Order Distribution Function Research Articles

Li2O concentration influenced local structure and properties of molten LiCl salt by machine learning driven molecular dynamics simulation

Pyroprocessing is one of the promising technologies for the reprocessing of spent nuclear fuel. In the electrolytic reduction process of pyroprocessing, LiCl serves as the electrolyte with a minor addition of Li2O as the initial oxygen ion input. Investigating the impact of Li2O concentration on the molten salt system is essential for enhancing the efficiency of electrolytic reduction. In the present study, the LiCl-Li2O system is simulated using deep potential molecular dynamics simulation. The properties including self-diffusion coefficient, shear viscosity, ionic conductivity, heat capacity, radial distribution functions, coordination numbers, short-range order, medium-range order, Voronoi structure, and angle distribution functions are explored at different Li2O concentrations. This study reveals that the variations of physical properties at different Li2O concentrations in LiCl molten salt can be attributed to the changes in local structure. For example, unnormal high proportions of two Voronoi structures are found in the molten salt when the Li2O concentration increases, which may explain the changes of properties. These findings offer valuable insights for refining the parameters of electrolytic reduction and elucidating the correlation between microscopic and macroscopic phenomena.

Deviation from the prediction of the Maier-Saupe theory of mixtures of charged discotic Gay-Berne and Lennard-Jones particles

ABSTRACT We report an analysis of the orientational order and orientational distribution functions of mixtures of discotic charged Gay-Berne (GB) and Lennard-Jones (LJ) particles as models of ionic liquid crystals and colloidal suspensions. We have studied three different stoichiometries (GB:LJ of 1:2, 1:1 and 2:1), with the opposite charges on the two particles selected to guarantee electroneutrality. We have found that for relatively low values of the scaled charge the dependence of the fourth-rank orientational order parameter, <P 4>, on the second-rank orientational order parameter, <P 2>, is in very good agreement with the prediction of the Maier-Saupe theory. In contrast, for relatively high values of the charge a deviation is observed which is in opposite directions for mixtures with an excess for GB particles and mixtures with an excess of LJ particles.

Drift kinetic theory of neoclassical tearing modes in tokamak plasmas: polarisation current and its effect on magnetic island threshold physics

A nonlinear 4-dimensional drift island theory derived in (Imada et al 2019 Nucl. Fusion 59 046016 and references therein) provides qualitative predictions of the plasma response to a stationary neoclassical tearing mode (NTM) magnetic island in a low beta, large aspect ratio tokamak plasma. (Dudkovskaia et al 2021 Plasma Phys. Control. Fusion 63 054001) refines a model for the magnetic drift frequency and exploits the limit of rare collisions, reducing this theory to 3-dimensional and thus providing a more accurate treatment of the trapped-passing boundary layer. The drift island theory is further improved in (Dudkovskaia et al 2023 Nucl. Fusion 63 016020) by introducing plasma shaping and finite beta effects. In the present paper, an improved model is adopted to resolve the drift island separatrix boundary layer, allowing one to investigate the polarisation current contribution that exists around the magnetic island separatrix, including in the presence of the background electric field. In particular, different magnetic topologies from both sides of the separatrix generate a radial discontinuity in the distribution function gradient there, when collisions are neglected. Allowing for collisional dissipation in the leading order distribution function around the separatrix resolves this discontinuity, smoothing the density distribution. The overall effect of the polarisation current on the NTM threshold is then combined from the outer contributions that exist outside the layer, as well as the separatrix layer piece, and self-consistently accounts for the electrostatic potential reconstructed from plasma quasi-neutrality. The corresponding NTM threshold is quantified and compared with previous predictions of (Dudkovskaia et al 2021 Plasma Phys. Control. Fusion 63 054001, Dudkovskaia et al 2023 Nucl. Fusion 63 016020).

Analytical Model for Determination of Size-Distribution of Colloidal Silver Nanoparticles from Surface Plasmon Resonance Wavelength and Dielectric Functions.

In this work it is shown that the size of silver nanoparticles in a colloidal solution can be determined only from the wavelength of the surface plasmon resonance and material and medium dielectric functions. The size dependence of dielectric functions of silver nanoparticles becomes noticeable in nanoparticles which are smaller than 30 nm in size, which is in accordance with Mie scattering theory applicability. The novelty of this work is in the development of an analytical model for the determination of the size of silver nanoparticles derived from applying shift functions to the UV-Vis spectra, resulting in well-known characteristic diameters of log-normal size distribution function. The purpose of these shift functions is the reconstruction of experimental UV–Vis spectra from simulated ones based on the Beer–Lambert law and log-normal distribution function in order to find the mode diameters of colloidal silver nanoparticles. The introduction of Lagrangian analogue of extinction cross section explains the redshift constant characteristic for given nanoparticle material and the size distribution of nanoparticles. Therefore, the size determination of colloidal silver nanoparticles is possible only through UV–Vis spectroscopy.

Model Comparison of the Transverse Momentum Spectra of Charged Hadrons Produced in P b P b Collision at s N N = 5.02 TeV

Transverse momentum, p T , spectra are of prime importance in order to extract crucial information about the evolution dynamics of the system of particles produced in the collider experiments. In this work, the transverse momentum spectra of charged hadrons produced in P b P b collision at 5.02 TeV have been analyzed using different distribution functions in order to gain strong insight into the information that can be extracted from the spectra. We have also discussed the applicability of the unified statistical framework on the spectra of charged hadron at 5.02 TeV

On the multiscale analysis of a two phase material: crystal plasticity versus mean field

In this paper, a comparison is made between two multiscale methods, namely crystal plasticity finite element and mean field on a material composed of two phases. Both methods are used to homogenize a given microstructure. In order to obtain macroscopic behavior, in the mean field approach, a Self-Consistent scheme is used to evaluate stress and strain partitioning among the phases. In this method, an average of the fields is estimated and local distributions cannot be captured. In parallel, crystal plasticity simulations on Representative Volume Elements (RVEs) composed of hexagonal grains are performed. In these simulations, grain orientations are attributed randomly respecting Mackenzie's distribution function in order to achieve isotropic behavior and macroscopic hardening is extracted from the simulations. The results on macroscopic hardening of both methods are compared to distinguish the extents of validity of mean field homogenization. In addition to Self- Consistent, other mean field schemes such as Voigt, Reuss and Bound-Interpolation are compared in terms of efficiency and accuracy. The comparison manifests that Self-Consistent scheme is capable of predicting material behavior well.

Finite System-size Effects in Self-organized Criticality Systems

Abstract We explore upper limits for the largest avalanches or catastrophes in nonlinear energy dissipation systems governed by self-organized criticality. We generalize the idealized “straight” power-law size distribution and Pareto distribution functions in order to accommodate incomplete sampling, limited instrumental sensitivity, finite system-size effects, and “Black Swan” and “Dragon King” extreme events. Our findings are as follows. (i) Solar flares show no finite system-size limits up to L ≲ 200 Mm, but solar flare durations reveal an upper flare duration limit of ≲6 hr. (ii) Stellar flares observed with Kepler exhibit inertial ranges of E ≈ 1034–1037 erg, finite system-size ranges of E ≈ 1037–1038 erg, and extreme events at E ≈ (1–5) × 1038 erg. (iii) The maximum flare energies of different spectral type stars (M, K, G, F, A, giants) reveal a positive correlation with the stellar radius, which indicates a finite system-size limit imposed by the stellar surface area. Fitting our finite system-size models to terrestrial data sets (earthquakes, wildfires, city sizes, blackouts, terrorism, words, surnames, web links) yields evidence (in half of the cases) for finite system-size limits and extreme events, which can be modeled with dual power-law size distributions.

Numerical Characterization of Corona Spark Plugs and Its Effects on Radicals Production

A mono-dimensional code for the simulation of the effects of High Frequency Ignition systems (HFI) on the production of chemical radicals was developed and here presented. The simulations were carried out by considering the typical environmental thermodynamic conditions of a nowadays engine at full load. An electron transport model is linked with a Boltzmann solver coupled with a chemistry solver, affecting the Electron Energy Distribution Function (EEDF) in order to obtain the physical conditions leading to the production of radical components for a given fuel mixture. The transport equations for the electrons, the positive and the negative ions, and the Gauss’ law in a steady-state plasma region. Then the Boltzmann equation for the electrons, in a spatially homogeneous steady-state case, is solved in order to obtain the EEDF. Finally the chemical kinetics model is employed assuming a fuel-air mixture neglecting the fuel carbon atoms due to the assumption that electron-impact dissociation reactions, which initiate the combustion, exhibit a greater reaction rate compared to those based on hydrocarbon thermal dissociation and therefore can be neglected in this work. Results show the production of the hydrogen (H), nitrogen (N), and oxygen (O) radicals and the radius of the initial discharge under different simulated engine operating conditions characterizing the role of a plasma corona effect for the induced chemical ignition in gasoline-powered engines.

Determination of Optimal Parametric Distribution and Technical Evaluation of Wind Resource Characteristics for Wind Power Potential at Jhimpir, Pakistan

The objective of this research work is to analyze wind characteristics and to assess wind power potential by selecting the best fit probability distribution function of Jhimpir Sindh Pakistan. This type of detailed investigation helps wind power generation companies in selecting suitable wind turbine and provides information of wind characteristics of potential site. Eight probability distribution functions are tested on the wind speed data from January 2015 to July 2018. Frequency bins of Weibull and Rayleigh distribution with maximum probabilities of 0.1210 and 0.1143 are most closest representation of our data. In order to, quantitatively analysis which distribution function is best fitting the local wind regime, we have applied the coefficient-of-determination, Kolmogorov-Smirnov, Chi square, Cramer-von Mises, Anderson-Darling tests along with Akaike information and Bayesian information criterion. These statistical test are used to rank the empirical distribution functions in order to identify two distribution function better fitting the actual wind speed data. After selecting two best fitted distribution functions, we analyze wind power potential and compare the error of wind power density based on these distribution functions (Weibull and Rayleigh). The power densities reported varied from 73.67 to 648.73W/m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> . Results indicate that power densities of Weibull and Rayleigh for the candidate site are 84.67-698.65W/m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> and 83.67-1021.4W/m <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> , respectively. The highest error for Weibull and Rayleigh are 0.1850 and 0.5745, respectively. Whereas lowest error are 0.0178 and 0.0180, respectively. Complete analysis suggested that Weibull distribution function is the most suitable for Jhimpir Sindh Pakistan and the studied site is suitable for wind power production. In addition, comprehensive analysis of wind direction at the candidate site suggested that Eastern and Southeastern wind directions are predominant with 38.52% and 33.24% of the total time.

A Phase-Type Distribution for the Sum of Two Concatenated Markov Processes Application to the Analysis Survival in Bladder Cancer

Stochastic processes are useful and important for modeling the evolution of processes that take different states over time, a situation frequently found in fields such as medical research and engineering. In a previous paper and within this framework, we developed the sum of two independent phase-type (PH)-distributed variables, each of them being associated with a Markovian process of one absorbing state. In that analysis, we computed the distribution function, and its associated survival function, of the sum of both variables, also PH-distributed. In this work, in one more step, we have developed a first approximation of that distribution function in order to avoid the calculation of an inverse matrix for the possibility of a bad conditioning of the matrix, involved in the expression of the distribution function in the previous paper. Next, in a second step, we improve this result, giving a second, more accurate approximation. Two numerical applications, one with simulated data and the other one with bladder cancer data, are used to illustrate the two proposed approaches to the distribution function. We compare and argue the accuracy and precision of each one of them by means of their error bound and the application to real data of bladder cancer.

Kinetic derivation of diffuse-interface fluid models.

We present a full derivation of capillary fluid equations from the kinetic theory of dense gases. These equations involve van der Waals' gradient energy, Korteweg's tensor, and Dunn and Serrin's heat flux as well as viscous and heat dissipative fluxes. Starting from macroscopic equations obtained from the kinetic theory of dense gases, we use a second-order expansion of the pair distribution function in order to derive the diffuse interface model. The capillary extra terms and the capillarity coefficient are then associated with intermolecular forces and the pair interaction potential.

Concentration and Magnetic Field Effects on Thermal Fluctuation of Magnetic Weight of Magnetite Nanoparticles During Agglomeration Under Magnetic Field

Agglomeration process of the magnetic nanoparticles under the magnetic field is studied by monitoring the magnetic weight of the sample, the magnetic force that the magnetic sample experiences under the magnetic field. The magnetic weight of the single domain magnetite nanoparticles in aqueous solution increases slowly with fluctuation as the nanoparticles agglomerate. The fluctuation of the magnetic weight coincides with the temperature change. We observe the thermal fluctuation of the magnetic weight of the samples of different concentrations at different magnetic fields. We employ the energy distribution function in order to simulate the thermal fluctuation of the magnetic weight. The simulation results suggest that the interparticle interactions, which restrict the motions of nanoparticles, play important roles in the agglomeration of high concentration samples at high magnetic fields. The interparticle interactions make the effective temperature lower than the experimental temperature by raising the magnetic anisotropy energy barrier.

A Single Molecular Stoichiometric P‐Source for Phase‐Selective Synthesis of Crystalline and Amorphous Iron Phosphide Nanocatalysts

AbstractThe formation of iron phosphide nanoparticles (FexP NPs) is a well‐studied process. It usually uses air‐sensitive phosphorus precursors such as n‐trioctylphosphine or white phosphorus. In this study, we report the synthesis and characterization of a remarkably stable tetrakis(acyl)cyclotetraphosphane, P4(MesCO)4. We demonstrate that this compound can be used as a stoichiometric source of P(0) species in order to synthesize FeP and Fe2P nanoparticles at only 250 °C. This tunable process provides a route to monodisperse nanoparticles with different compositions and crystallinities. We combine X‐Ray photoelectron spectroscopy (XPS) and atomic pair distribution function (PDF) in order to study the local order and bonding in the amorphous and crystalline materials. We show that crystalline FeP forms via an intermediate amorphous phase (obtained at a lower temperature) that presents local order similar to that of the crystalline sample. From the results of this work, a better understanding of the mechanism of the formation of amorphous and crystalline FexP NPs is provided which relies on the use of a stoichiometric and single P‐source. We then explore the electrocatalytic properties of FexP nanoparticles for the hydrogen evolution reaction (HER) in acidic and neutral electrolytes. In both electrolytes, amorphous FeP is a more efficient catalyst than crystalline FeP, itself more efficient than crystalline Fe2P. Our study paves the way for a more systematic investigation of amorphous metal phosphide phases in electrocatalysis. It also shows the beneficial properties of PDF on the characterization of such nanomaterials, which is highly challenging.

Thermodynamic perturbation theory for a valence-limited model of colloidal systems

Thermodynamic perturbation theory for central force associating potential is extended and applied to describe the properties of the valence-limited model of colloidal fluids. The model, which has been developed by Speedy and Debenedetti in early 1990s (R. J. Speedy, P. G. Debenedetti, Mol. Phys. 81, 237(1994)), is represented by the fluid of non-additive square-well hard spheres with a predefined maximum number of bonds that each particle can form. The theory takes into account ring formation and higher order distribution functions of the reference system. To assess the accuracy of the theory, we perform extensive Monte Carlo simulations for the original version of the model and its limiting version with square-well potential represented by the sticky Baxter interaction. Theoretical predictions for thermodynamic properties (pressure, energy, entropy) and fractions of n-time bonded particles are in good agreement with corresponding computer simulation predictions. Results of the theory for the liquid–gas phase diagram of the model with are less accurate.

Heisenberg's uncertainty conditions for various higher order probability distribution functions based on Budiyono–Rohrlich statistical model of quantum mechanics

This report discusses the explicit form of Heisenberg's uncertainty conditions based on recently proposed Budiyono–Rohrlich quantum interpretation which is formulated in terms of modified classical statistical mechanics within the framework of Hamilton–Jacobi formalism. This new statistical interpretation of quantum mechanics is remarkably compatible with the Copenhagen interpretation. We consider various probability distribution functions in the form of symmetric and localized higher order Gaussian, Cauchy-Lorentz and t− distribution functions. The characteristics of all those higher order distribution functions and the related uncertainty conditions are discussed, and we show that all those conditions satisfy the Heisenberg–Kennard uncertainty relation, as expected.

WIND SPEED ANALYSIS AT IKEJA, NIGERIA USING THE CONVENTIONAL PROBABILITY DENSITY FUNCTIONS

&lt;p&gt;The wind energy potential at Ikeja (Lat. 6.35 °N; Long. 3.20 °E), Nigeria was statistically analyzed using three of the mostly utilized conventional Probability Distribution Functions (PDFs) in order to determine which of these distributions would give the best means of analysis for wind in this particular location. The best fit test for these PDFs were determined from Akaike Information Criteria, Bayesian Information Criteria, Kolmogorov-Smirnov test, Cramer-von Mises statistics, Anderson-Darling Statistic, Mean Square Error and Chi-Square Test using Maximum Likelihood Estimation and Method of Moments as parameter estimates. The Weibull distribution gave the best fit in this location.&lt;/p&gt;

WIND SPEED ANALYSIS AT IKEJA, NIGERIA USING THE CONVENTIONAL PROBABILITY DENSITY FUNCTIONS

The wind energy potential at Ikeja (Lat. 6.35 N; Long. 3.20 E), Nigeria was statistically analyzed using three of the mostly utilized conventional Probability Distribution Functions (PDFs) in order to determine which of these distributions would give the best means of analysis for wind in this particular location. The best fit test for these PDFs were determined from Akaike Information Criteria, Bayesian Information Criteria, Kolmogorov-Smirnov test, Cramer-von Mises statistics, Anderson-Darling Statistic, Mean Square Error and Chi-Square Test using Maximum Likelihood Estimation and Method of Moments as parameter estimates. The Weibull distribution gave the best fit in this location.

A relativistic formulation of the de la Peña-Cetto stochastic quantum mechanics

A covariant generalization of a non-relativistic stochastic quantum mechanics introduced by de la Peña and Cetto is formulated. The analysis is done in space-time and avoids the use of a non-covariant time evolution parameter in order to search for Lorentz invariance. The covariant form of the set of iterative equations for the joint coordinate and momentum distribution function Q(x; p) is derived and expanded in power series of the coupling of the particle with the stochastic forces. Then, particular solutions of the zeroth order in the charge of the iterative equations for Q(x; p) are considered. For them, it follows that the space-time probability density ρ(x) and the function S(x) which gradient defines the mean value of the momentum at the space time point x, define a complex function ψ(x) which exactly satisfies the Klein-Gordon (KG) equation. These results for the zeroth order solution reproduce the ones formerly and independently derived in the literature. It is alsoargued that when the KG solution is either of positive or negative energy, the total number of particles conserves in the random motion. Other solutions for the joint distribution function in lowest order, satisfying the positive condition are also presented here. The are consistent with the assumed lack of stochastic forces implied by the zeroth order equations. It is also argued that such joint distributions, after considering the action of the stochastic forces, might furnish an explanation of the quantum mechanical properties, as associated to ensembles of particles in which the vacuum makes such particles behave in a similar way as Couder’s droplets moving over oscillating liquid surfaces. Some remarks on the solutions of the positive joint distribution problem proposed in the Olavos’s analysis are also presented.

Possible ergodic-nonergodic regions in the quantum Sherrington-Kirkpatrick spin glass model and quantum annealing.

We explore the behavior of the order parameter distribution of the quantum Sherrington-Kirkpatrick model in the spin glass phase using Monte Carlo technique for the effective Suzuki-Trotter Hamiltonian at finite temperatures and that at zero temperature obtained using the exact diagonalization method. Our numerical results indicate the existence of a low- but finite-temperature quantum-fluctuation-dominated ergodic region along with the classical fluctuation-dominated high-temperature nonergodic region in the spin glass phase of the model. In the ergodic region, the order parameter distribution gets narrower around the most probable value of the order parameter as the system size increases. In the other region, the Parisi order distribution function has nonvanishing value everywhere in the thermodynamic limit, indicating nonergodicity. We also show that the average annealing time for convergence (to a low-energy level of the model, within a small error range) becomes system size independent for annealing down through the (quantum-fluctuation-dominated) ergodic region. It becomes strongly system size dependent for annealing through the nonergodic region. Possible finite-size scaling-type behavior for the extent of the ergodic region is also addressed.

Coupled spin-charge dynamics in helical Fermi liquids beyond the random phase approximation

We consider a helical system of fermions with a generic spin (or pseudospin) orbit coupling. Using the equation of motion approach for the single-particle distribution functions, and a mean-field decoupling of the higher order distribution functions, we find a closed form for the charge and spin density fluctuations in terms of the charge and spin density linear response functions. Approximating the nonlocal exchange term with a Hubbard-like local-field factor, we obtain coupled spin and charge density response matrix beyond the random phase approximation, whose poles give the dispersion of four collective spin-charge modes. We apply our generic technique to the well-explored two-dimensional system with Rashba spin-orbit coupling and illustrate how it gives results for the collective modes, Drude weight, and spin-Hall conductivity which are in very good agreement with the results obtained from other more sophisticated approaches.