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At least 73 records · Page 4

Load biaxiality and fracture - Synthesis and summary

The question of load biaxiality strongly affecting almost all of the characteristics of brittle fracture behavior of a cracked body is investigated. Results of research published piecemeal over the years by the authors have shown that the stress and displacement fields, the elastic strain energy density, and the maximum shear stress near the crack tip are all altered by loads applied parallel to the crack, as are the angle of initial crack extension, the strain energy of the entire body, the fracture load, and the rate of fatigue crack growth. A synthesis and summary of this research is presented showing the shortcomings inherent in both Griffith's global energy rate theory for crack instability and Irwin's local crack-tip stress intensity theory for fracture toughness. In both theories only the tensile load perpendicular to the crack influences fracture behavior of the body.

Eftis, J.↗

Postcollapse hydrodynamics of SN 1987A - Two-dimensional simulations of the early evolution

The first few seconds of the explosion of SN 1987A are modeled here using a 2D cylindrical geometry smooth particle hydrodynamics code. The success of the explosion is determined to be sensitive to the duration of the infall, the timing of the bounce, and the subsequent neutrino heating. A semianalytical model for the initial structure of the collapsed object is used to present two simulations that differ by the mass that has been allowed to collapse into a neutron star prior to the bounce. In the case of a short initial infall, the explosion fails due to excessive cooling. For a longer initial infall, the cooling is less and the explosion is successful although relatively weak. It is shown that in this case, a successful explosion is brought about by the presence of an entropy gradient which, combined with the gravitational pull of the neutron star, leads to extremely strong instabilities. The critical importance of the global circulation for the success of the explosion is demonstrated.

Herant, Marc↗

The Magnetosphere Ionosphere Electron Precipitation Dynamics and Their Geospace Consequences During the 17 March 2013 Storm

During geomagnetic storms and substorms, the magnetosphere and ionosphere are strongly coupled by precipitating magnetospheric electrons from the Earth's plasma sheet and driven by both magnetospheric and ionospheric processes. Magnetospheric wave activity initiates electron precipitation, and the ionosphere and upper atmosphere further facilitate this process by enhancing the value of precipitated energy uxes via connection of two magnetically conjugate regions and multiple atmospheric reections. This paper focuses on the resulting electron energy uxes and afliated heightintegrated Pedersen and Hall conductances in the auroral regions produced by multiple atmospheric reections during the 17 March 2013 geomagnetic storm and their effects on the inner magnetospheric electric eld and ring current. Our study is based on the magnetically and electrically selfconsistent Rice ConvectionModelEquilibrium of the inner magnetosphere with SuperThermal Electron Transport modied electron energy uxes that take into account the electron energy interplay between the two magnetically conjugate ionospheres. SuperThermal Electron Transportmodied energy ux in the Rice ConvectionModelEquilibrium leads to a signicant difference in the global conductance pattern, ionospheric electric eld formation, Birkeland current structure, ring current energization and its energy content, subauroral polarization drifts intensications and their spatial locations, interchange instability redistribution, and overall energy interplay on the global scale.

Khazanov, George V.↗

Interfacial wave theory for dendritic structure of a growing needle crystal. I - Local instability mechanism. II - Wave-emission mechanism at the turning point

The complicated dendritic structure of a growing needle crystal is studied on the basis of global interfacial wave theory. The local dispersion relation for normal modes is derived in a paraboloidal coordinate system using the multiple-variable-expansion method. It is shown that the global solution in a dendrite growth process incorporates the morphological instability factor and the traveling wave factor.

Xu, Jian-Jun↗

Characterization of frequency standard instability by estimation of their covariance matrix

The popular 3-cornered hat method used for evaluating the noise contributions of individual frequency standards is revisited. This method is used in several cases, but sometimes the results are not consistent because one or more estimated clock variances turn out to be negative. Different causes of this unacceptable result have been conjectured: among them one regards the hypothesis of uncorrelated clocks, essential in this method. Since recently realistic cases of correlation between clocks, mainly due to the environmental conditions, have been observed, this paper proposes an entirely revisited version of the 3-cornered hat method which permits to evaluate the individual variances and also the possible covariances between clocks, by relaxing the hypothesis of uncorrelation. The uncertainty and the lack of contemporaneity of the measurement series are assumed to be negligible. The lack of the uncorrelation hypothesis calls for a more general mathematical model leading to an underdetermined linear system. The estimates of the (co)variances of the measurement series us well us those of the individual clocks are introduced by means of the scalar product of the related time series and arranged in the respective covariance matrices S and R. Since covariance matrix is positive definite by definition, the problem consists in estimating the unknown R, subject to the constraint of positive definiteness, from the known S. Unfortunately, this constraint is not sufficient to estimate R. Therefore a suitable optimization criterion is proposed, which assures the positive definiteness of R and, at the same time, minimizes the global correlation among clocks. Examples of frequency instability measurements processed by the "classical" 3-cornered hat method and the here-revisited method are presented showing that the solutions are identical only when the uncorrelation hypothesis doesn't violate the positive definiteness of R.

PatriziaTravella↗

Jeans criterion in a turbulent medium

According to the classical Jeans analysis, all the molecular clouds of mass larger than a few 100 M(solar), size larger than about 1pc and kinetic temperature Tk less than 30K are gravitationally unstable. We have shown that in clouds supported by internal supersonic motions, local gravitational instabilities may appear within molecular clouds which are globally stable. The argument is threefold: (1) when the turbulent kinetic energy is included into the internal energy term, the virial equilibrium condition shows that molecular clouds such as those observed, which are gravitationally unstable according to the Jeans criterion, are indeed globally stable if supported by a turbulent velocity field of power spectrum steeper than 3; (2) 2D compressible hydrodynamical simulations show that a supersonic turbulent velocity field generates a turbulent pressure within clouds, the gradients of which stabilize the unstable scales (i.e., the largest scales and the cloud itself) against gravitational collapse; (3) an analysis similar to the Jeans approach but including the turbulent pressure gradient term, gives basically the same results as those given in (1). Clouds of mean density lower than a critical value are found to be stable even though more massive than their Jeans mass. In clouds of mean density larger than that critical value, the gravitational instability appears only over a range of scales smaller than the cloud size, the largest scales being stable. In practice, the observed mean densities are lower than this critical value: the observation of a small number of cores and stars of a few solar masses embedded in clouds of several hundred solar masses can only be understood in terms of small scale density fluctuations of large amplitude generated by the supersonic turbulence which would occasionally overtake the limit of gravitational stability.

Bonazzola, S.↗

Planetary Geophysics and Tectonics

Research supported by grant NAGW-1928 has addressed a variety of problems related to planetary evolution. One important focus has been on questions related to the role of chemical buoyancy in planetary evolution with application to both Venus and the Moon. We have developed a model for the evolution of the Moon (Hess and Parmentier, 1995) in which dense, highly radioactive, late stage magma ocean cumulates sink forming a core. This core heats the overlying, chemically layered mantle giving rise to a heated, chemically well-mixed layer that thickens with time. This Mixed layer eventually becomes hot enough and thick enough that its top begins to melt at a pressure low enough that melt is buoyant, thus creating mare basalts from a high pressure source of the correct composition and at an appropriate time in lunar evolution. In work completed during the last year, numerical experiments on convection in a chemically stably stratified fluid layer heated from below have been completed. These results show us how to calculate the evolution of a mixed layer in the Moon, depending on the heat production in the ilmenite- cumulate core and the chemical stratification of the overlying mantle. Chemical stratification of the mantle after its initial differentiation is would trap heat in the deep interior and prevent the rapid rise of plumes with accompanying volcanism. This trapping of heat in the interior can explain the thickness of the lunar lithosphere as a function of time as well as the magmatic evolution. We show that heat transported to the base of the lithosphere at a rate determined by current estimates of radioactivity in the Moon would not satisfy constraints on elastic lithosphere thickness from tectonic feature associated with basin loading. Trapping heat at depth by a chemically stratified mantle may also explain the absence of global compressional features on the surface that previous models predict for an initially hot lunar interior. For Venus, we developed a model in which the chemical buoyancy of crust and a depleted mantle layer stabilizes the lithosphere for long periods of time and provides a mechanism of episodic planetary evolution (Parmentier and Hess, 1992). Continued thickening of a residual depleted mantle layer eventually suppresses pressure release melting and the creation of depleted mantle. Continued cooling then allows the lithosphere to become heavier than the underlying hotter, undepleted mantle. This repeated instability can occur on time scales appropriate for episodic global resurfacing on Venus. We have also examined the role of the gabbro-eclogite phase transformation on crust and lithosphere stability and as a mechanism of crustal recycling in the absence of plate tectonics. Our work thus far concentrates on the scale of instability that would occur due to cooling or crustal thickening associated with horizontal shortening. Whether repeated overturn can explain the evolution of Venus depends in part on whether sufficient heat transfer can occur between overturns and on constraints provided by understanding observed surface features and evolution.

Parmentier, E. M.↗

Imaging Plasma Density Structures in the Soft X-Rays Generated by Solar Wind Charge Exchange with Neutrals

Both heliophysics and planetary physics seek to understand the complex nature of the solar wind's interaction with solar system obstacles like Earth's magnetosphere, the ionospheres of Venus and Mars, and comets. Studies with this objective are frequently conducted with the help of single or multipoint in situ electromagnetic field and particle observations, guided by the predictions of both local and global numerical simulations, and placed in context by observations from far and extreme ultraviolet (FUV, EUV), hard X-ray, and energetic neutral atom imagers (ENA). Each proposed interaction mechanism (e.g., steady or transient magnetic reconnection, local or global magnetic reconnection, ion pick-up, or the Kelvin- Helmholtz instability) generates diagnostic plasma density structures. The significance of each mechanism to the overall interaction (as measured in terms of atmospheric/ionospheric loss at comets, Venus, and Mars or global magnetospheric/ionospheric convection at Earth) remains to be determined but can be evaluated on the basis of how often the density signatures that it generates are observed as a function of solar wind conditions. This paper reviews efforts to image the diagnostic plasma density structures in the soft (low energy, 0.1-2.0 keV) X-rays produced when high charge state solar wind ions exchange electrons with the exospheric neutrals surrounding solar system obstacles.

Sibeck, David G.↗

Dynamics, winds, circulation and turbulence in the atmosphere of Venus

With the possible exception of the lowest one or two scale heights, the dominant mode of circulation of Venus' atmosphere is a rapid, zonal, retrograde motion. Global albedo variations in the ultraviolet may reflect planetary scale waves propagating relative to the zonal winds. Other special phenomena such as cellular convection in the subsolar region and internal gravity waves generated in the interaction of the zonal circulation with the subsolar disturbance may also be revealed in ultraviolet imagery of the atmosphere. We discuss the contributions of experiments on the Orbiter and Entry Probes of Pioneer Venus toward unravelling the mystery of the planet's global circulation and the role played by waves, instabilities and convection therein

Schubert, G.↗

Reliability Sensitivity Analysis and Design Optimization of Composite Structures Based on Response Surface Methodology

This report discusses the development and application of two alternative strategies in the form of global and sequential local response surface (RS) techniques for the solution of reliability-based optimization (RBO) problems. The problem of a thin-walled composite circular cylinder under axial buckling instability is used as a demonstrative example. In this case, the global technique uses a single second-order RS model to estimate the axial buckling load over the entire feasible design space (FDS) whereas the local technique uses multiple first-order RS models with each applied to a small subregion of FDS. Alternative methods for the calculation of unknown coefficients in each RS model are explored prior to the solution of the optimization problem. The example RBO problem is formulated as a function of 23 uncorrelated random variables that include material properties, thickness and orientation angle of each ply, cylinder diameter and length, as well as the applied load. The mean values of the 8 ply thicknesses are treated as independent design variables. While the coefficients of variation of all random variables are held fixed, the standard deviations of ply thicknesses can vary during the optimization process as a result of changes in the design variables. The structural reliability analysis is based on the first-order reliability method with reliability index treated as the design constraint. In addition to the probabilistic sensitivity analysis of reliability index, the results of the RBO problem are presented for different combinations of cylinder length and diameter and laminate ply patterns. The two strategies are found to produce similar results in terms of accuracy with the sequential local RS technique having a considerably better computational efficiency.

Rais-Rohani, Masoud↗

Gravitational Effects on Flow Instability and Transition in Low Density Jets

Recent experiments have shown that low-density gas jets injected into a high-density ambient gas undergo an instability mode, leading to highly-periodic oscillations in the flow-field for certain conditions. The transition from laminar to turbulent flow in these jets is abrupt, without the gradual change in scales. Even the fine scale turbulent structure repeats itself with extreme regularity from cycle to cycle. Similar observations were obtained in buoyancy-dominated and momentum-dominated jets characterized by the Richardson numbers, Ri = [gD(rho(sub a)-rho(sub j))/rho(sub j)U(sub j)(exp 2) ] where g is the gravitational acceleration, D is the jet diameter, rho(sub a) and rho(sub a) are, respectively, the free-stream and jet densities, and U(sub j) is the mean jet exit velocity. At high Richardson numbers, the instability is presumably caused by buoyancy since the flow-oscillation frequency (f) or the Strouhal number, St = [fD/U(sub j)] scales with Ri. In momentum-dominated jets, however, the Strouhal number of the oscillating flow is relatively independent of the Ri. In this case, a local absolute instability is predicted in the potential core of low-density jets with S [= rho(sub j)/rho(sub a)] < 0.7, which agrees qualitatively with experiments. Although the instability in gas jets of high Richardson numbers is attributed to buoyancy, direct physical evidence has not been acquired in experiments. If the instability is indeed caused by buoyancy, the near-field flow structure of the jet will change significantly when the buoyancy is removed, for example, in the microgravity environment. Thus, quantitative data on the spatial and temporal evolutions of the instability, length and time scale of the oscillating mode and its effects on the mean flow and breakdown of the potential core are needed in normal and microgravity to delineate gravitational effects in buoyant jets. In momentum dominated low-density jets, the instability is speculated to originate in the potential core. However, experiments have not succeeded in identifying the direct physical cause of the instability. For example, the theory predicts an oscillating mode for S<0.62 in the limit of zero momentum thickness, which contradicts with the experimental findings of Kyle and Sreenivasan. The analyses of momentum-dominated jets neglect buoyancy effects because of the small Richardson number. Although this assumption is appropriate in the potential core, the gravitational effects are important in the annular region surrounding the jet, where the density and velocity gradients are large. This reasoning provides basis for the hypothesis that the instability in low Richardosn number jets studied by Kyle and Sreenivasan and Monkewitz et al. is caused by buoyancy. The striking similarity in characteristics of the instability and virtually the identical conclusions reached by Subbarao and Cantwell in buoyant (Ri>0.5) helium jets on one hand and by Kyle and Sreenivasan in momentum-dominated (Ri<1x10(exp -3)) helium jets on the other support this hypothesis. However, quantitative experiments in normal and microgravity are necessary to obtain direct physical evidence of buoyancy effects on the flow instability and structure of momentum-dominated low-density jets. The primary objective of this new research project is to quantify how buoyancy affects the flow instability and structure in the near field of low-density jets. The flow will be described by the spatial and temporal evolutions of the instability, length and time scales of the oscillating mode, and the mean and fluctuating concentration fields. To meet this objective, concentration measurements will be obtained across the whole field using quantitative Rainbow Schlieren Deflectometry, providing spatial resolution of 0.1mm and temporal resolution of 0.017s to 1ms. The experimental effort will be supplemented with linear stability analysis of low-density jets by considering buoyancy. The first objective of this research is to investigate the effects of gravity on the flow instability and structure of low-density jets. The flow instability in these jets has been attributed to buoyancy. By removing buoyancy in our experiments, we seek to obtain the direct physical evidence of the instability mechanism. In the absence of the instability, the flow structure will undergo a significant change. We seek to quantify these changes by mapping the flow field (in terms of the concentration profiles) of these jets at non-buoyant conditions. Such information is presently lacking in the existing literature. The second objective of this research is to determine if the instability in momentum-driven, low-density jets is caused by buoyancy. At these conditions, the buoyancy effects are commonly ignored because of the small Richardson based on global parameters. By eliminating buoyancy in our experiments, globally as well as locally, we seek to examine the possibility that the instability mechanism in self-excited, buoyant or momentum-driven jets is the same. To meet this objective, we would quantify the jet flow in normal and microgravity, while systematically decreasing the Richardson number from buoyancy-driven to momentum driven flow regime. The third objective of this research is to perform a linear stability analysis of low-density gas jets by including the gravitational effects. The flow oscillations in these jets are attributed to an absolute instability, whereby the disturbance grows exponentially at the site to ultimately contaminate the entire flow field. We seek to study the characteristics of both convective and absolute instabilities and demarcate the boundary between them.

Agrawal A. K.↗

Accretion disk oscillations - A local analysis in a disk of finite thickness

Two types of oscillations are observed to occur in dwarf novae: 'coherent' and 'quasi-periodic' oscillations. These may be associated with the pulsation of the white dwarf or the accretion disk components of the dwarf nova. Here a local (short-wavelength) analysis is utilized to study the oscillation of a self-consistent, two-dimensional model of an accretion disk. The linearized equations describing adiabatic, inviscid, nonaxisymmetric oscillations are used to derive a fifth-order algebraic equation for the (complex) pulsation frequency of the disk. The solutions of this equation for various values of the wavevector k reveal that the disk is capable of supporting (1) a pair of high-frequency acoustic modes (p-modes); (2) a pair of intermediate-frequency modes which may share the characteristics of internal gravity waves (g-modes) and inertial waves; and (3) a mode associated with a dynamical instability (purely imaginary frequency). The role played by the shear in determining the stability or instability of these modes is also considered. Finally, the global oscillation frequencies of the disk are discussed.

Carroll, B. W.↗

Nonaxisymmetric instabilities in rotating shear flows - Internal gravity modes in stratified media and analogies with plane flows

The role of the internal gravity modes in mediating the growth of nonaxisymmetric instabilities is investigated by studying the instability of stratified incompressible differentially rotating fluid cylinders to global nonaxisymmetric modes. The results indicate that, in addition to a modified version of the well-known principal branch mediated by surface modes of the system (analogous to f-modes of stars), there exist unstable branches of the dispersion relation mediated by internal gravity modes of the system (similar to the g-modes of stars). These branches arise due to the interaction between the g-modes. It is shown that the maximum growth rate on one of the new branches can sometimes equal or exceed that on the principal branch, thus modifying the principal branch.

Ghosh, P.↗

A Normal Incidence X-ray Telescope (NIXT) Sounding Rocket Payload

The solar corona, and the coronae of solar-type stars, consist of a low-density magnetized plasma at temperatures exceeding 10(exp 6) K. The primary coronal emission is therefore in the UV and soft X-ray range. The observed close connection between solar magnetic fields and the physical parameters of the corona implies a fundamental role for the magnetic field in coronal structuring and dynamics. Variability of the corona occurs on all temporal and spatial scales - at one extreme, as the result of plasma instabilities, and at the other extreme driven by the global magnetic flux emergence patterns of the solar cycle.

Golub, Leon↗

Extratropical Large-Scale Traveling Weather Systems in the Southern Hemisphere on Mars

From late-autumn through early-spring, the middle- and high-latitudes of both hemispheres of Mars and its predominantly carbon-dioxide atmosphere support mean equator-to-pole thermal contrasts, and then, support a strong mean westerly polar vortex. Observations from orbiting spacecraft indicate that this intense mean baroclinicity-barotropicity supports large-scale eastward traveling weather systems (i.e., transient, traveling synoptic-period waves, on the order of the Rossby deformation scale). On Earth, extratropical weather disturbances arise from wind-shear instabilities, and these are critical components of the terrestrial global circulation. So it is the case for Mars. Large-scale traveling weather systems on Mars serve as agents in the transport of heat, momentum and scalar and tracer quantities (e.g., atmospheric dust, watervapor, ice clouds, chemical species, etc). Such weather systems interact with other large-scale atmospheric circulation components, namely, quasi-stationary (i.e., forced Rossby) modes; global thermal tidal modes; and then, upon large-/continental- geographical scales, upslope/ down-slope flows amongst high relief, low relief, impact basins, and volcanic rises, and more. The character of Mars' traveling extratropical weather disturbances in its southern hemisphere during late winter through early spring is investigated using a high-resolution Mars global climate model (i.e., Mars GCM), and one from the Agency's Mars Climate Modeling Center (MCMC) based at the NASA Ames Research Center. The climate model includes several complex atmospheric physical packages. With such physics modules, our global climate simulations present comparatively well with observations of the planet's current water cycle (Haberle et al.,2019). The climate model is "forced" with an annual dust cycle (i.e., nudged based on MGS/TES observations). Compared to the northern-hemisphere counterparts, the southern synoptic-period weather disturbances and accompanying frontal waves have smaller meridional and zonal scales, and are less intense. Influences of the zonally asymmetric (i.e., east-west varying) topography on southern large-scale weather are investigated, in addition to large-scale up-slope/down-slope flows and the diurnal cycle. A southern storm zone in late winter and early spring presents in the western hemisphere via orographic influences from the Tharsis highlands, and the Argyre and Hellas impact basins. Geographically localized transient-wave activity diagnostics are constructed that illuminate dynamical differences amongst the simulations and these are presented.

Hollingsworth, Jeffery L.↗

Observations of the 2-day wave in NMC stratospheric analyses

Observational characteristics of the 2-day wave, a westward-propagating zonal wave 3 oscillation in the summer subtropical upper stratosphere and mesosphere, are studied based on five years of National Meteorological Center (NMC) operational stratospheric analyses. These data show episodic occurrence of the 2-day wave in the upper stratosphere in January (centered near 20 deg S) and July - August (centered near 20 deg N). These episodes are strongly correlated with observed reversals of the zonal mean potential vorticity gradient near the core of the summer easterly jet, consistent with previous suggestions that the 2-day wave is generated by an in situ instability of this jet. On the other hand, the horizontal and vertical structure of the waves is very similar to that calculated by Salby for a global normal-mode Rossby wave. The combination of normal-mode structure and instability signature suggests that the 2-day wave is a near-resonant mode forced by dynamical instability.

Randel, William J.↗

Cosmic Complexity

What explains the extraordinary complexity of the observed universe, on all scales from quarks to the accelerating universe? My favorite explanation (which I certainty did not invent) ls that the fundamental laws of physics produce natural instability, energy flows, and chaos. Some call the result the Life Force, some note that the Earth is a living system itself (Gaia, a "tough bitch" according to Margulis), and some conclude that the observed complexity requires a supernatural explanation (of which we have many). But my dad was a statistician (of dairy cows) and he told me about cells and genes and evolution and chance when I was very small. So a scientist must look for me explanation of how nature's laws and statistics brought us into conscious existence. And how is that seemll"!gly Improbable events are actually happening a!1 the time? Well, the physicists have countless examples of natural instability, in which energy is released to power change from simplicity to complexity. One of the most common to see is that cooling water vapor below the freezing point produces snowflakes, no two alike, and all complex and beautiful. We see it often so we are not amazed. But physlc!sts have observed so many kinds of these changes from one structure to another (we call them phase transitions) that the Nobel Prize in 1992 could be awarded for understanding the mathematics of their common features. Now for a few examples of how the laws of nature produce the instabilities that lead to our own existence. First, the Big Bang (what an insufficient name!) apparently came from an instability, in which the "false vacuum" eventually decayed into the ordinary vacuum we have today, plus the most fundamental particles we know, the quarks and leptons. So the universe as a whole started with an instability. Then, a great expansion and cooling happened, and the loose quarks, finding themselves unstable too, bound themselves together into today's less elementary particles like protons and neutrons, liberating a little energy and creating complexity. Then, the expanding universe cooled some more, and neutrons and protons, no longer kept apart by immense temperatures, found themselves unstable and formed helium nuclei. Then, a little more cooling, and atomic nuclei and electrons were no longer kept apart, and the universe became transparent. Then a little more cooling, and the next instability began: gravitation pulled matter together across cosmic distances to form stars and galaxies. This instability is described as a "negative heat capadty" in which extracting energy from a gravitating system makes it hotter -- clearly the 2nd law of thermodynamics does not apply here! (This is the physicist's part of the answer to e e cummings' question: what is the wonder that's keeping the stars apart?) Then, the next instability is that hydrogen and helium nuclei can fuse together to release energy and make stars burn for billions of years. And then at the end of the fuel source, stars become unstable and explode and liberate the chemical elements back into space. And because of that, on planets like Earth, sustained energy flows support the development of additional instabilities and all kinds of complex patterns. Gravitational instability pulls the densest materials into the core of the Earth, leaving a thin skin of water and air, and makes the interior churn incessantly as heat flows outwards. And the heat from the sun, received mostly near the equator and flowing towards the poles, supports the complex atmospheric and oceanic circulations. And because or that, the physical Earth is full of natural chemical laboratories, concentrating elements here, mixing them there, raising and lowering temperatures, ceaselessly experimenting with uncountable events where new instabilities can arise. At least one of them was the new experiment called life. Now that we know that there are at least as many planets as there are stars, it is hard to imagine that nature's ceasess experimentation would not be able to produce life elsewhere -- but we don't know for sure. And life went on to cause new Instabilities, constantly evolving, with living things in an extraordinary range of environments, changing the global environment, with boom-and-bust cycles. with predators for every kInd of prey, with criminals for every possible crime, with governments to prevent them, and instabilities of the governments themselves. One of the instabilities Is that humans demand new weapons and new products of all sort, leading to serious investments in science and technology. So the natural/human world of competition and combat is structured to lead to advanced weaponry and cell phones. So here we are In 2012, with people writing essays and wondering whether their descendents will be artificial life forms travelling back into space. And, pondering what are the origins of those forces of nature that give rise to everything. Verllnde has argued that gravitation, the one force that has so far resisted our efforts at a Quantum description, is not even a fundamental force, but is itself it a statistical force, like osmosis. What an amazing turn of events! But after all I've just said, I should not be surprised a bit.

Mather, John C.↗

Optimal Control via Self-Generated Stochasticity

The problem of global maxima of functionals has been examined. Mathematical roots of local maxima are the same as those for a much simpler problem of finding global maximum of a multi-dimensional function. The second problem is instability even if an optimal trajectory is found, there is no guarantee that it is stable. As a result, a fundamentally new approach is introduced to optimal control based upon two new ideas. The first idea is to represent the functional to be maximized as a limit of a probability density governed by the appropriately selected Liouville equation. Then, the corresponding ordinary differential equations (ODEs) become stochastic, and that sample of the solution that has the largest value will have the highest probability to appear in ODE simulation. The main advantages of the stochastic approach are that it is not sensitive to local maxima, the function to be maximized must be only integrable but not necessarily differentiable, and global equality and inequality constraints do not cause any significant obstacles. The second idea is to remove possible instability of the optimal solution by equipping the control system with a self-stabilizing device. The applications of the proposed methodology will optimize the performance of NASA spacecraft, as well as robot performance.

Zak, Michail↗