Statistical Equilibrium Research Articles

Insights into application of novel citric acid modified Saccharum munja biosorbent for facile removal of fuchsin basic dye, crystal violet dye and copper metal ion: statistical modelling, kinetics, thermodynamics and equilibrium studies

Insights into application of novel citric acid modified Saccharum munja biosorbent for facile removal of fuchsin basic dye, crystal violet dye and copper metal ion: statistical modelling, kinetics, thermodynamics and equilibrium studies

Isoscaling properties for neutron-rich fragments in highly asymmetric heavy ion collision systems* *Supported by the National Natural Science Foundation of China (12375123, 11975091) and the Program for Innovative Research Team (in Science and Technology) in University of Henan Province (21IRTSTHN011), China

Traditionally, isoscaling has been interpreted and applied within the framework of the grand canonical ensemble, based on the assumption that fragment production occurs following the attainment of a statistical equilibrium state. However, the influence of the symmetry energy can lead to differences in the neutron and density distribution in neutron-rich nuclei. This in turn may impact the isoscaling parameters (usually denoted by α and β). We examine the isoscaling properties for neutron-rich fragments produced in highly asymmetric systems on inverse kinematics, namely Ca and Ni + Be at 140 MeV per nucleon. We evaluate α and β values and sort them as a function of the neutron excess . The significant differences in α extracted from fragments within different ranges of I emphasize the importance of understanding the dependence of isoscaling parameters on fragments generated in various collision regions. Furthermore, the value for a specific fragment in small size and highly isospin asymmetry systems can serve as a probe to detect the variations in neutron density and proton density in different regions of the nucleus and indicate the limitations of theoretical models in investigating these issues.

Modeling hydraulic conductivity function of frozen soil

Hydraulic conductivity function for frozen soils (HCFF) is crucial for accurately simulating the water transfer process in cold regions, impacting hydrological states and frost heave diseases. However, the HCFF model capturing the relation between hydraulic conductivity and unfrozen water content (θ) or temperature (T) remains an open question. This study delves into HCFF encompassing both empirical and prediction models. This study begins with introducing θ-form and innovative T-form empirical HCFF models, showcasing their solid performance in fitting measured hydraulic conductivity data. Furthermore, the extension of the T-form empirical model to incorporate vapor flow and bimodal soils, through the introduction of maximum vapor conductivity and weighting factors, demonstrates a closer alignment with physical mechanisms and observed trends. In terms of predicting HCFF, the study provides a theoretical foundation through statistical hydraulic conductivity models and thermodynamic equilibrium in frozen soils. Additionally, it clarifies three routes for HCFF prediction—single Soil Freeze Characteristic Curve (SFCC), single Soil Water Characteristic Curve (SWCC), and a combination of the two—and validates their effectiveness through test results and comparison of HCFF prediction outcomes using SWCC and SFCC data from specific soil samples. In practice, the empirical and prediction models are recommended for available hydraulic conductivity data and available SFCC or SWCC data, respectively. Overall, this study not only lays the theoretical groundwork for most prediction models but also presents a valid empirical equation for modeling hydraulic conductivity function tailored specifically for frozen soils.

Collisional effects in modeling solar polarized lines

Context. Rigorous implementation of the effects of collisions in modeling the formation of the polarized solar lines is of utmost importance in order to realistically analyze the available, highly sensitive solar spectropolarimetric observations. Indeed, even when an observation seems to fit well with theory, one can misinterpret results if important effects due to collisions are not correctly implemented in the modeling process. Aims. We point out inconsistencies in the models adopted to implement the Paschen Back effect together with collisional effects on the solar linear polarization formed by scattering of anisotropic radiation. Because the significance of these inconsistencies increases as polarization becomes increasingly responsive to collisions, we investigate the range of hydrogen densities nH to which the polarization is sensitive. Methods. We used the density matrix formalism in the tensorial irreducible basis, which was developed within the theory of atom-radiation interaction and of atomic collisions. We solved the statistical equilibrium equations for multi-level atoms with hyperfine structure (HFS) in order to evaluate the collisional depolarization of levels of the D1-D2 lines of the K I atom. Results. We find that collisions play a prominent role, particularly at hydrogen densities of between 1013 and 1016 cm−3. Conclusions. So far, analyses of polarized lines formed in the presence of solar magnetic field have incorporated, if at all, collisional rates calculated assuming zero magnetic field. This could be a good approximation in the Hanle regime but not in the Paschen Back regime. For typical quiet Sun magnetic fields, the latter regime could be reached, and level-crossing takes place in several atomic systems. Therefore, one must be careful when using collisional rates calculated in the zero-field case to interpret linear polarization formed in magnetized media.

Probabilistic measures for biological adaptation and resilience.

This paper introduces an approach to quantifying ecological resilience in biological systems, particularly focusing on noisy systems responding to episodic disturbances with sudden adaptations. Incorporating concepts from nonequilibrium statistical mechanics, we propose a measure termed "ecological resilience through adaptation," specifically tailored to noisy, forced systems that undergo physiological adaptation in the face of stressful environmental changes. Randomness plays a key role, accounting for model uncertainty and the inherent variability in the dynamical response among components of biological systems. Our measure of resilience is rooted in the probabilistic description of states within these systems and is defined in terms of the dynamics of the ensemble average of a model-specific observable quantifying success or well-being. Our approach utilizes stochastic linear response theory to compute how the expected success of a system, originally in statistical equilibrium, dynamically changes in response to a environmental perturbation and a subsequent adaptation. The resulting mathematical derivations allow for the estimation of resilience in terms of ensemble averages of simulated or experimental data. Finally, through a simple but clear conceptual example, we illustrate how our resilience measure can be interpreted and compared to other existing frameworks in the literature. The methodology is general but inspired by applications in plant systems, with the potential for broader application to complex biological processes.

Photodissociation of CO2 via the 1Πg state: Wavelength-dependent imaging studies of O(1D2) photoproducts.

Photodissociation of CO2 via the 1Πg state is investigated using a time-sliced velocity-mapped ion imaging apparatus combined with a tunable vacuum ultraviolet photolysis source. The main O(1D2) + CO(X1Σ+) channel is directly observed from the measured images of O(1D2) photoproducts at 129.08-134.76nm. The total kinetic energy release spectra determined based on these images show that the energetic thresholds for the O(1D2) + CO(X1Σ+) photoproducts correspond to the thermochemical thresholds for the photodissociation of CO2(v2 = 0) and CO2(v2 = 1). One significant difference among the CO(X1Σ+, v) vibrational distributions for the predominant CO2(v2 = 0) dissociation is that the population of CO(v = 0) becomes favorable at 130.23-133.45nm compared to the Boltzmann-like component (v > 0) that always exists at 129.08-134.76nm. The wavelength dependences of the overall β are found to follow the variation trend of the CO(v = 0) abnormal intensity. The vibrational state-specific β values present a roughly decreasing trend with an increase in v, whereas β(v = 0) appears to be significantly larger than β(v = 1) at 130.23-133.45nm compared to 134.76 and 129.08nm. The non-statistical CO(v = 0) with larger β values at 130.23-133.45nm implies that an additional pathway may open through the conical intersection coupling to the dissociative 21A' state, except for the ever-existing pathway that yields the Boltzmann-like component. In contrast, at 129.08nm, the restoration of the statistical equilibrium in the CO(X1Σ+, v) vibrational distribution may be caused by the emergence of novel dissociation pathways arising from the participation of the 31A″ state.

Reduced Basis modelling of turbulence with well-developed inertial range

In this work, we introduce a Reduced Basis model for turbulence at statistical equilibrium. This is based upon an a-posteriori error estimation procedure that measures the distance from a trial solution to the K41 theory energy spectrum. We apply this general idea to build a Reduced Basis Smagorinsky turbulence model through a Greedy Algorithm. We derive some error estimates that make apparent the role of the energy spectrum in the ROM approximation. We carry on some tests for some academic unsteady 2D flows at large Reynolds number, that present well developed inertial spectrum. The methods presents a high efficiency, as the error achieved with the reduced method is 3 to 4 times the ones achieved if the exact error is used in the Greedy Algorithm.

A physics-informed data-driven algorithm for ensemble forecast of complex turbulent systems

A new ensemble forecast algorithm, named the physics-informed data-driven algorithm with conditional Gaussian statistics (PIDD-CG), is developed to predict the probability density functions (PDFs) of complex turbulent systems with partial observations. The PIDD-CG algorithm integrates a unique multiscale statistical closure modeling strategy with a highly efficient nonlinear data assimilation scheme to create a mixture of conditional statistics. An effective data-driven modeling method is integrated with the dominant conditional statistics to serve as the forecast ensemble members that can significantly reduce the high computational cost of recovering high-dimensional PDFs. The multiscale features in the time evolution of these conditional statistics ensembles are effectively predicted by an appropriate combination of physics-informed analytic formulae and recurrent neural networks. An information metric is adopted as the loss function for the latter to more accurately capture the desirable turbulent features. The proposed algorithm displays effective forecasting performance in both the transient and statistical equilibrium non-Gaussian PDFs of strongly turbulent systems with intermittency, regime switching, and extreme events. It also facilitates the development of efficient statistical reduced-order models in recovering and predicting the large-scale coherent structures of a large group of multiscale complex systems.

Аssessment of the importance of physical qualities in the military physical training of military

Taking into account the current state of modernization of weapons, equipment, improvement of forms and methods of conducting combat operations and comprehensive provision of units of the Ukrainian forces in accordance with NATO standards (world standards), it is urgent to make changes to the existing programs of professional education of future officers, in particular, programs of special physical training. In this work, we conducted a comparative analysis of the assessment of the importance of the physical qualities of military personnel according to physical training and sports instructors and students of participants of professional development courses. 29 physical training and sports instructors and 155 participants of professional development courses of the Vasyl Vyshyvany training center of the National Guard of Ukraine participated in the study. We found that the opinions of physical training and sports instructors and participants of professional development courses were similar for almost all qualities, the differences in the priority of physical qualities were in the time of reaction to a choice, the time of a simple reaction to a visual stimulus, and the ability to maintain statistical equilibrium (р<0.05). A survey of physical training and sports instructors showed that the most important physical qualities for military personnel are the time of a simple reaction to a visual stimulus (4.59±0.74 points), the ability to maintain statistical balance (4.52±0.63 points) and coordination of movements (4.48±0.63 points). For the participants of professional development courses, coordination of movements was the most important (4.34±0.75 points), strength endurance (4.29±0.75 points), speed (4.28±0.84 points) and speed strength (4.28±0.77 points).

Investigation of crack recognition and spatio-temporal evolution pattern in coal samples damage

Understanding the evolution mechanism of cracks helps to evaluate the behavior and performance of rock masses and provides a theoretical basis for the mechanism of crack propagation and instability. For this purpose, a rock mechanics testing system and an acoustic emission monitoring system were used to conduct acoustic emission positioning experiments on coal samples under uniaxial compression. According to clustering theory, the distribution pattern of microcracks and the dynamic evolution process of multiple cracks were studied. Subsequently, the reasons for the change in the spatio-temporal entropy (H) and fractal dimension (D) of a single crack were revealed. The research results show that microcracks present a statistical equilibrium distribution, the Gaussian distribution model is applicable to cluster crack distribution patterns, and a machine learning method can effectively identify cracks. The fractal dimension reflects the spatial characteristics of three-dimensional elliptical cracks, and low-dimensional cluster cracks are more likely to develop into macroscopic cracks. The change of H is related to the formation process of cracks, and an abnormal H (sudden increase and sudden decrease) could provide precursor information for the instability of coal samples. This research provides a new method to study crack distributions and formations and shows the competitiveness of the method in evaluating the damage state of coal.

Methodical support for controlling safety of cereals for children (exemplified by furan and methylfuran)

Introduction. The study addresses issues related to developing a procedure for identification of chemicals in food products in practical instrumental investigations. We have validated the method for quantification of a heterocyclic compound (furan) and sylvan (methylfuran) in grain-based cereals for children.
 The aim of this study was to develop a precise GC-MS-method for quantifying a heterocyclic compound and sylvan in food products to control their safety for children, especially infants.
 Materials and methods. The research objects were quantification means (QM) as a certain amount of an analyzed heterocyclic compound and sylvan (the mass share of the analyzed compound is 99%) provided by Sigma Aldrich Corporation (USA), as well as milk and milk-free dry cereals for babies. The study involved using an Agilent 7890А gas chromatographer with 5975С quadrupole mass-spectrometric detector. Sample preparation involved extraction and concentration of furan and methylfuran from food samples by statistical vapour-liquid equilibrium analysis and subsequent gas-chromatographic analysis of vapour phase.
 Results. The procedure for quantification of furan and methylfuran is an original scientific and technical development based on experimental data. It gives an opportunity to identify furan and methylfuran micro-admixtures in food samples with high precision and sensitivity with a range of concentrations between 0.93 and 9.37 ng and between 0.91 and 9.13 ng accordingly. The ultimate indicators describing acceptability of the results obtained by furan and methylfuran quantification included error not higher than 24%, пintra-laboratory precision (σRл ) not higher than 10%, correctness (± σCл ) not higher than 22%.
 Conclusion. The developed technique has shown high selectivity, sensitivity, reliability and satisfactory accuracy. The methodology meets the criteria of the State Standard of the Russian Federation GOST R ISO 5725-1-6-2002 and can be used for laboratory studies of food safety by enterprises and institutions engaged in quality control and research of food products and food raw materials.

Effects of fracture aperture distribution on the performances of the enhanced geothermal system using supercritical CO2 as working fluid

Enhanced Geothermal Systems (EGS) technology has the potential to be a significant source of clean, renewable energy worldwide. A promising alternative to water as the working fluid in EGS is the supercritical carbon dioxide (scCO2), which simultaneously contributes to reducing the atmospheric greenhouse gas emissions. The existing thermal-hydraulic coupled numerical models for non-isothermal two-phase flow in fractured porous media overlook the fracture aperture distributions, which significantly affects EGS performance. This study employs a discrete fracture model with a normal distribution of fracture apertures to investigate the EGS energy performance and carbon sequestration ability. The Monte Carlo method is applied to ensure the simulation results reach a statistical equilibrium from multiple realizations. Results show that the aperture distribution significantly affects EGS performances. The cumulative energy output and total sequestered scCO2 mass can be roughly divided into three stages based on fracture aperture distributions. On the other hand, the effects of aperture distribution become more important as the increase of mean fracture aperture and the reduction of injection pressures. Furthermore, comparing the performances of the EGS using scCO2 and H2O as working fluid, the study found that scCO2-EGS performs better with larger injection pressure, but it is more sensitive to aperture distribution.

Plasma diagnostics and Alfvén wave heating of solar prominences by multiwavelength observations

Abstract Solar prominences are cool and dense plasma supported by the magnetic field in the solar corona. They are composed of fine-scale structures called threads. Prominences are heated by the incident radiation from the solar atmosphere, but previous studies have shown that additional heating is necessary to maintain the temperature of prominences of about 104 K. This study aims to investigate quantitatively the mechanical heating of the prominences from observations. We performed spectroscopic observations of prominences in Hα (6563 Å), Hβ (4861 Å), and Ca ii IR (8542 Å) with the Domeless Solar Telescope at Hida observatory. The plasma parameters of the prominences are estimated by fittings of line profiles using the single-slab model and by solving the statistical equilibrium equation. By assuming that the turbulent motion is the manifestation of propagating Alfvén waves, net radiative losses and Alfvén wave energy flux in the prominences are estimated from these parameters. As a result, it was found that the energy flux by Alfvén waves is sufficient to compensate for the net radiative losses in most regions of the central part of the prominences. On the other hand, Alfvén wave energy flux tends to be insufficient at the outer part of prominences. In such regions, another heating mechanism such as enthalpy flux of mixing with coronal plasma needs to be considered.

Maximum entropy distributions of dark matter in ΛCDM cosmology

Context. Small-scale challenges to ΛCDM cosmology require a deeper understanding of dark matter physics. Aims. This paper aims to develop the maximum entropy distributions for dark matter particle velocity (denoted by X), speed (denoted by Z), and energy (denoted by E) that are especially relevant on small scales where system approaches full virialization. Methods. For systems involving long-range interactions, a spectrum of halos of different sizes is required to form to maximize system entropy. While the velocity in halos can be Gaussian, the velocity distribution throughout the entire system, involving all halos of different sizes, is non-Gaussian. With the virial theorem for mechanical equilibrium, we applied the maximum entropy principle to the statistical equilibrium of entire system, such that the maximum entropy distribution of velocity (the X distribution) could be analytically derived. The halo mass function was not required in this formulation, but it did indeed result from the maximum entropy. Results. The predicted X distribution involves a shape parameter α and a velocity scale, v0. The shape parameter α reflects the nature of force (α → 0 for long-range force or α → ∞ for short-range force). Therefore, the distribution approaches Laplacian with α → 0 and Gaussian with α → ∞. For an intermediate value of α, the distribution naturally exhibits a Gaussian core for v ≪ v0 and exponential wings for v ≫ v0, as confirmed by N-body simulations. From this distribution, the mean particle energy of all dark matter particles with a given speed, v, follows a parabolic scaling for low speeds (∝v2 for v ≪ v0 in halo core region, i.e., “Newtonian”) and a linear scaling for high speeds (∝v for v ≫ v0 in halo outskirt, i.e., exhibiting “non-Newtonian” behavior due to long-range gravity). We compared our results against N-body simulations and found a good agreement.

The He I 10 830 Å line: Radiative transfer and differential illumination effects

We study the formation of the Stokes profiles of the He I multiplet at 10 830 Å when relaxing two of the approximations that are typically considered in the modeling of this multiplet. Specifically, these are the lack of self-consistent radiation transfer and the assumption of equal illumination of the individual multiplet components. This He I multiplet is among the most important for the diagnostics of the outer solar atmosphere from spectropolarimetric observations, especially in prominences, filaments, and spicules. However, the aptness of these approximations is yet to be assessed, especially in situations where the optical thickness is on the order of one (or greater) and the radiation transfer has a significant impact in the local anisotropy as well as the ensuing spectral line polarization. This issue becomes particularly relevant in the ongoing development of new inversion tools that take into account multi-dimensional radiation transfer effects. To relax these approximations, we generalized the multi-term equations for the atomic statistical equilibrium to allow for a differential illumination of the multiplet components and implement them in a one-dimensional (1D) radiative transfer code. We find that even for this simple geometry and relatively small optical thickness, both radiation transfer and differential illumination effects have a significant impact on the emergent polarization profiles. These effects should be taken into account in order to avoid potentially significant errors when inferring the magnetic field vector.

Tracer Particles for Core-collapse Supernova Nucleosynthesis: The Advantages of Moving Backward

After decades, the theoretical study of core-collapse supernova explosions is moving from parameterized, spherically symmetric models to increasingly realistic multidimensional simulations. However, obtaining nucleosynthesis yields based on such multidimensional core-collapse supernova simulations is not straightforward. Frequently, tracer particles are employed. Tracer particles may be tracked in situ during the simulation, but often they are reconstructed in a post-processing step based on the information saved during the hydrodynamic simulation. Reconstruction can be done in a number of ways, and here we compare the approaches of backward and forward integration of the equations of motion to the results based on inline particle trajectories. We find that both methods agree reasonably well with the inline results for isotopes for which a large number of particles contribute. However, for rarer isotopes that are produced only by a small number of particle trajectories, deviations can be large. For our setup, we find that backward integration leads to better agreement with the inline particles by more accurately reproducing the conditions following freeze-out from nuclear statistical equilibrium, because the establishment of nuclear statistical equilibrium erases the need for detailed trajectories at earlier times. Based on our results, if inline tracers are unavailable, we recommend backward reconstruction to the point when nuclear statistical equilibrium was last applied, with an interval between simulation snapshots of at most 1 ms for nucleosynthesis post-processing.

Modeling of Particle Size Distributions in Industrial Poly(vinyl chloride) Suspension Polymerization Reactors

In the present paper, a mathematical model is built and implemented to describe the trajectories of mass inventories, pressures and polymer properties with emphasis on final particle size distributions of industrial scale poly(vinyl chloride) suspension polymerization reactors. The model comprises the mass balances, statistical moment balances, equilibrium relationships and population balance equations. A discretization scheme is employed to transform the integro-differential equations resulting from the population balance model into a system of differential equations. The obtained results show, for the first time, that classical breakage and coalescence kernels described in the literature can provide very good fittings of actual industrial scale data when coupled with proper parameter estimation procedures, so that the proposed model is able to represent the available operation data with good accuracy at distinct conditions. Particularly, it is also shown that the use of a top condenser for control of the reactor temperature can lead to changes of parameters that control the particle size distributions.

Comparison of chromospheric diagnostics in a 3D model atmosphere

Context. The Hα line, one of the most studied chromospheric diagnostics, is a tracer of magnetic field structures, while the intensity of its line core provides an estimate of the mass density. The interpretation of Hα observations is complicated by deviations from local thermodynamic equilibrium (LTE) or instantaneous statistical equilibrium conditions. Meanwhile, millimetre (mm) continuum radiation is formed in LTE, and therefore the brightness temperatures from Atacama Large Millimetre-submillimetre Array (ALMA) observations provide a complementary view of the activity and the thermal structure of stellar atmospheres. These two diagnostics together can provide insights into the physical properties of stellar atmospheres, such as their temperature stratification, magnetic structures, and mass density distribution. Aims. In this paper, we present a comparative study between synthetic continuum brightness temperature maps at mm wavelengths (0.3 mm to 8.5 mm) and the width of the Hα 6565 Å line. Methods. We used the 3D radiative-transfer codes Multi3D and Advanced Radiative Transfer (ART) to calculate synthetic spectra for the Hα line and the mm continua, respectively, from an enhanced network atmosphere model with non-equilibrium hydrogen ionisation generated with the state-of-the-art 3D radiation magnetohydrodynamics (rMHD) code Bifrost. We use a Gaussian point spread function (PSF) to simulate the effect of ALMA’s limited spatial resolution and calculate the Hα versus mm continuum correlations and slopes of scatter plots for the original and degraded resolution of the whole box, quiet sun, and enhanced network patches separately. Results. The Hα linewidth and mm brightness temperatures are highly correlated and the correlation is highest at a wavelength of 0.8 mm, that is, in ALMA Band 7. The correlation systematically increases with decreasing resolution. On the other hand, the slopes decrease with increasing wavelength. The degradation of resolution does not have a significant impact on the calculated slopes. Conclusions. With decreasing spatial resolution, the standard deviations of the observables, Hα linewidth, and brightness temperatures decrease and the correlations between them increase, but the slopes do not change significantly. These relations may therefore prove useful in calibrating the mm continuum maps observed with ALMA.

AXIOMATIC PRINCIPLES AND DETAILED BALANCE

This article presents an analysis of scientific papers and research on axiomatic principles and detailed balance, we are convinced that even today, in accordance with modern requirements, there is still a need to address axiomatic principles and detailed balance, methods and methods for their study. As mentioned earlier, the axiomatics of statistical physics is reduced to the principle of equal probability of the existence of an equilibrium closed physical system in all microstates accessible to it. This postulate, in turn, suggests that the time-averaged probability of the direct and reverse transition of the system between two selected groups of microstates in the accessible region of the phase space must be the same in both directions (this follows from the definition of an equilibrium state, which contains the requirement of stationarity). In fairness, it should be noted that the principle of detailed balance is not a consequence of the axiomatic principles of statistical physics, and therefore, strictly speaking, is not required to be applied within the framework of this axiomatics. There are situations and outcomes we have given in this article, when the principle of equal probability of available microstates in a closed system is satisfied, but the principle of detailed statistical equilibrium is not.

Fermi gas and modified gravity

We derive the equations of state of Fermi gas by maximizing the Fermi-Dirac entropy in modified gravity in relativistic and non-relativistic case. It will be demonstrated that the microphysics must depend on a given theory of gravity in order to consistently describe a physical system at a statistical equilibrium state.