An axiomatic explanation of complete self- reproduction.
Axiomatic explanation of complete self reproduction, noting logical mathematical biological reasoning and evolution theories
Loefgren, L.↗
SEARCH · Engineering Papers
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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Nucleation and growth control in protein crystallization
The five topics summarized in this final report are as follows: (1) a technique for the expedient, semi-automated determination of protein solubilities as a function of temperature and application of this technique to proteins other than lysozyme; (2) a small solution cell with adjustable temperature gradients for the growth of proteins at a predetermined location through temperature programming; (3) a microscopy system with image storage and processing capability for high resolution optical studies of temperature controlled protein growth and etching kinetics; (4) growth experiments with lysozyme in thermosyphon flow ; and (5) a mathematical model for the evolution of evaporation/diffusion induced concentration gradients in the hanging drop protein crystallization technique.
Rosenberger, Franz↗
On-Line, Real-Time Diagnostics of a Single Fluid Atomization System
A drop tube-Impulse Atomization technique was used to produce copper droplets. In this method, energy is transferred to a liquid by plunger movement resulting in spherical droplets emanating from orifices. A mathematical model of the evolution of droplet velocity and temperature at various heights for different sized droplets was developed. A two-color pyrometer, DPV-2000, and a shadowgraph were used to measure droplets radiant energy, diameter and velocity. The temperature values from the model were used to assess the two color pyrometer assumption over the temperature range of measurement. The DVP 2000 measurements were found to be dependent of droplet size wavelength and position of droplets below the atomizing nozzle. By calibrating the instrument for effective emissivity over the range of measurements, the thermal history of droplets may be recorded using a single color pyrometer approach.
DelshadKhatibi, P.↗
A novel physics-based and data-supported microstructure model for part-scale simulation of laser powder bed fusion of Ti-6Al-4V
The elasto-plastic material behavior, material strength and failure modes of metals fabricated by additive manufacturing technologies are significantly determined by the underlying process-specific microstructure evolution. In this work a novel physics-based and data-supported phenomenological microstructure model for Ti-6Al-4V is proposed that is suitable for the part-scale simulation of laser powder bed fusion processes. The model predicts spatially homogenized phase fractions of the most relevant microstructural species, namely the stable β-phase, the stable α s -phase as well as the metastable Martensite α m -phase, in a physically consistent manner. In particular, the modeled microstructure evolution, in form of diffusion-based and non-diffusional transformations, is a pure consequence of energy and mobility competitions among the different species, without the need for heuristic transformation criteria as often applied in existing models. The mathematically consistent formulation of the evolution equations in rate form renders the model suitable for the practically relevant scenario of temperature- or time-dependent diffusion coefficients, arbitrary temperature profiles, and multiple coexisting phases. Due to its physically motivated foundation, the proposed model requires only a minimal number of free parameters, which are determined in an inverse identification process considering a broad experimental data basis in form of time-temperature transformation diagrams. Subsequently, the predictive ability of the model is demonstrated by means of continuous cooling transformation diagrams, showing that experimentally observed characteristics such as critical cooling rates emerge naturally from the proposed microstructure model, instead of being enforced as heuristic transformation criteria. Eventually, the proposed model is exploited to predict the microstructure evolution for a realistic selective laser melting application scenario and for the cooling/quenching process of a Ti-6Al-4V cube of practically relevant size. Numerical results confirm experimental observations that Martensite is the dominating microstructure species in regimes of high cooling rates, e.g., due to highly localized heat sources or in near-surface domains, while a proper manipulation of the temperature field, e.g., by preheating the base-plate in selective laser melting, can suppress the formation of this metastable phase.
Inverse parameter identification↗
Evolution of heuristics by human operators in control systems.
Decision making mathematical model for control system operation modes, generating human operators heuristics evolution
Thomas, R. E.↗
Low order dynamical models for mixing layers
The goal of this project was to investigate the feasibility of developing useful low order dynamical systems to allow one to determine cheaply the effect of various initial conditions on the evolution of mixing layers. A mathematically rigorous approach for a time evolving base flow as found in a mixing layer seems to be the singular value decomposition of the linear operator transforming some initial perturbations into the solution at a given later time. Unfortunately, this is very costly, if at all feasible, and only deals with the linear evolution of a disturbance. A different approach based on weakly nonlinear analysis was attempted, but numerous difficulties were encountered. Several formulations were proposed which may be ill-posed. The reasons for this possible failure of the attempted approach is related to the fundamental limitations of weakly nonlinear analysis. The clarification of these issues is attempted in this report.
Riahi, D. N.↗
Quantifying disorder one atom at a time using an interpretable graph neural network paradigm
Abstract Quantifying the level of atomic disorder within materials is critical to understanding how evolving local structural environments dictate performance and durability. Here, we leverage graph neural networks to define a physically interpretable metric for local disorder, called SODAS. This metric encodes the diversity of the local atomic configurations as a continuous spectrum between the solid and liquid phases, quantified against a distribution of thermal perturbations. We apply this methodology to four prototypical examples with varying levels of disorder: (1) grain boundaries, (2) solid-liquid interfaces, (3) polycrystalline microstructures, and (4) tensile failure/fracture. We also compare SODAS to several commonly used methods. Using elemental aluminum as a case study, we show how our paradigm can track the spatio-temporal evolution of interfaces, incorporating a mathematically defined description of the spatial boundary between order and disorder. We further show how to extract physics-preserved gradients from our continuous disorder fields, which may be used to understand and predict materials performance and failure. Overall, our framework provides a simple and generalizable pathway to quantify the relationship between complex local atomic structure and coarse-grained materials phenomena.
36 MATERIALS SCIENCE↗
Force Density Function Relationships in 2-D Granular Media
An integral transform relationship is developed to convert between two important probability density functions (distributions) used in the study of contact forces in granular physics. Developing this transform has now made it possible to compare and relate various theoretical approaches with one another and with the experimental data despite the fact that one may predict the Cartesian probability density and another the force magnitude probability density. Also, the transforms identify which functional forms are relevant to describe the probability density observed in nature, and so the modified Bessel function of the second kind has been identified as the relevant form for the Cartesian probability density corresponding to exponential forms in the force magnitude distribution. Furthermore, it is shown that this transform pair supplies a sufficient mathematical framework to describe the evolution of the force magnitude distribution under shearing. Apart from the choice of several coefficients, whose evolution of values must be explained in the physics, this framework successfully reproduces the features of the distribution that are taken to be an indicator of jamming and unjamming in a granular packing. Key words. Granular Physics, Probability Density Functions, Fourier Transforms
Youngquist, Robert C.↗
Posiva's Onkalo{sup R} FST (Full-Scale In Situ System Test) - 20051
The FST - Full-scale In Situ System Test - is a unique full-scale demonstration of disposal system in crystalline host rock. The FST was constructed in ONKALO{sup R} demonstration area at the disposal depth of 420 metres, in Posiva's actual final disposal facility at Olkiluoto, Finland. The demonstration has included design, manufacture, installation and comprehensive instrumentation for monitoring the evolution of the disposal system and its components. The demonstration tunnel and experimental deposition holes were excavated in 2010 in ONKALO to address that they can be excavated to meet the requirements set for them. Two experimental deposition holes, bored in the floor of the tunnel, host each a canister surrounded by bentonite clay buffer rings/segments in the holes. Inside the canisters are heating elements to simulate decay heat emitted by spent fuel. The tunnel part used for the test is about 50 m long and it was filled with bentonite clay backfill after the installation of the canisters and buffer components. The tunnel is closed with a steel-reinforced concrete plug. The test is equipped with 500 sensors to monitor early evolution of the system. To forecast the evolution of the system, a mathematical model has been created. (authors)
12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
Elucidating Cycling Rate-Dependent Electrochemical Strains in Sodium Iron Phosphate Cathodes for Na-ion Batteries
Battery electrodes materials undergo significant mechanical instabilities which affects their longevity and exert rate-limitations during the cycling process. In this study, we investigate the rate-dependent mechanical response of sodium iron phosphate (NaFePO4, NFP) cathodes during Na intercalation via galvanostatic cycling at different rates by employing digital image correlation, electrochemical methods, and mathematical model. The mechanical behaviour of the electrode shows strong dependance on the applied scan rate. At slower rates, electrode shows asymmetrical strain generation between anodic and cathodic cycles, which is attributed to the formation of cathode-electrolyte interface layers. The electrode undergoes smaller strain generation when cycled at slower rates when the same amount of Na ions is removed or inserted into the electrode. A mathematical model was developed to predict strain evolution in the composite electrode as well as the concentration profile of the Na ions in the electrode particles. Rate-dependent and time dependent factors on the strain generation in the electrode are attributed to the capacity-dependent intercalation strains, rate-dependent mismatch strains, and time-dependent irreversible strains. The combination of in situ strain measurements with the analytical model provided new insight into the electrochemically induced mechanical deformations in Na-ion cathode electrodes.
Ozdogru, Bertan↗
Kinematic Flow and the Emergence of Time
Perhaps the most basic question we can ask about cosmological correlations is how their strength changes as we smoothly vary kinematic parameters. The answer is encoded in differential equations that govern this evolution in kinematic space. In this Letter, we introduce a new perspective on these differential equations. We show that, in the simplified setting of conformally coupled scalars in power-law Friedmann-Robertson-Walker spacetimes, the equations for arbitrary tree-level processes can be obtained from a small number of simple combinatorial rules. While this “kinematic flow” is defined purely in terms of boundary data, it reflects the physics of bulk time evolution. The unexpected regularity of the equations suggests the existence of an autonomously defined mathematical structure from which cosmological correlations and the time evolution of the associated spacetime emerge.
79 ASTRONOMY AND ASTROPHYSICS↗
On principles of emergent organization
After more than a century of concerted effort, physics still lacks basic principles of spontaneous organization. To appreciate why, we first state the problem, outline historical approaches, and survey the present state of the physics of self-organization. This frames the particular challenges arising from mathematical intractability and the resulting need for computational approaches, as well as those arising from a chronic failure to define structure. Then an overview of two modern mathematical formulations of organization—intrinsic computation and evolution operators—lays out a way to overcome these challenges. Together, the vantage point they afford shows how to account for the emergence of structured states via a statistical mechanics of systems arbitrarily far from equilibrium. The result is a constructive path forward to principles of organization that builds on mathematical identification of structure.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Mathematical Modeling of the Potential and Time Dependence of Ir Dissolution from Hydrous Ir Oxide Oxygen Evolution Catalysts
One of the main degradation mechanisms of hydrous iridium oxide acidic oxygen evolution reaction (OER) catalysts is dissolution and loss into the acidic membrane. While degradation models have been proposed, there is a gap in understanding the potential and time dependence of the iridium dissolution reaction and its mechanistic underpinnings. In this work, Ir dissolution rates measured as a function of time and potential via time-resolved inductively-coupled plasma mass spectrometry (ICP-MS) in aqueous acidic electrolyte are used to establish a mathematical model for Ir dissolution. The mathematical model is generated using proposed formation and dissolution reactions for Ir species. Through comparison with the ICP-MS data and existing information on the potential-dependent Ir phase, we find that the potential and time-dependence of dissolution can be modeled as dissolution of an oxide phase, here represented as IrO 2 , with potential dependent kinetics and formation of a passivating species, a process with a rate-limiting step that is not potential dependent. This understanding of the potential dependence of dissolution and passivation kinetics using aqueous electrolyte half-cell measurements can be used to predict the degradation of Ir oxide in operating energy conversion devices relying on the OER, such as proton-exchange membrane water electrolyzers.
Kariuki, Nancy N. [Argonne National Laboratory (AN↗
A mathematical framework for ejecta cloud dynamics with application to source models and piezoelectric mass measurements
We present a mathematical framework for describing the dynamical evolution of an ejecta cloud generated by a generic ejecta source model. We consider a piezoelectric sensor fielded in the path of an ejecta cloud, for experimental configurations in which the ejecta are created at a singly shocked planar surface and fly ballistically through vacuum to the stationary sensor. To do so, we introduce the concept of a time- and velocity-dependent ejecta “areal mass function.” We derive expressions for the analytic (“true”) accumulated ejecta areal mass at the sensor and the measured (“inferred”) value obtained via the standard method for analyzing piezoelectric voltages. In this way, we derive an exact expression and upper bound for the error imposed upon a piezoelectric ejecta mass measurement (in a perfect system) by the assumption of instantaneous creation, which is commonly required for momentum diagnostic analyses. This error term is zero for truly instantaneous source models; otherwise, the standard piezoelectric analysis is guaranteed to overestimate the true mass. When combined with a piezoelectric dataset, this framework provides a unique solution for the ejecta particle velocity distribution, subject to the assumptions inherent in the data analysis. The framework also leads to strong boundary conditions that any ejecta source model must satisfy in order to be consistent with apparently global properties of piezoelectric measurements from a wide range of experiments. We demonstrate this methodology by applying it to the Richtmyer–Meshkov instability+self-similar velocity distribution ejecta source model currently under development at Los Alamos National Laboratory.
97 MATHEMATICS AND COMPUTING↗
Exploring temporal community evolution: algorithmic approaches and parallel optimization for dynamic community detection
Abstract Dynamic (temporal) graphs are a convenient mathematical abstraction for many practical complex systems including social contacts, business transactions, and computer communications. Community discovery is an extensively used graph analysis kernel with rich literature for static graphs. However, community discovery in a dynamic setting is challenging for two specific reasons. Firstly, the notion of temporal community lacks a widely accepted formalization, and only limited work exists on understanding how communities emerge over time. Secondly, the added temporal dimension along with the sheer size of modern graph data necessitates new scalable algorithms. In this paper, we investigate how communities evolve over time based on several graph metrics under a temporal formalization. We compare six different algorithmic approaches for dynamic community detection for their quality and runtime. We identify that a vertex-centric (local) optimization method works as efficiently as the classical modularity-based methods. To its advantage, such local computation allows for the efficient design of parallel algorithms without incurring a significant parallel overhead. Based on this insight, we design a shared-memory parallel algorithm DyComPar , which demonstrates between 4 and 18 fold speed-up on a multi-core machine with 20 threads, for several real-world and synthetic graphs from different domains.
97 MATHEMATICS AND COMPUTING↗
Advection versus diffusion in Richtmyer-Meshkov mixing
The Richtmyer-Meshkov (RM) instability is one of the most severe degradation mechanisms for inertial confinement fusion (ICF), and mitigating it has been a priority for the global ICF effort. In this Letter, the instability's ability to atomically mix is linked to its background decay of residual turbulent energy. Here, we show how recently derived inequalities from the mathematical theory of PDEs constrain the evolution. A model RM process at leading order may diffusively mix or retain imprints of its initial structures indefinitely, depending on initial conditions, and there exists a theoretical range of zero-mixing for certain values of parameters. The results may apply to other systems resembling scalar transport in decaying turbulence.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Transmission Line Based Sensor Design for FMCW Radar Processing of Collision Damage
This report presents a framework for transmission line ( T-L ) sensor design in Frequency Modulated Continuous Wave (FMCW) radar applications, with particular emphasis on modeling collision damage effects. Classical electromagnetic (EM) propagation theory is combined with impact mechanics to develop a model for analyzing transmission line behavior as a sensor under high-velocity impact conditions. The framework includes detailed mathematical derivations, spatial and temporal damage evolution models, and practical implementation considerations.
42 ENGINEERING↗
Chronology of the early lunar crust
The Rb-Sr systematics of lunar 'anorthositic' rocks was studied in an effort to understand the evolution of the lunar crust. The contamination by KREEP of the anorthositic crust is corrected using chemical mixing models; cumulate geochemical models are used to establish the chronology of the early lunar crust; a method is presented to derive an estimate of the Rb/Sr ratio of the moon. A mathematical model for the Rb-Sr evolution of the lunar crust that includes mare basalt genesis is presented.
Schonfeld, E.↗