate. A central aim of this document is to define a parallel runtime interface in standard Fortran syntax, which enables us to leverage Fortran to succinctly express various properties of the procedure interfaces, including argument attributes.

97 MATHEMATICS AND COMPUTING↗

Parallel Runtime Interface for Fortran (PRIF) Design Document (Rev. 0.2)

This design document proposes an interface to support the parallel features of Fortran, named the Parallel Runtime Interface for Fortran (PRIF). PRIF is a proposed solution in which the runtime library is responsible for coarray allocation, deallocation and accesses, image synchronization, atomic operations, events, and teams. In this interface, the compiler is responsible for transforming the invocation of Fortran-level parallel features into procedure calls to the necessary PRIF procedures. The interface is designed for portability across shared- and distributed-memory machines, different operating systems, and multiple architectures. Implementations of this interface are intended as an augmentation for the compiler's own runtime library. With an implementation-agnostic interface, alternative parallel runtime libraries may be developed that support the same interface. One benefit of this approach is the ability to vary the communication substrate. A central aim of this document is to define a parallel runtime interface in standard Fortran syntax, which enables us to leverage Fortran to succinctly express various properties of the procedure interfaces, including argument attributes.

97 MATHEMATICS AND COMPUTING↗

Parallel Runtime Interface for Fortran (PRIF) Specification (Rev. 0.4)

This document specifies an interface to support the parallel features of Fortran, named the Parallel Runtime Interface for Fortran (PRIF). PRIF is a proposed solution in which the runtime library is responsible for coarray allocation, deallocation and accesses, image synchronization, atomic operations, events, and teams. In this interface, the compiler is responsible for transforming the invocation of Fortran-level parallel features into procedure calls to the necessary PRIF procedures. The interface is designed for portability across shared- and distributed-memory machines, different operating systems, and multiple architectures. Implementations of this interface are intended as an augmentation for the compiler's own runtime library. With an implementation-agnostic interface, alternative parallel runtime libraries may be developed that support the same interface. One benefit of this approach is the ability to vary the communication substrate. A central aim of this document is to define a parallel runtime interface in standard Fortran syntax, which enables us to leverage Fortran to succinctly express various properties of the procedure interfaces, including argument attributes.

97 MATHEMATICS AND COMPUTING↗