Calculation Of Distribution Function Research Articles

An Analysis and Optimization of Distortion Effect Caused by Pupil Decentering in Optical Gun Scope

During the use of optical gun scopes, slight movements between the human eye and the instrument can cause the pupil to offset from the optical axis, resulting in a dynamic distortion effect. This affects the accuracy and stability of aiming. Based on the mechanism, this study established parameters of the centroid’s deviation of image spots for marginal field points under pupil decentering and centering conditions and their differences to quantitatively evaluate the distortion. These evaluation parameters were obtained by performing a double integral calculation of the ray aberration distribution function over the entire designed exit pupil. Based on this evaluation method, three optical design strategies for reducing the distortion were proposed: optimizing ray aberrations, optimizing centroid shift of image spots, and utilizing vignetting effects. An optimization process was established by combining increasing vignetting and suppressing centroid shift. For a gun scope with significant distortion, the distortion effect was significantly weakened by increasing the vignetting factor and optimizing the centroid shift of image spots. This proved the effectiveness of the proposed analysis, evaluation, and optimization design methods.

Solvent diffusion mechanism of gun propellant revealed through molecular dynamics simulation

Drying is an important operational unit in the preparation of nitrocellulose-based gun propellant, which affects the drying quality and drying rate of the product. The diffusion properties of solvents during the drying process determine the rate of internal solvent removal from the gun propellant, so the diffusion behaviors of ethanol and acetone in the gun propellant were investigated based on molecular dynamics simulations. Three models of single-, double- and triple-base gun propellant components were established, and the interactions between the solvent and the components of gun propellant were investigated by radial distribution function, hydrogen bonding and interaction energy calculations, and the free volumes, diffusion coefficients and the activation energies of the solvents were used to describe the solvent diffusion performances. The results showed that the interaction between ethanol and the components of the gun propellant was mainly hydrogen bonding, and the interaction between acetone and the components was mainly van der Waals forces. When the mass ratio of ethanol and acetone is 1:1, the interaction energy between ethanol and the components is greater due to the presence of strong hydrogen bonding, which resulted in a higher diffusion activation energy of ethanol. However, since the molecular volume of ethanol is higher than that of acetone, it makes the diffusion coefficient of ethanol larger. Compared with single-base gun propellant, after adding nitroglycerin and nitroguanidine, the free volume fraction decreases, the sum of the interaction energies between the solvent and the components in gun propellant increases, and the diffusion activation energy increases. Hence, this present work regarding the study of solvent diffusion mechanism of gun propellant can provide theoretically guiding suggestion to the actual drying process and manufacture of gun propellant.

Renormalization of asymmetric staple-shaped Wilson-line operators in lattice and continuum perturbation theory

In this work, we study the renormalization of nonlocal quark bilinear operators containing an asymmetric staple-shaped Wilson line at the one-loop level in both lattice and continuum perturbation theory. These operators enter the first-principle calculation of transverse momentum-dependent parton distribution functions (TMDPDFs) in lattice QCD using the formulation of large momentum effective theory. We provide appropriate RI′-type conditions that address the power and logarithmic divergences, as well as the mixing among staple operators of different Dirac structures, using a number of different possible projectors. A variant of RI′, including calculations of rectangular Wilson loops, which cancel the pinch-pole singularities of the staple operators at infinite length and reduce residual power divergences, is also employed. We calculate at one-loop order the conversion matrix, which relates the quasi-TMDPDFs in the RI′-type schemes to the reference scheme MS¯ for arbitrary values of the renormalization momentum scale and of the dimensions of the staple. Published by the American Physical Society 2024

Nucleon helicity parton distribution function in the continuum limit with self-renormalization

We present the first lattice calculation of the nucleon isovector helicity parton distribution function (PDF) in the framework of large-momentum effective theory (LaMET) that uses the hybrid scheme with self-renormalization. We use ensembles generated by the MILC collaboration at lattice spacings a={0.1207,0.0888,0.0582} fm, with Nf=2+1+1 flavors of highly improved staggered quarks at sea pion mass of Mπ≈315 MeV. We use clover-improved action for our valence quarks with nucleon boost momentum Pz≈1.75 GeV and high-statistics measurements for the LaMET matrix elements. We perform an extrapolation to the continuum limit and improve the handling of systematic errors using renormalization-group resummation (RGR) and leading-renormalon resummation (LRR). Our final nucleon helicity PDF is renormalized in the MS‾ scheme at energy scale μ=2.0 GeV. We compare our results with and without the two systematic improvements of RGR and LRR at each lattice spacing as well as the continuum limit, and we see that the application of RGR and LRR greatly reduces the systematic errors across the whole x range. Our continuum results with both RGR and LRR show a small positive antiquark region for the nucleon helicity PDF as well as a change of as much as a factor of two in the central values compared to results with neither RGR or LRR. By contrast, the application of RGR and LRR only changes the central values by about 5% in the quark region. We compare our lattice results with the global fits by the JAM, NNPDF and DSSV collaborations, and we observe some tension between our results.

Rapid simulation of two-dimensional spectra with correlated anisotropic dimensions.

A new algorithm has been developed to simulate two-dimensional (2D) spectra with correlated anisotropic frequencies faster and more accurately than previous methods. The technique uses finite-element numerical integration on the sphere and an interpolation scheme based on the Alderman-Solum-Grant algorithm. This method is particularly useful for numerical calculations of joint probability distribution functions involving quantities with a parametric orientation dependence. The technique's efficiency also allows for practical least-squares fitting of experimental 2D solid-state nuclear magnetic resonance (NMR) datasets. The simulation method is illustrated for select 2D NMR methods, and a least-squares analysis is demonstrated in the extraction of paramagnetic shift and quadrupolar coupling tensors and their relative orientation from the experimental shifting-d echo 2H NMR spectrum of a NiCl2 · 2D2O salt.

Molecular dynamics simulation, thermodynamic parameters and solute–solvent molecular interactions of cilostazol (form A) dissolution in (ethylene glycol / ethanol + water) mixtures

This research work reports the cilostazol (form A) dissolution in (ethylene glycol / ethanol + water) mixtures. The co-solvency phenomenon only occurs in mixture of ethanol + water, the maximum solubility in mole fraction is 3.034 × 10-3 at the composition of 0.85. It was found that the solvation performance of cilostazol in two mixtures mainly depend on the ability of forming hydrogen bond (H-bond) of the solutions and van der Waals interaction. According to the preferential solvation results, it is conjecturable that cilostazol molecules are preferentially solvated by water in water-rich regions. With the increase of alcohol concentration, the destruction of water molecular ordered structure by alcohol through hydrogen bond, and solute molecules are preferentially solvated by ethanol and EG. Nonetheless, when 0.86 < x1 < 1 in mixture of ethanol + water, solute molecules are preferentially solvated by water again. The calculation of radial distribution function (RDF) between the atoms of H and O for ethanol and the atoms of N and H for solute is to achieve the interaction of the solute and solvents. The correlation fitting was performed for the solubility data through Jouyban Acree model and its derivative models, and the statistical analysis showed that the Apelblat-Jouyban Acree model is more suitable to present the solubility correlation. Meanwhile, the values of apparent molar standard dissolution enthalpy (ΔHsolo) and apparent molar standard dissolution entropy (ΔSsolo) are positive in each solvents, which reveals that the dissolution process of cilostazol form A is endothermic and entropy favorable within the given temperature range.

Kinetic Modeling of Ionospheric Outflows in Pressure Cooker Environments

AbstractPlasma escape from the high‐latitude ionosphere (ion outflow) serves as a significant source of heavy plasma to the magnetospheric plasma sheet and ring current regions. Outflows alter mass density and reconnection rates, hence global responses of the magnetosphere. A new fully kinetic and semi‐kinetic model, KAOS (Kinetic model of Auroral ion OutflowS), is constructed from first principles which traces large numbers of individual O+ ion macro‐particles along curved magnetic field lines, using a guiding‐center approximation, in order to facilitate calculation of ion distribution functions and moments. Particle forces include mirror and parallel electric field forces, a self‐consistent ambipolar electric field, and a parameterized source of ion cyclotron resonance wave heating, thought to be central to the transverse energization of ions. The model is initiated with a steady‐state ion density altitude profile and Maxwellian velocity distribution and particle trajectories are advanced via a direct simulation Monte Carlo scheme. This outlines the implementation of the kinetic outflow model, demonstrates the model's ability to achieve near‐hydrostatic equilibrium necessary for simulation spin‐up, and investigates L‐shell dependent wave heating and pressure cookers scenarios. This paper illustrates the model initialization process and numerical investigations of L‐shell dependent outflows and pressure cooker environments and serves to advance our understanding of the drivers and particle dynamics in the auroral ionosphere.

Diffusion Monte Carlo and PIMD calculations of radial distribution functions using an updated CCSD(T) potential for CH5 +

We report a new permutationally invariant polynomial (PIP) fit to CCSD(T)/aug-cc-pVTZ energies for CH 5 + that provides fast analytical forces, unlike the original PIP fit of 2006. The new fit, which is slightly more precise than the previous one, is used in classical molecular dynamics, diffusion Monte Carlo and path integral molecular dynamics calculations of CH and HH radial distribution functions (RDFs) at temperatures of 10 and 50 K . Corresponding RDFs are also reported for CD 3 H 2 + . The well-known quantum localisation of the H atoms to the diatomic site from previous and present DMC calculations is maintained at 10 K but shows additional delocalisation to the ‘ CH 3 + ’ site at 50 K .

Pyrrole/MXene membranes with simultaneously high structural stability and permeability for nanofiltration: Implication for water transport

Laminar MXene membranes hold great promise for aqueous separation applications. However, their susceptibility to oxidation in water cause chemical degradation and functional loss, impeding their separation efficiency and durability. In this study, an enhanced MXene nanofiltration membrane was fabricated by simply incorporating pyrrole with Ti3C2Tx, resulting in significantly improved oxidation resistance and permeability. Compared with pure MXene membrane, the pyrrole/MXene membrane exhibited a 3.52-fold increase in water permeance (465.9 L m−2 h−1 bar−1) and achieved excellent rejection performance for various dye molecules. The molecular dynamics simulations revealed that the pyrrole/MXene system presented a higher diffusion coefficient due to the weaker interaction energy at the interface between water molecule and pyrrole/MXene membrane. Normally, a larger transmembrane energy barrier meant a higher transport resistance that prevented the molecule from passing through the membrane. In this way, the determination of activation energy showed that the introduction of pyrrole facilitated a reduction in the requisite activation energy of water transfer from 9.37 to 4.86 kJ mol−1. More importantly, we explored the fact that the stabilization of MXene membranes had a significant impact on their separation performance during a long-term operation. Compared with pristine MXene membrane, the pyrrole/MXene membrane maintained initial two-dimensional structure and stable nanofiltration performance after prolonged operation. The radial distribution function calculations demonstrated that the chemical interactions between Ti3C2Tx and pyrrole were strong and involved the formation of Ti–C bonding and intermolecular interaction. This research provides a facile and effective method to prepare a high-performance and stable MXene nanofiltration membrane.

High-temperature impedance properties of Sr1-xCaxTiO3 ceramics for lead-free capacitor applications

ABSTRACT Lead-free Sr0.6Ca0.4TiO3 ceramic was prepared by solid-state reaction route. X-ray diffraction technique showed the phase purity and identified the orthorhombic perovskite structure. Scanning Electronic Microscopy observation evidenced homogeneous morphology and dense microstructure. Electrical conduction and dielectric relaxation mechanisms at high temperature have been studied by complex impedance measurement techniques over a wide range of frequencies and temperatures, from 100 Hz to 1 MHz and from 573 K to 783 K. Fitting of impedance measurements allowed us to study grains and grain boundaries electrical characteristics and their contribution to the conduction and dielectric relaxation processes in the ceramic. Electrical conduction in grains is due to oxygen vacancy jumps for temperatures below 733 K and to polarons above 763 K. Electrical DC conductivity in grains and grain boundaries is mainly due to oxygen vacancies. Impedance measurements and relaxation time distribution function calculations show non-Debye-type relaxation effects for both grains and grain boundaries.

Temperature dependent molecular dynamics simulation study to understand the stabilizing effect of NADES on the protein [formula omitted]-Lactoglobulin

The thermal stability of a protein is an important concern for its practical application in food processing industries. In this study, we have carried out classical molecular dynamics simulations to systematically investigate the effect of NADES (natural deep eutectic solvent) on the stabilization of the protein β-Lactoglobulin (BLG) at different temperatures. This study sheds light on the very aspects of NADES composed of betaine and sorbitol on the stability of the protein. NADES provides better stability to the protein up to a temperature of 400 K than in water. It is observed that the protein starts to unfold above temperature 400 K in spite of the presence of NADES which is quiet evident from the root mean square deviation (RMSD) and radius of gyration (Rg) plots. The decreasing average solvent accessible surface area (SASA) values and increasing intra-protein hydrogen bonds indicate better stability of the protein in NADES medium than in water at temperatures 300 K and 400 K. At high temperatures viz. 450 K and 500 K the number and distribution of solvent species (betaine and sorbitol) around the protein surface show an increment that are evident from the calculations of solvation shell, radial and spatial distribution functions. Increased number of betaine molecules that interact with the protein through electrostatic interaction may lead to destabilization of the protein at these temperatures. This study suggests that NADES could be used as an ideal medium for thermal stability of the protein BLG up to a temperature of 400 K. Beyond this temperature, NADES used for this study fails to exert stabilization effect on the protein.

Leading power accuracy in lattice calculations of parton distributions

In lattice-QCD calculations of parton distribution functions (PDFs) via large-momentum effective theory, the leading power (twist-three) correction appears as O(ΛQCD/Pz) due to the linear-divergent self-energy of Wilson line in quasi-PDF operators. For lattice data with hadron momentum Pz of a few GeV, this correction is dominant in matching, as large as 30% or more. We show how to eliminate this uncertainty through choosing the mass renormalization parameter consistently with the resummation scheme of the infrared-renormalon series in perturbative matching coefficients. An example on the lattice pion PDF data at Pz=1.9 GeV shows an improvement of matching accuracy by a factor of more than 3∼5 in the expansion region x=0.2∼0.5.

Theoretical Two Dimensional Infrared Spectroscopy of Aqueous Solutions of tert-Butyl Alcohol: Variation of the Dynamics of Spectral Diffusion along the Percolation Transition.

Binary mixtures of water and tert-butyl alcohol (TBA) are known to exhibit the so-called percolation transition where small clusters of TBA molecules span into large aggregates beyond a threshold concentration of the alcohol. In the present study, we have investigated the linear and two-dimensional infrared spectral features of aqueous solutions of TBA for varying concentration of the alcohol along the percolation transition. The percolation transition is characterized through calculations of intermolecular radial distribution functions and average size of the largest cluster of TBA molecules. It is found that, with variation of alcohol concentration, the radial distribution functions of the central carbon atoms of TBA molecules show a nonmonotonic change in the height of the first peak and also the size of the largest cluster of TBA molecules show a jump in the increase of its size for TBA mole fraction between 0.04 and 0.06 corresponding to a transition from smaller clusters to larger spanning aggregates. However, it is found that the linear infrared spectrum of water does not exhibit any noticeable changes on variation of TBA concentration along the percolation transition. Subsequently, two-dimensional infrared (2DIR) spectra and vibrational frequency time correlation function of water are calculated for all the TBA-water solutions considered in this study. The spectral diffusion of water calculated from 2DIR is found to slow down with increase of the TBA concentration. The time scales of spectral diffusion of water, as characterized by the relaxation of frequency time correlation function, 2DIR metric of central line slope, and also the hydrogen bond time correlation functions, are found to exhibit a noticeable jump along the percolation transition. The hydrophilic group of TBA is found to retard the water dynamics more effectively than the hydrophobic groups. Also, the jump in the dynamical slowdown along the percolation transition is found to be more significant for water molecules at the hydrophilic sites.

Available and total phosphorus background levels in soils: a calcareous and semi-arid region

It is critical to understand the risk of element pollution in soils by evaluating their background levels. Phosphorus (P) content in agricultural soils needs to be assessed from agronomic and environmental standpoints. The current study intended to calculate the background levels of available and total P in soils. To achieve this goal, 50 sites without human activities were selected. Soils were sampled from the surface and subsurface of each site (100 soil samples). The available P forms in soils were extracted using the water-extractable P (WEP), calcium chloride-extractable P (CCEP), and Olsen-extractable P (OEP) methods. The first two extractants are being used to evaluate P leaching from soils, while the last one is being used as an agronomic indicator. The methods used to calculate background levels were the iterative 2-δ technique (2-δ) and the calculated distribution function (CDF). Results showed that the upper limits of background levels using 2-δ method were 1.45, 0.92, 8.12, and 424.4mgkg-1 for WEP, CCEP, OEP, and total P, respectively. Also, the upper limits of background levels using CDF method were 1.42, 1.15, 12.09, and 447.6mgkg-1, for WEP, CCEP, OEP, and total P, respectively. It can be concluded that using these background levels, which for the first time were calculated for P, would enable us to have an accurate examination of P excess as a result of human activities.

Enhancing Heat Transfer Behaviour of Ethylene Glycol by the Introduction of Silicon Carbide Nanoparticles: An Experimental and Molecular Dynamics Simulation Study.

As the critical component of automotive engine coolant, ethylene glycol (E.G.) significantly matters in heat dissipation. In this study, the key aim is to investigate the heat transfer behaviour of E.G. as nano-additives base fluid. The heat transfer capability of E.G./SiC nanofluid (N.F.) was experimentally and theoretically evaluated via transient hot wire methods and equilibrium molecular dynamics (EMD) simulation, respectively. M.D. simulation exhibited a great ability to accurately forecast the thermal conductivity of N.F. compared with the experiment results. The results confirmed that the thermal stability of N.F. is relatively greater than that of E.G. base fluids. An improvement mechanism of thermal conductivity and thermal stability under an atomic scale via the analysis of mean square displacement (MSD) and radial distribution function (RDF) calculation was elaborately presented. Ultimately, the results indicated that the diffusion effect and the increasing transition rate of liquid atoms are responsible for thermal conductivity enhancement.

Estimation of Nitrate Background Value in Groundwater under the Long-Term Human Impact

This study demonstrates an approach to estimate the background value of nitrate as a basis for better groundwater management and protection in areas under long-term human impact. The aim was to determine the ambient background value (ABV) of nitrate in the catchment area of the Velika Gorica well field, a hydrogeologically homogeneous area within the Zagreb aquifer. ABVs are determined using four well-known model-based objective methods (the iterative 2-σ technique, IT; the calculated distribution function, CDF; the cumulative frequency curve, CFC; and the probability plot, PP), while simultaneously testing the reliability of the results of each method. If the results are not statistically significant, data selection is performed. The results show that using data without selection can lead to statistically non-significant ABVs, but with the additional selection of data, a statistically non-significant result became a statistically significant one. In summary, all final ABVs must be statistically significant and determined using as large a data set as possible. Reducing the size of the data set is acceptable only in the case of a statistically non-significant result.

Mechanistic insights into the crystallization of coamorphous drug systems.

In our previous study, the coamorphous formulation of lurasidone hydrochloride (LH) with saccharin (SAC) showed significantly enhanced dissolution and physical stability compared to crystalline/amorphous LH. However, the coamorphous system is still in amorphous state, and has the tendency to recrystallization, which will in turn result in the loss of above advantages. In this study, the crystallization kinetics under isothermal and non-isothermal conditions was investigated. Compared to amorphous LH, coamorphous LH-SAC showed 68.3-361.2 and 2.6-6.1 times lower crystallization rates in glassy state and supercooled liquid state, respectively. After co-amorphization, the addition of SAC changed the crystallization mechanism of amorphous LH from nucleation-controlled to diffusion-controlled manner. Amorphous LH followed the site-saturated nucleation, whereas the coamorphous system exhibited a fixed number of nuclei. The non-isothermal crystallization indicated amorphous LH and coamorphous LH-SAC showed two-dimensional (JMAEK 2) and three-dimensional (JMAEK 3) growth of nuclei, respectively. Furthermore, coamorphous LH-SAC exhibited higher molecular mobility and dynamic fragility (mD) than amorphous LH, which is kinetically unfavorable for its physical stability. However, from thermodynamic perspective, coamorphous LH-SAC had a higher configurational entropy, i.e., a higher entropy barrier for crystallization, which is beneficial to hinder its crystallization. Therefore, it was concluded that the higher configurational entropy rather than the molecular mobility was proposed to be responsible for its improved stability. In addition, molecular dynamics simulations with miscibility, radial distribution function and binding energy calculations suggested coamorphous components exhibited good miscibility and strong intermolecular interactions, which was also conductive to the enhancement in its stability. This study offers an in-depth understanding about the effect of the coformer on the crystallization kinetics of coamorphous systems, and points out the important contribution of the configurational entropy in stabilizing the coamorphous systems.

Computational Study of the Physical Properties of a High Temperature Molten Salt Mixture of FLiNaK and CeF3

In this work, we study the diffusion characteristics and structure of the molten salt FLiNaK with dissolved CeF3 in the operating temperature range of the molten-salt reactor. The temperature dependence of the self-diffusion coefficients of the ions that make up the salt mixture is represented with good accuracy as a linear dependence, except for the case of self-diffusion of Ce ions. As a rule, Li and F ions are more mobile than Na and K ions and significantly more so than slow Ce ions. The coordination numbers and their increase upon dissolution of CeF3 in FLiNaK were determined based on the calculation of partial radial distribution functions. The detailed structure of the melt is studied based on the construction of Voronoi polyhedra. The obtained topological characteristics indicate a predominantly tetrahedral type of distribution of Ce ions over the bulk of the system. Rotational symmetry of the 5th order prevails in the structure of the Li and F subsystems, and symmetries of the 3rd and 4th orders prevail in the Na and K subsystems, respectively. The simulation results can be used to search for actinide, which can be replaced by cerium in real experiments.

Implementation of a cylindrical distribution function for the analysis of anisotropic molecular dynamics simulations.

The cylindrical distribution function (CDF) is a convenient anisotropic analogue of the radial distribution function, the difference being the use of cylindrical shells for binning. As such, CDF analysis can be a powerful tool for the analysis of positional correlations within anisotropic systems, such as liquid crystals. Here we describe a lightweight Python tool, cylindr, for the calculation of cylindrical distribution function, which is compatible with the output of a number of popular MD engines. We demonstrate the use of cylindr in computing the CDF of a number of exemplar materials: classical and ferroelectric nematics; lamellar and columnar liquid crystals.

Sonochemically synthesized Zn (II) and Cd (II) based metal-organic frameworks as fluoroprobes for sensing of 2,6-dichlorophenol

A sonochemical route for the synthesis of 2-D Zn (II) and Cd (II) based metal - organic frameworks (MOF) formulated as [Zn(apca)2]n and [CdCl2(apca)]n (Hapca ​= ​3-aminopyrazine-2-carboxylic acid) was developed. The MOFs synthesized were characterized using PXRD, FT-IR, SEM, and TGA analysis. The impact of different irradiation time and precursor concentration were investigated for attaining repetitious morphology. The DFT studies provide the detailed calculation of charge density distribution and electron localization function (ELF) of MOFs. The selectivity of the as-synthesized MOFs was studied for detecting phenolic structural analogs such as phenol, 2,6-dichlorophenol (2,6-DCP), 2,4-dichlorophenol (2,4-DCP), 4-chlorophenol (4-CP), 2-Chlorophenol (2-CP), 2,4,6-trichlorophenol(2,4,6-TCP), 2-methoxyphenol (2-MP), 2-nitrophenol (2-NP), and 4-hydroxyphenol (4-HP) out under optimal conditions. The results revealed that our proposed probes are equipped with excellent recognition ability for almost exclusively 2,6-DCP. Both the MOFs exhibit a good linearity between the fluorescence intensity and analyte concentration in the range of 2–30 ​μmol ​L−1. The calculated limit of detection (LOD) for Zn-MOF and Cd-MOF was 5.6 ​μmol ​L−1 and 2.2 ​μmol ​L−1, respectively. The studies were further extended to fabrication of Zn-MOF@chitosan and Cd-MOF@chitosan membranes and proposed as solid fluoroprobes for detection of 2,6-DCP in real sample analysis.