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DOE OSTI2024

Challenging Common Assumptions of Thick-Wall Chamber Dynamics in Inertial Fusion Systems Using MOOSE-based Multiphysics Simulations

As an increasing number of companies look toward commercial Inertial Fusion Energy (IFE) designs, there is a pressing need to understand the physics of thick-wall chamber gas dynamics. The thick liquid wall approach implements a renewable wall to mitigate the fusion target emissions, thereby reducing the radiation damage rate and significantly extending the lifetime of chamber structures, leading to increased plant availability and reduced waste streams in comparison to dry wall chamber designs. It is necessary, however, to assess the critical performance and safety aspects of these systems. For example, it is crucial to predict (1) where the mass ablated from the liquid walls will vent, which determines the placement of condensing surfaces; (2) debris propagation up the beam lines, which provides essential information for design and protection requirements; (3) peak pressures and impulse on chamber walls, which affect chamber structural design; and (4) momentum transfer to the liquid jets, which constrains the shape and positioning of the jets. In turn, the chamber design and its liquid walls affect shielding requirements, material activation, and tritium fuel cycle. Currently available simulation tools, however, are unable to accurately capture key thick-wall chamber dynamics. Significant assumptions are often made to simplify the system and reduce computational cost and modeling capability needs, but the impact of these assumptions on simulation predictions has not been evaluated. For example, no three-dimensional simulations can be found in the open literature to evaluate gas venting and momentum transfer to the jets with simulations using two-dimensional domains to represent complex three-dimensional geometries. Moreover, limited studies have been dedicated to jet breakup due to both turbulence and neutron heating, and no studies have been found that evaluate how jet breakup can impact shock-jet interaction. Furthermore, effects of radiative heat transfer have rarely been included for the hydrodynamic phase of shock propagation, and integration of proper equations of state in shock dynamics codes has been mostly exploratory. In this study, we use the flexible, high-fidelity Multiphysics Object-Oriented Simulation Environment (MOOSE) to model these complex phenomena and inform design and safety studies. Capabilities to model thick-wall chamber gas dynamics are being developed, and the impact of the assumptions listed above (i.e., two-dimensional vs three-dimensional, absence of jet breakout, no radiative heat transfer, and ideal gas behavior) are being quantified.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2024

Challenging Common Assumptions of Thick-Wall Chamber Dynamics in Inertial Fusion Systems using MOOSE

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2023

Can we observe the ion-neutral drift velocity in prestellar cores?

Given the low-ionization fraction of molecular clouds, ambipolar diffusion is thought to be an integral process in star formation. However, chemical and radiative-transfer effects, observational challenges, and the fact that the ion-neutral drift velocity is inherently very small render a definite detection of ambipolar diffusion extremely non-trivial. Here, we study the ion-neutral drift velocity in a suite of chemodynamical, non-ideal magnetohydrodynamic (MHD), two-dimensional axisymmetric simulations of prestellar cores where we alter the temperature, cosmic-ray ionization rate, visual extinction, mass-to-flux ratio, and chemical evolution. Subsequently, we perform a number of non-local thermodynamic equilibrium (non-LTE) radiative-transfer calculations considering various idealized and non-idealized scenarios in order to assess which factor (chemistry, radiative transfer, and/or observational difficulties) is the most challenging to overcome in our efforts to detect the ion-neutral drift velocity. We find that temperature has a significant effect in the amplitude of the drift velocity with the coldest modelled cores (T = 6 K) exhibiting drift velocities comparable to the sound speed. Against expectations, we find that in idealized scenarios (where two species are perfectly chemically co-evolving) the drift velocity ‘survives’ radiative-transfer effects and can in principle be observed. However, we find that observational challenges and chemical effects can significantly hinder our view of the ion-neutral drift velocity. Finally, we propose that HCN and HCNH + ⁠, being chemically co-evolving, could be used in future observational studies aiming to measure the ion-neutral drift velocity.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2021

Configuration mixing in 28 Mg and the 26 Mg (t,p) 28 Mg reaction

We have studied the 26 Mg(t,p) 28 Mg reaction. The nucleus 28 Mg lies between 24 Mg and 32 Mg, the latter of which is central to the “island of inversion” characterized by low-lying neutron fp-shell configurations. The present results show that the second-excited 0 + state in 28 Mg contains large fp-shell occupation for the neutrons. The experiment was performed in inverse kinematics using the HELIcal Orbit Spectrometer (HELIOS) at Argonne National Laboratory. Shell-model calculations using the SDPF-MU interaction yielded level energies and two-neutron transfer amplitudes that were used in one-step distorted-wave Furthermore, born approximation calculations to provide theoretical predictions of the proton angular distributions. In many, but not all cases, the data were in good agreement with theoretical predictions.

20 ≤ A ≤ 38↗

DOE OSTI2023

A Refined Understanding of the Ice Cloud Longwave Scattering Effects in Climate Model

Abstract Because longwave (LW) absorption by greenhouse gases and clouds is more significant than the LW scattering effect by clouds, most climate models neglect cloud LW scattering to save computational costs. Ignoring cloud LW scattering directly overestimates outgoing longwave radiation (OLR). This study included ice‐cloud LW scattering treatment in the Exascale Energy Earth System Model (E3SM) version 2 and ran fully‐coupled simulations, prescribed sea surface temperature simulations, and offline radiative transfer calculations to comprehensively assess the impact of ice‐cloud LW scattering on global climate simulation. The instantaneous effect due to ice‐cloud LW scattering reduces the OLR by ∼1 W/m 2 on the global average and 2 W/m 2 on the tropical average. Tropospheric warming and high cloud amount reduction act to partially compensate for such instantaneous OLR reduction caused by the inclusion of LW scattering. When the simulation reaches the equilibrium, the surface warms by 0.66 K on average with respect to the simulation without LW scattering, with the Arctic surface temperature differences more than twice as large as that of the global mean. The impact of including LW scattering on the simulated climate change in response to 4 × CO 2 is also assessed. While including the cloud LW scattering does not significantly modify radiative forcing and total radiative feedback under such a scenario, it results in a 10% more positive cloud feedback.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Dynamical Unification of Tidal Disruption Events

The ~100 tidal disruption events (TDEs) observed so far exhibit a wide range of emission properties both at peak and over their lifetimes. Some TDEs radiate predominantly at X-ray energies, while others radiate chiefly at UV and optical wavelengths. While the peak luminosities across TDEs show distinct properties, the evolutionary behavior can also vary between TDEs with similar peak emission properties. In particular, for optical TDEs, while their UV and optical emissions decline somewhat following the fallback pattern, some events can greatly rebrighten in X-rays at late time. In this Letter, we conduct three-dimensional general relativistic radiation magnetohydrodynamics simulations of TDE accretion disks at varying accretion rates in the regime of super-Eddington accretion. We make use of Monte Carlo radiative transfer simulations to calculate the reprocessed spectra at various inclinations and at different evolutionary stages. We confirm the unified model proposed by Dai et al., which predicts that the observed emission largely depends on the viewing angle of the observer with respect to the disk orientation. Furthermore, we find that disks with higher accretion rates have elevated wind and disk densities, which increases the reprocessing of the high-energy radiation and thus generally augments the optical-to-X-ray flux ratio along a particular viewing angle. This implies that at later times, as the accretion level declines, we expect that more X-rays will leak out along intermediate viewing angles. Such dynamical model for TDEs can provide a natural explanation for the diversity in the emission properties observed in TDEs at peak and along their temporal evolution.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2020

Assessment of various tar and soot treatment methods and a priori analysis of the steady laminar flamelet model for use in coal combustion simulation

Soot formed in the fuel-rich regions of coal flames is known to have a significant impact on the radiative heat transfer characteristics of the flame. It is therefore important to account for the effect of soot radiation when simulating coal combustion systems. Several recent coal combustion studies have used acetylene as a surrogate for devolatilized tar and neglect soot formation altogether, while others have utilized empirical models for tar and soot or even chemical mechanisms which include tar and soot as species. In this work, we investigate several methods of treating coal-derived tar and soot and the impact each treatment has on predicted furnace temperature, particle mass loss, and other quantities of interest. Furthermore, we perform a priori comparisons of simulation results to calculations from a steady laminar flamelet model in order to assess the accuracy of a flamelet approach for each tar and soot treatment considered. Data used as a basis for the study is generated through One-Dimensional Turbulence (ODT) simulation of a coal combustion system in which high- fidelity models are used for gas phase chemistry and devolatilization, where char combustion is neglected.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2022

Experiments and numerical modeling of surrogate droplet combustion for a 93 octane gasoline calibration fuel

Gasoline is the world’s most prolific liquid transportation fuel for ground transportation vehicles. Yet, a fundamental understanding of its burning characteristics is still lacking. Complicating this matter is the highly multicomponent nature of gasoline (comprised of hundreds of chemical species) and the seasonable variability of its composition due to variations in the crude oil feedstocks used in refining. The need to bring order to this complex problem has led to development of calibration fuels (Tier II in presented study) which on average will provide repeatable metrics that replicate performance of refined gasoline for various engine designs. This study presents results of experiments using the configuration of an isolated droplet to study the combustion dynamics of calibration fuel and three different surrogates (S4, S5, S6) for the calibration fuel. Droplet burning is under microgravity conditions, where gas transport is determined entirely by fuel evaporation in order to promote spherical symmetry in the burning process. The initial droplet diameters ranged between 0.55 mm and 0.60 mm. The droplets were spark-ignited and their burning histories were recorded by digital video cameras to obtain quantitative data. For each fuel, the evolutions of droplet, flame, and soot-shell diameters were measured to calculate the burn rates, flame-droplet diameter ratios (FSR) and soot-droplet diameter ratios. Additionally, a detailed numerical modeling is presented. This simulation includes multicomponent phase equilibrium, unsteady gas and liquid transport, radiative heat transfer, internal liquid diffusion and detailed combustion chemistry of different fuels during their burning process. Experiment results show that the calibration fuel and surrogates have a close burn rates and FSR, and S5 presents a relatively similar results with calibration fuel. Predictions from the numerical simulation using the surrogate are compared with experiment measurements, which showed a good agreement with the experiment results, including the droplet burning rate and FSR.

Guo, Songtao↗

DOE OSTI2021

Seasonal Cycle of Idealized Polar Clouds: Large Eddy Simulations Driven by a GCM

The uncertainty in polar cloud feedbacks calls for process understanding of the cloud response to climate warming. As an initial step toward improved process understanding, we investigate the seasonal cycle of polar clouds in the current climate by adopting a novel modeling framework using large eddy simulations (LES), which explicitly resolve cloud dynamics. Resolved horizontal and vertical advection of heat and moisture from an idealized GCM are prescribed as forcing in the LES. The LES are also forced with prescribed sea ice thickness, but surface temperature, atmospheric temperature, and moisture evolve freely without nudging. A semigray radiative transfer scheme without water vapor and cloud feedbacks allows the GCM and LES to achieve closed energy budgets more easily than would be possible with more complex schemes. This enables the mean states in the two models to be consistently compared, without the added complications from interaction with more comprehensive radiation. Furthermore, we show that the LES closely follow the GCM seasonal cycle, and the seasonal cycle of low-level clouds in the LES resembles observations: maximum cloud liquid occurs in late summer and early autumn, and winter clouds are dominated by ice in the upper troposphere. Large-scale advection of moisture provides the main source of water vapor for the liquid-containing clouds in summer, while a temperature advection peak in winter makes the atmosphere relatively dry and reduces cloud condensate. The framework we develop and employ can be used broadly for studying cloud processes and the response of polar clouds to climate warming.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

Linear Time-Invariant Models of a Large Cumulus Ensemble

Abstract Methods in system identification are used to obtain linear time-invariant state-space models that describe how horizontal averages of temperature and humidity of a large cumulus ensemble evolve with time under small forcing. The cumulus ensemble studied here is simulated with cloud-system-resolving models in radiative–convective equilibrium. The identified models extend steady-state linear response functions used in past studies and provide accurate descriptions of the transfer function, the noise model, and the behavior of cumulus convection when coupled with two-dimensional gravity waves. A novel procedure is developed to convert the state-space models into an interpretable form, which is used to elucidate and quantify memory in cumulus convection. The linear problem studied here serves as a useful reference point for more general efforts to obtain data-driven and interpretable parameterizations of cumulus convection.

Meteorology & Atmospheric Sciences↗

DOE OSTI2025

Structural uncertainty assessment for fire-engulfed objects in crosswind: Establishing credibility for a multiphysics wall-modeled large-eddy simulation paradigm

A structural uncertainty validation study for a large-scale, fire-engulfed, elevated object subjected to crosswind is presented to establish the credibility of a high-fidelity, low-Mach, turbulent reacting flow wall-modeled large-eddy simulation (WMLES) approach that includes multiphysics coupling to participating media radiation and conjugate heat transfer. To establish that WMLES can accurately predict surface quantities including drag and pressure coefficient in the low-Mach crosswind regime, a foundational elevated isothermal cylinder validation case is presented at a similar gap-to-diameter ratio of 0.25, spanning the subcritical to supercritical drag regime (Re 𝐷 = 1.1 × 10 5 and 4.3 × 10 5 , respectively). Here, this study exercised both static and dynamic coefficient LES (Smagorinsky and 𝑘 sgs ) with both local and exchange-based velocity sampling. Results showcase that the drag crisis (or the sudden drop in drag coefficient at increased Re 𝐷 ) is well captured when using an exchange-based dynamic coefficient WMLES methodology, while noting lack of mesh convergence and overall drag and pressure coefficient predictively when using a static coefficient, local velocity sampling WMLES. For the 𝒪⁡(10) m JP-8 liquid pool fire crosswind validation study presented, two experimental crosswind configurations (2 m/s and 9.5 m/s) are showcased for a fire-engulfed mock fuselage roughly 4 m in diameter. Using the best model-form practices identified in the isothermal study, dynamic coefficient 𝑘 sgs exchange-based WMLES fire validation findings demonstrate accurate peak irradiation and skin temperature predictions as a function of crosswind magnitude. Excessive yaw in the low-crosswind fuselage configuration, consistent with experimental findings, captured a significant predicted asymmetry in flame attachment and heat flux toward the downwind cylindrical cap—indicative of axial vortex structures transporting the flame along the upper and lower fuselage leeward surface. All fire mesh resolution simulations captured the experimental finding that as crosswind increased, predicted flame shape and peak irradiation magnitude onto the fuselage transitioned from a windward to a leeward cylinder location due to the migration of the upper- to lower-shear fuel/air mixing layer thereby demonstrating the novelty, significance, and credibility of this high-fidelity WMLES reacting flow framework.

Domino, Stefan Paul [Sandia National Laboratories ↗

DOE OSTI2020

Modeling the Transmission of Optical Lightning Signals Through Complex 3‐D Cloud Scenes

Abstract Space‐based lightning imagers have shown that complex cloud scenes consisting of multiple tall convective features, anvil clouds, and warm boundary cloud layers are illuminated by lightning in many different ways depending on where the lightning occurs and how energetic it is. Modifications to the optical lightning signals from radiative transfer in the cloud medium can lead to reductions in detection efficiency and location accuracy for these instruments and can also cause some of the optical signals that are detected to have unexpected spatial energy distributions. In this study, we perform Monte Carlo radiative transfer simulations of optical lightning emissions in clouds with complex 3‐D geometries to shed some light on the origins of certain irregular radiance patterns that have been recorded from orbit. We show that diffuse reflections off nearby cloud faces can explain lightning signals in nonelectrified clouds, tall clouds can result in poor optical transmission and suppressed radiances that could lead to missed events and that particularly favorable viewing conditions can cause otherwise normal lightning to produce a superbolt that is orders of magnitude brighter than the same flash seen from a different angle.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2023

Improved Particle Heat Transfer by way of Bimodal Particle Distributions for High Temperature Solar Thermal Energy

High temperature solar thermal facilities are looking to increase operating temperatures through novel heat transfer media, one such being solid particles. These particles operating at high temperatures will require transferring their thermal energy into another working fluid like supercritical carbon dioxide which can be used in advanced power cycles. Achieving high heat transfer between the particles and supercritical carbon dioxide is essential to high efficiency and low-cost operation. Therefore, optimizing the thermal conductivity of these particles is one potential way to ensure high performance. Traditionally, unimodal particle distributions have been employed in high temperature particle solar power plants. However, ambient temperature testing of bimodal particle distributions has revealed a superior thermal conductivity when compared to its unimodal counterpart at the same temperature. This data was obtained by certified, off-the-shelf instruments that can effectively simulate the conditions a particle would be exposed to in a high temperature solar thermal system. Data obtained in this way suggests that the increased thermal conductively imputed by a bimodal particle distribution is significant at working temperatures in solar facilities. Furthermore, the thermal conductivity of these bimodal particle distributions peaks when the best combination of large and small particles is applied. At high temperatures, binary particle distributions are compared to monodispersed distributions of larger particles where heat transfer is more prolific due to the increased surface radiation. Various thermal conductivity, porosity and heat exchanger models are explored in conjunction with data acquired up to 700 C.

Stout, Dallin (ORCID:0009000294586091)↗

DOE OSTI2021

Pressurizer dynamic model and emulated programmable logic controllers for nuclear power plants cybersecurity investigations

This work demonstrates the functionality of the pressurizer using a fast-running three regions, non-equilibrium model and control programs of emulated PLCs. The state variables from an integrated model of primary loop in a representative PWR plant are communicated to the pressurizer’s emulated PLCs using a synchronized data transfer function. In turn, the PLCs communicate back instructions to the pressurizer model to adjust the pressure and water level to remain within preprogramed setpoints. Pressurizer model simultaneously solves the coupled mass and energy conservation equations in the saturated vapor and saturated and subcooled liquid regions using fixed step solver. Results demonstrate the response of the pressurizer model linked to an emulated pressure and water level PLCs in a simulated transient involving surge-in and surge-out events. The 50 ms response delay time for the emulated PLC insignificantly affects operation and predictions of the pressurizer model.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2022

Analysis of Postulated Accident Scenarios for the Transformational Challenge Reactor

The Transformational Challenge Reactor (TCR) is a helium-cooled, yttrium-hydride-moderated reactor that was designed for the U.S. Department of Energy Office of Nuclear Energy. A key objective of the TCR was to employ advanced manufacturing techniques in a nuclear system and demonstrate their potential for revolutionizing the nuclear reactor design process. One purpose of the present work is to demonstrate the safety of the TCR under postulated accidents. Based on RELAP5-3D and COMSOL analyses, the TCR remained below all current safety limits and far below the expected failure limits for the core materials. Another purpose of this work is to provide useful insights and recommendations regarding the application of RELAP5-3D to gas-cooled or other advanced reactors. A novel approach was implemented for simultaneously modeling conduction and radiation in RELAP5-3D, which was found to provide reasonable predictions of radial core, vessel, and ex-vessel heat transfer during postulated events. A multicode approach was also applied, in which high-fidelity COMSOL calculations were used to tune the radial heat transfer parameters in RELAP5-3D. The tuned RELAP5-3D model demonstrated comparable peak temperature predictions as COMSOL, despite a coarse treatment of the core in RELAP5-3D consisting of only two lumped heat structures. This high-fidelity tuning approach enabled enhanced accuracy as well as minimal complexity within the RELAP5-3D model, even for complex fuel geometric designs as in the TCR. Finally, investigations were made into the potential for flow reversal during a pressurized loss-of-forced-flow event in the TCR. The TCR is designed with downward helium flow through the core during normal operation. The RELAP5-3D model predicted that this downward flow would persist, without flow reversal, up to several days after the circulator trip. This was attributed to natural circulation hysteresis effects as have been noted in similar thermofluidic systems. Although flow stagnation and eventual reversal did not lead to unsafe TCR conditions, interesting spatial effects were observed which may have safety relevance for other reactor system designs and coolant types that are designed for downward core flow during normal operation, warranting closer investigation of the flow reversal phenomenon.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2024

MOOSE-Based Fast Reactor Core Bowing Capabilities: Coupled Structural Mechanics – Thermal Fluids Demonstration and Related Verification Efforts

Under the U.S. Department of Energy Office of Nuclear Energy’s Advanced Modeling and Simulation (NEAMS) Program, an integrated multiphysics approach is being developed to model the core bowing phenomena important to liquid metal-cooled fast reactors. Core bowing is an important passive safety mechanism in liquid metal-cooled fast reactors and involves multiphysics effects including radiation transport, fluid flow, heat transfer, and mechanical response to temperature and flux gradients. Verification and assessment efforts continued on the Multiphysics Object Oriented Simulation Environment (MOOSE) capabilities relevant for modeling thermo-mechanical core bowing behavior. IAEA Verification Problem 4, which was started in FY23, was further examined with MOOSE capabilities to rectify discrepancies observed in previous years when compared to IAEA benchmark participant data. Meshing and postprocessing capabilities in MOOSE were also advanced by other teams and utilized this year. A thermal fluids-structural mechanical coupling demonstration has performed on 7-assemblyand 19-assembly fast reactor assembly configurations using MOOSE. Subchannel capabilities are used to calculate coolant temperature, and heat conduction capabilities calculate duct wall temperature as well as heat transfer through the inter-assembly gap. Structural mechanical capabilities then deform the mesh, accounting for contact between assemblies, according to the temperature gradients calculated by the thermal solvers. Power distributions are imposed rather than calculated to demonstrate different deformations.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2026

HTGR Multiphysics Application Drivers FY26 Updates

This report summarizes FY26 progress under the Nuclear Energy Advanced Modeling and Simulation (NEAMS) program's high-temperature gas-cooled reactor (HTGR) application driver work, covering a wide range of activities such as code validation and multi-physics code assessment. 1) A detailed SAM model of the High-Temperature Engineering Test Reactor (HTTR) was developed using a unique-block grouping approach, with an extended parallel thermal network method to capture block-to-block conduction and radiation heat transfer, and applied to steady-state simulations of the HTTR 30~MW and 9~MW cases. 2) In another activity, SAM's newly implemented multi-component gas flow model was validated against the Natural convection Shutdown heat removal Test Facility (NSTF) argon ingress experiment, correctly capturing the density-driven suppression and thermal recovery of natural circulation observed when argon is introduced into the air-cooled Reactor Cavity Cooling System (RCCS) loop. 3) For the OECD/NEA High Temperature Test Facility (HTTF) benchmark, we co-led the international benchmark activities as well as the OECD/NEA final benchmark report to be released at the end of this year. 4) Finally, the coupled Griffin-SAM modeling capability for pebble-bed HTGRs was advanced by verifying the Griffin neutronics solution against Serpent Monte Carlo for a realistic non-uniform temperature distribution, resolving several deficiencies in the SAM-to-Griffin temperature transfer scheme, and enabling distinct fuel kernel, moderator, and coolant temperatures for cross section feedback. These new features were demonstrated in a PBR load-following transient.

Lee, Alvin↗

DOE OSTI2021

Numerical analysis of particle dispersion and deposition in coal combustion using large-eddy simulation

High-fidelity modeling provides a useful approach to investigate the particle dispersion and deposition mechanism in pulverized coal combustion. To be able to analyze these detailed mechanisms, this work couples detailed multiphysics models for poly-dispersed turbulent, particle-laden flow, particle and gas phase reaction chemistry, convective, conductive and radiative heat transfer, ash formation and deposition with a Large-Eddy Simulation (LES) approach to numerically simulate coal combustion in a downfired self-sustained oxy-fuel combustor (OFC). It is necessary to explicitly capture all but the highest frequency dynamics of the turbulence and its coupling with each of the other physical phenomena using LES. Effects of subgrid-scale unresolved turbulence on the particle motions are also analyzed by a novel Stokes number analysis. Due to the inherent relation ship between coal combustion and ash deposition, this study integrates the improved ash deposition model into the numerical simulation. Overall simulation results are compared with experimentally measured data from the OFC. The simulation and measured data for the averaged gas temperature and deposition rates agree with 5% and 28%. This study shows that high-fidelity LES coupled with other detailed multiphysics models running on a exascale computing facility can provide a good representation of complex coal combustion and deposition in a laboratory-scale furnace.

multiphysics model↗