Homogeneous Gas Research Articles

Local Density Approximation for Excited States

The ground state of an homogeneous electron gas is a paradigmatic state that has been used to model and predict the electronic structure of matter at equilibrium for nearly a century. For half a century, it has been successfully used to predict ground states of quantum systems via the local density approximation (LDA) of density functional theory (DFT), and systematic improvements in the form of generalized gradient approximations and evolution thereon. Here, we introduce the LDA for excited states by considering a particular class of nonthermal ensemble states of the homogeneous electron gas. These states find sound foundation and application in ensemble DFT—a generalization of DFT that can deal with ground and excited states on equal footing. The ensemble LDA is shown to successfully predict difficult low-lying excitations in atoms and molecules for which approximations based on local spin density approximation and time-dependent LDA fail. Published by the American Physical Society 2024

First Detection of Molecular Gas in the Giant Low Surface Brightness Galaxy Malin 1

After over three decades of unsuccessful attempts, we report the first detection of molecular gas emission in Malin 1, the largest spiral galaxy observed to date, and one of the most iconic giant low surface brightness galaxies. Using Atacama Large Millimeter/submillimeter Array, we detect significant 12CO (J = 1–0) emission in the galaxy’s central region and tentatively identify CO emission across three regions on the disk. These observations allow for a better estimate of the H2 mass and molecular gas mass surface density, both of which are remarkably low given the galaxy’s scale. By integrating data on its H i mass, we derive a very low molecular-to-atomic gas mass ratio. Overall, our results highlight the minimal presence of molecular gas in Malin 1, contrasting sharply with its extensive, homogeneous atomic gas reservoir. For the first time, we position Malin 1 on the Kennicutt–Schmidt diagram, where it falls below the main sequence for normal spirals, consistent with previous upper limits but now with more accurate figures. These findings are crucial for constraining our understanding of star formation processes in environments characterized by extremely low molecular gas densities and for refining models of galaxy formation, thereby improving predictions concerning the formation, evolution, and distribution of these giant, elusive galaxies.

Pressure Change in a Duct with a Flow of a Homogeneous Gaseous Substance in the Presence of a Point Mass and Momentum Sink of Gas

The flow characteristics of homogeneous gases in complex systems are an important issue in many areas, including underground mines. The flow in mine excavations and ventilation systems is described by known mathematical relationships that could be applied to various cases. In this paper, a flow in a duct with a local sink of mass and momentum for multiple variants of cooperation of a mechanical fan was analyzed. The relationships for the total and static pressure of air in the duct were derived. In the next stage, a calculation example of how the mass flow rate of air, and the total and static pressure of the flowing air will change in the tested sections for the duct with and without a sink, is presented. The derived formulas and calculated values for the considered calculation case allow the verification of the obtained relationships at the measurement station. Analyzing the results of the examples presented in the article, it can be concluded that the total and static pressure at the sink point differ depending on the equation of motion used. In the case of the classic equation, the value of total pressure is lower than the value calculated from the new equation of motion, and the difference between them is about 20 Pa. In the case of static pressure, this difference is about 46 Pa. Qualitative differences in the static pressure distribution at the release location were also demonstrated. Depending on the applied approach, positive or negative changes in the static pressure are noticed. The presented form of the equation of motion made it possible to determine the flow characteristics in the duct with a point mass and momentum sink in the case of the operation with and without a fan.

Accelerating the convergence of coupled cluster calculations of the homogeneous electron gas using Bayesian ridge regression.

The homogeneous electron gas is a system that has many applications in chemistry and physics. However, its infinite nature makes studies at the many-body level complicated due to long computational run times. Because it is size extensive, coupled cluster theory is capable of studying the homogeneous electron gas, but it still poses a large computational challenge as the time needed for precise calculations increases in a polynomial manner with the number of particles and single-particle states. Consequently, achieving convergence in energy calculations becomes challenging, if not prohibited, due to long computational run times and high computational resource requirements. This paper develops the sequential regression extrapolation (SRE) to predict the coupled cluster energies of the homogeneous electron gas in the complete basis limit using Bayesian ridge regression and many-body perturbation theory correlation energies to the second order to make predictions from calculations at truncated basis sizes. Using the SRE method, we were able to predict the coupled cluster double energies for the electron gas across a variety of values of N and rs, for a total of 70 predictions, with an average error of 5.20 × 10-4 hartree while saving 88.9h of computational time. The SRE method can accurately extrapolate electron gas energies to the complete basis limit, saving both computational time and resources. Additionally, the SRE is a general method that can be applied to a variety of systems, many-body methods, and extrapolations.

Simulation of gas mixture dynamics in a pipeline network using explicit staggered-grid discretization

We develop an explicit staggered finite difference discretization scheme for simulating the transport of highly heterogeneous gas mixtures through pipeline networks. This study is motivated by the proposed blending of hydrogen into natural gas pipelines to reduce end use carbon emissions while using existing pipeline systems throughout their planned lifetimes. Our computational method accommodates an arbitrary number of constituent gases with very different physical properties that may be injected into a network with significant spatiotemporal variation. In this setting, the gas flow physics are highly location- and time- dependent, so that local composition and nodal mixing must be accounted for. The resulting conservation laws are formulated in terms of pressure, partial densities and flows, and volumetric and mass fractions of the constituents. We include non-ideal equations of state that employ linear approximations of gas compressibility factors, so that the pressure dynamics propagate locally according to a variable wave speed that depends on mixture composition and density. We derive compatibility relationships for network edge boundary values that are more complex than for a homogeneous gas. The simulation method is evaluated on initial boundary value problems for a single pipe and a small network, is cross-validated with a lumped element simulation, and used to demonstrate a local monitoring and control policy for maintaining allowable concentration levels.

Quantum Confinement and End-Sealing Effects for Highly Sensitive and Stable Nitrogen Dioxide Detection: Homogeneous Integration of Ti3C2Tx-Based Flexible Gas Sensors.

The real-time and room-temperature detection of nitrogen dioxide (NO2) holds significant importance for environmental monitoring. However, the performance of NO2 sensors has been hampered by the trade-off between the high sensitivity and stability of conventional sensitive materials. Here, we present a novel fully flexible paper-based gas sensing structure by combining a homogeneous screen-printed titanium carbide (Ti3C2Tx) MXene-based nonmetallic electrode with a MoS2 quantum dots/Ti3C2Tx (MoS2 QDs/Ti3C2Tx) gas-sensing film. These precisely designed gas sensors demonstrate an improved response value (16.3% at 5 ppm) and a low theoretical detection limit of 12.1 ppb toward NO2, which exhibit a remarkable 3.5-fold increase in sensitivity compared to conventional Au interdigital electrodes. The outstanding performance can be attributed to the integration of the quantum confinement effect of MoS2 QDs and the conductivity of Ti3C2Tx, establishing the main active adsorption sites and enhanced charge transport pathways. Furthermore, an end-sealing effect strategy was applied to decorate the defect sites with naturally oxygen-rich tannic acid and conductive polymer, and the formed hydrogen bonding network at the interface effectively mitigated the oxidative degradation of the Ti3C2Tx-based gas sensors. The exceptional stability has been achieved with only a 1.8% decrease in response over 4 weeks. This work highlights the innovative design of high-performance gas sensing materials and homogeneous gas sensor techniques.

Numerical Modeling of the Interaction of a Monodisperse Gas Suspension with a Shock Wave Moving at an Angle to the Separation Boundary of a Homogeneous Gas and a Gas Suspension

The work is devoted to the study of the influence of the dispersed phase on the dynamics of gas suspensions during numerical modeling of the dynamics of gas suspensions. In this study, based on the continuum technique of dynamics of inhomogeneous media, the interaction of a shock wave propagating from a homogeneous gas with a gas suspension was numerically simulated. For each of the components of the mixture, a complete hydrodynamic system of equations of motion was solved, which included the equations of conservation of density, the equations of conservation of the spatial components of the momentum of the mixture components, and the equations of conservation of energy of the components. The carrier medium was described as a viscous, compressible heat-conducting gas. The mathematical model took into account interfacial heat transfer. The mathematical model also took into account the interphase exchange of momentum, which included the force of aerodynamic drag, the dynamic force of Archimedes and the force of added masses. The system of equations of the mathematical model was integrated using the finite difference method. To suppress numerical oscillations, a nonlinear correction scheme was used. Large volumetric contents of the dispersed phase were considered. The influence of interfacial interaction on the process of shock wave propagation has been studied.

Classical density functional theory: The local density approximation

We prove that the lowest free energy of a classical interacting system at temperature [Formula: see text] with a prescribed density profile [Formula: see text] can be approximated by the local free energy [Formula: see text], provided that [Formula: see text] varies slowly over sufficiently large length scales. A quantitative error on the difference is provided in terms of the gradient of the density. Here [Formula: see text] is the free energy per unit volume of an infinite homogeneous gas of the corresponding uniform density. The proof uses quantitative Ruelle bounds (estimates on the local number of particles in a large system), which are derived in an appendix.

New Functional Orbital-free Within DFT for Metallic Systems

I present the continuation of a study on Laplacian Level Kinetic Energy (KE) functionals applied to metallic nanosystems. The development of novel Kinetic Energy functionals is an important topic in density functional theory (DFT). The nanoparticles are patterned using gelatin spheres of different sizes, background density and number of electrons. To reproduce the correct kinetic and potential energy density of the various nanoparticles, the use of semilocal descriptors is necessary. Need an explicit density functional expression for the kinetic energy of electrons, including the first e second functional derivative, i.e. the kinetic potential and the kinetic kernel, respectively. The exact explicit form of the non interacting kinetic energy, as a functional of the electron density, is known only for the homogeneous electron gas (HEG), i.e., the Thomas-Fermi (TF) local functional and for 1 and 2 electron systems, i.e., the von Weizsacker (VW) functional. In between these two extreme cases, different semilocal or non local approximations were developed in recent years. Most semilocal KE functionals are based on modifications of the second-order gradient expansion (GE2) or fourth-order gradient expansion (GE4). I find that the Laplacian contribute is fundamental for the description of the energy and the potential of nanoparticles. I propose a new LAP2 semilocal functional which, better than the previous ones, allows us to obtain fewer errors both of energy and potential. More details of the previous calculations can be found in my 2 previous works which will be cited in the text.

Approximate Functionals for Multistate Density Functional Theory.

Recently Lu and Gao [J. Phys. Chem. Lett. 2022, 13 (33), 7762-7769] published a new, rigorous density functional theory for excited states and proved that the projection of the kinetic and electron-repulsion operators into the subspace of the lowest electronic states are a universal functional of the matrix density D(r). This is the first attempt to find an approximation to the multistate universal functional . It is shown that (i) does not explicitly depend on the number of electronic states and (ii) is an analytic matrix functional. The Thomas-Fermi-Dirac-von Weizsäcker model and the correlation energy of the homogeneous electron gas are turned into matrix functionals guided by two principles: that each matrix functional should transform properly under basis set transformations and that the ground state functional should be recovered for a single electronic state. Lieb-Oxford-like bounds on the average kinetic and electron-repulsion energies in the subspace are given. When evaluated on the numerically exact matrix density of LiF, this simple approximation reproduces the matrix elements of the electron-repulsion operator in the basis of the exact eigenstates accurately for all bond lengths. In particular the off-diagonal elements of the effective Hamiltonian that come from the interactions of different electronic states can be calculated with the same or better accuracy than the diagonal elements. Unsurprisingly, the largest error comes from the kinetic energy functional. More exact conditions that constrain the functional form of are needed to go beyond the local density approximation.

Condensate and superfluid fraction of homogeneous Bose gases in a self-consistent Popov approximation

We study the condensate and superfluid fraction of a homogeneous gas of weakly interacting bosons in three spatial dimensions by adopting a self-consistent Popov approximation, comparing this approach with other theoretical schemes. Differently from the superfluid fraction, we find that at finite temperature the condensate fraction is a non-monotonic function of the interaction strength, presenting a global maximum at a characteristic value of the gas parameter, which grows as the temperature increases. This non-monotonic behavior has not yet been observed, but could be tested with the available experimental setups of ultracold bosonic atoms confined in a box potential. We clearly identify the region of parameter space that is of experimental interest to look for this behavior and provide explicit expressions for the relevant observables. Finite size effects are also discussed within a semiclassical approximation.

Circumnuclear Gas of a Quasar in Absorption and Emission Lines

We present a detailed analysis of the unusual absorption- and emission-line spectrum of the quasar SDSS J074850.39+442439.0 (hereafter J0748+4424) at a redshift of z = 2.18. The archival SDSS optical spectrum is abundant in narrow absorption lines (NALs) originating from mostly singly ionized iron, nickel, and silicon ions at both ground and excited levels. With the aid of the photoionization simulations, we find that these NALs can be reasonably well reproduced by a homogeneous gas slab with a neutral hydrogen column density of 1021.6–1021.9 cm−2 and a number density of 106.0–106.6 cm−3 illuminated by the quasar central engine with an ionization parameter of 10−2.8–10−2.1. We infer the gas is located at a distance of ∼30–130 pc from the black hole. This circumnuclear gas can reveal itself in emission lines of a width of ∼1000 km s−1. Such intermediate-width emission lines (IELs) are indeed dominant in the observed Lyα emission, as the Lyα broad emission line (BEL) is mostly eaten up by the expected damped Lyα absorption (DLA). The IELs, though rather weak, are also detected in Hα and [O iii] emission lines. The IEL intensities largely agree with the predicted values by the simplified photoionization models using the parameters derived from the absorption lines and a covering fraction of 10%. The intrinsic DLA in J0748+4424, while itself contains abundant information on the circumnuclear environment, may serve as a “natural coronagraph” at the line of sight, exposing the IELs that are otherwise overwhelmed by the BELs.

First step toward a parameter-free, nonlocal kinetic energy density functional for semiconductors and simple metals.

The accuracy of orbital-free density functional theory depends on the approximations made for a Kinetic Energy (KE) functional. Until now, the most accurate KEDFs are based on non-local kernels constructed from the linear response theory of homogeneous electron gas. In this work, we explore beyond the HEG by employing a more general kernel based on the jellium-with-gap model (JGM). The proposed functional incorporates several new features, such as (i) having the correct low momentum(q) limit of the response function for metals and semiconductors without any modeling term, (ii) the underlying kernel is density-independent, and most importantly, (iii) parameter-free. The accuracy and efficiency of the proposed JGM NL-KEDF have been demonstrated for several semiconductors and metals. The encouraging results indicate the utility and predictive power of the JGM kernel for NL KEDF developments. This approach is also physically appealing and practically useful as we have presented a general formalism to incorporate the gap kernel in all existing Lindhard-based functionals.

Kinetic and thermodynamic approach to precisely solve the unsteady Rayleigh flow problem of a rarefied homogeneous charged gas under external force influence

Abstract An extension and further development of our previous article [J. Non-equilibrium Thermodyne. 37 (2012), 119–141] is presented. We study the irreversible non-equilibrium thermodynamics (INT) properties of the exact solution to the dilute homogeneously charged gas problem with unsteady Rayleigh flow. In contrast to previous research, the charged gas flows under the influence of an external force, the flat plate oscillates, and the displacement current term is considered, leading to significant advancements in understanding natural plasma dynamics. We are solving the Boltzmann kinetic equation (BKE) Krook model supplemented by Maxwell’s equations. We used a travelling wave and moments method with an electron velocity distribution function (EVDF). To the best of our knowledge, as three new scientific achievements, we introduced a new mathematical model for calculating the thermodynamic forces, kinetic coefficients, and fluxes variables, Equations (28–40) and (50–54). Second, we determined, with reasonable accuracy, the thermodynamic equilibrium time of electrons, t equ = 26.7955, under an external force. We clarify the difference between equilibrium EVDF and perturbed EVDF and take advantage of BKE to account for non-equilibrium thermodynamic principles. For diamagnetic and paramagnetic plasmas, the extended Gibbs equation predicts ratios between various contributions to the internal energy change (IEC) is presented. A standard laboratory argon plasma model is used to apply the results.

Numerical analysis of biomass gasification in a fluidized bed reactor using a computational fluid dynamics model integrated with reduced-order reaction kinetics

The use of detailed reaction kinetics in a computational fluid dynamics (CFD) model for simulating the complex reactive gas-solid flow during fluidized bed gasification of biomass (FBGB) is extremely intensive in computations. A reduced-order reaction kinetics model was thus developed and validated that can be integrated with a CFD model to improve the prediction of the formation of tar and syngas components during FBGB at various sizes and chemical compositions of biomass particles. The simulations by the integrated CFD model and reduced-order kinetics showed that pyrolytic products were released from biomass at various temperatures and rates, which created large variations in the concentrations of tar compounds and syngas, and the oxygen to fuel ratio in the bed. The CFD simulations showed that H2 and CO were generated in both heterogeneous phase of the expanded bed and homogenous gas phase in the freeboard region while large portions of CO2 and CH4 were generated in the gas phase near to the top freeboard. Optimization of syngas residence time at a specific gasification temperature can thus reduce the formation of tar, CO2 and CH4.

Radiative transfer of excitation: Lévy flights and self-similarity

The Green function of the Biberman–Holstein integral equation, both nonstationary (instantaneous point flash) and stationary (stationary point source) is studied. The point flash produces a self-similar spherical wave of excitation in homogenous gas medium. The transfer of excitation is due to the Lévy flights of resonance line photons. The properties of the wave – its shape, time evolution and propagation – are found for arbitrary line profile. The cases of Doppler, Lorentz and Voigt profiles are considered in some detail. For the Doppler broadened line, the structure of the self-similar wave is given by a rational function. The properties of the Green function of stationary Biberman–Holstein equation are reviewed. Some unexpected parallels with non-stationary case are found. The spherically-symmetric version of the longest flight approximation is discussed and the condition of its validity is formulated.

A Note on the Binding Energy for Bosons in the Mean-Field Limit

We consider a gas of N weakly interacting bosons in the ground state. Such gases exhibit Bose–Einstein condensation. The binding energy is defined as the energy it takes to remove one particle from the gas. In this article, we prove an asymptotic expansion for the binding energy, and compute the first orders explicitly for the homogeneous gas. Our result addresses in particular a conjecture by Nam (Lett Math Phys 108(1):141–159, 2018), and provides an asymptotic expansion of the ionization energy of bosonic atoms.

Methane cracking in molten tin for hydrogen and carbon production—a comparison with homogeneous gas phase process

Methane cracking in molten tin for hydrogen and carbon production—a comparison with homogeneous gas phase process

Effect of hydrogen ratio on leakage and explosion characteristics of hydrogen-blended natural gas in utility tunnels

Based on computational fluid dynamics technology, the effect of hydrogen blending ratio (HBR) on the concentration distribution of leaked gas diffusion in utility tunnels was investigated, and based on this, the explosion characteristics of hydrogen-blended natural gas (HBNG) were studied in an inhomogeneous concentration field. The results showed that the concentration field of HBNG gradually stabilized in the downstream of the leak site, and the peak concentration increased linearly with HBR. When HBR≤5%, a high concentration region above the upper explosive limit is formed inside the gas cloud. This characteristic of the distribution induces secondary combustion in utility tunnels. The maximum flame velocity and steady acceleration distance increase with the increase of HBR. The flame shape is significantly affected by the concentration field distribution. The explosion overpressure induced by the real concentration field created multiple peak structures that exacerbated the explosion disaster complexity. The first overpressure peak at the ends was formed by the superposition of the precursor shock wave and its reflected wave, and those at other locations are caused by the shock waves. However, all maximum overpressure peaks are formed by the superposition of multiple reflections of the explosion wave. The maximum peak overpressure at both ends of the tunnel is higher than that in the middle. The explosion overpressure induced by the inhomogeneous gas cloud is lower than that caused by homogeneous gas cloud under the same volume. The research results can provide an effective reference for the anti-explosion design and risk assessment of utility tunnel.

Analysis and Calculation of Two-Phase Flow in Industrial Pipelines Using Regime Classification

The analysis shows that using regime classification for individual phases, it is possible to obtain a more reliable design scheme for two phase flows. In contrast to the flow structure, the concept of mode is more accessible for calculating an industrial pipeline. In this case, transient processes can be determined and calculated. The analysis shows that in field conditions it is very difficult to determine transition boundaries for flow structures. However, taking into account the structural approach, it is very difficult to determine the boundaries of the flow, and based on the laws of hydrodynamics of a homogeneous liquid and gas, it is possible to determine the transition of one regime to another using the Reynolds number. This technique is based on the theory of the great Russian scientist Academician A.P. Krylov. Let us note that this theory has not yet lost its specialty in the fishing industry. Based on numerous data, a method for calculating the gas-liquid mixture in horizontal pipes is proposed. Based on the laws of homogeneous liquid and gas, an equation for the distribution of speed, flow and pressure loss in a pipeline is obtained. The analysis shows that, based on the laws of homogeneous liquid and gas, it is possible to propose a method for calculating the hydrodynamic parameters of a two-phase flow, such as liquid and gas in a round pipe. This technique is based on the theory of Academician A.P. Krylov, which characterizes the reliability of this technique.