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NASA NTRS2022

Parallel Grand-Canonical Monte Carlo (ParaGrandMC) User’s Manual Version 2.0

This manual describes the commands and command line options for the Parallel Grand Canonical Monte Carlo version 2.0 (ParaGrandMC.2.0) simulation code. This is a highly scalable parallel FORTRAN 2003 code for simulating the thermodynamic evolution of materials at the atomic level, and predicting their thermodynamic state, phase diagram, chemical composition and mechanical properties. The code is specifically designed to simulate multi-component alloy systems, predict solid-state phase transformations such as austenite-martensite transformations, precipitate formation, recrystallization, capillary effects at interfaces, surface absorption, etc., which can aid the design of novel metallic alloys. While the software is mainly tailored for modeling metal alloys, it can also be used for other types of solid-state systems, and to some degree for liquid or gaseous systems, including multiphase systems forming solid-liquid-gas interfaces. In addition to performing Monte Carlo (MC) simulations, the code can also perform Molecular Dynamics (MD) and Langevin Dynamics (LD) simulations, which can be combined and interchanged with MC for faster and more efficient system evolution. A detailed description of the MC part of the code is provided in the NASA ParaGrandMC report: NASA/CR–2016-219202; http://www.sti.nasa.gov.

High performance computing↗
NASA NTRS2004

Complexity of life via collective mind

e mind is introduced as a set of simple intelligent units (say, neurons, or interacting agents), which can communicate by exchange of information without explicit global control. Incomplete information is compensated by a sequence of random guesses symmetrically distributed around expectations with prescribed variances. Both the expectations and variances are the invariants characterizing the whole class of agents. These invariants are stored as parameters of the collective mind, while they contribute into dynamical formalism of the agents' evolution, and in particular, into the reflective chains of their nested abstract images of the selves and non-selves. The proposed model consists of the system of stochastic differential equations in the Langevin form representing the motor dynamics, and the corresponding Fokker-Planck equation representing the mental dynamics (Motor dynamics describes the motion in physical space, while mental dynamics simulates the evolution of initial errors in terms of the probability density). The main departure of this model from Newtonian and statistical physics is due to a feedback from the mental to the motor dynamics which makes the Fokker-Planck equation nonlinear. Interpretation of this model from mathematical and physical viewpoints, as well as possible interpretation from biological, psychological, and social viewpoints are discussed. The model is illustrated by the dynamics of a dialog.

collective intelligence↗
NASA NTRS2009

Complexity for Survival of Living Systems

A logical connection between the survivability of living systems and the complexity of their behavior (equivalently, mental complexity) has been established. This connection is an important intermediate result of continuing research on mathematical models that could constitute a unified representation of the evolution of both living and non-living systems. Earlier results of this research were reported in several prior NASA Tech Briefs articles, the two most relevant being Characteristics of Dynamics of Intelligent Systems (NPO- 21037), NASA Tech Briefs, Vol. 26, No. 12 (December 2002), page 48; and Self-Supervised Dynamical Systems (NPO- 30634) NASA Tech Briefs, Vol. 27, No. 3 (March 2003), page 72. As used here, living systems is synonymous with active systems and intelligent systems. The quoted terms can signify artificial agents (e.g., suitably programmed computers) or natural biological systems ranging from single-cell organisms at one extreme to the whole of human society at the other extreme. One of the requirements that must be satisfied in mathematical modeling of living systems is reconciliation of evolution of life with the second law of thermodynamics. In the approach followed in this research, this reconciliation is effected by means of a model, inspired partly by quantum mechanics, in which the quantum potential is replaced with an information potential. The model captures the most fundamental property of life - the ability to evolve from disorder to order without any external interference. The model incorporates the equations of classical dynamics, including Newton s equations of motion and equations for random components caused by uncertainties in initial conditions and by Langevin forces. The equations of classical dynamics are coupled with corresponding Liouville or Fokker-Planck equations that describe the evolutions of probability densities that represent the uncertainties. The coupling is effected by fictitious information-based forces that are gradients of the information potential, which, in turn, is a function of the probability densities. The probability densities are associated with mental images both self-image and nonself images (images of external objects that can include other agents). The evolution of the probability densities represents mental dynamics. Then the interaction between the physical and metal aspects of behavior is implemented by feedback from mental to motor dynamics, as represented by the aforementioned fictitious forces. The interaction of a system with its self and nonself images affords unlimited capacity for increase of complexity. There is a biological basis for this model of mental dynamics in the discovery of mirror neurons that learn by imitation. The levels of complexity attained by use of this model match those observed in living systems. To establish a mechanism for increasing the complexity of dynamics of an active system, the model enables exploitation of a chain of reflections exemplified by questions of the form, "What do you think that I think that you think...?" Mathematically, each level of reflection is represented in the form of an attractor performing the corresponding level of abstraction with more details removed from higher levels. The model can be used to describe the behaviors, not only of biological systems, but also of ecological, social, and economics ones.

Zak, Michail↗
NASA NTRS2003

Self-Supervised Dynamical Systems

Some progress has been made in a continuing effort to develop mathematical models of the behaviors of multi-agent systems known in biology, economics, and sociology (e.g., systems ranging from single or a few biomolecules to many interacting higher organisms). Living systems can be characterized by nonlinear evolution of probability distributions over different possible choices of the next steps in their motions. One of the main challenges in mathematical modeling of living systems is to distinguish between random walks of purely physical origin (for instance, Brownian motions) and those of biological origin. Following a line of reasoning from prior research, it has been assumed, in the present development, that a biological random walk can be represented by a nonlinear mathematical model that represents coupled mental and motor dynamics incorporating the psychological concept of reflection or self-image. The nonlinear dynamics impart the lifelike ability to behave in ways and to exhibit patterns that depart from thermodynamic equilibrium. Reflection or self-image has traditionally been recognized as a basic element of intelligence. The nonlinear mathematical models of the present development are denoted self-supervised dynamical systems. They include (1) equations of classical dynamics, including random components caused by uncertainties in initial conditions and by Langevin forces, coupled with (2) the corresponding Liouville or Fokker-Planck equations that describe the evolutions of probability densities that represent the uncertainties. The coupling is effected by fictitious information-based forces, denoted supervising forces, composed of probability densities and functionals thereof. The equations of classical mechanics represent motor dynamics that is, dynamics in the traditional sense, signifying Newton s equations of motion. The evolution of the probability densities represents mental dynamics or self-image. Then the interaction between the physical and metal aspects of a monad is implemented by feedback from mental to motor dynamics, as represented by the aforementioned fictitious forces. This feedback is what makes the evolution of probability densities nonlinear. The deviation from linear evolution can be characterized, in a sense, as an expression of free will. It has been demonstrated that probability densities can approach prescribed attractors while exhibiting such patterns as shock waves, solitons, and chaos in probability space. The concept of self-supervised dynamical systems has been considered for application to diverse phenomena, including information-based neural networks, cooperation, competition, deception, games, and control of chaos. In addition, a formal similarity between the mathematical structures of self-supervised dynamical systems and of quantum-mechanical systems has been investigated.

Zak, Michail↗
NASA NTRS2016

Real-time Identification and Control of Satellite Signal Impairments Solution and Application of the Stratonovich Equation Part 1. Theoretical Development

As satellite communications systems become both more complex and reliant with respect to their operating environment, it has become imperative to be able to identify, during real-time operation, the onset of one or more impairments to the quality of overall communications system integrity. One of the most important aspects to monitor of a satellite link operating within the Earth's atmosphere is the signal fading due to the occurrence of rain and/or phase scintillations. This, of course, must be done in the presence of the associated measurement uncertainty or potentially faulty measurement equipment such as in the Advanced Communication Technology Satellite (ACTS) experiment. In the present work, an approach originally suggested in 1991, and apparently still considered iconoclastic, will be significantly developed and applied to the satellite communications link on which the deleterious composite signal fade is the result of one or many component fade mechanisms. Through the measurement (with the attendant uncertainty or 'error' in the measurement) of such a composite fading satellite signal, it is desired to extract the level of each of the individual fading mechanisms so they can be appropriately mitigated before they impact the overall performance of the communications network. Rather than employing simple-minded deterministic filtering to the real-time fading, the present approach is built around all the models and/or descriptions used to describe the individual fade components, including their dynamic evolution. The latter is usually given by a first-order Langevin equation. This circumstance allows the description of the associated temporal transition probability densities of each of the component processes. By using this description, along with the real-time measurements of the composite fade (along with the measurement errors), one can obtain statistical estimates of the levels of each of the component fading mechanisms as well as their predicted values into the future. This is all accomplished by the use of the well-known Stratonovich integro-differential equation that results from the model of the measured signal fade that is also tailored to adaptively adjust the values of the parameters used in the statistical models of the individual fade mechanisms. Three examples of increasing complexity are addressed and solved for the iterative determination of fade component levels from the measured composite signal fade in the presence of measurement error and, in the last case, with uncertainty in the model parameters.

Countermeasure↗
NASA NTRS1996

On the Stochastic Quantization Method: Characteristics and Applications to Singular Systems

Introducing the generalized Langevin equation, we extend the stochastic quantization method so as to deal with singular dynamical systems beyond the ordinary territory of quantum mechanics. We also show how the uncertainty relation is built up to the quantum mechanical limit with respect to fictitious time, irrespective of its initial value, within the framework of the usual stochastic quantization method.

Kanenaga, Masahiko↗
NASA NTRS1975

The simulated depth history of dust grains in the lunar regolith

Trajectories giving the individual depth variations of lunar dust grains with time are randomly generated by a Monte Carlo code, where the variables are the mass and speed distribution of meteorites at the lunar surface and the geometrical shape of impact craters. A statistical analysis of a great number of such trajectories is then used to define the 'average' depth history of lunar dust grains for two grain radii: 1 and 50 microns. This yields: (1) estimates for time constants involved during the dynamic evolution of the regolith, (2) a model for the layering of the regolith, and (3) a better understanding of the basic dust-grain mechanisms responsible for the formation of the most mature lunar soil samples. The validity of various soil models proposed for the dynamic evolution of the regolith is discussed in terms of experimental constraints on the models.

Duraud, J. P.↗
NASA NTRS1984

Description of quantum noise by a Langevin equation

General features of the quantum noise problem expressed as the equations of motion for a particle coupled to a set of oscillators are investigated analytically. Account is taken of the properties of the companion oscillators by formulating quantum statistical correlation Langevin equations (QSLE). The frequency of the oscillators is then retained as a natural cut-off for the quantum noise. The QSLE is further extended to encompass the particle trajectory and is bounded by initial and final states of the oscillator. The states are expressed as the probability of existence at the moment of particle collision that takes the oscillator into a final state. Two noise sources then exist: a statistical uncertainty of the initial state and the quantum dynamical uncertainty associated with a transition from the initial to final state. Feynman's path-integral formulation is used to characterize the functional of the particle trajectory, which slows the particle. It is shown that the energy loss may be attributed to friction, which satisfies energy conservation laws.

Metiu, H.↗
NASA NTRS1989

The formation of topological defects in phase transitions

It was argued, and fought through numerical work that the results of non-dynamical Monte Carlo computer simulations cannot be applied to describe the formation of topological defects when the correlation length at the Ginzburg temperature is significantly smaller than the horizon size. To test the current hypothesis that infinite strings at formation are essentially described by Brownian walks of size the correlation length at the Ginzburg temperature, fields at the Ginzburg temperature were equilibrated. Infinite structure do not exist in equilibrium for reasonable definitions of the Ginzburg temperature, and horizons must be included in a proper treatment. A phase transition, from small-scale to large-scale string or domain wall structure, is found to occur very close to the Ginzburg temperature, in agreement with recent work. The formation process of domain walls and global strings were investigated through the breaking of initially ordered states. To mimic conditions in the early Universe, cooling times are chosen so that horizons exist in the sample volume when topological structure formation occurs. The classical fields are evolved in real-time by the numerical solution of Langevin equations of motion on a three dimensional spatial lattice. The results indicate that it is possible for most of the string energy to be in small loops, rather than in long strings, at formation.

Hodges, Hardy M.↗
NASA NTRS2005

The Atmospheres of Saturn and Titan in the Near-Infrared: First Results of Cassini/VIMS

The wide spectral coverage and extensive spatial, temporal, and phase-angle mapping capabilities of the Visual Infrared Mapping Spectrometer (VIMS) onboard the Cassini-Huygens Orbiter are producing fundamental new insights into the nature of the atmospheres of Saturn and Titan. For both bodies, VIMS maps over time and solar phase angles provide information for a multitude of atmospheric constituents and aerosol layers, providing new insights into atmospheric structure and dynamical and chemical processes. For Saturn, salient early results include evidence for phosphine depletion in relatively dark and less cloudy belts at temperate and mid-latitudes compared to the relatively bright and cloudier Equatorial Region, consistent with traditional theories of belts being regions of relative downwelling. Additional Saturn results include (1) the mapping of enhanced trace gas absorptions at the south pole, and (2) the first high phase-angle, high-spatial-resolution imagery of CH4 fluorescence. An additional fundamental new result is the first nighttime near-infrared mapping of Saturn, clearly showing discrete meteorological features relatively deep in the atmosphere beneath the planet's sunlit haze and cloud layers, thus revealing a new dynamical regime at depth where vertical dynamics is relatively more important than zonal dynamics in determining cloud morphology. Zonal wind measurements at deeper levels than previously available are achieved by tracking these features over multiple days, thereby providing measurements of zonal wind shears within Saturn's troposphere when compared to cloudtop movements measured in reflected sunlight. For Titan, initial results include (1) the first detection and mapping of thermal emission spectra of CO, CO2, and CH3D on Titan's nightside limb, (2) the mapping of CH4 fluorescence over the dayside bright limb, extending to approximately 750 km altitude, (3) wind measurements of approximately 0.5 ms(exp -1), favoring prograde, from the movement of a persistent (multiple months) south polar cloud near 88 deg S latitude, and (4) the imaging of two transient mid-southern-latitude cloud features.

Cassini Mission↗
NASA NTRS2023

ICARUS: in-Situ Studies of the Solar Corona Beyond Parker Solar Probe and Solar Orbiter

The primary scientific goal of ICARUS (Investigation of Coronal AcceleRation and heating of solar wind Up to the Sun), a mother-daughter satellite mission, proposed in response to the ESA “Voyage 2050” Call, will be to determine how the magnetic field and plasma dynamics in the outer solar atmosphere give rise to the corona, the solar wind, and the entire heliosphere. Reaching this goal will be a Rosetta Stone step, with results that are broadly applicable within the fields of space plasma physics and astrophysics. Within ESA’s Cosmic Vision roadmap, these science goals address Theme 2: “How does the Solar System work?” by investigating basic processes occurring “From the Sun to the edge of the Solar System”. ICARUS will not only advance our understanding of the plasma environment around our Sun, but also of the numerous magnetically active stars with hot plasma coronae. ICARUS I will perform the first direct in situ measurements of electromagnetic fields, particle acceleration, wave activity, energy distribution, and flows directly in the regions in which the solar wind emerges from the coronal plasma. ICARUS I will have a perihelion altitude of 1 solar radius and will cross the region where the major energy deposition occurs. The polar orbit of ICARUS I will enable crossing the regions where both the fast and slow winds are generated. It will probe the local characteristics of the plasma and provide unique information about the physical processes involved in the creation of the solar wind. ICARUS II will observe this region using remote-sensing instruments, providing simultaneous, contextual information about regions crossed by ICARUS I and the solar atmosphere below as observed by solar telescopes. It will thus provide bridges for understanding the magnetic links between the heliosphere and the solar atmosphere. Such information is crucial to our understanding of the plasma physics and electrodynamics of the solar atmosphere. ICARUS II will also play a very important relay role, enabling the radio-link with ICARUS I. It will receive, collect, and store information transmitted from ICARUS I during its closest approach to the Sun. It will also perform preliminary data processing before transmitting it to Earth. Performing such unique in situ observations in the area where presumably hazardous solar energetic particles are energized, ICARUS will provide fundamental advances in our capabilities to monitor and forecast the space radiation environment. Therefore, the results from the ICARUS mission will be extremely crucial for future space explorations, especially for long-term crewed space missions.

Solar wind↗