Macroscopic Field Research Articles

An efficient and high-fidelity local multi-mesh finite volume method for heat transfer and fluid flow problems in metal additive manufacturing

The multi-scale and nonlinear feature of additive manufacturing problems poses great challenges to numerical algorithms regarding computational efficiency and fidelity. In this work, we propose a novel local multi-mesh finite volume method for heat transfer and fluid flow problems in the additive manufacturing process. In this method, two sets of meshes (coarse base mesh and finer overlay mesh) are used to resolve the macroscopic temperature field of the whole domain and the mesoscopic heat transfer and fluid flow problem within a relatively small region covering the melt pool, respectively. The interaction between the base mesh and the overlay mesh is handled by the Dirichlet boundary conditions on the interface following the refinement-by-superposition idea, such that the powder-scale simulation is available with high efficiency. The finer mesh with cells of sub-powder size uses the arbitrary Lagrangian–Eulerian description and moves with the heat source to keep coverage of the region with high solution gradients. According to the moving feature of the finer mesh, a particle-volume fraction conversion scheme is introduced to update the material distribution. The local multi-mesh finite volume method is further combined with the discrete element method as well as a surface reconstruction method to alternatively solve the powder layering process and the laser melting process. A set of numerical cases is presented, and the numerical results are compared with analytical and experimental data from the literature, with good agreement in cases where such data is available. Moreover, the computational efficiency of the proposed method is proved to be dozens of times (16∼50 for the given size ratios of the melt pool to the whole domain) of the finite volume method using a uniform structured mesh. It is expected to be a powerful tool for efficiently achieving powder-scale simulation of the additive manufacturing process and other similar multi-scale problems.

Ferroelectricity and negative piezoelectric coefficient in orthorhombic phase pure ZrO2 thin films

A new approach for epitaxial stabilisation of ferroelectric orthorhombic (o-) ZrO2 films with negative piezoelectric coefficient in ∼ 8nm thick films grown by ion-beam sputtering is demonstrated. Films on (011)-Nb:SrTiO3 gave the oriented o-phase, as confirmed by transmission electron microscopy and electron backscatter diffraction mapping, grazing incidence x-ray diffraction and Raman spectroscopy. Scanning probe microscopy techniques and macroscopic polarization-electric field hysteresis loops show ferroelectric behavior, with saturation polarization of ∼14.3 µC/cm2, remnant polarization of ∼9.3 µC/cm2 and coercive field ∼1.2 MV/cm. In contrast to the o-films grown on (011)-Nb:SrTiO3, films grown on (001)-Nb:SrTiO3 showed mixed monoclinic (m-) and o-phases causing an inferior remnant polarization of ∼4.8 µC/cm2, over 50% lower than the one observed for the film grown on (011)-Nb:SrTiO3. Density functional theory (DFT) calculations of the SrTiO3/ZrO2 interfaces support the experimental findings of a stable polar o-phase for growth on (011) Nb:SrTiO3, and they also explain the negative piezoelectric coefficient.

Reduced state of the field and classicality of quantum Gaussian evolution

The notion of classicality of quantum evolution of light is an object of both conceptual and practical importance. The main goal of this work is to derive the exact conditions for the classicality of quantum Gaussian evolution, i.e., the evolution of Gaussian states of light and their convex combinations, a model which is of great significance in quantum optics and information. According to our findings, quantum Gaussian evolution should be considered classical if the Hamiltonian and Lindblad operators generating it correspond to passive optical transformations. This is illustrated with several explicit examples, ranging from Gaussian thermal operations to entanglement-maximizing dissipative engineering. Our results are obtained using the recently introduced mesoscopic formalism of the reduced state of the field, which was originally devised as as a description of macroscopic quantum fields. Here, to make the framework suitable for our goal, we redevelop it as a tool for probing classicality, which constitutes our second main contribution.

‘Another wall of turf’

Excavation of a well-preserved stretch of the rampart of the Antonine Wall east of Watling Lodge, at Laurieston, allowed for the first micromorphological study of its earthen building materials. This revealed that the rampart core, as well as the cheeks, were constructed in well layered courses of turf blocks – but sourced from different grasslands. The evidence differs from macroscopic observations made at other sections in this area where the rampart material had been interpreted as representing a loose earth core with clay cheeks. Our results show that even when the characteristic striped sections indicative of turf are not visible in the field, thin-section analysis can confirm the use of intact soil blocks with the remains of grassed surfaces. It now seems possible that the visible variation between materials in the eastern and western sectors of the Antonine Wall may simply be due to different types of turf used, varying in subsoil composition and topsoil formation, and representing differences in landscape management and survival of vegetation. Combined with macroscopic field recording to identify Roman building practices, our analysis of this section at Laurieston also shows the care that was taken to construct a level, well-draining base for the rampart to avoid slumping and moisture build-up. Further excavations and thin-section analysis elsewhere along the Wall are now needed to confirm whether turf was more extensively used than so far anticipated for the eastern sector and whether the Antonine Wall could possibly have been built completely of turf. Such conclusions would suggest a much more standardised construction process and more extensive grassland exploitation than considered up until now. While our results demonstrate the importance of micromorphological analysis for understanding this earthen UNESCO World Heritage site, our interdisciplinary approach may also have wider relevance for research on linear earthworks in different geographical and chronological settings.

High-resolution investigation of a conflagration event in the North-East Temple at Lachish via integration of forensic, stratigraphic and geoarchaeological evidence: A model for studying architectural destruction by fire

Burnt structures are well known archaeologically throughout the Near East. This study proposes an integrated interpretational framework for reconstructing fires in mud-brick structures using macro- and micro-archaeological types of evidence employing well-established tools. While previous research often utilized either macroscopic field evidence or micro-geoarchaeological data, here we present the integration of stratigraphy, architecture and location of artefacts in the framework of archaeology of crisis, spatial reconstruction of fire temperatures using micro-geoarchaeology, insights from experimental archaeology, and concepts from fire investigation. We demonstrate the utility of this integrative framework in a high-resolution reconstruction of a destructive fire event that occurred in the Late Bronze Age North-East Temple at Tel Lachish, ca. 1210–1126 BCE. We identify the area of ignition and the fire propagation path, and propose the cause of the fire in relation to the archaeology and history of the site in the 12th century BCE.

Combining Rankine–Hugoniot relations, ion dynamics in the shock front, and the cross-shock potential

Rankine–Hugoniot relations (RH) connect the upstream and downstream plasma states. They allow us to determine the magnetic compression, the density compression, and the plasma heating as functions of the Mach number, shock angle, and upstream temperature. RH are based on the conservation laws in the hydrodynamical form. In collisionless shocks, the ion distributions behind the shock transition are determined by ion dynamics in the macroscopic fields of the shock front. The ion parameters upon crossing the shock are directly related to the magnetic compression and the cross-shock potential. For given upstream parameters, RH provide the magnetic compression. If there is no substantial overshoot, an analytical estimate provides the cross-shock potential as a function of the magnetic compression and the Mach number. Numerical tracing of ions across a shock profile with the derived parameters provides the ion pressure, which is in good agreement with the combination of the two theoretical approaches.

Hydrodynamic phase field crystal approach to interfaces, dislocations, and multi-grain networks

We derive a phase field crystal model that couples the diffusive evolution of a microscopic structure with the fast dynamics of a macroscopic velocity field, explicitly accounting for the relaxation of elastic excitations. This model captures better than previous formulations the dynamics of complex interfaces and dislocations in single crystals as well as grain boundary migration in poly-crystals where the long-range elastic field is properly relaxed. The proposed model features a diffusivity that depends non-linearly on the local phase. It induces more localized interfaces between a disordered phase (liquid-like) and an ordered phase, e.g., stripes or crystal lattices. For stripes, the interface dynamics are shown to be strongly anisotropic. We also show that the model is able to evolve the classical PFC at mechanical equilibrium. However, in contrast to previous approaches, it is not restricted to a single-crystal configuration or small distortions from a fixed reference lattice. To showcase the capabilities of this approach, we consider a few examples, from the annihilation of dislocation loops in a single crystal at mechanical equilibrium to the relaxation of a microstructure including crystalline domains with different orientations and grain boundaries. During the self-annihilation of a mixed type dislocation loop (i.e., not shear or prismatic), long-range elastic effects cause the loop to move out of plane before the annihilation event.

Progress of Laser Processing Technology in Ferroelectric Nanocomposites

Although polymer-based nanocomposites have great application potential in many fields, compared with the application of ferroelectric nanocomposites in functional microscale structures and devices, especially in the field of photonics microdevices fabricated by laser processing, the development of polymer-based nanocomposites is relatively lagging behind. In this study, the polyvinylidene fluoride ferroelectric composite material was taken as the research object, and the preparation method of polymer nanocomposite material suitable for laser microstructure processing was solved by exploring the material functionalization method. The control of the optical properties of polyvinylidene fluoride ferroelectric composites was achieved through material design, control of the size of nanoparticles in the prepared polymer nanocomposites, and characterization of their structures and properties. Two-dimensional and three-dimensional structures of polymer nanocomposites were prepared by laser microstructure processing technology, and the optical properties of the microstructures were evaluated. When the applied stress field was zero, the macroscopic coercive field was larger, and the hystereswas loop was wider, while the butterfly curve changed rapidly near the coercive field, and the strain was negative. From the test results of the scanning electron microscope, it can be concluded that the lowest average power to find ablation traces was 0.06 mw, and the affected area was very small, and there was no damage to the surrounding nanotubes. Therefore, this paper believes that the damage threshold of carbon nanotubes was slightly less than 0.06 mw. This study contributes to the development of nanocomposite preparation methods for laser micromachining.

Temperature transitions and degeneracy in the control of small clusters with a macroscopic field

We present a numerical investigation of the control of few-particle fluctuating clusters with a macroscopic field. Our goal is to reach a given target cluster shape in minimum time. This question is formulated as a first passage problem in the space of cluster configurations. We find the optimal policy to set the macroscopic field as a function of the observed shape using dynamic programming. Our results show that the optimal policy is non-unique, and its degeneracy is mainly related to symmetries shared by the initial shape, the force and the target shape. The total fraction of shapes for which optimal choice of the force is non-unique vanishes as the cluster size increases. Furthermore, the optimal policy exhibits a discrete set of transitions when the temperature is varied. Each transition leads to a discontinuity in the derivative of the time to reach with target with respect to temperature. As the size of the cluster increases, the change in the policy due to temperature transitions grows like the total number of configurations and a continuum limit emerges.

Derivation of a second-order acoustic wave equation in an air-saturated porous medium from a volume-averaged transport model

For propagation of high-amplitude acoustic waves in a rigid porous frame saturated by air, significant departures from a constant flow resistivity model have been observed. This departure can be modeled as a quadratic modification to the linear Darcy’s drag law, known as Forchheimer’s correction. To study the physical cause and relative significance of this nonlinear correction with respect to convective nonlinearity, a second-order acoustic wave equation is derived from volume-averaged equations of mass, momentum, and entropy conservation. Due to the scale separation between the wavelength and the porous structure, the particle velocity is approximated as the sum of irrotational macroscopic and incompressible microscopic fields. The porosity, tortuosity, and permeability are defined and incorporated into the macroscopic conservation equations. Porous drag terms are also derived in the macroscopic momentum equation for Darcy’s law and Forchheimer’s correction. Conservation equations for fluid parameter perturbations are obtained, and a second-order wave equation is derived. Dimensional analysis, in terms of the acoustic Reynolds number and Darcy number, describes the criteria for significant Forchheimer and convective nonlinearity. A case is obtained for a Westervelt-like equation for approximately progressive plane waves. These results inform modeling of nonlinearities for sound propagation in porous media under practical conditions.

Discharge of elongated grains in silos under rotational shear.

The discharge of elongated particles from a silo with rotating bottom is investigated numerically. The introduction of a slight transverse shear reduces the flow rate Q by up to 70% compared with stationary bottom, but the flow rate shows a modest increase by further increasing the external shear. Focusing on the dependency of flow rate Q on orifice diameter D, the spheres and rods show two distinct trends. For rods, in the small-aperture limit Q seems to follow an exponential trend, deviating from the classical power-law dependence. These macroscopic observations are in good agreement with our earlier experimental findings [Phys. Rev. E 103, 062905 (2021)2470-004510.1103/PhysRevE.103.062905]. With the help of the coarse-graining methodology we obtain the spatial distribution of the macroscopic density, velocity, kinetic pressure, and orientation fields. This allows us detecting a transition from funnel to mass flow pattern caused by the external shear. Additionally, averaging these fields in the region of the orifice reveals that the strong initial decrease in Q is mostly attributed to changes in the flow velocity, while the weakly increasing trend at higher rotation rates is related to increasing packing fraction. Similar analysis of the grain orientation at the orifice suggests a correlation of the flow rate magnitude with the vertical orientation and the packing fraction at the orifice with the order of the grains. Lastly, the vertical profile of mean acceleration at the center of the silo denotes that the region where the acceleration is not negligible shrinks significantly due to the strong perturbation induced by the moving wall.

Structure of conformal gravity in the presence of a scale breaking scalar field

We revisit the structure of conformal gravity in the presence of a c-number, conformally coupled, long range, macroscopic scalar field. And in the static, spherically symmetric case discuss two classes of exact exterior solutions. In one solution the scalar field has a constant value and in the other solution, which is due to Brihaye and Verbin, it has a dependence on the radial coordinate, with the two exterior solutions being relatable by a conformal transformation. In light of these two solutions Horne and then Hobson and Lasenby raised the concern that the fitting of conformal gravity to galactic rotation curves had been misapplied and thus called the successful fitting of the conformal theory into question. In this paper we show that the analysis of Brihaye and Verbin needs to reappraised, with their reported result not being as general as they had indicated, but nonetheless being valid in the particular case that they studied. For the analyses of Horne and of Hobson and Lasenby we show that this macroscopic scalar field is not related to the mass generation that is required in a conformal theory. Rather, not just in conformal gravity, but also in standard Einstein gravity, the presence of such a long range scalar field would lead to test particles whose masses would be of the same order as the masses of the galaxies around which they orbit. Since particle masses are not at all of this form, such macroscopic fields cannot be responsible for mass generation; and the existence of any such mass-generating scalar fields can be excluded, consistent with there actually being no known massless scalar particles in nature. Instead, mass generation has to be due to c-number vacuum expectation values of q-number fields. Such expectation values are microscopic not macroscopic and only vary within particle interiors, giving particles an extended, baglike structure, as needed for localization in a conformal theory. And being purely internal they have no effect on galactic orbits, to thus leave the good conformal gravity fitting to galactic rotation curves intact.

Dynamic Simulation of Electron Emission Characteristics Based on Different Numerical Models of a Nanoscale Micro-Protrusion

It is well known that electron emission is one of the key factors to cause electrical breakdown in vacuum gaps. In previous studies, it tended to use simplified numerical models with uniform electric field on emission region to investigate the electron emission characteristics at the cathode micro-protrusion and the influence of the materials of the micro-protrusions. The objective of this article is to introduce an improved numerical model of a nanoscale micro-protrusion with nonuniform electrical field on the emission region, which could be used for micro-protrusions with various irregular geometries. The improved numerical model is used in this article to study the dynamic characteristics of the electron emission of Cu and Cr micro-protrusions under different macroscopic electric fields. First, the electric field distribution is obtained by solving Laplace equation based on finite difference method (FDM). Then, the emission current and Nottingham effect are obtained by calculating the general thermal-field (GTF) equations based on the electric field distribution. Finally, the dynamic characteristics of the electron emission current and temperature distribution are iteratively calculated considering the Joule heating and Nottingham effect. The calculation results of the improved numerical model are compared with those of the previous simplified numerical model. The results show that for Cu and Cr micro-protrusions, the Joule heating, and Nottingham effect would play different roles in the emission process. In general, it is more likely for the Cr micro-protrusions to evaporate than the Cu micro-protrusions. The results of this article may provide some useful information to further understand the vacuum breakdown initiated by electron emission.

A framework to enable microstructure-sensitive location-specific fatigue life analysis of components and connectivity to the product lifecycle

Traditionally, aerospace components are treated as monolithic structures during lifing analyses, wherein distinct microstructural information at individual locations is not necessarily considered. In components with gradient microstructures, the resulting material allowables are conservative and associated with large uncertainty bounds. To improve precision in the life estimates, a location-specific lifing framework is developed, which tracks manufacturing processes and retrieves microstructural information at distinct locations for use within a crystal plasticity fatigue life prediction model. A use case for the lifing of a dual microstructure heat treated turbine disk component is demonstrated near the bore (fine grains) and rim (coarse grains) regions. We employ the framework to access (a) the grain size statistics and (b) the macroscopic strain fields to inform precise boundary conditions for the crystal plasticity analysis. The proposed location-specific lifing framework presents new opportunities for simultaneously designing the component and tailoring the microstructures to meet the targeted performance.

Modeling of the temperature field induced during electrical discharge machining

Electrical discharge machining is a process with main thermal active principal. Thus, for example for steel materials it is unavoidable to modify the rim zone of the final workpiece. Knowledge or even prediction of these modifications would improve industrial applications. Basis for this is the information about the time and locally resolved temperature field, which is not available in that form today. Hence the objective of this work is to establish a model of the temperature field within the electrodes rim zone during electrical discharge machining process. In this work, this field is modeled for the electrical discharge machining process based on the measurable discharge energy of a single discharge. First, an energy dissipation model for a single discharge is presented. In the next step, the interaction of two consecutive discharges is analyzed. Both results are the inputs for a macroscopic process model to calculate the temperature field of the whole workpiece. Finally, by coupling this macroscopic temperature field and the single discharge model it is possible to determine the locally resolved temperature field at any time of the process. For typical conditions, it is very unlikely that two discharges affect each other regarding overlaying temperature fields in the micro range but over time, a macroscopic heating could take place depending on the dielectric cooling efficiency.

Transport across thin membranes: Effective solute flux jump

A model to describe the transport across membranes of chemical species dissolved in an incompressible flow is developed via homogenization. The asymptotic matching between the microscopic and macroscopic solute concentration fields leads to a solute flux jump across the membrane, quantified through the solution of diffusion problems at the microscale. The predictive model, written in a closed form, covers a wide range of membrane behaviors, in the limit of negligible Reynolds and Péclet numbers inside the membrane. The closure problem at the microscale, found via homogenization, allows one to link the membrane microstructure to its effective macroscopic properties, such as solvent permeability and solute diffusivity. After a validation of the model through comparison with the corresponding full-scale solution, an immediate application is provided, where the membrane behavior is a priori predicted through an analysis of its microscopic properties. The introduced tools and considerations may find applications in the design of thin microstructured membranes.

Maximizing the electromomentum coupling in piezoelectric laminates

Asymmetric piezoelectric composites exhibit coupling between their macroscopic linear momentum and electric field, a coupling that does not appear at the microscopic scale. This electromomentum coupling constitutes an additional knob to tailor the dynamic response of the medium, analogously to the Willis coupling in elastic composites. Here, we employ topology- and free material optimization approaches to maximize the electromomentum coupling of periodic piezoelectric laminates in the low frequency, long-wavelength limit. We find that the coupling can be enhanced by orders of magnitude, depending on the degrees of freedom in the optimization process. The optimal compositions that we find provide guidelines for the design of metamaterials with maximum electromomentum coupling, paving the way for their integration in wave control applications.

Momentum, angular momentum, and spin of waves in an isotropic collisionless plasma

We examine the momentum and angular momentum (including spin) properties of linear waves, both longitudinal (Langmuir) and transverse (electromagnetic), in an isotropic nonrelativistic collisionless electron plasma. We focus on conserved quantities associated with the translational and rotational invariance of the wave fields with respect to the homogeneous medium; these are sometimes called pseudomomenta. There are two types of the momentum and angular momentum densities: (i) the kinetic ones associated with the energy flux density and the symmetrized (Belinfante) energy-momentum tensor and (ii) the canonical ones associated with the conserved Noether currents and canonical energy-momentum tensor. We find that the canonical momentum and spin densities of Langmuir waves are similar to those of sound waves in fluids or gases; they are naturally expressed via the electron velocity field. In turn, the momentum and spin densities of electromagnetic waves can be written either in the forms known for free-space electromagnetic fields, involving only the electric field, or in the dual-symmetric forms involving both electric and magnetic fields, as well as the effective permittivity of plasma. We derive these properties both within the phenomenological macroscopic approach and microscopic Lagrangian field theory for the coupled electromagnetic fields and electrons. Finally, we explore implications of the canonical momentum and spin densities in transport and electrodynamic phenomena: the Stokes drift, the wave-induced magnetization (inverse Faraday effect), etc.

Controlling the Shape of Small Clusters with and without Macroscopic Fields.

Despite major advances in the understanding of the formation and dynamics of nanoclusters in the past decades, theoretical bases for the control of their shape are still lacking. We investigate strategies for driving fluctuating few-particle clusters to an arbitrary target shape in minimum time with or without an external field. This question is recast into a first passage problem, solved numerically, and discussed within a high temperature expansion. Without field, large-enough low-energy target shapes exhibit an optimal temperature at which they are reached in minimum time. We then compute the optimal way to set an external field to minimize the time to reach the target, leading to a gain of time that grows when increasing cluster size or decreasing temperature. This gain can shift the optimal temperature or even create one. Our results could apply to clusters of atoms at equilibrium, and colloidal or nanoparticle clusters under thermo- or electrophoresis.

Chemical Solution Deposition of Barium Titanate Thin Films with Ethylene Glycol as Solvent for Barium Acetate.

Chemical solution deposition (CSD) of BaTiO3 (BT) or BT-based thin films relies on using a carboxylic acid and alcohol as the solvents for alkaline-earth carboxylate and transition-metal alkoxide, respectively; however, the esterification reaction of the solvents may lead to in-situ water formation and precipitation. To avoid such an uncontrolled reaction, we developed a route in which ethylene glycol (EG) is used as the solvent for Ba-acetate. The EG-based BT coating solutions are stable for at least a few months. The thermal decomposition of the BT xerogel obtained by drying the EG-based solutions depends on the choice of the solvent for the Ti-alkoxide as well: in the case of EG and 2-methoxyethanol solvents carbon residues are removed at only about 1100 °C, while in the case of ethanol it is concluded at about 700 °C. About 100 nm thick BT films derived from the EG-ethanol solution deposited on platinized silicon reveal dense, crack-free columnar microstructure. They exhibit local ferro- and piezoelectric properties. The macroscopic polarization-electric field loops were obtained up to a quite high electric field of about 2.4 MV/cm. The EG-ethanol based CSD route is a viable alternative to the established acetic acid–alcohol route for BT and BT-based films.