On balance equations for heterogeneous continua.
Balance equations for heterogeneous continua - substances consisting of many distinct, possibly interacting constituents derived from classical continuum physics viewpoint
BALANCE EQUATION↗
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Terminal Model Of Newtonian Dynamics
Paper presents study of theory of Newtonian dynamics of terminal attractors and repellers, focusing on issues of reversibility vs. irreversibility and deterministic evolution vs. probabilistic or chaotic evolution of dynamic systems. Theory developed called "terminal dynamics" emphasizes difference between it and classical Newtonian dynamics. Also holds promise for explaining irreversibility, unpredictability, probabilistic behavior, and chaos in turbulent flows, in thermodynamic phenomena, and in other dynamic phenomena and systems.
Zak, Michail↗
Strongly magnetized classical plasma models
Discrete particle processes in the presence of a strong external magnetic field were investigated. These processes include equations of state and other equilibrium thermodynamic relations, thermal relaxation phenomena, transport properties, and microscopic statistical fluctuations in such quantities as the electric field and the charge density. Results from the equilibrium statistical mechanics of two-dimensional plasmas are discussed, along with nonequilibrium statistical mechanics of the electrostatic guiding-center plasma (a two-dimensional plasma model).
Montgomery, D.↗
Gravitational tides in the outer planets. I - Implications of classical tidal theory. II - Interior calculations and estimation of the tidal dissipation factor
Classical tidal theory is applied to the atmospheres of the outer planets. The tidal geopotential due to satellites of the outer planets is discussed, and the solution of Laplace's tidal equation for Hough modes appropriate to tides on the outer planets is examined. The vertical structure of tidal modes is described, noting that only relatively high-order meridional mode numbers can propagate vertically with growing amplitude. Expected magnitudes for tides in the visible atmosphere of Jupiter are discussed. The classical theory is extended to planetary interiors taking the effects of spherically and self-gravity into account. The thermodynamic structure of Jupiter is described and the WKB theory of the vertical structure equation is presented. The regions for which inertial, gravity, and acoustic oscillations are possible are delineated. The case of a planet with a neutral interior is treated, discussing the various atmospheric boundary conditions and showing that the tidal response is small.
Ioannou, Petros J.↗
Thermodynamic Behavior of Nano-sized Gold Clusters on the (001) Surface
We have studied thermal expansion of the surface layers of the hexagonally reconstructed Au (001) surface using a classical Molecular Dynamics (MD) simulation technique with an Embedded Atomic Method (EAM) type many-body potential. We find that the top-most hexagonal layer contracts as temperature increases, whereas the second layer expands or contracts depending on the system size. The magnitude of expansion coefficient of the top layer is much larger than that of the other layers. The calculated thermal expansion coefficients of the top-most layer are about -4.93 x 10(exp -5)Angstroms/Kelvin for the (262 x 227)Angstrom cluster and -3.05 x 10(exp -5)Angstroms/Kelvin for (101 x 87)Angstrom cluster. The Fast Fourier Transform (FFT) image of the atomic density shows that there exists a rotated domain of the top-most hexagonal cluster with rotation angle close to 1 degree at temperature T less than 1000Kelvin. As the temperature increases this domain undergoes a surface orientational phase transition. These predictions are in good agreement with previous phenomenological theories and experimental studies.
Paik, Sun M.↗
Transport Processes in Dendritic Crystallization
Free dentritic growth refers to the unconstrained development of crystals within a supercooled melt, which is the classical dendrite problem. The development of theoretical understanding of dendritic growth and its experimental status is sketched showing that transport theory and interfacial thermodynamics (capillarity theory) are insufficient ingredients to develop a truly predictive model of dendrite formation. The convenient, but incorrect, notion of maximum velocity was used for many years to estimate the behavior of dendritic transformations until supplanted by modern dynamic stability theory. The proper combinations of transport theory and morphological stability seem to be able to predict the salient aspects of dendritic growth, especially in the neighborhood of the tip.
Glicksman, M. E.↗
The rate parameters for coupled rotation-vibration-dissociation phenomenon in H2
The effects of molecular rotation on coupled vibration-dissociation phenomena in H2 undergoing a nonequilibrium relaxation in a heating and cooling environment were studied theoretically. The rate coefficients for the collisional bound-bound and bound-free transitions, calculated by a quasi-classical trajectory method, were fed into the master equation, which was numerically solved to determine the rotational and vibrational population densities and bulk thermodynamic properties. Results indicate that the vibrational transition rates of H2 increase monotonically with the vibrational levels, faster than in the Landau-Teller (1936) model, and that the rotation of the molecules helps relax the low vibrational levels, serves as a temporary storage of vibrational energy during the relaxation, and thereby delays the dissociation process. The average energy loss due to the dissociation was determined to be about 80-90 percent of the total dissociation energy.
Sharma, Surendra P.↗
Diatomic molecule variations
The rotational energy is separated from vibrational energy in the two-particle, steady-state wave equation and to first order the solutions are harmonic oscillator functions. The classical phase integral gives a partition function valid only at high temperature, but the quantum summation is easily performed to give analytic expressions for all the thermodynamic properties of the harmonic oscillator at all temperatures. Anharmonic effects are treated by small perturbation solutions to the wave equation and the relation between energy levels and a series expansion of the perturbation potential is derived. Next, the quantum solutions for an oscillator with a Morse-function potential are derived in terms of Laguerre polynomials.
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Machine Learning Approaches for Rare-Earth Silicate Environmental Barrier Coating Thermochemical and Thermomechanical Property Predictions
Environmental barrier coatings (EBCs) are a necessary enabling technology for the transition from superalloys to silicon carbide (SiC) ceramic matrix composites (CMCs) in gas turbine engines for increased efficiency and decreased fuel costs. SiC-based CMCs are prone to oxidation-based degradation in the engine hot section, and rare-earth (RE) silicates are promising candidates for EBCs due to their close thermal expansion match to the composite substrate and oxidation resistance. However, the design of EBCs is hindered by the large chemical space of candidate materials and the difficulty in obtaining material properties for engineering optimization. This is especially difficult as research continues into mixed-cation or “high-entropy” RE silicates. First-principles computational methods such as density functional theory (DFT) are highly effective at calculating material properties to guide coating design but are limited by their computational cost. Atomistic simulations have the potential to both accelerate property calculations and expand the properties able to be calculated due to their lower computational compared to DFT. However, they require interatomic potentials (IAPs) specific to the material system of interest, and, to our knowledge, there are no suitable IAPs for RE silicates. Machine learning (ML) is a promising technique to accelerate material property predictions indirectly by generating IAPs for atomistic simulations or via direct prediction. In this work, we present two ML approaches to accelerate the calculation of RE silicate properties relevant to EBC design: 1) a ML-derived interatomic potential (IAP) for atomistic simulations of yttrium disilicate (Y2Si2O7) from DFT training data, and 2) a neural network (NN) model to directly predict thermochemical properties of RE silicates and oxides directly from easily obtainable unit cell parameters. Classical MD simulations using the IAP yield lattice properties and bond lengths in good agreement with both DFT and experimental results from x-ray diffraction. Thermodynamic properties calculated using the finite-displacement phonon method and quasi-harmonic approximation were orders of magnitude faster than DFT with good agreement to the DFT results. The IAP was also used to calculate properties such as coefficient of thermal expansion (CTE) that require large simulation supercells and are therefore difficult with DFT. The IAP correctly predicted the anisotropic nature of the CTE in three different phases of Y2Si2O7. The NN model predicts constant pressure heat capacity, Cp, orders of magnitude faster than DFT calculations, which can enable its use as a surrogate model for multiscale simulations. The two methods presented in this work demonstrate the utility of ML for accelerating the prediction of RE silicate properties, which can in turn accelerate EBC design and optimization.
machine learning↗
Scalar/Vector potential formulation for compressible viscous unsteady flows
A scalar/vector potential formulation for unsteady viscous compressible flows is presented. The scalar/vector potential formulation is based on the classical Helmholtz decomposition of any vector field into the sum of an irrotational and a solenoidal field. The formulation is derived from fundamental principles of mechanics and thermodynamics. The governing equations for the scalar potential and vector potential are obtained, without restrictive assumptions on either the equation of state or the constitutive relations or the stress tensor and the heat flux vector.
Morino, L.↗
Mechanics and thermodynamics in lubrication
The causes for breakdown in the lubricant film of mineral oils are discussed. It is stated that the critical point is caused by desorption of the naturally occurring surface active agent and can be described by thermodynamic analysis. The effect of different metals in lubrication is surveyed. The problem of breakdown in elastohydrodynamic lubrication is treated phenomenologically by studying traction. The topics considered are classical and non-Newtonian explanations, anomalous film thickness and viscosity effects, surface roughness contributions, and solidification of the lubricant. Reasons for the apparent granular traction characteristics are examined.
Cameron, A.↗
Characteristics of Distinctive Regions Comprising Stellar Atmospheres
Empirically identified atmospheric regions whose existence and properties generally have no classical-theoretical basis are discussed. The quasi-thermal photosphere, chromosphere, lower corona, upper corona, non-decelerated post corona, decelerated post corona, and the H sub alpha emission envelope are defined. The observational phenomena, thermodynamic mechanisms, and diagnostic aspects associated with each of the atmospheric layers are described.
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Electrical double layers at the oil/water interface
This review presents the historical development and current status of the theory of the electrical double layer at a liquid/liquid interface. It gives rigorous thermodynamic definitions of all basic concepts related to liquid interfaces and to the electrical double layer. The difference between the surface of a solid electrode and the interface of two immiscible electrolyte solutions (ITIES) is analyzed in connection to their electrical properties. The most important classical relationships for the electrical double layer are presented and critically discussed. The generalized adsorption isotherm is derived. After a short review of the classical Gouy-Chapman and Verwey-Niessen models, more recent developments of the double layer theory are presented. These include effects of variable dielectric permittivity, nonlocal electrostatics, hydration forces, the modified Poisson-Boltzmann equation and the ion-dipole plasma. The relative merits of different theories are estimated by comparing them with computer simulation of the ITIES and electrical double layer. Special attention is given to the structure of ITIES and its variation due to adsorption of ions and amphiphilic molecules.
Non-NASA Center↗
An approximate theoretical method for modeling the static thrust performance of non-axisymmetric two-dimensional convergent-divergent nozzles
An analytical/numerical method has been developed to predict the static thrust performance of non-axisymmetric, two-dimensional convergent-divergent exhaust nozzles. Thermodynamic nozzle performance effects due to over- and underexpansion are modeled using one-dimensional compressible flow theory. Boundary layer development and skin friction losses are calculated using an approximate integral momentum method based on the classic karman-Polhausen solution. Angularity effects are included with these two models in a computational Nozzle Performance Analysis Code, NPAC. In four different case studies, results from NPAC are compared to experimental data obtained from subscale nozzle testing to demonstrate the capabilities and limitations of the NPAC method. In several cases, the NPAC prediction matched experimental gross thrust efficiency data to within 0.1 percent at a design NPR, and to within 0.5 percent at off-design conditions.
Hunter, Craig A.↗
Free dendritic growth
Free dendritic growth refers to the unconstrained development of crystals within a supercooled melt, which is the classical 'dendrite problem'. Great strides have been taken in recent years in both the theoretical understanding of dendritic growth and its experimental status. The development of this field will be sketched, showing that transport theory and interfacial thermodynamics (capillarity theory) were sufficient ingredients to develop a truly predictive model of dendrite formation. The convenient, but incorrect, notion of 'maximum velocity' was used for many years to estimate the behavior of dendritic transformations until supplanted by modern dynamic stability theory. The proper combinations of transport theory and morphological stability seem to able to predict the salient aspects of dendritic growth, especially in the neighborhood of the tip. The overall development of cast microstructures, such as equiaxed zone formation, rapidly solidified microstructures, etc., also seems to contain additional non-deterministic features which lie outside the current theories discussed here.
Glicksman, M. E.↗
On the dynamic response of pressure transmission lines in the research of helium-charged free piston Stirling engines
In free piston Stirling engine research the integrity of both amplitude and phase of the dynamic pressure measurements is critical to the characterization of cycle dynamics and thermodynamics. It is therefore necessary to appreciate all possible sources of signal distortion when designing pressure measurement systems for this type of research. The signal distortion inherent to pressure transmission lines is discussed. Based on results from classical analysis, guidelines are formulated to describe the dynamic response properties of a volume-terminated transmission tube for applications involving helium-charged free piston Stirling engines. The scope and limitations of the dynamic response analysis are considered.
Miller, Eric L.↗
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↗
A cumulative damage model for continuous fiber composite laminates with matrix cracking and interply delaminations
The present cumulative damage model for the prediction of stiffness loss in graphite/epoxy laminates applies a thermomechanical constitutive theory for elastic composites with distributed damage. The model proceeds from a continuum mechanics and thermodynamics approach in which the distributed damage is characterized by a set of second-order tensor-valued internal state variables. A set of damage-dependent laminated plate equations is obtained; this is developed by modifying classical Kirchhoff plate theory.
Allen, David H.↗