SEARCH · Engineering Papers

Results for “Stokes equations”

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.

SourceResearch connectionFrom yearThrough year

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 343 records · Page 19

All sources NASA NTRS DOE OSTI

DOE OSTI2022

Shock-driven dispersal of a corrugated finite-thickness particle layer

A research area emerging in the multiphase flow community is the study of shock-driven multiphase instability (SDMI), a gas–particle analog of the traditional fluid-fluid Richtmyer–Meshkov instability (RMI). In this work, we study the interaction of planar air shocks with corrugated glass particle curtains through the use of numerical simulations with an Eulerian–Lagrangian approach. One objective of this study is to compare the simulated particle curtains to a comparable set of shock tube experiments performed to analyze traditional RMI of a gas curtain. The simulations are set to match the experimental shock Mach numbers and perturbation wavelengths (3.6 and 7.2 mm) while also matching the Atwood number of the experiments to the multiphase Atwood number of the simulations. Varying particle diameters are tested in the simulations to explore the impact of particle diameter on the evolution of the particle curtain. This simulation setup allows for a one-to-one comparison between RMI and SDMI under comparable conditions while also allowing for a separate study into the validity of the use of the multiphase Atwood number to compare the single-phase and multiphase instabilities. In particular, we show that the comparison depends on the diameter of the particles (thus, dependent on the Stokes number of the flow). A second objective of this study is to analyze the effect of the initial particle volume fraction on the evolution of the curtain and the behavior of the instability. This is done through analyzing the effect of the multiphase terms of the vorticity evolution equation on the vorticity deposition in SDMI. Also discussed is the effect of the particle diameter on the multiphase generation terms as well as in the baroclinic vorticity generation term in SDMI as the shock passes over the curtain.

42 ENGINEERING↗

DOE OSTI2022

On the hot surface ignition of a wall-stagnating spray flame

The ignition of fuel sprays due to interaction with hot surfaces is an important phenomenon in the safety analysis of many engineering systems. We perform a parametric study of the hot surface ignition (HSI) of a fuel spray approaching a heated surface caused by the accidental leakage of a fuel line. Here, to this end, we employ a one-dimensional Eulerian-Eulerian formulation with a non-equilibrium evaporation model and a realistic chemical mechanism to describe $n$-dodecane fuel chemistry. We first describe and analyze the phenomenology of the unsteady processes leading to ignition using non-dimensionalized quantities. Through consideration of the temporal development of the most reactive mixture, we demonstrate that ignition occurs at a fuel-lean composition in a premixed region near the hot surface. Using non-dimensional parameters identified from the governing equations, we perform a parametric study of the time, location and local mixture composition at ignition and determine the ignition limits. We then identify the most important parametric sensitivities for physical analysis using a data-driven classification method. Our analysis demonstrates a contraction of the ignition limits with increased Stokes number and a regime of parametric insensitivity of igniting mixture composition. We also show that at high Damköhler numbers, the ignition location conforms to the parametric behavior of the thermal boundary layer, whereas at low Damköhler numbers approaching the ignition limit it reaches a near-unity value of the quenching Peclet number. We then compare the demonstrated parametric dependencies to the results of the quasi-steady asymptotic ignition literature, showing that our results are consistent with those obtained analytically within the limitations imposed by the simplified formulation of the latter.

42 ENGINEERING↗

DOE OSTI2021

Improvement of Numerical Methods in Pronghorn

During the fiscal year of 2021, the finite-volume method (FVM) was deployed in Pronghorn to provide improved efficiency, stability, and accuracy for coarse-mesh, thermal-hydraulics problems. While the main goals of fiscal year 2021 were met, several issues emerged from the early deployment of the finite-volume method in Pronghorn. These issues were: The compressible and incompressible formulations that were implemented are inadequate for many nuclear reactor flow problems; Omission of terms accounting for the porosity and Darcy-Forchheimer body force discontinuities in the Rhie-Chow interpolation lead to oscillations in pressure and velocity at these discontinuities; The FVM lacks a correction for non-orthogonal grids for computing accurate pressure gradient leading to loss of accuracy in regions with skewed elements; The FVM currently uses a monolithic solver. Monolithic solvers have issues dealing with the saddle-point nature of the discretized fluid equations. The result are bad convergence if direct factorization is not used and large memory consumption when direct factorization is used. These four issues are addressed in this report. In particular, we report the completion of the following task: Implementation of a weakly compressible formulation in the MOOSE Navier-Stokes module; Implementation of Moukalled’s method for including body forces in the RCI. Additionally, we identified the need to smooth the porosity using Moukalled’s face-cell smoothing operator; Implementation of a non-orthogonal correction for the Green-Gauss gradient computation; Preliminary implementation of a SIMPLE segregated solver.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Transport coefficients of quasiparticle models within a new relaxation time approximation of the Boltzmann equation

We investigate the transport properties of a kinetic theory model that is tuned to describe the thermodynamic properties of QCD at zero chemical potential using a new formulation of the relaxation time approximation. In contrast to previous approaches, the latter is constructed to preserve the fundamental properties of the collision term of the Boltzmann equation for any energy dependence of the relaxation time. A novel choice of matching conditions is implemented to ensure that the background mean-field depends only on the temperature even when the system is out of equilibrium. We provide a consistent analysis of how the transport coefficients of relativistic Navier-Stokes theory vary with the energy dependence of the relaxation time. We also show that the entropy production of this theory is consistent with the second law of thermodynamics and verify that it is independent of the matching conditions employed. We used this fact to calculate the matching independent combination of transport coefficients.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2023

High-Fidelity Energy Deposition Ignition Model Coupled with Flame Propagation Models at Engine-like Flow Conditions

With the heightened pressure on car manufacturers to increase the efficiency and reduce the carbon emissions of their fleets, more challenging engine operation has become a viable option. Highly dilute, boosted, and stratified charge, among others, promise engine efficiency gains and emissions reductions. At such demanding engine conditions, the spark-ignition process is a key factor for the flame initiation propagation and the combustion event. From a computational standpoint, there exist multiple spark-ignition models that perform well under conventional conditions but are not truly predictive under strenuous engine operation modes, where the underlying physics needs to be expanded. In this paper, a hybrid Lagrangian-Eulerian spark-ignition (LESI) model is coupled with different turbulence models, grid sizes, and combustion models. The ignition model, previously developed, relies on coupling Eulerian energy deposition with a Lagrangian particle evolution of the spark channel, at every time-step. The spark channel is attached to the electrodes and allowed to elongate at a speed derived from the flow velocity. The LESI model is used to simulate spark ignition in a nonquiescent crossflow environment at engine-like conditions, using converge commercial computational fluid dynamics (CFD) solver. The results highlight the consistency, robustness, and versatility of the model in a range of engine-like setups, from typical with Reynolds-averaged Navier-Stokes (RANS) and a larger grid size to high fidelity with large-eddy simulation (LES) and a finer grid size. The flame kernel growth is then evaluated against Schlieren images from an optical constant volume ignition chamber with a focus on the performance of flame propagation models, such as G-equation and thickened flame model, versus the baseline well-stirred reactor model. Finally, future development details are discussed.

Advanced ignition modeling↗

DOE OSTI2025

Topological contribution to the Bogoliubov coefficient for cosmological particle production

Particle production in cosmology is often efficiently computed in terms of Bogoliubov transforms. Restricting to a particular class of dispersion relationships, we identify a map between the number of particles produced in a special kinematic limit and a Stokes phenomena related topology of analytic continuation of the Bogoliubov coefficient functions. Intuitively, this kinematic limit corresponds to the long wavelength limit although a more precise description depends on the nature of the curved spacetime. To identify the topology, we reformulate the usual Bogoliubov computations as a type of SU(1, 1) gauged differential equation and utilize a special gauge together with a discrete symmetry that naturally characterizes the dispersion relationship. Using a dark matter model and a nonzero constant spatial curvature model, we estimate how such topological contributions will arise in physical applications. Published by the American Physical Society 2025

Chung, Daniel J. H. (ORCID:0000000343998504)↗

DOE OSTI2021

Large Eddy Simulation of Lean Mixed-Mode Combustion Assisted by Partial Fuel Stratification in a Spark-Ignition Engine

Partial fuel stratification (PFS) is a promising fuel injection strategy to improve the stability of lean combustion by applying a small amount of pilot injection right before spark timing. Mixed-mode combustion, which makes use of end-gas autoignition following conventional deflagration-based combustion, can be further utilized to speed up the overall combustion. In this study, PFS-assisted mixed-mode combustion in a lean-burn direct injection spark-ignition (DISI) engine is numerically investigated using multi-cycle large eddy simulation (LES). A previously developed hybrid G-equation/well-stirred reactor combustion model for the well-mixed operation is extended to the PFS-assisted operation. The experimental spray morphology is employed to derive spray model parameters for the pilot injection. The LES-based model is validated against experimental data and is further compared with the Reynolds-averaged Navier–Stokes (RANS)-based model. Overall, both RANS and LES predict the mean pressure and heat release rate traces well, while LES outperforms RANS in capturing the cycle-to-cycle variation (CCV) and the combustion phasing in the mass burned space. Liquid and vapor penetrations obtained from the simulations agree reasonably well with the experiment. Detailed flame structures predicted from the simulations reveal the transition from a sooting diffusion flame to a lean premixed flame, which is consistent with experimental findings. LES captures more wrinkled and stretched flames than RANS. Finally, the LES model is employed to investigate the impacts of fuel properties, including heat of vaporization (HoV) and laminar burning speed (SL). Combustion phasing is found more sensitive to SL than to HoV, with a larger fuel property sensitivity of the heat release rate from autoignition than that from deflagration. Moreover, the combustion phasing in the PFS-assisted operation is shown to be less sensitive to SL compared with the well-mixed operation.

fuel property sensitivity↗

DOE OSTI2024

Revisiting shear stress tensor evolution: Nonresistive magnetohydrodynamics with momentum-dependent relaxation time

This study aims to develop second-order relativistic viscous magnetohydrodynamics (MHD) derived from kinetic theory within an extended relaxation time approximation (momentum/energy dependent) for the collision kernel. The investigation involves a detailed examination of shear stress tensor evolution equations and associated transport coefficients. The Boltzmann equation is solved using a Chapman-Enskog-like gradient expansion for a charge-conserved conformal system, incorporating a momentum-dependent relaxation time. The derived relativistic nonresistive, viscous second-order MHD equations for the shear stress tensor reveal significant modifications in the coupling with dissipative charge current and magnetic field due to the momentum dependence of the relaxation time. By utilizing a power law parametrization to quantify the momentum dependence of the relaxation time, the anisotropic magnetic field-dependent shear coefficients in the Navier-Stokes limit have been investigated. The resulting viscous coefficients are seen to be sensitive to the momentum dependence of the relaxation time.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2022

A Study of Propane Combustion in a Spark-Ignited Cooperative Fuel Research (CFR) Engine

Liquefied petroleum gas (LPG), whose primary composition is propane, is a promising candidate for heavy-duty vehicle applications as a diesel fuel alternative due to its CO 2 reduction potential and high knock resistance. To realize diesel-like efficiencies, spark-ignited LPG engines are proposed to operate near knock-limit over a wide range of operating conditions, which necessitates an investigation of fuel-engine interactions that leads to end-gas autoignition with propane combustion. This work presents both experimental and numerical studies of stoichiometric propane combustion in a sparkignited (SI) cooperative fuel research (CFR) engine. Engine experiments are initially conducted at different compression ratio (CR) values, and the effects of CR on engine combustion are characterized. A three-pressure analysis (TPA) model based on the two-zone combustion concept is developed in GT-Power and validated using test results to estimate in-cylinder wall temperatures, residual gas fraction, etc. This model is further utilized to examine end-gas chemistry by enabling the SI turbulent flame combustion and unburned gas chemical kinetics modules. Finally, a three-dimensional (3D) computational fluid dynamic (CFD) model of the CFR engine is developed in CONVERGE, where the G-equation and SAGE detailed chemical kinetics models are implemented for combustion modeling. Here, a 153 species reduced chemical kinetics mechanism derived from the detailed NUIGMech1.1 mechanism based on the ignition delay and laminar flame speed (LFS) studies is used to generate an LFS lookup table and to describe end-gas autoignition chemistry. Multi-cycle Reynolds-averaged Navier-Stokes (RANS) simulations are then performed for the tested CRs, and the numerical model is shown to be capable of predicting the propane combustion characteristics, particularly the end-gas autoignition behavior.

20 FOSSIL-FUELED POWER PLANTS↗

DOE OSTI2022

Space-Time Block Preconditioning for Incompressible Flow

Parallel-in-time methods have become increasingly popular in the simulation of time-dependent numerical PDEs, allowing for the efficient use of additional message passing interface processes when spatial parallelism saturates. Most methods treat the solution and parallelism in space and time separately. In contrast, all-at-once methods solve the full space-time system directly, largely treating time as simply another spatial dimension. All-at-once methods offer a number of benefits over separate treatment of space and time, most notably significantly increased parallelism and faster time to solution (when applicable). However, the development of fast, scalable all-at-once methods has largely been limited to time-dependent (advection-)diffusion problems. This paper introduces the concept of space-time block preconditioning for the all-at-once solution of incompressible flow. By extending well-known concepts of spatial block preconditioning to the space-time setting, we develop a block preconditioner whose application requires the solution of a space-time (advection-)diffusion equation in the velocity block, coupled with a pressure Schur complement approximation consisting of independent spatial solves at each time-step, and a space-time matrix-vector multiplication. The new method is tested on four classical models in incompressible flow. Finally, the results indicate perfect scalability in refinement of spatial and temporal mesh spacing, perfect scalability in nonlinear Picard iteration count when applied to a nonlinear Navier--Stokes problem, and minimal overhead in terms of number of preconditioner applications compared with sequential time-stepping.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

NEAMS TH CRAB

The MOOSE framework is a library designed to make it straightforward for physicists and engineers to model partial differential equations using finite element and finite volume methods. Finite elements have been a part of the framework library since MOOSE's inception over a decade ago. Initial finite volume capability, however, was added only as recently as May of 2020. Since that time, significant work has been conducted to develop fluid modeling capability based on the finite volume method. Much of this work has taken place in MOOSE's navier_stokes module and in the NEAMS program's coarse mesh CFD code Pronghorn. We report here on development in MOOSE and Pronghorn of incompressible, porous incompressible, and weakly compressible finite volume simulation capabilities and their application to modeling of MSR and FHR advanced reactor concepts.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

DOE OSTI2022

Local correlation-based transition models for high-Reynolds-number wind-turbine airfoils

Abstract. Modern wind-turbine airfoil design requires robust performance predictions for varying thicknesses, shapes, and appropriate Reynolds numbers. The airfoils of current large offshore wind turbines operate with chord-based Reynolds numbers in the range of 3–15 million. Turbulence transition in the airfoil boundary layer is known to play an important role in the aerodynamics of these airfoils near the design operating point. While the lack of prediction of lift stall through Reynolds-averaged Navier–Stokes (RANS) computational fluid dynamics (CFD) is well known, airfoil design using CFD requires the accurate prediction of the glide ratio (L/D) in the linear portion of the lift polar. The prediction of the drag bucket and the glide ratio is greatly affected by the choice of the transition model in RANS CFD of airfoils. We present the performance of two existing local correlation-based transition models – one-equation model (γ− SA) and two-equation model (γ-Reθt‾- SA) coupled with the Spalart–Allmaras (SA) RANS turbulence model – for offshore wind-turbine airfoils operating at a high Reynolds number. We compare the predictions of the two transition models with available experimental and CFD data in the literature in the Reynolds number range of 3–15 million including the AVATAR project measurements of the DU00-W-212 airfoil. Both transition models predict a larger L/D compared to fully turbulent results at all Reynolds numbers. The two models exhibit similar behavior at Reynolds numbers around 3 million. However, at higher Reynolds numbers, the one-equation model fails to predict the natural transition behavior due to early transition onset. The two-equation transition model predicts the aerodynamic coefficients for airfoils of various thickness at higher Reynolds numbers up to 15 million more accurately compared to the one-equation model. As a result, the two-equation model predictions are more comparable to the predictions from eN transition model. However, a limitation of this model is observed at very high Reynolds numbers of around 12–15 million where the predictions are very sensitive to the inflow turbulent intensity. The combination of the two-equation transition model coupled with the Spalart–Allmaras (SA) RANS turbulence model is a good method for performance prediction of modern wind-turbine airfoils using CFD.

17 WIND ENERGY↗

DOE OSTI2020

A passive model for the evolution of subgrid-scale instabilities in turbulent flow regimes

In this work, a zero-dimensional model for the development of turbulent mixing layers driven by Rayleigh–Taylor (RT) or Richtmyer–Meshkov (RM) instabilities is presented, for application in Reynolds-Averaged Navier–Stokes (RANS) simulations. The model approximates the behavior of the turbulent mixing layer at a passively advected tracer particle that sits on the material interface of interest in the simulation, and is used to provide initial conditions for the RANS model once the mixing layer width has developed to a size that may be resolved on the computational mesh. The model relies on approximations to the Besnard–Harlow–Rauenzahn (BHR) RANS closure equations and is thus consistent the turbulent development of the mixing layer, unlike previous models of this type which have focused on the early-time laminar development of RT or RM instabilities. These instabilities will often grow through an initially laminar state before developing into turbulence, and criteria for switching from an existing laminar model to the proposed turbulent model are considered. The proposed model reproduces the mixing layer development of RT and RM instabilities seen in mixed width resolving BHR RANS simulations to a reasonable degree of accuracy, and relaxes the need for the RANS simulation to resolve the mixed width as soon as the mixing layer becomes turbulent, which may be impractical in cases where the mixing layer grows through a wide range of scales.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2025

Extended Galerkin Neural Network Approximation of Singular Variational Problems with Error Control

We present extended Galerkin neural networks, a variational framework for approximating general boundary value problems (BVPs) with error control. The main contributions of this work are (1) a rigorous theory guiding the construction of new weighted least squares variational formulations suitable for use in neural network approximation of general BVPs, and (2) an “extended” feedforward network architecture which incorporates and is even capable of learning singular solution structures, thus greatly improving approximability of singular solutions. Furthermore, numerical results are presented for several problems, including steady Stokes flow around reentrant corners and in convex corners with Moffatt eddies in order to demonstrate efficacy of the method.

a posteriori error estimate↗

DOE OSTI2021

Optimal Iteration and its Application to Some Problems in Aerosol Science and Particle Dynamics

Iteration is a common technique for finding the solutions to an equation. It is easy to code, straightforward to apply, readily comprehensible, and can be run indefinitely until a given accuracy is attained. However, for a given equation there are multiple iteration schemes that can be employed, with different convergence rates, and there is no obvious way to determine a priori which is best. In this work, the convergence rates of different approaches to simple iteration schemes are analyzed and the new technique of optimal iteration, which determines the scheme that maximizes the convergence rate, is introduced and illustrated by its application to several common problems in aerosol and particle dynamics. The first application is determination of the mobility diameter of an aerosol particle from the measured mobility, which is complicated by the nonlinearity of the Cunningham correction. This same equation occurs in the determination of the diameter of multiply-charged particles with the same mobility diameter as singly-charged particles. The next application is determination of the aerodynamic diameter from the mobility diameter for situations in which the Cunningham correction must be taken into account. The final two applications are determination of the terminal velocity from the diameter, and of the diameter from the terminal velocity, for particles sufficiently large that Stokes’ Law does not apply. The technique is easy to apply and can be employed in a number of situations.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

A robust spectral element implementation of the $k - τ$ RANS model in Nek5000/NekRS

The $k - ω$ Reynolds Averaged Navier Stokes (RANS) model is one of the industry standard approaches for modeling of turbulent flows. It performs better than the $k - ϵ$ model for low Reynolds number flows and is also more suitable for boundary layers with adverse pressure gradients. Major drawback of the model, however, is that the asymptotic value of $ω$ at the walls is singular, necessitating the use of a contrived “sufficiently” large value for $ω$ as the boundary condition for its transport equation. Here, this invariably leads to the solution being sensitive to near wall grid spacing. While an acceptable solution for low order (finite volume) methods, the excessive near wall gradients lead to persistent numerical stability issues in high order codes. To alleviate the problem, specifically in the context of the high order spectral element code Nek5000, a regularized $k - ω$ approach was formulated in our prior work (Tomboulides et al., 2018). The formulation, however, relies on the use of wall distance and its gradients for modeling the closure terms and can pose problems for simulations in complex geometries. This work presents a novel implementation of the $k - τ$ RANS model in Nek5000, where $τ = 1/ω$, eliminating the need for regularization, owing to the asymptotically bounded behavior of the source terms in the $τ$ transport equation, and also eliminating dependence on wall distance. Robustness and stability of the $k - τ$ model is ensured through implicit treatment of the source terms and their careful numerical implementation and demonstrated through several cases aimed at verification and validation. Studies include both canonical and engineering relevant problems, viz., turbulent channel flow, pipe flow, backward facing step, flow over NACA 0012 airfoil and flow in a T-junction. Results from the $k - τ$ model are shown to be consistent with regularized $k - ω$ model and also with the $k - ω$ SST model in OpenFOAM (for select studies). Comparison with experimental data is also shown, where available, to bolster validation efforts for the $k - τ$ model implementation through prediction of key turbulent quantities of interest.

Nek5000↗

DOE OSTI2025

Recent Improvements in Pronghorn for Advanced Reactor Modeling

Pronghorn is a thermal-hydraulics computational tool developed using the Idaho National Laboratory's Multiphysics Object-Oriented Simulation Environment (MOOSE). It is designed to support Computational Fluid Dynamics (CFD) modeling, ranging from subchannel and porous media analysis to Reynolds Averaged Navier-Stokes (RANS) turbulence modeling. As an integral part of the MOOSE-based suite of tools, Pronghorn seamlessly couples with other MOOSE-based applications to simulate a variety of physical phenomena. This article highlights recent significant enhancements to Pronghorn's CFD modeling capabilities and demonstrates their application to advanced nuclear reactor designs. The recent improvements in Pronghorn primarily focus on modifications to its turbulence modeling capabilities, near-wall corrections and numerical schemes. In terms of turbulence modeling, the two-equation $k-\epsilon$ and $k-\omega$ SST models have been implemented and validated with both equilibrium and non-equilibrium wall treatments. Additionally, corrections for wall roughness, and curvature, and wall-channeling in pebble beds have been introduced in the near-wall modeling. These developments enable more accurate simulations of advanced nuclear reactors. Two case studies are presented in this work: a pool-type Molten Chloride Reactor and a salt-cooled Pebble-Bed High Temperature Reactor. In both cases, the previous models in Pronghorn are compared with the new implementations, demonstrating the improved accuracy achieved with the updated models.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2021

Scalar mixing in a Kelvin-Helmholtz shear layer and implications for Reynolds-averaged Navier-Stokes modeling of mixing layers

Large-eddy simulation of a temporally evolving Kelvin-Helmholtz (KH) mixing layer is performed with the tenth-order compact difference code miranda to examine the steady-state behavior of a passive scalar in a shear-driven mixing layer. It is shown that the integral behavior of scalar variance in a KH mixing layer behaves similarly to the integral behavior of scalar variance in a Rayleigh-Taylor (RT) mixing layer, and mixedness of the simulated KH shear layer tends towards a value of about 0.8. It is further shown that if the k-L-a-V Reynolds-averaged Navier-Stokes (RANS) model [B. E. Morgan et al., Phys. Rev. E 98, 033111 (2018)], calibrated to reproduce steady-state mixing in an RT layer, is applied to simulate a KH mixing layer, the RANS model will significantly overpredict the magnitude of scalar variance in the KH layer. A straightforward addition to the k-L-a-V model is then suggested, and self-similarity analysis is applied to determine constraints on model coefficients. Furthermore, it is shown that with the addition of a buoyancy production term in the model equation for scalar variance, it becomes possible to eliminate the model deficiency and match steady-state mixedness in simulations of both RT and KH mixing layers with a single model calibration.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗