Scalar Density Research Articles

On the kinetic physical and mathematical metal creep theory controlled by thermally activated dislocation sliding

The rationale for the prospects of using the physical and mathematical theory of metal creep in creep computations is carried out by a comparative analysis of the classical phenomenological and physical and mathematical metal creep theories. On the example of the description by both theories specific results of non-stationary creep experiments and analysis of the theories equations it is shown that implementing the physical kinetic equation for the actual structural parameter of the material, namely the scalar density of immobile dislocations, makes the physical and mathematical theory universal for solving non-stationary metal creep problems with multiaxial loading, when change, including abruptly, temperature, forces and loading rates.

Extraordinary Nature of the Nucleon Scalar Charge and Its Densities as a Signal of Nontrivial Vacuum Structure of QCD

It is widely known that the nucleon scalar charge is proportional to the pion–nucleon sigma term as one of the important low-energy observables of QCD. Especially interesting to us is the physics of the nucleon scalar charge densities. This comes from the fact that the corresponding operator has the same quantum number as the physical vacuum. It indicates unusual behavior of the nucleon scalar density as a function of the distance r from the nucleon center. Namely, it would not be reduced down to zero at the spatial infinity but rather approach some nonzero constant corresponding to the vacuum quark condensate. Naturally, this unique nature of the nucleon scalar density in the position space also affects the corresponding density in the momentum space, i.e., the corresponding parton distribution function (PDF) as a function of the Bjorken variable x. This PDF is known as the chiral-odd twist-3 PDF e(x). We argue that e(x) is likely to have a delta-function-type singularity at x=0 and that the appearance of this singularity can be interpreted as a signal of the nontrivial vacuum structure of QCD.

Periodic Bonding Behaviors of Actinide Atoms (An = Th-Cm) with Negatively Curved Nanographene.

The nanographene with negative curvature has been extensively studied due to its interesting properties and potential applications. In the present work, we have performed all-electron scalar relativistic density functional theory (DFT) calculations to understand the periodic interaction mechanisms of actinide atoms (An = Th, Cm) with the TB8C nanographene. The encapsulated complexes (An@TB8C) were formed due to the octagonal vacancy in the TB8C nanographene. TB8C shows fairly high affinity toward An atoms, especially for Th and Pa. AIMD simulations further confirmed the effective trapping of An atom with TB8C. The partial covalent characters of An-C bonds in An@TB8C were revealed through various bond analysis methods. The 6d electrons of An play an important role in the participation of chemical bonds. The delocalization index (DI) is proposed as a useful descriptor in the study of bond strength involving the actinides. Electronic absorption spectra were simulated for further identification in the experiments. The current work has expanded the potential molecular properties and applications of nanographene.

Reactivity of Zinc Fingers in Oxidizing Environments: Insight from Molecular Models Through Activation Strain Analysis.

The reactivity of Zn2+ tetrahedral complexes with H2O2 was investigated in silico, as a first step in their disruption process. The substrates were chosen to represent the cores of three different zinc finger protein motifs, i. e., a Zn2+ ion coordinated to four cysteines (CCCC), to three cysteines and one histidine (CCCH), and to two cysteines and two histidines (CCHH). The cysteine and histidine ligands were further simplified to methyl thiolate and imidazole, respectively. H2O2 was chosen as an oxidizing agent due to its biological role as a metabolic product and species involved in signaling processes. The mechanism of oxidation of a coordinated cysteinate to sulfenate-κS and the trends for the different substrates were rationalized through activation strain analysis and energy decomposition analysis in the framework of scalar relativistic Density Functional Theory (DFT) calculations at ZORA-M06/TZ2P ae // ZORA-BLYP-D3(BJ)/TZ2P. CCCC is oxidized most easily, an outcome explained considering both electrostatic and orbital interactions. The isomerization to sulfenate-κO was attempted to assess whether this step may affect the ligand dissociation; however, it was found to introduce a kinetic barrier without improving the energetics of the dissociation. Lastly, ligand exchange with free thiolates and selenolates was investigated as a trigger for ligand dissociation, possibly leading to metal ejection; molecular docking simulations also support this hypothesis.

Cooperative Mission Planning Using Rollout Policy Optimization

This paper proposes a novel cooperative mission planning for uncrewed aerial systems (UAS), using roll-out policy optimization and a blend of straight and double-Archimedean-spiral (DAS) paths. Typical mission tasks using UAS, possibly multiple, include visiting distinct locations/waypoints and covering specific areas of interest (AOIs). For the UAS, to guarantee the coverage of the AOI, the algorithm generates a DAS path that even accounts for the sensor’s field-of-view constraints. A scalar spiral density parameter in the algorithm effectively provides customized adjustments to the length of the DAS over an AOI while developing mission plans. A lower and upper bound value for the spiral density parameter and the dependency of the parameter on the coverage of an AOI are derived. This scalar parameter gives the users potential flexibility in the design of mission plans. Roll-out policy optimization minimizes the overall path length for the cooperative UAS mission and, as a direct consequence, minimizes time and fuel. This method leads to finding a near-optimal path in that the computation time does not grow exponentially with the number of UAS. Results from the simulation studies with several cooperative mission scenarios, including multiple UASs visiting several waypoints and AOIs starting from identical and distinct initial locations, demonstrate the efficacy of the proposed concept. The results from a data-based complex test case using the LiDAR data set further demonstrate the adaptability of the proposed mission planning approach in a real-world setting.

Simulations of Stochastic Fluid Dynamics near a Critical Point in the Phase Diagram.

We present simulations of stochastic fluid dynamics in the vicinity of a critical endpoint belonging to the universality class of the Ising model. This study is motivated by the challenge of modeling the dynamics of critical fluctuations near a conjectured critical endpoint in the phase diagram of quantum chromodynamics (QCD). We focus on the interaction of shear modes with a conserved scalar density, which is known as model H. We show that the observed dynamical scaling behavior depends on the correlation length and the shear viscosity of the fluid. As the correlation length is increased or the viscosity is decreased we observe a crossover from the dynamical exponent of critical diffusion, z≃4, to the expected scaling exponent of model H, z≃3. We use our method to investigate the time-dependent correlation function of non-Gaussian moments M^{n}(t) of the order parameter. We find that the relaxation time depends in a nontrivial manner on the power n.

Theoretical study of the ability of symmetric and asymmetric N-donor ligands to separate Am(III) and Eu(III) and the bonding nature

In the reprocessing of spent nuclear fuel, nitrogen-donor extractants are more effective in separating actinides and lanthanides. In this article, a series of heterocyclic N-donor ligands with different backbones and different side chain substituents are systematically investigated to analyze their extraction selectivity and complexation abilities for Am(Ⅲ) and Eu(Ⅲ) by using scalar relativistic density functional theory (DFT). Through the analysis of geometric structures and bond properties of the complexes by means of the NBO and QTAIM methods, it was observed that the coordination ability of the N-donor ligand with Am(Ⅲ) was stronger than with Eu(Ⅲ). Thermodynamic analysis showed that these ligands have good extraction ability and separation performance for Am(III) and Eu(III), the backbone and side chain substituents of the ligands and also the organic solvents have significant influences on the extraction selectivity of the ligands for Am(III) and Eu(III) ions. This work provides some theoretical insights for the design of N-donor extractants with good separation performance for lanthanides and actinides.

Exploring the bonding and extraction separation effects of N donor ligands with different skeletons on Am(III) and Eu(III)

Designing ligands for effective separation of actinide(III)/lanthanide(III) is one of the key issues in the treatment of spent nuclear fuel. However, due to the chemical similarity of trivalent actinides and lanthanides, their separation faces a great challenge in the reprocessing of spent nuclear fuel. Nitrogen donor extractants are considered as promising reagents for separation of trivalent actinides and lanthanides. To the best of our knowledge, the pre-organized structure of the ligand has a strong influence on the extraction separation capacity. In this work, we designed four N-donor ligands (L1 and L2 with pyridine and bipyridine skeletons, respectively, and L3 and L4 both with phenanthroline skeletons) with different pre-organized structures and investigated their selective extraction for Am(III) and Eu(III) by using scalar relativistic density functional theory (DFT). The absolute minimum ESP values of these ligands and the higher HOMO level suggest that the ligand L2 may have a stronger affinity for Am(III)/Eu(III) ions than other ligands. The three average bond lengths of each complex indicate that the Am(III) and Eu(III) ions have larger bond lengths with N2 atoms than with N1 atoms. Various theoretical approaches have been used to evaluate the properties of the four ligands as well as the coordination structures, bonding properties and thermodynamic properties of the complexes of the four ligands with Am(III) and Eu(III). The WBIs, QTAIM, NBO, DOS and EDA analysis indicate that the metal–ligand bonds are mainly ionic in character, the Am-N bond has more covalency than the Eu-N bond because the Am 5f orbitals are more involved in bonding with ligand than Eu 4f orbitals. According to the extended transition state and natural orbital chemical valence theory (ETS-NOCV) analysis, electrons are obviously transferred from the lone pair of the ligand N atom to the hybrid s, d and f orbitals of the metal ion. The thermodynamic results show that the four ligands can coordinate well with the Am and Eu ions, and also have suitable separation capacity for Am and Eu. Among the four ligands, the L2 and L3 ligands have the strongest coordination ability for metals and the best extraction separation effect for Am and Eu. It can be seen that the bridging skeleton of the ligand and the number of N atoms on the five-membered ring and also different organic solvents have obvious effects on the extraction and separation capacity of the ligand. This study provides a theoretical basis for the efficient separation of Am(III)/Eu(III) by adjusting the preorganization level of ligands, and provides a theoretical basis for the design and screening of ligands by preorganization.

Multivariate and Matrix-Variate Logistic Models in the Real and Complex Domains

Several extensions of the basic scalar variable logistic density to the multivariate and matrix-variate cases, in the real and complex domains, are given where the extended forms end up in extended zeta functions. Several cases of multivariate and matrix-variate Bayesian procedures, in the real and complex domains, are also given. It is pointed out that there are a range of applications of Gaussian and Wishart-based matrix-variate distributions in the complex domain in multi-look data from radar and sonar. It is hoped that the distributions derived in this paper will be highly useful in such applications in physics, engineering, statistics and communication problems, because, in the real scalar case, a logistic model is seen to be more appropriate compared to a Gaussian model in many industrial applications. Hence, logistic-based multivariate and matrix-variate distributions, especially in the complex domain, are expected to perform better where Gaussian and Wishart-based distributions are currently used.

Fully non-Gaussian Scalar-Induced Gravitational Waves

Scalar-Induced Gravitational Waves (SIGWs) represent a particular class of primordial signals which are sourced at second-order in perturbation theory whenever a scalar fluctuation of the metric is present. They form a guaranteed Stochastic Gravitational Wave Background (SGWB) that, depending on the amplification of primordial scalar fluctuations, can be detected by GW detectors. The amplitude and the frequency shape of the scalar-induced SGWB can be influenced by the statistical properties of the scalar density perturbations. In this work we study the intuitive physics behind SIGWs and we analyze the imprints of local non-Gaussianity of the primordial curvature perturbation on the GW spectrum. We consider all the relevant non-Gaussian contributions up to fifth-order in the scalar seeds without any hierarchy, and we derive the related GW energy density ΩGW(f). We perform a Fisher matrix analysis to understand to which accuracy non-Gaussianity can be constrained with the LISA detector, which will be sensitive in the milli-Hertz frequency band. We find that LISA, neglecting the impact of astrophysical foregrounds, will be able to measure the amplitude, the width and the peak of the spectrum with an accuracy up to 𝒪(10-4), while non-Gaussianity can be measured up to 𝒪(10-3). Finally, we discuss the implications of our non-Gaussianity expansion on the fraction of Primordial Black Holes.

Dynamical system analysis of scalar field cosmology in coincident f(Q) gravity

In this article, we investigate scalar field cosmology in the coincident f(Q) gravity formalism. We calculate the motion equations of f(Q) gravity under the flat Friedmann-Lemaître-Robertson-Walker background in the presence of a scalar field. We consider a non-linear f(Q) model, particularly f(Q) = − Q + α Q n , which is nothing but a polynomial correction to the Symmetric Teleparallel Equivalent to General Relativity (STEGR) case. Further, we assumed two well-known specific forms of the potential function, specifically the exponential from V(ϕ) = V 0 e −β ϕ and the power-law form V(ϕ) = V 0 ϕ −k . We employ some phase-space variables and transform the cosmological field equations into an autonomous system. We calculate the critical points of the corresponding autonomous systems and examine their stability behaviors. We discuss the physical significance corresponding to the exponential case for parameter values n = 2 and n = − 1 with β = 1, and n = − 1 with β=3 . Moreover, we discuss the same corresponding to the power-law case for the parameter value n = − 2 and k = 0.16. We also analyze the behavior of corresponding cosmological parameters such as scalar field and dark energy density, deceleration, and the effective equation of state parameter. Corresponding to the exponential case, we find that the results obtained for the parameter constraints in Case III is better among all three cases, and that represents the evolution of the Universe from a decelerated stiff era to an accelerated de-Sitter era via matter-dominated epoch. Further, in the power-law case, we find that all trajectories exhibit identical behavior, representing the evolution of the Universe from a decelerated stiff era to an accelerated de-Sitter era. Lastly, we conclude that the exponential case shows better evolution as compared to the power-law case.

Dipole symmetries from the topology of the phase space and the constraints on the low-energy spectrum

We demonstrate the general existence of a local dipole conservation law in bosonic field theory. The scalar charge density arises from the symplectic form of the system, whereas the tensor current descends from its stress tensor. The algebra of spatial translations becomes centrally extended in presence of field configurations with a finite nonzero charge. Furthermore, when the symplectic form is closed but not exact, the system may, surprisingly, lack a well-defined momentum density. This leads to a theorem for the presence of additional light modes in the system whenever the short-distance physics is governed by a translationally invariant local field theory. We also illustrate this mechanism for axion electrodynamics as an example of a system with Nambu-Goldstone modes of higher-form symmetries.

High-valent actinyl (AnO2; An = U, Np and Pu) complexation with TEtraQuinoline (TEQ) ligand - a DFT study.

A recently synthesised novel macrocycle composed of four quinoline units called TEtraquinoline (TEQ) (J. Am. Chem. Soc., 2023, 145(4), 2609-2618) was reported to exhibit transition metal complexation ability. Meanwhile, there is a growing interest in different binding motifs for radioactive and toxic actinides. In this study, we modelled high-valent actinyl (AnO2)n+, An = U, Np, Pu; n = 1, 2, 3 complexes of TEQ and studied their geometric and electronic properties using scalar relativistic density functional theory (SR-DFT). The calculated results showed that the equatorial An-N and axial AnO bonds were polar bonds with a high degree of covalence, the former being longer than the latter. Natural bond orbital (NBO) analysis of the An-N bond orders decreased from complexes of uranyl to plutonyl and from complexes of heptavalent to pentavalent actinyls. This was due to the localization of the 5f orbital in the heavier actinyl and the high charge on An. The charge analysis showed a ligand-to-metal charge transfer (LMCT) on complexation. It was interesting to observe metal-to-ligand spin delocalization only in the [AnVI/VIIO2L]2+/3+ complexes, where the spin density on An was observed to increase on complexation. Based on the assigned oxidation states, it was observed that the heptavalent neptunyl cation retained its formal high oxidation state on complexation with TEQ. The energetics associated with the formation reaction of all the actinyl-TEQ complexes suggest spontaneity at lower temperatures (i.e., lower than 298.15 K). The energy decomposition analysis (EDA) indicates that the electrostatic energy contributions were predominant in the [AnVO2L]+ complexes, while covalent (orbital) energy contributions were higher in the [AnVIO2L]2+ and [AnVIIO2L]3+ complexes. The extended transition state-natural orbitals for chemical valence (ETS-NOCV) analysis confirmed the prominent covalent character in [AnVIIO2L]3+ over [AnVIO2L]2+ and [AnVO2L]+and the back donation of charges from An to N that stabilizes TEQ.

Parallel optimization approaches for scattering source term and angle merging in MOC high-order anisotropic computation on GPUs

The introduction of high-order anisotropic scattering and thousand-group calculations significantly increases the computational workload of the MOC method, posing difficulties for practical parallel computation on GPUs. In this paper, a GPU-based MOC algorithm is optimized, focusing on the performance optimization of the kernel function that merges high-order anisotropic angular flux density into scalar flux density moments, as well as the optimization of the scattering source term calculation method in thousand-group calculations. Two parallel algorithms based on azimuthal and polar angles are proposed for high-order anisotropic scattering. For the thousand-group calculation, a data structure is designed according to the physical characteristics of the anisotropic scattering matrix, and then two optimization algorithms are proposed from the perspectives of memory access and parallelism. Based on the KAIST-3A reference problem, the parallel expansion of the polar angle in the merging calculation is more advantageous. Based on the KAIST-3A reference problem, the parallel expansion of the polar angle in the merging calculation is found to be more advantageous. Based on a self-designed fast reactor fuel lattice, it is concluded that the parallelism-oriented calculation method for the thousand-group anisotropic scattering source term is more efficient. Finally, the Roofline model is used to analyze the advantages of the algorithm.

One-sided friction stir welding of 1565сhM alloy plates

The results of experimental studies of the features of the structure of butt joints of 1565chM alloy plates with a thickness of 25 mm obtained by one-sided friction stir welding are presented. It is established that the structure of the mixing zone (weld metal) is a dynamically and primarily recrystallized region. The grain size in the weld metal varies depending on the distance from the front surface of the weld from 5.16 μm (upper part of the joint) to 2.93 μm (root part of the joint). The separation of intermetallic compounds in the mixing zone for Al—Mg system alloys helps to reduce the average grain size. In the bodies of grains at the level of half the thickness of the plate, there are both chaotically distributed dislocations and dislocation clusters mainly in the form of dislocation walls. In this case, the scalar density of dislocations at this level exceeds the values of the scalar density of dislocations in the upper and root parts of the weld. In the mixing zone of the joints of the 1565chM alloy plates the microstructure at different levels of horizontal sections along the thickness of the plate is very homogeneous, which indicates the mechanism of layer-by-layer transfer, which is macroscopic.

Heterocyclic Ligands with Different N/O Donor Modes for Am(III)/Eu(III) Separation: A Theoretical Perspective.

Excellent "CHON" compatible ligands based on a heterocyclic skeleton for the separation of trivalent actinides [An(III)] from lanthanides [Ln(III)] have been widely explored, the aim being spent nuclear fuel reprocessing. The combination mode of a soft/hard (N/O) donor upon the coordination chemistry of An(III) and Ln(III) should play a vital role with respect to the performance of ligands. As such, in this work, two typical experimentally available phenanthroline-derived tetradentate ligands, CyMe4-BTPhen (L1) and Et-Tol-DAPhen (L4), and two theoretically designed asymmetric tetradentate heterocyclic ligands, L2 and L3, with various N/O donors were investigated using scalar relativistic density functional theory. We have evaluated the electronic structures of L1-L4 and their coordination modes, bonding properties, and extraction reactions with Am(III) and Eu(III). We found that the Am/Eu-N interactions play a more important role in the orbital interactions between the ligand and Am(III)/Eu(III) ions. Compared with those of L1, the coordinated O atoms of L2 and L4 weaken the metal-N bonds. The Am(III)/Eu(III) selectivity follows the order L1 > L2 > L4 based on the change in Gibbs free energy, reflecting the fact that the Am(III)/Eu(III) selectivity of the ligand is affected by the number of coordinated N atoms. In addition, L3 displays the strongest binding ability for Am(III)/Eu(III) ions and the smallest Am(III)/Eu(III) selectivity among the four ligands, due to its structural preorganization. This work clarifies the influence of the number of coordinated N and O atoms of ligands on Am(III)/Eu(III) selectivity, which provides valuable fundamental information for the design of efficient ligands with N and O donors for An(III)/Ln(III) separation.

Deep Learning of Joint Scalar PDFs in Turbulent Flames from Sparse Multiscalar Data

ABSTRACT We investigate the reconstruction of multi-dimensional joint scalar probability density functions starting with sparse multiscalar data in turbulent flames using deep operator networks (DeepONets). The formulation is based on 1) a dimensionality reduction to reduce the complexity of modeling the PDF using principal component analysis (PCA), and 2) the implementation of the deep operator neural network (or DeepONet) to construct a generalizable joint PDF of the principal components (PCs). We demonstrate the accuracy and generalizability of the DeepONet on the Sandia turbulent non-premixed flames D, E and F where the DeepONet is trained on data for flame E and is evaluated for the 3 flames. The DeepONet-based approach is able to construct multiple PDF shapes based on the PCs for all conditions. Combined with a recently proposed method for evaluating thermochemical scalar means conditioned on the PCs, the convolution of these means with the joint PDFs yields good predictions of thermochemical scalars’ unconditional means profiles in the flames.

Stochastic modeling of turbulent mixing based on a hierarchical swapping of fluid parcels

AbstractTurbulent mixing is an omnipresent phenomenon that constantly affects our everyday life and plays an important role in a variety of industrial applications. The simulation of turbulent mixing poses great challenges, since the full resolution of all relevant length and time scales is associated with an immense computational effort. This limitation can be overcome by only resolving the large‐scale effects and completely model the sub‐grid scales. The development of an accurate sub‐grid mixing model is therefore a key challenge to capture all interactions in the sub‐grid scales. At this place, the hierarchical parcel‐swapping (HiPS) model formulated by A.R. Kerstein [J. Stat. Phys. 153, 142–161 (2013)] represents a computationally efficient and scale‐resolving turbulent mixing model. HiPS mimics the effects of turbulence on time‐evolving, diffusive scalar fields. In HiPS, the diffusive scalar fields or a state space is interpreted as a binary tree structure, which is an alternative approach compared to the most common mixing models. Every level of the tree represents a specific length and time scale, which is based on turbulence inertial range scaling. The state variables are only located at the base of the tree and are treated as fluid parcels. The effects of turbulent advection are represented by stochastic swaps of sub‐trees at rates determined by turbulent time scales associated with the sub‐trees. The mixing only takes places between adjacent fluid parcels and at rates consistent with the prevailing diffusion time scales. In this work, the HiPS model formulation for the simulation of passive scalar mixing is detailed first. Preliminary results for the mean square displacement, passive scalar probability density function (PDF) and scalar dissipation rate are given and reveal the strengths of the HiPS model considering the reduced order and computational efficiency. These model investigations are an important step of further HiPS advancements. The integrated auxiliary binary tree structure allows HiPS to satisfy a large number of criteria for a good mixing model. From this point of view, HiPS is an attractive candidate for modeling the mixing in transported PDF methods.

Monopole and Instanton Effects on Connected and Disconnected Correlations for Scalar Density

Monopole and Instanton Effects on Connected and Disconnected Correlations for Scalar Density

Theoretical Study on the Coordination and Separation Capacity of Macrocyclic N-Donor Extractants for Am(III)/Eu(III).

Designing ligands that can effectively separate actinide An(III)/lanthanide Ln(III) in the solvent extraction process remains one of the key issues in the treatment of accumulated spent nuclear fuel. Nitrogen donor ligands are considered as promising extractants for the separation of An(III) and Ln(III) due to their environmental friendliness. Four new macrocyclic N-donor hexadentate extractants were designed and their coordination with Am(III) and Eu(III), as well as their extraction selectivity and separation performance for Am(III) and Eu(III), were investigated by scalar relativistic density functional theory. A variety of theoretical methods have been used to evaluate the properties of the four ligands and the coordination structures, bonding properties, and thermodynamic properties of the complexes formed by the four ligands with Am(III) and Eu(III). The results of various wavefunction analysis methods including NBO analysis, quantum theory of atoms in molecules (QTAIM) analysis, and so on show that Am(III) has a stronger coordination ability with the ligands than Eu(III) due to the Am 5f orbitals more involved in bonding with the ligands than the Eu 4f orbitals, and the bonding environment of the N-donor in the ligand has a significant effect on its coordination ability of the metal ions. Thermodynamic analysis of the solvent extraction process shows that all of the four N-containing macrocyclic ligands have good extraction selectivity and separation performance for Am(III) and Eu(III). This study provides theoretical support for designing potential nitrogen-containing macrocyclic extractants with excellent separation performance.