Assumption Of Equilibrium Research Articles

On particle scattering in Gross-Pitaevskii theory and implications for dark matter halos

Bose-Einstein-condensed dark matter (BEC-DM), also called scalar field dark matter (SFDM), has become a popular alternative to the standard, collisionless cold dark matter (CDM) model, due to its long-held potential to resolve the small-scale crisis of CDM. Halos made of BEC-DM have been modelled using the Gross-Pitaevskii (GP) equation coupled to the Poisson equation; the so-called GPP equations of motion. These equations are based on fundamental microphysical conditions that need to be fulfilled in order for the equations to be valid in the first place, related to the diluteness of the DM gas and the nature of the particle scattering model. We use these conditions in order to derive the implications for the BEC-DM parameters, the 2-particle self-interaction coupling strength g and the particle mass m. We compare the derived bounds with the constraint that results from the assumption of virial equilibrium of the central cores of halos, deriving a relationship that connects g and m. We find that the GPP conditions are greatly fulfilled, for BEC-DM particle masses of interest, if such models also obey the virial condition that turns out to be the strongest constraint. We also derive the implications for the elastic scattering cross section (per particle mass) in BEC-DM halos, based on the scattering model of GPP, and find a huge range of possible values, depending on the self-interaction regime. We put our results into context to recent literature which predicts sub-kpc core size in BEC-DM halos.

Fourth-order accurate numerical modeling of the multi-fluid plasma equations with adaptive mesh refinement

This work develops a multi-fluid plasma modeling capability in extension of a parallel, adaptive, fourth-order, finite-volume method, computational fluid dynamics algorithm. The governing equations of the multi-fluid plasma model are derived from moments of the Boltzmann equation, under the assumption of local thermodynamic equilibrium. Maxwell's equations describe the electromagnetic field evolution and are coupled to the fluid equations of charged species. The present work concentrates on two, charged, collisionless fluids as the first step, although the algorithm is designed to accommodate more fluids, both charged and neutral, and collisions between fluids; the extension to multiple fluids is straightforward. The numerical algorithm featuring parallel, high-order (≥4 for smooth flows), adaptive mesh refinement is expected to help cope with the inherent stiffness of the physics involved. The standard, fourth-order Runge-Kutta scheme is used to evolve the solution in time. The current study is primarily focused on verification and testing of the new, adaptive algorithm; we demonstrate 4th-order accuracy using problems with exact solutions and benchmark our solutions for common plasma simulations against references from literature. Using the 4th-order scheme, our multi-fluid model is shown to provide accurate solutions to plasma problems using half the cell count as traditional, 2nd-order methods. Furthermore, adaptive mesh refinement is successfully applied to three, plasma test problems, providing a significant reduction in mesh size. In subsequent work, an optimized version of our multi-fluid plasma algorithm will be applied to plasma test cases with more practical configurations, with a rigorous assessment of the improvements to computational efficiency afforded by our adaptive, higher-order scheme.

Disequilibrium and complexity across scales: a patch-dynamics framework for organizational ecology

Based on equilibrium assumptions, traditional ecological models have been widely applied in the fields of management and organization studies. While research using these models is still ongoing, studies have nonetheless struggled with ways to address multiple levels of analysis, uncertainty, and complexity in their analyses. This paper conceptualizes the dynamic co-evolution mechanisms that operate in an ecosystem across multiple organizational scales. Specifically, informed by recent advances in modelling in biology, a general ‘patch-dynamics’ framework that is theoretically and methodologically able to capture disequilibrium, uncertainty, disturbances, and changes in organizational populations or ecosystems, as complex and dynamically evolving resource environments are introduced. Simulation models are built to show the patch-dynamics framework’s functioning and test its robustness. The patch-dynamics framework and modelling methodology integrates equilibrium and disequilibrium perspectives, co-evolutions across multiple organization levels, uncertainties, and random disturbances into a single framework, opening new avenues for future research on topics in the field of management and organization studies, as well as on the mechanisms that shape ecosystems. Such a framework has the potential to help analyse the sustainability and healthiness of the business environment, and deserves more attention in future research on management and organization theory, particularly in the context of significant uncertainty and disturbances in business and management practice. Overall, the paper offers a distinct theoretical perspective and methodology for modelling population and ecosystem dynamics across different scales.

Validity of Local Thermal Equilibrium Assumption for Heat Transfer in a Saturated Soil Layer

The assumption of local thermal equilibrium (LTE) between solid and fluid phases commonly is used for studies of heat transfer in saturated soil and is valid for a wide range of conditions. However, for certain conditions, the heat transfer process may give rise to local thermal nonequilibrium (LTNE) in which adjacent solid and fluid phases have different temperatures. This note presents the results of a numerical study of the validity of the LTE assumption for one-dimensional heat transfer in a saturated soil layer with fluid flow. For the conditions investigated, the LTE assumption holds for soil with particle sizes smaller than the gravel range. For soil with particles sizes in the gravel range and larger, the LTE assumption may be valid or invalid, depending primarily on fluid discharge velocity, with higher fluid velocity values more likely to produce LTNE conditions.

Hydrodynamics of a Multi-Component Bosonic Superfluid

We obtain the superfluid hydrodynamic equations of a multi-component Bose gas with short-ranged interactions at zero temperature under the local equilibrium assumption and show that the quantum pressure is generally present in the nonuniform case. Our approach can be extended to systems with long-range interactions such as dipole-dipole interactions by treating the Hartree energy properly. For a highly symmetric superfluid, we obtain the excitation spectrum and show that except for the density phonon, all other excitations are all degenerate. The implication of our results is discussed.

Phenotype, allele and genotype frequency distribution of ABO and Rh(D) blood group among blood donors attending regional blood transfusion centre in Delhi, India.

The ABO and Rh blood group phenotypes, alleles, and genotype frequencies have many biological and medical implications. The frequency differs broadly according to races, geographical borders and ethnicity, even within the same region. This study was designed to determine the frequency of ABO and Rh blood groups among blood donors attending the regional blood transfusion centre in Delhi. The gel card method was used to determine the ABO and Rh(D) blood groups of donors who donated blood between January 1, 2020, and June 30, 2022. The assumption of Hardy-Weinberg equilibrium was used to determine allele and genotype frequencies of blood donors. A total of 16,925 blood units were donated during the study period. Donors phenotype frequencies of ABO were as follows: 'A' (23.88%), 'B' (37.38%), 'AB' (9.97%) and 'O '(29.27%). Rh(D)+Ve (D) were (94.9%) and Rh(D)-Ve (d) were (5.01%), which follow an order of B > O > A > AB and Rh-D > d for Rh. Donors ABO and Rh (D) allele frequencies were IA-0.183, IB-0.277, IO-0.541 and ID-0.776, Id-0.224 respectively. Allele frequencies follow an order of IO > IB > IA and Rh- ID > Id. Donors ABO genotype frequencies were AA-0.0333, AO-0.198, BB-0.0768, BO-0.30, AB-0.101, OO-0.293 and Rh(D) genotype frequencies were DD-0.602, Dd-0.347, dd-0.0501. Genotype frequencies follow an order of BO > OO > AO > AB > BB > AA and DD > Dd > dd. Among our donors, which were mostly from northern India, the ABO and Rh(D) blood groups have the highest proportion of ABO-B and Rh(D)+Ve and the lowest proportion of ABO-AB and Rh(D)-Ve, with a stable order of B > O > A > AB and D > d for phenotype, IO > IB > IA and ID > Id for allele and BO > OO > AO > AB > BB > AA and DD > Dd > dd for genotype.

CO2 storage in porous media unsteady thermosolutal natural convection -Application in deep saline aquifer reservoirs

In this paper, the storage of CO2 is investigated numerically under supercritical conditions in deep saline aquifer reservoirs. The simulations were performed on a non-deformable, saturated porous material inside a vertical enclosure that was assumed to be impermeable and insulated on three sides. The porous medium is homogeneous and isotropic with constant thermo-physical properties except for the fluid density, which varies according to Boussinesq approximations. A dynamic model assumes that flow is two-dimensional and obeys Darcy's motion law. The thermal equilibrium assumption (LTE) is also considered. The set of conservation equations and the appropriate initial and boundary conditions have been resolved numerically by the classical finite volume method. Spatio-temporal variations of different state variables such as pressure, velocity, temperature, and concentration were numerically simulated and plotted versus controlling parameters, particularly the thermal and solutal Rayleigh numbers, RaT and RaS; the Lewis number, Le; and the reservoir's aspect ratio, A. According to regulating factors, and physical and geological qualities, we could predict the behavior of CO2 that would be stored in a geologic reservoir that is thought to be porous media. We could also estimate the time and direction of CO2 mass transfer based on the abovementioned factors. Great attention was paid to examining the sensitivity of fluid flow, heat, and mass transfer rates according to the reservoir form and the operating conditions.

A Historically Driven Spinup Procedure for Soil Carbon Modeling

Soil process models such as RothC typically assume soil organic carbon (SOC) is in equilibrium at the beginning of each simulation run. This is not likely to be true in the real world, since recalcitrant SOC pools (notably, humified material) take many decades to re-stabilize after a land use change. The equilibrium assumption stems from a spinup method in which the model is run under a single land use until all SOC pools stabilize. To overcome this, we demonstrate an alternative spinup procedure that accounts for historical land use changes. The “steady-state” and “historical” spinup methods both impute unknown C inputs such that the modeled SOC matches empirical measurements at the beginning of the simulation and set initial SOC fractions. Holding all other parameters equal, we evaluated how each spinup affects SOC projections in simulations of agricultural land use change in the U.S. state of Vermont. We found that projected SOC trajectories for all land use scenarios are sensitive to the spinup procedure. These differences are due to disparities in imputed below-ground plant-derived carbon between the two procedures. Compared to the steady-state, imputed C in the historical spinup is higher for land uses that increase SOC (e.g., adoption of regenerative practices) and lower for land uses that decrease SOC (e.g., a transition from pasture to crops), due to the time window within which land use changes are assumed to have occurred. The novel historical spinup procedure captures important dynamics commonly missing in previous studies, representing an advancement in soil process modeling.

Local equilibrium in liquid phase shock waves.

We have assessed the assumption of local thermodynamic equilibrium in a shock wave by comparing local thermodynamic data generated with nonequilibrium molecular dynamics (NEMD) simulations with results from corresponding equilibrium simulations. The shock had a Mach number approximately equal to 2 in a Lennard-Jones spline liquid. We found that the local equilibrium assumption holds perfectly well behind the wave front, and is a very good approximation in the front itself. This was supported by calculations of the excess entropy production in the shock front with four different methods that use the local equilibrium assumption in different ways. Two of the methods assume local equilibrium between excess thermodynamic variables by treating the shock as an interface in Gibbs's sense. The other two methods are based on the local equilibrium assumption in a continuous description of the shock front. We show for the shock studied in this work that all four methods give excess entropy productions that are in excellent agreement, with an average variance of 3.5% for the nonequilibrium molecular dynamics (NEMD) simulations. In addition, we solved the Navier-Stokes (N-S) equationsnumerically for the same shock wave using an equilibrium equationof state (EoS) based on a recently developed perturbation theory. The results for the density, pressure, and temperature profiles agree well with the profiles from the NEMD simulations. For instance, the shock waves generated in the two simulations travel with almost the same speed; the average absolute Mach-number deviation of the N-S simulations relative to NEMD is 2.6% in the investigated time interval.

Measuring Galactic dark matter through unsupervised machine learning

ABSTRACTMeasuring the density profile of dark matter in the Solar neighbourhood has important implications for both dark matter theory and experiment. In this work, we apply autoregressive flows to stars from a realistic simulation of a Milky Way-type galaxy to learn – in an unsupervised way – the stellar phase space density and its derivatives. With these as inputs, and under the assumption of dynamic equilibrium, the gravitational acceleration field and mass density can be calculated directly from the Boltzmann equation without the need to assume either cylindrical symmetry or specific functional forms for the galaxy’s mass density. We demonstrate our approach can accurately reconstruct the mass density and acceleration profiles of the simulated galaxy, even in the presence of Gaia-like errors in the kinematic measurements.

Gas condensate well productivity in fractured vuggy carbonate reservoirs: A numerical modeling study

The spatial distribution of fractures and cavities may generate important impact on the fluid flow behavior in fractured vuggy carbonate reservoirs. However, the recovery mechanism of gas condensate wells is not well understood due to the lack of effective reservoir simulation methods that coupled porous-medium and free flows occurring in fractured vuggy carbonate reservoirs. In this work, a novel compositional reservoir model is developed for modeling the production dynamics of gas-condensate well in complex fractured vuggy reservoirs. The compositional multiphase fluid flow through rock matrix and fractures is assumed to follow Darcy's law, while the free flow in cavities is modeled based on the assumptions of instantaneous thermodynamic equilibrium and phase segregation controlled by gravity. An advanced numerical calculation method combining finite volume method (FVM) and embedded discrete fracture-vug model (EDFVM) is developed to efficiently solve the multi-component multiphase flow problem. Case studies are conducted to investigate the gas-condensate flow behavior and well production performance under various configurations of fracture-cavity patterns. Two scenarios are considered by placing the production well at the top and bottom of the models, which aim to mimic different locations of directional well target. The results indicate that when cavities are present, condensate oil accumulates mainly beneath the cavities due to the effect of gravity segregation. Thus, more condensate oil may be produced with depletion at the bottom of the reservoir. However, condensate oil distributes surrounding the production well when cavities are absent, and the production performance of gas-condensate well is less affected by depletion location. Furthermore, the cumulative condensate oil and gas production are higher when cavities are present because of the continuous supplement of condensate gas by cavities. Our research findings have important implication for the design of directional well planning in the fractured vuggy gas condensate reservoirs.

Technoeconomic Analysis of a Small-Scale Downdraft Gasification-Based Cogeneration Power Plant Using Green Wastes

Abstract In this work, the technoeconomic assessment of a small-scale gasification-based cogeneration plant (25–50 kWe) fed with green wastes (fallen leaves, spent coffee grounds, and paperboard) is presented. The cogeneration power plant is modeled using Thermoflex software under thermochemical equilibrium and steady-state assumptions. Subsequently, the performance of the cogeneration plant is numerically analyzed as a function of the feedstock moisture content (6–30%), air–waste equivalence ratio (0.20–0.55), and the system load (6.25–25 kWe). The results show that the best energy performance of the cogeneration plant is achieved with a feedstock moisture of 6.05%, an equivalence ratio of 0.358, and a load of 25 kWe. At this best performance mode, the electric generation and cogeneration efficiencies are 19.33% and 49.71%, respectively, with a specific biomass consumption of 1.19 kg/kWh. Two scenarios are established for the economic assessment. The baseline scenario considers a 25-kWe cogeneration plant, while, in the second one, the generation capacity of the system was assumed to be doubled (50 kWe). The financial results show that the power generation has an energy levelized cost of 11.7 ¢$/kWh and 8.4 ¢$/kWh for 25 kWe and 50 kWe, respectively. Nevertheless, none of the proposed scenarios were found to be economically feasible based on the negative net present value obtained. Therefore, further energy laws and regulations are required seeking to support the small-scale auto-generation units based on biomass gasification.

Islands in the fluid: islands are common in cosmology

We discuss the possibility of entanglement islands in cosmological spacetimes with a general perfect fluid with an equation of state w. We find that flat universes with time-symmetric slices where the Hubble parameter vanishes always have islands on that slice. We then move away from such slices, considering still universes with a general perfect fluid. Under the local thermal equilibrium assumption, the comoving entropy density sc is constant. As a result, the conditions for an island become an inequality between the energy density (or Hubble parameter) and the temperature at some time of normalization. The consequences are that islands can exist for practically all fluids that are not radiation, i.e. w ≠ 1/3. We also discuss the ramifications of our results for universes with spatial curvature. Finally, we show that islands occur in the Simple Harmonic Universe model which has no classical singularity at the background level, in contrast to all previous examples where islands occurred only in space-times with singularities.

Non-equilibrium extension of the explicit algebraic subgrid-scale stress model with application to turbulent channel flow at low Reynolds numbers

An extension of the explicit algebraic subgrid-scale (SGS) stress model (EASSM) of Marstorp et al. [J. Fluid Mech. 639, 403–432 (2009)] is proposed to account for the non-local equilibrium between the production, P, and viscous dissipation, ϵ, of the SGS turbulent kinetic energy in its formulation. The original derivation of the EASSM uses the equilibrium assumption P=ϵ, whereas in the current new derivation, a cubic algebraic equation is extracted for P/ϵ from the modeled transport equation for the SGS stress anisotropy, which can be solved to improve the EASSM predictions with less than 4% additional computational costs per time step. The performance of the extended EASSM is assessed in large-eddy simulation of plane turbulent channel flow at Reτ=587 and 179 for a wide range of resolutions, where deviations from the local equilibrium assumption are expected at the vicinity of the walls. The enhanced EASSM formulation lowers resolution dependence of the model predictions and improves its predictions at low resolutions. The improvements affected major one-point turbulence statistics of interest, such as the wall shear stress, mean velocity, Reynolds stresses, and SGS dissipation as well as the two-point velocity correlations and premultiplied spanwise spectra of the streamwise velocity. The predicted mean P/ϵ also reasonably agrees with the filtered direct numerical simulation data.

The Halo Mass–Temperature Relation for Clusters, Groups, and Galaxies

The halo mass–temperature (M–T) relation for a sample of 216 galaxy clusters, groups, and individual galaxies observed by the Chandra X-ray Observatory is presented. Using accurate spectral measurements of their hot atmospheres, we derive the M–T relation for systems with temperatures ranging between 0.4 and 15.0 keV. We measure the total masses of the clusters, groups, and galaxies at radius R 2500, finding that the M 2500 ∝ T α relation follows a power law with α = 1.65 ± 0.06. Our relation agrees with recent lensing studies of the M–T relation at R 200 and is consistent with self-similar theoretical predictions and recent simulations. This agreement indicates that the M–T relation is weakly affected by nongravitational heating processes. Using lensing masses within R 200 we find M 200–T follows a power law with a slope of 1.61 ± 0.19, consistent with the M 2500–T relation. No evidence for a break or slope change is found in either relation. Potential biases associated with sample selection, evolution, and the assumption of hydrostatic equilibrium that may affect the scaling are examined. No significant impacts attributable to these biases are found. Non-cool-core clusters and early spirals produce higher scatter in the M–T relation than cool-core clusters and elliptical galaxies.

The Temperature Dependent Boltzmann Equation with Reservoir of Radiation Photons

Usually, the temperature is introduced by the Boltzmann distribution function under the local equilibrium assumption. In this manuscript, we propose a temperature dependent Boltzmann equation, where the temperature is taken into account by the collision of transport particles and the particles in the reservoir, and we assume the reservoir remain in an equilibrium or local equilibrium state with an external temperature. Different from the usual Boltzmann equation, our temperature dependent Boltzmann equation obtains a new damping force which originates from the collision between transport particle and reservoir and is contrary to the external force applied to the system, meanwhile the relaxation time is also affected by the derivative of the damping force. In our study, the reservoir are consist of the radiations of photons, so the Compton scattering happens between the transport particle and the photon. Finally, we illustrate them by the example of one-dimensional transport process, the damping force and the non-equilibrium temperature defined by us are shown.

Droplet evaporation in inert gases

A general mixed kinetic-diffusion boundary condition is formulated to account for the out-of-equilibrium kinetics in the Knudsen layer. The mixed boundary condition is used to investigate the problem of quasi-steady evaporation of a droplet in an infinite domain containing inert gases. The widely adopted local thermodynamic equilibrium assumption is found to be the limiting case of infinitely large kinetic Péclet number ${{Pe}_k}$ , and it introduces significant error for ${{Pe}_k} \leqslant O(10)$ , which corresponds to a typical droplet radius $a$ of a few micrometres or smaller. When compared with experimental data, solutions based on the mixed boundary condition, which take into account the temperature jump across the Knudsen layer, better predict the time evolution of $a$ than the classical $D^2$ -law (i.e. $a^2 \propto t$ , where $t$ denotes time). In the slow evaporation limit, an analytical solution is obtained by linearising the full formulation about the equilibrium condition, which shows that the $D^2$ -law can be recovered only in the large ${{Pe}_k}$ limit. For small ${{Pe}_k}$ , where the process is dominated by kinetics, a linear relation, i.e. $a \propto t$ , emerges. When the gas phase density approaches the liquid density (e.g. at high-pressure or low-temperature conditions), the increase in the chemical potential of the liquid phase due to the presence of inert gases needs to be accounted for when formulating the mixed boundary condition, an effect largely ignored in the literature so far.

Study of the 6.x nm short wavelength radiation spectra of laser-produced erbium plasmas for BEUV lithography

Beyond extreme ultraviolet (BEUV) radiation with a wavelength of 6.x nm for lithography is responsible for reducing the source wavelength to enable continued miniaturization of semiconductor devices. In this work, the Required BEUV light at 6.x nm wavelength was generated in dense and hot Nd:YAG laser-produced Er plasmas. The spectral contributions from the 4p–4d and 4d–4f transitions of singly, doubly and triply excited states of Er XXIV–Er XXXII in the BEUV band were calculated using Cowan and the Flexible Atomic Code. It was also found that the radiative transitions between multiply excited states dominate the narrow wavelength window around 6.x nm. Under the assumption of collisional radiative equilibrium of the laser-produced Er plasmas, the relative ion abundance in the experiment was inferred. Using the Boltzmann quantum state energy level distribution and Gram–Charlier fitting function of unresolved transition arrays (UTAs), the synthetic spectrum around 6.x nm was finally obtained and compared with the experimental spectrum. The spatio-temporal distributions of electron density and electron temperature were calculated based on radiation hydrodynamic simulation in order to identify the contributions of various ionic states to the UTAs arising from the Er plasmas near 6.x nm.

First detection of radio recombination lines of ions heavier than helium

We report the first detection of radio recombination lines (RRLs) of ions heavier than helium. In a highly sensitive multi-band (12–50 GHz) line survey toward Orion KL with the TianMa 65-m Radio Telescope (TMRT), we successfully detected more than fifteen unblendedαlines of RRLs of singly ionized species (XII) recombined from XIII. TheKa-band (26–35 GHz) spectrum also shows tentative signals ofβlines of ions. The detected lines can be successfully crossmatched with the rest frequencies of RRLs of C IIand/or O II. This finding greatly expands the scope of our understanding of ion RRLs, since prior to this work, only two blended lines (105αand 121α) of He IIhad been reported. Our detected lines can be fitted simultaneously under assumption of local thermodynamic equilibrium (LTE). An abundance of C IIIand O IIIof 8.8×10−4was obtained, avoiding the complexities of optical and infrared observations and the blending of RRLs of atoms. It is consistent with but approaches the upper bound of the value (10−4–10−3) estimated from optical and infrared observations. The effects of dielectronic recombination may contribute to enhancing the level populations even at largen. We expect future observations using radio interferometers could break the degeneracy between C and O, while also helping to reveal the ionization structure and dynamical evolution of various ionized regions.

Preface

Preface