Search Results (124)

In this work, we propose the general idea of using a path-finding algorithm to solve a variational problem. By interpreting a variational problem of finding the function that minimizes a functional integral as a shortest path finding, we can apply the shortest path-finding algorithm to numerically estimate the optimal function. This can be achieved by discretizing the continuous domain of the variational problem into a spatially weighted graph. The weight of each edge is defined according to the function of the original problem. We adopt the Moser lattice as the discretization scheme since it provides adjustable connections around a vertex. We find that this number of connections is crucial to the estimation of an accurate optimal path. Dijkstra’s shortest path-finding algorithm was chosen due to its simplicity and convenience in implementation. We validate our proposal by applying Dijkstra’s path-finding algorithm to numerically solve three famous variational problems, i.e., the optical ray tracing, the brachistochrone, and the catenary problems. The first two are examples of problems with no constraint. The standard Dijkstra’s algorithm can be directly applied. The third problem is an example of a problem with an isoperimetric constraint. We apply the Lagrangian relaxation technique to relax the optimization in the standard Dijkstra algorithm to incorporate the constraint. In all cases, when the number of sublattices is large enough, the results agree well with the analytic solutions. In all cases, the same path-finding code is used, regardless of the problem details. Our approaches provide more insight and promise to be more flexible than conventional numerical methods. We expect that our method can be useful in practice when an investigation of the optimal path in a complex problem is needed. Full article

In this study, microstructure evolution during prior austenite decomposition and reverse phase transformation processes was revealed in a high-strength medium-Mn steel. Furthermore, the relationship between deformed prior austenite characteristics and deformation behavior was studied. The results indicated that the recovery and recrystallization of the deformed prior austenite were significantly inhibited during hot rolling in the non-recrystallized zone, the grain size was obviously refined along the normal direction (ND), and that the strain hardening of prior austenite via hot deformation could increase the resistance of shear transformation, resulting in the preservation of high-density lattice defects in the quenched martensite matrix. Before the nucleation of intercritical austenite, the dislocation and grain boundary can provide fast diffusion paths for C and Mn, and the enrichment of C and Mn before intercritical austenite formation can reduce the critical temperature of ferrite/austenite transformation. The nucleated sites and driving force for intercritical austenite were strongly increased by rolling in the non-recrystallization region. The resistance of crack propagation was found to be enhanced by the sustained transformation-induced plasticity (TRIP) effect (via retained austenite with different stability) and for the laminated microstructure, the optimum properties were obtained as being a combination of yield strength of 748 MPa, tensile strength of 952 MPa, and total elongation of 26.2%. Full article

This study investigates the design of additive manufacturing for controlled crack propagation using process parameters and lattice structures. We examine two lattice types—octet-truss (OT) and diamond (DM)—fabricated via powder bed fusion with Ti-6Al-4V. Lattice structures are designed with varying densities (10%, 30%, and 50%) and process using two different laser energies. Using additive-manufactured specimens, Charpy impact tests are conducted to evaluate the fracture behavior and impact energy levels of the specimens. Results show that the type of the lattice structures, the density of the lattice structures, and laser energy significantly influence crack propagation patterns and impact energy. OT exhibits straighter crack paths, while DM demonstrates more random fracture patterns. Higher-density lattices and increased laser energy generally improve the impact energy. DM consistently outperformed OT in the impact energy for angle specimens, while OT showed superior performance in stair specimens. Finally, a case study demonstrates the potential for combining OT and DM structures to guide crack propagation along predetermined paths, offering a novel approach to protect critical components during product failure. Full article

We present a new formulation of the central moment lattice Boltzmann (LB) method based on a minimal continuous Fokker-Planck (FP) kinetic model, originally proposed for stochastic diffusive-drift processes (e.g., Brownian dynamics), by adapting it as a collision model for the continuous Boltzmann equation (CBE) for fluid dynamics. The FP collision model has several desirable properties, including its ability to preserve the quadratic nonlinearity of the CBE, unlike that based on the common Bhatnagar-Gross-Krook model. Rather than using an equivalent Langevin equation as a proxy, we construct our approach by directly matching the changes in different discrete central moments independently supported by the lattice under collision to those given by the CBE under the FP-guided collision model. This can be interpreted as a new path for the collision process in terms of the relaxation of the various central moments to “equilibria”, which we term as the Markovian central moment attractors that depend on the products of the adjacent lower order moments and a diffusion coefficient tensor, thereby involving of a chain of attractors; effectively, the latter are nonlinear functions of not only the hydrodynamic variables, but also the non-conserved moments; the relaxation rates are based on scaling the drift coefficient by the order of the moment involved. The construction of the method in terms of the relevant central moments rather than via the drift and diffusion of the distribution functions directly in the velocity space facilitates its numerical implementation and analysis. We show its consistency to the Navier-Stokes equations via a Chapman-Enskog analysis and elucidate the choice of the diffusion coefficient based on the second order moments in accurately representing flows at relatively low viscosities or high Reynolds numbers. We will demonstrate the accuracy and robustness of our new central moment FP-LB formulation, termed as the FPC-LBM, using the D3Q27 lattice for simulations of a variety of flows, including wall-bounded turbulent flows. We show that the FPC-LBM is more stable than other existing LB schemes based on central moments, while avoiding numerical hyperviscosity effects in flow simulations at relatively very low physical fluid viscosities through a refinement to a model founded on kinetic theory. Full article

Martensitic transformations, viewed as continuous mappings between triply periodic minimal surfaces (TPMSs), as suggested by Hyde and Andersson (Z. Kristallogr. 1986, 174, 225–236), are extended to include paths between the initial and final phases. Reversible transformations, which correspond to shape-memory materials, occur only if lattice points remain at flat points on a TPMS throughout a continuous transformation. For the shape-memory material NiTi, the density functional calculations by Hatcher et al. [Phys. Rev. B2009, 80, 144203] yield irreversible and reversible paths with and without energy barriers, respectively, in agreement with our theory. Although there are TPMSs for face-centered and body-centered cubic crystals for iron, the deformation between them is not reversible, in agreement with the non-vanishing energy barriers obtained from the density functional calculations of Zhang et al. (RSC Advances2021, 11, 3043–3048). Full article

Sn–Bi-based, low-temperature solder alloys are being developed to offer the electronics manufacturing industry a path to lower temperature processes. A critical challenge is the significant microstructural and lattice parameter changes that these alloys undergo at typical service temperatures, largely due to the variable solubility of Bi during the Sn phase. The influence of alloying additions in improving the performance of these alloys is the subject of much research. This study aims to enhance the understanding of how alloying with In influences these properties, which are crucial for improving the alloy’s reliability. Using in situ heating synchrotron powder X-ray diffraction (PXRD), we investigated the Sn–57 wt% Bi–xIn (x = 0, 0.2, 0.5, 1, 3 wt%) alloys during heating and cooling. Our findings reveal that In modifies the microstructure, promoting more homogeneous Bi distribution during thermal cycling. This study not only provides new insights into the dissolution and precipitation behaviour of Bi in Sn–Bi-based alloys, but also demonstrates the potential of In to improve the thermal stability of these alloys. These innovations contribute significantly to advancing the performance and reliability of Sn–Bi-based, low-temperature solder alloys. Full article

Electric multirotor plant protection unmanned aerial vehicles (UAVs) are widely used in China for efficient and precise plant protection at low altitude for low volumes. Unstructured farmland in China has various types of obstacles, and UAVs usually use a detour path to avoid obstacles due to flight altitude limitations. However, existing UAV spray systems do not spray when in obstacle neighborhoods during obstacle avoidance, resulting in insufficient droplet coverage and reduced plant protection quality in the area. To improve the droplet coverage in obstacle neighborhoods, this article carries out a study of side spray technology with an electric quadrotor UAV, and proposes the design and development of a side spray device. The relationship between the obstacle avoidance path of the UAV and the spray pattern of the side spray device and their effect on droplet coverage in obstacle neighborhoods was explored. An accurate measurement method of the relative position between the UAV and obstacles was proposed. Spray angle calculations and nozzle selection for the side spray device were carried out in conjunction with the relative position. A rotor wind field simulation model was designed based on the lattice Boltzmann method (LBM), and the spatial layout of the side spray device on the UAV was designed based on the simulation results. To explore suitable spray patterns for the side spray device, comparative experiments of droplet coverage in obstacle neighborhoods were carried out under different environments, spray patterns, and flight parameter combinations. The relationship between the flight parameter combinations and the distribution uniformity of droplets and the effective swath width of the side spray device was explored. The experimental results were analyzed by an analysis of variance (ANOVA) and a relationship model was obtained. The results showed that the side spray device can effectively improve droplet coverage in obstacle neighborhoods compared to a device without side spray using the same flight parameter combinations. The effective swath width in obstacle neighborhoods can be increased by a minimum of 6.35%, maximum of 35.32%, and average of 15.25% using the side spray device. The error between the predicted values of the relational model and the field experiment results was less than 15%. The results verify the effectiveness and rationality of the method proposed in this article. This study can provide technical and theoretical references for improving the plant protection quality of UAVs in obstacle environments. Full article

Heterostructures of visible light-absorbing semiconductors were prepared through the growth of ZnIn₂S₄ crystallites in the presence of CdS nanostructures. A variety of hybrid compositions was synthesized. Both reference samples and heterostructured materials were characterized in detail, regarding their morphology, crystalline character, chemical speciation, as well as vibrational properties. The abovementioned physicochemical characterization suggested the absence of doping phenomena, such as the integration of either zinc or indium ions into the CdS lattice. At specific compositions, the growth of the amorphous ZnIn₂S₄ component was observed through both XRD and Raman analysis. The development of heterojunctions was found to be composition-dependent, as indicated by the simultaneous recording of the Raman profiles of both semiconductors. The optical band gaps of the hybrids range at values between the corresponding band gaps of reference semiconductors. The photocatalytic activity was assessed in both organic dye degradation and hydrogen peroxide evolution. It was observed that the hybrids demonstrating efficient photocatalytic activity in dye degradation were rather poor photocatalysts for hydrogen peroxide evolution. Specifically, the hybrids enriched in the CdS component were shown to act efficiently for hydrogen peroxide evolution, whereas ZnIn₂S₄-enriched hybrids demonstrated high potential to photodegrade an azo-type organic dye. Furthermore, scavenging experiments suggested the involvement of singlet oxygen in the mechanistic path for dye degradation. Full article

This study investigated the migration patterns of oxygen in the deoxidation process of Ti-48Al alloy scrap using electromagnetic levitation (EML) technology. Scanning electron microscopy (SEM), X-ray diffraction (XRD), and X-ray photoelectron spectroscopy (XPS) were employed to analyze the oxygen distribution patterns and migration path during EML. The refining process resulted in three types of oxygen migration: (1) escape from the lattice and evaporation in the form of AlO, Al₂O; (2) formation of metal oxides and remaining in the alloy melt; (3) attachment to the quartz tube wall in the form of metal oxides such as Al₂O₃ and Cr₂O₃. The oxygen content of the scrap was dropped with a deoxidation ratio of 62%. It indicated that EML can greatly promote the migration and removal of oxygen elements in Ti-Al alloy scrap. Full article

For silicon-based epitaxial quantum dot lasers (QDLs), the mismatches of the lattice constants and the thermal expansion coefficients lead to the generation of threaded dislocations (TDs), which act as the non-radiative recombination centers through the Shockley–Read–Hall (SRH) recombination. Based on a three-level model including the SRH recombination, the nonlinear properties of the silicon-based epitaxial QDLs under optical injection have been investigated theoretically. The simulated results show that, through adjusting the injection parameters including injection strength and frequency detuning, the silicon-based epitaxial QDLs can display rich nonlinear dynamical states such as period one (P1), period two (P2), multi-period (MP), chaos (C), and injection locking (IL). Relatively speaking, for a negative frequency detuning, the evolution of the dynamical state with the injection strength is more abundant, and an evolution path P1-P2-MP-C-MP-IL has been observed. Via mapping the dynamical state in the parameter space of injection strength and frequency detuning under different SRH recombination lifetime, the effects of SRH recombination lifetime on the nonlinear dynamical state of silicon-based epitaxial QDLs have been analyzed. Full article

The investigation of iron under high pressure and temperatures is crucial to understand the Earth’s core structure and composition and the generation of magnetic fields. Here, we present new in situ XRD measurements for iron in an off-Hugoniot state by laser-driven ramp compression at pressure of 200–238 GPa. The lattice parameters for the hexagonal (hcp)-Fe phase and the c/a ratios were obtained to compare them with previous static and dynamical data, which provides the direct confirmation of such parameters via the different compression paths and strain rates. This work indicates that laser ramp compression can be utilized to provide crystal structure information and direct key information on the crystal structure of Fe at the ultrahigh pressure–temperature conditions relevant for planetology. Full article

Continuous-fiber-reinforced composite lattice structures (CFRCLSs) have garnered attention due to their lightweight and high-strength characteristics. Over the past two decades, many different topological structures including triangular, square, hexagonal, and circular units were investigated, and the basic mechanical responses of honeycomb structures under various load conditions, including tension, compression, buckling, shear, and fatigue were studied. To further improve the performance of the honeycombs, appropriate optimizations were also carried out. However, the mechanical properties of a single lattice often struggle to exceed the upper limit of its structure. This paper investigates the effect of permutation and hybrid mode on the mechanical properties of CFRCLSs by comparing five structures: rhomboid (R-type), octagon orthogonal array (OOA-type), octagon hypotenuse array (OHA-type), octagon nested array (ONA-type), and rhomboid circle (RC-type), with the conventional hexagonal structure (H-type). CFRCLS samples are fabricated using fused filament fabrication (FFF), with carbon-fiber-reinforced polylactic acid (PLA) as the matrix. The in-plane compression properties, energy absorption characteristics, and deformation behaviors of the hybrid structures were studied by experimental tests. The results demonstrate that different permutation and hybrid modes alter the deformation behaviors and mechanical properties of the structures. Taking elastic modulus as an example, the values of H-type, R-type, OOA-type, OHA-type, ONA-type, and RC-type are, respectively, 6.08 MPa, 5.76 MPa, 19.0 MPa, 10.3 MPa, 31.7 MPa, and 73.2 MPa, while the ratio of their masses is 1:1:1.10:1.52:1.66. Furthermore, hybrid lattice structures exhibit significantly improved mechanical properties compared to single lattice structures. Compared to the single structure R-type, the RC-type increases elastic modulus, yield strength, and energy absorption, respectively, by 12.7 times, 5.4 times, and 4.4 times. Full article

First, a recently developed eigenfunction expansion technique, based in part on the separation of the thickness variable and partly utilizing a modified Frobenius-type series expansion technique in conjunction with the Eshelby–Stroh formalism, is employed to derive three-dimensional singular stress fields in the vicinity of the front of an interfacial crack weakening an infinite bicrystalline superlattice plate, made of orthorhombic (cubic, hexagonal, and tetragonal serving as special cases) phases of finite thickness and subjected to the far-field extension/bending, in-plane shear/twisting, and anti-plane shear loadings, distributed through the thickness. Crack-face boundary and interface contact conditions as well as those that are prescribed on the top and bottom surfaces of the bicrystalline superlattice plate are exactly satisfied. It also extends a recently developed concept of the lattice crack deflection (LCD) barrier to a superlattice, christened superlattice crack deflection (SCD) energy barrier for studying interfacial crack path instability, which can explain crack deflection from a difficult interface to an easier neighboring cleavage system. Additionally, the relationships of the nature (easy/easy, easy/difficult, or difficult/difficult) interfacial cleavage systems based on the present solutions with the structural chemistry aspects of the component phases (such as orthorhombic, tetragonal, hexagonal, as well as FCC (face-centered cubic) transition metals and perovskites) of the superlattice are also investigated. Finally, results pertaining to the through-thickness variations in mode I/II/III stress intensity factors and energy release rates for symmetric hyperbolic sine-distributed loads and their skew-symmetric counterparts that also satisfy the boundary conditions on the top and bottom surfaces of the bicrystalline superlattice plate under investigation also form an important part of the present investigation. Full article

The problem of finding the best path trajectory in a graph is highly complex due to its combinatorial nature, making it difficult to solve. Standard search algorithms focus on selecting the best path trajectory by introducing constraints to estimate a suitable solution, but this approach may overlook potentially better alternatives. Despite the number of restrictions and variables in path planning, no solution minimizes the computational resources used to reach the goal. To address this issue, a framework is proposed to compute the best trajectory in a graph by introducing the mathematical morphology concept. The framework builds a lattice over the graph space using mathematical morphology operators. The searching algorithm creates a metric space by applying the morphological covering operator to the graph and weighing the cost of traveling across the lattice. Ultimately, the cumulative traveling criterion creates the optimal path trajectory by selecting the minima/maxima cost. A test is introduced to validate the framework’s functionality, and a sample application is presented to validate its usefulness. The application uses the structure of the avenues as a graph. It proposes a computable approach to find the most suitable paths from a given start and destination reference. The results confirm that this is a generalized graph search framework based on morphological operators that can be compared to the Dijkstra approach. Full article

Graphs are a powerful tool for solving various mathematical problems. One such task is the representation of discrete structures. Combinatorial generation methods make it possible to obtain algorithms that can create discrete structures with specified properties. This article is devoted to issues related to the construction of such combinatorial generation algorithms for a wide class of directed lattice paths. The main method used is based on the representation of a given combinatorial set in the form of an AND/OR tree structure. To apply this method, it is necessary to have an expression for the cardinality function of a combinatorial set that satisfies certain requirements. As the main result, we have found recurrence relations for enumerating simple directed lattice paths that satisfy the requirements of the applied method and have constructed the corresponding AND/OR tree structure. Applying the constructed AND/OR tree structure, we have developed new algorithms for ranking and unranking simple directed lattice paths. Additionally, the obtained results were generalized to the case of directed lattice paths. Full article