Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Computing continuum”

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.

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

At least 451 records · Page 25

Investigation of mode activity in NBI-heated experiments of Wendelstein 7-X

The 2018 operation phase (OP 1.2b) of the stellarator Wendelstein 7-X (W7-X) included, for the first time, neutral beam injection (NBI) to heat the plasma. Since the injection geometry at W7-X is not parallel, this generates both passing and trapped fast particles. During longer phases of NBI injection, with the primary purpose to study the heating efficiency of this system, Alfvén eigenmodes (AEs) were observed by a number of diagnostics, including the phase contrast imaging (PCI) system, the magnetic pick-up coils (Mirnov coils), and the soft x-ray multi-camera tomography system (XMCTS). Alfvén eigenmodes are of great interest for future fusion reactors as it has been shown that the resonant interaction of fast ions with self-excited AEs can lead to enhanced transport of fast ions and potentially to energy losses. This is especially true for so-called gap-modes, Alfvén eigenmodes with frequencies in gaps of the continuous spectrum, since they lack continuum damping. These modes are commonly known to be excited by fast ions, but other destabilizing mechanisms, e.g. the electron-pressure gradient are also possible. In this article we present a first analysis of the experimentally observed frequencies from the theoretical side. The calculation of shear Alfvén wave continua for selected cases and the assignment of observed frequencies to the gaps of the continuous spectra are presented. Using the ideal-MHD code CKA (Könies A. 2007 10th IAEA TM on Energetic Particles in Magnetic Confinement System), we find gap modes that match the experimental measurements in terms of the observed frequencies. We emphasize the crucial roles played by the coupling of sound and Alfvén waves as well as of the Doppler shift arising as a consequence of the radial electric field in W7-X. We employ the perturbative gyrokinetic code CKA-EUTERPE (Feh´er 2013 Simulation of the interaction between Alfv´en waves and fast particles), using a slowing-down distribution function for the fast ions as calculated by the Monte-Carlo particle following code ASCOT (Hirvijoki et al 2014 Comput. Phys. Commun. 185 1310–21) to assess the fast-ion drive. Here we find that the fast-ion drive is insufficient to overcome the background-plasma damping. The fact that unstable modes were observed experimentally may point to problems with the modelling or indicate the existence of other destabilizing mechanisms, e.g. associated with the electron-pressure gradient (Windisch et al 2017 Plasma Phys. Control. Fusion 59 105002) that sensitively depend on the profiles of the background plasma.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Galerkin formulation of path integrals in lattice field theory

We present a mathematical framework for Galerkin formulations of path integrals in lattice field theory. The framework is based on using the degrees of freedom (DOFs) associated to a Galerkin discretization as the fundamental lattice variables. We formulate standard concepts in lattice field theory, such as the partition function and correlation functions, in terms of the DOFs. For example, using continuous finite element spaces, we show that the two-point spatial correlation function can be defined between any two points on the domain (as opposed to at just lattice sites) and furthermore, this two-point function satisfies a weak propagator (or Green’s function) identity, in analogy to the continuum case, as well as a convergence estimate obtained from the standard finite element techniques. Furthermore, this framework leads naturally to higher-order formulations of lattice field theories by considering higher-order finite element spaces for the Galerkin discretization. We consider analytical and numerical examples of scalar field theory to investigate how increasing the order of piecewise polynomial finite element spaces affect the approximation of lattice observables. Finally, we sketch an outline of this Galerkin framework in the context of gauge field theories.

97 MATHEMATICS AND COMPUTING↗

Modeling heat pipe startup and noncondensable gases in Sockeye

For this work, a one-dimensional gas mixture flow model was developed and implemented in the heat pipe code Sockeye to model the effects of noncondensable gases. Additionally, a startup model based on the dusty gas model was implemented to model the transition from rarefied gas dynamics to continuum flow, which occurs during the frozen startup of high-temperature heat pipes. Multiple startup and noncondensable gas models were tested against experimental data for sodium heat pipes, showing excellent agreement. Additionally, the newly developed gas mixture model for modeling noncondensable gas is further tested with a theoretical case study with arbitrary heating configurations. Finally, several recommendations and conclusions are made from the studies in this work to guide future heat pipe modeling efforts.

97 - MATHEMATICS AND COMPUTING↗

Radiation driven diffusion in γU-Mo

A monolithic fuel design based on a U-Mo alloy has been selected as the fuel type for conversion of the United States High-Performance Research Reactors (HPRRs). A critical phenomenon of interest with U-Mo monolithic fuel is the large amount of swelling that takes place during operation, particularly at high fission densities. The accurate prediction of fuel evolution under irradiation requires implementation of correct thermodynamic and kinetic properties into mesoscale and continuum level fuel performance modeling codes. One such property where there exists incomplete data is the diffusion of relevant species under irradiation. Fuel performance swelling predictions rely on an accurate representation of diffusion in order to determine the rate of fission gas swelling and the local microstructural evolution. In this work, we present molecular dynamics simulations of the radiation driven diffusion of U, Mo and Xe in U-Mo nuclear fuels. Diffusion coefficients for each species are determined over a range of temperatures and compositions. In this work, updated diffusion coefficients are presented that are applicable under irradiation that incorporate both intrinsic and radiation driven diffusion.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗

Continuum Damage Mechanics Modeling of High-Temperature Flaw Propagation: Application to Creep Crack Growth In 316H Standardized Specimens and Nuclear Reactor Components

Predicting creep crack growth (CCG) of flaws found during operation in high-temperature alloy components is essential for assessing the remaining lifetime of those components. While defect assessment procedures are available for this purpose in design codes, these are limited in their range of applicability. This study assesses the application of a local damage-based finite-element methodology as a more general technique for the prediction of CCG at high temperatures on a variety of structural configurations. Numerical results for stainless steel 316H, which are validated against experimental data, show the promise of this approach. This integration of continuum damage mechanics (CDM) based methodologies, together with adequate inelastic models, into assessment procedures can therefore inform the characterization of CCG under complex operating conditions, while avoiding excessive conservatism. This article shows that such modeling frameworks can be calibrated to experimental data and used to demonstrate that the degree of tri-axiality ahead of a growing creep crack affects its rate of growth. The framework is also successfully employed in characterizing CCG in a realistic reactor pressure vessel geometry under an arbitrary loading condition. These results are particularly relevant to the nuclear power industry for defect assessment and inspections as part of codified practices of structural components with flaws in high-temperature reactors.

42 ENGINEERING↗

Unconventional Charge Transport in MgCr 2 O 4 and Implications for Battery Intercalation Hosts

Ion transport in solid-state cathode materials prescribes a fundamental limit to the rates batteries can operate; therefore, an accurate understanding of ion transport is a critical missing piece to enable new battery technologies, such as magnesium batteries. Based on our conventional understanding of lithium-ion materials, MgCr 2 O 4 is a promising magnesium-ion cathode material given its high capacity, high voltage against an Mg anode, and acceptable computed diffusion barriers. Electrochemical examinations of MgCr 2 O 4 , however, reveal significant energetic limitations. Motivated by these disparate observations; herein, we examine long-range ion transport by electrically polarizing dense pellets of MgCr 2 O 4 . Our conventional understanding of ion transport in battery cathode materials, e.g., Nernst-Einstein conduction, cannot explain the measured response since it neglects frictional interactions between mobile species and their nonideal free energies. In this work, we propose an extended theory that incorporates these interactions and reduces to the Nernst-Einstein conduction under dilute conditions. This theory describes the measured response, and we report the first study of long-range ion transport behavior in MgCr 2 O 4 . We conclusively show that the Mg chemical diffusivity is comparable to lithium-ion electrode materials, whereas the total conductivity is rate-limiting. Given these differences, energy storage in MgCr 2 O 4 is limited by particle-scale voltage drops, unlike lithium-ion particles that are limited by concentration gradients. Future materials design efforts should consider the interspecies interactions described in this extended theory, particularly with respect to multivalent-ion systems and their resultant effects on continuum transport properties.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Distance-dependent dielectric constant at the calcite/electrolyte interface: Implication for surface complexation modeling

Hypothesis: The electrical double layer formed at the mineral/electrolyte interface is often modeled using mean-field approaches based on a continuum description of the solvent whose dielectric constant is assumed to decrease monotonically with decreasing distance to the surface. In contrast, molecular simulations show that the solvent polarizability oscillates near the surface similar to the water density profile - as shown previously, for example, by Bonthuis et al. (D.J. Bonthuis, S. Gekle, R.R. Netz, Dielectric Profile of Interfacial Water and its Effect on Double-Layer Capacitance, Phys Rev Lett 107(16) (2011) 166102). Here, we showed that molecular and mesoscale pictures agree by spatially averaging the dielectric constant obtained from molecular dynamics simulations over the distances relevant to the mean-field representation. In addition, the values of capacitances used to describe the electrical double layer in Surface Complexation Models (SCMs) of the mineral/electrolyte interface can be estimated using molecularly informed spatially averaged dielectric constants and positions of hydration layers. Experiments: First, we used molecular dynamics simulations to model the calcite 101¯4/electrolyte interface. Next, by using atomistic trajectories, we calculated the distance-dependent static dielectric constant and water density in the direction normal to the. Finally, we applied spatial compartmentalization consistent with the model of parallel-plate capacitors connected in series to estimate SCM capacitances. Findings: Computationally expensive simulations are required to determine the dielectric constant profile of interfacial water near the mineral surface. On the other hand, water density profiles are readily assessable from much shorter simulation trajectories. Our simulations confirmed that dielectric and water density oscillations at the interface are correlated. Here, we parametrized linear regression models to estimate the dielectric constant directly from the local water density. This is a significant computational shortcut compared to slowly converging calculations relying on total dipole moment fluctuations. The amplitude of the interfacial dielectric constant oscillation can exceed the dielectric constant of the bulk water, suggesting an ice-like frozen state, but only if there are no electrolyte ions. The interfacial accumulation of electrolyte ions causes a decrease in the dielectric constant due to the reduction of water density and re-orientation of water dipoles in ion hydration shells. Finally, we show how to use the computed dielectric properties to estimate SCM's capacitances.

58 GEOSCIENCES↗

Ensemble Simulations and Experimental Free Energy Distributions: Evaluation and Characterization of Isoxazole Amides as SMYD3 Inhibitors

Optimization of binding affinities for ligands to their target protein is a primary objective in rational drug discovery. Herein, we report on a collaborative study that evaluates various compounds designed to bind to the SET and MYND domain-containing protein 3 (SMYD3). SMYD3 is a histone methyltransferase and plays an important role in transcriptional regulation in cell proliferation, cell cycle, and human carcinogenesis. Experimental measurements using the scintillation proximity assay show that the distributions of binding free energies from a large number of independent measurements exhibit non-normal properties. We use ESMACS (enhanced sampling of molecular dynamics with approximation of continuum solvent) and TIES (thermodynamic integration with enhanced sampling) protocols to predict the binding free energies and to provide a detailed chemical insight into the nature of ligand-protein binding. Our results show that the 1-trajectory ESMACS protocol works well for the set of ligands studied here. Although one unexplained outlier exists, we obtain excellent statistical ranking across the set of compounds from the ESMACS protocol and good agreement between calculations and experiments for the relative binding free energies from the TIES protocol. ESMACS and TIES are again found to be powerful protocols for the accurate comparison of the binding free energies.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Sodium tracer measurements of an expanded dense aluminum plasma from e-beam isochoric heating

Spatially and temporally resolved visible absorption spectroscopy is performed on sodium D-lines present as surface contaminants on an expanded dense aluminum plasma plume. An 80-ns FWHM, intense, relativistic electron beam deposits 5.4 J into a 100- μ m-thick Al foil, which isochorically heats and subsequently hydrodynamically expands the material through the warm dense matter state and into a classical-like plasma state, with a coupling parameter of approximately 0.2 and a degeneracy parameter of approximately 270. The Na contamination, carried along with the expanding plume, shows saturated absorption features in the dense Al continuum for λ > 450 nm. X-ray photoelectron spectroscopy and laser-induced breakdown spectroscopy confirm Na is a surface contaminant with an atomic concentration of ~ 0.1 % when interrogating identical foil samples. Additioanlly, a spectroscopic-quality radiation transport model is used to post-process 2D hydrodynamic simulations to interpret the plasma conditions based on the measured Na 3p-3s doublet line profiles. A sodium number density of 3 × 10 15 cm -3 best matches the experimental spectra, which originate from a dense surface plasma with n e = 3.0 ± 0.8 × 10 18 cm -3 .

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

A Continuum Dislocation Dynamics Crystal Plasticity Approach to Irradiated Body-Centered Cubic α-Iron

Radiation-induced embrittlement of reactor pressure vessel (RPV) steels can potentially limit the operating life of nuclear power plants. Over extended exposure to radiation doses, these body-centered cubic (BCC) irons demonstrate irradiation damage. Here, we present a continuum dislocation density (CDD) crystal plasticity model to capture the interaction among dislocations and self-interstitial atom (SIA) loops in α-iron. We demonstrate the importance of modeling cross slip using a combined stochastic Monte Carlo approach and the role of slip system strength anisotropy in capturing stochastic cross slip interactions. Through these captured interactions, the CDD crystal plasticity model can capture both the stress response and the physical evolution of dislocations on different slip system planes. Single-crystal verification experiments are used to calibrate the CDD crystal plasticity model, and a set of simplified polycrystalline simulations demonstrates the model’s ability to capture the stress response from tensile experiments on α-iron.

36 MATERIALS SCIENCE↗

Effect of diffusion constant on the morphology of dendrite growth in lithium metal batteries

Lithium dendrites can lead to a short circuit and battery failure, and developing strategies for their suppression is of considerable importance. In this work, we study the growth of dendrites in a simple model system where the solvent is a continuum and the lithium ions are hard spheres that can deposit by sticking to existing spheres or the electrode surface. Using stochastic dynamics simulations, we investigate the effect of applied voltage and diffusion constant on the growth of dendrites. We find that the diffusion constant is the most significant factor, and the inhomogeneity of the electric field does not play a significant role. Additionally, the growth is most pronounced when the applied voltage and diffusion constant are both low. We observe a structural change from broccoli to cauliflower shape as the diffusion constant is increased. The simulations suggest that a control of electrolyte parameters that impact lithium diffusion might be an attractive route to controlling dendrite growth.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

SOMAFOAM: An OpenFOAM based solver for continuum simulations of low-temperature plasmas

Here, we report the development of SOMAFOAM, a finite volume framework for performing continuum simulations of low-temperature plasmas. The primary goal of this work is to discuss the features of SOMAFOAM along with representative results provided as examples for a range of operating conditions and geometries. This includes plasma and plasma–dielectric systems operating in direct current, radio frequency, and microwave regimes from pressures as low as 100 mTorr to atmospheric pressure. The code has several useful features including the ability to run massively parallel simulations using arbitrary geometries, structured/unstructured meshes, choice of models such as drift–diffusion/full-momentum at runtime, and species-dependent timesteps to name a few. The verification/validation studies presented include comparison with previously published continuum simulations (low-pressure direct current and radio frequency plasma), with experiments (Gaseous Electronics Conference Reference Cell and microwave microplasma ignited in a split ring resonator), and previously published kinetic simulations (low-pressure radio frequency plasma). Other examples provided include a direct current atmospheric pressure microplasma bounded by dielectric sidewalls and a helium–nitrogen plasma ignited using a needle electrode facing a dielectric. The performance of the code is also discussed with serial and distributed memory parallel runs demonstrated up to 512 cores. The design and implementation of the code in a modular object-oriented framework allows for easy extension and seamless coupling with other codes and can be expected to play an important role in both academia and industry.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DFT-based investigation of solvation of Nd(III)/Yb(III) cations in room-temperature ionic-liquid

We report a DFT study on the solvation of bare rare-earth (RE) cations [Nd(III) and Yb(III)] in the room-temperature ionic-liquid (RTIL) based on 1,3-dimethyl-imidazolium + , PF 6 - , [MMI][PF 6 ]. In the present article, we aim to investigate whether the chosen RTIL can preferentially solvate any of the RE cations under study. First, the RTIL binding to the RE cation is studied in the gas phase, and then explored with continuum solvation model employing RTIL parameters. First, we considered the formation of the first solvation shell, where the PF 6 - anions directly bond with the Ln(III) cation. We then further surrounded the first solvation shell with [MMI]+ cations to form the second solvation shell. The stability of PF 6 - coordinated complexes is studied by calculating the binding energy values. The number of PF 6 - anions for both Ln(III) cations starts with three ligands and goes until the maximum binding energy in the RTIL medium is reached. The coordination number and binding modes of PF 6 - depend on the size of the RE cation. Comparing the binding energy values between the RE cations for the first solvation shell complexes, it is noticed that Yb-complexes have relatively greater binding energy than Nd-complexes. We have further performed a Boltzmann population analysis to find out the most dominant conformer among each category of PF 6 - coordinated complexes. A study using Natural Population Analysis shows that after complexation with PF 6 - the charge on the Yb-centers lower to a greater extent than Nd-centers, implying stronger bonding between Yb and PF 6 - , which is in harmony with the binding energy analysis. Overall, the computational investigation provides an in-depth understanding of the complexation phenomena of RE cations in RTIL, which can be useful for the practical separation of RE cations using RTIL.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Modeling the formation of Sedan Crater using the FLAG and HOSS codes

Numerical modeling of explosion crater formation requires accounting for complex physical processes. Numerical validation of explosion cratering is an important step in modeling and requires experimental data for comparison. Models using discrete elements and continuum models have both benefits and drawbacks to their approaches. In this work, we consider both an arbitrary Lagrangian–Eulerian (ALE) hydrocode and a finite discrete element method (FDEM) approach to modeling the formation of the Sedan crater, the largest human-made crater in the United States. The Sedan crater formed from an underground nuclear detonation in the Nevada desert as part of Project Plowshare. Our models show that the continuum approach of the hydrocode matched well compared to early test time prior to the mound rupture and subsequent fireball venting, when most of the alluvium exhibited fluid behavior. Our FDEM approach matched the final crater dimensions well, after material had settled back into the crater, when material strength and solid mechanics play key roles. Our work shows how leveraging the benefits of multiple numerical approaches can lead to better understanding of complex physical problems, especially problems with limited experimental data. By using a continuum approach to early-time hydrodynamics and an FDEM approach to later-time solid mechanics, we can better understand the different physical regimes of explosion crater formation.

36 MATERIALS SCIENCE↗

A micromorphic filter for determining stress and deformation measures from direct numerical simulations of lower length scale behavior

A micromorphic filter is presented for the extraction of stress and deformation measures from underlying direct numerical simulation (DNS) of microstructural mechanical response. The filter is consistent with the micromorphic continuum theory of Eringen and Suhubi (1964), and allows the interrogation of a DNS to generate higher order constitutive models. The filter adopts aspects of the overlap coupling techniques for atomistic-continuum scale-bridging in order to update the nodal degrees of freedom of the finite-element-based filter. Here, two methods for the extraction of quantities of interest from the underlying DNS are presented. The first is a least squares fitting technique which is appropriate for finite-element-style macro-scale domains, and the second is a variationally based approach which generalizes the method to any macro-scale domain which has a variational form. No restrictions on the form of the micro-scale simulation are inherent to the approach, provided that the required quantities (stress, position, etc.) can be provided. The filter is applied to a simple homogeneous medium undergoing homogeneous deformation to demonstrate the recovery of a classical continuum response, what we call the null case. We then apply the framework to the same homogeneous medium with a central and edge penny-shaped crack to show micromorphic effects. We demonstrate that varying the size of the filter causes the micromorphic behaviors to arise and then dissipate as the filter becomes smaller than the crack's length scale. Additionally we show the effect of filter size on a chiral element network along with a plate perforated with evenly spaced and perturbed holes through the thickness. The micromorphic effects are shown to be present for the chiral elements under any loading but become most pronounced when a single element is located within each averaging domain. Micromorphic effects become pronounced for the plate upon the onset of localization.

97 MATHEMATICS AND COMPUTING↗

A spline-based method to obtain spatially dependent viscosity in confined flows

Coupling chemical physics to continuum theories is a critical step to understanding multi-scale phenomena. This paper will connect non-equilibrium molecular dynamics simulations to a continuum-based Navier-Stokes equation that has relaxed the assumption of spatial uniformity in viscosity. Using a form for viscosity based on spline interpolation, viscosity as a function of position is obtained from the least squares fit of the velocity profile measured from molecular simulations of flow in a nanochannel. Viscosity can vary widely, particularly near the channel boundaries, indicating that uniform viscosity is no longer appropriate. Variations of the viscosity near the channel surfaces imply that considering solution and surface chemistry could be necessary to rigorously understand molecular-scale flows in nanochannels.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Finite spatial-grid effects in energy-conserving particle-in-cell algorithms

Finite-grid (or aliasing) instabilities are pervasive in particle-in-cell (PIC) plasma simulation algorithms, and force the modeler to resolve the smallest (Debye) length scale in the problem regardless of dynamical relevance. These instabilities originate in the aliasing of interpolation errors between mesh quantities and particles (which live in the space–time continuum). Recently, strictly energy-conserving PIC (EC-PIC) algorithms have been developed that promise enhanced robustness against aliasing instabilities. In this study, we confirm by analysis that EC-PIC is stable against aliasing instabilities for stationary plasmas. For drifting plasmas, we demonstrate by analysis and numerical experiments that, while EC-PIC algorithms are not free from these instabilities in principle, they feature a benign stability threshold for finite-temperature plasmas that make them usable in practice for a large class of problems (featuring ambipolarity and realistic ion-electron mass ratios) without the need to consider the size of the Debye length. We also demonstrate that this threshold is absent for the popular momentum-conserving PIC algorithms, which are therefore unstable for both drifting and stationary plasmas beyond a threshold in cell size compared to Debye length. Finite-grid (or aliasing) instabilities are pervasive in particle-in-cell (PIC) plasma simulation algorithms, and force the modeler to resolve the smallest (Debye) length scale in the problem regardless of dynamical relevance. These instabilities originate in the aliasing of interpolation errors between mesh quantities and particles (which live in the space–time continuum). Recently, strictly energy-conserving PIC (EC-PIC) algorithms have been developed that promise enhanced robustness against aliasing instabilities. In this study, we confirm by analysis that EC-PIC is stable against aliasing instabilities for stationary plasmas. For drifting plasmas, we demonstrate by analysis and numerical experiments that, while EC-PIC algorithms are not free from these instabilities in principle, they feature a benign stability threshold for finite-temperature plasmas that make them usable in practice for a large class of problems (featuring ambipolarity and realistic ion-electron mass ratios) without the need to consider the size of the Debye length. Finally, we also demonstrate that this threshold is absent for the popular momentum-conserving PIC algorithms, which are therefore unstable for both drifting and stationary plasmas beyond a threshold in cell size compared to Debye length.

97 MATHEMATICS AND COMPUTING↗

A Numerical Simulation of a Single Shock-Accelerated Particle

Particle drag models, which capture macro viscous and pressure effects, have been developed over the years for various flow regimes to enable cost effective simulations of particle-laden flows. The relatively recent derivation by Maxey and Riley has provided an exact equation of motion for spherical particles in a flow field based on the continuum assumption. Many models that have been simplified from these equations have provided reasonable approximations; however, the sensitivity of particle-laden flows to particle drag requires a very accurate model to simulate. To develop such a model, a 2D axisymmetric Navier-Stokes direct numerical simulation of a single particle in a transient, shock-driven flow field was conducted in the hydrocode FLAG. FLAG’s capability to run arbitrary Lagrangian-Eulerian hydrodynamics coupled with solid mechanic models makes it an ideal code to capture the physics of the flow field around and in the particle as it is shock-accelerated – a challenging regime to study. The goal of this work is twofold: to provide a validation for FLAG’s Navier-Stokes and heat diffusion solutions, and to provide a rationale for recent experimental particle drag measurements.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗