Present Model Research Articles

A full operating conditions ejector model for refrigeration systems driven by low-grade heat sources

The ejector refrigeration technology driven by low-grade heat sources constitutes as one of the crucial means to solve the energy shortage in present-day society and to reduce the global environmental pollution. Thermodynamics ejector models are the basis of performance prediction, system control and structural design in ejector refrigeration systems driven by low-grade heat sources. However, the majority of present ejector models are unable to simultaneously meet the general feasibility of full operating conditions and the level of prediction accuracy for improving the energy efficiency of the refrigeration system. In this study, a novel theoretical model of ejectors is successfully derived based on the foundation of compound-choking theory and gas dynamic relations, which easily predicts the entrainment performance under the on-design and off-design conditions in ejector refrigeration systems. Indeed, a direct solution algorithm is presented to quickly and accurately solve this model and a linear correlation is employed between the mixing loss coefficient and the back pressure at the subcritical mode. The developed model is verified with experimental results in R245fa, R134a and R600a ejector refrigeration system. The results show that the model provides a precise estimation of the entrainment performance with the mean relative errors of 2.45%, 5.49% and 3.67% for R245fa, R134a and R600a refrigerants at full working conditions, while the prediction of critical condensing temperatures is considerably approximated by the experimental measurements. In the comparative analysis with the previous model, this model demonstrates a superior prediction performance, especially in the subcritical mode using the linear function mixing loss coefficient. This study will be a valuable aid in the improvement of energy efficiency in ejector refrigeration systems.

Stability of plane parallel flow revisited for particle-fluid suspensions

Abstract An alternative model is proposed for hydrodynamic stability of plane parallel flow of an incompressible Newtonian fluids with suspended solid particles. For heavy particle-laden dusty gases with negligible particle volume fraction, the effective complex-form mean velocity in the modified Orr-Sommerfeld equation derived by the present model is showed to be essentially identical to the well-known Saffman's classical results. In the limit cases of small or large Stokes number of particles, simple formulas are derived for the effective Reynolds number ratio of the particle-laden suspension to the clear fluid without particles under otherwise identical conditions. The derived formula for particles of finite particle-to-fluid density ratio and small Stokes number is verified by comparing predicted results with known data, although a comparison of the derived formula with known results for particles of finite density ratio and large Stokes number cannot be made here due to the lack of available data. It is hoped that the present work could offer a conceptually novel and relatively simplified model for hydrodynamics of solid particle-fluid suspensions.

UNVEILING THE INFLUENCE OF ONE-LEG STANCE AND STANDING UP FROM A CHAIR ON HUMAN HIP JOINT PROSTHESIS USING FINITE ELEMENT CONCEPTS

The hip joint plays an important role in providing stability to the human body. Factors such as aging, wear, and tear, make the hip joint degenerate and, in such cases, the same to be replaced through hip arthroplasty surgeries. The background of this study aims to investigate the contact consequence between the artificial femoral head and the acetabular cup for different bearing couples during one-leg stance and standing up from a chair, utilizing the finite element method. The three-dimensional finite dynamic contact model has been developed with different material combinations. The results obtained by the present finite element model align well with the previously available literature. The parameters investigated include maximum von Mises stress, maximum contact pressure and deformation for different material combinations. The results reveal that the pair i.e., Alumina on Ultra-high molecular weight polyethylene (UHMWPE) exhibits lower contact pressure, von Mises Stress and deformation. Therefore, the material pair i.e., Alumina on UHMWPE can be employed in the Total hip replacement (THR) to mitigate contact consequences under both static and dynamic loading conditions, thereby enhancing the durability of the artificial joints.

Performance Correction and Parameters Identification Considering Non-Uniform Electric Field in Cantilevered Piezoelectric Energy Harvesters

In the current electromechanical model of cantilevered piezoelectric energy harvesters, the assumption of uniform electric field strength within the piezoelectric layer is commonly made. This uniform electric field assumption seems reasonable since the piezoelectric layer looks like a parallel-plate capacitor. However, for a piezoelectric bender, the strain distribution along the thickness direction is not uniform, which means the internal electric field generated by the spontaneous polarization cannot be uniform. In the present study, a non-uniform electric field in the piezoelectric layer is resolved using electrostatic equilibrium equations. Based on these, the traditional distributed parameter electromechanical model is corrected and simplified to a practical single mode one. Compared with a traditional model adopting a uniform electric field, the bending stiffness term involved in the electromechanical governing equations is explicitly corrected. Through comparisons of predicted power output with two-dimensional finite element analysis, the results show that the present model can better predict the power output performance compared with the traditional model. It is found that the relative corrections to traditional model have nothing to do with the absolute dimensions of the harvesters, but only relate to three dimensionless parameters, i.e., the ratio of the elastic layer’s to the piezoelectric layer’s thickness; the ratio of the elastic modulus of the elastic layer to the piezoelectric layer; and the piezoelectric materials’ electromechanical coupling coefficient squared, . It is also found that the upper-limit relative corrections are only related to , i.e., the higher is, the larger the upper-limit relative corrections will be. For a PZT-5 unimorph harvester, the relative corrections of bending stiffness and corresponding resonant frequency are up to 17.8% and 8.5%, respectively. An inverse problem to identify the material parameters based on experimentally obtained power output performance is also investigated. The results show that the accuracy of material parameters identification is improved when considering a non-uniform electric field.

Study on the mixed lubrication of rough planar extrusion considering surface texture

Surface texture plays a crucial role in fluid dynamic lubrication. The non-Newtonian thermal elastohydrodynamic lubrication problem involving rough surfaces with texture has not been investigated to date. In this paper, a model for non-Newtonian thermal elastohydrodynamic lubrication incorporating rough surfaces and texture morphology is developed, focusing on the problem of mixed lubrication in planar extrusion with texture. The model builds upon the Reynolds equation with flow factor introduced. It considers the effects of rough surface texture, thermal effects, and non-Newtonian effects. The Reynolds equation is numerically solved using the Semi-System method to calculate the oil film pressure in full film region and contact pressure in dry contact area. The DC-FFT algorithm is employed to calculate surface elastic deformation. Comparing the calculated friction coefficient of the present model with the measured values in literature experiments, the average error is only 6.94%. Furthermore, the study investigates the effects of texture, temperature, and non-Newtonian on interfacial lubrication performance under mixed lubrication conditions. It’s found that compared to untextured surface, the average film thickness of textured surface increased by a maximum of 10.8%, and the friction coefficient decreased by a maximum of 67.4%; Compared to Newtonian fluids, shear thinning fluids reduce temperature by 0.18%, and shear thickening fluids are more conducive to improving mixed lubrication performance. A stepped pit texture is designed based on the dynamic pressure mechanism of the texture, indicating that the circular stepped pit texture has the best load-bearing capacity improvement.

Study of Magnetization Variation in Magnetic Nanomaterials Having Wide Applications in Making Anti-Corrosion Coatings Using Qualitative Approach

Nanostructured magnetic nanoparticles and nanocomposites possess exceptional properties and serve and act as an interface between physics and engineering. Innovations in nano-scale material science can be utilized to solve the issue of marine biofouling by creating anti-corrosion coatings that are not harmful to wildlife and the environment. In this paper, the author has studied the impact of size, dimension, and shape on the Saturation magnetisation of magnetic nanomaterials having wide applications using a qualitative model. It is known that Curie temperature and saturation magnetisation of magnetic materials are linearly related and also the Curie temperature varies linearly with melting temperature. A qualitative model is proposed in the present study extending the relation between Curie temperature and Saturation magnetisation to study the size and shape effect on magnetisation (MS) in nano solids. The nanomaterials considered to study the size and shape impact on Saturation magnetisation with size are Fe, Ni, Co, Fe3O4, MnFe2O4, and CoFe2O4.The Saturation magnetisation is found to reduce with size reduction at nano level due to the drastic increase in the surface area to volume ratio in nano solids with size reduction to nanoregime. The results obtained using the model are compared with the available experimental data. The variation in magnetisation is studied for shapes viz. nanowires, thin films, spherical, tetrahedral, octahedral, dodecahedral and icosahedral nanosolids. A good consistency is obtained between the present model results and the experimental results available that justify the validity of the model proposed.

Settling velocity characteristics of inertial particles in turbulent and wave-induced environments

In the present study, a theoretical model is proposed to calculate the settling velocity of solid particles in turbulence generated by both oscillatory and nearly horizontal flow motions. In contrast to other previous models that typically compartmentalize two flow conditions in their studies, this study takes a more comprehensive approach by considering the combined effects of both conditions. Taking into account the influence of drag nonlinearity, virtual mass and Basset history forces, the new theoretical model is formulated. The proposed model is obtained by solving the particle motion in fluid flow under some reasonable assumptions. Accordingly, we obtain a new dimensionless term to better take into account the effect of turbulence anisotropy on the settling velocity and the role of the sediment damping coefficient. Application of this term for other conditions is discussed in the paper. The present model shows satisfactory agreement with a wide range of experimental and numerical data and with different flow conditions found in the existing literature. These data include homogeneous isotropic turbulence with high resolution direct numerical simulations (DNS), turbulent open channel and vertical oscillation.

A new mechanistic model to predict liquid loading in inclined natural gas wells

Accurately predicting the critical gas velocity and inclination angle is crucial for gas field development. However, the mechanism of liquid loading remains elusive due to insufficient attention given to the multivaluedness of flow structures and phase non-uniformity. This paper theoretically studied the flow pattern and gas-liquid configuration in wellbore based on the minimum energy principle. The Kelvin-Helmholtz instability of liquid film was analyzed, and a new correlation for the interfacial friction factor was proposed based on wave properties. The results indicated that the flow pattern transitioned from stratified to annular flow as the inclination angle increased. The gas-liquid interface presented a curved shape, with the interface curvature being influenced by various factors such as fluid properties, tube diameter, inclination angle, and gas and liquid velocities. As the inclination angle increases, the critical gas velocity first increases and then decreases, reaching a peak between 44° and 59°, aligning well with experimental and conventional results. Larger tube diameter, higher liquid density, and viscosity result in a higher critical gas velocity. Waves are more prone to develop in inclined pipes, and capillary waves can break up liquid film due to instability, leading to a discontinuous flow in inclined tubes. Film instability is exacerbated by a smaller diameter, higher liquid holdup, or greater inclination angle. Finally, a new model was devised to predict liquid loading in inclined natural gas wells, demonstrating better performance than existing models. In practice, the present model can achieve real-time prediction of critical gas velocity and continuously monitor the location of liquid accumulation in gas wells over the lifespan.

Three-dimensional simulation of a proton exchange membrane fuel cell with non-integrated metal foam as flow distributor

In proton exchange membrane fuel cells (PEMFCs), the presence of metal foam in the flow channels improves the polarity diagram and increases the cell generated power, but this leads to an increase in pressure drop and, as a result, an increase in parasitic power. In this study, two types of non-integrated arrangements of metal foam are introduced, which, in addition to having high generated power, have lower pressure drop, and subsequently, lower parasitic power, and will also result in a more uniform distribution of temperature and current density. In the first arrangement, which is called IPTG, an abbreviation of Increased Porosity Toward the gas diffusion layer (GDL), the channels are divided into four equal parts with variable porosities from 0.65 to 0.95, in such a way that the metal foam layer with the highest porosity (0.95) is located in the closest area to the GDL. In the second arrangement which is called Reduced Porosity Toward the GDL, the metal foam layer with the least porosity (0.65) is located in the closest area to the GDL. To make a better comparison between the present model and the conventional one, the net power parameter with subtracting parasitic power from generated electrical power of the fuel cell is calculated for all models. The numerical study of this paper is conducted by developing a three-dimensional computational fluid dynamics model by employing user-defined functions. The results show that the net power of the PEMFC with IPTG arrangement is 3.8 % higher than that of the one with integrated metal foam arrangement with a porosity of 0.95. Also, the higher the pores per inch (PPI) of metal foam used in the non-integrated metal foam model, the greater the net power of the fuel cell, so that, the net power of PEMFC with IPTG arrangement with PPI=80 is 3.2 % more than that of PPI=20.

Performance assessment of firefighter protective clothing under different thermal environments: Impact of the variation of thickness in inter-layer airgap and microclimate

Personal protective equipment for firefighters can effectively prevent skin burns and ensure firefighters' safety. Considering a variety of fire environments faced by a firefighter, the present study is devoted to showing the role of the inter-layer fabric airgap and its variation in thickness on skin burns under high intensity heat flux. The present numerical model is formulated by considering a coupled conduction and radiation heat interaction in the porous fabric medium and the Pennes bioheat transfer model for the multi-layered skin. The study considers the effect of variation in airgap thickness, variation in heat transfer coefficient, and duration of exposure on the thermal damage of the firefighter's skin subjected to different harsh thermal environments. The results found that increasing the thickness of AG1 and AG2 does not yield a significant impact during the exposure time. Conversely, AG3 and AG4 lead to considerable temperature reductions at the basal layer, with AG3 causing a decrease of 2.6 °C to 2.9 °C and AG4 causing a decrease of 11.9 °C to 17.0 °C under all exposure conditions. Additionally, when the heat transfer coefficient increases during post-exposure, temperature drops of 9.17 °C to 10.72 °C, 9.81 °C to 11.46 °C, 10.0 °C to 11.64 °C, and 8.68 °C to 10.07 °C are observed for AG1, AG2, AG3, and AG4, respectively, across all exposure conditions. However, both the airgaps have a substantial effect on thermal protection during the post exposure period. In addition, the nature of the variation of stored and transmitted energy in fabric assembly shows an opposite trend during both the exposure and post exposure period in contrast to the third and fourth airgaps for all the considered thermal environments.

Modeling of the fracture behaviors of concrete using 3D discrete element method with softening effect

Understanding the fracture mechanism of concrete is very important for the safety design of concrete structures. We develop a 3D discrete element model with softening effect to study the fracture behaviors of quasi-brittle materials. The basic ideas of our model inspired from the flat-joint concept and the cohesive crack model are implemented in the framework of MUSEN, which is an open source discrete element software with CPU–GPU accelerating computation. The placement-package-compaction method is proposed together with laser scanning technology to construct the meso-scale geometric model of concrete. The meso-parameters of 3D discrete element model developed are calibrated by uniaxial compression and splitting tension tests of concrete. The validation of the present model is verified by the laboratory test of concrete. Compared with the results predicted by the flat-joint model, the F-CMOD curves and fracture parameters simulated by our model are in good agreement with that of the laboratory tests of concrete. Finally, it is concluded that the fracture strain of bond significantly affects the fracture behavior but the softening mode does not. It is found that the linear one is better choice among three softening modes in the present model.

Grids of stellar models with rotation. VIII. Models from 1.7 to 500 M⊙ at metallicity Z = 10-5

Grids of stellar evolution models with rotation using the Geneva stellar evolution code ( Genec ) have been published for a wide range of metallicities. We introduce the last remaining grid of Genec models, with a metallicity of $Z=10^ $. We study the impact of this extremely metal-poor initial composition on various aspects of stellar evolution, and compare it to the results from previous grids at other metallicities. We provide electronic tables that can be used to interpolate between stellar evolution tracks and for population synthesis. Using the same physics as in the previous papers of this series, we computed a grid of stellar evolution models with Genec spanning masses between 1.7 and 500\,$M_ with and without rotation, at a metallicity of Due to the extremely low metallicity of the models, mass-loss processes are negligible for all except the most massive stars. For most properties (such as evolutionary tracks in the Hertzsprung-Russell diagram, lifetimes, and final fates), the present models fit neatly between those previously computed at surrounding metallicities. However, specific to this metallicity is the very large production of primary nitrogen in moderately rotating stars, which is linked to the interplay between the hydrogen- and helium-burning regions. The stars in the present grid are interesting candidates as sources of nitrogen-enrichment in the early Universe. Indeed, they may have formed very early on from material previously enriched by the massive short-lived Population III stars, and as such constitute a very important piece in the puzzle that is the history of the Universe.

An innovative design and metrological testing to evaluate the performance of UV phototherapy devices

Narrowband UVB is the main type of light used to treat various dermatological conditions by administering appropriate doses. In this study, a new design was developed for an open-plan phototherapy device and assessed whether this could improve uniformity and deliver a higher dose, thus reducing treatment times. On the other hand, the uniformity and irradiation dose of a current model of (UV) phototherapy device were investigated. A simulation software was used to present the comparison of the simulated irradiation measurements and uniformity estimation for both the present device and the proposed device. In comparison to a present model of UV therapy device measurements, the results showed that the suggested (UV) phototherapy design device increased the irradiation dose value by 10%, improved the uniformity by 9.3%, and consequently reducing the exposure time by 13%. On the other hand, for both the current (UV) phototherapy equipment and the suggested design device, the irradiation loss value resulting from any UV lamp inefficiency was also calculated. The current model device’s loss value percentage was 15%, however, the loss value of the suggested design for the UV phototherapy device was between 3 and 4%. Based on the results discussed throughout the paper, the findings indicate that the suggested design is promising for UV phototherapy applications.

Travels with BERT: Surfacing the intertextuality in Hans Christian Andersen's travel writing and fairy tales through the network lens of large language model‐based topic modeling

AbstractHans Christian Andersen's fairy tales have garnered the greatest popular and scholarly attention despite the interdependence of works across the broad range of his artistic production. We read Andersen's fairy tales in concert with his travel writing to highlight the intertextual aspects that cross these seemingly distinct genres. We leverage recent advances in large language models (LLM) and network theory to generate representations that facilitate user exploration of these intertextual interdependencies across genres and across time. In the first part of our study, we use BERTopic and an LLM model fine‐tuned for nineteenth‐century Danish literary language to present independent and combined topic models of the two corpuses. This approach supports multi‐scalar analysis of intertextual elements within and across these corpuses, thereby implementing a method for macroscopic reading. In the second part of the study, we develop a series of networked representations of the dependencies between fairy tales, where these dependencies are generated on the basis of the shared intertextual topic space of the fairy tales and the travel writing.

A Simple Model for the Pauli Repulsion with Possible Utility in QM, MM and Chemical Education.

The Pauli repulsion is the intermolecular force responsible for the volume and low compressibility of condensed-phase matter at normal conditions. A simple model for this force is presented, wherein per-atom electron densities are represented as spherical charge distributions that are prevented from significantly overlapping. In the example of two noble gas atoms approaching one another beyond their van der Waals radii, the distance between the centers of the electronic charge distributions becomes larger than the distance between the nuclei, giving rise to an unfavorable electrostatic interaction. For the purpose of calculating this interaction, the model is further simplified by representing the per-atom electron density as a negative point charge, loosely inspired by the classical Drude oscillator. The dispersion interaction is simplified to an R-6 term, centered on the aforementioned point charges. Despite the gross simplicity of the resulting formalism, near-quantitative agreement with high-level QM interaction energies of noble gas dimers is achieved. Accordingly, the present model is thought to have utility in force fields, in post-HF and post-DFT dispersion corrections, and in chemical education.

Mouse Model of Parkinson's Disease with Bilateral Dorsal Striatum Lesion with 6-Hydroxydopamine Exhibits Cognitive Apathy-like Behavior.

Among the symptoms of Parkinson's disease (PD), apathy comprises a set of behavioral, affective, and cognitive features that can be classified into several subtypes. However, the pathophysiology and brain regions that are involved in these different apathy subtypes are still poorly characterized. We examined which subtype of apathy is elicited in a mouse model of PD with 6-hydroxydopamine (6-OHDA) lesions and the behavioral symptoms that are exhibited. Male C57/BL6J mice were allocated to sham (n = 8) and 6-OHDA (n = 13) groups and locally injected with saline or 4 µg 6-OHDA bilaterally in the dorsal striatum. We then conducted motor performance tests and apathy-related behavioral experiments. We then pathologically evaluated tyrosine hydroxylase (TH) immunostaining. The 6-OHDA group exhibited significant impairments in motor function. In the behavioral tests of apathy, significant differences were observed between the sham and 6-OHDA groups in the hole-board test and novelty-suppressed feeding test. The 6-OHDA group exhibited impairments in inanimate novel object preference, whereas social preference was maintained in the three-chamber test. The number of TH+ pixels in the caudate putamen and substantia nigra compacta was significantly reduced in the 6-OHDA group. The present mouse model of PD predominantly showed dorsal striatum dopaminergic neuronal loss and a decrease in novelty seeking as a symptom that is related to the cognitive apathy component.

Modeling Plutonium Decorporation in a Female Nuclear Worker Treated with Ca-DTPA after Inhalation Intake.

The present work models plutonium (Pu) biokinetics in a female former nuclear worker. Her bioassay measurements are available at the US Transuranium and Uranium Registries. The worker was internally exposed to a plutonium-americium mixture via acute inhalation at a nuclear weapons facility. She was medically treated with injections of 1 g Ca-DTPA on days 0, 5, and 14 after the intake. Between days 0 and 20, fecal and urine samples were collected and analyzed for 239Pu and 241Am. Subsequently, she was followed up for bioassay monitoring over 14 y, with additional post-treatment urine samples collected and analyzed for 239Pu. The uniqueness of this dataset is due to the availability of: (1) both early and long-term bioassay data from a female with plutonium intake; (2) data on chelation therapy for a female; and (3) fecal measurement results. Chelation therapy with Ca- and/or Zn-salts of DTPA is known to aid in reducing the internal radiation dose by enhancing the excretion of plutonium and americium from the body. Such enhancement affects plutonium biokinetics in the human body, posing a challenge to the internal dose assessment. The current radiation dose assessment practice is to exclude the data affected by Ca-DTPA from the analysis. The present analysis is the first to explicitly model the chelation-affected bioassay data in a female by using a newly developed chelation model. Thus, the bioassay data collected during and after the Ca-DTPA administrations were used for biokinetic modeling and dose assessment. The Markov Chain Monte Carlo method was used to investigate model parameter uncertainty, based on the bioassay data and assumed prior probability distributions. A χ2/nData (number of data points) ≈ 1 was observed in this study, which indicates self-consistency of the data with the model. Results of this study show that the worker's 239Pu intake was 12 Bq, with a committed effective dose to the whole-body of 1.2 mSv and a committed equivalent dose to the bone surfaces, liver, and lungs of 37.8, 9.1, and 0.8 mSv, respectively. This study also discusses the worker's dose reduction due to chelation treatment.

Computational modeling of cell motility and clusters formation in enzyme-sensitive hydrogels

AbstractIn this paper, we propose an extension of a previous model of cell motility in tissue engineering applications recently developed by the authors. Achieving large-scale production of neo-tissue through biofabrication technologies remains challenging owing to the need of thoroughly optimizing all the relevant process variables, a task hardly attainable through solely trial and error approaches. Therefore, the present work is intended to provide a valid and effective computational-based support for neo-tissue formation, with a specific focus on the preliminary phase of such process, in which cells move through a polymeric scaffold (hydrogel) and then compact into clusters. Cell motility is modeled by resorting to the phase-field method, and by incorporating diffusion of nutrients from the external culture bath as well as the expression by cells of chemoattractant substances that bias the random path they otherwise would follow. The previous model has been enriched by additionally encompassing the secretion of enzymes by cells that cleave the crosslinks between the hydrogel polymer chains. As such, in the present model hydrogel degradation exhibits spatio-temporal variations in its chemo-physical properties related to the local amount of enzymes, which deeply affects cell motility. Numerical results showcase the pivotal importance of the cells micro-environment properties for their crawling in hydrogel scaffolds, opening towards the development of a predictive computational-aided optimization tool for neo-tissue growth in bioprinted scaffolds.

Modelling of evaporative falling-film heat transfer over a horizontal tube

This article focuses on evaporative falling film heat transfer through numerical simulations. A two-dimensional symmetric liquid film flowing outside a single horizontal tube was simulated using the open-source CFD software OpenFOAM. The Tanasawa model was employed to consider mass transfer at the liquid–vapour interface, and the isoAdvector VOF method was used for interface tracking. The simulations explored the impact of film flow rate, tube surface heat flux, and tube diameter on the liquid film thickness and surface heat transfer coefficient. Additionally, the critical heat flux and operational limits were considered. The results demonstrate the accurate reproduction of evaporative falling film heat transfer performance by the present model. The film thickness exhibits a similar profile to adiabatic and sensible falling film heat transfer but provides smaller values. Similarly, the evaporative heat transfer coefficient exhibits significantly higher values and a gentle peripheral variation. The influence of heat flux on evaporative falling film heat transfer is contingent on the film flow rate; it can either enhance or weaken the process. Notably, a larger tube diameter negatively affects heat transfer, suppressing the impact of heat flux, and also increases the risk of liquid film dryout. For a given film flow rate, the average heat transfer coefficient increases initially, reaches a maximum value, and then decreases as the wall heat flux is increased. The peak heat flux, termed critical heat flux, increases with film flow rate but decreases with tube diameter. An operational limit exists where the heat flux is lower than the critical heat flux and the film flow rate is higher than the critical film flow rate; under these conditions, evaporative falling film heat transfer operates in a fully wetting status.

Thermal pairing treatment within the path integral formalism

Abstract A method for the treatment of the pairing correlations at finite temperature is proposed within the path integral formalism. It is based on the square root extraction of the pairing term in the Hamiltonian of the system. Gap equations, as well as expressions of the pairing gap parameter Δ, the energy E and the heat capacity C are established. The formalism is first tested using the Richardson model which enables comparison with exact solution. The results obtained using the present formalism are also compared to the Finite Temperature BCS (FTBCS) ones. An improvement compared to the FTBCS model is noted especially at low temperature. Indeed, it is shown that the agreement between the Δ values of the present work and the exact ones is very good at low temperature. This leads to a better agreement between the values of E and C of the present model and the exact values than with the FTBCS values. However, a critical value of the temperature still exists.
Realistic cases are then considered using single-particle energies of a deformed Woods-Saxon mean-field for the nuclei ¹⁶²Dy and ¹⁷²Yb. It is shown that in the framework of the present approach, the pairing effects persist beyond the FTBCS critical temperature. Moreover, at low temperature, a good agreement between the present model results and semiexperimental values of the heat capacity is observed. A clear improvement compared to the FTBCS method is noted. It is no more the case at higher temperature.