Numerical Verification of Affine Systems with up to a Billion Dimensions

Affine systems reachability is the basis of many verification methods. With further computation, methods exist to reason about richer models with inputs, nonlinear differential equations, and hybrid dynamics. As such, the scalability of affine systems verification is a prerequisite to scalable analysis for more complex systems. In this paper, we improve the scalability of affine systems verification, in terms of the number of dimensions (variables) in the system. The reachable states of affine systems can be written in terms of the matrix exponential, and safety checking can be performed at specific time steps with linear programming. Unfortunately, for large systems with many state variables, this direct approach requires an intractable amount of memory while using an intractable amount of computation time. We overcome these challenges by combining several methods that leverage common problem structure. Memory is reduced by exploiting initial states that are not full-dimensional and safety properties (outputs) over a few linear projections of the state variables. Computation time is saved by using numerical simulations to compute only projections of the matrix exponential relevant for the verification problem. Since large systems often have sparse dynamics, we use Krylov-subspace simulation approaches based on the Arnoldi or Lanczos iterations. Our method produces accurate counter-examples when properties are violated and, in the extreme case with sufficient problem structure, can analyze a system with one billion real-valued state variables

Exploring the Formation of Resistive Pseudodisks with the GPU Code Astaroth

Pseudodisks are dense structures formed perpendicular to the direction of the magnetic field during the gravitational collapse of a molecular cloud core. Numerical simulations of the formation of pseudodisks are usually computationally expensive with conventional CPU codes. To demonstrate the proof-of-concept of a fast computing method for this numerically costly problem, we explore the GPU-powered MHD code Astaroth, a 6th-order finite difference method with low adjustable finite resistivity implemented with sink particles. The formation of pseudodisks is physically and numerically robust and can be achieved with a simple and clean setup for this newly adopted numerical approach for science verification. The method's potential is illustrated by evidencing the dependence on the initial magnetic field strength of specific physical features accompanying the formation of pseudodisks, e.g. the occurrence of infall shocks and the variable behavior of the mass and magnetic flux accreted on the central object. As a performance test, we measure both weak and strong scaling of our implementation to find most efficient way to use the code on a multi-GPU system. Once suitable physics and problem-specific implementations are realized, the GPU-accelerated code is an efficient option for 3-D magnetized collapse problems.Comment: 29 pages, 1 table, 15 figures, Accepted for publication in the Astrophysical Journa

FOULING AND ITS MITIGATION ON HEAT EXCHANGER SURFACES BY ADDITIVES AND CATALYTIC MATERIALS

Calcium carbonate (CaCO3) fouling is the most commonly observed fouling phenomenon in cooling water applications. Fouling happens when a process uses cooling water supersaturated with mineral salt crystals (i.e. hard water). Precipitation deposits on heat transfer surfaces whenever these inversely-soluble salt crystals, like dissolved calcium ions, are exposed to high temperature. An online-monitoring system for fouling phenomena was studied experimentally using a mixture of sodium bicarbonate and calcium chloride for carbonate fouling salt in de-ionized water. The effects of different parameters such as surface temperature, flow velocity, and concentration on the calcium carbonate scale formation process were experimentally investigated by using the developed monitoring system. The calcium carbonate deposition rates on five different metal surfaces (Stainless steel 316, brass, copper, aluminum and carbon steel) were investigated. The surface was analyzed by analytical microscopy to investigate the morphology of the deposit layer. The results revealed that SS316 yielded the lowest deposition on the surface. Nowadays, hazardous chemical additives are often used to mitigate fouling but chemicals are expensive and pose problems to the environment. Physical water treatment (PWT), a non-chemical method is good alternative for fouling mitigation method. PWT using zinc and tourmaline as catalytic materials is presented in this research work. Fouling tests were conducted for verification of this PWT method. Artificially-hardened water at 300 mgL-1 was utilized as the fluid medium to form fouling deposits. The hard water flow velocities were varied from 0.15 ms-1 to 0.45 ms-1 and the artificially-hardened water temperature was maintained at 25 oC and the experimental time was set to 72 hours for each run. The results revealed that in the PWT-treatment case, the deposition of calcium carbonate particle is lower compared to those in the No-treatment case. Furthermore, mitigation of calcium carbonate fouling by applying EDTA, EDTA-MWCNT and DTPA-MWCNT-based water nanofluids on heat exchanger surfaces were reported. Investigation of additive (benign to the environment) on the fouling rate of deposition was performed. Assessment of the deposition of calcium carbonate on the heat exchanger surfaces with respect to the inhibition of crystal growth was conducted by Scanning Electron Microscope (SEM). The results showed that the formation of calcium carbonate crystals can be retarded significantly by adding MWCNT-DTPA additives as inhibition in the solution. Moreover, investigation was extended by introducing a non-invasive-monitoring of concentrations of calcium hardness in cooling water. Investigation was conducted with a 2.5 GHz microwave cavity resonator. The principle of electric dipole moment theories were used to analyse the sample solution that occurs as a function of calcium ion content. The sample was centrally positioned in the electric field of the TM010 mode of a resonant cylindrical cavity. COMSOL simulation package was used to compare and validate the experimental cavity resonator frequency. Transmission signal (S21) measurements via Vector Network Analyser (VNA) with different concentrations were investigated and observed linear relationship in amplitude with frequency changes. These research successfully introduce a novel technique of monitoring of water hardness concentration by using non-invasive microwave sensor

Analysis and Simulation of Hypervelocity Gouging Impacts

In this work, a summary of past and present research efforts, as well as the theoretical foundation, of hypervelocity gouging is presented. As the Holloman AFB High Speed Test Track (HHSTT) sled\u27s speed has increased to Mach 8.5, material interactions develops which causes gouging - this can result in catastrophic failure. A characterization of gouging, including a thermodynamic history, is developed from an examination of a gouged rail. An extensive study is performed that determines the specific material flow models for VascoMax 300 and 1080 steel. The models are validated utilizing several experimental tests which are successfully simulated using CTH - a state-of-the-art shock wave physics hydrocode. Additionally, a penetration theory is developed which provides insight into the gouging problem using an analytic approach that does not require the use of computationally intensive codes. Based on the detailed examination of the materials and the validation of the material models within CTH, an evaluation of the HHSTT gouging phenomenon is performed. These simulations of the gouging problem replicate the experimentally observed characteristics and lead to recommendations to mitigate the occurrence of hypervelocity gouging

National Aeronautics and Space Administration (NASA)/American Society for Engineering Education (ASEE) Summer Faculty Fellowship Program, 1994, volume 1

The JSC NASA/ASEE Summer Faculty Fellowship Program was conducted by Texas A&M University and JSC. The objectives of the program, which began nationally in 1964 and at JSC in 1965 are to: (1) further the professional knowledge of qualified engineering and science faculty members, (2) stimulate an exchange of ideas between participants and NASA, (3) enrich and refresh the research and teaching activities of participants' institutions, and (4) contribute to the research objectives of the NASA centers. Each faculty fellow spent at least 10 weeks at JSC engaged in a research project in collaboration with a NASA JSC colleague. This document is a compilation of the final reports on the research projects completed by the faculty fellows during the summer of 1994