Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “diffusion couples”

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 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Mediated Electrochemical Probing: A Systems-Level Tool for Redox Biology

Biology uses well-known redox mechanisms for energy harvesting (e.g., respiration), biosynthesis, and immune defense (e.g., oxidative burst), and now we know biology uses redox for systems-level communication. Currently, we have limited abilities to “eavesdrop” on this redox modality, which can be contrasted with our abilities to observe and actuate biology through its more familiar ionic electrical modality. In this Perspective, we argue that the coupling of electrochemistry with diffusible mediators (electron shuttles) provides a unique opportunity to access the redox communication modality through its electrical features. Here, we highlight previous studies showing that mediated electrochemical probing (MEP) can “communicate” with biology to acquire information and even to actuate specific biological responses (i.e., targeted gene expression). We suggest that MEP may reveal an extent of redox-based communication that has remained underappreciated in nature and that MEP could provide new technological approaches for redox biology, bioelectronics, clinical care, and environmental sciences.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Complete quasilinear model for the acceleration-driven lower hybrid drift instability and a computational assessment of its validity

A complete quasilinear model is derived for the electrostatic acceleration-driven lower hybrid drift instability in a uniform two-species low-beta plasma in which current is perpendicular to the background magnetic field. The model consists of coupled nonlinear velocity space diffusion equations for the volume-averaged ion and electron distribution functions. Each species' diffusion coefficient depends on a time-evolving spectral density of the electric-field energy per unit volume and a time-evolving dispersion relation. The dispersion relation is expressed analytically in integral form without the use of asymptotic limits and applies to arbitrary distribution functions, so long as they can be expressed as a function of one velocity coordinate, e.g., f⁡(vy) or f⁡(v⊥). The quasilinear model conserves energy and is complete in that it fully describes the evolution of the distribution functions, including resonant and nonresonant particle-wave interactions, while accounting for distribution-function-dependent mixed-complex frequencies. Further, the quasilinear diffusion model is solved numerically and self-consistently using a Crank-Nicolson temporal discretization and a second-order finite-volume velocity-space discretization. Numerical solutions are compared to nonlinear fourth-order accurate continuum kinetic Vlasov-Poisson simulations. Evolution of electric-field energy, growth rates, distribution functions, and diffusion coefficients are shown to be in agreement with Vlasov simulations. The quasilinear model is shown to predict anomalous transport terms, like resistivity and heating, to within a factor of order unity. Discrepancies between the quasilinear model and Vlasov simulations are assessed and attributed primarily to lack of damping in the quasilinear description and to the use of unperturbed-orbit susceptibilities in the linear theory dispersion relation. The results illuminate the predictive accuracy of the quasilinear model, place approximate bounds on its validity, and provide much needed vetting of quasilinear theory's ability to predict the nonlinear state of a microturbulent plasma.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Multi-domain automated patterning of DNA-functionalized hydrogels

DNA-functionalized hydrogels are capable of sensing oligonucleotides, proteins, and small molecules, and specific DNA sequences sensed in the hydrogels’ environment can induce changes in these hydrogels’ shape and fluorescence. Fabricating DNA-functionalized hydrogel architectures with multiple domains could make it possible to sense multiple molecules and undergo more complicated macroscopic changes, such as changing fluorescence or changing the shapes of regions of the hydrogel architecture. However, automatically fabricating multi-domain DNA-functionalized hydrogel architectures, capable of enabling the construction of hydrogel architectures with tens to hundreds of different domains, presents a significant challenge. We describe a platform for fabricating multi-domain DNA-functionalized hydrogels automatically at the micron scale, where reaction and diffusion processes can be coupled to program material behavior. Using this platform, the hydrogels’ material properties, such as shape and fluorescence, can be programmed, and the fabricated hydrogels can sense their environment. DNA-functionalized hydrogel architectures with domain sizes as small as 10 microns and with up to 4 different types of domains can be automatically fabricated using ink volumes as low as 50 μL. We also demonstrate that hydrogels fabricated using this platform exhibit responses similar to those of DNA-functionalized hydrogels fabricated using other methods by demonstrating that DNA sequences can hybridize within them and that they can undergo DNA sequence-induced shape change.

Rubanov, Moshe (ORCID:0000000180507407)↗
DOE OSTI2023

Outlook on texture evolution in additively manufactured stainless steels: Prospects for hydrogen embrittlement resistance, overview of mechanical, and solidification behavior

Abstract Realizing application specific manufacture with fusion-based additive manufacturing (F-BAM) processes requires understanding of the physical phenomena that drive evolution of microstructural attributes, such as texture. Current approaches for understanding texture evolution in F-BAM are majorly considerate of the phenomena occurring only during solidification. This hinders the comprehensive understanding and control of texture during F-BAM. In this perspective article, we discuss several physical phenomena occurring during and after solidification that can determine texture in F-BAM processed stainless steels (SS). A crystal plasticity-coupled hydrogen adsorption-diffusion modeling framework is also leveraged to demonstrate the prospects of grain boundary engineering with F-BAM for enhanced hydrogen embrittlement resistance of SS. Implications of varying thermokinetics in F-BAM for solidification behavior of SS are discussed. Additionally, microstructural attributes that are key to high temperature mechanical performance of SS are highlighted. Considerations as outlined in this perspective article will enable grain boundary engineering and application specific microstructural design of SS with F-BAM. Graphical abstract

36 MATERIALS SCIENCE↗
DOE OSTI2025

Destructive PIE and Safety Testing of Six AGR-5/6/7 Capsule 2 Compacts

This study evaluates fission product retention and particle failure mechanisms in AGR-5/6/7 Capsule 2 uranium carbide and uranium oxide (UCO) tristructural isotropic (TRISO) fuel under high-temperature gas reactor accident-relevant conditions using high-temperature safety tests and destructive postirradiation examination. Three Capsule 2 compacts were held isothermally at 1600°C for approximately 300 hours and one compact at 1800°C for approximately 300 hours; two additional compacts were examined in the as-irradiated state. Post-test deconsolidation–leach–burn–leach (DLBL) quantified nuclide inventories in matrix and particles. Individual particles were surveyed for radioisotope inventories, and microanalytical approaches resolved microstructural evolution and fission product distributions within the coating layers. At 1600°C, no krypton was detected above the minimum detectable limit, and cesium releases were far below a single particle equivalent, indicating the absence of full TRISO failure or SiC failures. Silver releases were limited and primarily reflected depleted postirradiation inventories, consistent with prior compact-level exams indicating substantial in-pile 110mAg loss. At 1800°C, cumulative 134Cs release of approximately 2.5 particle equivalents and delayed 85Kr totaling approximately 0.53 particle equivalents were consistent with one full TRISO failure and two SiC failures. Europium and strontium releases were roughly one order of magnitude higher than at 1600°C and comparable to AGR-1/AGR-2 high-temperature tests, with sustained late-hold rates indicating diffusion through intact coatings coupled with matrix depletion. Overall, AGR-5/6/7 Capsule 2 UCO fuel demonstrated fission product retention during safety testing consistent with prior AGR campaigns, while distinctive in-pile 110mAg depletion and measurable 1600°C europium loss motivate targeted follow-on studies.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2025

Destructive PIE and Safety Testing of Six AGR-5/6/7 Capsule 2 Compacts

This study evaluates fission product retention and particle failure mechanisms in AGR-5/6/7 Capsule 2 uranium carbide and uranium oxide (UCO) tristructural isotropic (TRISO) fuel under high-temperature gas reactor accident-relevant conditions using high-temperature safety tests and destructive post-irradiation examination. Three Capsule 2 compacts were held isothermally at 1600°C for approximately 300 hours and one compact at 1800°C for approximately 300 hours; two additional compacts were examined in the as-irradiated state. Post-test deconsolidation–leach–burn–leach (DLBL) quantified nuclide inventories in matrix and particles. Individual particles were surveyed for radioisotope inventories, and microanalytical approaches resolved microstructural evolution and fission product distributions within the coating layers. At 1600°C, no krypton was detected above the minimum detectable limit, and cesium releases were far below a single particle equivalent, indicating the absence of full TRISO failure or SiC failures. Silver releases were limited and primarily reflected depleted post-irradiation inventories, consistent with prior compact-level exams indicating substantial in-pile 110m Ag loss. At 1800°C, cumulative 134 Cs release of approximately 2.5 particle equivalents and delayed 85 Kr totaling approximately 0.53 particle equivalents were consistent with one full TRISO failure and two SiC failures. Europium and strontium releases were roughly one order of magnitude higher than at 1600°C and comparable to AGR-1/AGR-2 high-temperature tests, with sustained late-hold rates indicating diffusion through intact coatings coupled with matrix depletion. Overall, AGR-5/6/7 Capsule 2 UCO fuel demonstrated fission product retention during safety testing consistent with prior AGR campaigns, while distinctive in-pile 110m Ag depletion and measurable 1600°C europium loss motivate targeted follow-on studies.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2022

Supporting hierarchical soil biogeochemical modeling: version 2 of the Biogeochemical Transport and Reaction model (BeTR-v2)

Abstract. Reliable soil biogeochemical modeling is a prerequisite for credible projections of climate change and associated ecosystem feedbacks. This recognition has called for frameworks that can support flexible and efficient development and application of new or alternative soil biogeochemical modules in Earth system models (ESMs). The the Biogeochemical Transport and Reaction model version 1 (BeTR-v1) code (i.e., CLM4-BeTR) is one such framework designed to accelerate the development and integration of new soil biogeochemistry formulations into ESMs and to analyze structural uncertainty in ESM simulations. With a generic reactive transport capability, BeTR-v1 can represent multiphase (e.g., gaseous, aqueous, and solid), multi-tracer (e.g., nitrate and organic carbon), and multi-organism (e.g., plants, bacteria, and fungi) dynamics. Here, we describe the new version, Biogeochemical Transport and Reaction model version 2 (BeTR-v2), which adopts more robust numerical solvers for multiphase diffusion and advection and coupling between biogeochemical reactions and improves code modularization over BeTR-v1. BeTR-v2 better supports different mathematical formulations in a hierarchical manner by allowing the resultant model be run for a single topsoil layer or a vertically resolved soil column, and it allows the model to be fully coupled with the land component of the Energy Exascale Earth System Model (E3SM). We demonstrate the capability of BeTR-v2 with benchmark cases and example soil biogeochemical (BGC) implementations. By taking advantage of BeTR-v2's generic structure integrated in E3SM, we then found that calibration could not resolve biases introduced by different numerical coupling strategies of plant–soil biogeochemistry. These results highlight the importance of numerically robust implementation of soil biogeochemistry and coupling with hydrology, thermal dynamics, and plants – capabilities that the open-source BeTR-v2 provides. We contend that Earth system models should strive to minimize this uncertainty by applying better numerical solvers.

58 GEOSCIENCES↗
DOE OSTI2020

Optically pumped spin polarization as a probe of many-body thermalization

Disorder and many body interactions are known to impact transport and thermalization in competing ways, with the dominance of one or the other giving rise to fundamentally different dynamical phases. Here we investigate the spin diffusion dynamics of 13 C in diamond, which we dynamically polarize at room temperature via optical spin pumping of engineered color centers. We focus on low-abundance, strongly hyperfine-coupled nuclei, whose role in the polarization transport we expose through the integrated impact of variable radio-frequency excitation on the observable bulk 13 C magnetic resonance signal. Unexpectedly, we find good thermal contact throughout the nuclear spin bath, virtually independent of the hyperfine coupling strength, which we attribute to effective carbon-carbon interactions mediated by the electronic spin ensemble. In particular, observations across the full range of hyperfine couplings indicate the nuclear spin diffusion constant takes values up to two orders of magnitude greater than that expected from homo-nuclear spin couplings.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Indistinguishable telecom band photons from a single Er ion in the solid state

Atomic defects in the solid state are a key component of quantum repeater networks for long-distance quantum communication1. Recently, there has been significant interest in rare earth ions, in particular Er 3+ for its telecom band optical transition that allows long-distance transmission in optical fibres. However, the development of repeater nodes based on rare earth ions has been hampered by optical spectral diffusion, precluding indistinguishable single-photon generation. Here, we implant Er 3+ into CaWO 4 , a material that combines a non-polar site symmetry, low decoherence from nuclear spins and is free of background rare earth ions, to realize significantly reduced optical spectral diffusion. For shallow implanted ions coupled to nanophotonic cavities with large Purcell factor, we observe single-scan optical linewidths of 150 kHz and long-term spectral diffusion of 63 kHz, both close to the Purcell-enhanced radiative linewidth of 21 kHz. This enables the observation of Hong–Ou–Mandel interference between successively emitted photons with a visibility of V = 80(4)%, measured after a 36 km delay line. We also observe spin relaxation times T 1,s = 3.7 s and T 2,s > 200 μs, with the latter limited by paramagnetic impurities in the crystal instead of nuclear spins. Furthermore, this represents a notable step towards the construction of telecom band quantum repeater networks with single Er 3+ ions.

42 ENGINEERING↗
DOE OSTI2026

NOCI-F Electronic Couplings in Assemblies of Indolonaphthyridine Molecules: From Dimers to the Full Stack

Key electronic processes related to molecular excitonic states of finite stacks of indolonaphthyridine molecules are analyzed via the non-orthogonal configuration interaction with fragments (NOCI-F) method. Indolonaphthyridine is an organic chromophore that can undergo several electronic photoexcitation-related intermolecular processes, such as exciton and electron transfer. The structures studied here are noncrystalline arrangements built as either ordered stacks of indolonaphthyridine or stacks extracted from molecular dynamics simulations including thermal disorder. Taking dimers or trimers from either model, we performed CASSCF and NOCI-F calculations to quantify the intermolecular electronic couplings governing singlet fission, excited singlet and triplet diffusion, and hole and electron diffusion processes. Also, comparing the results for the different models, we studied the effect of structural disorder and distortion on these couplings. Finally, we present a newly developed, advanced postanalysis tool. It takes the NOCI-F data as input to carry out a multifragment full Hamiltonian procedure that involves the complete stack, providing physical information not available from the dimer/trimer models, hence giving access to additional insight into the material’s properties.

coupling reactions↗
DOE OSTI2025

Annihilation-limited long-range exciton transport in high-mobility conjugated copolymer films

A combination of ultrafast, long-range, and low-loss excitation energy transfer from the photoreceptor location to a functionally active site is essential for cost-effective polymeric semiconductors. Delocalized electronic wavefunctions along π-conjugated polymer (CP) backbone can enable efficient intrachain transport, while interchain transport is generally thought slow and lossy due to weak chain–chain interactions. In contrast to the conventional strategy of mitigating structural disorder, amorphous layers of rigid CPs, exemplified by highly planar poly(indacenodithiophene-co-benzothiadiazole) (IDT-BT) donor-accepter copolymer, exhibit trap-free transistor performance and charge-carrier mobilities similar to amorphous silicon. Here, we report long-range exciton transport in HJ -aggregated IDTBT thin-film, in which the competing exciton transport and exciton–exciton annihilation (EEA) dynamics are spectroscopically separated using a phase-cycling-based scheme and shown to depart from the classical diffusion-limited and strong-coupling regime. In the thin film, we find an annihilation-limited mechanism with ≪100% per-encounter annihilation probability, facilitating the minimization of EEA-induced excitation losses. In contrast, excitons on isolated IDTBT chains diffuse over 350 nm with 0.56 cm 2 s −1 diffusivity, before eventually annihilating with unit probability on first contact. We complement the pump–probe studies with temperature-dependent photocurrent and EEA measurements from 295 K to 77 K and find a remarkable correspondence of annihilation rate and photocurrent activation energies in the 140 K to 295 K temperature range.

Shi, Yuping (ORCID:0000000318289415)↗
DOE OSTI2025

Osmotic control of the spacing of parallel shear cracks in shale growing subcritically in geologic past

The geological genesis of natural cracks in sedimentary rocks such as shale is a problem that needs to be understood to improve the technology of hydraulic fracturing as well as deep sequestration of harmful fluids. Why are the vertical natural cracks roughly parallel and equidistant, and why is the spacing roughly 10 cm rather than 1 cm or 100 cm? Fracture mechanics of critical cracks cannot answer this question. Neither can the material heterogeneity. The growth of critical parallel cracks is impossible because the relative crack face displacements would immediately localize into one crack, leading to an earthquake. The cracks must have formed, on the tectonic time scale, by a slow growth of subcritical shear cracks governed by the Charles-Evans law. The idea advanced here is that what controls the crack spacing is the balance between the reduction, due to shear dilatancy, of the concentration of ions such as Na + and Cl - in each fracture process zone (PFZ), which decelerates the cracks, and the restoration of ion concentration by diffusion of ions from the space between the cracks into the FPZ. This diffusion of water is driven mainly by the osmotic pressure gradient, which offsets the deceleration and depends strongly on the crack spacing. A simple analytical solution of the steady state is rendered possible by approximating the ion concentration profiles between adjacent cracks by parabolic arcs. Applying this theory to Woodford shale yields the approximate crack spacing of 10 cm, which is realistic. Furthermore, the stability of unlimited parallel mode II frictional crack growth is proven by examining the second variation of the free energy. Water concentration drop in the FPZ due to shear dilatancy and its restoration by water diffusion from the inter-crack space have similar effect, although probably much weaker.

42 ENGINEERING↗
DOE OSTI2023

Energy coupling and stoichiometry of Zn 2+ /H + antiport by the prokaryotic cation diffusion facilitator YiiP

YiiP from Shewanella oneidensis is a prokaryotic Zn 2+ /H + antiporter that serves as a model for the Cation Diffusion Facilitator (CDF) superfamily, members of which are generally responsible for homeostasis of transition metal ions. Previous studies of YiiP as well as related CDF transporters have established a homodimeric architecture and the presence of three distinct Zn 2+ binding sites named A, B, and C. In this study, we use cryo-EM, microscale thermophoresis and molecular dynamics simulations to address the structural and functional roles of individual sites as well as the interplay between Zn 2+ binding and protonation. Structural studies indicate that site C in the cytoplasmic domain is primarily responsible for stabilizing the dimer and that site B at the cytoplasmic membrane surface controls the structural transition from an inward facing conformation to an occluded conformation. Binding data show that intramembrane site A, which is directly responsible for transport, has a dramatic pH dependence consistent with coupling to the proton motive force. A comprehensive thermodynamic model encompassing Zn 2+ binding and protonation states of individual residues indicates a transport stoichiometry of 1 Zn 2+ to 2–3 H + depending on the external pH. This stoichiometry would be favorable in a physiological context, allowing the cell to use the proton gradient as well as the membrane potential to drive the export of Zn 2+ .

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2024

Structure and Dynamics of Aqueous Electrolytes at Quartz (001) and (101) Surfaces

Here, understanding and describing reactivity at mineral-water interfaces such as ion adsorption, the kinetics of dissolution, or surface charge development depends on our ability to improve the accuracy of electrical double layer (EDL) models. While molecular dynamics (MD) simulations are routinely used to investigate the structure and energetics of adsorbed ions comprising the EDL, less attention is paid to their self-diffusion dynamics, which can uniquely inform on coupling to interfacial reactions. Here we use MD to investigate both the organization and diffusion dynamics of water and electrolyte ions (NaCl, KCl, CaCl 2 ) at hydroxylated quartz (001) and (101) surfaces, a comparison which allowed us to assess surface structural effects of corrugation and silanol density. We found that inner- versus outer-sphere complex formation depends on cation size and charge but not necessarily hydration energies. Participation of surface silanols in the hydration spheres of Na + and K + generally indicated their preference for inner-sphere complexation, but this depends strongly on the orientation of the surface considered through its influence over the organization and dynamics of adsorbed water layers. In particular, surface orientation substantially affects the diffusive behavior of the near-surface water. Na + was found to decrease the mobility of water in the first layer, consistent with an increasing frequency of hydrolysis implied by faster quartz dissolution rates observed in experiments via the well known salt effect. Our results are also in good agreement with the observed dissolution rate of quartz vs. surface adsorption strength measure by Dove and Nix. This study sets the stage for a forthcoming paper examining how the dynamics at quartz/electrolyte interfaces are influenced by externally applied electric fields.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Scattered-light uniformity imager for diagnosing laser absorption asymmetries on OMEGA

Light scattered from a target is the most-direct measurement for diagnosing laser absorption in a direct-drive implosion. Observations from OMEGA implosions show much larger scattered-light asymmetries than predictions. A new instrument has been developed to absolutely measure the scattered-light intensity and nonuniformity for the purpose of diagnosing the asymmetry. The scattered-light uniformity imager (SLUI) diagnostic records the variation in scattered-light intensity over a transmission diffuser using a charge-coupled device (CCD)/lens assembly. At the standard operating position, an 11.3° (f/2.5) cone of light is collected. A stray light baffle, debris shield, and antireflection absorbing filter are also incorporated into the diagnostic payload inserted into the target chamber. The imaging parts of the diagnostic (light baffle, vacuum window, filters, lens, and CCD camera) are located outside the target chamber. Five SLUIs have been built and deployed in OMEGA’s ten-inch manipulator diagnostic ports, covering almost 5% of the emission surface, enabling an absolute scattered-light measurement should be within a few percent of the global average. Each SLUI system is calibrated offline, providing absolute scattered-light intensity measurements. Based on the measured point spread function, each diffuser plate image contains over 20 000 independent scattered-light absolute-intensity measurements of the variation over the collection cone. SLUI provides a platform to study scattered light and absorption asymmetries, and their possible sources.

47 OTHER INSTRUMENTATION↗
DOE OSTI2023

Optically Enhanced Solid-State 1 H NMR Spectroscopy

Low sensitivity is the primary limitation to extending nuclear magnetic resonance (NMR) techniques to more advanced chemical and structural studies. Photochemically induced dynamic nuclear polarization (photo-CIDNP) is an NMR hyperpolarization technique where light is used to excite a suitable donor–acceptor system, creating a spin-correlated radical pair whose evolution drives nuclear hyperpolarization. Systems that exhibit photo-CIDNP in solids are not common, and this effect has, up to now, only been observed for 13 C and 15 N nuclei. However, the low gyromagnetic ratio and natural abundance of these nuclei trap the local hyperpolarization in the vicinity of the chromophore and limit the utility for bulk hyperpolarization. Here, we report the first example of optically enhanced solid-state 1 H NMR spectroscopy in the high-field regime. This is achieved via photo-CIDNP of a donor–chromophore–acceptor molecule in a frozen solution at 0.3 T and 85 K, where spontaneous spin diffusion among the abundant strongly coupled 1 H nuclei relays polarization through the whole sample, yielding a 16-fold bulk 1 H signal enhancement under continuous laser irradiation at 450 nm. These findings enable a new strategy for hyperpolarized NMR beyond the current limits of conventional microwave-driven DNP.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Exploring the energy landscape of RBMs: reciprocal space insights into bosons, hierarchical learning and symmetry breaking

Deep generative models have become ubiquitous due to their ability to learn and sample from complex distributions. Despite the proliferation of various frameworks, the relationships among these models remain largely unexplored, a gap that hinders the development of a unified theory of AI learning. In this work, we address two central challenges: clarifying the connections between different deep generative models and deepening our understanding of their learning mechanisms. We focus on Restricted Boltzmann Machines (RBMs), a class of generative models known for their universal approximation capabilities for discrete distributions. By introducing a reciprocal space formulation for RBMs, we reveal a connection between these models, diffusion processes, and systems of coupled bosons. Our analysis shows that at initialization, the RBM operates at a saddle point, where the local curvature is determined by the singular values of the weight matrix, whose distribution follows the Marc̆enko-Pastur law and exhibits rotational symmetry. During training, this rotational symmetry is broken due to hierarchical learning, where different degrees of freedom progressively capture features at multiple levels of abstraction. This leads to a symmetry breaking in the energy landscape, reminiscent of Landau’s theory. This symmetry breaking in the energy landscape is characterized by the singular values and the weight matrix eigenvector matrix. We derive the corresponding free energy in a mean-field approximation. We show that in the limit of infinite size RBM, the reciprocal variables are Gaussian distributed. Our findings indicate that in this regime, there will be some modes for which the diffusion process will not converge to the Boltzmann distribution. To illustrate our results, we trained replicas of RBMs with different hidden layer sizes using the MNIST dataset. Our findings not only bridge the gap between disparate generative frameworks but also shed light on the fundamental processes underpinning learning in deep generative models.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

On the Spectral Evolution of Hot White Dwarf Stars. II. Time-dependent Simulations of Element Transport in Evolving White Dwarfs with STELUM

White dwarf stars are subject to various element transport mechanisms that can cause their surface composition to change radically as they cool, a phenomenon known as spectral evolution. In this paper, we undertake a comprehensive theoretical investigation of the spectral evolution of white dwarfs. First, we introduce STELUM, a new implementation of the stellar evolutionary code developed at the Université de Montréal. We provide a thorough description of the physical content and numerical techniques of the code, covering the treatment of both stellar evolution and chemical transport. Then, we present two state-of-the-art numerical simulations of element transport in evolving white dwarfs. Atomic diffusion, convective mixing, and mass loss are considered simultaneously as time-dependent diffusive processes and are fully coupled to the cooling. We first model the PG 1159-DO-DB-DQ evolutionary channel: a helium-, carbon-, and oxygen-rich PG 1159 star transforms into a pure-helium DB white dwarf due to gravitational settling and then into a helium-dominated, carbon-polluted DQ white dwarf through convective dredge-up. We also compute for the first time the full DO-DA-DC evolutionary channel: a helium-rich DO white dwarf harboring residual hydrogen becomes a pure-hydrogen DA star through the float-up process and then a helium-dominated, hydrogen-bearing DC star due to convective mixing. We demonstrate that our results are in excellent agreement with available empirical constraints. In particular, our DO-DA-DC simulation perfectly reproduces the lower branch of the bifurcation observed in the Gaia color–magnitude diagram, which can therefore be interpreted as a signature of spectral evolution.

79 ASTRONOMY AND ASTROPHYSICS↗