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In this paper, a pre-compressed one-dimensional granular crystal model is studied. The bright analytic single and multiple solitary wave solutions in more general forms than those obtained the KdV system in the previous studies are derived by using the homogeneous balance principle and Hirota’s bilinear method. The difference between the present solutions and those from the KdV system are investigated both analytically and numerically. By analyzing the dispersion relation and the collision process of solitary waves, we find that there are two types of double-solitary waves in the pre-compressed granular crystal model. The geometric and numerical analysis of dynamic behaviors of the solutions is presented with emphasis on the relation between the double-solitary waves and elastic collision between single-solitary waves. We find that the opposite collision between single-solitary waves may be stable and thus generate a stable double-solitary wave. It is concluded that the collision is a special stable double-solitary wave solution. We further propose a possible way to determine the stability of multiple solitary waves qualitatively. The results of this paper provide a theoretical basis for finding stable multiple solitary wave solutions.

Since the edge-to-edge matching relationship of close-packed planes on an incoherent interphase boundary was found, the one-dimensional ledge migration mechanism has been put forward. However, owing to the lack of direct experimental evidence, the existence of the one-dimensional ledge is still questioned and it is thus usually treated as just an assumption. In this study, focusing on the existence of one-dimensional ledges and the migration mechanism of incoherent interphase boundaries, an atomic scale investigation on the migration of incoherent interphase boundaries in a body- to face-centered cubic transformation has been carried out using the phase-field crystal model. Simulation results demonstrated the presence of one-dimensional ledges on incoherent interphase boundaries, but only on those boundaries with high atomic densities. The simulation results further showed that the interphase boundaries with one-dimensional ledges migrate as a result of the nucleation and extension of the one-dimensional ledge, similar to the mechanism for two-dimensional ledges; meanwhile the interphase boundaries without one-dimensional ledges migrate according to a continuous mechanism by random atomic jumping. Because it is difficult for one-dimensional ledges to nucleate under low driving forces, interphase boundary migration based on the one-dimensional ledge mechanism is slower than that based on the continuous mechanism. This study reveals the structures and mechanisms of complex transitions of incoherent interphase boundaries and can aid a deeper understanding of solid phase transformations.

The phase-field crystal equation is a sixth-order nonlinear parabolic equation and have received increasing attention in the study of the microstructural evolution of two-phase systems on atomic length and diffusive time scales. This model can be applied to simulate various phenomena such as epitaxial growth, material hardness and phase transition. Compared with the classical local gradient flow and phase field models, the nonlocal models such as nonlocal phase-field crystal equation equipped with nonlocal diffusion operator can describe more practical phenomena for modeling phase transitions. We propose linear semi-implicit approach and scalar auxiliary variable approach with unconditional energy stability for the nonlocal phase-field crystal equation. The first contribution is that we have proved the unconditional energy stability for nonlocal phase-field crystal model and its semi-discrete schemes carefully and rigorously. Secondly, we found a fast procedure to reduce the computational work and memory requirement which the non-locality of the nonlocal diffusion term generates huge computational work and memory requirement. Finally, several numerical simulations are demonstrated to verify the accuracy and efficiency of our proposed schemes.

Grain-oriented (GO) sheet steels are widely used as the core material in large power transformers. The strong magnetostriction in GO sheet steels, however, causes undesirable vibrations and acoustic noises, and is difficult to estimate in the design optimization of power transformers. This article proposes a new magnetostriction model of GO sheet steels by combining the Becker-Doring crystal model and the dynamic Jiles-Atherton hysteresis model. Incorporated in the finite-element analysis (FEA), the new model can correctly simulate the butterfly loops of magnetostriction in GO sheet steels. The effectiveness and accuracy of the proposed model are verified by the experimental measurement results on a single sheet sample in a free state with no external stress.

Formation of quasicrystal structures has always been mysterious since the discovery of these magic structures. In this work, the nucleation of decagonal, dodecagonal, heptagonal, and octagonal quasicrystal structures controlled by the coupling among multiple length scales is investigated using a dynamic phase-field crystal model. We observe that the nucleation of quasicrystals proceeds through local rearrangement of length scales, i.e., the generation, merging and stacking of 3-atom building blocks constructed by the length scales, and accordingly, propose a geometric model to describe the cooperation of length scales during structural transformation in quasicrystal nucleation. Essentially, such cooperation is crucial to quasicrystal formation, and controlled by the match and balance between length scales. These findings clarify the scenario and microscopic mechanism of the structural evolution during quasicrystal nucleation, and help us to understand the common rule for the formation of periodic crystal and quasicrystal structures with various symmetries.

In this paper, we develop a new square phase-field crystal model using the L 2 -gradient flow approach, where the total mass of atoms is conserved through a nonlocal Lagrange multiplier. We construct a fast, provably unconditionally energy stable, second-order scheme by using the recently developed SAV approach with the stabilization technique, where an extra stabilization term is added to enhance the stability and keep the required accuracy while using large time steps. Through the comparisons with the classical Cahn–Hilliard type square phase-field crystal model and the non-stabilized SAV scheme for simulating some benchmark numerical examples, we demonstrate the robustness of the new model, as well as the stability and the accuracy of the developed scheme, numerically.

The phase-field crystal model is one of the most successful models with which to describe crystallization at a near-atomic scale with a larger timescale compared with other atomistic methods when direct correlation functions (DCFs) for the desired lattice are specified. However, the DCFs are, in general, not known and are hard to obtain from essential material information, such as primitive lattice vectors and atom positions. In this paper, we propose a method of obtaining two-point DCFs for desired two-dimensional lattices. The proposed optimization scheme is simple in that it minimizes the temporal change in free energy with respect to the target lattice using a gradient descent. In numerical experiments, we successfully obtained DCFs not only for well-known two-dimensional lattices (i.e., triangular, square, rectangular, honeycomb, and kagome lattices) but also for five nontrivial lattices (i.e., maple leaf, ladybug, trellis, Lieb, and CaVO lattices). We also show that these five lattices can be simulated using a phase-field crystal with at least five modes.

In this work, we have introduced theoretically a novel design of a 1D phononic crystal model acting as a sensor for gasoline components (blends). The proposed sensor is prepared to distinguish between different components of gasoline with high performance. The sensor is designed from a defect layer filled with one of the gasoline blends in the middle of a 1D multilayer phononic crystal configured as, [(lead/ epoxy)2 gasoline [(lead / epoxy)2] . The numerical investigations are obtained based on the transfer matrix method and the acoustic properties of the constituent materials. The numerical results showed that our sensing tool can distinguish between different gasoline blends with high selectivity and sensitivity at the same time. In addition, the monitoring of these blends could be obtained. The proposed sensor provides high sensitivity and quality factor that can reach 2.97×107 Hz and 5034, respectively.

The phase-field crystal equation is a sixth-order nonlinear parabolic equation and can be applied to simulate various phenomena such as epitaxial growth, material hardness, and phase transition. We propose a series of efficient modified stabilized invariant energy quadratization approaches with unconditional energy stability for the phase-field crystal model. Firstly, we propose a more suitable positive preserving function strictly in square root and consider a modified invariant energy quadratization (MIEQ) approach. Secondly, a series of efficient and suitable functionals H(ϕ) in square root are considered and the modified stabilized invariant energy quadratization (MSIEQ) approaches are developed. We prove the unconditional energy stability and optimal error estimates for the semi-discrete schemes carefully and rigorously. A comparative study of classical IEQ, MIEQ, and MSIEQ approaches is considered to show the accuracy and efficiency. Finally, we present various 2D numerical simulations to demonstrate the stability and accuracy.

Migration mechanisms of interphase boundaries (IPBs) are essential for understanding solid phase transformations. Most studies of the migration mechanisms of IPBs are focused on transformations under rational or near-rational orientation relationships. However, for cases of irrational orientation relationships that widely exist in massive transformations and grain boundary (GB) precipitations, knowledge remains extremely lacking. In this study, taking a triangular-square massive transformation as an example, we explored the migration mechanisms of IPBs with irrational orientation relationships at atomic scales by using the phase-field crystal method. Crystallography analysis based on near-coincidence site calculations also were conducted to verify simulated IPBs structures. Both massive transformations and precipitation transformations were reproduced using the phase-field crystal model. The simulation results show that, similar to the case of rational orientation relationships, the IPBs with irrational orientation relationships migrate by a ledge mechanism due to the satisfying of the edge-to-edge matching relationship. Further simulations on the interactions between IPBs and GBs indicate that GBs can make the newly generated massive phase change its orientation during the process of massive phase transfer across some low-angle GBs.

The article describes the solution to the problem of placing elements in blocks on a crystal model based on a genetic algorithm (GA), which allows creating an algorithmic environment in the field of genetic search for solving the problem of placing elements on a crystal, taking into account the criterion for the maximum number of linear segments. The purpose of this work is to find ways of placing elements in blocks based on a genetic algorithm. The scientific novelty lies in the development of a modified genetic algorithm for computer-aided design of very large-scale integrated circuits, taking into account the criterion for the maximum number of line segments. The problem statement in this work is as follows: to optimize the placement of elements in blocks by using a modified GA taking into account the criterion for the maximum number of line segments. A fundamental difference from the known approaches in the use of new modified genetic structures in computer-aided design, in addition, the paper presents a new method for placing elements on a crystal, based on a modified GA, taking into account the criterion for the maximum number of linear segments. Thus, the problem of creating methods, algorithms and software for automated placement of elements on a chip is currently of particular relevance.

Roles of non-/symmetric triple and quadruple junctions on plasticity of ploycrystals are examined using phase-filed crystal model combined with an isovolumetric deformation technique. We designed four polycrystalline samples containing the four types of junctions respectively to simulate the deformation process under a strain rate comparable to practical situations. Our results uncover relationships between the ability of resistances to external deformations and the deformation mechanisms. For the ploycrystals containing quadruple junctions, the symmetric junction is beneficial to maintain the stability of the junctions during deformations, while asymmetric ones would be disjointed and result in formation and growth of sub-grains. For the polycrystals containing triple junctions, the stability of the junction is strongly related to the misorientation angles of the associated grains. The triple junction composed with high-angle GBs exhibits excellent stability under successive deformations and the deformation is dominated by GB migrations. Low-angle GBs migrate more easily than the high-angle ones.

Time crystal is defined as a phase of matter spontaneously exhibiting a periodicity in time. Previous studies focused on discrete quantum time crystals under periodic drive. Here, we propose a time crystal model based on a levitated charged nanoparticle in a static magnetic field without drive. Both the classical time crystal in thermal equilibrium and the quantum time crystal in the ground state can emerge in the spin rotational mode, under the strong magnetic field or the large charge-to-mass ratio limit. Besides, for the first time, the \emph{time polycrystal} is defined and naturally appears in this model. Our model paves a way for realizing time crystals in thermal equilibrium., Comment: 10 pages, 7 figures

Elucidating the interplay of defect and stress at the microscopic level is a fundamental physical problem that has strong connection with materials science. Here, based on the two-dimensional crystal model, we show that the instability mode of vacancies with varying size and morphology conforms to a common scenario. A vacancy under compression is fissioned into a pair of dislocations that glide and vanish at the boundary. This neat process is triggered by the local shear stress around the vacancy. The remarkable fractionalization of vacancies creates rich modes of interaction between vacancies and other topological defects, and provides a new dimension for mechanical engineering of defects in extensive crystalline structures., Comment: 7 pages, 6 figures

Abstract. Active matter systems often are well approximated as overdamped, meaning that any inertial momentum is immediately dissipated by the environment. On the other hand, especially for macroscopic systems but also for many mesoscopic ones particle mass can become relevant for the dynamics. For such systems we recently proposed an underdamped continuum model which captures translationally inertial dynamics via two contributions. First, convection and second a damping time scale of inertial motion. In this paper, we ask how both of these features influence the collective behavior compared to overdamped dynamics by studying the example of the active phase field crystal model. We first focus on the case of suppressed convection to study the role of the damping time. We quantify that the relaxation process to the steady collective motion state is considerably prolonged with damping time due to the increasing occurrence of transient groups of circularly moving density peaks. Finally, we illustrate the fully underdamped case with convection. Instead of collective motion of density peaks we then find a coexistence of constant high and low density phases reminiscent of motility-induced phase separation. Graphical abstract

A phase-field crystal model that spontaneously undergoes displacive phase transitions is introduced by explicitly studying a two-component two-dimensional square crystal reminiscent of a perovskite. When the intercomponent free energy is a simple polynomial, the crystal undergoes displacive transitions in the $\ensuremath{\langle}10\ensuremath{\rangle}$ and $\ensuremath{\langle}11\ensuremath{\rangle}$ directions. When the interaction is a correlation function, displacements in any direction can occur. This displacive phase-field crystal (DPFC) model maps to Landau-Ginzburg-Devonshire (LGD) theories for ferroelectrics, and the DPFC and LGD models are compared in terms of phase transitions and domain walls. Dynamical simulations of quadrijunctions were also performed and found stable spiraling quadrijunctions and unstable nonspiraling quadrijunctions. Last, domain coarsening across a small-angle grain boundary demonstrates multiple forms of non-mean-curvature-driven growth.

We have extended the multiconfigurational Ehrenfest (MCE) approach to investigate the dynamics of a one-dimensional Holstein molecular crystal model. It has been shown that the extended MCE approach yields results in perfect agreement with benchmark calculations by the hierarchy equations of motion method. The accuracies of the MCE approach in describing the dynamical properties of the Holstein polaron over a wide range of exciton transfer integrals and exciton-phonon couplings are carefully examined by a detailed comparison with the fully variational multiple Davydov D2 ansatz. It is found that while the MCE approach and the multi-D2 ansatz produce almost exactly the same results for a small transfer integral, the results obtained by the multi-D2 ansatz start to deviate from those by the MCE approach at longer times for a large transfer integral. A large number of coherent state basis functions are required to characterize the delocalized features of the phonon wavefunction in the case of large transfer integral, which becomes computationally too demanding for the multi-D2 ansatz. The MCE approach, on the other hand, uses hundreds to thousands of trajectory guided basis functions and converges very well, thus providing an effective tool for accurate and efficient simulations of polaron dynamics.

An electronic phase-field crystal model is proposed where the thermodynamics of electrons are considered in a free-energy-functional formulation. The free-electron-gas system is considered initially as the noninteracting limit of the model. The excess free-energy contribution to the functional is incorporated by including Coulombic repulsions among electrons and exchange-correlation interactions. The evolution of an electron mean field is considered in the low-temperature limit using diffusive dynamics. Three-dimensional Wigner crystallization can be achieved from the model when the density of the system is lowered sufficiently. Through this approach, we are able to provide insight into topological defect formation and evolution during Wigner crystallization.

Shape instability belongs to one of significant types of violation for disposable structural elements under high-stress levels. Due to lack of fundamental data on materials, it is quite problematic to consider the shape instability in the design of disposable structural elements. The crystal plastic finite element method is proposed to investigate the dispersion of shape instability life data. It allows these data to be obtained from traditional material parameters. The shape instability behavior is described with the constitutive crystal model of plastic damage accumulation. Then, to improve the accuracy of life prediction, the new method is developed to construct the simulation model of true microstructure. A modeling algorithm based on the image processing technology is provided to reduce the virtual stresses from the transient crystal plastic modeling method. Comparison of experimental and predicted results shows good agreement at high stresses close to the elastic limit of the material.

Coarsening is a common physical process that occurs in polydisperse two-phase mixture systems, which had been widely studied for decades. However, accurate prediction of the volume fraction dependence of the diffusion-controlled coarsening kinetic process is still very difficult. In this work, by using the atomic-scale phase-field crystal model, we investigated the coarsening kinetics of crystalline nanoparticles in the semi-solid region. The results showed that the details of the atomic-scale nature of particles do not affect the kinetics of coarsening for low solid volume fractions and the coarsening process of the nanoparticles is in agreement with the classical coarsening theory. While, for high solid volume fractions, our simulation results show that the coarsening rates of crystalline particles decrease with the solid volume fraction, which runs counter to the theoretical models based on mean-field theories. By checking the competitive growth process of all the particles, we found the appearance of grain rotation and volume diffusion mechanisms leads to the failure of the classical coarsening models.

Branching is a fundamental mechanism for lamellar spacing adjustment during eutectic solidification. However, the kinetic mechanism of branching is still unclear due to the lack of in-situ observations. In this work, utilizing the binary phase-field crystal model, we investigated the lamellar branching process during eutectic directional growth on an atomic scale. By visualizing the new lamella creation process, we found that new α lamellae form from heterogeneous nucleation at the front of the β/liquid interface. After further simulating eutectic solidification with different temperatures and lattice-mismatches, we found that the conditions that promote the heterogeneous nucleation could also stimulate lamellar branching. Conversely, if we suppress the heterogeneous nucleation process, lamellar branching will be hard to emerge, and the eutectic morphology will be a 2λ oscillating pattern.

A self-contained theoretical analysis of the bandgap opening and merging behavior for the designed phononic crystal model which is composed of three-component coated ball and four short connecting plates is reported in this study by finite element numerical simulations. The results show that there are multiple bandgaps of the designed model in the middle and low frequency range simultaneously. The structure symmetry is reduced to open a new bandgap via the separation of resonance modes, and an ultra-wide bandgap obtained. Especially, the equivalent spring mass model is constructed and the corresponding calculation formula of torsional resonance frequency is presented. In addition, the influence of the structural parameters on the band structure is investigated.

The model, which effectively contributes to creation of maximum reasonable value of construction projects, was proposed. The proposed system is characterized by the fact that due to its convenient coherence, it adjusts the influence of its separate methods (elements) on project value in a cumulative manner. The need for such a model was driven by global challenges, such as necessity to reduce greenhouse gas emissions and to increase power efficiency of satisfaction of social needs. Characteristic feature of the proposed model is that it is composed of six interacting components, which collectively are self-sufficient for efficient engineering and management of construction projects. This concept is presented in the form of a "crystal" of cumulative application of three pairs of methods. The first pair includes value engineering and building information model. The second pair includes "benefits-costs" analysis and the theory of dynamics of project value. The third pair includes profiling of contract systems and pricing strategies. Each element of the proposed model, playing its natural role, coherently complements and reinforces its other elements. This model allows balanced decision making in terms of availability of various competing priorities of all stakeholders. The key priority of the cumulative model is preventive reaction to potential problems in the course of project implementation. It was established that the aforementioned pairs of methods and the model in general bring convenient and efficient synergy to architecture, engineering and management of construction projects. The synergy, which is a basic feature of the proposed model, provides a presence of two characteristics at the same time: complete coverage of project tasks that are solved and convenient compactness. It is the main advantage of the Crystal model of value management. Dynamics of usefulness and value of the project of office center construction within several consecutive sessions of model application model was calculated, it was shown that quality of project result almost reached its maximum. It demonstrates feasibility of further research in this direction and expansion of a range of projects of model application

This work deals with the quantification and application of the modified two-mode phase-field crystal model (M2PFC; Asadi and Asle Zaeem, 2015) for face-centered cubic (FCC) metals at their melting point. The connection of M2PFC model to the classical density functional theory is explained in this article. M2PFC model in its dimensionless form contains three parameters (two independent and one dependent) which are determined using an iterative procedure based on the molecular dynamics and experimental data. The quantification process and computer simulations are performed for Ni and Al as two case studies. The quantitative M2PFC models are used in series of numerical simulations to determine the two-phase FCC-liquid coexisting and the bulk properties at the melting points of Ni and Al. The calculated and predicted properties are the expansion in melting, elastic constants, solid-liquid interface free energy, and surface anisotropy, which are also compared with their available experimental or computational counterparts in the literature.

A tube-type piezoelectric phononic crystal model is proposed to study interaction between locally resonant and Bragg band gaps, which is arrayed periodically by metal and piezoelectric segments. Each piezoelectric segment consists of a shell with series-connected and opposite directions polarized double layers and a resonant shunting circuit. According to the interaction between Bragg scattering and local electromagnetic oscillation, three regions corresponding to the inductance can be divided as follows: quasi-short circuits region, coupling region, and quasi-open circuits region. Some interesting phenomena are found from the coupling between Bragg scattering and locally resonant of electromagnetic oscillation. (1) In the coupling region, a pass band splits a Bragg band gap into two band gaps. But the cut-off frequency of the second band gap does not change with the inductance. (2) In the quasi-open circuits region, Bragg and locally resonant band gaps exist independently. (3) The first band gap transits from Bragg scattering to local resonance when the inductance increases from quasi-short circuits region to quasi-open circuits region. (4) The cut-off frequency of the first band gap is always less than the estimated resonant frequency of inductor-capacitor oscillators. Finally, the theoretical result is validated by two kinds of finite element models based on ANSYS.

Investigation of the heteroepitaxial film growth for anisotropic systems has been carried out by means of the anisotropic phase-field crystal model. Numerical simulations have been performed by varying the anisotropic parameters, orientations, and lattice misfit between isotropic substrate and anisotropic film layers. The simulation results demonstrate the formation of dislocations during the growth of layers with non-cubic anisotropic lattice in the presence of the elastic strain caused by the lattice misfits. It is shown that for any particular choice of misfit, both the lattice anisotropy of the film and the orientation of the substrate influence the parameters of dislocation formation such as the number of dislocations, the characteristic distance at which dislocations begin to nucleate, and the excess elastic energy.

The structure of an M-type lead hexaferrite (magnetoplumbite) crystal is studied via the diffraction of synchrotron radiation. The crystal model contains two iron ions positions with dynamic disorder. The dynamics of the crystal lattice in the temperature range of 80 to 775 K is studied by Raman scattering. Particular attention is given to the discussing the nature of the local disorder of iron ions in the trigonal bipyramidal environment of oxygen ions.

Atomically thin 2-dimensional heterostructures are a promising, novel class of materials with groundbreaking properties. The possiblity of choosing the many constituent components and their proportions allows optimizing these materials to specific requirements. The wide adaptability comes with a cost of large parameter space making it hard to experimentally test all the possibilities. Instead, efficient computational modelling is needed. However, large range of relevant time and length scales related to physics of polycrystalline materials poses a challenge for computational studies. To this end, we present an efficient and flexible phase-field crystal model to describe the atomic configurations of multiple atomic species and phases coexisting in the same physical domain. We extensively benchmark the model for two-dimensional binary systems in terms of their elastic properties and phase boundary configurations and their energetics. As a concrete example, we demonstrate modelling lateral heterostructures of graphene and hexagonal boron nitride. We consider both idealized bicrystals and large-scale systems with random phase distributions. We find consistent relative elastic moduli and lattice constants, as well as realistic continuous interfaces and faceted crystal shapes. Zigzag-oriented interfaces are observed to display the lowest formation energy., Comment: 17 pages, 13 figures

With the help of the McMillan formula and virtual crystal model, we predict $T_c$ may exceed 34 K in a beryllium-based alloy with a specific composition, reminiscent of $T_c$ = 35 K in the first cuprate superconductor. This may similarly inspire research efforts to seek high temperature superconductors in ambient., Comment: Accepted by Solid State Communications on 23/10/19

This paper introduces improvements to the amplitude expansion of the phase-field crystal model that enable the simulation of grains within a full range of orientations. The unphysical grain boundary between grains, rotated by a crystal's symmetry rotation, is removed using a combination of the auxiliary rotation field described in our previous work and an algorithm that correctly matches the complex amplitudes according to the differences in local rotation.

In this work, we propose a method to compute TOF resolutions from TOF-PET emission data using a crystal model. For each line of response, the TOF resolutions were computed as the hypotenuse of crystal timing resolutions of the crystals in coincidence. We find that the accuracy of the crystal timing resolutions highly depends on the average count per crystal. In the phantom study, we observe a small global shift in the TOF-resolution, which we believe to be due to the scans being performed at different count rates. However, the whole body patient study shows that the count rate possibly is not the only factor influencing the crystal timing properties. The effect of the TOF resolution on joint reconstructions (and more so on standard reconstructions) seems to be limited as long as the mean crystal TOF resolution is modelled during reconstruction.

In this paper, we consider numerical approximations for the anisotropic phase-field crystal model. The model is a sixth-order nonlinear equation with an anisotropic Laplace operator. To develop easy-to-implement and unconditionally energy stable time marching schemes, we combine the scalar auxiliary variable (SAV) approach with the stabilization method, where two extra stabilization terms are added to enhance the stability and keep the required accuracy while using large time steps. By using the first-order backward Euler and second-order backward differentiation formula, we obtain two highly efficient and linear numerical schemes and prove their unconditional energy stabilities rigorously. We demonstrate the accuracy, stability, and efficiency of the developed schemes through numerous benchmark numerical experiments.

High resolution EBSD studies on a deformed copper polycrystal have been carried out to quantify the microstructural residual stress distributions, and those of stress state including triaxiality of importance in defect nucleation studies. Crystal plasticity analysis of a representative, similarly textured, model polycrystal has been carried out showing that the experimental distributions of microstructural residual stress components, effective stress, hydrostatic stress and stress triaxiality are well captured. The crystal model enables point-wise microstructural Schmid factors to be calculated both globally (ie with respect to the macroscopic remote loading) and locally from full knowledge of the grain-level stress state. Significant differences are demonstrated such that global Schmid analysis tends to overestimate slip activity and the frequency of high Schmid factors, indicating that the local microstructural heterogeneity is significant and caution is necessary in interpreting polycrystal behaviour using global Schmid factors. A stored energy criterion for fatigue crack nucleation indicates that preferential sites for fatigue crack nucleation are local to grain boundaries (as opposed to triple junctions), and that hard-soft grain interfaces where high GND densities develop are preferable.

A computationally efficient plasticity model for HCP crystals is developed for use in simulations where the constitutive model evaluations account for a significant fraction of the total analysis time. Combined pyramidal and prismatic slip is represented as an isotropic function while slip along the basal plane and extension twinning are maintained as distinct mechanisms. Additional efficiency is gained by deferring the updates of the rate-independent twinning and basal system strengths until the following time step, which allows precomputation of the inverses of the slip interaction matrices. Comparisons are made with single crystal pure Mg experimental data, as well as rolled polycrystal AZ31B data. The computational efficiency is evaluated by comparing simulation times from the current model with J2-Flow theory plasticity and a full crystal plasticity model. The reduced crystal plasticity model retains essential crystallographic features that govern macroscale mechanical response of HCP metals at approximately five times the computational expense of a J2-Flow theory calculation.

The degree of agglomeration and the aggregate shape influence the quality of crystalline products and the ease of downstream processing. Studying the shape of primary particles in an aggregate can lead to a better understanding of the underlying aggregation mechanism. We present an automatic image processing procedure for identifying the shape, size, and position of each primary particle in microcomputed tomography (μCT) images of potash alum aggregates. Splitting an aggregate into primary particles is based on recombining watershed-transform regions, where concavity points are considered as indicators of correct segmentation. The shape identification algorithm uses the Hough transform to identify visible face normals and matches them to the set of face normals defined by a crystal model. In principle, the algorithm is applicable to other crystalline compounds provided that sufficient symmetry is present to determine the shape of a primary particle from its visible part.

International audience; Understanding the driving forces observed during the first steps of beta-hematin crystal formation is vital in view of developing new therapeutic treatments against malaria. In this context a new additive Amber force field specific to the cyclic dimer of ferriprotoporphyrin IX coordinated via Fe-O propionate bonds (FPD) was developed and validated in the context of a crystal model. The structure and dynamics of small clusters or oligomers of the FPD entity were studied by molecular dynamics in condensed phase. New hydrogen bond patterns were identified in the dynamical process of the simulations: the characteristic pair of coplanar hydrogen bonds reported in crystallographic structures between FPD sheets (Pagola et al. Nature 2000, 404, 307) is found to be in a subtle equilibrium with new hydrogen bonds between FPD located within the same sheet. Hydrophobic interactions appeared to play a key role in oligomer cohesion: clusters with intersheet hydrogen bonds are found unstable compared to clusters with embedded-type molecular systems. We propose that oligomers enclosing this kind of embedded structure could serve as elementary building motifs for crystal growth in the digestive vacuole of Plasmodium, and could represent an attractive target for impairing hemozoin formation in a therapeutic approach.

Molecular dynamics simulation is employed to study the tension and compression deformation behaviors of magnesium single crystals with different orientations. The angle between the loading axis and the basal direction ranges from 0° to 90°. The simulation results show that the initial defects usually nucleate at free surfaces, but the initial plastic deformation and the subsequent microstructural evolutions are various due to different loading directions. The tension simulations exhibit the deformation mechanisms of twinning, slip, crystallographic reorientation and basal/prismatic transformation. The twinning, crystallographic reorientation and basal/prismatic transformation can only appear in the crystal model loaded along or near the a-axis or c-axis. For the compression simulations, the basal, prismatic and pyramidal slips are responsible for the initial plasticity, and no twinning is observed. Moreover, the plastic deformation models affect the yield strengths for the samples with different orientations. The maximum yield stresses for the samples loaded along the c-axis or a-axis are much higher than those loaded in other directions.

The Peierls structural transition in quasi-one-dimensional organic crystals of TTF-TCNQ is investigated in the frame of a more complete physical model. The two most important electron-phonon interaction mechanisms are taken into account simultaneously. One is similar of that of deformation potential and the other is of polaron type. For simplicity, the 2D crystal model is considered. The renormalized phonon spectrum and the phonon polarization operator are calculated in the random phase approximation for different temperatures. The effects of interchain interaction on renormalized acoustic phonons and on the Peierls critical temperature are analyzed.

The conservative Swift&ndash, Hohenberg equation was introduced to reformulate the phase-field crystal model. A challenge in solving the conservative Swift&ndash, Hohenberg equation numerically is how to treat the nonlinear term to preserve mass conservation without compromising efficiency and accuracy. To resolve this problem, we present a linear, high-order, and mass conservative method by placing the linear and nonlinear terms in the implicit and explicit parts, respectively, and employing the implicit-explicit Runge&ndash, Kutta method. We show analytically that the method inherits the mass conservation. Numerical experiments are presented demonstrating the efficiency and accuracy of the proposed method. In particular, long time simulation for pattern formation in 2D is carried out, where the phase diagram can be observed clearly. The MATLAB code for numerical implementation of the proposed method is provided in Appendix.

The current study is based on employing the torsional test parameters to observe the texture evolution of Al–Mg alloy with the face-centered cubic structure. We considered the Mg content in the alloy, which is an alloying composition, as our prime test parameter and examined how its variations are related to the test variables, such as temperature and strain rate. To confirm the torsion texture evolution of Al–Mg alloy, it was tested using the electron backscattered diffraction method and represented using a pole figure and an orientation distribution function. In the Al–Mg alloy, the change of Mg content causes a transformation of the physical properties, such as the stacking fault energy. Therefore, the difference in the shear texture evolution is observed to be remarkable. Further, the test results were compared to examine the validity of the rate sensitive crystal model. As the Mg content and strain rate increase, a specific face-centered cubic texture has been pronounced. Furthermore, as the temperature rises, the intensity of A fiber weakens, and the overall orientation distribution becomes random. From the results, this shear texture is discovered to be well suited for the rate sensitive crystal model, which demonstrates that the orientation persistence increases with increasing Mg content, higher strain rate, and lower temperatures.

The phase-field crystal (PFC) equation is derived by the gradient flow for the Swift–Hohenberg free energy functional; thus, the numerical method requires the energy of the functional to decrease. Convex Splitting Runge–Kutta (CSRK) methods can be suitably applied to achieve high-order temporal accuracy as well as unconditional energy stability and unique solvability. For the PFC equation, we prove the unconditional energy stability and unique solvability of the CSRK methods and provide one family of parameters of the second-order CSRK methods and possible examples of third-order CSRK methods. We present numerical experiments to demonstrate the accuracy and energy stability of the methods. Specifically, based on the high-order accuracy and energy stability of the CSRK method, we propose an indicator function capable of characterizing the pattern formation of the phase-field crystal model for long-time simulation.

Wax precipitation is a major flow assurance issue for petroleum production, oil blending, downstream processing, and oil products usage. While numerous thermodynamic models have been proposed to calculate wax appearance temperature (WAT) and precipitation profile at temperatures below WAT, the existing models are correlative in nature and fail to comply with phase behavior experimentally observed for wax precipitation. This work presents a predictive thermodynamic model for wax precipitation based on an explicit co-crystal formation assumption for precipitated wax, a treatment consistent with experimental findings. With a simple Flory-Huggins expression accounting for the liquid phase nonideality and the treatment of lamella structure for wax precipitation below WAT, the model satisfactorily predicts WAT at low pressures for multicomponent paraffin mixtures and wax precipitation amounts and contents as the temperature drops below WAT.

We propose a new chirality-imbalance phenomenon arising in baryonic/high dense matters under a magnetic field. A locally chiral-imbalanced (parity-odd) domain can be created due to the electromagnetically induced $U(1)_A$ anomaly in high-dense matters. The proposed local-chiral imbalance generically possesses a close relationship to a spacial distribution of an inhomogeneous chiral (pion)-vector current coupled to the magnetic field. To demonstrate such a nontrivial correlation, we take the skyrmion crystal approach to model baryonic/high dense matters. Remarkably enough, we find the chirality-imbalance distribution takes a wave form in a high density region (dobbed ``chiral-imbalance density wave''), when the inhomogeneous chiral condensate develops to form a chiral density wave. This implies the emergence of a nontrivial density wave for the explicitly broken $U(1)_A$ current simultaneously with the chiral density wave for the spontaneously broken chiral-flavor current. We further find that the topological phase transition in the skyrmion crystal model (between skyrmion and half-skyrmion phases) undergoes the deformation of the chiral-imbalance density wave in shape and periodicity. The emergence of this chiral-imbalance density wave could give a crucial contribution to studies on the chiral phase transition, as well as the nuclear matter structure, in compact stars under a magnetic field., 11 pages, 16 figures

The orientation relationships and interfaces between α′-Al13Cr4Si4 and the matrix in Al-Si-Cr-Mg alloy are characterized by HAADF-STEM electron microscopy. Multiple orientation relationships are found between α′-Al13Cr4Si4 and Al matrix in Al-Si-Cr-Mg and four of them are rarely common. By unraveling the atomic structure of dispersoids, the crystal model of α′-Al13Cr4Si4 is approved by the atomic-resolution for the first time. The interface we investigated proves that orientation relationships always rely on specific planes of Al matrix.

In this paper, we consider numerical approximations for solving a modified phase-field crystal model with a strong nonlinear vacancy potential. We develop an efficient time marching numerical scheme which combines the newly developed SAV approach with the traditional stabilization technique, where a new auxiliary variable is introduced to reformulate the model and a crucial linear stabilization term is added to stabilize the scheme and keep the required accuracy while using large time steps. We prove the unconditional energy stability of the developed scheme rigorously and perform numerous benchmark numerical examples in 2D and 3D. Through the comparisons with the non-stabilized SAV scheme, the stability and accuracy of the proposed scheme are demonstrated numerically.

Phase-field crystal model with one mode is introduced to describe morphological transition. The relationship between growth morphology and smooth density distribution was investigated. The results indicate that the pattern selection of dendrite growth is caused by the competition between interface energy anisotropy and interface kinetic anisotropy based on the 2D phase diagram. When the calculation time increases, the crystal grows to secondary dendrite at the dimensionless undercooling equal to − 0.4. Moreover, when noise is introduced in the growth progress, the symmetry is broken in the growth mode, and there becomes irregular fractal-like growth morphology. Furthermore, the single crystal shape develops into polycrystalline when the noise amplitude is large enough. When the dimensionless undercooling is less than − 0.3, the noise has a significant effect on the growth shape. In addition, the growth velocity of crystal near to liquid phase line is slow, while the shape far away from the liquid adapts to fast growth. Based on the simulation results, the method was proved to be effective, and it can easily obtain different crystal shapes by choosing the different points in 2D phase diagram.

The conserved Swift-Hohenberg equation (or phase-field-crystal [PFC] model) provides a simple microscopic description of the thermodynamic transition between fluid and crystalline states. Combining it with elements of the Toner-Tu theory for self-propelled particles, Menzel and Lowen [Phys. Rev. Lett. 110, 055702 (2013)PRLTAO0031-900710.1103/PhysRevLett.110.055702] obtained a model for crystallization (swarm formation) in active systems. Here, we study the occurrence of resting and traveling localized states, i.e., crystalline clusters, within the resulting active PFC model. Based on linear stability analyses and numerical continuation of the fully nonlinear states, we present a detailed analysis of the bifurcation structure of periodic and localized, resting and traveling states in a one-dimensional active PFC model. This allows us, for instance, to explore how the slanted homoclinic snaking of steady localized states found for the passive PFC model is amended by activity. A particular focus lies on the onset of motion, where we show that it occurs either through a drift-pitchfork or a drift-transcritical bifurcation. A corresponding general analytical criterion is derived.

We explore magnetic field effects on the nuclear matter based on the skrymion crystal approach for the first time. It is found that the magnetic effect plays the role of a catalyzer for the topological phase transition (topological deformation for the skyrmion crystal configuration from the skrymion phase to half-skyrmion phase). Furthermore, we observe that in the presence of the magnetic field, the inhomogeneous chiral condensate persists both in the skyrmion and half-skyrmion phases. Explicitly, as the strength of magnetic field gets larger, the inhomogeneous chiral condensate in the skyrmion phase tends to be drastically localized, while in the half-skyrmion phase the inhomogeneity configuration is hardly affected. It also turns out that a large magnetic effect in a low density region distorts the baryon shape to an elliptic form but the crystal structure is intact. However, in a high density region, the crystal structure is strongly effected by the strong magnetic field. A possible correlation between the chiral inhomogeneity and the deformation of the skrymion configuration is also addressed. The results obtained in this paper might be realized in the deep interior of compact stars., Comment: 13 pages, 31 figures, minor corrections made, some revision made, references added

The chiral soliton lattice (CSL) has been studied in condensed-matter system such as chiral magnets, which arises as a parity-violating topological soliton. In hadron physics, various attempts have also been made to apply the idea of CSL to baryonic matter. In this work, we explore the CSL effects on the baryonic matter based on the skrymion crystal approach. It is found that the CSL causes an inverse catalysis for the topology change in the dense baryonic matter. Furthermore, we observe that the CSL makes the single-baryon shape deformed to be highly oscillating as the frequency of the CSL gets larger, which leads to the enhancement of a baryon energy. Of interest is that in a high density region, the CSL goes away due to the topology change in the baryonic matter. What we find here might deepen our understanding of dense matter systems as well as compact stars., Comment: 12 pages, 29 figures