Modeling asteroid collisions and impact processes

As a complement to experimental and theoretical approaches, numerical modeling has become an important component to study asteroid collisions and impact processes. In the last decade, there have been significant advances in both computational resources and numerical methods. We discuss the present state-of-the-art numerical methods and material models used in "shock physics codes" to simulate impacts and collisions and give some examples of those codes. Finally, recent modeling studies are presented, focussing on the effects of various material properties and target structures on the outcome of a collision.Comment: Chapter to appear in the Space Science Series Book: Asteroids IV. Includes minor correction

P/2010 A2 LINEAR II: dynamical dust modelling

P/2010 A2 is an object on an asteroidal orbit that was observed to have an extended tail or debris trail in January 2010. In this work, we fit the outburst of P/2010 A2 with a conical burst model, and verify previous suspicions that this was a one--time collisional event rather than an sustained cometary outburst, implying that P/2010 A2 is not a new Main Belt Comet driven by ice sublimation. We find that the best--fit cone opening angle is about 40 to 50 degrees, in agreement with numerical and laboratory simulations of cratering events. Mapping debris orbits to sky positions suggests that the distinctive arc features in the debris correspond to the same debris cone inferred from the extended dust. From the velocity of the debris, and from the presence of a velocity maximum at around 15 cm/s, we infer that the surface of A2 probably has a very low strength (<1 kPa), comparable to lunar regolith.Comment: 14 pages, 25 figures; accepted by Astronomy and Astrophysic

Impact crater scaling laws

Impact craters are numerous on planetary bodies and furnish important information about the composition and past histories of those bodies. The interpretation of that information requires knowledge about the fundamental aspects of impact cratering mechanics. Since the typical conditions of impacts are at a size scale and velocity far in excess of experimental capabilities, direct simulations are precluded. Therefore, one must rely on extrapolation from experiments of relatively slow impacts of very small bodies, using physically based scaling laws, or must study the actual cases of interest using numerical code solutions of the fundamental physical laws that govern these processes. A progress report is presented on research on impact cratering scaling laws, on numerical studies that were designed to investigate those laws, and on various applications of the scaling laws developed by the author and his colleagues. These applications are briefly reviewed

Outline of a Decision Support System for Area-Wide Water Quality Planning

This working paper outlines requirements for an implementation of a computerized decision support system which addresses the technical aspects of area-wide water quality planning. The framework for this work is in the context of the environmental law adopted in the United States during 1972. This law, known as the Federal Water Pollution Control Act Amendments of 1972, specifies various requirements that both municipal and industrial discharges must eventually conform. By 1977 municipal waste treatment plants must have in place secondary treatment facilities and for industry it is necessary to utilize what is referred to as "best practical technology" for waste treatment. Under certain circumstances as described in section 303 of the law further treatment may be required to meet water quality standards. Section 208 of the Federal Water Pollution Control Act Amendments of 1972 calls for area-wide implementation of technical and management planning, with the objectives of meeting 1983 water quality goals and establishing a plan for municipal and industrial facilities construction over a twenty year period. Emphasis is placed on locally controlled planning, on dealing with non-point sources as well as point sources, and on consideration of both structural and nonstructural control methods. The scope of present examination is limited to those aspects of technical planning which are amenable to implementation within the framework of a computerized decision support system

Antecedents and Outcomes of the Flow Experience: An Empirical Study in the Context of Online Gaming

This study uses flow theory and the technology acceptance model (TAM) to provide new insight into the impact of enjoyment, one important dimension of flow, on user satisfaction, user beliefs, and behavioral intention to use. In addition, based on the propositions that knowledge results in an increased ability for activity and that flow is an emotional state of activity, this paper adopts a process view of knowledge to examine the role of knowledge in predicting enjoyment. The foregoing concepts are represented in a nomological network of enjoyment. Associated hypotheses are tested by using questionnaire responses of 253 online game players

Energy coupling in catastrophic collisions

The prediction of events leading to the catastrophic collisions and disruption of solar system bodies is fraught with the same difficulties as are other theories of impact events; since one simply cannot perform experiments in the regime of interest. In the catastrophic collisions of asteroids that regime involves bodies of a few tons to hundred of kilometers in diameter, and velocities of several kilometers pre second. For hundred kilometer bodies, gravitational stresses dominate material fracture strengths, but those gravitational stresses are essentially absent for laboratory experiments. Only numerical simulations using hydrocodes can in principle analyze the true problems, but they have their own major uncertainties about the correctness of the physical models and properties. The question of the measure of the impactor and its energy coupling is investigated using numerical code calculations. The material model was that of a generic silicate rock, including high pressure melt and vapor phases, and includes material nonlinearity and dissipation via a Mie-Gruniesen model. A series of calculations with various size ratios and impact velocities are reported

Nonadiabatic extension of the Heisenberg model

The localized states within the Heisenberg model of magnetism should be represented by best localized Wannier functions forming a unitary transformation of the Bloch functions of the narrowest partly filled energy bands in the metals. However, as a consequence of degeneracies between the energy bands near the Fermi level, in any metal these Wannier functions cannot be chosen symmetry-adapted to the complete paramagnetic group M^P. Therefore, it is proposed to use Wannier functions with the reduced symmetry of a magnetic subgroup M of M^P [case (a)] or spin dependent Wannier functions [case (b)]. The original Heisenberg model is reinterpreted in order to understand the pronounced symmetry of these Wannier functions. While the original model assumes that there is exactly one electron at each atom, the extended model postulates that in narrow bands there are as many as possible atoms occupied by exactly one electron. However, this state with the highest possible atomiclike character cannot be described within the adiabatic (or Born-Oppenheimer) approximation because in the (true) nonadiabatic system the electrons move on localized orbitals that are still symmetric on the average of time, but not at any moment. The nonadiabatic states have the same symmetry as the adiabatic states and determine the commutation properties of the nonadiabatic Hamiltonian H^n. The nonadiabatic Heisenberg model is a purely group- theoretical model which interprets the commutation properties of H^n that are explicitly given in this paper for the two important cases (a) and (b). There is evidence that the occurrence of these two types of Wannier functions in the band structure of a metal is connected with the occurrence of magnetism and superconductivity, respectively

Projectile-shape dependence of impact craters in loose granular media

We report on the penetration of cylindrical projectiles dropped from rest into a dry, noncohesive granular medium. The cylinder length, diameter, density, and tip shape are all explicitly varied. For deep penetrations, as compared to the cylinder diameter, the data collapse onto a single scaling law that varies as the 1/3 power of the total drop distance, the 1/2 power of cylinder length, and the 1/6 power of cylinder diameter. For shallow penetrations, the projectile shape plays a crucial role with sharper objects penetrating deeper.Comment: 3 pages, 3 figures; experimen

Impactor flux and cratering on Ceres and Vesta: Implications for the early Solar System

We study the impactor flux and cratering on Ceres and Vesta caused by the collisional and dynamical evolution of the asteroid Main Belt. We develop a statistical code based on a well-tested model for the simultaneous evolution of the Main Belt and NEA size distributions. This code includes catastrophic collisions and noncollisional removal processes such as the Yarkovsky effect and the orbital resonances. The model assumes that the dynamical depletion of the early Main Belt was very strong, and owing to that, most Main Belt comminution occurred when its dynamical structure was similar to the present one. Our results indicate that the number of D > 1 km Main Belt asteroids striking Ceres and Vesta over the Solar System history are approximately 4 600 and 1 100 respectively. The largest Main Belt asteroids expected to have impacted Ceres and Vesta had diameters of 71.7 km and 21.1 km. The number of D > 0.1 km craters on Ceres is \sim 3.4 \times 10^8 and 6.2 \times 10^7 on Vesta. The number of craters with D > 100 km are 47 on Ceres and 8 on Vesta. Our study indicates that the D = 460 km crater observed on Vesta had to be formed by the impact of a D \sim 66.2 km projectile, which has a probability of occurr \sim 30% over the Solar System history. If significant discrepancies between our results about the cratering on Ceres and Vesta and data obtained from the Dawn Mission were found, they should be linked to a higher degree of collisional evolution during the early Main Belt and/or the existence of the late heavy bombardment. An increase in the collisional activity in the early phase may be provided for an initial configuration of the giant planets consistent with, for example, the Nice model. From this, the Dawn Mission would be able to give us clues about the initial configuration of the early Solar System and its subsequent dynamical evolution.Comment: Accepted for publication in Astronomy and Astrophysic

Wind tunnel investigation of supersonic wing-tail flutter

A flutter model, consisting of a wing, horizontal tail, and splitter plate/fuselage mechanism, was tested in a 4-foot transonic tunnel in the Mach number range 1.1 to 1.3. Two types of flutter were encountered during the testing: a wing-tail flutter bending-torsion flutter mode. The wing-tail flutter speed was found to be a minimum at M = 1.2 for the configuration tested. Recorded model test data were digitized for a power spectral density (PSD) analysis and Random Decrement (Randomdec) analysis. Comparisons between the frequency and damping obtained from the PSD plots and the Randomdec signatures agreed very well. A limited flutter analysis was conducted using a Mach box unsteady aerodynamics method which accounted for interference and airfoil thickness. Analytical comparisons with experimental flutter speeds agreed well. The analyses assuming zero thickness predicted flutter speeds higher than those measured, ranging from 1 percent at M = 1.12 to 8 percent at M = 1.28. With the airfoil thickness included, the correlation was improved such that predicted flutter speeds for all cases investigated were within 2 percent of experimental speeds