Power-law Interpolation Research Articles

Contamination Level Prediction: Progress in Species Separation by TGA/MS

Molecular contamination can be detrimental to spacecraft life expectancy as it may induce changes to the properties of the surfaces on which it deposits. In order to control these potential issues, manufacturers need to assess in-flight contamination levels in the quite early design phases, possibly leading to design changes or extra material bake-out to fulfil requirements. The accuracy of model assessments may thus have direct impacts on missions and costs. Prediction of outgassing and deposition at mission timescale is done by extrapolating short-term on-ground experimental results, by fitting the latter with some empirical or physical laws. Common methods are the power law interpolation (in isothermal conditions) or the residence time approach (with thermally activated time constants), which leads to exponential decays in isothermal conditions. Although they allow fitting the measured outgassed flux over few-day-long experiments, their extrapolation to ten or fifteen-year-long missions is more challenging. Validating empirical laws might involve long-term empirical comparisons, while obviously the validation of physical models should start with checking their physics. In spite of many years trying, a basic difficulty was yet found to block significant progress on physical validation. As long as measurements are limited to the total mass on QCMs it looks possible to fit data as a sum of almost any law, such as residence time or diffusion models e.g. for outgassing. Following this observation, a conclusion was drawn that the only way to discriminate between two different physics was to characterize contamination at chemical species level. Such characterizations are a prerequisite to unravel the physics at play during several phenomena: outgassing, deposit films dynamics, photochemistry, environment/ATOX interactions, etc. This innovative approach, presented herein, aims at identifying outgassed contaminants by means of coupled thermogravimetric analysis and mass spectrometry. For this purpose, this paper reports the successful species separation and identification of contaminants outgassed from a material used in space applications: the epoxy adhesive Scotchweld EC-9323-2.

Effect of polyurea coating on the ductility of aluminum foam

The closed-cell metal foams are utilized in various industrial applications due to their impact and energy absorption capacity, noise cancelation, and lightweight properties. Additionally, the manufacturing methods of stochastic foams with blowing agents or inert gas injection are well known. However, the poor mechanical strength and high brittleness are restricting the application of these materials. A method of increasing the ductility, plastic deformation, and fracture toughness of these materials is the integration of elastomer coating. Polyurea is widely used in applications where water-proofing and high ductility are aimed. In this study, two types of polyurea coatings as MS950 and MS955 are sprayed over the aluminum foam with three densities as 0.508, 0.557, and 0.624 g/cm3 to evaluate the effect of coating on the ductility and fracture toughness of samples considering the tensile behavior and 4 densities as 0.508, 0.538, 0.557, and 0.624 g/cm3 for the flexural bending test. The MS955 polyurea coating elevated the ultimate tensile strength and elasticity modulus of all specimens with a maximum of 239% and a minimum of 70%. However, the MS950 coating did not result in a significant rise in tensile strength. The main advantage of the MS950 coating is in the amount of strain increment with 374% in maximum and 181% in minimum resulting in higher ductility and fracture toughness. Additionally, the bending characteristics of MS950 coating demonstrate a drastic increase in both load and strain which recommend the usage of this coating in bending and impact applications. Finally, an analytical evaluation of the coated and uncoated specimens in the elastic region and the elastoplastic region is provided using linear and power-law interpolation. In tensile tests, the MS955 coating resulted in higher elasticity modulus and fracture toughness. However, in bending applications, the MS950 coating demonstrated higher load strength with elevated ductility.

Novel methodology of Non-probabilistic Reliability-based Topology Optimization (NRBTO) for multi-material layout design via interval and convex mixed uncertainties

This paper proposes an efficient topology optimization strategy for seeking the optimal layout of multi-material structures with mixed uncertainties of interval and convexity. In conjunction with the safety criterion for local displacement and the extended power-law interpolation scheme for the material property, the task of the optimization problem is formulated as to minimize the total volume of different materials while satisfying reliability requirement. By introducing the set-theoretical convex method, uncertainty quantification analysis under mixture of interval and convex uncertainties is firstly conducted for exploring boundary rules of considered responses. Combined with the area-ratio principle and the shortest distance judgment, a novel reliability index with favorable mathematical characteristics is then defined. Moreover, for guarantee the computational efficiency as well as the iterative convergence, the adjoint-variable model is also established and the investigated minimization issue can be solved by a gradient-based optimization algorithm. Eventually, several numerical applications are given to demonstrate the validity and reasonability of the present topology optimization methodology.

Mass accumulation of earth from interplanetary dust, meteoroids, asteroids and comets

Using new data and recent models this paper derives a total combined flux model of the mass reaching Earth as interplanetary material. For the small sizes the interplanetary flux model by Grün et al. (1985) was used which describes the mass flux at 1AU for meteoroids in the mass range 10–21kg to about 10−1kg. For the large objects the flux models by Brown et al. (2002) were used which were derived for bodies greater than 1m and are based on sensor data of fireballs that entered the Earth atmosphere. For the intermediate size range interpolations and alternative models based on meteor and fireball data were used. All flux models were converted to an altitude of 100km above the Earth surface to make them comparable. The total combined flux model covers more than 34 orders of magnitude in mass. Using recent measurements and alternative flux models the uncertainties of the obtained model were estimated. Recent measurements include in-situ impact data on retrieved space hardware and optical meteor and fireball data. Depending on the models and interpolation used the interplanetary material that enters the Earth atmosphere per day is in the range of 30−180t with a best guess value of 54t per day for an upper cut-off size of 1km. If the upper size limit is placed at 0.5m which is the largest size where statistically a daily impact is expected, the expected mass influx is slightly more than 32t per day. The combined models with interpolations suggest deviations from a simple power law. The flux in the diameter range of 0.01–0.1m appears not as large as suggested by a simple power law interpolation.

Optimal topology design for stress-isolation of soft hyperelastic composite structures under imposed boundary displacements

Soft hyperelastic composite structures that integrate soft hyperelastic material and linear elastic hard material can undergo large deformations while isolating high strain in specified locations to avoid failure. This paper presents an effective topology optimization-based methodology for seeking the optimal united layout of hyperelastic composite structures with prescribed boundary displacements and stress constraints. The optimization problem is modeled based on the power-law interpolation scheme for two candidate materials (one is soft hyperelastic material and the other is linear elastic material). The ź-relaxation technique and the enhanced aggregation method are employed to avoid stress singularity and improve the computational efficiency. Then, the topology optimization problem can be readily solved by a gradient-based mathematical programming algorithm using the adjoint variable sensitivity information. Numerical examples are given to show the importance of considering prescribed boundary displacements in the design of hyperelastic composite structures. Moreover, numerical solutions demonstrate the validity of the present model for the optimal topology design with a stress-isolated region.

Topology optimization of reinforced concrete structures considering control of shrinkage and strength failure

To take into account the shrinkage effect in the early stage of Reinforced Concrete (RC) design, an effective continuum topology optimization method is presented in this paper. Based on the power-law interpolation, shrinkage of concrete is numerically simulated by introducing an additional design-dependent force. Under multi-axial stress conditions, the concrete failure surface is well fitted by two Drucker–Prager yield functions. The optimization problem aims at minimizing the cost function under yield strength constraints on concrete elements and a structural shrinkage volume constraint. In conjunction with the adjoint-variable sensitivity information, the enhanced aggregation method is utilized to efficiently reduce the computational effort arisen from large-scale strength constraints. Numerical results reveal that the proposed approach can produce a reasonable solution with the least steel reinforcements to ensure the structural safety under the combined action of external loads and shrinkage.

An Immersed Boundary Method Based on Volume Fraction

The immersed boundary method(IBM) was rapid developed in recent years, because of the ability for the complex configurations and moving bodies simulations. Most of the research on the IBM were focused on the low Mach numberflow, few researchers applied this method to the high Mach number flow problems. A new IB method developed in current paper, which applied the volume fraction to get the cut cell average variables. The values of the variables in the cells that located in the body was determined by the ghost cell method, and the value located in the flow field were gained by power law interpolation. The cases that transonic flow round airfoil and Ma 1.3 shock wave cross wedge were simulated, which showed that the new method could captured the shock wave, expansion wave, shock-vortex interaction, shock reflection, and this method is suitable for the high-speed flow problems.

The Selection of the Difference Scheme in Numerical Simulation of Low-Rise Gable Roof Surface Pressure

Using the FLUENT software, this paper taking the wind load shape coefficient in the current code for the design of building structures as the comparison standard, have numerical wind tunnel simulation of the wind the surface wind pressure on low layer double slope roof. It focused on the effect of four convective term difference schemes on the numerical simulation, such as First-Order Upwind, Second-Order Upwind, Power Law and Quadratic Upwind Interpolation for ConvectiveKinematics. It provided reasonable reference for selection of convective term difference format.

Optimal topology design of steel–concrete composite structures under stiffness and strength constraints

This study presents a three-phase topology optimization model and an effective solution procedure to generate optimal material distributions for complex steel–concrete composite structures. The objective is to minimize the total material cost (or mass) while satisfying the specified structural stiffness requirements and concrete strength constraints. Based on the Drucker–Prager criterion for concrete yield behaviour, the extended power-law interpolation for material properties and a cosine-type relaxation scheme for Drucker–Prager stress constraints are adopted. An enhanced aggregation method is employed to efficiently treat the large number of stress constraints, and the optimal topology is obtained through a standard gradient-based search. Several examples are provided to demonstrate the capability of the proposed optimization method in automatically finding the reasonable composite layout of steel and concrete.

The Influence of the Convective Terms Discretization Scheme on the Simulation Results of Architectural Numerical Wind Tunnel

The numerical simulation of construction is to obtain the desired accuracy. It depends on the theoretical basis of the calculator and selection of the various important factors in the actual operation. For this problem, this paper adopting the current code for the design of building structures as the comparison standard, using the FLUENT software, taking the numerical simulation results of a high building’s wind load shape coefficient of for example, discussing the influence of four kinds of the convective terms discretization scheme, respectively the first-order upwind, the second order upwind , power law and Quadratic upwind interpolation for convective kinematics, on the simulation results of architectural numerical wind tunnel, provides the reference for the rational use of numerical wind tunnel method.

Maximal Stiffness Design of Two-Material Structures by Topology Optimization with Nonprobabilistic Reliability

Basedon the multi-ellipsoid convex modelandthe quantified measure of the nonprobabilistic reliability, topology optimization of two-material structures in the presence of parameter uncertainties is investigated. The task of the optimal design problem is to distribute a given amount of two candidate materials into the design domain for acquiring the maximal stiffness while satisfying the reliability requirement. The extended power-law interpolation scheme for material properties is employed for relaxing the two-material topological design problem into a continuous-valued optimization problem. In addition, through transforming the minimax-type optimization problemintoaseriesofdeterministiconesbyusingasequentialapproximateprogrammingstrategy,thispaperaims tomaketheoptimizationdesignnumericallytractable.Theresultingmathematicalprogrammingproblemsarethen efficientlysolvedbytheassociationofthemethodofmovingasymptoteswithaheuristiciterativemanner.Numerical investigations reveal that system uncertainties may have considerable effects on the optimal material layout of twomaterial structures. The proposed topology optimization methodology could yield a more reasonable two-material structuraldesignthan theconventional deterministic counterpart whenthe samereliabilityrequirements need tobe achieved.

Layout design of reinforced concrete structures using two-material topology optimization with Drucker–Prager yield constraints

This paper aims to develop a method that can automatically generate the optimal layout of reinforced concrete structures by incorporating concrete strength constraints into the two-material topology optimization formulation. The Drucker---Prager yield criterion is applied to predict the failure behavior of concrete. By using the power-law interpolation, the proposed optimization model is stated as a minimum compliance problem under the yield stress constraints on concrete elements and the material volume constraint of steel. The ?-relaxation technique is employed to prevent the stress singularity. A hybrid constraint-reduction strategy, in conjunction with the adjoint-variable sensitivity information, is integrated into a gradient-based optimization algorithm to overcome the numerical difficulties that arise from large-scale constraints. It can be concluded from numerical investigations that the proposed model is suitable for obtaining a reasonable layout which makes the best uses of the compressive strength of concrete and the tensile strength of steel. Numerical results also reveal that the hybrid constraint-reduction strategy is effective in solving the topology optimization problems involving a large number of constraints.

Topology optimization of continuum structures with Drucker–Prager yield stress constraints

This paper presents an efficient topology optimization strategy for seeking the optimal layout of continuum structures exhibiting asymmetrical strength behaviors in compression and tension. Based on the Drucker–Prager yield criterion and the power-law interpolation scheme for the material property, the optimization problem is formulated as to minimize the material volume under local stress constraints. The ε-relaxation of stress constraints is adopted to circumvent the stress singularity problem. For improving the computational efficiency, a grouped aggregation approach based on the Kreisselmeier–Steinhauser function is employed to reduce the number of constraints without much sacrificing the approximation accuracy of the stress constraints. In conjunction with the adjoint-variable sensitivity analysis, the minimization problem is solved by a gradient-based optimization algorithm. Numerical examples demonstrate the validity of the present optimization model as well as the efficiency of the proposed numerical techniques. Moreover, it is also revealed that the optimal design of a structure with pressure-dependent material may exhibit a considerable different topology from the one obtained with pressure-independent material model.

Thermal and Nonthermal Infrared Emission from M87

We discuss images of M87 from 3.6 to 160 μm obtained with Spitzer. As found previously, there is an excess in the far-infrared over a simple power-law interpolation from the radio to the resolved nonthermal features in the mid-infrared and optical. We show that this excess is most likely due to warm dust in the galaxy itself and that the properties of this emission component are similar to the far-infrared emission of normal giant elliptical galaxies. The new observations allow us to determine the spectrum of the jet and surrounding lobes of nonthermal emission. We find that even in the lobes, the synchrotron break frequency is in the optical, probably requiring in situ particle acceleration not only in the jet but in the lobes as well.

A Modified Power Law for Creep Analysis

The creep strengths for an annealed Ni-33Fe-25Cr alloy, UNS N08120 (HAYNES® HR-120® alloy) are presented from 593°C to 1204°C at every 56°C for lives up to 30,000 hours. The creep data are used as a basis for converting the power law method (log stress versus log time at a defined temperature) to the usefulness of the Larson-Miller method for design creep analysis. A new empirical relationship was developed between stress, temperature and creep rupture life. Power Law equations were generated at each temperature using linear regression of the transformed data to obtain the best-fit constants. The constants were then plotted and a best-fit polynomial of the constants as a function of temperature was determined. The polynomial then replaced the constants in the original power law equation to obtain a single expression of stress as a function of time and temperature. Using this new Modified Power Law (MPL) equation, interpolation or extrapolation to obtain stress becomes possible for any temperature and time.

The Nature of Associated Absorption and the Ultraviolet–X‐Ray Connection in 3C 288.1

We discuss new Hubble Space Telescope spectroscopy of the radio-loud quasar 3C 288.1. The data cover ~590 to ~1610 A in the quasar rest frame. They reveal a wealth of associated absorption lines (AALs) with no accompanying Lyman-limit absorption. The metallic AALs range in ionization from C III and N III to Ne VIII and Mg X. We use these data and photoionization models to derive the following properties of the AAL gas: (1) There are multiple ionization zones within the AAL region, spanning a factor of at least ~50 in ionization parameter. (2) The overall ionization is consistent with the warm X-ray continuum absorbers measured in Seyfert 1 nuclei and other QSOs. (3) However, the column densities implied by the AALs in 3C 288.1 are too low to produce significant bound-free absorption at any UV-X-ray wavelengths. Substantial X-ray absorption would require yet another zone, having a much higher ionization or a much lower velocity dispersion than the main AAL region. (4) The total hydrogen column density in the AAL gas is log NH(cm-2) ≈ 20.2. (5) The metallicity is roughly half solar. (6) The AALs have deconvolved widths of ~900 km s-1, and their centroids are consistent with no shift from the quasar systemic velocity (conservatively, within ±1000 km s-1). (7) There are no direct indicators of the absorber's location in our data, but the high ionization and high metallicity both suggest a close physical relationship to the quasar/host galaxy environment. Finally, the UV continuum shape gives no indication of a blue bump at higher energies. There is a distinct break of unknown origin at ~1030 A, and the decline toward higher energies (with spectral index α ≈ -1.73, for fν ∝ να) is even steeper than a single power-law interpolation from 1030 A to soft X-rays.

Determination of resting free calcium in barnacle muscle using modified aequorins, buffered calcium injections, and simultaneous image-intensified video microscopy.

Knowing the resting free calcium is important in understanding the role of calcium as an intracellular second messenger. We used a bracketing (null) technique with a luminescent calcium indicator, aequorin, microinjection and image-intensification to measure free calcium in single muscle fibres from the barnacle, Balanus nubilus. We injected modified aequorins (recombinant, and hch-) which after a 30 min diffusion gave reasonable resting glows. Subsequent injection of calcium (strongly buffered with either EGTA or BAPTA, 10 mM) increased or decreased the resting glow depending on the free calcium level in the injected buffer solution. This bracketing (null) method is inherently accurate, but mechanical artifacts on calcium injection reduce the accuracy when total light emission is measured. We therefore used image-intensified video-microscopy of the injected region and video processing (Image-1) of artifact-free regions, to greatly improve the consistency. The luminescence in a pre-selected region of the muscle fibre was measured as a function of time during the injection. Solution calciums were chosen so that if the first injection decreased the resting glow, the second increased it, or vice versa, thus bracketing the true resting value. We used two methods to determine the true value bracketed by our injections: (1) a linear interpolation using the fractional changes in luminescence or (2) a power law interpolation assuming a 2.2 or 2.5 power relationship between luminescence and free calcium. Using these methods, we estimated the free calcium level in the lateral depressor fibres of freshly dredged barnacles to be 279 +/- 36 nM (+/- SD), 339 +/- 42 nM, or 352 +/- 45 nM for the linear, 2.2 and 2.5 powers respectively under the conditions of hch-aequorin and BAPTA buffers (using a K'Ca for BAPTA of 3.0 x 10(6) M-1 for our conditions). Recombinant-aequorin gave essentially the same result while EGTA buffers yielded a somewhat higher value but because of influences of pH on the K'Ca for EGTA (taken as 6.7 x 10(6) M-1 for our conditions) was considered less reliable. Minor changes in [Mg2+] upon buffer injection can lead to underestimates of the true resting [Ca2+] by at most 10%. Thus, we estimate the resting free calcium in barnacle muscle fibres to be 300-380 nM.

Gasdynamic approach to small plumes computation

The semi-inverse marching characteristics scheme SIMA was extended to treat rotational flows; it is applied to computation of free plumes, starting out from non-uniform nozzle exit flow that reflects substantial viscous effects. For lack of measurements of exit flow in small nozzles, the exit plane flow is approximated by introducing a Power Law Interpolation (PLI) between the exit plane center and lip values. Exit plane flow variables thus approximated, are Mach number, pressure, flow angle and stagnation temperature. This choice is guided by gasdynamic considerations of exhaust flow from small nozzles into vacuum. The PLI is adjusted so as to obtain a match between computations and measurements at intermediate range from the nozzle. Computed plumes were found to be in good agreement with five different sets of small plume experiments. Comparative computations were performed using two alternate methods: the Boynton-Simons point-source approximation, and SIMA computation that started out from a uniform exit flow. It is demonstrated that for small nozzles having an exit flow dominated by viscous effects, the combined SIMA/PLI computational method is reasonably accurate and is dearly superior to either of the two alternate methods. 14 refs.

Computation of concentration distribution in natural streams

A unified approach has been presented for the computation of concentration distributions in streams. Starting from the Cartesian-coordinates equation governing mass transport in a stream of constant width, the equation describing mass transport in a stream of variable width can be obtained using transformed coordinates. For these coordinates the solution domain is rectangular. Due to the mathematical similarity between the two equations, a common numerical discretization procedure can be employed. The procedure is based on the use of the control volume approach and the power-law interpolation scheme between nodes. The resulting computer program was used for computation of the transverse mixing coefficient in a riverine reach.

X-ray and gamma-ray upper limits for pulsed emission from radio pulsars

Results are given for an HEAO 1 search for pulsed emissions from 11 radio pulsars, in the 15 keV-11 MeV energy range. The upper limits of the Vela pulsar are found to fall below the low-energy extrapolation of the more than 50 MeV pulsed spectrum observed by the COS B satellite, and while consistent with predictions of a polar cap acceleration model, seem barely consistent with a single power-law interpolation between optical intensity and the 50 MeV intensity. High energy X-ray upper limits for seven of the ten other pulsars, which were chosen on the basis of proximity to earth, high rotational energy loss rates and short periods, are found to be only a few percent of their rotational energy losses, assuming a moment of inertia, an emission solid angle, and a pulse duty cycle, that are all similar to the high energy X-ray duty cycle of the Crab pulsar. These upper limits are below the corresponding fraction for the Crab pulsar in the cases of the Vela pulsar, PSR 1929+10 and PSR 1642-03.