Strip Domain Research Articles

The global well-posedness of solutions to compressible isentropic two-fluid magnetohydrodynamics in a strip domain

The global well-posedness of solutions to compressible isentropic two-fluid magnetohydrodynamics in a strip domain

Manipulation of Moiré Superlattice in Twisted Monolayer-multilayer Graphene by Moving Nanobubbles.

In the heterostructure of two-dimensional (2D) materials, many novel physics phenomena are strongly dependent on the Moiré superlattice. How to achieve the continuous manipulation of the Moiré superlattice in the same sample is very important to study the evolution of various physical properties. Here, in minimally twisted monolayer-multilayer graphene, we found that bubble-induced strain has a huge impact on the Moiré superlattice. By employing the AFM tip to dynamically and continuously move the nanobubble, we realized the modulation of the Moiré superlattice, like the evolution of regular triangular domains into long strip domain structures with single or double domain walls. We also achieved controllable modulation of the Moiré superlattice by moving multiple nanobubbles and establishing the coupling of nanobubbles. Our work presents a flexible method for continuous and controllable manipulation of Moiré superlattices, which will be widely used to study novel physical properties in 2D heterostructures.

Synergistic effects of laser powder bed fusion and annealing on the texture-selective recrystallization of magnetostrictive Fe-Ga-NbC alloys for biomedical applications

IntroductionMagnetostrictive Fe-Ga alloys have garnered extensive attention owing to their excellent magnetic properties and acceptable biocompatibility. Nevertheless, the polycrystalline Fe-Ga alloys currently available tend to display random texture orientations, which constrain their magnetostrictive performance. ObjectivesTo regulate the texture orientation of Fe-Ga-NbC alloys and thereby enhancing magnetostriction. MethodsIn this study, a processing route comprising laser powder bed fusion (LPBF) followed by secondary recrystallization annealing (800, 1000, and 1200 °C, respectively) was developed to prepare Fe-Ga-NbC alloys. ResultsThe results showed that the LPBF-ed (Fe81Ga19)99(NbC)1 alloys exhibited a high content of high energy grain boundaries (HEGBs) due to the repeated melting and solidification. In subsequent annealing process, the migration of HEGBs induced the rearrangement and recrystallization of grains, during which NbC was found to locate at the grain boundaries and influence the migration path of HEGBs via selective pinning, thereby resulting in a strong Goss texture. With the rise in annealing temperature, the content of Goss texture gradually increased from the initial 3.9 % to 71.3 % at 1200 °C, leading to enhanced magnetostriction, lower saturation magnetization and coercivity. Furthermore, in alternating magnetic fields, the alloys annealed at 1200 °C also exhibited higher magnetostriction than the LPBF-ed alloys. And a noteworthy grain coarsening was also observed after annealing, accompanied by a discernible inclination of magnetic domains towards strip domains. Additional, cell tests demonstrated that the prepared alloys had satisfactory biocompatibility and the ability to promote osteogenic differentiation. ConclusionThese findings indicated that the LPBF-ed and annealed Fe-Ga-NbC alloys might be a promising alternative as magnetostrictive-driven materials for biomedical applications.

A Study of Singular Similarity Solutions to Laplace’s Equation with Dirichlet Boundary Conditions

A Study of Singular Similarity Solutions to Laplace’s Equation with Dirichlet Boundary Conditions

Dynamic inverse plane characteristics of circular holes in a strip-shaped medium under line source excitation

Based on the complex variable function method and the wave function expansion method, the dynamic anti-plane characteristics of circular holes in the strip domain under line source excitation were studied. The total wave field in the strip domain is constructed using the concept of infinite mirroring, which eliminates the mutual impact of the wave field under the action of the upper and lower limits of the strip domain. To determine the overall wave field, solve the wave field's unknown coefficients in accordance with the boundary conditions. The right number of mirror images is found using the dynamic stress distribution of a circular hole in the band-shaped domain as a specific calculation example. The effect of altering the incident frequency and band-shaped domain width on the dynamic stress concentration coefficient surrounding the circular hole is also explored. As a consequence of the findings, the dynamic stress concentration coefficient around the circular hole in the zone domain at low frequencies is substantially bigger than it is at medium and high frequencies. Under identical conditions, the dynamic stress concentration coefficient will exhibit periodic extreme values and converge as the distance increases between the lower boundary and the circular hole’s center.

Vanishing capillarity–viscosity limit of the incompressible Navier–Stokes–Korteweg equations with slip boundary condition

In this paper, we investigate the vanishing capillarity–viscosity limit of the incompressible Navier–Stokes–Korteweg (NSK) equations in a three-dimensional horizontally periodic strip domain, in which the velocity of the fluid is supplemented with slip boundary condition and the gradient of density with Dirichlet boundary condition on the boundary. We prove that there exists an positive constant T0 independent on the capillarity and viscosity coefficients, such that the incompressible NSK equations have a unique strong solution on [0,T0] and the solution is uniformly bounded in H3. Based on the uniform estimates, we further give the convergence rate in H1 from the solutions of the incompressible NSK equations to the solution of the inhomogeneous incompressible Euler equations as the capillarity and viscosity coefficients go to zero simultaneously.

Octonionic monogenic and slice monogenic Hardy and Bergman spaces

Abstract In this paper we discuss some basic properties of octonionic Bergman and Hardy spaces. In the first part we review some fundamental concepts of the general theory of octonionic Hardy and Bergman spaces together with related reproducing kernel functions in the monogenic setting. We explain how some of the fundamental problems in well-defining a reproducing kernel can be overcome in the non-associative setting by looking at the real part of an appropriately defined para-linear octonion-valued inner product. The presence of a weight factor of norm 1 in the definition of the inner product is an intrinsic new ingredient in the octonionic setting. Then we look at the slice monogenic octonionic setting using the classical complex book structure. We present explicit formulas for the slice monogenic reproducing kernels for the unit ball, the right octonionic half-space and strip domains bounded in the real direction. In the setting of the unit ball we present an explicit sequential characterization which can be obtained by applying the special Taylor series representation of the slice monogenic setting together with particular octonionic calculation rules that reflect the property of octonionic para-linearity.

Enhanced insulation and ferro/piezo-electric properties of BiFeO3–BaTiO3via synchronous B-site co-doping and quenching treatment

Lead-free piezoelectric ceramics 0.7BiFe1-x(Zn0.5Sn0.5)xO3-0.3BaTiO3 [BF(ZS)x-BT] were successfully prepared using the solid-state reaction method. The dual effects of B-site Zn/Sn co-doping and quenching on the structure and piezoelectricity of BF(ZS)x-BT were investigated. All samples showed a distinct perovskite structure, characterized by the simultaneous presence of rhombohedral (R) and pseudo-cubic (pC) phases. The insulation and electrical properties were significantly increased by appropriate Zn/Sn co-doping and quenching treatment. The long parallel strip domains and enhanced lattice distortion synergistically contribute to the outstanding piezoelectricity (d33 = 203 pC/N) and a high Curie temperature (Tc = 493 °C) in quenched BF(ZS)0.003-BT. Furthermore, the quenching treatment was found to further improve the piezoelectric property and enhance its high-temperature stability, as demonstrated by the in-situ electromechanical coupling coefficient (kp) and thermal depolarization test. The d33 of the quenched BF(ZS)0.003-BT was maintained at 186 pC/N around 400 °C, highlighting its promising applications in medium-high temperature conditions.

Study of quantum calculus for a new subclass of $ q $-starlike bi-univalent functions connected with vertical strip domain

<abstract><p>In this study, using the ideas of subordination and the quantum-difference operator, we established a new subclass $ \mathcal{S} ^{\ast }\left(\delta, \sigma, q\right) $ of $ q $-starlike functions and the subclass $ \mathcal{S}_{\Sigma }^{\ast }\left(\delta, \sigma, q\right) $ of $ q $-starlike bi-univalent functions associated with the vertical strip domain. We examined sharp bounds for the first two Taylor-Maclaurin coefficients, sharp Fekete-Szegö type problems, and coefficient inequalities for the function $ h $ that belong to $ \mathcal{S}^{\ast }\left(\delta, \sigma, q\right) $, as well as sharp bounds for the inverse function $ h $ that belong to $ \mathcal{S}^{\ast }\left(\delta, \sigma, q\right) $. We also investigated some results for the class of bi-univalent functions $ \mathcal{S}_{\Sigma }^{\ast }\left(\delta, \sigma, q\right) $ and well-known corollaries were also highlighted to show connections between previous results and the findings of this paper.</p></abstract>

Manipulation of BiFeO3 nanostructure by substrate terrace morphology

Topological domain structures, such as vortex and center domain have been found in BiFeO3 nanoislands fabricated by self-assemble approaches, which exhibit great application potential in nonvolatile storage. However, how to control the self-assembled nanostructure during preparation process is still an open question. Here, we successfully grew BiFeO3 films with nano-stripe, nano-maze and dense nanoisland structures on LaAlO3 (001) substrate by pulsed laser deposition. We found the formation of different nanostructures is related to the terrace morphology of the substrate. Nano-stripe structure with strip domain and high conduction tail-to-tail domain wall preferred to form on wide terrace, nano-maze structure with three-fold or four-fold center-type domain usually form on bunched terrace, while dense nanoisland structure with two/three-fold domain preferred to from on the narrow or rough terrace LaAlO3 substrate. These findings provide guidance for manipulating the ferroelectric topological domain structure during film preparation process.

Polar topological superdomain arrays in PMN-PT crystals engineered via a voltage-free method

Domain engineering is an active field of research that aims to enhance the functional properties of ferroelectric materials for various applications. This work presents a voltage-free method for fabricating topological superdomain arrays in 0.72Pb(Mg1/3Nb2/3)O3-0.28PbTiO3 (PMN-28PT) crystals. During the cooling process from high-temperature paraelectric phase to room temperature ferroelectric phase, the out-of-plane polarization of PMN-28PT crystals in contact with aluminum can be fully regulated downward, attributed to the difference in the work function of aluminum and PMN-28PT. In conjunction further with photolithography and ultraviolet light illumination, it is easy to obtain periodic strip domain structures with alternating up and down polarization. Moreover, this method can also control in-plane polarization, resulting in a large-scale central divergent/convergent topological superdomain array. These findings provide insights into ferroelectric domain engineering and have implications for the development of electromechanical, piezoelectronic, and photonic devices.

Global well-posedness of 2D Hyperbolic perturbation of the Navier–Stokes system in a thin strip

In this paper, we study a hyperbolic version of the Navier–Stokes equations, obtained by using the approximation by relaxation of the Euler system, evolving in a thin strip domain. The formal limit of these equations is a hyperbolic Prandtl type equation, our goal is to prove the existence and uniqueness of a global solution to these equations for analytic initial data in the tangential variable, under a uniform smallness assumption. Then we justify the limit from the anisotropic hyperbolic Navier–Stokes system to the hydrostatic hyperbolic Navier–Stokes system with small analytic data.

New Subclass of Close-to-convex Functions Associated with the Vertical Strip Domains

New Subclass of Close-to-convex Functions Associated with the Vertical Strip Domains

Gevrey-Class-3 Regularity of the Linearised Hyperbolic Prandtl System on a Strip

In the present paper, we address a physically-meaningful extension of the linearised Prandtl equations around a shear flow. Without any structural assumption, it is well-known that the optimal regularity of Prandtl is given by the class Gevrey 2 along the horizontal direction. The goal of this paper is to overcome this barrier, by dealing with the linearisation of the so-called hyperbolic Prandtl equations in a strip domain. We prove that the local well-posedness around a general shear flow U_{textrm{sh}}in W^{3, infty }(0,1) holds true, with solutions that are Gevrey class 3 in the horizontal direction.

The Effect of Annealing on the Soft Magnetic Properties and Microstructure of Fe82Si2B13P1C3 Amorphous Iron Cores.

This research paper investigated the impact of normal annealing (NA) and magnetic field annealing (FA) on the soft magnetic properties and microstructure of Fe82Si2B13P1C3 amorphous alloy iron cores. The annealing process involved various methods of magnetic field application: transverse magnetic field annealing (TFA), longitudinal magnetic field annealing (LFA), transverse magnetic field annealing followed by longitudinal magnetic field annealing (TLFA) and longitudinal magnetic field annealing followed by transverse magnetic field annealing (LTFA). The annealed samples were subjected to testing and analysis using techniques such as differential scanning calorimetry (DSC), transmission electron microscopy (TEM), X-ray diffraction (XRD), magnetic performance testing equipment and magneto-optical Kerr microscopy. The obtained results were then compared with those of commercially produced Fe80Si9B11. Fe82Si2B13P1C3 demonstrated the lowest loss of P1.4T,2kHz = 8.1 W/kg when annealed in a transverse magnetic field at 370 °C, which was 17% lower than that of Fe80Si9B11. When influenced by the longitudinal magnetic field, the magnetization curve tended to become more rectangular, and the coercivity (B3500A/m) of Fe82Si2B13P1C3 reached 1.6 T, which was 0.05 T higher than that of Fe80Si9B11. During the 370 °C annealing process of the Fe82Si2B13P1C3 amorphous iron core, the internal stress in the strip gradually dissipated, and impurity domains such as fingerprint domains disappeared and aligned with the length direction of the strip. Consequently, wide strip domains with low resistance and easy magnetization were formed, thereby reducing the overall loss of the amorphous iron core.

Fuzzy response to SH guided-wave scattering by semicircular depressions on the boundary of a ribbon-shaped elastic plate

In this paper, the fuzzy scattering problem with semicircular depressions on the boundary of a band-shaped elastic plate with steady SH guided wave incident is studied and an analytical solution is given. First, the SH guided wave is constructed by the guided wave expansion method, and then the scattered wave satisfying the free condition of the boundary stress of the strip domain is constructed by the cumulative mirror method. Finally, a definite solution equation is obtained based on the fact that the shear stress at the edge of the semi-circular recessed hole is zero. In this paper, the ambiguity of the number of waves and the width of the bands is taken into account. In order to avoid the irreversibility of interval algorithm and the difficulty of solving non-linear equations, the membership function of fuzzy quantity is segmented to make the membership degree and fuzzy quantity correspond respectively. A deterministic problem that translates into piecewise processing. Two numerical examples are given to examine the changes in fuzzy response of different numbers of fuzzy waves and fuzzy thicknesses to the dynamic stress concentration factor of the hoop at the collapse limit.

Asymptotic stability and sharp decay rates to the linearly stratified Boussinesq equations in horizontally periodic strip domain

We consider an initial boundary value problem of the multi-dimensional Boussinesq equations in the absence of thermal diffusion with velocity damping or velocity diffusion under the stress free boundary condition in horizontally periodic strip domain. We prove the global-in-time existence of classical solutions in high order Sobolev spaces satisfying high order compatibility conditions around the linearly stratified equilibrium, the convergence of the temperature to the asymptotic profile, and sharp decay rates of the velocity field and temperature fluctuation in all intermediate norms based on spectral analysis combined with energy estimates. To the best of our knowledge, our results provide first sharp decay rates for the temperature fluctuation and the vertical velocity to the linearly stratified Boussinesq equations in all intermediate norms.

Effect of magnetic field annealing on the soft magnetic properties of CoFeSiB ribbon and its fluxgate performance

As a key part of fluxgate, the properties of magnetic core determine the performance of fluxgate sensor. We studied the effects of zero magnetic field annealing (ZFA) and longitudinal magnetic field annealing (LFA) on soft magnetic properties, magnetic anisotropy and magnetic domain structure of the Co70Fe5Si15B10 amorphous ribbon and its fluxgate sensor performance. It is found that LFA can effectively modulate the magnetic domain from irregular shape and size to wide regular strip domains. As a result, pinning effect, magnetic anisotropy and coercivity decrease, while the initial permeability increases. And finally, the sensitivity of the fluxgate become higher, and noise become less. The results show that the optimal soft magnetic properties of the ribbons are obtained after LFA at 440 °C, with the initial permeability of 21,020 and the coercivity of 0.2 A/m. We applied a square wave excitation signal of current 30 mA and frequency 2.4 kHz to test the performance of the fluxgates. It is found that the fluxgate sensitivity increases from the original 36.54 to 41.82 mV/μT after magnetic field annealing treatment, and the peak-to-peak noise (Noisep-p) value at 10 Hz bandwidth in 250 s decreases from the original 5.22 to 2.14 nT. The results show that the LFA treatment of the core has a significant effect on its magnetic properties and fluxgate performance enhancement, and these results have good implications for the construction of high-performance fluxgate.

On λ-pseudo starlike functions associated with vertical strip domain

We consider the class of [Formula: see text]-pseudo starlike functions [Formula: see text] such that [Formula: see text] maps the open unit disk [Formula: see text] onto a strip domain [Formula: see text] with [Formula: see text] for some [Formula: see text], [Formula: see text]. We estimate [Formula: see text], [Formula: see text] and solve the Fekete–Szegö problem for functions in this class.

Empirical vulnerability estimation models considering updating the structural earthquake damage database

The seismic vulnerability of regional buildings is a fundamental index to effectively predict and estimate the seismic resilience of urban and rural areas. The structural empirical vulnerability database can be used to develop and generate relatively accurate multidimensional vulnerability models. With the development of instrument intensity and the updating of macroseismic intensity scales, the structural vulnerability assessment model established using the traditional regional structural empirical vulnerability database shows features of low accuracy. Therefore, using innovative methods to update the conventional vulnerability estimation model has become a fundamental scientific problem to be urgently solved. In this study, the mixed effects of instrument intensity and macrointensity and their evaluation scale were sufficiently considered, and the traditional vulnerability level quantification scale was improved. The structural empirical vulnerability database of three typical earthquakes in China (Wenchuan in 2008, Yushu in 2010, and Jiuzhaigou in 2017) has been comprehensively updated, and the multiscale statistical and computational model has been developed. A nonlinear regression model based on multidimensional vulnerability quantification parameters was proposed. A comparison model for predicting the actual seismic vulnerability of four types of buildings considering typical earthquakes was developed. The traditional vulnerability index algorithm was updated, and the point cloud and strip domain quantitative model based on the updated empirical vulnerability database (27,394 buildings) was established.