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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 163 records · Page 9

Fermi LAT Observations of the Crab Nebula During the Exceptional April 2011 Outburst

The Crab Nebula, formerly thought to be steady in gamma rays, shows unexpected and occasionally dramatic variability in high-energy gamma rays. The Large Area Telescope (LAT) on Fermi recorded several strong outbursts, including dedicated pointed observations of the brightest yet seen, a spectacular flare in April 2011. These observations provide a particularly detailed look at the temporal and spectral characteristics of the nebula during the flare. The LAT data show an additional component in the spectral energy distribution that peaks at a maximum of $375\pm26~\mathrm{MeV}$. In the probable scenario that this component is synchrotron emission, the electrons are accelerated to extreme energies that are difficult to reconcile with the very rapid change in flux and the expectation for acceleration processes and conditions occurring within the pulsar wind nebula. The physical location and mechanism driving the flares remains undetermined despite observations across the spectrum made by a variety of instruments including the Hubble Space Telescope, the Chandra X-ray Observatory, and the Very Large Array. I will present timing and spectral studies of the high-energy gamma-ray data, discuss implications for the origin of the flares, and highlight preparations for the next major flare.

Hays, Elizabeth↗

Acquisition and Early Losses of Rare Gases from the Deep Earth

Direct observations show that the deep Earth contains rare gases of solar composition distinct from those in the atmosphere. We examine the implications of mantle rare gas characteristics on acquisition of rare gases from the solar nebula and subsequent losses due to a large impact. Deep mantle rare gas concentrations and isotopic compositions can be obtained from a model of transport and distribution of mantle rare gases. This model assumes the lower mantle closed early, while the upper mantle is open to subduction from the atmosphere and mass transfer from the lower mantle. Constraints are derived that can be incorporated into models for terrestrial volatile acquisition: (1) Calculated lower-mantle Xe-isotopic ratios indicate that the fraction of radiogenic Xe produced by I-129 and Pu-244 during the first about 10(exp 8) yr was lost, a conclusion also drawn for atmospheric Xe. Thus, either the Earth was made from materials that had lost >99% of rare gases about (0.7-2) x 10(exp 8) yr after the solar system formed, or gases were then lost from the fully formed Earth. (2) Concentrations of 3He and 20Ne in the lower mantle were established after these losses. (3) Neon-isotopic data indicates that mantle Ne has solar composition. The model allows for solar Ar/Ne and Xe/Ne in the lower mantle if a dominant fraction of upper mantle Ar and Xe are subduction-derived. If Earth formed in the presence of the solar nebula, it could have been melted by accretional energy and the blanketing effect of a massive, nebula-derived atmosphere. Gases from this atmosphere would have been sequestered within the molten Earth by dissolution at the surface and downward mixing. It was found that too much Ne would be dissolved in the Earth unless the atmosphere began to escape when the Earth was only partially assembled. Here we consider conditions required to initially dissolve sufficient rare gases to account for the present lower mantle concentrations after subsequent losses at 10(exp 8) yr. It is assumed that equilibration of the atmosphere with a thoroughly molten mantle was rapid, so that initial abundances of gases retained in any mantle layer reflected surface conditions when the layer solidified. For subsequent gas loss of 99.5% and typical solubility coefficients, a total pressure of 100 atm was required for an atmosphere of solar composition. Calculations of the pressure at the base of a primordial atmosphere indicate that this value might be exceeded by an order of magnitude or more for an atmosphere supported by accretional energy. Surface temperatures of about 4000 K would have been produced, probably high enough to melt the deep mantle. Initial distributions of retained rare gases would then be determined by the history of surface pressure and temperature during mantle cooling and solidification, i.e., the coupled cooling of Earth and atmosphere. The Earth's thermal state was determined by its surface temperature and the efficiency of convection in the molten mantle, estimated to be sufficient to maintain an adiabatic gradient. Because the melting curve is steeper than the adiabat, solidification of the mantle proceeded outward from the interior. Incorporation of atmospheric gases in the mantle therefore occurred over a range in surface temperature of a few thousand degrees Kelvin. The thermal state of the atmosphere was controlled by total luminosity of the Earth (energy) released by accreting planetesimals and the cooling Earth), nebular temperature and pressure, and atmospheric opacity. The energy released by accretion declined with time as did nebular pressure. Analytical solutions for an idealized (constant opacity radiative atmosphere show that declining energy sources under constant nebular conditions result in slowly diminishing surface temperature but dramatically increasing surface pressure. For such an atmosphere with declining nebular pressure but constant total luminosity, surface pressure decreases gradually with decreasing temperaure. A decline in accretion luminosity might be compensated by energy released as the mantle cools for about 10(exp 5) year, after which luminosity must decline. The total complement of dissolved rare gases will depend on the particular evolutionary path determined by the declining accretional luminosity, the Earth thermal history, removal of the nebula, and opacity variations of the atmosphere. Models for these coupled evolutionary histories for Earth's acquisition of nebular-derived noble gases are in progress. The later losses required at about 10(exp 8) yr (depleting the interior concentrations of the sequestered solar gases by a factor of > 100) were presumably related to the major impact in which the Moon formed.

Porcelli, D.↗

Investigation of the Stability of Very Flat Spins and Analysis of Effects of Applying various Moments Utilizing the Three Moment Equations of Motion

Based on linearized equations of motion utilizing only the three moment equations and assuming only flat-spin conditions, it appears that contemporary designs (with the moment of inertia about the wing axis I(sub Y) considerably greater than the moment of inertia about the fuselage axis I(sub X) having positive values of C(sub l, sub p) (rolling-moment coefficient due to rolling) or positive values of C(sub l, sub beta) (rolling-moment coefficient due to sideslip) will probably not have a stable spin in the flat-spin region near an angle of attack of 90 deg. If the damping in pitch in flat-spin attitudes is zero, stable flat-spin conditions may not be possible on an airplane having the mass primarily distributed along the wings. The effect of moving ailerons with the spin or the effect of applying a positive pitching moment producing recovery for contemporary fighter designs will be greatest for large negative values of C(sub n, sub beta) (yawing-moment coefficient due to sideslip). In addition, for a certain critical value of positive C(sub n, sub beta), the rolling moment applied by moving ailerons with the spin or the application of a positive pitching moment will have no effect on reducing the spin rate.

Klinar, Walter J.↗

A statistical model for interpreting computerized dynamic posturography data

Computerized dynamic posturography (CDP) is widely used for assessment of altered balance control. CDP trials are quantified using the equilibrium score (ES), which ranges from zero to 100, as a decreasing function of peak sway angle. The problem of how best to model and analyze ESs from a controlled study is considered. The ES often exhibits a skewed distribution in repeated trials, which can lead to incorrect inference when applying standard regression or analysis of variance models. Furthermore, CDP trials are terminated when a patient loses balance. In these situations, the ES is not observable, but is assigned the lowest possible score--zero. As a result, the response variable has a mixed discrete-continuous distribution, further compromising inference obtained by standard statistical methods. Here, we develop alternative methodology for analyzing ESs under a stochastic model extending the ES to a continuous latent random variable that always exists, but is unobserved in the event of a fall. Loss of balance occurs conditionally, with probability depending on the realized latent ES. After fitting the model by a form of quasi-maximum-likelihood, one may perform statistical inference to assess the effects of explanatory variables. An example is provided, using data from the NIH/NIA Baltimore Longitudinal Study on Aging.

NASA Discipline Neuroscience↗

Existence, uniqueness and regularity of a time-periodic probability density distribution arising in a sedimentation-diffusion problem

The sedimentation and diffusion of a nonneutrally buoyant Brownian particle in vertical fluid-filled cylinder of finite length which is instantaneously inverted at regular intervals are investigated analytically. A one-dimensional convective-diffusive equation is derived to describe the temporal and spatial evolution of the probability density; a periodicity condition is formulated; the applicability of Fredholm theory is established; and the parameter-space regions are determined within which the existence and uniqueness of solutions are guaranteed. Numerical results for sample problems are presented graphically and briefly characterized.

Nitsche, Ludwig C.↗

Turbulent plane Couette flow using probability distribution functions

A numerical scheme employing a combination of the discrete ordinate method and finite differences is developed for solving the one-dimensional form of Lundgren's (1967) model equation for turbulent plane Couette flow. The approach used requires no a priori assumption about the form of the turbulent distribution function, and the numerical solution is obtained directly from the governing differential equations. Two different types of boundary conditions (zero-gradient and Chapman-Enskog) for the distribution function are evaluated by comparing the numerical results with experimental data. It is found that: (1) the present approach gives convergent and stable results over a wide range of Reynolds numbers; (2) Lundgren's equation yields results that compare well with experimental data for mean velocity and skin friction in the case of simple Couette flow; (3) the zero-gradient boundary condition leads to a logarithmic flow profile; and (4) the Chapman-Enskog boundary condition provides very good agreement with experimental data when applied within the near-wall region.

Srinivasan, R.↗

Quantum-Classical Hybrid for Information Processing

Based upon quantum-inspired entanglement in quantum-classical hybrids, a simple algorithm for instantaneous transmissions of non-intentional messages (chosen at random) to remote distances is proposed. The idea is to implement instantaneous transmission of conditional information on remote distances via a quantum-classical hybrid that preserves superposition of random solutions, while allowing one to measure its state variables using classical methods. Such a hybrid system reinforces the advantages, and minimizes the limitations, of both quantum and classical characteristics. Consider n observers, and assume that each of them gets a copy of the system and runs it separately. Although they run identical systems, the outcomes of even synchronized runs may be different because the solutions of these systems are random. However, the global constrain must be satisfied. Therefore, if the observer #1 (the sender) made a measurement of the acceleration v(sub 1) at t =T, then the receiver, by measuring the corresponding acceleration v(sub 1) at t =T, may get a wrong value because the accelerations are random, and only their ratios are deterministic. Obviously, the transmission of this knowledge is instantaneous as soon as the measurements have been performed. In addition to that, the distance between the observers is irrelevant because the x-coordinate does not enter the governing equations. However, the Shannon information transmitted is zero. None of the senders can control the outcomes of their measurements because they are random. The senders cannot transmit intentional messages. Nevertheless, based on the transmitted knowledge, they can coordinate their actions based on conditional information. If the observer #1 knows his own measurements, the measurements of the others can be fully determined. It is important to emphasize that the origin of entanglement of all the observers is the joint probability density that couples their actions. There is no centralized source, or a sender of the signal, because each receiver can become a sender as well. An observer receives a signal by performing certain measurements synchronized with the measurements of the others. This means that the signal is uniformly and simultaneously distributed over the observers in a decentralized way. The signals transmit no intentional information that would favor one agent over another. All the sequence of signals received by different observers are not only statistically equivalent, but are also point-by-point identical. It is important to assume that each agent knows that the other agent simultaneously receives the identical signals. The sequences of the signals are true random, so that no agent could predict the next step with the probability different from those described by the density. Under these quite general assumptions, the entangled observers-agents can perform non-trivial tasks that include transmission of conditional information from one agent to another, simple paradigm of cooperation, etc. The problem of behavior of intelligent agents correlated by identical random messages in a decentralized way has its own significance: it simulates evolutionary behavior of biological and social systems correlated only via simultaneous sensoring sequences of unexpected events.

Zak, Michail↗

Measurement of the Errors of Service Altimeter Installations During Landing-Approach and Take-Off Operations

The overall errors of the service altimeter installations of a variety of civil transport, military, and general-aviation airplanes have been experimentally determined during normal landing-approach and take-off operations. The average height above the runway at which the data were obtained was about 280 feet for the landings and about 440 feet for the take-offs. An analysis of the data obtained from 196 airplanes during 415 landing approaches and from 70 airplanes during 152 take-offs showed that: 1. The overall error of the altimeter installations in the landing- approach condition had a probable value (50 percent probability) of +/- 36 feet and a maximum probable value (99.7 percent probability) of +/- 159 feet with a bias of +10 feet. 2. The overall error in the take-off condition had a probable value of +/- 47 feet and a maximum probable value of +/- 207 feet with a bias of -33 feet. 3. The overall errors of the military airplanes were generally larger than those of the civil transports in both the landing-approach and take-off conditions. In the landing-approach condition the probable error and the maximum probable error of the military airplanes were +/- 43 and +/- 189 feet, respectively, with a bias of +15 feet, whereas those for the civil transports were +/- 22 and +/- 96 feet, respectively, with a bias of +1 foot. 4. The bias values of the error distributions (+10 feet for the landings and -33 feet for the take-offs) appear to represent a measure of the hysteresis characteristics (after effect and recovery) and friction of the instrument and the pressure lag of the tubing-instrument system.

Gracey, William↗

CFDP Performance over Weather-Dependent Ka-Band Channel

This study presents an analysis of the delay performance of the CCSDS File Delivery Protocol (CFDP) over weather-dependent Ka-band channel. The Ka-band channel condition is determined by the strength of the atmospheric noise temperature, which is weather dependent. Noise temperature data collected from the Deep Space Network (DSN) Madrid site is used to characterize the correlations between good and bad channel states in a two-state Markov model. Specifically, the probability distribution of file delivery latency using the CFDP deferred Negative Acknowledgement (NAK) mode is derived and quantified. Deep space communication scenarios with different file sizes and bit error rates (BERs) are studied and compared. Furthermore, we also examine the sensitivity of our analysis with respect to different data sampling methods. Our analysis shows that while the weather-dependent channel only results in fairly small increases in the average number of CFDP retransmissions required, the maximum number of transmissions required to complete 99 percentile, on the other hand, is significantly larger for the weather-dependent channel due to the significant correlation of poor weather states.

weather↗

CFDP Performance over Weather-dependent Ka-band Channel

This study presents an analysis of the delay performance of the CCSDS File Delivery Protocol (CFDP) over weather-dependent Ka-band channel. The Ka-band channel condition is determined by the strength of the atmospheric noise temperature, which is weather dependent. Noise temperature data collected from the Deep Space Network (DSN) Madrid site is used to characterize the correlations between good and bad channel states in a two-state Markov model. Specifically, the probability distribution of file delivery latency using the CFDP deferred Negative Acknowledgement (NAK) mode is derived and quantified. Deep space communication scenarios with different file sizes and bit error rates (BERs) are studied and compared. Furthermore, we also examine the sensitivity of our analysis with respect to different data sampling methods. Our analysis shows that while the weather-dependent channel only results in fairly small increases in the average number of CFDP retransmissions required, the maximum number of transmissions required to complete 99 percentile, on the other hand, is significantly larger for the weather-dependent channel due to the significant correlation of poor weather states.

deep space communications↗

Electrified Aircraft Propulsion Systems: Potential Failure Modes and Failure Mitigation Strategies

Electrified aircraft propulsion (EAP) systems hold great potential for the reduction of aircraft fuel burn, emissions, and noise. Currently, NASA and other organizations are actively working to identify and mature technologies necessary to bring EAP designs to reality. A requirement for the development of any civil aircraft and its systems is to ensure that potential hazards in the design are identified and appropriately mitigated to ensure that the system is safe. During aircraft development, a system safety assessment that consists of a functional hazard assessment is conducted to identify all potential failure conditions of each function, and classify those failures according to the severity of their effects on the aircraft or its occupants. The more severe a function's failure condition classification, the greater the development assurance level required for the function to ensure that the probability of the hazard is acceptably low. Today, aircraft engines and their control systems receive type certificate approval as a stand-alone system to signify their airworthiness. However, the complex coupling and distributed nature of EAP designs are expected to place added challenges on the certification of these systems. This presentation will provide an initial high-level review of the potential failure modes and hazards posed by a generic EAP system along with potential mitigation strategies for those failures. The EAP system is assumed to be a hybrid design consisting of gas turbine engines, mechanical drives, electric machines, power electronics and distribution systems, energy storage devices, and motor driven propulsors. The functionality provided by each of these EAP subsystems will be discussed along with the potential failure modes they may encounter. This will include a discussion of coupled failure effects, where a fault in one EAP subsystem effects the operation of other subsystems in the architecture. Next, potential failure mitigation strategies are discussed including both software-based and hardware-based mitigation strategies. The presentation will conclude with an example evaluation of the potential failure modes and mitigation strategies for a concept EAP system proposed by NASA.

Simon, Donald L.↗

Gravity and count probabilities in an expanding universe

The time evolution of nonlinear clustering on large scales in cold dark matter, hot dark matter, and white noise models of the universe is investigated using N-body simulations performed with a tree code. Count probabilities in cubic cells are determined as functions of the cell size and the clustering state (redshift), and comparisons are made with various theoretical models. We isolate the features that appear to be the result of gravitational instability, those that depend on the initial conditions, and those that are likely a consequence of numerical limitations. More specifically, we study the development of skewness, kurtosis, and the fifth moment in relation to variance, the dependence of the void probability on time as well as on sparseness of sampling, and the overall shape of the count probability distribution. Implications of our results for theoretical and observational studies are discussed.

Bouchet, Francois R.↗

Icing tunnel tests of a composite porous leading edge for use with a liquid anti-ice system

The efficacy of liquid ice protection systems which distribute a glycol-water solution onto leading edge surfaces through a porous skin was demonstrated in tests conducted in the NASA Lewis icing research tunnel using a composite porous leading edge panels. The data obtained were compared with the performance of previously tested stainless steel leading edge with the same geometry. Results show: (1) anti-ice protection of a composite leading edge is possible for all the simulated conditions tested; (2) the glycol flow rates required to achieve anti-ice protection were generally much higher than those required for a stainless steel panel; (3) the low reservoir pressures of the glycol during test runs indicates that more uniform distribution of glycol, and therefore lower glycol flow rates, can probably be achieved by decreasing the porosity of the panel; and (4) significant weight savings can be achieved in fluid ice protection systems with composite porous leading edges. The resistance of composite panels to abrasion and erosion must yet be determined before they can be incorporated in production systems.

Kohlman, D. L.↗

Service Life Extension of the Propulsion System of Long-Term Manned Orbital Stations

One of the critical non-replaceable systems of a long-term manned orbital station is the propulsion system. Since the propulsion system operates beginning with the launch of station elements into orbit, its service life determines the service life of the station overall. Weighing almost a million pounds, the International Space Station (ISS) is about four times as large as the Russian space station Mir and about five times as large as the U.S. Skylab. Constructed over a span of more than a decade with the help of over 100 space flights, elements and modules of the ISS provide more research space than any spacecraft ever built. Originally envisaged for a service life of fifteen years, this Earth orbiting laboratory has been in orbit since 1998. Some elements that have been launched later in the assembly sequence were not yet built when the first elements were placed in orbit. Hence, some of the early modules that were launched at the inception of the program were already nearing the end of their design life when the ISS was finally ready and operational. To maximize the return on global investments on ISS, it is essential for the valuable research on ISS to continue as long as the station can be sustained safely in orbit. This paper describes the work performed to extend the service life of the ISS propulsion system. A system comprises of many components with varying failure rates. Reliability of a system is the probability that it will perform its intended function under encountered operating conditions, for a specified period of time. As we are interested in finding out how reliable a system would be in the future, reliability expressed as a function of time provides valuable insight. In a hypothetical bathtub shaped failure rate curve, the failure rate, defined as the number of failures per unit time that a currently healthy component will suffer in a given future time interval, decreases during infant-mortality period, stays nearly constant during the service life and increases at the end when the design service life ends and wear-out phase begins. However, the component failure rates do not remain constant over the entire cycle life. The failure rate depends on various factors such as design complexity, current age of the component, operating conditions, severity of environmental stress factors, etc. Development, qualification and acceptance test processes provide rigorous screening of components to weed out imperfections that might otherwise cause infant mortality failures. If sufficient samples are tested to failure, the failure time versus failure quantity can be analyzed statistically to develop a failure probability distribution function (PDF), a statistical model of the probability of failure versus time. Driven by cost and schedule constraints however, spacecraft components are generally not tested in large numbers. Uncertainties in failure rate and remaining life estimates increase when fewer units are tested. To account for this, spacecraft operators prefer to limit useful operations to a period shorter than the maximum demonstrated service life of the weakest component. Running each component to its failure to determine the maximum possible service life of a system can become overly expensive and impractical. Spacecraft operators therefore, specify the required service life and an acceptable factor of safety (FOS). The designers use these requirements to limit the life test duration. Midway through the design life, when benefits justify additional investments, supplementary life test may be performed to demonstrate the capability to safely extend the service life of the system. An innovative approach is required to evaluate the entire system, without having to go through an elaborate test program of propulsion system elements. Evaluating every component through a brute force test program would be a cost prohibitive and time consuming endeavor. ISS propulsion system components were designed and built decades ago. There are no representative ground test articles for some of the components. A 'test everything' approach would require manufacturing new test articles. The paper outlines some of the techniques used for selective testing, by way of cherry picking candidate components based on failure mode effects analysis, system level impacts, hazard analysis, etc. The type of testing required for extending the service life depends on the design and criticality of the component, failure modes and failure mechanisms, life cycle margin provided by the original certification, operational and environmental stresses encountered, etc. When specific failure mechanism being considered and the underlying relationship of that mode to the stresses provided in the test can be correlated by supporting analysis, time and effort required for conducting life extension testing can be significantly reduced. Exposure to corrosive propellants over long periods of time, for instance, lead to specific failure mechanisms in several components used in the propulsion system. Using Arrhenius model, which is tied to chemically dependent failure mechanisms such as corrosion or chemical reactions, it is possible to subject carefully selected test articles to accelerated life test. Arrhenius model reflects the proportional relationship between time to failure of a component and the exponential of the inverse of absolute temperature acting on the component. The acceleration factor is used to perform tests at higher stresses that allow direct correlation between the times to failure at a high test temperature to the temperatures to be expected in actual use. As long as the temperatures are such that new failure mechanisms are not introduced, this becomes a very useful method for testing to failure a relatively small sample of items for a much shorter amount of time. In this article, based on the example of the propulsion system of the first ISS module Zarya, theoretical approaches and practical activities of extending the service life of the propulsion system are reviewed with the goal of determining the maximum duration of its safe operation.

Kamath, Ulhas↗

Loss of Control Detection for Commercial Transports Using Conditional Variational Autoencoders

This work describes a detector for the loss of control of a commercial transport in flight. The detector has a belief state defined by the latent variable stochastic modeling of a conditional variational autoencoder (CVAE) constructed with bidirectional recurrent layers. In 2000, the Boeing Company and the NASA Langley Research Center jointly developed a quantitative set of metrics for defining loss-of-control (LOC) for a commercial transport. We use the thresholds for these quantitative metrics to define a condition vector for training the CVAE. We demonstrate through experimentation that reconstruction probability is an accurate indicator that the vehicle has shifted to an LOC state. Second, we introduce a technique for inferring that the vehicle is experiencing a flight state change is approaching by measuring a shift in the sampling Gaussian distributions of the latent space. We provide an analysis of its applicability to flight data from a NASA generic commercial transport-type aircraft.

Newton H Campbell↗

Simulation of Vacuum Chamber Pressure Distribution with Surrogate Modeling and Uncertainty Quantification

A major challenge in understanding differences in electric propulsion performance in ground tests and in space operations concerns the pressure distribution within the test vacuum chamber. The chamber backpressure is much higher than experienced in space, modifying thruster performance and plume dynamics. Numerical simulation is a key element to determining the background conditions in non-ideal vacuum chamber environments. An important parameter for the accurate simulation of chamber backpressure is the probability that an atom will stick to a cryogenic panel used to pump away the plume gases. This quantity can be used to model vacuum pumps in particle-based kinetic numerical methods. In this work, a three-dimensional direct simulation Monte Carlo code is used to model neutral xenon atoms flowing from the anode of the H9 Hall Effect Thruster within the University of Michigan’s Large Vacuum Test Facility. Simulated pressures are compared with ion gauge pressure measurements to infer the effective sticking coefficient of the chamber’s vacuum pumps. A pressure predicting surrogate model is developed for inference of pump sticking coefficients and for uncertainty quantification. This information enables accurate and useful kinetic simulations of electric propulsion thruster plasma plumes in vacuum chambers.

DSMC↗

Chance-Constrained Guidance With Non-Convex Constraints

Missions to small bodies, such as comets or asteroids, require autonomous guidance for descent to these small bodies. Such guidance is made challenging by uncertainty in the position and velocity of the spacecraft, as well as the uncertainty in the gravitational field around the small body. In addition, the requirement to avoid collision with the asteroid represents a non-convex constraint that means finding the optimal guidance trajectory, in general, is intractable. In this innovation, a new approach is proposed for chance-constrained optimal guidance with non-convex constraints. Chance-constrained guidance takes into account uncertainty so that the probability of collision is below a specified threshold. In this approach, a new bounding method has been developed to obtain a set of decomposed chance constraints that is a sufficient condition of the original chance constraint. The decomposition of the chance constraint enables its efficient evaluation, as well as the application of the branch and bound method. Branch and bound enables non-convex problems to be solved efficiently to global optimality. Considering the problem of finite-horizon robust optimal control of dynamic systems under Gaussian-distributed stochastic uncertainty, with state and control constraints, a discrete-time, continuous-state linear dynamics model is assumed. Gaussian-distributed stochastic uncertainty is a more natural model for exogenous disturbances such as wind gusts and turbulence than the previously studied set-bounded models. However, with stochastic uncertainty, it is often impossible to guarantee that state constraints are satisfied, because there is typically a non-zero probability of having a disturbance that is large enough to push the state out of the feasible region. An effective framework to address robustness with stochastic uncertainty is optimization with chance constraints. These require that the probability of violating the state constraints (i.e., the probability of failure) is below a user-specified bound known as the risk bound. An example problem is to drive a car to a destination as fast as possible while limiting the probability of an accident to 10(exp -7). This framework allows users to trade conservatism against performance by choosing the risk bound. The more risk the user accepts, the better performance they can expect.

FROM↗

Dicarboxylic acids generated by thermal alteration of kerogen and humic acids

Significant amounts (up to 2 percent of organic geopolymers) of low-molecular-weight (LMW) dicarboxylic acids (C2-C10) have been detected during thermal alteration (270 C, 2 h) of kerogens and humic acids isolated from young or ancient lithified sediments. Their distribution is characterized by the predominance of oxalic acid followed by succinic, fumaric, and methylsuccinic acids. These acids are probably released by the breakdown of macromolecular structures, which have incorporated biogenic organic compounds, including diacids, during early digenesis in sediments. Because of their reactivity, LMW diacids may play geochemically important roles under natural conditions.

Kawamura, Kimitaka↗