Boundary Behavior Research Articles

Nonlinear elliptic problem in exterior domains: exact boundary behavior of blow-up positive solutions

Nonlinear elliptic problem in exterior domains: exact boundary behavior of blow-up positive solutions

Frustrated metastable-to-equilibrium grain boundary structural transition in NbMoTaW due to segregation and chemical complexity

Grain boundary structural transitions can lead to significant changes in the properties and performance of materials. In multi-principal element alloys, understanding these transitions becomes complex due to phenomena such as local chemical ordering and multi-component segregation. Using atomistic simulations, we explore a metastable-to-equilibrium grain boundary structural transition in NbMoTaW. The transition, characterized by structural disordering and reduced free volume, shows high sensitivity to its local chemical environment. Most notably, the transition temperature range of the alloy is more than twice that of a pure metal. Differences in composition between coexisting metastable and equilibrium structures highlight the change in local site availability due to structural relaxation. Further examination of grain boundaries with fixed chemical states at varying temperatures reveals that the amount of segregation significantly influences the onset temperature yet has minimal effect on the transition width. These insights underscore the profound effect of chemical complexity and ordering on grain boundary transitions in complex concentrated alloys, marking a meaningful advancement in our understanding of grain boundary behavior at the atomic level.

Microscopic-plastic deformation behavior of grain boundary precipitates in an Al–Zn–Mg alloy

The nano-precipitates with minimal misfit strengthen Al–Zn–Mg alloys by impeding dislocation motion. However, grain boundary precipitates (GBPs) are known to have a completely incoherent relationship with the matrix, making them less effective in strengthening the alloys. Instead, GBPs are recognized for preoccupying elements such as Zn or Mg, thereby diminishing the quantity of nano-strengthening phases. GBPs significantly influence the deformation and fracture behaviors of Al–Zn–Mg alloys by accelerating stress localization and crack formation. In this study, we investigated how the accumulation of dislocations in the GBP areas leads to stress localization and subsequent cracking, using micropillar tests and crystal plasticity finite element method (CP-FEM) analysis. The dislocation pile-up in the GBPs causes stress localization around the grain boundaries, inducing crack initiation and leading to intergranular fracture. These findings enhance our understanding of the role of GBPs in the deformation and cracking of Al–Zn–Mg alloys and may pave the way for new concepts in managing GBPs.

On some properties of generalized squeezing functions and Fridman invariants

AbstractThe purpose of this paper is twofold. The first aim is to study the comparison of generalized squeezing functions and Fridaman invariants of some special domains. Then, the second aim is to give estimates for these two invariants and discuss their boundary behavior near inessential boundary points.

A semi-analytical pressure and rate transient analysis model for inner boundary and propped fractures exhibiting dynamic behavior under long-term production conditions

The loss of hydrocarbon production caused by the dynamic behavior of the inner boundary and propped fractures under long-term production conditions has been widely reported in recent studies. However, the quantitative relationships for the variations of the inner boundary and propped fractures have not been determined and incorporated in the semi-analytical models for the pressure and rate transient analysis. This work focuses on describing the variations of the inner boundary and propped fractures and capturing the typical characteristics from the pressure transient curves.A generalized semi-analytical model was developed to characterize the dynamic behavior of the inner boundary and propped fractures under long-term production conditions. The pressure-dependent length shrinkage coefficients, which quantify the length changes of the inner zone and propped fractures, are modified and incorporated into this multi-zone semi-analytical model. With simultaneous numerical iterations and numerical inversions in Laplace and real-time space, the transient solutions to pressure and rate behavior are determined in just a few seconds. The dynamic behavior of the inner boundary and propped fractures on transient pressure curves is divided into five periods: fracture bilinear flow (FR1), dynamic PFs flow (FR2), inner-area linear flow (FR3), dynamic inner boundary flow (FR4), and outer-area dominated linear flow (FR5). The early hump during FR2 period and a positive upward shift during FR4 period are captured on the log-log pressure transient curves, reflecting the dynamic behavior of the inner boundary and propped fractures during the long-term production period.The transient pressure behavior will exhibit greater positive upward trend and the flow rate will be lower with the shrinkage of the inner boundary. The pressure derivative curve will be upward earlier as the inner boundary shrinks more rapidly. The lower permeability caused by the closure of un-propped fractures in the inner zone results in greater upward in pressure derivative curves. If the permeability loss for the dynamic behavior of the inner boundary caused by the closure of un-propped fractures is neglected, the flow rate will be overestimated in the later production period.

The role of in-situ Al3Ti formed during solidification in improving the high-temperature properties of Al-Cu alloy

In this paper, in-situ Al3Ti-reinforced Al-Cu alloys were fabricated by Ti alloying and exhibit outstanding high-temperature properties. The results show that when the volume fraction of Al3Ti is 7.8%, the ultimate strengths of the alloy can reach 203.9MPa and 144.1MPa at 300°C and 350°C, which are 31.0% and 51.4% higher than the base alloy, respectively. The analysis indicates that in addition to precipitation strengthening, dislocation strengthening, and load-transfer strengthening, low-angle grain boundaries also play an important role in improving the high-temperature properties of the alloy. When the Ti concentration in the alloy melt is high, Al3Ti grows into the two-dimensional lamellar dendrite with a complex structure and serves as the heterogeneous nucleation site of multiple α-Al cores, which results in the abnormal grain growth behavior and increase of low-angle grain boundaries. Moreover, fracture mechanism analysis suggests that the existence of Al3Ti increases the number of initial cracks, which increases the risk of splitting the matrix. The deformation behavior of Al3Ti is mainly controlled by twins, stacking faults, and dislocations. Under tensile stress, cracks first form in Al3Ti and then evolve into non-equiaxed voids in the matrix, which eventually connect and lead to the fracture of the alloy.

Boundary behaviors of spacelike constant mean curvature surfaces in Schwarzschild spacetime

Boundary behaviors of spacelike constant mean curvature surfaces in Schwarzschild spacetime

On angular limits of quasiregular mappings

We investigate Lindelöf and Koebe type boundary behavior results for bounded quasiregular mappings in n-dimensional Euclidean space. Our results give sufficient conditions for existence of non-tangential limits at a boundary point.

Weak solutions to the heat conducting compressible self-gravitating flows in time-dependent domains

In this paper, we consider the heat-conducting compressible self-gravitating fluids in time-dependent domains, which typically describe the motion of viscous gaseous stars. The flow is governed by the 3D Navier–Stokes–Fourier–Poisson equations where the velocity is supposed to fulfill the full-slip boundary condition and the temperature on the boundary is given by a non-homogeneous Dirichlet condition. We establish the global-in-time weak solution to the system. Our approach is based on the penalization of the boundary behavior, viscosity, and the pressure in the weak formulation. Moreover, to accommodate the non-homogeneous boundary heat flux, the concept of ballistic energy is utilized in this work.

Stability estimate for an inverse stochastic parabolic problem of determining unknown time-varying boundary *

Stochastic parabolic equations are widely used to model many random phenomena in natural sciences, such as the temperature distribution in a noisy medium, the dynamics of a chemical reaction in a noisy environment, or the evolution of the density of bacteria population. In many cases, the equation may involve an unknown moving boundary which could represent a change of phase, a reaction front, or an unknown population. In this paper, we focus on an inverse problem with the goal is to determine an unknown moving boundary based on data observed in a specific interior subdomain for the stochastic parabolic equation. The uniqueness of the solution of this problem is proved, and furthermore a stability estimate of log type is derived. This allows us, theoretically, to track and to monitor the behavior of the unknown boundary from observation in an arbitrary interior domain. The primary tool is a new Carleman estimate for stochastic parabolic equations. As a byproduct, we obtain a quantitative unique continuation property for stochastic parabolic equations.

Solvable non-Hermitian skin effects and real-space exceptional points: non-Hermitian generalized Bloch theorem

Non-Hermitian systems can exhibit extraordinary boundary behaviors, known as the non-Hermitian skin effects, where all the eigenstates are localized exponentially at one side of lattice model. To give a full understanding and control of non-Hermitian skin effects, we have developed the non-Hermitian generalized Bloch theorem to provide the analytical expression for all solvable eigenvalues and eigenstates, in which translation symmetry is broken due to the open boundary condition. By introducing the Vieta’s theorem for any polynomial equation with arbitrary degree, our approach is widely applicable for one-dimensional non-Hermitian tight-binding models. With the non-Hermitian generalized Bloch theorem, we can analyze the condition of existence or non-existence of the non-Hermitian skin effects at a mathematically rigorous level. Additionally, the non-Hermitian generalized Bloch theorem allows us to explore the real-space exceptional points. We also establish the connection between our approach and the generalized Brillouin zone method. To illustrate our main results, we examine two concrete examples including the Su–Schrieffer–Heeger chain model with long-range couplings, and the ladder model with non-reciprocal interaction. Our non-Hermitian generalized Bloch theorem provides an efficient way to analytically study various non-Hermitian phenomena in more general cases.

A fractional Hopf Lemma for sign-changing solutions

In this paper we prove some results on the boundary behavior of solutions to fractional elliptic problems. Firstly, we establish a Hopf Lemma for solutions to some integro-differential equations. The main novelty of our result is that we do not assume any global condition on the sign of the solutions. Secondly, we show that non-trivial radial solutions cannot have infinitely many zeros accumulating at the boundary. We provide concrete examples to show that the results obtained are sharp.

Setting our boundaries: The role of gender, values, and role salience in work–home boundary permeability

AbstractAlthough women make up nearly half of the U.S. workforce, gender role stereotypes persist, and gender roles may relate to how men and women manage work–home boundaries. In this study, we explore gender differences in how employee values (tradition, achievement) translate into role identity salience, and in turn, boundary management preferences and behaviour. With data collected in two waves from 200 employees, we examined how the personal values of tradition and achievement relate differently by gender to role identity salience and in turn, boundary management. We found that men who more strongly value tradition have higher levels of work identity salience and both prefer and create an impermeable boundary around work to prevent intrusion from home. Men who valued tradition more also preferred and crafted a permeable home boundary to allow work intrusion. In contrast, women with higher tradition values reported higher home identity salience, which was associated with preferring segmentation in both work‐to‐home and home‐to‐work directions, and to behaviorally protecting home from work. Contrary to expectations, achievement values did not relate to a boundary management process via role identity salience for either gender. We discuss implications for a more nuanced, values‐driven, and gendered perspective on boundary management.

Polyharmonic potential theory on the Poincaré disk

We consider the open unit disk D equipped with the hyperbolic metric and the associated hyperbolic Laplacian L. For λ∈C and n∈N, a λ-polyharmonic function of order n is a function f:D→C such that (L−λI)nf=0. If n=1, one gets λ-harmonic functions. Based on a Theorem of Helgason on the latter functions, we prove a boundary integral representation theorem for λ-polyharmonic functions. For this purpose, we first determine nth-order λ-Poisson kernels. Subsequently, we introduce the λ-polyspherical functions and determine their asymptotics at the boundary ∂D, i.e., the unit circle. In particular, this proves that, for eigenvalues not in the interior of the L2-spectrum, the zeroes of these functions do not accumulate at the boundary circle. Hence the polyspherical functions can be used to normalise the nth-order Poisson kernels. By this tool, we extend to this setting several classical results of potential theory: namely, we study the boundary behaviour of λ-polyharmonic functions, starting with Dirichlet and Riquier type problems and then proceeding to Fatou type admissible boundary limits.

Exploring the thermal behavior and diffusive functionality of structural defects and phase boundaries in near-stoichiometric chromium diborides by in situ scanning transmission electron microscopy

Exploring the thermal behavior and diffusive functionality of structural defects and phase boundaries in near-stoichiometric chromium diborides by <i>in situ</i> scanning transmission electron microscopy

Differences in boundary behavior in the 3D vertex and Voronoi models.

An important open question in the modeling of biological tissues is how to identify the right scale for coarse-graining, or equivalently, the right number of degrees of freedom. For confluent biological tissues, both vertex and Voronoi models, which differ only in their representation of the degrees of freedom, have effectively been used to predict behavior, including fluid-solid transitions and cell tissue compartmentalization, which are important for biological function. However, recent work in 2D has hinted that there may be differences between the two models in systems with heterotypic interfaces between two tissue types, and there is a burgeoning interest in 3D tissue models. Therefore, we compare the geometric structure and dynamic sorting behavior in mixtures of two cell types in both 3D vertex and Voronoi models. We find that while the cell shape indices exhibit similar trends in both models, the registration between cell centers and cell orientation at the boundary are significantly different between the two models. We demonstrate that these macroscopic differences are caused by changes to the cusp-like restoring forces introduced by the different representations of the degrees of freedom at the boundary, and that the Voronoi model is more strongly constrained by forces that are an artifact of the way the degrees of freedom are represented. This suggests that vertex models may be more appropriate for 3D simulations of tissues with heterotypic contacts.

Optimizing strategy for the discovery of compositionally-biased or low-complexity regions in proteins

Proteins can contain tracts dominated by a subset of amino acids and that have a functional significance. These are often termed ‘low-complexity regions’ (LCRs) or ‘compositionally-biased regions’ (CBRs). However, a wide spectrum of compositional bias is possible, and program parameters used to annotate these regions are often arbitrarily chosen. Also, investigators are sometimes interested in longer regions, or sometimes very short ones. Here, two programs for annotating LCRs/CBRs, namely SEG and fLPS, are investigated in detail across the whole expanse of their parameter spaces. In doing so, boundary behaviours are resolved that are used to derive an optimized systematic strategy for annotating LCRs/CBRs. Sets of parameters that progressively annotate or ‘cover’ more of protein sequence space and are optimized for a given target length have been derived. This progressive annotation can be applied to discern the biological relevance of CBRs, e.g., in parsing domains for experimental constructs and in generating hypotheses. It is also useful for picking out candidate regions of interest of a given target length and bias signature, and for assessing the parameter dependence of annotations. This latter application is demonstrated for a set of human intrinsically-disordered proteins associated with cancer.

Flutter investigation and deep learning prediction of FG composite wing reinforced with carbon nanotube

Abstract The flutter of a composite wing reinforced with functionally graded carbon nanotubes (CNTs) has been investigated. A rectangular plate models a supersonic wing with cantilever boundary conditions. To determine displacement fields of a moderately thick plate, shear deformation theory is used. Using the Hamilton principle, a first-order piston theory was used to simulate supersonic airflow. This study examines four types of CNT thickness. Also, four different CNT distribution patterns are investigated. In a two-layer asymmetric composite, the effects of patch mass, mass distribution, fiber orientation angle, and distribution of CNTs were examined. Moreover, the results are compared and verified with other studies. A greater mass ratio led to a smaller flutter boundary, while a longer added mass increased the flutter boundary. A variation in the distribution pattern in CNT fiber orientation results in a distinct behavior of the flutter boundary for asymmetric composites with increasing orientation angles. The artificial neural network is utilized to predict the damping ratio, and the results showed great accuracy compared to the study results. Hyperparameter tuning is employed for better optimizing the predictive models.

Heterogeneities of grain boundary contact for simulation of laboratory-scale mechanical behavior of granitic rocks

From a practical point of view, grain structure heterogeneities are key parameters that control the rock response and still remains a challenge to incorporate in a quantitative manner. One of the less discussed topics in the context of the grain-based model (GBM) in the particle flow code (PFC) is the contact heterogeneities and the appropriate contact model to mimic the grain boundary behavior. Generally, the smooth joint (SJ) model and linear parallel bond (LPB) model are used to simulate the grain boundary behavior. However, the literature does not document the suitability of different models for specific problems. Another challenge in implementing GBM in PFC is that only a single bonding parameter is used at the grain boundaries. The aim of this study is to investigate the responses of a laboratory-scale specimen with SJ and LPB models, considering grain boundary heterogeneous and homogeneous contact parameters. Uniaxial and biaxial compression tests are performed to calibrate the response of Creighton granite. The stress–strain curves, volumetric dilation, inter-crack (crack in the grain boundary), and intra-crack (crack within the grain) development, and failure patterns associated with different contact models are examined. It was found that both the SJ and LPB models can reproduce the pre-peak behavior observed for a granitic rock type. However, the LPB model is unable to reproduce the post-peak behavior. Due to the large interlocking effect originating from the balls in contact and the ball size in the LPB model, local dilation is induced at the grain boundaries. This overestimates the volumetric dilation and residual shear strength. The LPB model tends to result in discontinuous inter-cracks and stress localization in the rock specimen, resulting in fine fragments at the rock surface during failure.

Micro-crystallographically revealing the plasticity-evolved behaviors of thick Ti–6Al–4V laser-arc hybrid welded joint

Revealing the plasticity-evolved behaviors is of great significance for developing high-reliability thick Ti–6Al–4V welded joint for deep-sea exploration equipment. This research effort entailed a collaborative utilization of transmission electron microscopy (TEM) and electron backscatter diffraction (EBSD) techniques to reveal the evolution behaviors of microstructure, weld texture, and grain boundaries for thick Ti–6Al–4V laser-arc hybrid welded joint with thickness of up to 40 mm. The discerned outcomes of this study underscored that the mixture strategy of large-sized lath martensite, densely entangled dislocations, and dislocations pile up at grain boundaries in distinct welding layers significantly enlarged the inhomogeneous plasticity of thick Ti–6Al–4V welded joint. Besides, the intensified cylindrical-texture within the weld leads to a substantial augmentation in the occurrence of Schmidt Factor concentrations above 0.3, indicative of a larger fraction of grains assuming a soft-orientation. Furthermore, the investigation unveiled an increase in the proportion of low angle grain boundaries demonstrably augmented the distribution density of geometrically necessary dislocations (GNDs) within the welds, which in conjunction with the enhanced cylindrical texture substantially elevated the grains deformability, consequently reinforcing the plasticity of welded joint. This work has provided insights into the evolution behavior of thick Ti–6Al–4V welded joint for greatly improving the plastic properties of welded structure, and substantially enhancing the service safety for deep-sea exploration equipment.