Expansion Calculations Research Articles

Deformation tracking of honeycomb structure based on image skeletonization and branch point matching

Honeycomb structures have attracted much attention in various engineering fields due to its superiorities in high specific strength, high specific stiffness and excellent energy-absorbing characteristics. Therefore, it is very important to obtain the deformation state of honeycomb structure in the studies of its manufacturing process and mechanical behavior. In this study, a simple and efficient strategy for tracking the deformation of thin-walled honeycomb structure based on image skeletonization and branch points matching is presented. Principle and process of the new proposed strategy are first detailed, including image skeletonization, branch points selection, matching expansion and deformation calculation, etc. Simulations and experiments with compression and tensile deformations are performed to verify the efficiency of the proposed strategy. The results indicate that the displacement measurements based on the proposed strategy are able to provide subpixel-level accuracy, even though some interference branch points are generated during deformation. In addition, the limitations of the proposed strategy are discussed, which points out the train of thought for the subsequent research.

Thermal expansion calculation using FBGS in cryogenic applications

This study presents the measurement of the thermal expansion of aluminum alloy 6061 at cryogenic temperatures using Helium as the cooling medium. Three distinct tests were conducted to evaluate thermal expansion: two with gradual and natural heating of the material, and a third with temperature stabilization at key points. Measurements were carried out using Fiber Bragg Grating Sensors (FBGS), which provided precise and reliable data on the material's thermal behavior. The obtained results were compared with reference curves from the National Institute of Standards and Technology (NIST), showing good agreement and validation of the employed methods. This research highlights the effectiveness of using FBGS in measuring thermal expansion under cryogenic conditions and the importance of heating procedures in obtaining accurate data.

Structure Factors for Hot Neutron Matter from AbInitio Lattice Simulations with High-Fidelity Chiral Interactions.

We present the first abinitio lattice calculations of spin and density correlations in hot neutron matter using high-fidelity interactions at next-to-next-to-next-to-leading order in chiral effective field theory. These correlations have a large impact on neutrino heating and shock revival in core-collapse supernovae and are encapsulated in functions called structure factors. Unfortunately, calculations of structure factors using high-fidelity chiral interactions were well out of reach using existing computational methods. In this Letter, we solve the problem using a computational approach called the rank-one operator (RO) method. The RO method is a general technique with broad applications to simulations of fermionic many-body systems. It solves the problem of exponential scaling of computational effort when using perturbation theory for higher-body operators and higher-order corrections. Using the RO method, we compute the vector and axial static structure factors for hot neutron matter as a function of temperature and density. The abinitio lattice results are in good agreement with virial expansion calculations at low densities but are more reliable at higher densities. Random phase approximation codes used to estimate neutrino opacity in core-collapse supernovae simulations can now be calibrated with abinitio lattice calculations.

Experimental and simulation study on the expansion mechanism of polyurethane grout

Understanding the expansion mechanism of polyurethane polymer grout can supply guidance for accurate grouting. However, most of the polymer grout expansion calculations were defined simplistically by the polymer density-expansion pressure empirical relationship expression, which failed to meet the time history of the expansion pressure during the polymer reaction process. The objective of this paper was to investigate the expansion mechanism of polyurethane foam in various constraint conditions during the whole polymer reaction process. A model describing the expansion mechanism of polyurethane foam was established based on the energy conservation principle, the chemical reaction kinetic equation solved by the Runge-Kutta method, and the ideal gas state equation. The model was proved applicable compared to the experiments under fixed volume and fixed confining pressure boundaries. In addition, the effects of grouting quantity, confining pressure, initial temperature, and physical foaming agent content on the grout expansion pressure, density, and components conversions were discussed. The results showed that the expansion pressure of polymer grout gradually increased with time under the fixed volume conditions, and the grout expansion pressure increased as the density increased. The final grout expansion pressure will increase with the increase of initial temperature or the content of physical blowing agent. Under the fixed confining pressure condition, the polymer grout density gradually decreased with time, the grout density increased as the confining pressure increased while the conversions of the two components alcohol and isocyanate increased. The final density decreases with the increase of initial temperature or the content of physical blowing agent.

Sub-stoichiometry and vacancy structures in V/Nb carbide precipitates by cluster expansion and first-principles calculations

Carbide precipitates, particularly V/Nb carbides, play a vital role in modulating many properties, including strength, hardness, wear resistance and hydrogen embrittlement (HE) susceptibility of steels. Our work presented a comprehensive study employing a cluster expansion (CE) approach combined with first-principles calculations to investigate the sub-stoichiometry induced by C vacancies within V/Nb carbides, an important aspect lacking sufficient understanding. Ground-state sub-stoichiometric V/Nb carbide compounds as the C composition varies were predicted, consistent with experimental observations. The predictions were further supported by the good agreement between the calculated bulk moduli and experimental measurements. The elastic moduli of carbides were shown to monotonically decrease as the C composition decreases, attributed to pd bonds being replaced by dd bonds with the introduction of vacancies. We have demonstrated that C vacancies in the carbides would arrange into particular patterns, with notable preference to form 3NN vacancy pairs and triplets. Such vacancy pattern formation was elucidated to be mainly driven by the elastic interaction between vacancies. The present study provides critical new knowledge regarding sub-stoichiometry and vacancy structures in carbide precipitates in steels. The findings are critical for an accurate understanding of the structures and properties of carbides and offer essential inputs for engineering steels of enhanced performance.

Ab initio study of nuclear clustering in hot dilute nuclear matter

We present a systematic ab initio study of clustering in hot dilute nuclear matter using nuclear lattice effective field theory with an SU(4)-symmetric interaction. We introduce a method called light-cluster distillation to determine the abundances of dimers, trimers, and alpha clusters as a function of density and temperature. Our lattice results are compared with an ideal gas model composed of free nucleons and clusters. Excellent agreement is found at very low density, while deviations from ideal gas abundances appear at increasing density due to cluster-nucleon and cluster-cluster interactions. In addition to determining the composition of hot dilute nuclear matter as a function of density and temperature, the lattice calculations also serve as benchmarks for virial expansion calculations, statistical models, and transport models of fragmentation and clustering in nucleus-nucleus collisions.

Hydrodynamics of polydisperse gas-solid flows: Kinetic theory and multifluid simulation

Polydisperse gas-solid flows, which is notoriously difficult to model due to the complex gas-particle and particle-particle interactions, are widely encountered in industry. In this article, a refined kinetic theory for polydisperse flow is developed, which features single-parameter Chapman-Enskog expansion (the Knudsen number) and exact calculation of the integrations related to pair distribution function of particle velocity without any mathematical approximations. The Navier-Stokes order constitutive relations for multifluid modeling of polydisperse gas-solid flow are then obtained analytically, including the solid stress tensor, the solid-solid drag force, the granular heat flux and the energy dissipation rate. Finally, the model is preliminarily validated by comparing to the discrete element simulation data of one-dimensional granular shear flow and by showing that the hydrodynamic characteristics of gas-solid flows in a bubbling fluidized bed containing bidisperse particles can be successfully predicted.

Evolution of coal permeability during gas/energy storage

Both carbon dioxide and hydrogen can be stored in coal seams as two enabling components of energy transition from fossil-based systems to renewable sources. In both cases, understanding the evolution of coal permeability under the influence of gas adsorption is extremely important. The gas sorption-induced deformation is commonly treated by analogous calculation of thermal expansion. This assumption has long been proved to be inconsistent with observations as reported in the literature. In this study, we hypothesize that the difference between the assumption and the reality is due to self-constrained/facilitated swelling phenomena during gas injection. Under this new hypothesis, coal could be constrained or facilitated depending on coal internal structures and processes. A concept of fictitious stress is introduced to quantify coal self-constrained or facilitated degree and converted into the equivalent effective stress. This conversion has transformed the conventional effective stress principle to unconventional one. This has led to new generic coal permeability model, which has been validated by experimental data. An analysis of stress state evolution during gas storage process is conducted. Our results suggest that our coal permeability model is a valuable tool for evaluation of gas storage in coal seams.

Manual versus deep learning measurements to evaluate cumulus expansion of bovine oocytes and its relationship with embryo development in vitro

Cumulus expansion is an important indicator of oocyte maturation and has been suggested to be indicative of greater oocyte developmental capacity. Although multiple methods have been described to assess cumulus expansion, none of them is considered a gold standard. Additionally, these methods are subjective and time-consuming. In this manuscript, the reliability of three cumulus expansion measurement methods was assessed, and a deep learning model was created to automatically perform the measurement. Cumulus expansion of 232 cumulus-oocyte complexes was evaluated by three independent observers using three methods: (1) measurement of the cumulus area, (2) measurement of three distances between the zona pellucida and outer cumulus, and (3) scoring cumulus expansion on a 5-point Likert scale. The reliability of the methods was calculated in terms of intraclass-correlation coefficients (ICC) for both inter- and intra-observer agreements. The area method resulted in the best overall inter-observer agreement with an ICC of 0.89 versus 0.54 and 0.30 for the 3-distance and scoring methods, respectively. Therefore, the area method served as the base to create a deep learning model, AI-xpansion, which reaches a human-level performance in terms of average rank, bias and variance. To evaluate the accuracy of the methods, the results of cumulus expansion calculations were linked to embryonic development. Cumulus expansion had increased significantly in oocytes that achieved successful embryo development when measured by AI-xpansion, the area- or 3-distance method, while this was not the case for the scoring method. Measuring the area is the most reliable method to manually evaluate cumulus expansion, whilst deep learning automatically performs the calculation with human-level precision and high accuracy and could therefore be a valuable prospective tool for embryologists.

Calculation and analysis of compression and expansion in a piston hybrid power machine with regenerative heat exchange in pump mode

Calculation and analysis of compression and expansion in a piston hybrid power machine with regenerative heat exchange in pump mode

The zero-point vibration contributions to energy and compressibility of light rare-gas solids

The zero-point vibration energy, Gruneisen coefficient, and zero-point vibration pressure of light rare-gas solids (LRGS)(He, Ne, Ar) are calculated within a certain range of atomic spacing using many-body expansion and ab initio calculation methods based on quantum and atomic cluster theories. The results are then compared with the previous theoretical calculations and experimental data. It is concluded that the smaller the molar volume of LRGS, the greater the crystal's zero-point vibration energy and vibration frequency. The zero-point vibration energy of LRGSis only 6% of the total many-body interaction energy but should not be neglected. The Grüneisen coefficient of LRGS increases as the molar volume increases. The zero-point vibration pressure is smaller, which is about 3% of the total pressure. The error caused by the pressure calculation is not significant, but when the molar volume is reduced to a fixed value, the zero-point vibration pressure must be considered and cannot be ignored. In addition, the calculation results of zero-point vibration pressure are compared to the previous theoretical calculations and experimental results.

Chemically aware unitary coupled cluster with abinitio calculations on an ion trap quantum computer: A refrigerant chemicals' application.

Circuit depth reduction is of critical importance for quantum chemistry simulations on current and near term quantum computers. This issue is tackled by introducing a chemically aware strategy for the unitary coupled cluster ansatz. The objective is to use the chemical description of a system to aid in the synthesis of a quantum circuit. We combine this approach with two flavors of symmetry verification for the reduction of experimental noise. These methods enable the use of Quantinuum's System Model H1 ion trap quantum computer for a 6-qubit quantum subspace expansion calculation. We present (i) calculations to obtain methane's optical spectra; (ii) an atmospheric gas reaction simulation involving [CH3⋅-H-OH]‡. Using our chemically aware unitary coupled cluster state-preparation strategy in tandem with state of the art symmetry verification methods, we improve device yield for CH4 at 6 qubits. This is demonstrated by a 90% improvement in two-qubit gate count and a reduction in relative error to 0.2% for electronic energy calculated on System Model H1.

Model of SPS Two-Stadium Synthesis and Densification Reactor Applied for Ultrafine Zirconium Nitride Powder

The volumetric changes and variable porosity due to the concentration expansion of the solid phase in the synthesis of zirconium nitride (ZrN) are studied. The model of two-stage reactor based on spark plasma sintering (SPS) is proposed. At the first stage the synthesis for the given kinetics is simulated. At the second stage the densification of ZrN using the Olevsky’s sintering model [1-5] is applied. The synthesis and densification processes using the prescribed heat sources, at the given positions inside the reactor is simulated. The generalization of the two-temperature model [6] and the formula of the porosity in the densification using calculation of the solid concentration expansion and thermal dispersion is proposed. The concentration expansion coefficients in the process of zirconium nitrogenating at a given initial density values and coefficients of expansion of reagents .is studied The temperature at the stage of ZrN synthesis and porosity variation at the stage of densification are in satisfactory agreement with experimental results [2,7,8]

Vibrational response functions for multidimensional electronic spectroscopy in nonadiabatic models.

The interplay of nuclear and electronic dynamics characterizes the multidimensional electronic spectra of various molecular and solid-state systems. Theoretically, the observable effect of such interplay can be accounted for by response functions. Here, we report analytical expressions for the response functions corresponding to a class of model systems. These are characterized by coupling between the diabatic electronic states and the vibrational degrees of freedom, resulting in linear displacements of the corresponding harmonic oscillators, and by nonadiabatic couplings between pairs of diabatic states. In order to derive the linear response functions, we first perform the Dyson expansion of the relevant propagators with respect to the nonadiabatic component of the Hamiltonian, then derive and expand with respect to the displacements the propagators at given interaction times, and finally provide analytical expressions for the time integrals that lead to the different contributions to the linear response function. The approach is then applied to the derivation of third-order response functions describing different physical processes: ground state bleaching, stimulated emission, excited state absorption, and double quantum coherence. Comparisons between the results obtained up to sixth order in the Dyson expansion and independent numerical calculation of the response functions provide evidence of the series convergence in a few representative cases.

QED mα7 effects for triplet states of heliumlike ions

We perform ab initio calculations of the QED effects of order $m{\ensuremath{\alpha}}^{7}$ for the $2^{3}S$ and $2^{3}P$ states of He-like ions. The computed effects are combined with previously calculated energies [V. A. Yerokhin and K. Pachucki, Phys. Rev. A 81, 022507 (2010)], thus improving the theoretical accuracy by an order of magnitude. The obtained theoretical values for the $2\phantom{\rule{0.16em}{0ex}}^{3}S\ensuremath{-}2\phantom{\rule{0.16em}{0ex}}^{3}P_{0,2}$ transition energies are in good agreement with available experimental results and with previous calculations performed to all orders in the nuclear binding strength parameter $Z\ensuremath{\alpha}$. For the ionization energies, however, we find some inconsistency between the $Z\ensuremath{\alpha}$-expansion and all-order calculations, which might be related to a similar discrepancy between the theoretical and experimental results for the ionization energies of helium [V. Patk\'o\ifmmode \check{s}\else \v{s}\fi{} et al., Phys. Rev. A 103, 042809 (2021)].

Novel Carbene Hydroxymethylene Derivatives: Gibbs free energy, NBO, AIM, and Hammett approaches via DFT and MP2 methods

Density functional theory (DFT) and the Møller-Plesset expansion (MP2) calculations were benchmarked to characterize the structure of novel derivatives of carbene hydroxymethylene. In this regard, eleven numbers of primary aldehydes including formaldehyde, acetaldehyde, formyl chloride, 2-chloroacetaldehyde, formyl fluoride, 2-fluoroacetaldehyde, formic acid, propionaldehyde, glyoxal, methyl formate, and formyl bromide (1H-11Br) were scrutinized, at the B3LYP/6-311++G(3d,3p) level of theory. Thereafter, the process of keto-enol tautomerism via a [1,2]-H-shift of 1H-11Br was monitored to reach their corresponding enol forms (1P-11P). For all species (except for one structure), the TS involves a triangle structure of C-O-H and yields cis or trans isomers of a singlet ground-state (S) carbene that contrasts the multiplicity of ordinary carbenes. The bond dissociation energy (BDE) calculations were carried out for the homolytic cleavage of C−H bonds of 1H-11Br. The AIM, as a promising analysis that definitely reveals the nature of the bond, was conducted to characterize the eigenvalues at the bond critical points (BCPs). In addition, the relation between the Hammett equation and thermodynamic parameters was obtained. Our investigation suggests new stable S derivatives of carbene hydroxymethylene that can be isolated.

STUDY ON VIBRATION AND THERMAL EXPANSION OF HEATING FURNACE MANIFOLD BASED ON FLUID-STRUCTURE INTERACTION METHOD

In the petrochemical industry, the manifolds are usually adopted as the distributor of the heating furnace. The structure of the manifold plays a crucial role in the safe operation of the heating furnace. For the straight tube structure and fishbone structure of the manifold, thermal expansion calculation was carried out in this paper. The expansion amount of each branch pipe was obtained, and the maximum expansion amount of the branch pipe was 91.8% of the reserved size. The accuracy of the design of the branch pipe wall clearance allowance was verified. Numerical simulations of the fluid-structure interaction were carried out for both structures, which showed that the two structures have similar deformation and frequency in terms of overall structural vibration. However, in the branch vibration, the stress and vibration frequency of the fishbone branch increase by 12.6% and 25.3%, respectively, compared to the straight tube branch, which is caused by the presence of large vortices in the branch of the fishbone structure. Finally, modal analyses were performed for both structures, and the results can be used to estimate whether the vibration frequencies of the two structures avoid the natural frequencies.

Excitation of a rectangular resonator through communication windows in the conveyor installation of microwave heating

Abstract Based on the excitation theory of L.A. Vainstein obtained simple and convenient iterative relations for excitation of a resonator in the form of a rectangular parallelepiped with a dielectric layer through several coupling windows in its walls. Theexpansion of the field in terms of the complete system of solenoidal functions of a rectangular resonator is used. Solenoidality is due to the fact that the electric fields of excitation in the openings of rectangular waveguides on the resonator walls, fed through coaxial-waveguide transitions, are tangent to the boundaries of the heated dielectric layer. Simple formulas for expansion coefficients and calculation of fields are obtained. It is convenient to solve the obtained implicit formulas iteratively; in this case, it is possible to take into account both a linear dielectric and a nonlinear dielectric, the permittivity of which depends on the square of the electric field. The algorithm is implemented to simulate a conveyor installation of microwave heating. It is possible to modify the algorithm by introducing potential basic subsystems of functions for the case of modeling complex dielectric inclusions. The results are suitable for modeling other nonlinear inclusions, as well as in problems when using volumetric given sources instead of surface ones. For given electric fields in the coupling windows, the power entering the resonator is calculated on the basis of the Poynting vector.

Analytical solution to wave diffraction by a hemisphere in infinite water depth using the multipole expansion method

Linear water wave diffraction by a hemisphere in infinite water depth is investigated using the multipole expansion method in this paper. In the spherical coordinate system, the diffraction potential is expressed in the form of multipole wave potentials and the wave-free potential, as derived by Hulme (1982) for radiation potentials. The issues associated with the high-order multipole expansion are solved in this paper. The new method can calculate the multipole wave potentials at arbitrary orders and thus successfully calculate the diffraction potentials on the body surface and free surface around a hemisphere. The wave exciting forces acting on hemispheres are calculated using the near-field and far-field methods, which utilizes the radiation potential computed by Hulme's (1982) method to verify the accuracy of the analytical solution in this paper. Compared with the far-field method, the analytical solution in this paper converges more quickly as the truncation term N increases, especially when the wavenumber Ka is large. In this paper, the theory of applying the multipole expansion method to solve hydrodynamic problems with a hemisphere on the free surface is completed, which makes the multipole expansion method no longer limited to low-order expansion calculations and can be applied to more fields.

To the cusp and back: resurgent analysis for modular graph functions

Modular graph functions arise in the calculation of the low-energy expansion of closed-string scattering amplitudes. For toroidal world-sheets, they are SL(2, ℤ)-invariant functions of the torus complex structure that have to be integrated over the moduli space of inequivalent tori. We use methods from resurgent analysis to construct the non-perturbative corrections arising for two-loop modular graph functions when the argument of the function approaches the cusp on this moduli space. SL(2, ℤ)-invariance will in turn strongly constrain the behaviour of the non-perturbative sector when expanded at the origin of the moduli space.