CORRECTION TO THE SECOND APPROXIMATION CALCULATION OF THE GEOMAGNETIC FIELD, SOLAR WIND INTERFACE
Correction to second approximation calculation of geomagnetic field, solar wind interface
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Correction to second approximation calculation of geomagnetic field, solar wind interface
Correction for ‘Interfacial rheology of lanthanide binding peptide surfactants at the air–water interface’ by Stephen A. Crane et al. , Soft Matter , 2024, 20 , 9161–9173, https://doi.org/10.1039/D4SM00493K.
New composite materials possess attractive properties for use in advanced aircraft. A necessary requirement for their introduction into aeronautic use is an accurate understanding of their long term aging processes so that proper design criteria can be established. In order to understand those properties, these composites must be exposed to thermal and load cycles that are characteristic of flight conditions. Additionally, airline companies will require nondestructive evaluation (NDE) methods that can be used in the field to assess the condition of these new materials as they age. As part of an effort to obtain the required information about new composites for aviation use, we are performing ultrasonic measurements both in the NDE laboratory and in the materials testing laboratory at NASA. The materials testing laboratory is equipped with environmental chambers mounted on load frames so that composite samples can be exposed to thermal and loading cycles representative of flight protocols. Applying both temperature and load simultaneously will help to highlight temperature and load interactions during the aging of these composite materials. This study reports on our initial ultrasonic attenuation results from thermoset and thermoplastic composite samples. Ultrasonic attenuation measurements have been used reliably to assess the effects of material degradation. For example, recently, researchers have shown that by using frequencies of ultrasound on the order of 24 MHz, they could obtain adequate contrast in the evaluation of thermal degradation in these composites. This paper will present data that shows results at a lower frequency range. In addition, we report results on the frequency dependence of attenuation as the slope of attenuation with respect to frequency, beta = delta alpha (f) / delta f. The slope of attenuation is an attractive parameter since it is quantitative, yet does not require interface corrections like conventional quantitative attenuation measurements. This is a consequence of the assumption that interface correction terms are frequently independent. Uncertainty in those corrections terms compromises the value of conventional quantitative attenuation data.
As part of an effort to obtain the required information about new composites for aviation use, materials and NDE researchers at NASA are jointly performing mechanical and NDE measurements on new composite materials. The materials testing laboratory at NASA is equipped with environmental chambers mounted on load frames that can expose composite materials to thermal and loading cycles representative of flight protocols. Applying both temperature and load simultaneously will help to highlight temperature and load interactions during the aging of these composite materials. This report highlights our initial ultrasonic attenuation results from thermoplastic composite samples that have undergone over 4000 flight cycles to date. Ultrasonic attenuation measurements are a standard method used to assess the effects of material degradation. Recently, researchers have shown that they could obtain adequate contrast in the evaluation of thermal degradation in thermoplastic composites by using frequencies of ultrasound on the order of 24 MHz. In this study, we address the relationship of attenuation measured at lower frequencies in thermoplastic composites undergoing both thermal and mechanical loading. We also compare these thermoplastic results with some data from thermoset composites undergoing similar protocols. The composite s attenuation is reported as the slope of attenuation with respect to frequency, defined as b = Da(f)/Df. The slope of attenuation is an attractive parameter since it is quantitative, yet does not require interface corrections like conventional quantitative attenuation measurements. This latter feature is a consequence of the assumption that interface correction terms are frequency independent. Uncertainty in those correction terms can compromise the value of conventional quantitative attenuation data. Furthermore, the slope of the attenuation more directly utilizes the bandwidth information and in addition, the bandwidth can be adjusted in the post processing stage to compensate for the loss of dynamic range of the signal as the composites age.
The Direct Discontinuous Galerkin (DDG (Liu and Yan, 2008)) method and a counterpart with Interface Correction (DDGIC (Danis and Yan, 2022)) are extended to compute diffusion terms that arise when solving the compressible multi-component flow equations in thermochemical nonequilibrium. Thermodynamic properties, transport properties, chemical reaction rates, and energy exchange terms are computed using Mutation++ (Scoggins et al., 2020). The DG method is applied on unstructured grids, where the accuracy and convergence rates can be sensitive to the numerical method chosen for parabolic terms. A method for determining the homogeneity tensor of the flow equations required for DDGIC is shown. The convergence properties of the DDG methods are studied and compared to the Interior Penalty (IP) method. A number of numerical experiments are conducted to assess the accuracy and performance of the method. The numerical results and convergence studies indicate that DDG and DDGIC provide accurate solutions and perform well for general flows in thermochemical nonequilibrium.
This study is devoted to a comparative analysis of three 'Adaptive ZOOM' (ZOom Overlapping Multi-level) methods based on similar concepts of hierarchical multigrid local refinement: LDC (Local Defect Correction), FAC (Fast Adaptive Composite), and FIC (Flux Interface Correction)--which we proposed recently. These methods are tested on two examples of a bidimensional elliptic problem. We compare, for V-cycle procedures, the asymptotic evolution of the global error evaluated by discrete norms, the corresponding local errors, and the convergence rates of these algorithms.
A wall interference assessment and correction method for subsonic two-dimensional wind tunnel testing is presented. This method calculates a pressure coefficient and angle of attack correction based on velocity measurements on interfaces inside of the wind tunnel. A mathematical representation of the test article is not required. An experimental verification of the suggested technique is given. A NACA 0012 airfoil is tested at a Mach number of 0.70 and at two different angles of attack. Calculated blockage corrections show reasonable agreement with results based on Hackett's method. Corrected surface pressures compare favorably to free-air flow field data if the tunnel flow field is subsonic. The present wall interference correction method can be applied to transonic tunnel flow fields with some restrictions. Errors are estimated and it is shown that the expected error in calculating the pressure coefficient correction on the model surface is in the order of the error of pressure coefficient measurement on interfaces. Necessary testing equipment in existing tunnels can easily be modified if the present method is applied.
Solution of the steady 2-D Euler equations using mesh embedding, or local grid refinement, with a cell-centered finite volume scheme is investigated. Embedded regions which are topologically similar to the global grid are considered. An isoenergetic model for the governing equations is used in Jameson's finite volume multistage scheme with modifications to the boundary conditions and smoothing. A detailed study of the embedding interface flux and smoothing formulations is conducted. Taylor expansion analysis reveals that local second order spatial accuracy is not possible if a conservative interface flux formulation is used. The analysis also gives constraints for local first order accuracy. An energy stability analysis indicates that downwind weighting of interface fluxes causes local instabilities. Analysis shows that conservative interface smoothing formulations must have a locally convective component, but that correct interface formulations allow globally dissipative smoothing. Embedded mesh solutions obtained with this scheme are presented for a transonic airfoil. They show that if embedding interfaces are close to the shocks, then small modifications in the interface location can have large effects on converge and solution accuracy.
While new versions of automated control systems such as flight guidance systems are introduced at a rapid pace, it is widely recognized that user interaction with these machines is increasingly problematic. One cause for this difficulty that is commonly cited in the literature, is the discrepancy between the machine's behavior and the operator's (e.g., pilot) expectations. This paper discusses a formal approach to the analysis of operator's interaction with complex automated control systems. We focus attention on the issue of interface correctness; that is, on the question whether the display provides adequate information about the machine's configurations (states, modes, and associated parameters) and transitions, so as to enable the operator to successfully perform the specified set of tasks. To perform the analysis several assumptions are made: (1) A complete formal model of the machine's behavior is available (e.g., as a state transition system, or as a hybrid-machine); (2) A specification of operator's tasks is available and can be formally described (e.g., the reliable and predictable transition between activities involved in executing a climb to a new altitude); (3) The pilot is well trained and has a correct 'mental' model of the machine's response-map. By 'comparing' the machine's model with the set of operator's tasks we formally (i.e., mathematically) evaluate two questions: 1) does the machine's output interface (display) enable the operator to determine, unambiguously, what the current configuration (e.g., mode) of the machine is, and 2) does the display enable the operator to determine, unambiguously, what the next configuration of the machine will be, in response to a specified interaction by the operator (e.g., engaging a mode or changing a parameter such as a speed or target altitude). This paper describes a methodology for conducting such an evaluation using examples from automated flight control systems of modem 'glass cockpit' jetliners. Taxonomy of the different types of discrepancies that lead to pilot inability to resolve the current and next configuration of the machine is suggested. Data from incident reports involving 'mode confusion' is used to corroborate these discrepancies. Finally, means for compensating, either by augmenting the display and/or the operator's 'mental model' are briefly mentioned.
We propose a fourth order Navier-Stokes solver based on the immersed interface method (IIM), for flow problems with stationary and one-way coupled moving boundaries and interfaces. Our algorithm employs a Runge-Kutta-based projection method that maintains high-order temporal accuracy in both velocity and pressure for steady and unsteady velocity boundary conditions. Fourth order spatial accuracy is achieved through a novel fifth order IIM discretization scheme for the advection term, as well as existing high-order interface-corrected finite difference schemes for the other differential operators. Using a set of manufactured flow problems with stationary and moving boundaries, we demonstrate fourth order convergence of velocity and pressure in the infinity norm, both inside the domain and on the immersed boundaries. The solver’s performance is further validated through a range of practical flow simulations, highlighting its efficiency over a second order scheme. Finally, we showcase the ability of our immersed discretization scheme to handle interface-coupled multiphysics problems by solving a conjugate heat transfer problem with multiple immersed solids. Overall, the proposed approach robustly combines the efficiency of high order discretization schemes with the flexibility of immersed discretizations for flow problems with complex, moving boundaries and interfaces.
Higher order software (HOS) is concerned only with computable functions and relationships. The HOS methodology can be used for the definition of software for multiprogrammed, multiprocessor, or multicomputer systems. A description of HOS methodology is presented, giving attention to questions of formulation, interface correctness, specification language principles, and HOS analyzers. Aspects of system design are considered, and details of software management are discussed. Attention is given to modularity as defined by HOS, frozen module management, the assembly control supervisor, and aspects of reliability and efficiency.
In this paper we review the existing and develop new continuous Galerkin methods for solving time dependent partial differential equations with higher order derivatives in one and multiple space dimensions. We review local discontinuous Galerkin methods for convection diffusion equations involving second derivatives and for KdV type equations involving third derivatives. We then develop new local discontinuous Galerkin methods for the time dependent bi-harmonic type equations involving fourth derivatives, and partial differential equations involving fifth derivatives. For these new methods we present correct interface numerical fluxes and prove L(exp 2) stability for general nonlinear problems. Preliminary numerical examples are shown to illustrate these methods. Finally, we present new results on a post-processing technique, originally designed for methods with good negative-order error estimates, on the local discontinuous Galerkin methods applied to equations with higher derivatives. Numerical experiments show that this technique works as well for the new higher derivative cases, in effectively doubling the rate of convergence with negligible additional computational cost, for linear as well as some nonlinear problems, with a local uniform mesh.
In this poster, we describe a web-based tool for verification and automatic generation of user interfaces. The verification component of the tool accepts as input a model of a machine and a model of its interface, and checks that the interface is adequate (correct). The generation component of the tool accepts a model of a given machine and the user's task, and then generates a correct and succinct interface. This write-up will demonstrate the usefulness of the tool by verifying the correctness of a user interface to a flight-control system. The poster will include two more examples of using the tool: verification of the interface to an espresso machine, and automatic generation of a succinct interface to a large hypothetical machine.
This report addresses the design of human-automation interaction from a formal perspective that focuses on the information content of the interface, rather than the design of the graphical user interface. It also addresses the, issue of the information provided to the user (e.g., user-manuals, training material, and all other resources). In this report, we propose a formal procedure for generating interfaces and user-manuals. The procedure is guided by two criteria: First, the interface must be correct, i.e., that with the given interface the user will be able to perform the specified tasks correctly. Second, the interface should be as succinct as possible. The report discusses the underlying concepts and the formal methods for this approach. Several examples are used to illustrate the procedure. The algorithm for constructing interfaces can be automated, and a preliminary software system for its implementation has been developed.
This report addresses the design of human-automation interaction from a formal perspective that focuses on the information content of the interface, rather than the design of the graphical user interface. It also addresses the issue of the information provided to the user (e.g., user-manuals, training material, and all other resources). In this report, we propose a formal procedure for generating interfaces and user-manuals. The procedure is guided by two criteria: First, the interface must be correct, that is, with the given interface the user will be able to perform the specified tasks correctly. Second, the interface should be succinct. The report discusses the underlying concepts and the formal methods for this approach. Two examples are used to illustrate the procedure. The algorithm for constructing interfaces can be automated, and a preliminary software system for its implementation has been developed.
Radiation transport arises in various scientific, industrial, and medical fields, and understanding its effect in applications is needed to make accurate predictions, safety assessments and performance optimizations. Solving the Radiation Transport Equation (RTE) is challenging due to its integro-differential nature, which involves both differential and integral terms. The differential term describes the change in radiation intensity due to absorption and emission, while the integral term accounts for scattering. The accurate modeling of radiation is further complicated in many applications due to the complex, irregular geometries. Various methods exist for solving the RTE, including the zonal, Monte Carlo, spherical harmonics, discrete ordinates, and finite volume methods. Traditional mesh-based approaches, which rely on structured or unstructured meshes, struggle with irregular geometries due to: a) the difficulty of conforming structured grids to irregular domains, b) challenges in enforcing boundary conditions correctly, and c) the additional computational cost of unstructured mesh methods. This work presents a second-order accurate method for solving the RTE in irregular geometries. The radiation intensity is discretized using the finite-volume method in both spatial and angular directions on regular Cartesian grid blocks. Leveraging the block-structured adaptive mesh refinement (AMR) framework provided by AMReX, our method refines the grid locally to reduce spatial discretization error, ensuring a converged numerical solution while minimizing computational costs elsewhere. A two-stage deferred correction approach is employed: First, a first-order discretization on grid blocks is solved using an algebraic multigrid method in HYPRE. Second, a correction term is applied explicitly to achieve second-order accuracy. The correction term is calculated by approximating the radiation flux on cell faces using a Total Variation Diminishing (TVD) scheme. This approach ensures quick convergence of the multigrid method while preserving higher-order accuracy of the numerical solution. Irregular geometries are resolved as embedded boundaries (EB), resulting in both cut cells and regular cells. In cut cells, we modify the fluxes using face fractions and incorporate additional contributions from EB boundary conditions. To ensure higher-order convergence near the EB interface, the correction term is modified by interpolating the radiation intensity to fictitious ghost points. The implementation takes advantage of modern supercomputers by leveraging AMReX’sMPI/X parallelization strategy where X can be MPI or a GPU accelerator including CUDA, HIP and DPC++. We validate our solver using classical test cases, both with and without EB, demonstrating accuracy and efficiency. Additionally, we analyze the impact of adaptive mesh refinement on solution accuracy and computational cost, highlighting the advantages of our approach for high-resolution radiation transport simulations.
Conventional continuum solvation models are ubiquitous in computational catalysis, including for describing metal/water interfaces, which are relevant to both solution-phase heterogeneous catalysis and electrocatalysis. Nonetheless, we find that such continuum models qualitatively fail to describe both the adsorption free energy and conformational preference for many organic molecules at such interfaces, largely due to the failure of continuum models to incorporate the role of competitive water adsorption. We develop a simple phenomenological model that accounts for competitive water adsorption and show that the model, when used in conjunction with continuum solvation, provides a dramatic improvement in the description of both adsorption and conformational preference. The model is also extended to additionally incorporate the influence of applied potential at the electrode surface, thus facilitating computationally efficient applications to scenarios including electrocatalysis.
A plan has been formulated and selected for a NASA Phase 2 SBIR award for using the VLBA tape recorder for recording general data. The VLBA tape recorder is a high-speed, high-density linear tape recorder developed for Very Long Baseline Interferometry (VLBI) which is presently capable of recording at rates up to 2 Gbit/sec and holding up to 1 Terabyte of data on one tape, using a special interface and not employing error correction. A general-purpose interface and error correction will be added so that the recorder can be used in other high-speed, high-capacity applications.