Evolution of heuristics by human operators in control systems.
Mathematical model for decision making /heuristics/ by human operators in control systems
Thomas, R. E.↗
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Results for “MATHEMATICAL EVOLUTION”
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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Designing a Unique Single Point Cross Over Method
The idea behind genetic algorithms is to extract optimization strategies nature uses successfully - known as Darwinian Evolution - and transform them for application in mathematical optimization theory to find the global optimum in a defined phase space. One could imagine a population of individual 'explorers' sent into the optimization phase-space. Each explorer is defined by its genes, what means, its position inside the phase-space is coded in his genes. Every explorer has the duty to find a value of the quality of his position in the phase space. (Consider the phase-space being a number of variables in some technological process, the value of quality of any position in the phase space - in other words: any set of the variables - can be expressed by the yield of the desired chemical product.) Then the struggle of 'life' begins. The three fundamental principles are selection, mating/crossover, and mutation. Only explorers (= genes) sitting on the best places will reproduce and create a new population. This is performed in the second step (mating/crossover). The 'hope' behind this part of the algorithm is, that 'good' sections of two parents will be recombined to yet better fitting children. In fact, many of the created children will not be successful (as in biological evolution), but a few children will indeed fulfill this hope. These good sections are named in some publications as building blocks. Now there appears a problem. Repeating these steps, no new area would be explored. The two former steps would only exploit the already known regions in the phase space, which could lead to premature convergence of the algorithm with the consequence of missing the global optimum by exploiting some local optimum. The third step, mutation, ensures the necessary accidental effects. One can imagine the new population being mixed up a little bit to bring some new information into this set of genes. Whereas in biology a gene is described as a macro-molecule with four different bases to code the genetic information, a gene in genetic algorithms is usually defined as a bitstring (a sequence of b 1's and 0's).
Wilson, Richard Phillip↗
On the theory of the structure of Mars.
Martian structure theory, comparing mathematical model based on earth long term evolution and ad hoc models
Lyttleton, R. A.↗
Numerical Calculation of the Morphology of a Solid/Liquid Interface Near an Insoluble Particle
A numerical mathematical model capable of accurately describing the evolution of the shape of the solid/liquid interface in the proximity of a foreign particle is presented in this paper. The model accounts for the influence of the temperature gradient and the Gibbs-Thomson and disjoining pressure effects. It shows that for the systems characterized by k(sub P) < k(sub L) the disjoining pressure causes the interface curvature to change its sign in the close-contact particle/interface region. It also shows that the increase of the temperature gradient diminishes the effect of the disjoining pressure. Calculated critical solidification velocities for the pushing/engulfment transition are compared with experimental measurements performed in microgravity conditions.
Catalina, Adrian V.↗
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↗
JOINT APPOINTEE: Evolution of ferroelectric properties in SmxBi1-xFeO3 via automated Piezoresponse Force Microscopy across combinatorial spread libraries
Combinatorial spread libraries offer a innovative approach to explore the evolution of material properties over broad concentration, temperature, and growth parameter spaces. However, traditional limitation of this approach is the requirement for the read-out of functional properties across the library. Here we develop automated Piezoresponse Force Microscopy (PFM) for the exploration of combinatorial spread libraries and demonstrate its application in the SmxBi1-xFeO3 system with the ferroelectric-antiferroelectric morphotropic phase boundary. This approach relies on the synergy of the quantitative nature of PFM and the implementation of automated experiments that allow PFM-based sampling over macroscopic samples. The concentration dependence of pertinent ferroelectric parameters has been determined and used to develop the mathematical framework based on Ginzburg-Landau theory describing the evolution of these properties across the concentration space. We pose that a combination of automated scanning probe microscope and combinatorial spread library approach will emerge as an efficient research paradigm to close the characterization gap in the high-throughput materials discovery. We make the data sets open to the community and hope that this will stimulate other efforts to interpret and understand the physics of these systems.
Automated Microscopy, Combinatorial Library, Ferro↗
Scale covariant gravitation. V - Kinetic theory. VI - Stellar structure and evolution
A scale covariant kinetic theory for particles and photons is developed. The mathematical framework of the theory is given by the tangent bundle of a Weyl manifold. The Liouville equation is derived, and solutions to corresponding equilibrium distributions are presented and shown to yield thermodynamic results identical to the ones obtained previously. The scale covariant theory is then used to derive results of interest to stellar structure and evolution. A radiative transfer equation is derived that can be used to study stellar evolution with a variable gravitational constant. In addition, it is shown that the sun's absolute luminosity scales as L approximately equal to GM/kappa, where kappa is the stellar opacity. Finally, a formula is derived for the age of globular clusters as a function of the gravitational constant using a previously derived expression for the absolute luminosity.
Hsieh, S.-H.↗
Efficient inverse design optimization through multi-fidelity simulations, machine learning, and boundary refinement strategies
Not Available
97 MATHEMATICS AND COMPUTING↗
Spatially Patterned Architectures to Modulate CO 2 Reduction Cascade Catalysis Kinetics
Electrochemical CO 2 reduction using renewable sources of electrical energy holds promise for converting CO 2 into fuels and chemicals. The complex interactions among chemical/electrochemical reactions and mass transport make it difficult to analyze the effect of an individual process on electrode performance based only on experimental methods. Here, we developed a generalized steady-state simulation to describe an electrode surface in which sequential cascade catalysts are patterned in a periodic trench design. If appropriately constructed, this trench geometry is hypothesized to be able to yield a higher net current density for a CO 2 reduction (CO 2 R) cascade reaction. We have used realistic experimental reaction kinetics to investigate the role of trench geometry in mass transport, local microenvironments, and selectivity for a model CO 2 R cascade reaction. The model considers local concentration gradients of bicarbonate species at quasi-equilibrium and catalytic surface reactions based on concentration-dependent Butler–Volmer kinetics. Our results suggest that varying the spatial distribution of active sites plays a significant role in facilitating effective mass transport between active sites, modulating selectivity for the cascade reaction, and enhancing the yield of desirable cascade products. Moreover, we observe that this trench geometry significantly alters the cascade reaction rate by affecting the local pH, which can cause inadvertent depletion of available aqueous CO 2 to limit the CO 2 R cascade kinetics and modest suppression of the hydrogen evolution reaction (HER). The results highlight the trade-offs between mass transport, pH, and reaction kinetics that become apparent only when considering the coupled physics of all processes at the electrode surface. Here, this model can thus serve as a primary tool to build more selective and efficient patterned architectures for the CO 2 R cascade catalysis.
CO2 reduction↗
LevSeq: Rapid Generation of Sequence-Function Data for Directed Evolution and Machine Learning
Sequence-function data provides valuable information about the protein functional landscape but is rarely obtained during directed evolution campaigns. Here, we present Long-read every variant Sequencing (LevSeq), a pipeline that combines a dual barcoding strategy with nanopore sequencing to rapidly generate sequence-function data for entire protein-coding genes. LevSeq integrates into existing protein engineering workflows and comes with open-source software for data analysis and visualization. The pipeline facilitates data-driven protein engineering by consolidating sequence-function data to inform directed evolution and provide the requisite data for machine learning-guided protein engineering (MLPE). LevSeq enables quality control of mutagenesis libraries prior to screening, which reduces time and resource costs. Simulation studies demonstrate LevSeq’s ability to accurately detect variants under various experimental conditions. Lastly, we show LevSeq’s utility in engineering protoglobins for new-to-nature chemistry. Widespread adoption of LevSeq and sharing of the data will enhance our understanding of protein sequence-function landscapes and empower data-driven directed evolution.
59 BASIC BIOLOGICAL SCIENCES↗
Nonlinear causality and strong hyperbolicity of baryon-rich Israel-Stewart hydrodynamics
We present the first set of fully-nonlinear, necessary and sufficient conditions guaranteeing causal evolution of the initial data for the Israel-Stewart hydrodynamic equations with shear and bulk viscosity coupled to a nonzero baryon current. These constraints not only provide nonlinear causality: they also (a) guarantee the existence of a locally well-posed evolution of the initial data (they enforce strong hyperbolicity) when excluding the endpoints of the bounds, (b) arise from purely algebraic constraints that make no underlying symmetry assumptions on the degrees of freedom and (c) propagate the relevant symmetries of the degrees of freedom over the entire evolution of the problem. Our work enforces a mathematically rigorous foundation for future studies of viscous relativistic hydrodynamics with baryon-rich matter including neutron star mergers and heavy-ion collisions.
Cordeiro, Ian [University of Illinois Urbana-Champ↗
Comparative evolution of the inverse problems (Introduction to an interdisciplinary study of the inverse problems)
The progressive realization of the consequences of nonuniqueness imply an evolution of both the methods and the centers of interest in inverse problems. This evolution is schematically described together with the various mathematical methods used. A comparative description is given of inverse methods in scientific research, with examples taken from mathematics, quantum and classical physics, seismology, transport theory, radiative transfer, electromagnetic scattering, electrocardiology, etc. It is hoped that this paper will pave the way for an interdisciplinary study of inverse problems.
Sabatier, P. C.↗
Abstracts for the International Conference on Asteroids, Comets, Meteors 1991
Topics addressed include: chemical abundances; asteroidal belt evolution; sources of meteors and meteorites; cometary spectroscopy; gas diffusion; mathematical models; cometary nuclei; cratering records; imaging techniques; cometary composition; asteroid classification; radio telescopes and spectroscopy; magnetic fields; cosmogony; IUE observations; orbital distribution of asteroids, comets, and meteors; solar wind effects; computerized simulation; infrared remote sensing; optical properties; and orbital evolution.
Source record↗
Direct numerical simulations of a reacting turbulent mixing layer by a pseudospectral-spectral element method
An account is given of the implementation of the spectral-element technique for simulating a chemically reacting, spatially developing turbulent mixing layer. Attention is given to experimental and numerical studies that have investigated the development, evolution, and mixing characteristics of shear flows. A mathematical formulation is presented of the physical configuration of the spatially developing reacting mixing layer, in conjunction with a detailed representation of the spectral-element method's application to the numerical simulation of mixing layers. Results from 2D and 3D calculations of chemically reacting mixing layers are given.
Mcmurtry, Patrick A.↗
Serious Gaming for Test & Evaluation of Clean-Slate (Ab Initio) National Airspace System (NAS) Designs
Incremental approaches to air transportation system development inherit current architectural constraints, which, in turn, place hard bounds on system capacity, efficiency of performance, and complexity. To enable airspace operations of the future, a clean-slate (ab initio) airspace design(s) must be considered. This ab initio National Airspace System (NAS) must be capable of accommodating increased traffic density, a broader diversity of aircraft, and on-demand mobility. System and subsystem designs should scale to accommodate the inevitable demand for airspace services that include large numbers of autonomous Unmanned Aerial Vehicles and a paradigm shift in general aviation (e.g., personal air vehicles) in addition to more traditional aerial vehicles such as commercial jetliners and weather balloons. The complex and adaptive nature of ab initio designs for the future NAS requires new approaches to validation, adding a significant physical experimentation component to analytical and simulation tools. In addition to software modeling and simulation, the ability to exercise system solutions in a flight environment will be an essential aspect of validation. The NASA Langley Research Center (LaRC) Autonomy Incubator seeks to develop a flight simulation infrastructure for ab initio modeling and simulation that assumes no specific NAS architecture and models vehicle-to-vehicle behavior to examine interactions and emergent behaviors among hundreds of intelligent aerial agents exhibiting collaborative, cooperative, coordinative, selfish, and malicious behaviors. The air transportation system of the future will be a complex adaptive system (CAS) characterized by complex and sometimes unpredictable (or unpredicted) behaviors that result from temporal and spatial interactions among large numbers of participants. A CAS not only evolves with a changing environment and adapts to it, it is closely coupled to all systems that constitute the environment. Thus, the ecosystem that contains the system and other systems evolves with the CAS as well. The effects of the emerging adaptation and co-evolution are difficult to capture with only combined mathematical and computational experimentation. Therefore, an ab initio flight simulation environment must accommodate individual vehicles, groups of self-organizing vehicles, and large-scale infrastructure behavior. Inspired by Massively Multiplayer Online Role Playing Games (MMORPG) and Serious Gaming, the proposed ab initio simulation environment is similar to online gaming environments in which player participants interact with each other, affect their environment, and expect the simulation to persist and change regardless of any individual player's active participation.
Allen, B. Danette↗
Ratchetting behavior in viscoplasticity - A technical note
Viscoplastic models that use the Armstrong and Frederick (1966) kinematic hardening relationship are known to generally overpredict the observed accumulation of ratchet strains. The reason for this behavior is a consequence of the mathematics used to describe Hooke's law and the evolution equations for plastic strain and back stress. Conditions for ratchetting exist whenever there is a cycle-averaged mean stress present over a cyclic loading path. Two types of controlled loading paths are often studied: cyclic relaxation is the ratchet mechanism associated with displacement (strain) control, while cyclic creep is the ratchet mechanism associated with load (stress) control. Overcoming the possible adverse trends in predicted ratchetting behavior is a difficult task, and how one ought to go about doing this is not yet completely clear. We therefore choose to discuss the mathematical cause of ratchetting and how it has been dealt with to date, but make no attempt to correct this flaw.
Freed, Alan D.↗
GenASiS Mathematics: Object-oriented manifolds, operations, and solvers for large-scale physics simulations (version 2)
We report GenASiS Mathematics provides modern Fortran classes furnishing extensible object-oriented functionality for the solution of fields governed by selected partial differential equations. The initial release included extensible object-oriented implementations of simple meshes and the evolution of generic conserved currents thereon. This revision - Version 2 of Mathematics - includes significant reorganization and streamlining of these classes, higher-order reconstruction by a different method, a Poisson solver, coarsening to avoid Courant time step limitations near coordinate singularities, and the offloading of computational kernels to GPUs.
97 MATHEMATICS AND COMPUTING↗
Bifurcation Analysis Reveals Solution Structures of Phase Field Models
The phase field method is playing an increasingly important role in understanding and predicting morphological evolution in materials and biological systems. Here, in this study, we develop a new analytical approach based on the bifurcation analysis to explore the mathematical solution structure of phase field models. Revealing such solution structures not only is of great mathematical interest but also may provide guidance to experimentally or computationally uncover new morphological evolution phenomena in materials undergoing electronic and structural phase transitions. To elucidate the idea, we apply this analytical approach to three representative phase field equations: the Allen-Cahn equation, the Cahn-Hilliard equation, and the Allen-Cahn-Ohta-Kawasaki system. The solution structures of these three phase field equations are also verified numerically by the homotopy continuation method.
97 MATHEMATICS AND COMPUTING↗