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All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Direct Measurement of Diffusion Coefficients: Evidence for Diffusive Stochastic Heating in Collisionless Plasmas

Open questions in collisionless plasma dissipation can be addressed using space-based observations in different astrophysical environments, with implications for both astrophysical and laboratory plasma systems. We study a low-𝛽, highly imbalanced, sub-Alfvénic stream observed by Parker Solar Probe (PSP) to identify and distinguish between signatures of stochastic heating (SH) and resonant heating (RH) by parallel ion cyclotron waves (∥-ICWs). Prior work studying this stream [Trevor A. Bowen et al., Stochastic heating in the sub-Alfvénic solar wind, Phys. Rev. Lett. 135, 255201 (2025)] showed that the SH rate, accounting for intermittency, matched the amplitude of the local energy transfer (LET) rate, while the RH rate did not. This comparison relied on a number of assumptions regarding the nature of the diffusive process and the calculation of the LET rate. We introduce a novel technique of inverting the proton guiding center equation to empirically measure velocity-space diffusion coefficients using three-dimensional proton velocity distribution functions, from the ion electrostatic analyzer (the Solar Probe Analyzer for Ions) on PSP. Measured diffusion coefficients are used to determine phase-space heating rates, leading to a calculation of a fully kinetic heating rate independent of assumptions made in prior work. We show that scale-dependent analytic expressions for SH via noncoherent fluctuations match the empirical measurements from PSP data, provided that we account for intermittency in the heating calculation. In contrast, the derived heating rates for SH that accounts for the effects of the helicity barrier and heating rates for RH via ∥-ICWs do not peak in the same region of velocity space as the empirical measurements, nor do they reach the required magnitude. Our approach provides novel methodology to uniquely identify and constrain heating processes in collisionless plasmas and shows evidence of a Fokker-Planck-like diffusive process in the near-Sun solar wind.

Plasma kinetic theory↗
DOE OSTI2023

Determination of Ce 3+ , Co 2+ , Mn 2+ and Fe 2+ diffusion coefficients in Nafion® membrane

Concentration gradient diffusion coefficients for Ce 3+ , Co 2+ , Mn 2+ and Fe 2+ cations are determined in Nafion®211 membranes over a wide range of environmental conditions. Measurements are made using finite-width cation-rich bands introduced to NR211 via a hot-pressing procedure. A robust method of accurate diffusion coefficient determination of the finite-width deposits is developed using a Fick's second law of diffusion solution for one-dimensional systems. The transition metal dications are found to have nearly identical NR211 diffusion coefficients under water saturated conditions over the 22–80 °C range. The powerful chemical mitigant, Ce 3+ , is about one-half as diffusive as the dications under identical conditions. Derived diffusion coefficients for Ce 3+ and Co 2+ are found to be independent of initial cation concentration over the range of 12.5–70 mol% exchange level. The diffusion behavior of Ce 3+ in 80 °C liquid water and saturated water vapor is identical. The diffusion coefficients of Ce 3+ are shown to have a strong dependence on membrane hydration level varying by a factor of more than 30 over the range of 95 to 40% RH. Finally, the implications of these new diffusion findings are applied to a discussion of potential guidelines for the development of highly durable fuel cell systems, which employ mobile metal cations as lifetime-extending redox stabilizers.

08 HYDROGEN↗
DOE OSTI2021

Mutual Diffusion Coefficients of Na 2 SO 4 at C = 0.02989 mol·dm -3 and 298.15 K by Using Rayleigh Interferometry with Free Diffusion Boundary Conditions: Experimental Test of the Effect of the C 3/2 Concentration Dependence of Refractive Index at Low Concentration

Rayleigh interferometry is one of the most precise and accurate methods for the experimental determination of the mutual diffusion coefficients of both electrolytes and non-electrolytes in liquid solutions. For binary solutions at moderate and high concentrations where the concentration dependences of both diffusion coefficient and refractive index can be assumed to be linear or almost linear and the concentration difference ΔC between a pair of solutions undergoing free diffusion is not large compared to their average concentration, and by using proper combinations of the interference fringe positions as they vary with time, under these conditions diffusion coefficients are obtained that are independent of the size of ΔC. However, this situation becomes more complicated at low concentrations for electrolyte solutions where the concentration dependences of both the diffusion coefficient and refractive index are non-linear, with C 1/2 dependence for the diffusion coefficient and C 3/2 dependence for the refractive index. As a test of these effects on calculated mutual diffusion of electrolyte solutions at low concentrations as measured by Rayleigh interferometry, apparent mutual diffusion coefficients D v,a (volume-fixed reference frame) were measured for fixed average concentrations C=(0.02989 ± 0.00001) mol·dm –3 of Na 2 SO 4 (aq) at 298.15 K while varying ΔC/C from 0.66673 to 2, a threefold variation. The dependence of the diffusion coefficient on ΔC/C was found to be linear, yielding D v = 1.041 6 × 10 –9 m 2 ·s –1 for an infinitely small concentration difference between the diffusing solutions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Resolution of a Few Problems in the Application of Quasilinear Theory to Calculating Diffusion Coefficients in Heliophysics

A theory of quasilinear diffusion for obliquely propagating electromagnetic waves was developed in the 1960's and applied in the 1970's to model scattering of relativistic electrons by a prescribed distribution of waves. In the latter work, a transformation of variables, from wavevector space to the temporal frequency and tangent of the wave normal angle, was used so that simple Gaussian functions of frequency and tangent of the wave normal angle could be multiplied together to define the distribution of wave power, although arbitrary distributions of power in these two variables is also permitted. Finally, in 2005, previous work was consolidated and has been widely used in heliophysics studies that require computation of quasilinear diffusion coefficients. Here it is shown that this transformation is inppropriate when the precise wave vector distribution is known. The correct transformation is derived and used to produce diffusion coefficients that can differ by orders of magnitude from those computed using the inappropriate transformation. The differences are largest when the distribution of wave power extends to wave normal angles near the resonance cone. When the ratio of the plasma frequency to the gyrofrequency is large, only low energies (keV) are affected, but as the ratio decreases higher energies (MeV) also show differences. It is also shown that the derivation from the 1960's uses a notation that results in the diffusion coefficients depending on the distribution of wave power with respect to the wave azimuthal angle whereas there should be no such dependence.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2023

Machine Learning Predictions of Simulated Self-Diffusion Coefficients for Bulk and Confined Pure Liquids

Diffusion properties of bulk fluids have been predicted using empirical expressions and machine learning (ML) models, suggesting that predictions of diffusion also should be possible for fluids in confined environments. The ability to quickly and accurately predict diffusion in porous materials would enable new discoveries and spur development in relevant technologies such as separations, catalysis, batteries, and subsurface applications. Here in this work, we apply artificial neural network (ANN) models to predict the simulated self-diffusion coefficients of real liquids in both bulk and pore environments. The training data sets were generated from molecular dynamics (MD) simulations of Lennard-Jones particles representing a diverse set of 14 molecules ranging from ammonia to dodecane over a range of liquid pressures and temperatures. Planar, cylindrical, and hexagonal pore models consisted of walls composed of carbon atoms. Our simple model for these liquids was primarily used to generate ANN training data, but the simulated self-diffusion coefficients of bulk liquids show excellent agreement with experimental diffusion coefficients. ANN models based on simple descriptors accurately reproduced the MD diffusion data for both bulk and confined liquids, including the trend of increased mobility in large pores relative to the corresponding bulk liquid.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Cross-correlation analysis of X-ray photon correlation spectroscopy to extract rotational diffusion coefficients

Coefficients for translational and rotational diffusion characterize the Brownian motion of particles. Emerging X-ray photon correlation spectroscopy (XPCS) experiments probe a broad range of length scales and time scales and are well-suited for investigation of Brownian motion. While methods for estimating the translational diffusion coefficients from XPCS are well-developed, there are no algorithms for measuring the rotational diffusion coefficients based on XPCS, even though the required raw data are accessible from such experiments. In this paper, we propose angular-temporal cross-correlation analysis of XPCS data and show that this information can be used to design a numerical algorithm (Multi-Tiered Estimation for Correlation Spectroscopy [MTECS]) for predicting the rotational diffusion coefficient utilizing the cross-correlation: This approach is applicable to other wavelengths beyond this regime. We verify the accuracy of this algorithmic approach across a range of simulated data.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Determination of the Diffusion Coefficients of Binary CH4 and C2H6 in a Supercritical CO2 Environment (500–2000 K and 100–1000 atm) by Molecular Dynamics Simulations

The self-diffusion coefficients of carbonaceous fuels in a supercritical CO2 environment provide transport information that can help us understand the Allam Cycle mechanism at a high pressure of 300 atm. The diffusion coefficients of pure CO2 and binary CO2/CH4 and CO2/C2H6 at high temperatures (500 K~2000 K) and high pressures (100 atm~1000 atm) are determined by molecular dynamics simulations in this study. Increasing the temperature leads to an increase in the diffusion coefficient, and increasing the pressure leads to a decrease in the diffusion coefficients for both methane and ethane. The diffusion coefficient of methane at 300 atm is approximately 0.012 cm2/s at 1000 K and 0.032 cm2/s at 1500 K. The diffusion coefficient of ethane at 300 atm is approximately 0.016 cm2/s at 1000 K and 0.045 cm2/s at 1500 K. The understanding of diffusion coefficients potentially leads to the reduction in fuel consumption and minimization of greenhouse gas emissions in the Allam Cycle.

Energy & Fuels↗
DOE OSTI2021

Mutual Diffusion Coefficients and Refractive Index Increments of K 2 SO 4 (aq) at 298.15 K from Rayleigh Interferometry

Here, isothermal mutual diffusion coefficients (interdiffusion coefficients) were measured for K 2 SO 4 (aq) at 298.15 ± 0.005 K, at numerous concentrations ranging from dilute solutions to near saturation (0.59648 mol∙dm -3 ; 0.61349 mol∙kg -1 ) under free diffusion boundary conditions, using high precision Rayleigh interferometry. Under the experimental conditions these diffusion coefficients are on the volume-fixed reference frame D v . Two series of experiments were performed, the first using the traditional experimental approach with a mercury lamp source and with the interference patterns being recorded on glass photographic plates, and the second with a He-Ne laser light source and computerized data acquisition using a photodiode array. The results from both series of experiments are in excellent agreement, and generally yield diffusion coefficients precise to at least 0.002 x 10 -9 m 2 ∙s 1 (0.15% to 0.19%) and in most cases to 0.001 x 10 -9 m 2 ∙s -1 (0.07% to 0.1%). These experiments also yield accurate values of the refractive index differences for the solution pairs used in the diffusion experiments. The new diffusion coefficients are compared to two sets of published values of diffusion coefficients for K 2 SO 4 (aq) which are somewhat discrepant from each other. This study extends and complements our earlier work on the diffusion coefficients of the most common brine salts: NaCl(aq), KCl(aq), MgCl 2 (aq), CaCl 2 (aq), Na 2 SO 4 (aq), ] MgSO 4 (aq), NaHCO 3 (aq), and KHCO 3 (aq) at 298.15 K.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Atomistic and mesoscale simulations to determine effective diffusion coefficient of fission products in SiC

The silicon carbide (SiC) layer in tristructural isotropic (TRISO) particles serves as the barrier to prevent escape of fission products produced in the fuel kernel. Knowing the diffusion coefficient of fission products through SiC is critical to determining whether fission gas can escape from the particle. It has been observed in experiments that Ag accumulated in grain boundaries and triple junctions in SiC. It is hypothesized that grain boundary diffusion is the primary pathway by which fission products penetrate the SiC layer. In this report, the effective diffusion coefficient of the fission product Ag through the grain boundary network is calculated using a combination of atomistic and phase-field methods. The grain boundary diffusion coefficient is calculated using molecular dynamics simulations. The bulk diffusion coefficient is determined using a combination of density functional theory and nudged elastic band methods. An effective diffusion coefficient is calculated, accounting for the grain structure using a phase-field method. The effective diffusion coefficient will be incorporated into Bison and fission product release calculations are compared to available experimental data.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2021

Using Computationally-Determined Properties for Machine Learning Prediction of Self-Diffusion Coefficients in Pure Liquids

The ability to predict transport properties of liquids quickly and accurately will greatly improve our understanding of fluid properties both in bulk and complex mixtures, as well as in confined environments. Such information could then be used in the design of materials and processes for applications ranging from energy production and storage to manufacturing processes. As a first step, we consider the use of machine learning (ML) methods to predict the diffusion properties of pure liquids. Recent results have shown that Artificial Neural Networks (ANNs) can effectively predict the diffusion of pure compounds based on the use of experimental properties as the model inputs. In the current study, a similar ANN approach is applied to modeling diffusion of pure liquids using fluid properties obtained exclusively from molecular simulations. A diverse set of 102 pure liquids is considered, ranging from small polar molecules (e.g., water) to large nonpolar molecules (e.g., octane). Self-diffusion coefficients were obtained from classical molecular dynamics (MD) simulations. Since nearly all the molecules are organic compounds, a general set of force field parameters for organic molecules was used. The MD methods are validated by comparing physical and thermodynamic properties with experiment. Computational input features for the ANN include physical properties obtained from the MD simulations as well as molecular properties from quantum calculations of individual molecules. Furthermore, fluid properties describing the local liquid structure were obtained from center of mass radial distribution functions (COM-RDFs). Feature sensitivity analysis revealed that isothermal compressibility, heat of vaporization, and the thermal expansion coefficient were the most impactful properties used as input for the ANN model to predict the MD simulated self-diffusion coefficients. The MD-based ANN successfully predicts the MD self-diffusion coefficients with only a subset (2 to 3) of the available computationally determined input features required. A separate ANN model was developed using literature experimental self-diffusion coefficients as model targets. Although this second ML model was not as successful due to a limited number of data points, a good correlation is still observed between experimental and ML predicted self-diffusion coefficients.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Estimating the Diffusion Coefficient of Lithium in Graphite: Extremely Fast Charging and a Comparison of Data Analysis Techniques

Galvanostatic intermittent titration experiments were performed in three-electrode cells to characterize the effect of C/2, 2-C and 4-C charge rates on the observed lithium diffusion coefficient. As part of the data analysis process, we compared the classic Weppner-Huggins analysis of polarization data with a newer (Wang et al.) analysis method for depolarization data. At low values of x in Li x C 6 , both analysis methods showed the same general trend in the apparent lithium diffusion coefficient, 4-C > 2-C > C/2. The two techniques differed in the magnitude of the estimated diffusion coefficient by about a factor of 100. The observed increase in diffusion coefficient does not last over a large compositional range. Since the estimates from the method of Weppner and Huggins may contain artifacts due to the use of particulate electrodes and high charge rates, the method of Wang et al. may produce better values.

25 ENERGY STORAGE↗
DOE OSTI2026

Challenges in Pulsed-Field Gradient Nuclear Magnetic Resonance on Magnetically Heterogeneous Interfaces: Sequence and Field-Dependent Apparent Diffusion Coefficients

It is well known that the internal gradient (gi) that exists within pores haunts the diffusion coefficient (D) as measured by the pulsed-field gradient (PFG) nuclear magnetic resonance (NMR). Several PFG-NMR methods developed to determine an accurate D were not successful. Then, the steady-state diffusion coefficient (Dapp,8) for the cation [C4mim]+ of [C4mim][Tf2N]; [1-butyl-3-methylimidazolium][bis(trifluoromethylsulfonyl)imde] ionic liquid confined in ordered mesoporous carbon (OMC) were determined by comparing Dapp,8 obtained from 1H PFG-NMR performed with three different stimulated echo sequences: STE, APFG, and MPFG under the two external magnetic field strength, B0 = 9.4 and 14.1 Tesla. The measured Dapp,8 which is an order of magnitude smaller than D of bulk [C4mim][Tf2N], is in good agreement between APFG and MPFG both in B0 = 9.4 and 14.1 Tesla. However, the strong gi artifact, which caused apparent diffusion coefficient (Dapp) depending strongly and weakly on B0 and temperature, respectively, in diffusion-time dependent Dapp, Dapp(?) obtained from a sequence with monopolar gradients (STE) was suppressed by using sequences employing bipolar gradients (APFG and MPFG) in the region of steady-state diffusion. But incompletely suppressed gi artifact resulting in the different behaviors of the early part of Dapp(?) between the sequences leads a ˜ 0.6 and 0.9 in MPFG and APFG, respectively, in the relationship between mean squared displacement and diffusion time: = 2Dta, where a = 0.5 and 1 for 1-dimensional single file diffusion and 3-dimensional bulk diffusion, respectively. The above observations clearly show that the diffusion behavior of ions/molecules within the pores and pore structure, such as the surface-to-volume ratio? (D?_app (?)=D_0 [1-4/(9vp) S/V v(D_0 ?)]) and tortuosity (T = D0/Dapp,8), are possible to be misunderstood, especially in the systems with a non-negligible gi. This work demonstrates that it may be necessary to test several PFG sequences under multiple external magnetic fields for the correct determination of the diffusion behavior of ions/molecules in the pores with a larger internal gradient, gi.

Han, Kee Sung↗
DOE OSTI2024

Parallel Diffusion Coefficient of Energetic Charged Particles in the Inner Heliosphere from the Turbulent Magnetic Fields Measured by Parker Solar Probe

Diffusion coefficients of energetic charged particles in turbulent magnetic fields are a fundamental aspect of diffusive transport theory but remain incompletely understood. In this work, we use quasi-linear theory to evaluate the spatial variation of the parallel diffusion coefficient κ ∥ from the measured magnetic turbulence power spectra in the inner heliosphere. We consider the magnetic field and plasma velocity measurements from Parker Solar Probe made during Orbits 5–13. The parallel diffusion coefficient is calculated as a function of radial distance from 0.062 to 0.8 au, and the particle energy from 100 keV to 1 GeV. We find that κ ∥ increases exponentially with both heliocentric distance and energy of particles. The fluctuations in κ ∥ are related to the episodes of large-scale magnetic structures in the solar wind. By fitting the results, we also provide an empirical formula of κ ∥ = (5.16 ± 1.22) × 10 18 r 1.17 ± 0.08 E 0.71 ± 0.02 (cm 2 s -1 ) in the inner heliosphere, which can be used as a reference in studying the transport and acceleration of solar energetic particles as well as the modulation of cosmic rays.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2024

Multitiered computational methodology for extracting three-dimensional rotational diffusion coefficients from x-ray photon correlation spectroscopy data without structural information

X-ray photon correlation spectroscopy (XPCS) is a powerful technique for analyzing particle systems by investigating their dynamics in suspensions across a broad range of temporal and spatial scales. This is done by illuminating samples with coherent x-ray beams and calculating the correlation function of the obtained x-ray scattering images. XPCS is uniquely suited for studying Brownian dynamics, consisting of translational and rotational diffusion. While traditional XPCS image analysis techniques can extract translational diffusion components, they are unable to estimate rotational diffusion coefficients. Here, we introduce a methodology that combines the angular-temporal cross-correlation analysis and a algorithmic framework called Multi-Tiered Estimation for Correlation Spectroscopy in 3D for estimating three-dimensional rotational diffusion coefficients from XPCS images of three-dimensional particle systems. We demonstrate our methodology for extracting rotational diffusion coefficients from XPCS data by applying it to simulated noisy x-ray images of systems of crossing nanotubes and proteins that evolve under translational and rotational Brownian motion for different diffusion rates. Furthermore, our results show that our approach determines rotational diffusion coefficients within a few percent error.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Henry’s Solubility and Diffusion Coefficients for 29 Volatile Organic Compounds in Polydimethylsiloxane Sylgard 184 at 293 K

Two-dimensional (2D) inverse gas chromatography (IGC) enables simultaneous determination of Henry’s solubility and Fickian diffusion coefficients for volatile organic compounds (VOCs) in polymer films. This technique offers a significant advantage over traditional cylindrical column IGC by providing precise control and measurement of the film thickness (here, 0.064 ± 0.002 mm), which is the critical length scale for accurate diffusivity determination. We apply this methodology to characterize VOC transport in Sylgard 184, a widely used polydimethylsiloxane (PDMS)-based polymer containing substantial silica filler content. At room temperature (20 °C), we measured solubility and diffusion coefficients for 29 common VOCs spanning diverse chemical functionalities, including alkanes, aromatics, chlorinated solvents, ketones, esters, and alcohols. Comparison with literature data for pure PDMS reveals that VOC solubility in Sylgard 184 is generally higher; for most non-hydrogen-bonding compounds it remains within a factor of 2 of pure PDMS, whereas alcohols are enhanced by roughly 1.8 to 3.7 times, which we attribute to favorable interactions with residual silanol groups on the silanized silica filler. Diffusion coefficients range from 1.0 × 10 –6 cm 2 /s (n-undecane) to 8.9 × 10–5 cm 2 /s (acetonitrile) and align well with extrapolated literature values for PDMS. This study provides essential thermodynamic and transport data for predicting VOC permeation in Sylgard 184 while demonstrating the utility of 2D IGC as a robust technique for characterizing rubbery polymer membranes across diverse industrial applications.

organic↗
DOE OSTI2022

Towards 2+1 Flavor Lattice QCD Results for the Heavy Quark Diffusion Coefficient

We apply and extend a novel approach to non-perturbatively estimate the heavy-quark momentum diffusion coefficient κ, which is a key input for the theoretical description of heavy quarkonium production in heavy ion collisions, and is important for the understanding of the elliptic flow and nuclear suppression factor of heavy flavor hadrons. In the heavy-quark limit, this coefficient is encoded in the spectral functions of color-electric and color-magnetic correlators that we calculate on the lattice to high pre cision by applying gradient flow. In a recent study we have considered quenched QCD at 1.5 T c , where we performed a detailed study of the lat tice spacing and flow time dependence of the color-electric correlator, and, using theoretically well-established model fits for the spectral reconstruc tion, we estimated the heavy-quark diffusion coefficient. Equipped with the experience obtained in quenched QCD, we estimate $κ$ from 2+1 flavor QCD ensembles at small but finite lattice spacing and flow time without increasing systematic errors significantly.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Mechanistic calculation of the effective silver diffusion coefficient in polycrystalline silicon carbide: Application to silver release in AGR-1 TRISO particles

The silicon carbide (SiC) layer in tristructural isotropic (TRISO) fuel particles serves as a barrier to prevent the escape of fission products produced and not retained in the fuel kernel. The release of silver (Ag) is a concern due to the long half-life of the 110m Ag isotope. However, accurately determining the fission gas release rate requires knowing the diffusion coefficient through the SiC layer. In this study, we leverage atomistic calculations of Ag diffusivity in SiC bulk and grain boundaries (GBs) to develop a mesoscale effective Ag diffusion coefficient (D eff ) in SiC. Since GBs serve as pathways for Ag diffusion, D eff is defined as a function of temperature and microstructure variables. In particular, the size of SiC grains in the direction perpendicular to diffusion is shown to significantly affect Ag diffusion. The prediction of the mechanistic, mesoscale approach falls within one order of magnitude of empirical values. The temperature and microstructure-dependent effective Ag diffusivity in SiC is implemented in the fuel performance code Bison with a correction factor to predict Ag release from AGR-1 TRISO fuel particles. We hereby quantify the impact of SiC grain size on Ag release and improve Bison’s predictions.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2024

Quark Mass Dependence of Heavy Quark Diffusion Coefficient from Lattice QCD

We present the first study of the quark mass dependence of the heavy quark momentum and spatial diffusion coefficients using lattice QCD with light dynamical quarks corresponding to a pion mass of 320 MeV. We find that, for the temperature range 195 MeV < 𝑇 < 293 MeV, the spatial diffusion coefficients of the charm and bottom quarks are smaller than those obtained in phenomenological models that describe the 𝑝 𝑇 spectra and elliptic flow of open heavy flavor hadrons.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗