Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Transition Model”

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 487 records · Page 27
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Chemical Complexity of Phosphorous-bearing Species in Various Regions of the Interstellar Medium

Phosphorus-related species are not known to be as omnipresent in space as hydrogen, carbon, nitrogen, oxygen, and sulfur-bearing species. Astronomers spotted very few P-bearing molecules in the interstellar medium and circumstellar envelopes. Limited discovery of the P-bearing species imposes severe constraints in modeling the P-chemistry. In this paper, we carry out extensive chemical models to follow the fate of P-bearing species in diffuse clouds, photon-dominated or photodissociation regions (PDRs), and hot cores/corinos. We notice a curious correlation between the abundances of PO and PN and atomic nitrogen. Since N atoms are more abundant in diffuse clouds and PDRs than in the hot core/corino region, PO/PN reflects <1 in diffuse clouds, ≪1 in PDRs, and >1 in the late warm-up evolutionary stage of the hot core/corino regions. During the end of the post-warm-up stage, we obtain PO/PN > 1 for hot core and <1 for its low-mass analog. We employ a radiative transfer model to investigate the transitions of some of the P-bearing species in diffuse cloud and hot core regions and estimate the line profiles. Our study estimates the required integration time to observe these transitions with ground-based and space-based telescopes. We also carry out quantum chemical computation of the infrared features of PH{sub 3}, along with various impurities. We notice that SO{sub 2} overlaps with the PH{sub 3} bending-scissoring modes around ∼1000–1100 cm{sup −1}. We also find that the presence of CO{sub 2} can strongly influence the intensity of the stretching modes around ∼2400 cm{sup −1} of PH{sub 3}.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2022

A Rapid Ionization Change in the Nebular-phase Spectra of the Type Ia SN 2011fe

Abstract We present three new spectra of the nearby Type Ia supernova (SN Ia) 2011fe covering ≈480–850 days after maximum light and show that the ejecta undergoes a rapid ionization shift at ∼500 days after explosion. The prominent Fe iii emission lines at ≈4600 Å are replaced with Fe i +Fe ii blends at ∼4400 Å and ∼5400 Å. The ≈7300 Å feature, which is produced by [Fe ii ]+[Ni ii ] at ≲400 days after explosion, is replaced by broad (≈±15,000 km s −1 ) symmetric [Ca ii ] emission. Models predict this ionization transition occurring ∼100 days later than what is observed, which we attribute to clumping in the ejecta. Finally, we use the nebular-phase spectra to test several proposed progenitor scenarios for SN 2011fe. Nondetections of H and He exclude nearby nondegenerate companions, [O i ] nondetections disfavor the violent merger of two white dwarfs, and the symmetric emission-line profiles favor a symmetric explosion.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Distributed Wind: Supporting the Clean Energy Transition

Distributed wind technologies have advanced a great deal over the last decade, developing from a very selective market to one that is poised to play a significant role in supporting a clean energy transition. Summarizing technical and modeling advances, most of them supported by program efforts undertaken by the Wind Energy Technology Office of the U.S. Department of Energy, this presentation provides an overview of the current state of distributed wind technologies and how the technology could support the wider distributed energy development. The presentation also provides an short introduction to the challenges and ongoing research to address these challenges.

distributed energy↗
DOE OSTI2023

Measuring Sustainability of PV in Energy Transition: Mass, Energy, and Circularity

Energy transition to a carbon-free energy system is crucial for global decarbonization and underpins circular economy (CE) goals. Photovoltaic (PV) technology is required for energy transition, but manufacturing and circular pathways can be material, energy, and carbon-intensive. Therefore, we need a prioritization of sustainability strategies for PV evolution. In this study, we compare sustainable PV module designs in terms of their entailed mass, energy, circularity, and carbon impacts to achieve Energy Transition. Results will support decision-makers through data-backed scenario and tradeoff analyses offering prioritization of sustainable PV module designs and CE pathways for meeting Energy Transition goals.

carbon↗
DOE OSTI2021

$\mathcal{g}$ modes of neutron stars with hadron-to-quark crossover transitions

Here we perform the first study of the principal core g-mode oscillation in hybrid stars containing quark matter, utilizing a crossover model for the hadron-to-quark transition inspired by lattice QCD. The ensuing results are compared with our recent findings of g-mode frequencies in hybrid stars with a first-order phase transition using Gibbs constructions. We find that models using Gibbs construction yield g-mode amplitudes and the associated gravitational energy radiated that dominate over those of the chosen crossover model owing to the distinct behaviors of the equilibrium and adiabatic sound speeds in the various models. Based on our results, we conclude that were g modes to be detected in upgraded LIGO and Virgo detectors it would indicate a first-order phase transition akin to a Gibbs construction.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Inverter Intensive Hybrid Power Plant Modeling with Small-Signal Stability Augmentation through Flexible Operation Mode Transition

Hybrid power plants (HPPs) prompt the penetration of inverter-based renewable energy sources (RES) in transmission systems; however, given their low-inertia nature, HPPs are dominated by power electronic inverters, so there are inevitable challenges in system stability when increasing numbers of HPPs are integrated into the modern power grids. To boost the penetration level of HPPs without jeopardizing system stability, it is desirable to equip them with operational characteristics (i.e., grid-forming capabilities) that are comparable to those of conventional power plants dominated by synchronous generators (SGs). In this paper, a holistic model of inverter intensive HPP is derived and a bi-level hierarchical control is developed to allow HPPs to flexibly switch among the designed operation modes (i.e., P-Q, P-V, and isochronous modes). Compared to SGs, which have limited controllability, the operation mode of each HPP could vary as requested. Such flexible mode transitions could be integrated into the secondary plant-level control and be leveraged as an additional control degree to further augment system stability. Further, the system small-signal stability margin is quantified with varying HPP operation modes. More importantly, modal analysis is thereby conducted to quantify the impacts of mode transition on the system oscillatory modes. The effectiveness of the proposed HPP bi-level hierarchical control is verified using extensive case studies based on the simplified real-world island power grid, and the results validate that the system small-signal stability margin can be enhanced with the additional degree of control flexibility enabled by HPP operation mode transition. The real-time hardware-in-the-loop (HIL) results are also provided to verify the proposed method.

grid-forming control↗
DOE OSTI2021

Spectral properties of three-dimensional Anderson model

The three-dimensional Anderson model represents a paradigmatic model to understand the Anderson localization transition. In this work we first review some key results obtained for this model in the past 50 years, and then study its properties from the perspective of modern numerical approaches. Our main focus is on the quantitative comparison between the level sensitivity statistics and the level statistics. While the former studies the sensitivity of Hamiltonian eigenlevels upon inserting a magnetic flux, the latter studies the properties of unperturbed eigenlevels. We define two versions of dimensionless conductance, the first corresponding to the width of the level curvature distribution relative to the mean level spacing, and the second corresponding to the ratio of the Heisenberg time and the Thouless time obtained from the spectral form factor. We show that both conductances look remarkably similar around the localization transition, in particular, they predict a nearly identical critical point consistent with other well-established measures of the transition. We then study some further properties of those quantities: for level curvatures, we discuss particular similarities and differences between the width of the level curvature distribution and the characteristic energy studied by Edwards and Thouless (1972) in their pioneering work, in which the hopping at one lattice edge is changed from periodic to antiperiodic boundary conditions. In the context of the spectral form factor, we show that at the critical point it enters a broad time-independent regime, in which its value is consistent with the level compressibility obtained from the level variance. Finally, we test the scaling solution of the average level spacing ratio in the crossover regime using the cost function minimization approach introduced recently in Šuntajs et al. (2020). The latter approach seeks for the optimal scaling solution in the vicinity of the crossing point, while at the same time it allows for the crossing point to drift due to finite-size corrections. We find that the extracted transition point and the scaling coefficient agree with those from the literature to high numerical accuracy.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2026

Understanding the causes of satellite–model discrepancies in aerosol–cloud interactions using near-LES simulations of marine boundary layer clouds

Aerosol–cloud interactions (ACI) remain the largest source of uncertainty in model estimates of anthropogenic radiative forcing, primarily because of deficiencies in representing aerosol–cloud microphysical processes that lead to inconsistent cloud liquid water path (LWP) responses to aerosol perturbations between observations and models. To investigate this discrepancy, we conducted a series of large-eddy-scale simulations driven by realistic meteorology over the eastern North Atlantic, and evaluated LWP susceptibility, precipitation processes, and boundary layer thermodynamics using satellite and ground-based observations. Simulated LWP responses show a strong dependence on cloud state. Non-precipitating thin clouds exhibit a modest LWP decrease with increasing cloud droplet number concentration (N d ), consistent in sign but weaker in magnitude than satellite estimates, reflecting enhanced turbulent mixing and evaporation. The largest model-observation discrepancy occurs in non-precipitating thick clouds, where simulated LWP susceptibilities are strongly positive (+0.32) while observations indicate large negative values (−0.69). This discrepancy stems from excessive precipitation driven by underestimated entrainment, overly active accretion, and overly broad drop-size distributions in polluted conditions. While our high-resolution setup mitigates the excessive drizzling common in coarser models and captures key regime transitions, these biases persist – highlighting that improved parameterizations of cloud-top processes, precipitation, and aerosol effects are needed beyond simply increasing model resolution. Additionally, misrepresented moisture inversions in reanalysis introduce a moist bias in cloud-top relative humidity, further amplifying positive LWP susceptibility. Our results also suggest that large negative N d –LWP relationships in observations may reflect internal cloud processes rather than true ACI effects.

Aerosol-cloud interaction↗
DOE OSTI2023

Hybrid interatomic potential for Sn

To design materials for extreme applications, it is important to understand and predict phase transitions and their influence on material properties under high pressures and temperatures. Atomistic modeling can be a useful tool to assess these behaviors. However, this can be difficult due to the lack of fidelity of the interatomic potentials in reproducing this high pressure and temperature extreme behavior. Here, in this work, a hybrid EAM-R—which is the combination of embedded atom method (EAM) and rapid artificial neural network potential—for Tin (Sn) is described which is capable of accurately modeling the complex sequence of phase transitions between different metallic polymorphs as a function of pressure. This hybrid approach ensures that a basic empirical potential like EAM is used as a lower energy bound. By using the final activation function, the neural network contribution to energy must be positive, assuring stability over the whole configuration space. This implementation has the capacity to reproduce density functional theory results at 6 orders of magnitude slower than a pair potential for molecular dynamics simulation, including elastic and plastic characteristics and relative energies of each phase. Using calculations of the Gibbs free energy, it is demonstrated that the potential precisely predicts the experimentally observed phase changes at temperatures and pressures across the whole phase diagram. At 10.2 GPa, the present potential predicts a first-order phase transition between body-centered tetragonal (BCT) β-Sn and another polymorph of BCT-Sn. This structure transforms into body-centered cubic near the experimentally reported value at 33 GPa. Thus, the Sn potential developed in this paper can be used to study complex deformation mechanisms under extreme conditions of high pressure and strain rates unlike existing potentials. Moreover, the framework developed in this paper can be extended for different material systems with complex phase diagrams.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Probabilistic Power Consumption Modeling for Commercial Buildings Using Logistic Regression Markov Chain

The total energy consumed by buildings takes up to 40% of U.S. energy use, in which a large portion is contributed by commercial buildings. Building performance optimization is desirable but requires accurate building models with uncertainties taken into account. This paper proposes a novel probabilistic modeling method using Logistic Regression Markov Chain (LRMC). The LRMC model enhances the performance of traditional Markov Chain (MC) models by adopting time-variant transition matrices calibrated using logistic regression with exogenous inputs. Compared with existing building models, the proposed model produces accurate multi-step modeling results with full probability distribution. The proposed probabilistic building model is tested using actual commercial building measurements and modeling performance is evaluated with two probabilisitc metrics. The results show that the LRMC model has higher accuracy than traditional MC model and Logistic Regression (LR) model in that it yields lower error scores under both evaluation metrics.

Building modeling↗
DOE OSTI2020

Equations of state, phase relations, and oxygen fugacity of the Ru-RuO 2 buffer at high pressures and temperatures

Experimental studies and measurements of inclusions in diamonds show that ferric iron components are increasingly stabilized with depth in the mantle. To determine the thermodynamic stability of such components, their concentration needs to be measured at known oxygen fugacities. The metal-oxide pair Ru and RuO 2 are ideal as an internal oxygen fugacity buffer in high-pressure experiments. Both phases remain solid to high temperatures and react minimally with silicates, only exchanging oxygen. To calculate oxygen fugacities at high pressure and temperature, however, requires information on the phase relations and equation of state properties of the solid phases. We have made in situ synchrotron X-ray diffraction measurements in a multi-anvil press on mixtures of Ru and RuO 2 to 19.4 GPa and 1473 K with which we have determined phase relations of the RuO 2 phases and derived thermal equations of state (EoS) parameters for both Ru and RuO 2 . Rutile-structured RuO 2 was found to undergo two phase transformations, first at ~7 GPa to an orthorhombic structure and then above 12 GPa to a cubic structure. The phase boundary of the cubic phase was constrained for the first time at high pressure and temperature. We have derived a continuous Gibbs free energy expression for the tetragonal and orthorhombic phases of RuO 2 by fitting the second-order phase transition boundary and P-V-T data for both phases, using a model based on Landau theory. The transition between the orthorhombic and cubic phases was then used along with EoS terms derived for both phases to determine a Gibbs free energy expression for the cubic phase. We have used these data to calculate the oxygen fugacity of the Ru + O 2 = RuO 2 equilibrium, which we have parameterized as a single polynomial across the stability fields of all three phases of RuO 2 . The expression is log 10 f O 2 (Ru – RuO 2 ) = (7.782 – 0.00996P + 0.001932P 2 – 3.76 × 10 –5 P 3 ) + (–13 763 + 592P – 3.955P 2 )/T + (–1.05 × 10 6 – 4622P)/T 2 , which should be valid from room pressure up to 25 GPa and 773–2500 K, with an estimated uncertainty of 0.2 log units. Our calculated fO 2 is shown to be up to 1 log unit lower than estimates that use previous expressions or ignore EoS terms.

Armstrong, Katherine↗
DOE OSTI2022

Automated Control for Nuclear Thermal Propulsion Start-Up using MOOSE-based Applications

This report presents a Griffin/Bison/RELAP-7 numerical model of a prototypical NTP system that features fuel assemblies arranged in rings, and which was designed to simulate rapid startup transients. The physics modeled include full-core neutronics, assembly-wise heat conduction, and conjugate heat transfer, with the balance of plant mainly imposed through boundary conditions. In addition, various forms of automated reactivity control were deployed by using the MOOSE to autonomously drive the model and simulate the reactor transitioning from assumed initial conditions to nominal power in a fraction of a minute. To generate the cross-sections of the neutronics model, and in an effort to simultaneously account for the tremendous axial temperature gradients in the reactor and to limit the number of state points required for cross-section generation, the average component temperatures and hydrogen densities in the cooling channels were correlated to the average fuel and moderator temperatures, and fixed axial profiles were derived for nominal conditions and then used during the transient. With this approximation, a tractable cross-section library tabulated with fuel/moderator temperatures and CD angles was generated using Serpent. The full-core SPH correction procedure and the CD decusping technology in Griffin, respectively, ensure preservation of the multiplication factor and reaction rates at state points, along with a reasonably accurate reactivity worth between tabulated CD angles, despite using a coarse mesh. Feedback from other physics was calculated by modeling one representative fuel assembly per ring, along with the corresponding fuel and moderator cooling channels. To limit power overshoots during startup, another layer of multiphysics coupling was added to the model in order to automatically control the drums. Two different technologies presented herein showed outstanding performance in this regard: (1) a novel hybrid PID controller based on both power and reactivity signals, and (2) a PGC that relies on kinetics parameters and reactivity coefficients to predict future behavior and adjust the desired signal accordingly. A challenging benchmark was devised, featuring a power demand curve that exponentially increases by a factor of 500 within 30 seconds, then levels out after that. Both control approaches create a simulated power curve that closely follows the power demand curve and limits power overshoots to 1% or less. While the former approach requires more tuning of the internal parameters, the latter requires additional knowledge of the reactivity feedback coefficients and rates of change of the corresponding variables, including fuel and moderator temperature, which could be difficult to dynamically measure for a real NTP system. Fortunately, some inaccuracy in these quantities will not drastically degrade the PGC performance. Subsequently, a more realistic startup sequence was considered, in which the mass flow rate and outlet pressures are ramped up to model bootstrap and thrust build-up phases prior to reaching steady-state conditions, demonstrating the ability of the hybrid PID and PGCs to handle such transients, with both types of controllers exhibiting very similar behavior. Nevertheless, a significant chamber temperature overshoot was observed, caused by the demanded power signal and assumed mass flow rate. This issue could be mitigated by deploying a reactor controller that follows the chamber temperature signal and actuates both the control valves and drums (rather than using a power signal based solely on the drums to control reactivity). Enhancement of the hydrogen fluid properties available in MOOSE, as well as a better understanding of prototypical initial conditions, are also needed to further enhance this startup model. Finally, a study was performed to model decay heat post-shutdown, and to prepare for extending this model to predict shutdown behavior and post-shutdown pulsed cooling requirements.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2020

Polarity dependent heating at the phase interface in metal-insulator transitions

We show that in a model of a metal photoexcited by a transient pump pulse resonant with a phonon mode, the absolute dc conductivity may become negative, depending on the interplay between the electronic structure, the phonon frequency, and the pump intensity. The analysis includes the effects of inelastic scattering and thermal relaxation. Results for the time evolution of the negative conductivity state are presented; the associated nonequilibrium physics may persist for long times after the pulse. Furthermore, our findings provide a theoretical justification for previously proposed phenomenology and indicate new routes to the generation and exploration of intrinsically nonequilibrium states.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2023

Resolving experimental biases in the interpretation of diffusion experiments with a user-friendly numerical reactive transport approach

The reactive transport code CrunchClay was used to derive effective diffusion coefficients (D e ), clay porosities (ε), and adsorption distribution coefficients (K D ) from through-diffusion data while considering accurately the influence of unavoidable experimental biases on the estimation of these diffusion parameters. These effects include the presence of filters holding the solid sample in place, the variations in concentration gradients across the diffusion cell due to sampling events, the impact of tubing/dead volumes on the estimation of diffusive fluxes and sample porosity, and the effects of O-ring-filter setups on the delivery of solutions to the clay packing. Doing so, the direct modeling of the measurements of (radio)tracer concentrations in reservoirs is more accurate than that of data converted directly into diffusive fluxes. While the above-mentioned effects have already been described individually in the literature, a consistent modeling approach addressing all these issues at the same time has never been described nor made easily available to the community. A graphical user interface, CrunchEase, was created, which supports the user by automating the creation of input files, the running of simulations, and the extraction and comparison of data and simulation results. While a classical model considering an effective diffusion coefficient, a porosity and a solid/solution distribution coefficient (D e –ε–K D ) may be implemented in any reactive transport code, the development of CrunchEase makes it easy to apply by experimentalists without a background in reactive transport modeling. CrunchEase makes it also possible to transition more easily from a D e –ε–K D modeling approach to a state-of-the-art process-based understanding modeling approach using the full capabilities of CrunchClay, which include surface complexation modeling and a multi-porosity description of the clay packing with charged diffuse layers.

58 GEOSCIENCES↗
DOE OSTI2024

Crescendo beyond the horizon: More gravitational waves from domain walls bounded by inflated cosmic strings

Gravitational-wave (GW) signals offer a unique window into the dynamics of the early universe. GWs may be generated by the topological defects produced in the early universe, which contain information on the symmetry of UV physics. We consider the case in which a two-step phase transition produces a network of domain walls bounded by cosmic strings. Specifically, we focus on the case in which there is a hierarchy in the symmetry-breaking scales, and a period of inflation pushes the cosmic string generated in the first phase transition outside the horizon before the second phase transition. We show that the GW signal from the evolution and collapse of this string-wall network has a unique spectrum, and the resulting signal strength can be sizeable. In particular, depending on the model parameters, the resulting signal can show up in a broad range of frequencies and can be discovered by a multitude of future probes, including the pulsar timing arrays and space- and ground-based GW observatories. As an example that naturally gives rise to this scenario, we present a model with the first phase transition followed by a brief period of thermal inflation driven by the field responsible for the second stage of symmetry breaking. Here, the model can be embedded into a supersymmetric setup, which provides a natural realization of this scenario. In this case, the successful detection of the peak of the GW spectrum probes the soft supersymmetry breaking scale and the wall tension.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

A Deep Potential model for liquid–vapor equilibrium and cavitation rates of water

Computational studies of liquid water and its phase transition into vapor have traditionally been performed using classical water models. Here, we utilize the Deep Potential methodology—a machine learning approach—to study this ubiquitous phase transition, starting from the phase diagram in the liquid–vapor coexistence regime. The machine learning model is trained on ab initio energies and forces based on the SCAN density functional, which has been previously shown to reproduce solid phases and other properties of water. Here, we compute the surface tension, saturation pressure, and enthalpy of vaporization for a range of temperatures spanning from 300 to 600 K and evaluate the Deep Potential model performance against experimental results and the semiempirical TIP4P/2005 classical model. Moreover, by employing the seeding technique, we evaluate the free energy barrier and nucleation rate at negative pressures for the isotherm of 296.4 K. Further, we find that the nucleation rates obtained from the Deep Potential model deviate from those computed for the TIP4P/2005 water model due to an underestimation in the surface tension from the Deep Potential model. From analysis of the seeding simulations, we also evaluate the Tolman length for the Deep Potential water model, which is (0.091 ± 0.008) nm at 296.4 K. Finally, we identify that water molecules display a preferential orientation in the liquid–vapor interface, in which H atoms tend to point toward the vapor phase to maximize the enthalpic gain of interfacial molecules. We find that this behavior is more pronounced for planar interfaces than for the curved interfaces in bubbles. This work represents the first application of Deep Potential models to the study of liquid–vapor coexistence and water cavitation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

Diagonal entropy and topological phase transitions in extended Kitaev chains

We investigate the diagonal entropy for ground states of the extended Kitaev chains with extensive pairing and hopping terms. The systems contain rich topological phases equivalently represented by topological invariant winding numbers and Majorana zero modes. Both the finite size scaling law and block scaling law of the diagonal entropy are studied, which indicates that the diagonal entropy demonstrates volume effect. The parameter of volume term is regarded as the diagonal entropy density, which can identify the critical points of symmetry-protected topological phase transitions efficiently in the studied models, even for those with higher winding numbers. The formulation of block scaling law and the capability of diagonal entropy density in detecting topological phase transitions are independent of the chosen bases. In order to manifest the advantage of diagonal entropy, we also calculate the global entanglement, which cannot show clear signatures of the topological phase transitions. This work provides a new quantum-informatic approach to characterize the feature of the topologically ordered states and may motivate a deep understanding of the quantum coherence and diagonal entropy in various condensed matter systems.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Finite-Size Scaling on a Digital Quantum Simulator Using Quantum Restricted Boltzmann Machine

The critical point and the critical exponents for a phase transition can be determined using the Finite-Size Scaling (FSS) analysis. This method assumes that the phase transition occurs only in the infinite size limit. However, there has been a lot of interest recently in quantum phase transitions occurring in finite size systems such as a single two-level system interacting with a single bosonic mode e.g., in the Quantum Rabi Model (QRM). Since these phase transitions occur at a finite system size, the traditional FSS method is rendered inapplicable for these cases. For cases like this, we propose an alternative FSS method in which the truncation of the system is done in the Hilbert space instead of the physical space. This approach has previously been used to calculate the critical parameters for stability and symmetry breaking of electronic structure configurations of atomic and molecular systems. We calculate the critical point for the quantum phase transition of the QRM using this approach. We also provide a protocol to implement this method on a digital quantum simulator using the Quantum Restricted Boltzmann Machine algorithm. Our work opens up a new direction in the study of quantum phase transitions on quantum devices.

Khalid, Bilal↗