Inhomogeneous Domain Research Articles

Space–time adaptive ADER-DG finite element method with LST-DG predictor and a posteriori sub-cell ADER-WENO finite-volume limiting for multidimensional detonation waves simulation

The space–time adaptive ADER–DG finite element method with LST–DG predictor and a posteriori sub–cell ADER–WENO finite–volume limiting was used for simulation of multidimensional reacting flows with detonation waves. The presented numerical method does not use any ideas of splitting or fractional time steps methods. The modification of the LST–DG predictor has been developed, based on a local partition of the time step in cells in which strong reactivity of the medium is observed. This approach made it possible to obtain solutions to classical problems of flows with detonation waves and strong stiffness, without significantly decreasing the time step. The results obtained show the very high applicability and efficiency of using the ADER–DG–PN method with a posteriori sub–cell limiting for simulating reactive flows with detonation waves. The numerical solution shows the correct formation and propagation of ZND detonation waves. The structure of detonation waves is resolved by this numerical method with subcell resolution even on coarse spatial meshes. The smooth components of the numerical solution are correctly and very accurately reproduced by the numerical method. Non–physical artifacts of the numerical solution, typical for problems with detonation waves, such as the propagation of non–physical shock waves and weak detonation fronts ahead of the main detonation front, did not arise in the results obtained. The results of simulating rather complex problems associated with the propagation of detonation waves in significantly inhomogeneous domains are presented, which show that all the main features of detonation flows are correctly reproduced by this numerical method. It can be concluded that the space–time adaptive ADER–DG–PN method with LST–DG predictor and a posteriori sub–cell ADER–WENO finite–volume limiting is perfectly applicable to simulating fairly complex reacting flows with detonation waves.

Instability, bifurcation and nonlinear dynamics of Poiseuille flow in fluid overlying an anisotropic and inhomogeneous porous domain

The present study focuses on the finite amplitude analysis of Poiseuille flow in an anisotropic and inhomogeneous porous domain that underlies a fluid domain. The nonlinear interactions are studied by imposing finite amplitude disturbances to the Poiseuille flow. The former interactions in terms of modal amplitudes dictate the fundamental mode, the distorted mean flow, the second harmonic and the distorted fundamental mode. The harmonics are solved progressively in increasing order of the least stable mode obtained from the linear theory to ascertain the cubic Landau equation, which in turn helps to determine the bifurcation phenomena. The presented weakly nonlinear theory predicts the existence of subcritical transition to turbulence of Poiseuille flow in such superposed systems. In general, on moving away from the bifurcation point, it is found that a decrease in the value of inhomogeneity (in terms of Ai), Darcy number (δ) and an increase in the value of depth ratio (dˆ; the ratio of fluid domain thickness to that of porous domain) favours subcritical bifurcation. For the considered variation of parameters, the bifurcation, either subcritical or supercritical, remains the same irrespective of the value of media anisotropy (ξ) in the vicinity of the bifurcation point except for dˆ=0.2,Ai=1. In such a situation, subcritical (supercritical) bifurcation is witnessed for ξ=0.001,0.01,0.1 (1,3). Furthermore, in contrast to isotropic and homogeneous porous media, both subcritical and supercritical bifurcations are observed when moving away from the bifurcation point. A correspondence between the type of mode via linear theory and the type of bifurcation via nonlinear theory is witnessed, which is further affirmed by the secondary flow patterns. Finally, the presented theoretical results reveal an early onset of subcritical transition to turbulence in comparison with isotropic and homogeneous porous media.

Angular Dependence of Hump‐Shape Hall Effects for Distinguishing between Karplus–Luttinger and Geometrical Origins

AbstractAmong the vast magnetic heterostructures explored in Condensed Matter Physics, two contrasting interpretations of the hump‐shaped Hall Effects remain ambiguous and debated, namely, the overlap of two opposite‐signed Karplus–Luttinger Hall loops associated with inhomogeneous collinear domains with perpendicular anisotropy, or the Geometrical/Topological Hall Effect emanated from hexagonal close‐packed lattice of Skyrmion ground state with smoothly varying non‐collinear moments. Their similarity in topology implies difficulty in discrimination via magnetic imaging. Here, this ambiguity is overcome and clarified by the divergence exponent of hump peak fields extracted from Hall measurements with magnetic field rotation on several heterostructures. Their difference in sensitivity to in‐plane fields reveals that the former mechanism involves higher uniaxial anisotropy than the latter, departing from the Skyrmion ground state regime by the Ginzburg–Landau framework of triple‐q spin‐wave superposition. Numerous material systems can be summarized into a single curve of divergence exponent versus the collinear quality factor, bridging the crossover of the two mentioned mechanisms.

Galerkin Method and Parallel Algorithm for Solving the Problem of EM-Wave Propagation in a Locally Inhomogeneous Medium with a Graphene Layer at the Boundary of the Inhomogeneity Domain

Galerkin Method and Parallel Algorithm for Solving the Problem of EM-Wave Propagation in a Locally Inhomogeneous Medium with a Graphene Layer at the Boundary of the Inhomogeneity Domain

Thermal cycle stability and microstructure of Pb(Mg1/3Nb2/3)O3-PbTiO3 single crystals

The Pb(Mg1/3Nb2/3)O3-PbTiO3 (PMN-PT) ferroelectric single crystals have been commercially available as important components in medical ultrasound transducers due to their excellent piezoelectric and electromechanical coupling performance. The variation in piezoelectric and dielectric properties of PMN-PT single crystals with ambient temperature is an important application indicator. In this work, the PMN-PT single crystals after direct current poling (DCP) and alternating current poling (ACP) were subjected to the cyclic thermal treatment process. The thermal cycling stability and microstructural changes in PMN-PT single crystals were investigated. The ACP single crystals exhibit a higher dielectric constant ε33T/ε0 (6500–7600) and piezoelectric coefficient d33 (2100–2500 pC N−1) compared to the DCP single crystals (ε33T/ε0 of 4100–5000, d33 of 1200–1300 pC N−1). Under thermal cycling at 60 °C, the DCP and ACP single crystals exhibit good thermal cycling stability after 150 cycles. Microstructural observations show that the domain structure of the DCP single crystals exhibits “staggered domain walls, inhomogeneous domain size, variety of domain structure,” while the relatively homogeneous stripe-like domains were observed in the ACP single crystals. After thermal cycling, new fine striped domains appear in both the DCP and ACP single crystals due to the instability of rotated polarization, but the piezoelectric and dielectric properties are not greatly affected. This work provides an intensive understanding of the effects of thermal cycling on the domain structure, which is useful for applications.

Modelling permanent magnet excited uniform fields with rational approximations

PurposeA novel method for modelling permanent magnets is investigated based on numerical approximations with rational functions. This study aims to introduce the AAA algorithm and other recently developed, cutting-edge mathematical tools, which provide outstandingly fast and accurate numerical computation of potentials and vector fields.Design/methodology/approachFirst, the AAA algorithm is briefly introduced along with its main variants and other advanced mathematical tools involved in the modelling. Then, the analysis of a circular Halbach array with a one-pole pair is carried out by means of the AAA-least squares method, focusing on vector potential and flux density in the bore and validating results by means of classic finite element software. Finally, the investigation is completed by a finite difference analysis.FindingsAAA methods for field analysis prove to be strikingly fast and accurate. Results are in excellent agreement with those provided by the finite element model, and the very good agreement with those from finite differences suggests future improvements. They are also easy programming; the MATLAB code is less than 200 lines. This indicates they can provide an effective tool for rapid analysis.Research limitations/implicationsAAA methods in magnetostatics are novel, but their extension to analogous physical problems seems straightforward. Being a meshless method, it is unlikely that local non-linearities can be considered. An aspect of particular interest, left for future research, is the capability of handling inhomogeneous domains, i.e. solving general interface problems.Originality/valueThe authors use cutting-edge mathematical tools for the modelling of complex physical objects in magnetostatics.

Inhomogeneous domain switching near an electrode edge in orthorhombic K0.5Na0.5NbO3 piezoceramic

To characterize the inhomogeneous field distributions and their effect on ferroelectric/ferroelastic domain switching in potassium sodium niobate-based piezoceramics, a partially electroded orthorhombic phase K0.5Na0.5NbO3 ceramic sample containing a distinct edge was investigated using micro-beam, high-energy XRD with applied fields. Under the field application, the partial-electrode sample exhibits orientation-dependent and position-sensitive domain switching. The experimental measurements of micro-scale domain texture correlate reasonably with simulated electric fields calculated from a finite element analysis. Both experimental and simulated results reveal that the domain switching is induced inhomogeneously up to the millimeter-scale across the sample and that the electric field is significantly concentrated near the electrode edge. Integrating the experimental results with the model demonstrates that the local electric field directions and amplitudes drive the local orientation dependence of domain switching and, conversely, the direction of the local electric field can be inferred from the direction in which the maximum domain switching is measured.

The excess loss analysis of an easy-plane FeSiAl@SiO2 soft magnetic composite with high permeability

The loss coming from the special eddy current caused by the inhomogeneous domain wall motion is usually used to explain the complex mechanisms of the excess loss below 200 kHz. In this work, an easy-plane FeSiAl@SiO2 SMC was fabricated to analyze the core loss. The prepared easy-plane FeSiAl@SiO2 SMC exhibits an initial permeability of 816 at 1 MHz and a domain wall resonance peak of 5.9 MHz. The core loss was measured up to 3 MHz and was separated into hysteresis loss, classical eddy current loss and excess loss. The excess loss was deeply analyzed by the theory of G. Bertotti. The results show the excess loss caused by localized eddy curreny is the main component of core loss in the range of 200 kHz to 3 MHz, and the domain wall resonance also exhibits the contribution on the core loss in the MHz band.

Thermoelastic analysis of a bi-layered system with the single domain inclusion-based boundary element method

When a bi-layered composite system is subjected to prescribed thermal and elastic boundary conditions, material mismatch of layers and inhomogeneities causes intensive stress concentration, particularly with an initial crack, which causes delamination of the system. This paper combines the boundary element method and our recent work on the dual equivalent inclusion method (DEIM), namely the inclusion-based boundary element method (iBEM), to simulate the thermoelastic behavior without the whole domain integral. Using Galerkin’s stress vector technique, the bimaterial thermoelastic Green’s function mathematically transforms the entire domain integral to boundary integral equations. Because the inhomogeneities and matrix generally exhibit thermal and mechanical material mismatch, the DEIM simulates the inhomogeneity problem by inclusion with continuously distributed polynomial-form eigentemperature and eigenstrain. Therefore, iBEM avoids conventional multi-region solution scheme and convert the entire domain into boundary integral equations plus domain integrals within the inhomogeneity domain. The energy release rate (J-integral) can be utilized to reveal and judge the stability of the crack. For elastic problems, when one of the layers becomes stiffer or is embedded with the stiffer inhomogeneity, the J-integral decreases, and the system is more stable. However, this conclusion is not established for thermoelastic problems. Moreover, locations, distribution, and material mismatches are essential in (modified) J-integrals. Numerical case studies validate the single-domain algorithm, and parametric studies illustrate the effects of inhomogeneities on the (modified) J-integral for a bi-layered system.

Effect of notch location on fatigue crack growth behavior for inhomogeneous material domains in friction stir welded magnesium alloy

The fatigue crack growth behavior of friction stir welded joints of AZ31 Mg alloy is investigated for three different notch locations. The extended finite element method based simulation is developed to capture the effect of stir zone on fatigue crack growth behavior. The notch locations with asymmetric material domain experience an asymmetric stress field, which leads to crack path deviation from the orthogonal direction to the applied force. This leads to a longer crack path. The near-tip stress field from the simulation enhances the understanding of unusual crack path. The experimental results including crack path trajectories from experiments compare well against the numerical predictions.

Future deceleration due to backreaction in a Universe with multiple inhomogeneous domains

Abstract We formulate a model of spacetime with inhomogeneous matter distribution in multiple domains. In the context of the backreaction framework using Buchert's averaging procedure, we evaluate the effect of backreaction due to the inhomogeneities on the late time global evolution of the Universe. Examining the future evolution of this universe, we find that it can transit from the presently accelerating phase to undergo future deceleration. The future deceleration is governed by our model parameters. We constrain the model parameters using observational analysis of the Union 2.1 supernova Ia data employing the Markov Chain Monte Carlo method.

Stability of non-isothermal Poiseuille flow in a fluid overlying an anisotropic and inhomogeneous porous domain

A two-domain approach is used to investigate the thermal convection of Poiseuille flow in an anisotropic and inhomogeneous porous domain underlying a fluid domain. The flow of the Newtonian fluid is regulated by Darcy's law in the porous domain with the implementation of the Beavers–Joseph condition at the interface. The impact of medium anisotropy and inhomogeneity is inspected by virtue of linear stability analysis along with other governing parameters such as depth ratio (ratio of depth of fluid domain to porous domain), Darcy number, Reynolds number and Prandtl number concerning the stability of the fluid–porous system. The neutral curves are found to be bimodal and unimodal in nature with the anisotropy and inhomogeneity leaving its imprint on parametric variation. An increase in anisotropy or decrease in the inhomogeneity parameter follows the modal change from unimodal (porous) to bimodal (both porous and fluid). Also, it has been identified that, irrespective of the considered variations in anisotropy and inhomogeneity, the least stable mode for the depth ratio ${<}0.05$ is porous and for the depth ratio ${>}0.16$ is fluid. Furthermore, energy budget analysis is carried out to classify the type of instability and validate the type of mode. The instability is found to be thermal–buoyant in nature with omission of low Reynolds numbers along with very low values of the ratio of permeability in the horizontal to vertical direction, where thermal–shear instability is witnessed. Likewise, secondary flow patterns in the context of the streamfunction and temperature contour are analysed to validate the least stable mode and the type of prevailing instability in the fluid–porous system. The presented numerical results find good experimental support from the results of Chen & Chen (J. Fluid Mech., vol. 207, 1989, pp. 311–321) in the limit of natural convection with an isotropic and homogeneous porous domain.

3D seismic response characteristics of a pile-mat-founded AP1000 nuclear-island building considering nonlinear hysteretic behavior of soil

Given the increase of nuclear power plants, it has become unavoidable for the pile-supported nuclear-island buildings to be constructed on the coastal deposits potentially influenced by strong earthquakes. The coupling influences of the hysteresis nonlinearity of soil and the soil-pile-structure interaction (SPSI) have not yet been considered comprehensively in the seismic response analysis of the nuclear-island building, although it is a vital issue. On the basis of a newly-developed generalized non-Masing hysteretic constitutive model, a 3D integrated simulation method is proposed to evaluate the seismic responses of the pile-mat-founded nuclear-island building system subjected to multidirectional earthquake motions. This integrated method involves an explicit parallel algorithm framework, comprising the nuclear-island building modeling, the pile-mat foundation modeling, the inhomogeneous soil domain modeling, and the artificial boundary condition. The bedrock records of near-field, moderate-far field and far-field earthquake scenarios are assumed for determining the bedrock motions of the ultimate and operational safety earthquakes. For an actual pile-mat-founded AP1000 nuclear-island building, the simulation results show the complexity and significance of the coupling effect of the site, the tridirectional earthquake shaking, and the secondary nonlinearity of soil. Such a complex coupling effect significantly increases the seismic responses of the pile-mat-founded nuclear-island building. A notable finding is that the scenario earthquakes with abundant long period components may have more destructive potential to the pile-mat-founded nuclear-island buildings than the scenario earthquakes with characteristics of abundant short period components and shorter durations. The results provide insights into the seismic design of the pile-mat-founded nuclear-island buildings, which could guide the design and construction of such similar facilities in the high seismic intensity regions.

The Thickness and Structure of Dip-Coated Polymer Films in the Liquid and Solid States.

Films formed by dip coating brass wires with dilute and semi-dilute solutions of polyvinyl butyral in benzyl alcohol were studied in their liquid and solid states. While dilute and semi-dilute solutions behaved as Maxwell viscoelastic fluids, the thickness of the liquid films followed the Landau-Levich-Derjaguin prediction for Newtonian fluids. At a very slow rate of coating, the film thickness was difficult to evaluate. Therefore, the dynamic contact angle was studied in detail. We discovered that polymer additives preserve the advancing contact angle at its static value while the receding contact angle follows the Cox–Voinov theory. In contrast, the thickness of solid films does not correlate with the Landau-Levich-Derjaguin predictions. Only solutions of high-molecular-weight polymers form smooth solid films. Solutions of low-molecular-weight polymers may form either solid films with an inhomogeneous roughness or solid polymer domains separated by the dry substrate. In technological applications, very dilute polymer solutions of high-molecular-weight polymers can be used to avoid inhomogeneities in solid films. These solutions form smooth solid films, and the film thickness can be controlled by the experimental coating conditions.

Nonlinear Evolutionary Problem of Filtration Consolidation With the Non-Classical Conjugation Condition

Finite-element solutions of the initial-boundary value problem for a nonlinear parabolic equation in an inhomogeneous domain with the conjugation condition of a non-ideal contact were found. The initial boundary value problem is a mathematical model of an important technical problem of filtration consolidation of inhomogeneous soils. Inhomogeneity is considered in terms of the presence of thin inclusions, physicochemical characteristics of which differ from those of the main soil. The problem of longterm consolidation is especially pronounced in soils with low filtration coefficient. Low permeability of the porous medium causes deviation from the linear relationship between the pressure gradient and the filtration rate.Weak formulation of the problem is suggested, and the accuracy of the approximate finite element solution, its existence and uniqueness are substantiated for the case of Darcy’s nonlinear law. A test example and the effect of the nonlinear filtration law for thin inclusion on the dynamics of scattering of excess pressures in the entire area of the problem are considered.

Complex-scaled infinite elements for resonance problems in heterogeneous open systems

The technique of complex scaling for time harmonic wave-type equations relies on a complex coordinate stretching to generate exponentially decaying solutions. In this work, we use a Galerkin method with ansatz functions with infinite support to discretize complex-scaled scalar Helmholtz-type resonance problems with inhomogeneous exterior domains. We show super-algebraic convergence of the method with respect to the number of unknowns in radial direction. Numerical examples underline the theoretical findings.

Cooperation enhanced by the interaction diversity for the spatial public goods game on regular lattices

We investigate the evolution of cooperative behaviors of the spatial public goods game on lattices where the number of interactive neighbors are not identical for all players in the population but they can randomly select the interactive objects from the immediate neighbors in the von Neumann or Moore neighborhood. Extensive numerical simulations indicate that the cooperation level is greatly enhanced by the interaction diversity compared with the traditional model in which the social scope is homogeneous. The mechanism that explains this improvement is based on the inhomogeneous interactive domain in which cooperators can maintain their strategies easily and stabilize the cooperative neighborhood, resulting in the emergence of close cooperation clusters. Moreover, increasing uncertainty in strategy adoption process can resolve the trapped condition with a strong synergy factor and help the system to achieve the full cooperation state when the diversity mechanism is considered.

Modeling and Simulation of Magnons Scattering Across Shear Spins in Multilayered Ferromagnetic Slabs

In this work, we introduce a computer model and theoretical approach based on the matching technique to investigate the spin precession and the magnetic properties of an ordered magnetic interface joining two ferromagnetic multilayers of type AB, made of 10 spin slabs, obtained by alternative two spin layers A and B. We simulate, particularly, the coherent magnon transmission through spins’ interface, in multilayered thin films, obtained by shearing a part of the film from the other at an angle of 30∘. The individual and total transmittance of bulk magnons of the thin film, scattering coherently at the shearing interface zone and the localized magnonic spin states, are calculated and analyzed. The transmission and reflection spin modes are derived as elements of a Landauer–Büttiker type scattering matrix. The results highlight the localized spin states on the interface shear domain and their interactions with incident magnons. The evolutions of the magnonic spectra can be presented for arbitrary directions of the incident magnons on the boundary zone, for all accessible frequencies in the propagating bands as well as for the magnetic exchange coupling between each spin A(B) and its adjacent sites and their spin intensity. The results demonstrate the dependence of the magnonic spectra for the perfect multilayered films and at the inhomogeneous domain of the interface shear. The analysis of the spectra illustrates the fluctuations, related to Fano resonances, due to the coupling between travelling magnons and the localized modes in the shear interface domain. The calculated spectra could yield useful information concerning the magnetic parameters of such interface slabs in multilayered films.

Inhomogeneous solutions to thermal Hartree–Fock equations in first-order phase transitions

It is shown that the damping algorithm for the density matrix in self-consistent-field iterations, originally proposed for quantum chemistry of molecules in the ground state, can yield convergent solutions to thermal Hartree–Fock equations representing inhomogeneous domain structures in first-order phase transitions. A lattice gas of spinless Fermions with nearest-neighbour attractive interaction is analysed as an illustration. In the metastable or unstable region of the phase diagram, numerical solutions converge to phase-separated states consisting of gas and liquid domains, characterised by a double-peak structure in the single-particle energy spectrum. Broadening of the energy spectrum due to quantum-mechanical tunnelling effect is also demonstrated. The present method would facilitate direct numerical access to phase-transition regions of various quantum/classical systems without causing breakdown.

Tailoring the microstructure and magnetic properties of (Nd,Pr)2Fe14B/α-Fe nanocomposite magnets via Ta addition

The effect of Ta addition on the microstructure and magnetic properties of (Nd0.4Pr0.6)9Fe85-xTaxB6 nanocomposite magnets prepared by melt spinning was studied. Microstructure studies reveal that Ta addition is effective in refining the microstructure of nanocomposite magnets. The temperature coefficient of coercivity (β) is improved from −0.350%/°C for x = 0 to −0.329%/°C for x = 2 in the temperature range 27 °C-175 °C. With the increase in x from 0 to 2, the coercivity of the alloys is improved remarkably from 6.1 kOe to 10.4 kOe at the expense of remanence. As a result, the optimal magnetic properties with Hci = 7.5 kOe and (BH)max = 23.4 MGOe have been achieved at x = 1. Minor hysteresis loops were analyzed to determine the coercivity of (Nd0.4Pr0.6)9Fe85-xTaxB6 nanocomposite magnets by inhomogeneous domain wall pinning mechanism. The significant enhancement of magnetic properties mainly results from grain refinement achieved by introducing Ta.