Diffusion Cross Research Articles

Representative deflection angle for the single-deflection method of direct simulation Monte Carlo.

The total cross sectionof binary collision is, in general, unbounded due to the long-range interations of molecules. It is conventional to truncate the small angle deflections of collisions. The present work suggests an alternative way of avoiding the difficulty of unboundedness. We employ the mean value theorem of definite integral over the deflection angle for the cross section. A series of numerical experiments were carried out to look for the representative collision cross sectionthrough which the single-angle simulation is amenable to the solution of the Boltzmann equation. Results show that the cross sectionshould be 〈Σ〉=Σ_{D}^{2}/(2Σ_{D}-Σ_{μ}), and the representative deflection for the single-angle simulation be cos〈χ〉=Σ_{μ}/Σ_{D}-1, where Σ_{D} is the diffusion cross sectionand Σ_{μ} is the viscosity cross section. The single-angle computations for the inverse power law and the Lennard-Jones force law perfectly reproduce the conventional scattering algorithms for one-dimensional (1D) simulations of transport coefficients and 1D shock thickness. The computation costs for Lennard-Jones molecules are comparable to the costs for inverse power-law models.

Cold collisions between alkali metals and alkaline-earth metals in the heteronuclear atom-ion system Li+Ba+

In a recent experiment [P. Weckesser et al., Nature (London) 600, 429 (2021)], the quantum $s$-wave regime was attained for an alkali-metal and alkaline-earth atom-ion combination $({\mathrm{LiBa}}^{+})$. We investigate possible outcomes from the interaction of this ion-atom pair at quantum regimes from a theoretical point of view. For this purpose, Born-Oppenheimer potential energy surfaces are constructed for the three lowest dissociation channels of the ${(\mathrm{Ba}\text{\ensuremath{-}}\mathrm{Li})}^{+}$ molecular system using a multireference configuration interaction electronic-structure calculation. We present elastic, spin-exchange (SE), and diffusion cross sections in different energy regimes. The collisional properties of this system are calculated in terms of the scattering phase shifts and scattering cross sections, and the semiclassical behavior at a relatively high energy limit is also examined. For SE collisions, phase locking is obtained towards lower partial waves.

Gas Diffusion Characteristics and Size Effect in Coal Particles with Different Degrees of Metamorphism

Coalbed methane (CBM) is a green unconventional energy source where the gas diffusion efficiency in coal directly limits the production capacity. Therefore, different gas adsorption experiments were used to determine the diffusion characteristics of coal samples with varying degrees of metamorphism. The influence law based on the gas type, pore structure, and coal sample size on the gas diffusion coefficient was analyzed, and the synergistic control effect of various factors on diffusion was discussed. The results show that when the particle size is the same, the diffusion coefficient of different gases shows the change rule of CO2 > N2 > CH4, and the diffusion coefficient of different samples is positively correlated with the degree of pore development. When the particle size is different, the diffusion coefficient is negatively correlated with the pore development degree and positively correlated with the sample particle size. The effective diffusion coefficient is consistent with the diffusion coefficient when the particle size of the sample is the same, and the effective diffusion coefficient is opposite to the diffusion coefficient when the particle size decreases. The analysis reveals that the diffusion coefficients of different gas are limited by the diameter of gas molecular dynamics, and the diffusion coefficient is reduced with the decrease in the diameter of the gas molecular dynamics. The change of diffusion coefficient caused by particle size change is positively correlated with the change of diffusion cross section caused by size effect. The difference between the effective diffusion coefficient and the diffusion coefficient mainly comes from whether the effective diffusion path is calculated. Therefore, when the particle size is constant, the effective diffusion coefficient can replace the diffusion coefficient to characterize the diffusion behavior. When the particle size is different, it is more appropriate to use the diffusion coefficient to characterize the gas diffusion behavior. The significance of the research findings in revealing gas transport in the coal matrix and coalbed methane formation is substantial.

Pattern Dynamics of Cross Diffusion Predator–Prey System with Strong Allee Effect and Hunting Cooperation

In this paper, we consider a Leslie–Gower cross diffusion predator–prey model with a strong Allee effect and hunting cooperation. We mainly investigate the effects of self diffusion and cross diffusion on the stability of the homogeneous state point and processes of pattern formation. Using eigenvalue theory and Routh–Hurwitz criterion, we analyze the local stability of positive equilibrium solutions. We give the conditions of Turing instability caused by self diffusion and cross diffusion in detail. In order to discuss the influence of self diffusion and cross diffusion, we choose self diffusion coefficient and cross diffusion coefficient as the main control parameters. Through a series of numerical simulations, rich Turing structures in the parameter space were obtained, including hole pattern, strip pattern and dot pattern. Furthermore, We illustrate the spatial pattern through numerical simulation. The results show that the dynamics of the model exhibits that the self diffusion and cross diffusion control not only form the growth of dots, stripes, and holes, but also self replicating spiral pattern growth. These results indicate that self diffusion and cross diffusion have important effects on the formation of spatial patterns.

Homonuclear ion-atom collisions: Application toLi+−Li

We present a theoretical framework for homonuclear, ground-state ion-atom collisions wherein the indistinguishability of direct elastic and resonant charge exchange (RCE) scattering channels is discussed. The discussion in terms of the total cross section(${\ensuremath{\sigma}}_{\text{tot}}$) is motivated and derived. The standard cross-section expressions for direct elastic(${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\sigma}}}_{\text{el}}$) and RCE (${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\sigma}}}_{\text{ce}}$) channels are obtained as high-energy approximations to ${\ensuremath{\sigma}}_{\text{tot}}$. We show that the total cross section resolves the inconsistency, at low energies, between the diffusion cross section (${\ensuremath{\sigma}}_{D}$) and the high-energy approximation to the total cross section (${\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\sigma}}}_{\text{tot}}$). The validity of the equivalence relation between the ${\ensuremath{\sigma}}_{D}$ and $2\ifmmode\times\else\texttimes\fi{}{\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{\ensuremath{\sigma}}}_{\text{ce}}$ is also discussed. The differences which result in cross sections which are frequently used in the description of ion-atom collision is illustrated with specific calculations for an ${\mathrm{Li}}^{+}\ensuremath{-}\mathrm{Li}$ system. The use of ${\ensuremath{\sigma}}_{\text{tot}}$ is advocated as a correct and consistent way to represent cross sections.

DONJON5/CLASS coupled simulations of MOX/UO2 heterogeneous PWR core

Most fuel cycle simulation tools are based either on fixed recipes or assembly calculations for reactor modeling. Due to the high number of calculations and extensive computational power requirements, full-core computations are often seen as not viable for this purpose. However, this leads to additional hypotheses and modeling biases, thus limiting the realism of the resulting fuel cycle. For several applications, the current modeling method is sufficient, but precise calculations of discharged fuel composition may require further refinements. CLASS (Core Library for Advanced Simulation Scenarios) is a dynamic fuel cycle simulation code developed since 2012 with reactor models based on neural networks to produce nuclear data and physical quantities. Past work has shown a first coupling between CLASS and DONJON5 to quantify neural networks approach biases. This work assesses the applicability of 3D full-core diffusion calculations using the DONJON5 code coupled with nuclear scenario simulations involving a realistic PWR core at equilibrium cycle conditions. DONJON5 interpolates burnup dependent diffusion coefficients and cross sections generated beforehand by DRAGON5, a deterministic lattice calculation tool. Whereas previous studies considered only homogeneous reactors (i.e. homogeneous assembly in terms of composition and enrichment as well as homogeneous core), the present contribution focuses on the integration of full-core calculations in CLASS for fuel cycles involving a MOX/UO2 PWR core (i.e. 1/3 MOx–2/3 UOx). The DONJON5 model considered in this work describes a core with critical boron concentration at each time step partially loaded with MOx heterogeneous assemblies composed of three enrichments. In fuel cycle calculations, the main issue is to adapt, in the fabrication stage, the fresh fuel composition for the reactor with regards to the isotopic composition of the available stocks. This work presents a fuel loading model based on power peaking factors minimization that respects irradiation cycle length, 235U enrichment as well as Pu concentration and fissile quality, hence, ensuring a more uniform power distribution in the core.

A Review on Chemical Permeation Enhancers used in the Formulation of Transdermal Drug Delivery System

Skin penetration enhancement technology is a rapidly evolving area that will greatly increase the quantity of transdermal drug delivery medications. Penetration enhancers are used to facilitate the movement of drugs through the skin barrier. Numerous methods exist for extending partition enhancement. The enhancers' contact with the polar head of the lipid groups is the potential means for increasing the penetration. Penetration enhancers improve the amount of free water molecules between the bilayer, leading to an improvement of the polar drug diffusion cross section. This article focuses on the different compounds assessed for improving penetration activity like sulphoxides, azones, pyrrolidones, alcohols and alkanols, glycols, surfactants and terpenes.

Ecofriendly lithium-sodium separation by diffusion processes using lithium composite membrane

• Effect of experimental parameters on recovered Li + concentration and recovery ratio. • Li + and Na + separation by diffusion dialysis and cross ionic dialysis. • Effect of feeding concentrations [Na + ]/[Li + ] ratio on recovered Li + concentration and selectivity. • Reusability tests of the Lithium Composite Membrane (LCM). Lithium procurement has become a worldwide policy due to the rapid development of Lithium Ion Batteries. However, during its extraction from natural sources, Li + /Na + separation remains challenging due to its similar characteristics. Herein, we investigate the Li + /Na + separation by two selective and environmentally friendly processes, diffusion dialysis (DD) and cross ion dialysis (CID), using Lithium Composite Membrane (LCM). Firstly, we studied the effect of several experimental parameters by DD (pH, co-ion nature, feed solution composition, treatment duration) and by CID (compositions of feed and receiver) on Li + diffusion through LCM.DD results have shown that Li + recovery rate reaches 22.1% of its initial feed concentration after 27 days of treatment, which is very efficient compared to the evaporation process. CID obtained results reveal that optimal Li + diffusion is achieved at 0.1 M HCl. Secondly, we examined the effect of [Na + ] F /[Li + ] F ratio in the feeding solution on membrane performances (recovered Li + concentration, selectivity coefficient S(Li + /Na + ) and recovery rate) by DD and CID. It was found that high recovered Li + concentration was reached even at high ratio. At [Na + ] F /[Li + ] F = 40 and after 24 h of treatment, we successfully extract 16.63% of Li + with only 0.003% of Na + and S(Li + /Na + ) = 5543 by DD and 36.78% of Li + with only 0.11% of Na + and S(Li + /Na + ) = 931 by CID. Finally, the reusability of LCM during DD was evaluated using two regeneration protocols, one with pure water and the other with a 0.1 M LiCl solution. Results reveal that the second protocol shows better preservation of the membrane selectivity. Thus, LCM is suitable for lithium recovery from its low-concentration sources (brines and seawater).

Analytical approximation of cross sections of collisions of electrons with atoms of inert gases

The paper presents an analysis of data on the cross sections of elastic and inelastic collisions of electrons with noble gas atoms. The transport (diffusion) cross sec-tion, the excitation and ionization cross sections are considered. For the selected sets of experimental and theoretical data, optimal analytical formulas are found and approximation coefficients are selected for them. The obtained semi-empirical formulas allow us to reproduce the cross section values in a wide range of colli-sion energies from 0.001 to 10000 eV with an accuracy of several percent.

Cross sections of electron collisions with noble gases atoms

Consideration is given to the analysis of data on the cross sections of elastic and inelastic col-lisions of electrons with noble gas atoms. The transport (diffusion) cross section, the excita-tion and ionization cross sections are studied. For the selected sets of experimental and theo-retical data, optimal analytical formulas are found and approximation coefficients are select-ed for them. The obtained semi-empirical formulas allow us to reproduce the cross section values in a wide range of collision energies from 0.001 to 10000 eV with an accuracy of sev-eral percent.

Analytical approximation of cross sections of collisions of electrons with atoms of inert gases

The paper presents an analysis of data on the cross sections of elastic and inelastic collisions of electronswith noble gas atoms. The transport (diffusion) cross section, the excitation and ionization cross sectionsare considered. The bibliography on the cross sections of electron-atomic collisions includes manythousands of works. But the critical analysis of the results of experimental data in the review work is verydifficult due to the fact that the necessary initial data can only be available to the authors of the work. Theerrors of the order of 1-3% given in the original works are contrasted with each other, sometimesdiffering by 50%. Comparisons of the electron cross sections sets in noble gases was made. For theselected sets of experimental and theoretical data, optimal analytical formulas are found andapproximation coefficients are selected for them. The obtained semi-empirical formulas allow us toreproduce the cross-section values for them in a wide range of collision energies from 0.001 to 10000 eVwith an accuracy of several percent. Key words: electron atomic collisions, transport cross section, excitation cross section, ionization crosssection, approximation of cross sections, noble gases.

Global existence and uniqueness for a volume-surface reaction-nonlinear-diffusion system

<p style='text-indent:20px;'>We prove a global existence, uniqueness and regularity result for a two-species reaction-diffusion volume-surface system that includes nonlinear bulk diffusion and nonlinear (weak) cross diffusion on the active surface. A key feature is a proof of upper <inline-formula><tex-math id="M1">\begin{document}$ L^{\infty} $\end{document}</tex-math></inline-formula>-bounds that exploits the entropic gradient structure of the system.

Experimental Investigation of FCCI Using Diffusion Couple Test Between UZr Fuel with Sb Additive and Cladding

Alloying additions are introduced into U-Zr fuel in order to bind lanthanides (e.g., cerium) and prevent their migration to the fuel-cladding interface. Antimony (Sb) is being investigated as a candidate additive. The present study focuses on the diffusion couple behavior of U-10Zr (wt%) alloy with Sb against cladding (iron or HT9) at 640°C. The diffusion cross sections were analyzed using a scanning electron microscope and X-ray diffraction. Zr-rind was found at the interface of the fuel alloy, Sb was found to be bound in Sb-Zr precipitates or Sb-Ce precipitates, and no reaction was found between Sb precipitates and the cladding materials.

Sensitivity boosts by the CPMAS CryoProbe for challenging biological assemblies

Despite breakthroughs in MAS NMR hardware and experimental methodologies, sensitivity remains a major challenge for large and complex biological systems. Here, we report that 3–4 fold higher sensitivities can be obtained in heteronuclear-detected experiments, using a novel HCN CPMAS probe, where the sample coil and the electronics operate at cryogenic temperatures, while the sample is maintained at ambient temperatures (BioSolids CryoProbe™). Such intensity enhancements permit recording 2D and 3D experiments that are otherwise time-prohibitive, such as 2D 15N-15N proton-driven spin diffusion and 15N-13C double cross polarization to natural abundance carbon experiments. The benefits of CPMAS CryoProbe-based experiments are illustrated for assemblies of kinesin Kif5b with microtubules, HIV-1 capsid protein assemblies, and fibrils of human Y145Stop and fungal HET-s prion proteins – demanding systems for conventional MAS solid-state NMR and excellent reference systems in terms of spectral quality. We envision that this probe technology will be beneficial for a wide range of applications, especially for biological systems suffering from low intrinsic sensitivity and at physiological temperatures.

Ab initio interaction potentials of the Ba, Ba+ complexes with Ar, Kr, and Xe in the lowest excited states.

The complexes of the Ba atom and Ba+ cation with the rare gas atoms Ar, Kr, and Xe in the states associated with the 6s → 5d, 6p excitations are investigated by means of the multireference configuration interaction techniques. Scalar relativistic potentials are obtained by the complete basis limit extrapolation through the sequence of aug-cc-pwCVnZ basis sets with the cardinal numbers n = Q, T, 5, combined with the suitable effective core potentials and benchmarked against the coupled cluster with singles, doubles, and non-iterative triples calculations and the literature data available for selected electronic states. Spin-orbit coupling is taken into account by means of the state-interacting multireference configuration interaction calculations performed for the Breit-Pauli spin-orbit Hamiltonian. The results show weak spin-orbit coupling between the states belonging to distinct atomic multiplets. General trends in the interaction strength and long-range anisotropy along the rare gas series are discussed. Vibronic spectra of the Ba and Ba+ complexes in the vicinity of the 1S → 1P° and 2S → 2P° atomic transitions and diffusion cross sections of the Ba(1S0, 3DJ) atom in high-temperature rare gases are calculated. Comparison with available experimental data shows that multireference calculations tend to underestimate the interaction strength for excited complexes.

Validation of the Serpent 2-DYNSUB code sequence using the Special Power Excursion Reactor Test III (SPERT III)

The Special Power Excursion Reactor Test III (SPERT III) is studied using the Serpent 2-DYNSUB code sequence in order to validate it for modeling reactivity insertion accidents (RIA) in PWRs. The SPERT III E-core was a thermal research reactor constructed to analyze reactor dynamics. Its configuration resembles a commercial PWR on terms of fuel type, choice of moderator, coolant flow and system pressure. The initial conditions of the rod ejection accident experiments (REA) performed cover cold startup, hot startup, hot standby and operating power scenarios. Eight of these experiments were analyzed in detail. Firstly, multi-dimensional nodal diffusion cross section tables were created for the three-dimensional reactor simulator DYNSUB employing the Monte Carlo neutron transport code Serpent 2. In a second step, DYNSUB stationary simulations were compared to Monte Carlo reference three-dimensional full scale solutions obtained with Serpent 2 (cold startup conditions) and Serpent 2/SUBCHANFLOW (operating power conditions) with a good agreement being observed. The latter tool is an internal coupling of Serpent 2 and the sub-channel thermal-hydraulics code SUBCHANFLOW. Finally, DYNSUB was utilized to study the eight selected transient experiments. Results were found to match measurements well. As the selected experiments cover much of the possible transient (delayed super-critical, prompt super-critical and super-prompt critical excursion) and initial conditions (cold and hot as well as zero, little and full power reactor states) one expects in commercial PWRs, the obtained results give confidence that the Serpent 2-DYNSUB tool chain is suitable to model REAs and other RIAs in PWRs.

Numerical investigation of flow and thermal pattern in unbounded flow using nanofluid - Case study: Laminar 2-D plane jet

In this article, a numerical study is carried out to analyze the effect of nanoparticle volume fraction over flow and thermal characteristics of laminar 2-D plane jet. Al2O3-water and TiO2-water nanofluids are considered in this investigation with lowest and highest values of particle volume concentration equals to 0 and 0.02 respectively. This paper propose four correlations for describing the relation between the solid volume fraction, ?t and ?u. The results show that the cross stream thermal diffusion depth and cross stream hydraulic diffusion depth are increased when particles volume concentration is increased and mean temperature and mean velocity decreases when the solid volume fraction is increased. The effects of nanoparticle volume fraction in velocity and temperature time histories are also studied and discussed.

Numerical investigation of flow and thermal pattern in unbounded flow using nanofluid - Case study: Laminar 2-D plane jet

In this article, a numerical study is carried out to analyze the effect of nanoparticle volume fraction over flow and thermal characteristics of laminar 2-D plane jet. Al2O3-water and TiO2-water nanofluids are considered in this investigation with lowest and highest values of particle volume concentration equals to 0 and 0.02 respectively. This paper propose four correlations for describing the relation between the solid volume fraction, δt and δu. The results show that the cross stream thermal diffusion depth and cross stream hydraulic diffusion depth are increased when particles volume concentration is increased and mean temperature and mean velocity decreases when the solid volume fraction is increased. The effects of nanoparticle volume fraction in velocity and temperature time histories are also studied and discussed.

Study on the adhering failure mechanism of cemented carbide inserts and element diffusion model during the heavy-duty cutting of water chamber head

In view of the serious adhering failure of cemented carbide inserts during the heavy-duty cutting of water chamber head, the adhering failure mechanism of inserts and the element diffusion model of the adhering process were investigated. First, based on cutting simulations, the cutting force was found to be as high as 45.2 kN while the maximum cutting temperature was 930 °C. Under the combined action of mechanical and thermal loads, element diffusion occurred between insert and workpiece and formed an adhering layer, resulting in the adhering failure of inserts. After that, the element diffusion dynamics equation of the adhering process was proposed according to Fick’s law. Based on the semi-infinite long-bar diffusion model and its initial conditions and boundary conditions, the dynamics equation was solved, with the element diffusion concentration model obtained. In the end, the experimental scheme of element diffusion was put forward, and the element diffusion between the cemented carbide insert and workpiece at elevated temperatures was experimentally investigated. The diffusion distance of Co in 508III steel was measured as 8 μm. The element diffusion concentration within the diffusion distance was compared with the value predicted by the model, with the effectiveness of the element diffusion model validated. The concentration distribution of diffusing elements in the diffusion cross section was characterized through experiments and compared with the theoretical concentration distribution. The research results can provide a basis for the in-depth study of the formation mechanism of insert-chip adhering layers and their influence on the cutting performance and service life of inserts.

Collisional relaxation of vibrational states of SrOH with He at 2 K

Vibrational relaxation of strontium monohydroxide (SrOH) molecules in collisions with helium (He) at 2 K is studied. We find the diffusion cross section of SrOH at 2.2 K to be and the vibrational quenching cross section for the (100) Sr–O stretching mode to be . The resulting ratio is more than an order of magnitude smaller than for previously studied few-atom radicals (Au et al 2014 Phys. Rev. A 90 032703 ). We also determine the Franck–Condon factor for SrOH () to be .