Local Equilibrium Approach Research Articles

Elastic and transport coefficients of the perfect hard-sphere crystal from the poles of the hydrodynamic spectral functions

The elastic and transport coefficients of a perfect face-centered cubic crystal of hard spheres are computed from the poles of the dynamic structure factor and of the spectral functions of transverse momentum density fluctuations. For such crystals, the relevant coefficients are the three isothermal elastic constants (C11T,C12T,C44T) , the heat conductivity κ, and the three viscosities (η11,η12,η44) (in Voigt’s notations), which are directly computed using molecular dynamics simulations. The elastic and transport coefficients are then compared to the values of the same coefficients obtained with the method of Helfand moments, showing good agreement and providing strong support for the microscopic hydrodynamic theory of perfect crystals based on the local-equilibrium approach.

Hydrodynamic correlation and spectral functions of perfect cubic crystals

We investigate the collective dynamics of the perfect cubic crystal by deriving from the hydrodynamic equations the time-dependent correlation and the spectral functions characterizing the fluctuations of mass and momentum densities. We show that the seven hydrodynamic modes of the perfect crystal can be identified from the resonances of these spectral functions. The comparison with those of a fluid is discussed. Using the numerical values of the thermodynamic, elastic, and transport coefficients computed in our previous paper (J Mabillard and P Gaspard 2024 J. Stat. Mech. 023208) for a system of hard spheres, the theoretical expressions for the correlation and spectral functions are compared to the same functions directly computed using molecular dynamics simulations. The excellent agreement between theory and simulation provides strong support for the microscopic hydrodynamic theory of perfect crystals based on the local-equilibrium approach. This work sheds light on the fundamental mechanisms governing the collective behavior of matter in the solid state.

Local Equilibrium Approach in the Problem of the Dynamics of a Plane Turbulent Wake in a Passively Stratified Medium

Local Equilibrium Approach in the Problem of the Dynamics of a Plane Turbulent Wake in a Passively Stratified Medium

Hydrodynamic properties of the perfect hard-sphere crystal: microscopic computations with Helfand moments

Within the framework of the local equilibrium approach, the equilibrium and nonequilibrium properties relevant to the hydrodynamics of the perfect hard-sphere crystal were obtained through molecular dynamics simulations using the Helfand moments associated with momentum and energy transport. Because this crystal is face-centered cubic, the hydrodynamic properties we considered were hydrostatic pressure, isothermal bulk modulus, specific heat capacities and their ratio, three isothermal elastic constants (C11T,C12T,C44T) , heat conductivity, and three viscosities (η11,η12,η44) (in Voigt’s notation). These properties were computed as a function of the particle density. The pressure and transport coefficients diverge near the close-packing density, as the collision frequency per particle also diverges.

The evolution of sulphur-bearing molecules in high-mass star-forming cores

Context. To understand the chemistry of sulphur (S) in the interstellar medium, models need to be tested by observations of S-bearing molecules in different physical conditions. Aims. We aim to derive the column densities and abundances of S-bearing molecules in high-mass dense cores in different evolutionary stages and with different physical properties. Methods. We analysed observations obtained with the Institut de RadioAstronomie Millimétrique (IRAM) 30 m telescope towards 15 well-known cores classified in the three main evolutionary stages of the high-mass star formation process: high-mass starless cores, high-mass protostellar objects, and ultracompact HII regions. Results. We detected rotational lines of SO, SO+, NS, C34S, 13CS, SO2, CCS, H2S, HCS+, OCS, H2CS, and CCCS. We also analysed the lines of the NO molecule for the first time to complement the analysis. From a local thermodynamic equilibrium approach, we derived the column densities of each species and excitation temperatures for those that are detected in multiple lines with different excitation. Based on a statistical analysis of the line widths and the excitation temperatures, we find that NS, C34S, 13CS, CCS, and HCS+ trace cold, quiescent, and likely extended material; OCS, and SO2 trace warmer, more turbulent, and likely denser and more compact material; SO and perhaps SO+ trace both quiescent and turbulent material, depending on the target. The nature of the emission of H2S, H2CS, and CCCS is less clear. The molecular abundances of SO, SO2, and H2S show the strongest positive correlations with the kinetic temperature, which is thought to be an indicator for evolution. Moreover, the sum of all molecular abundances shows an enhancement of gaseous S from the less evolved to the more evolved stages. These trends could be due to the increasing amount of S that is sputtered from dust grains owing to the increasing protostellar activity with evolution. The average abundances in each evolutionary group increase, especially in the oxygen-bearing molecules, perhaps due to the increasing abundance of atomic oxygen with evolution owing to photodissociation of water in the gas phase. Conclusions. Our observational work represents a test-bed for theoretical studies aimed at modelling the chemistry of sulphur during the evolution of high-mass star-forming cores.

Modelling of hydrogen diffusion in a steel containing micro-porosity. Application to the permeation experiment

Two numerical models based on non-equilibrium and local equilibrium approaches respectively were developed to simulate hydrogen transport in porous metals, taking account of gaseous hydrogen trapping inside the micro-porosities. They were applied to the case of hydrogen permeation in a cast steel at room temperature. Numerical simulations revealed that the two models are equivalent under certain conditions. A parametric analysis was performed to explore the effect of external hydrogen fugacity, hydrogen solubility and porosity fraction on the hydrogen diffusion behavior. A comparison between experimental permeation data and the numerical results showed reasonable agreement considering no input parameter was adjusted.

Quantum local-equilibrium approach to dissipative hydrodynamics.

The macroscopic hydrodynamic equationsare derived for many-body systems in the local-equilibrium approach, using the Schrödinger picture of quantum mechanics. In this approach, statistical operators are defined in terms of microscopic densities associated with the fundamentally conserved quantities and other slow modes possibly emerging from continuous symmetry breaking, as well as macrofields conjugated to these densities. Functional identities can be deduced, allowing us to identify the reversible and dissipative parts of the mean current densities, to obtain general equationsfor the time evolution of the conjugate macrofields, and to establish the relationship to projection-operator methods. The entropy production is shown to be nonnegative by applying the Peierls-Bogoliubov inequality to a quantum integral fluctuation theorem. Using the expansion in the gradients of the conjugate macrofields, the transport coefficients are given by Green-Kubo formulas and the entropy production rate can be expressed in terms of quantum Einstein-Helfand formulas, implying its nonnegativity in agreement with the second law of thermodynamics. The results apply to multicomponent fluids and can be extended to condensed matter phases with broken continuous symmetries.

CHEMOUT: CHEMical complexity in star-forming regions of the OUTer Galaxy

Context. The outer Galaxy is an environment with a lower metallicity than the regions surrounding the Sun and for this reason the formation and survival of molecules in star-forming regions located in the inner and outer Galaxy are expected to be different. Aims. To gain understanding of how chemistry changes throughout the Milky Way, it is crucial to observe the outer star-forming regions of the Galaxy in order to constrain models adapted for lower metallicity environments. Methods. The project ‘chemical complexity in star-forming regions of the outer Galaxy’ (CHEMOUT) is designed to address this problem by observing a sample of 35 star-forming cores at Galactocentric distances of up to ~23 kpc with the Institut de RadioAstronomie Millimétrique (IRAM) 30 m telescope in various 3 mm and 2 mm bands. In this work, we analyse observations of methanol (CH3OH), one of the simplest complex organic molecules and crucial for organic chemistry in star-forming regions, and of two chemically related species, HCO and formaldehyde (H2CO), towards 15 out of the 35 targets of the CHEMOUT sample. More specifically, we consider only the targets for which both HCO and H2CO were previously detected, which are precursors of CH3OH. Results. We detected CH3OH in all 15 targets. The emission is associated with an extended envelope, as the average angular size is ~47″ (i.e. ~2.3 pc at a representative heliocentric distance of 10 kpc). Using a local thermodynamic equilibrium approach, we derive CH3OH excitation temperatures in the range ~7–16 K and line widths ≤4 km s−1, which are consistent with emission from a cold and quiescent envelope. The CH3OH fractional abundances with respect to H2 range between ~0.6 × 10−9 and ~7.4 × 10−9. These values are comparable to those found in star-forming regions in the inner and local Galaxy. H2CO and CH3OH show well-correlated line velocities, line widths, and fractional abundances with respect to H2, indicating that their emission originates from similar gas. These correlations are not seen with HCO, suggesting that CH3OH is likely more chemically related to H2CO than to HCO. Conclusions. Our results have important implications for the organic and possibly pre-biotic chemistry occurring in the outermost star-forming regions of the Galaxy, and can help to set the boundaries of the Galactic habitable zone.

FAUST VI. VLA1623−2417 B: a new laboratory for astrochemistry around protostars on 50 au scale

ABSTRACT The ALMA (Atacama Large Millimeter Array) interferometer, with its unprecedented combination of high sensitivity and high angular resolution, allows for (sub-)mm wavelength mapping of protostellar systems at Solar system scales. Astrochemistry has benefitted from imaging interstellar complex organic molecules in these jet–disc systems. Here, we report the first detection of methanol (CH3OH) and methyl formate (HCOOCH3) emission towards the triple protostellar system VLA1623−2417 A1+A2+B, obtained in the context of the ALMA Large Programme FAUST (Fifty AU STudy of the chemistry in the disc/envelope system of solar-like protostars). Compact methanol emission is detected in lines from Eu = 45 K up to 61 K and 537 K towards components A1 and B, respectively. Large velocity gradient analysis of the CH3OH lines towards VLA1623−2417 B indicates a size of 0.11–0.34 arcsec (14–45 au), a column density $N_{\rm CH_3OH}$ = 1016–1017 cm−2, kinetic temperature ≥ 170 K, and volume density ≥ 108 cm−3. A local thermodynamic equilibrium approach is used for VLA1623−2417 A1, given the limited Eu range, and yields Trot ≤ 135 K. The methanol emission around both VLA1623−2417 A1 and B shows velocity gradients along the main axis of each disc. Although the axial geometry of the two discs is similar, the observed velocity gradients are reversed. The CH3OH spectra from B show two broad (4–5 km s−1) peaks, which are red- and blueshifted by ∼ 6–7 km s−1 from the systemic velocity. Assuming a chemically enriched ring within the accretion disc, close to the centrifugal barrier, its radius is calculated to be 33 au. The methanol spectra towards A1 are somewhat narrower (∼ 4 km s−1), implying a radius of 12–24 au.

Exact and approximate mean first passage times on trees and other necklace structures: a local equilibrium approach

In this work we propose a novel method to calculate mean first-passage times (MFPTs) for random walks on graphs, based on a dimensionality reduction technique for Markov state models, known as local-equilibrium (LE). We show that for a broad class of graphs, which includes trees, LE coarse-graining preserves the MFPTs between certain nodes, upon making a suitable choice of the coarse-grained states (or clusters). We prove that this relation is exact for graphs that can be coarse-grained into a one-dimensional lattice where each cluster connects to the lattice only through a single node of the original graph. A side result of the proof generalises the well-known essential edge lemma (EEL), which is valid for reversible random walks, to irreversible walkers. Such a generalised EEL leads to explicit formulae for the MFPTs between certain nodes in this class of graphs. For graphs that do not fall in this class, the generalised EEL provides useful approximations if the graph allows a one-dimensional coarse-grained representation and the clusters are sparsely interconnected. We first demonstrate our method for the simple random walk on the c-ary tree, then we consider other graph structures and more general random walks, including irreversible random walks.

Critical review on local thermal equilibrium and local thermal non-equilibrium approaches for the analysis of forced convective flow through porous media

Scientific community from the field of thermo-fluidics have focused extensive attention towards investigating techniques of enhancing the heat transfer in varied thermal systems. One of the most suitable techniques for augmenting the heat transfer is incorporating porous medium into thermal systems. The transport processes through porous media, which consists of a fluid phase and a solid matrix, can be modelled by either considering both to be in thermal equilibrium or in thermal non-equilibrium. Hence, two different modelling strategies viz. local thermal equilibrium (LTE) model and local thermal non-equilibrium (LTNE) model have been employed by different researchers. In this work, a comprehensive review of the published literatures in respect of the modelling approaches used for determining the implications of embedding porous media in different thermal systems from the perspective of heat transfer and entropy generation has been presented. The effects of various key determinants on the fluid flow, heat transfer characteristics and entropy generation in thermal systems are discussed. This discussion is then followed by a critical assessment of the applicability of LTE and LTNE approaches. At the end, conclusions and recommendations about the less explored systems and the areas that needs further investigations are summarized.

Nonequilibrium statistical mechanics of crystals

The local equilibrium approach previously developed by the authors (J Mabillard and P Gaspard 2020 J. Stat. Mech. 103203) for matter with broken symmetries is applied to crystalline solids. The macroscopic hydrodynamics of crystals and their local thermodynamic and transport properties are deduced from the microscopic Hamiltonian dynamics. In particular, the Green–Kubo formulas are obtained for all the transport coefficients. The eight hydrodynamic modes and their dispersion relation are studied for general and cubic crystals. In the same twenty crystallographic classes as those compatible with piezoelectricity, cross effects coupling transport between linear momentum and heat or crystalline order are shown to split the degeneracy of damping rates for modes propagating in opposite generic directions.

Thin Film Deposition by Atmospheric Pressure Dielectric Barrier Discharges Containing Eugenol: Discharge and Coating Characterizations.

Eugenol (4-Allyl-2-methoxyphenol) is the main constituent of clove oil. In addition to being widely used as a condiment, it has been recognized as a powerful bactericide. Owing to that, Eugenol has been used in several applications including odontology and as a conservative for food products. Aiming at the development of natural bactericide coatings, in this work, using an atmospheric pressure plasma in a dielectric barrier discharge (DBD) reactor Eugenol was deposited on stainless steel substrate, with argon as a carrier gas. The discharge power supply was a transformer at 14.4 kV peak-to-peak voltage and 60 Hz frequency. Operating with a gas flow rate at 4 L/min, the active power was around 1.2 W. The maximum plasma electron temperature of the plasma with monomers was about 1.5 eV, estimated by visible emission spectroscopy using a local thermodynamic equilibrium approach. The study also comprehended the analysis of the film structure, aging, and thermal stability using infrared reflectance spectroscopy, and its thicknesses and roughness by profilometry. The thickness of the films was in the range of 1000 to 2400 nm with a roughness of up to 800 nm with good adhesion on the substrate. The FTIR result shows a stable coating with a chemical structure similar to that of the monomer. Aging analysis showed that the film does not degrade, even after exposing the film for 120 days in ambient air and for 1.0 h under a high thermal UV-lamp.

Mixed thermomagnetic convection of ferrofluid in a porous cavity equipped with rotating cylinders: LTE and LTNE models

In the present study, the impressions of the MHD and porous medium on mixed convection of Fe3O4-water nanofluid in a cavity with rotating cylinders in three different temperature cases with local thermal equilibrium and local thermal non-equilibrium approaches were studied. The effect of the presence of cylinders in three different temperature cases to improve the heat transfer rate was investigated. A finite volume method was used to solve equations. The Richardson, Hartmann, and Darcy numbers ranges are 1 ≤ Ri ≤ 100, 0 ≤ Ha ≤ 30, 0.001 ≤ Da ≤ 0.1, respectively. The volume fraction of nanoparticles varies in the range of 0–3%. The results show that the use of porous media has a beneficial effect on increasing the heat transfer rate, but the combination of the porous medium and the magnetic field can increase or decrease the heat transfer. Also, the most effective and highest heat transfer rate was occurred at Da = 0.01 and Da = 0.1, respectively. In addition, when the cylinders are cold or hot, the highest and lowest heat transfer rates occur, respectively. Finally, it was concluded that the magnetic field could control the fluid flow inside the cavity.

Signatures of Helium Continuum in Cool Flare Loops Observed by SDO/AIA

Abstract We present an analysis of off-limb cool flare loops observed by the Solar Dynamics Observatory (SDO)/Atmospheric Imaging Assembly (AIA) during the gradual phase of SOL2017-09-10T16:06 X8.2-class flare. In the extreme-ultraviolet (EUV) channels starting from the 335 Å one, cool loops appear as dark structures against the bright loop arcade. These dark structures were precisely coaligned (spatially and temporally) with loops observed by Swedish Solar Telescope (SST) in emission lines of hydrogen and ionized calcium. A recently published semi-empirical model of cool loops based on SST observations serves to predict the level of hydrogen and helium recombination continua. The continua were synthesized using an approximate non-LTE (i.e., departures from local thermodynamic equilibrium) approach and theoretical spectra were then transformed to AIA signals. Comparison with signals detected inside the dark loops shows that only in AIA 211 Å channel the computed level of recombination continua is consistent with observations for some models, while in all other channels that are more distant from the continua edges the synthetic continuum is far too low. In analogy with on-disk observations of flares we interpret the surplus emission as due to numerous EUV lines emitted from hot but faint loops in front of the cool ones. Finally we briefly comment on failure of the standard absorption model when used for analysis of the dark-loop brightness.

Possible effect of flow velocity on thawing rock-water-ice systems under local thermal non-equilibrium conditions

Climate change causes thawing of many permafrost regions, increasing the rockfall and landslide hazard when the cementing ice melts and slopes become unstable. The thermo-hydro-mechanical processes are strongly coupled and complex to describe in those intrinsic multi-phase systems. So far, thermal models often utilize the local thermal equilibrium approach, assuming that all three phases (solid rock or soil, liquid water and ice) are in thermal equilibrium. While this approach is very tempting due to its easy implementation, there are situations especially during thawing in which temperature gradients exist between the involved phases. In such cases, the local thermal equilibrium approach has to be replaced by the more complex local thermal non-equilibrium approach in which the thermodynamic state of each phase is described by its own temperature. In those models, the heat transfer between the phases is described explicitly in dependence of the heat transfer coefficient and the contact area. Parameterization of the heat transfer coefficient is a challenging task and mostly relies on empirical values and relationships. Most models using the local thermal non-equilibrium approach utilize a constant heat transfer coefficient. However, experiments under geothermal temperature conditions prove that the heat transfer coefficient depends, among others, on flow velocity. This is of special interest as strong dynamics are characteristic for thawing system which impose a unique challenge to heat transfer models. For example, the volume fraction of the liquid domain increases significantly during thawing of rock-ice systems due to the melting of the ice phase. This again, directly influences flow velocity. In this work, the possible effect of a velocity dependent heat transfer coefficient on thawing rock-water-ice systems is investigated. With higher flow velocity, advection effects of the intruding fluid become more significant but also heat transfer is increased. When the intruding liquid water is colder than the surrounding rock, the melting rate is maximum for a specific flow velocity, as advection of cold water and heating from the rock counteract. While this is a purely synthetic study and no experimental data yet exists for validation of the proposed scheme, this study indicates the existence of a way more complex interaction between liquid fluid flow and melting processes as previously expected and way beyond state-of-the-art modeling.

Numerical investigation of rock-pile based waste heat storage for remote communities in cold climates

Remote communities in arctic climates are solely dependent on diesel generators for continuous power supply due to their detached loci from national power gridlines or natural gas pipelines. Moreover, to get along with the harsh, long winters, these communities directly or indirectly depend on fossil-fuel based heating systems. Due to the lower efficiency of the conventional diesel engines, these generators discard a significant amount of heat through the exhaust. Occasionally, during the wintertime, this waste heat from the exhaust is used directly as a heat source after recovery. However, during summer, when the heating demand is lower or nil, this heat is commonly discarded, and its energy potential wasted. A rock-pile based seasonal thermal energy storage is a viable solution that can sustainably resolve this issue. This paper presents a validated numerical study that focuses on the coupling of a waste heat recovery system to a diesel exhaust stream offering a performance assessment of the proposed rock-pile waste heat storage system in a remote, off-grid community located in northern Canada. It examines the impacts of local thermal equilibrium versus non-equilibrium approaches as well as temperature-dependent properties, variation of air mass flow rate, particle size and finally the thermo-physical properties on the proposed model. The presented results show that air should be treated as an ideal gas and that the local thermal non-equilibrium approach should be used for its considerably higher accuracy. Techno-economic assessment of the system resulted in a relatively short payback period of less than six years.

Exact analysis based on BDLTNE approach for thermal behaviour in living tissues during regional hyperthermia therapy

The present work highlights the attempt to develop a two-dimensional mathematical modelling of thermal characteristics in malignant tissues under a regional hyperthermia therapy based on the bi-dimensional local thermal non-equilibrium bioheat model. In the arena of biological heat transfer, a local thermal non-equilibrium model is preferred over a local thermal equilibrium approach, as skin tissues are a combination of highly non-uniform non-homogeneous structure of fluid and solid media (porous structure). The solution of the thermal response has been determined analytically by employing a ‘hybrid scheme’ composed of ‘shift of variables’ and ‘finite integral transform’ with the therapeutic boundary conditions and actual local coordinates dependent on the initial condition. The thermal behavioural study has been conducted with the influence of oscillating and constant heat flux imposed on the exposed surface of the diseased tissue. The results have been validated with the published experimental work. From the research output, it has been noticed that the sinusoidal therapeutic heat flux is better for the longer time of treatment in comparison with the constant heat flux heating. The treatment protocols of regional hyperthermia suggest that the size of the affected tissue (or organ) is larger in comparison with the localized hyperthermia. Hence, the multi-dimensional modelling should give better glimpse of results than the 1-D form of analysis. From the constructed 2-D thermal contours, it may be noted under the regional hyperthermia circumstance that the heat propagation in the living tissue is in two-directional nature, and thus 2-D analysis is necessary for predicting an accurate temperature response. The present analysis also highlights that a temperature range of 38–44 $$^\circ {\hbox {C}}$$ is possible to maintain in a prolonged therapeutic exposure time instead of maintaining $$50\,^\circ {\hbox {C}}$$ for 30 min described in the existing literature. Hence, this positive aspect obtained in the present work can avoid the collateral damage of healthy tissues in human bodies during the regional hyperthermia therapy.

Simulated laser-induced breakdown spectra of graphite and synthetic shergottite glass under Martian conditions

We report the results of a simulation of the laser-induced breakdown spectra of graphite and synthetic shergottite glass in an atmosphere similar to that of Mars using a 1-D, Lagrangian hydrodynamic model, a spherical geometry description of the laser ablation and plume expansion and a local thermodynamic equilibrium (LTE) approach for the emission spectra. We compare the LIBS spectra of two calibration targets on board of the Curiosity rover to the simulated ones calculated under nominally the same conditions as those encountered on Mars. The simulations provide an additional way, to laboratory based comparative studies, to better understand the effects of laser parameters and atmospheric pressures. We report on the effect of laser irradiance and ambient pressure on the electron and ion temperature, electron number density, and fluid velocity parameters characterizing the plasma. Finally, we show the effects of laser irradiance and ambient pressure on the simulated emission spectra of graphite and shergottite and compare them to those acquired by ChemCam. The agreement between the two is good, particularly for the prominent emission lines.

Effect of C and N and their absence on the kinetics of austenite-ferrite phase transformations in Fe-0.5Mn alloy

Investigating the partitioning effect of substitutional and interstitial elements on the migration of transformation interfaces during austenite-ferrite phase transformation in steels with the conventional experimental method is extremely challenging due to interaction between the solute atoms and the transformation interfaces. Additionally, the simultaneous nucleation of new phases during phase transformations limits the accuracy of extracted growth rates from experimental kinetics measurements of phase fractions. In a novel experimental approach, the cyclic partial phase transformation concept is used to avoid the effect of nucleation on total kinetics of phase transformations. In this study, a Fe-0.5Mn alloy in the presence and absence of interstitial C and N additions is subjected to different cyclic transformation routes to examine the possible interaction between solute atoms and migrating interfaces. The experimental results are in semi-quantitative agreement with modelling predictions made by the local equilibrium approach and provide indirect evidence of Mn partitioning at austenite/ferrite interface in absence of any interstitial elements. It is also confirmed that the presence of interstitial elements promotes Mn interaction with the interface, whereas N promotes more Mn partitioning at transformation interface compared to C.