Boundary Behavior Research Articles

The effects of hydrogen and vacancy on the tensile deformation behavior of Σ3 symmetric tilt grain boundaries in pure fe

The interplay of hydrogen, vacancy and grain boundary plays an important role in hydrogen induced premature fracture in the metallic materials. In this work, two models with the representative high angle grain boundaries with the low and high grain boundary energy have been built according to the coincidence site lattice theory. The effects of hydrogen and hydrogen-vacancy combination on the deformation behaviors of the two models were investigated by means of molecular dynamics simulation with the straining direction vertical to the grain boundary. It is found that in both cases hydrogen tends to segregate and maintain a high local stress state around the grain boundary, and promote the premature fracture compared with the hydrogen-free model. Vacancy enhanced the effects of hydrogen in the model with grain boundary of the lower energy. However, vacancy promoted the dislocation evolution behavior in the model with grain boundary of the higher energy. The simulation results were further explained by considering the effects of hydrogen on the generalized stacking fault energy and the work of separation of the grain boundary.

Tumor boundary instability induced by nutrient consumption and supply

We investigate the tumor boundary instability induced by nutrient consumption and supply based on a Hele-Shaw model derived from taking the incompressible limit of a cell density model. We analyze the boundary stability/instability in two scenarios: 1) the front of the traveling wave; 2) the radially symmetric boundary. In each scenario, we investigate the boundary behaviors under two different nutrient supply regimes, in vitro, and in vivo. Our main conclusion is that for either scenario, the in vitro regime always stabilizes the tumor's boundary regardless of the nutrient consumption rate. However, boundary instability may occur when the tumor cells aggressively consume nutrients, and the nutrient supply is governed by the in vivo regime.

Engineered Grain Boundary Enables the Room Temperature Solid-State Sodium Metal Batteries

The NASICON-type (Sodium Super Ionic Conductor) Na3Zr2Si2PO12 solid electrolyte is one of the most promising electrolytes for solid-state sodium metal batteries. When preparing Na3Zr2Si2PO12 ceramic using a traditional high-temperature solid-state reaction, the high-densification temperature would result in the volatilization of certain elements and the consequent generation of impurity phase, worsening the functional and mechanical performance of the NASICON electrolyte. We rationally introduced the sintering additive B2O3 to the NASICON matrix and systemically investigated the influence of B2O3 on the crystal structure, microstructure, electrical performance, and electrochemical performance of the NASICON electrolytes. The results reveal that B2O3 can effectively reduce the densification sintering temperature and promote the performance of the Na3Zr2Si2PO12 electrolyte. The Na3Zr2Si2PO12-2%B2O3-1150 ℃ achieves the highest ionic conductivity of 4.7 × 10−4 S cm−1 (at 25 °C) with an activation energy of 0.33 eV. Furthermore, the grain boundary phase formed during the sintering process could improve the mechanical behavior of the grain boundary and inhibit the propagation of metallic sodium dendrite within the NASICON electrolyte. The assembled Na/Na3Zr2Si2PO12-2%B2O3/Na3V1.5Cr0.5(PO4)3 cell reveals the initial discharge capacity of 98.5 mAh g−1 with an initial Coulombic efficiency of 84.14% and shows a capacity retention of 70.3% at 30 mA g−1 over 200 cycles.

Effect of rare earth element yttrium on migration behavior of twin boundary in magnesium alloys: a molecular dynamics study

The addition of rare earth (RE) elements can effectively improve the mechanical properties of Mg alloys, which is attributed to its ability to regulate the plastic deformation behavior of Mg alloys. Here, the effects of the concentration of RE element Y and temperature on the migration behavior of twin boundary (TB) in the Mg alloys are investigated by molecular dynamics simulation. The results show that Y element has a softening effect on the migration of TB and promoted TB migration in the Mg alloys. The higher concentration of Y element, the stronger the softening effect on TB migration, and also the faster the migration speed of TB. The results indicate that higher temperature is beneficial to TB migration, and the softening effect of Y element on TB migration in the Mg alloys decreases with the increase of temperature. In addition, the migration mechanism of TB in the Mg alloys is analyzed in detail. This work provides a theoretical basis for the design and preparation of high-performance Mg alloys.

Insights into the role of partially mixed zones in sulfide stress corrosion cracking of the inconel 625/X80 weld overlay

Sulfide stress corrosion cracking (SSCC) behavior of the fusion boundary (FB) region of Inconel 625/X80 weld overlay was investigated with a focus on the role of the beach and peninsula partially mixed zones (PMZs). Compared to the martensite-ferrite boundary, the large misorientation and low deformation compatibility of the austenite-martensite boundary promote the accumulation of hydrogen and thus increase the cracking susceptibility. Further, under the effect of local anodic dissolution and hydrogen accumulation due to the large dimension PMZ, the corrosion defect formed at the junction can be easily transformed into a crack. After SSCC initiation, the crack preferentially grows along the Inconel 625/PMZ interface while the austenite matrix may oblige the crack to propagate along the FB. In addition, the beach PMZ likely shows a higher SSCC susceptibility than the peninsula PMZ mainly because severe anodic dissolution in the peninsula structure blunts the crack tip along the FB during crack propagation.

The structure dependence of oxidation behavior of high-angle grain boundaries of alloy 600 in simulated pressurized water reactor primary water

The intergranular degradation of seven different types of high-angle grain boundaries (HAGBs) were investigated on Alloy 600 after exposure to simulated pressurized water reactor primary water. All boundaries are susceptible to preferential intergranular oxidation (PIO) except for ideal coherent twin boundary. Diffusion induced grain boundary migration (DIGM) normally occurs and its depth is positively correlated with the PIO extent. Interestingly, the PIO susceptibility is independent on the grain boundary misorientation angle or Σ value, but related to the grain boundary atom packing density (GBAPD). Grain boundaries with higher GBAPD values show higher PIO resistance as the element diffusion is slower.

Method of Suppressing Solidification Cracking by Laser Surface Melting and Epitaxial Growth Behavior for Directionally Solidified 247LC Superalloy

In this study, the relationship between solidification cracking and epitaxial growth behavior with the high-speed laser surface melting of a directionally solidified 247LC superalloys was fundamentally and metallurgically investigated, to develop a successful welding procedure for the next generation of gas turbine blades. Under typical laser surface melting conditions (scan speed: 50 mm/s, heat input: 40 J/mm), severe solidification cracking phenomena occurs. The key metallurgical factors of solidification cracking have been identified as solidification segregation-assisted pipeline diffusion behavior at the solidification grain boundary, and in the randomly formed polycrystalline melting zone microstructure. In addition, under extremely low heat input and high-speed laser beam scan conditions (scan speed: 1000 mm/s, heat input: 2 J/mm), an effective surface melting zone can be obtained within a single directionally solidified grain under a relatively high-energy beam density (65 J/mm2) using the characteristics of single-mode fiber lasers. Results reveal that the laser melting zone successfully shows a 99.9% epitaxial growth achievement ratio. Because of the superior epitaxial growth ratio within the laser surface melting zone, and the rapid solidification phenomena, formation of a solidification grain boundary and solidification segregation-assisted pipeline diffusion behavior can be suppressed. Finally, a solidification crack-free laser melting zone can thus be achieved.

The Leibniz rule for the Dirichlet and the Neumann Laplacian

We study the bilinear estimates in the Sobolev spaces with the Dirichlet and the Neumann boundary condition. The optimal regularity is revealed to get such estimates in the half space case, which is related to not only smoothness of functions and but also boundary behavior. The crucial point for the proof is how to handle boundary values of functions and their derivatives.

The Optimal Global Estimates and Boundary Behavior for Large Solutions to the k-Hessian Equation

In this paper, we consider the k-Hessian equation $${S_k}({D^2}u) = b(x)f(u)\,\,\,in\,\,\Omega,\,\,\,\,u = + \infty \,\,on\,\,\partial \Omega,$$ where Ω is a smooth, bounded, strictly convex domain in ℝN with N ≥ 2, b ∈ C∞ (Ω) is positive in Ω and may be singular or vanish on the boundary, f ∈ C∞ (0, +∞) ∩ C[0, +∞) (or f ∈ C∞ (ℝ)) is positive and increasing on [0, +∞) (or ℝ) and satisfies the Keller—Osserman type condition. We first prove an upper and lower solution method of classical k-convex large solutions to the above equation, and then we study the optimal global estimates and boundary behavior of large solutions. In particular, we investigate the asymptotic behavior of such solutions when the parameters on b tend to the corresponding critical values and infinity.

The reduced Bergman kernel and its properties

In this paper, we study some properties of the nth-order weighted reduced Bergman kernels for planar domains, [Formula: see text]. Specifically, we look at Ramadanov type theorems, localization, and boundary behavior of the weighted reduced Bergman kernel and its higher-order counterparts. We also give a transformation formula for these kernels under biholomorphisms.

Reliability Modeling and Assessment for a Cyber-Physical System With a Complex Boundary Behavior

This article investigates the reliability of a special cyber-physical system (CPS) with an unreliable service and a complex boundary behavior. A flat semi-dormant multicontroller (FSDMC) model is constructed on a special CPS named arbitrated networked control system (ANCS) with dual channels. In this study, the dual-channel ANCS is considered as a Markov repairable system, which integrates the binary state of physical device failure and the multistate of information flow. The FSDMC is modeled as an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">N/(d,c)-M/M/c/K/SMWV</i> queuing system with an unreliable service. A dual rate matrix method is proposed to solve the stationary distribution of the queuing system and obtain the closed-form matrix solution of the distribution. Based on the queuing model, an optimization model is established to minimize the proposed cost performance rate function. A particle swarm optimization algorithm is used to solve the optimization model and obtain the optimal values of the system parameters under stable conditions. The closed-form expression of the instantaneous availability of the FSDMC on the physical failure rate and repair rate of the controller is yielded iteratively. The linear relationship between system instantaneous failure rate and task instantaneous failure rate is expressed. The sensitivity of task failure rate to system parameters is analyzed. Several reliability metrics are used to evaluate system reliability and task reliability. Experiments are conducted in real application scenarios to compare the task reliability using redundancy technology and real parallel applications. Experiments show that the proposed reliability model can more effectively guarantee system reliability goals compared with its counterparts.

On the boundary behavior of weak (p; q)-quasiconformal mappings

On the boundary behavior of weak (p; q)-quasiconformal mappings

On the boundary behavior of weak (p,q)-quasiconformal mappings

Let $\Omega$ and $\widetilde{\Omega}$ be domains in the Euclidean space $\mathbb{R}^n$. We study the boundary behavior of weak $(p,q)$-quasiconformal mappings $\varphi:\Omega\to \widetilde{\Omega}$, $n-1&lt;q\leqslant p&lt;n$. The suggested method is based on the capacitary distortion properties of the weak $(p,q)$-quasiconformal mappings.

Instantons in AdS$$_4$$ from (anti)membranes wrapping $$S^7$$ to Bose–Fermi duality in CFT$$_3$$’s

We present new SO(4)-invariant and non-supersymmetric instanton solutions for the conformally coupled m^2=-2 and massive m^2=+4 (pseudo)scalars arising from a consistent truncation of 11-dimensional supergravity over AdS_4 x S^7/Z_k when the internal space is a S^1 Hopf fibration on CP^3, and we consider backreaction. In fact, the bulk configurations associate with (anti)membranes wrapped around mixed internal (and external) directions, which in turn probe the Wick-rotated or skew-whiffed background, break all supersymmetries as well as parity invariance. From near the boundary behavior of the closed solution for the coupled bulk (pseudo)scalar, we get a marginal triple-trace deformation with mixed boundary condition (valid also for the bulk massless m^2=0 (pseudo)scalar, raised when considering the external space backreaction, with Dirichlet boundary condition) and as a result, the corresponding boundary effective potential is unbounded from below and causes an instability because of the Fubini-like instanton. Presenting dual effective actions, we see that the boundary solutions and counterparts realize in singlet sectors of three-dimensional U(N) and O(N) Chern--Simons-matter field theories. In particular, we use versions of massless and mass-deformed regular and critical boson and fermion models, find instantons and confirm state-operator AdS_4/CFT_3 correspondence and also Bose-Fermi duality at the level of the solutions. In addition, we discuss on relations of our setups with Vasiliev's Higher-Spin theories, deformations of the Aharony-Bergman-Jafferis-Maldacena model and other related studies.

The non-tangential boundary behavior of the matrix-valued rational inner functions on bounded symmetric domain

Knese [Proc. LMS 111(2015), 1261-1306] proved every rational inner function on polydisc has a non-tangential limit at every point of the Shilov boundary. We extended his result to the case of functions on general bounded symmetric domains. Namely, every rational inner function on a bounded symmetric domain has a non-tangential limit of modulus 1 1 at every point of the Shilov boundary. We also prove that every matrix-valued rational inner function on tube-type domain has a unitary non-tangential limit at every point of the Shilov boundary.

The Wiener Criterion for Nonlocal Dirichlet Problems

We study the boundary behavior of solutions to the Dirichlet problems for integro-differential operators with order of differentiability \(s \in (0, 1)\) and summability \(p>1\). We establish a nonlocal counterpart of the Wiener criterion, which characterizes a regular boundary point in terms of the nonlocal nonlinear potential theory.

The effect of disorder on quenched and averaged large deviations for random walks in random environments: Boundary behavior

For a random walk in a uniformly elliptic and i.i.d. environment on Zd with d≥4, we show that the quenched and annealed large deviation rate functions agree on any compact set contained in the boundary ∂D≔{x∈Rd:|x|1=1} of their domain which does not intersect any of the (d−2)-dimensional facets of ∂D, provided that the disorder of the environment is low enough (depending on the compact set). As a consequence, we obtain a simple explicit formula for both rate functions on any such compact set of ∂D at low enough disorder. In contrast to previous works, our results do not assume any ballistic behavior of the random walk and are not restricted to neighborhoods of any given point (on the boundary ∂D). In addition, our results complement those in Bazaes et al. (2022), where, using different methods, we investigate the equality of the rate functions in the interior of their domain. Finally, for a general parametrized family of environments, we show that the strength of disorder determines a phase transition in the equality of both rate functions, in the sense that for each x∈∂D there exists ɛx such that the two rate functions agree at x when the disorder is smaller than ɛx and disagree when it is larger. This further reconfirms the idea, introduced in Bazaes et al. (2022), that the disorder of the environment is in general intimately related with the equality of the rate functions.

Properties of the moduli set of complete connected projective special real manifolds

We construct a compact convex generating set \(\mathcal {C}_n\) of the moduli set of closed connected projective special real manifolds of fixed dimension n. We show that a closed connected projective special real manifold corresponds to an inner point of \(\mathcal {C}_n\) if and only if it has regular boundary behaviour. Our results can be used to describe deformations of 5d supergravity theories with complete scalar geometries.

The Heston stochastic volatility model has a boundary trace at zero volatility

We establish boundary regularity results in Hölder spaces for the degenerate parabolic problem obtained from the Heston stochastic volatility model in Mathematical Finance set up in the spatial domain (upper half-plane) mathbb {H} = mathbb {R}times (0,infty )subset mathbb {R}^2. Starting with nonsmooth initial data u_0in H, we take advantage of smoothing properties of the parabolic semigroup textrm{e}^{-t{mathcal {A}}}:,Hrightarrow H, tin mathbb {R}_+, generated by the Heston model, to derive the smoothness of the solution u(t) = textrm{e}^{-t{mathcal {A}}} u_0 for all t>0. The existence and uniqueness of a weak solution is obtained in a Hilbert space H = L^2(mathbb {H};mathfrak {w}) with very weak growth restrictions at infinity and on the boundary partial mathbb {H}= mathbb {R}times { 0}subset mathbb {R}^2 of the half-plane mathbb {H}. We investigate the influence of the boundary behavior of the initial data u_0in H on the boundary behavior of u(t) for t>0.

материаловЭволюция границ зерен алюминия в процессе изотермического отжига

Using an example of textured aluminum foils, the possibilities of using the reflected electron diffraction method for in situ studies of the behavior of grain boundaries during isothermal annealing have been experimentally demonstrated. It is shown that there is no homogeneity of the microstructure in space and no continuity of its change in time during grain growth. The experimentally discovered rotation of the crystal lattice near the grain boundary in the region of a thermal etching groove can have a retarding effect on the movement of the boundary.