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At least 181 records · Page 10

The scaling of secondary craters

Secondary craters are common features around fresh planetary-scale primary impact craters throughout most of the Solar System. They derive from the ejection phase of crater formation, thus secondary scaling relations provide constraints on parameters affecting ejection processes. Secondary crater fields typically begin at the edge of the continuous ejecta blankets (CEB) and extend out several crater radii. Secondaries tend to have rounded rims and bilateral symmetry about an axis through the primary crater's center. Prominent secondary chains can extend inward across the CEB close to the rim. A simple method for comparing secondary crater fields was employed: averaging the diameters and ranges from the center of the primary crater of the five largest craters in a secondary crater field. While not as much information is obtained about individual crater fields by this method as in more complete secondary field mapping, it facilitates rapid comparison of many secondary fields. Also, by quantifying a few specific aspects of the secondary crater field, this method can be used to construct scaling relations for secondary craters.

Croft, Steven K.↗

Effective constitutive relations for the microstructure of periodic frames

Effective micro-structure properties of two-dimensional large repetitive frame-like structures are derived using straightforward combinations of energy methods of linear transformations. Once the actual structure is identified symmetry considerations are used in order to identify its independent property constants. The actual values of these constants are constructed according to a building block format which is carried out in the three consecutive steps: (1) all basic planar lattices are identified, (2) effective continuum properties are derived for each of these planar basic grids using energy methods, and (3) orthogonal transformations are finally used to determine the contribution of each basic set to the overall effective continuum properties of the structure.

Nayfeh, A. H.↗

On thick domain walls in general relativity

Planar scalar field configurations in general relativity differ considerably from those in flat space. It is shown that static domain walls of finite thickness in curved space-time do not possess a reflection symmetry. At infinity, the space-time tends to the Taub vacuum on one side of the wall and to the Minkowski vacuum (Rindler space-time) on the other. Massive test particles are always accelerated towards the Minkowski side, i.e., domain walls are attractive on the Taub side, but repulsive on the Minkowski side (Taub-vacuum cleaner). It is also proved that the pressure in all directions is always negative. Finally, a brief comment is made concerning the possibility of infinite, i.e., bigger than horizon size, domain walls in our universe. All of the results are independent of the form of the potential V(phi) greater than or equal to 0 of the scalar field phi.

Goetz, Guenter↗

Down-to-earth studies of carbon clusters

Recent advances in supersonic beam experiments with laser-vaporization sources of clusters have provided some interesting new insights into the nature of the small clusters of carbon, and the processes through which carbon condenses. One cluster in particular, C(sub 60), appears to play a central role. It is argued that this cluster takes the shape of a soccerball: a hollow sphere composed of a shell of 60 carbon atoms connected by a lattice of hexagonal and pentagonal rings, in a pattern of overall icosahedral symmetry. Although C(sub 60) appears to be uniquely stable due to its perfect symmetry, all other even-numbered carbon clusters in the 32 to 100+ atom size range seem to favor similar closed spheroidal forms. These species are interpreted as relatively unreactive side products in condensation reactions of carbon vapor involving spiraling graphitic sheets. The prevalence of C(sub 60) in laser-vaporized carbon vapors and sooting flames suggests that it may be formed readily whenever carbon condenses. Such ready formation and extraordinary stability may have substantial astrophysical implications.

Smalley, R. E.↗

Computation of three-dimensional turbulent boundary layers with heat transfer in a plane of symmetry using embedded wall-layer functions

In the calculation of turbulent boundary layers, a large number of mesh points are required to adequately resolve the intense variation in the velocity and enthalpy in the near-wall region. A substantial reduction in computational effort may be realized by representing the velocity and enthalpy profiles in the wall layer by analytical embedded functions. The effectively inviscid flow in the outer part of the boundary layer may then be resolved by employing a relatively coarser mesh. To obtain complete profiles, the outer numerical solution is matched asymptotically to the inner wall-layer analytical solution. To date, this approach has been restricted to two-dimensional flows; in the present study, a method which may be utilized for turbulent boundary layers with heat transfer in a plane of symmetry is developed as a first step in the application of the embedded-function method to full three-dimensional flows. The present method uses only about half as many mesh points as that required in a conventional procedure, which calculates the flow all the way to the wall, but there is no degradation in accuracy of the computed results.

Degani, A. T.↗

Solutions of some problems in applied mathematics using MACSYMA

Various Symbolic Manipulation Programs (SMP) were tested to check the functioning of their commands and suitability under various operating systems. Support systems for SMP were found to be relatively better than the one for MACSYMA. The graphics facilities for MACSYMA do not work as expected under the UNIX operating system. Not all commands for MACSYMA function as described in the manuals. Shape representation is a central issue in computer graphics and computer-aided design. Aside from appearance, there are other application dependent, desirable properties like continuity to certain order, symmetry, axis-independence, and variation-diminishing properties. Several shape representations are studied, which include the Osculatory Method, a Piecewise Cubic Polynomial Method using two different slope estimates, Piecewise Cubic Hermite Form, a method by Harry McLaughlin, and a Piecewise Bezier Method. They are applied to collected physical and chemical data. Relative merits and demerits of these methods are examined. Kinematics of a single link, non-dissipative robot arm is studied using MACSYMA. Lagranian is set-up and Lagrange's equations are derived. From there, Hamiltonian equations of motion are obtained. Equations suggest that bifurcation of solutions can occur, depending upon the value of a single parameter. Using the characteristic function W, the Hamilton-Jacobi equation is derived. It is shown that the H-J equation can be solved in closed form. Analytical solutions to the H-J equation are obtained.

Punjabi, Alkesh↗

Stiffness and strength tailoring in uniform space-filling truss structures

A deterministic procedure for tailoring the continuum stiffness and strength of uniform space-filling truss structures, through the appropriate selection of truss geometry and member sizes (flexural stiffness, axial stiffness, and length), is presented. The trusses considered herein are generated by uniform replication of a characteristic truss cell. The repeating cells are categorized by one of a set of possible geometric symmetry groups derived using crystallographic techniques. The elastic symmetry associated with each geometric symmetry group is identified to help select an appropriate truss geometry for a given application. Stiffness and strength tailoring of a given truss geometry is enabled through explicit expressions relating the continuum stiffnesses and failure stresses of the truss to the stiffnesses and failure loads of its members. These expressions are derived using an existing equivalent continuum analysis technique and a newly developed analytical failure theory for trusses. Several examples are presented to illustrate the application of these techniques and to demonstrate the usefulness of the information gained from this analysis.

Lake, Mark S.↗

Exact Integrations of Polynomials and Symmetric Quadrature Formulas over Arbitrary Polyhedral Grids

This paper is concerned with two important elements in the high-order accurate spatial discretization of finite volume equations over arbitrary grids. One element is the integration of basis functions over arbitrary domains, which is used in expressing various spatial integrals in terms of discrete unknowns. The other consists of quadrature approximations to those integrals. Only polynomial basis functions applied to polyhedral and polygonal grids are treated here. Non-triangular polygonal faces are subdivided into a union of planar triangular facets, and the resulting triangulated polyhedron is subdivided into a union of tetrahedra. The straight line segment, triangle, and tetrahedron are thus the fundamental shapes that are the building blocks for all integrations and quadrature approximations. Integrals of products up to the fifth order are derived in a unified manner for the three fundamental shapes in terms of the position vectors of vertices. Results are given both in terms of tensor products and products of Cartesian coordinates. The exact polynomial integrals are used to obtain symmetric quadrature approximations of any degree of precision up to five for arbitrary integrals over the three fundamental domains. Using a coordinate-free formulation, simple and rational procedures are developed to derive virtually all quadrature formulas, including some previously unpublished. Four symmetry groups of quadrature points are introduced to derive Gauss formulas, while their limiting forms are used to derive Lobatto formulas. Representative Gauss and Lobatto formulas are tabulated. The relative efficiency of their application to polyhedral and polygonal grids is detailed. The extension to higher degrees of precision is discussed.

Liu, Yen↗

Baryon symmetric big bang cosmology

Both the quantum theory and Einsteins theory of special relativity lead to the supposition that matter and antimatter were produced in equal quantities during the big bang. It is noted that local matter/antimatter asymmetries may be reconciled with universal symmetry by assuming (1) a slight imbalance of matter over antimatter in the early universe, annihilation, and a subsequent remainder of matter; (2) localized regions of excess for one or the other type of matter as an initial condition; and (3) an extremely dense, high temperature state with zero net baryon number; i.e., matter/antimatter symmetry. Attention is given to the third assumption, which is the simplest and the most in keeping with current knowledge of the cosmos, especially as pertains the universality of 3 K background radiation. Mechanisms of galaxy formation are discussed, whereby matter and antimatter might have collided and annihilated each other, or have coexisted (and continue to coexist) at vast distances. It is pointed out that baryon symmetric big bang cosmology could probably be proved if an antinucleus could be detected in cosmic radiation.

Stecker, F. W.↗

Constraints on the rheological structure of the mantle

Rheological models of the mantle are at present limited to radial symmetry, usually with homogeneous linearly viscous or viscoelastic incompressible layers. While such models are probably overly simple, they readily allow calculation of geophysical effects, such as post glacial rebound and related changes in the Earth's shape. They are also directly applicable to problems of global mantle flow and plate motions.

Oconnell, R. J.↗

Noninteractive macroscopic reliability model for ceramic matrix composites with orthotropic material symmetry

A macroscopic noninteractive reliability model for ceramic matrix composites is presented. The model is multiaxial and applicable to composites that can be characterized as orthotropic. Tensorial invariant theory is used to create an integrity basis with invariants that correspond to physical mechanisms related to fracture. This integrity basis is then used to construct a failure function per unit volume (or area) of material. It is assumed that the overall strength of the composite is governed by weakest link theory. This leads to a Weibull type model similar in nature to the principle of independent action (PIA) model for isotropic monolithic ceramics. An experimental program to obtain model parameters is briefly discussed. In addition, qualitative features of the model are illustrated by presenting reliability surfaces for various model parameters.

Duffy, Stephen F.↗

Noninteractive macroscopic reliability model for ceramic matrix composites with orthotropic material symmetry

A macroscopic noninteractive reliability model for ceramic matrix composites is presented. The model is multiaxial and applicable to composites that can be characterized as orthotropic. Tensorial invariant theory is used to create an integrity basis with invariants that correspond to physical mechanisms related to fracture. This integrity basis is then used to construct a failure function per unit volume (or area) of material. It is assumed that the overall strength of the composite is governed by weakest link theory. This leads to a Weibull type model similar in nature to the principle of independent action (PIA) model for isotropic monolithic ceramics. An experimental program to obtain model parameters is briefly discussed. In addition, qualitative features of the model are illustrated by presenting reliability surfaces for various model parameters.

Duffy, Stephen F.↗

Helicity fluctuations and turbulent energy production in rotating and non-rotating pipes

Finite-difference second-order accurate direct simulation of a turbulent pipe has been used to investigate how the turbulence production and dissipation change when a solid body rotation is applied. It is shown that when the helicity increases, the dissipation is reduced. It is asserted that to have a drag reduction the external action should be such as to disrupt the symmetry of right- and left-handed helical structures. In this study the Navier-Stokes equations in rotational form permit the turbulent energy production to be split into a part related to the energy cascade from large to small scales and into a part related to the convection by large scales. The full simulation data have shown the latter is greater than the former in the wall region and that, on the contrary, these two terms balance each other in the central region. From the pdf of the former, it has been shown how the vortical structures are changed in the wall region by the background radiation and how they are related to the changes in the energy production.

Orlandi, P.↗

Shape Parameter for a Non-Axisymmetric Isothermal Dendrite

In previous work, we found approximate solutions for paraboloids having perturbations with four-fold axial symmetry in order to model dendritic growth in cubic materials. These solutions provide self-consistent corrections through second order in a shape parameter e to the Peclet number-supercooling relation of the Ivantsov solution. The parameter e is proportional to the amplitude of the four-fold correction to the dendrite shape, as measured from the Ivantsov paraboloid of revolution. We calculate e by comparing the dendrite tip shape to the portion of the equilibrium shape near the growth direction, (001), for anisotropic surface free energy, where the ni are components of the unit normal of the crystal surface. This comparison results in epsilon = -2(epsilon 4), independent of the Peclet number. From the experimental value of epsilon 4, we find epsilon approximately 0.011, in good agreement with the measured value epsilon approximately 0.008 of LaCombe et al.

McFadden, G. B.↗

Assimilation of SMAP Observations Over Land Improves the Simulation and Prediction of Tropical Cyclone Idai

This work is focused on the role of soil moisture in the prediction of tropical cyclones (TCs) approaching land and after landfall. Soil moisture conditions can impact the circulation and structure of an existing tropical cyclone (TC) when part or all of the circulation is over land. For example, dry land surface conditions may lead to faster dissipation of a TC over land (often associated with changes in precipitation structure), whereas very wet conditions may help sustain or in rare cases re-intensify a TC. Moreover, the presence of strong soil moisture gradients may affect the symmetry and development of the TC circulation leading to changes in its over-land track. While the link between soil moisture conditions and TC evolution in proximity to land is relatively well understood in theory, applications of these findings in the context of numerical weather prediction (NWP) have been limited. Here we present a case study that explores the potential of improving TC predictions through an improved soil moisture initialization in an NWP framework. Specifically, we examine the impact of assimilating observations from the NASA Soil Moisture Active Passive (SMAP) mission into the NASA Goddard Earth Observing System (GEOS) global weather model on the prediction of South-West Indian Ocean TC Idai (2019). SMAP provides accurate L-band (1.4 GHz) brightness temperatures (Tb) observations that are sensitive to soil moisture globally and at high revisit times of 2-3 days. It has previously been shown that the assimilation of SMAP Tb observations significantly improves modeled land surface states. Thus, it is expected that SMAP can be used to constrain land surface initial conditions and potentially benefit TC forecasts. Here we present two sets of retrospective forecasts of TC Idai that are compared in an Observing System Experiment framework at ¼ degree resolution: (i) forecasts initialized from an analysis that is comparable to the GEOS operational analysis (without SMAP Tb assimilation) and (ii) forecasts initialized from an analysis that additionally assimilates SMAP brightness temperature observations over land using a weakly-coupled land analysis. We find that the assimilation of SMAP meaningfully improves the representation of TC Idai’s structure as well as the prediction of its intensity and track. The analyzed TC size, as measured by the wind speed radius, is improved by up to 18% in the analysis with SMAP assimilation relative to the control run. The forecast intensity error, measured against the observed intensity, is reduced by up to 23%. At the 1/4-degree resolution used here, GEOS unavoidably under-estimates TC intensity and over-estimates TC size. The SMAP assimilation therefore corrects the model in the right direction, leading to a storm that is more energetic and more compact. Furthermore, we find that the along-track forecast error is reduced by up to 34%, indicating a more accurate propagation speed, which is consistent with the fact that TC speed over land is strongly affected by surface processes. The impact of SMAP assimilation on the forecast cross-track error is neutral. Across the TC forecast skill metrics used here, the improvements from SMAP DA are largest at lead times of 36 to 72 hours, suggesting that the predictability of forecasts at shorter lead times may be dominated by short-term convective processes, while the land and its longer memory gains in importance as a source of predictability on a 2-3 day timescale. We further investigated the underlying mechanisms leading to the skill improvements from SMAP data assimilation by isolating the land areas that directly influence TC Idai using a back trajectory analysis. We find that the assimilation of SMAP leads to wetter soil moisture conditions that cause an increased latent heat flux, which ultimately results in TC analyzed representation that has higher column-integrated total moisture content and total energy compared to the analysis in the control run without SMAP assimilation. Overall, the results highlight that the assimilation of SMAP observations into a global numerical weather prediction model can lead to pronounced improvements of TC predictions. This is a crucial step towards a better mitigation of the socio-economic impact of landfalling TCs and thus safeguarding human lives. Finally, our study presents an event-based approach that assesses the impact of land data assimilation for a particular weather event rather than by globally averaging differences in skill. We argue that global skill assessments – while necessary – can mute the impact of land data assimilation, because the land’s influence on the atmosphere is constrained to certain locations and certain times. Instead, the event-based approach better highlights the true potential of land data assimilation in the context of NWP, especially for extreme events when accurate predictions are critical.

Jana Kolassa↗

Assimilation of SMAP Observations Over Land Improves the Simulation and Prediction of Tropical Cyclone Idai

This work is focused on the role of soil moisture in the prediction of tropical cyclones (TCs) approaching land and after landfall. Soil moisture conditions can impact the circulation and structure of an existing tropical cyclone (TC) when part or all of the circulation is over land. For example, dry land surface conditions may lead to faster dissipation of a TC over land (often associated with changes in precipitation structure), whereas very wet conditions may help sustain or in rare cases re-intensify a TC. Moreover, the presence of strong soil moisture gradients may affect the symmetry and development of the TC circulation leading to changes in its over-land track. While the link between soil moisture conditions and TC evolution in proximity to land is relatively well understood in theory, applications of these findings in the context of numerical weather prediction (NWP) have been limited. Here we present a case study that explores the potential of improving TC predictions through an improved soil moisture initialization in an NWP framework. Specifically, we examine the impact of assimilating observations from the NASA Soil Moisture Active Passive (SMAP) mission into the NASA Goddard Earth Observing System (GEOS) global weather model on the prediction of South-West Indian Ocean TC Idai (2019). SMAP provides accurate L-band (1.4 GHz) brightness temperatures (Tb) observations that are sensitive to soil moisture globally and at high revisit times of 2-3 days. It has previously been shown that the assimilation of SMAP Tb observations significantly improves modeled land surface states. Thus, it is expected that SMAP can be used to constrain land surface initial conditions and potentially benefit TC forecasts. Here we present two sets of retrospective forecasts of TC Idai that are compared in an Observing System Experiment framework at ¼ degree resolution: (i) forecasts initialized from an analysis that is comparable to the GEOS operational analysis (without SMAP Tb assimilation) and (ii) forecasts initialized from an analysis that additionally assimilates SMAP brightness temperature observations over land using a weakly-coupled land analysis. We find that the assimilation of SMAP meaningfully improves the representation of TC Idai’s structure as well as the prediction of its intensity and track. The analyzed TC size, as measured by the wind speed radius, is improved by up to 18% in the analysis with SMAP assimilation relative to the control run. The forecast intensity error, measured against the observed intensity, is reduced by up to 23%. At the 1/4-degree resolution used here, GEOS unavoidably under-estimates TC intensity and over-estimates TC size. The SMAP assimilation therefore corrects the model in the right direction, leading to a storm that is more energetic and more compact. Furthermore, we find that the along-track forecast error is reduced by up to 34%, indicating a more accurate propagation speed, which is consistent with the fact that TC speed over land is strongly affected by surface processes. The impact of SMAP assimilation on the forecast cross-track error is neutral. Across the TC forecast skill metrics used here, the improvements from SMAP DA are largest at lead times of 36 to 72 hours, suggesting that the predictability of forecasts at shorter lead times may be dominated by short-term convective processes, while the land and its longer memory gains in importance as a source of predictability on a 2-3 day timescale. We further investigated the underlying mechanisms leading to the skill improvements from SMAP data assimilation by isolating the land areas that directly influence TC Idai using a back trajectory analysis. We find that the assimilation of SMAP leads to wetter soil moisture conditions that cause an increased latent heat flux, which ultimately results in TC analyzed representation that has higher column-integrated total moisture content and total energy compared to the analysis in the control run without SMAP assimilation. Overall, the results highlight that the assimilation of SMAP observations into a global numerical weather prediction model can lead to pronounced improvements of TC predictions. This is a crucial step towards a better mitigation of the socio-economic impact of landfalling TCs and thus safeguarding human lives. Finally, our study presents an event-based approach that assesses the impact of land data assimilation for a particular weather event rather than by globally averaging differences in skill. We argue that global skill assessments – while necessary – can mute the impact of land data assimilation, because the land’s influence on the atmosphere is constrained to certain locations and certain times. Instead, the event-based approach better highlights the true potential of land data assimilation in the context of NWP, especially for extreme events when accurate predictions are critical.

Jana Kolassa↗

Video-Camera-Based Position-Measuring System

A prototype optoelectronic system measures the three-dimensional relative coordinates of objects of interest or of targets affixed to objects of interest in a workspace. The system includes a charge-coupled-device video camera mounted in a known position and orientation in the workspace, a frame grabber, and a personal computer running image-data-processing software. Relative to conventional optical surveying equipment, this system can be built and operated at much lower cost; however, it is less accurate. It is also much easier to operate than are conventional instrumentation systems. In addition, there is no need to establish a coordinate system through cooperative action by a team of surveyors. The system operates in real time at around 30 frames per second (limited mostly by the frame rate of the camera). It continuously tracks targets as long as they remain in the field of the camera. In this respect, it emulates more expensive, elaborate laser tracking equipment that costs of the order of 100 times as much. Unlike laser tracking equipment, this system does not pose a hazard of laser exposure. Images acquired by the camera are digitized and processed to extract all valid targets in the field of view. The three-dimensional coordinates (x, y, and z) of each target are computed from the pixel coordinates of the targets in the images to accuracy of the order of millimeters over distances of the orders of meters. The system was originally intended specifically for real-time position measurement of payload transfers from payload canisters into the payload bay of the Space Shuttle Orbiters (see Figure 1). The system may be easily adapted to other applications that involve similar coordinate-measuring requirements. Examples of such applications include manufacturing, construction, preliminary approximate land surveying, and aerial surveying. For some applications with rectangular symmetry, it is feasible and desirable to attach a target composed of black and white squares to an object of interest (see Figure 2). For other situations, where circular symmetry is more desirable, circular targets also can be created. Such a target can readily be generated and modified by use of commercially available software and printed by use of a standard office printer. All three relative coordinates (x, y, and z) of each target can be determined by processing the video image of the target. Because of the unique design of corresponding image-processing filters and targets, the vision-based position- measurement system is extremely robust and tolerant of widely varying fields of view, lighting conditions, and varying background imagery.

Lane, John↗

Stiffness and strength tailoring in uniform space-filling truss structures

This paper presents a deterministic procedure for tailoring the continuum stiffness and strength of uniform space-filling truss structures through the appropriate selection of truss geometry and member sizes (i.e., flexural and axial stiffnesses and length). The trusses considered herein are generated by replication of a characteristic truss cell uniformly through space. The repeating cells are categorized by one of a set of possible geometric symmetry groups derived using the techniques of crystallography. The elastic symmetry associated with each geometric symmetry group is identified to aid in the selection of an appropriate truss geometry for a given application. Stiffness and strength tailoring of a given truss geometry is enabled through explicit expressions relating the continuum stiffnesses and failure stresses of the truss to the stiffnesses and failure loads of its members. These expressions are derived using an existing equivalent continuum analysis technique and a newly developed analytical failure theory for trusses. Several examples are presented to illustrate the application of these techniques, and to demonstrate the usefulness of the information gained from this analysis.

Lake, Mark S.↗