Thin Domain Research Articles

Bi-spatial Pullback Attractors of Non-autonomous p-Laplacian Equations on Unbounded Thin Domains

Bi-spatial Pullback Attractors of Non-autonomous p-Laplacian Equations on Unbounded Thin Domains

Domain effects on the electro-optic properties of thin-film barium titanate

On-chip electro-optic modulation is essential to realize complex on-chip optical signal processing. Recent developments in thin-film ferroelectric oxide for high-speed electro-optical modulators have gained considerable interest in understanding and correlating the material property with the electro-optic response. Particularly, the effect of thin film, domain orientation, and polling on the electro-optic response is not well understood. In this article, we present the effect of ferroelectric domains of thin-film Barium Titanate on the electro-optic response in a waveguide configuration. We also show the impact of drive electrode orientation with respect to the in-plane polarization angle in a multi-domain structure. Our theoretical findings corroborate the experimental observations in the literature, which substantiate the theoretical framework.

Erratum to “Navier–Stokes equations in a curved thin domain, Part III: thin-film limit”

There are two flaws in the third part [3] of our study on the Navier--Stokes equations in a curved thin domain. The first one is that the form of Ladyzhenskaya's inequality on a closed surface taken from the arXiv version [2] of the second part of our study is incorrect. The second one is that a wrong claim is used in the proofs of lemmas in [3, Section 6.3] which give estimates for the weighed potential part of a tangential surface vector field. This erratum corrects these flaws.

Self-organization and dewetting kinetics in sub-10 nm diblock copolymer line/space lithography

In this work, we investigated the self-assembly of a lamellar block copolymer (BCP) under different wetting conditions. We explored the influence of the chemical composition of under-layers and top-coats on the thin film stability, self-assembly kinetics and BCP domain orientation. Three different chemistries were chosen for these surface affinity modifiers and their composition was tuned in order to provide either neutral wetting (i.e. an out-of-plane lamellar structure), or affine wetting conditions (i.e. an in-plane lamellar structure) with respect to a sub-10 nm PS-b-PDMSB lamellar system. Using such controlled wetting configurations, the competition between the dewetting of the BCP layer and the self-organization kinetics was explored. We also evaluated the spreading parameter of the BCP films with respect to the configurations of surface-energy modifiers and demonstrated that BCP layers are intrinsically unstable to dewetting in a neutral configuration. Finally, the dewetting mechanisms were evaluated with respect to the different wetting configurations and we clearly observed that the rigidity of the top-coat is a key factor to delay BCP film instability.

Angstrom-scale imaging of magnetization in antiferromagnetic Fe2As via 4D-STEM

We demonstrate a combination of computational tools and experimental 4D-STEM methods to image the local magnetic moment in antiferromagnetic Fe2As with 6 angstrom spatial resolution. Our techniques utilize magnetic diffraction peaks, common in antiferromagnetic materials, to create imaging modes that directly visualize the magnetic lattice. Using this approach, we show that center-of-mass analysis can determine the local magnetization component in the plane perpendicular to the path of the electron beam. Moreover, we develop Magnstem, a quantum mechanical electron scattering simulation code, to model electron scattering of an angstrom-scale probe from magnetic materials. Using these tools, we identify optimal experimental conditions for separating weak magnetic signals from the much stronger interactions of an angstrom-scale probe with electrostatic potentials. Our techniques should be useful for characterizing the local magnetic order in systems such in thin films, interfaces, and domain boundaries of antiferromagnetic materials, which are difficult to probe with existing methods.

Renormalizing Antiferroelectric Nanostripes in β′-In2Se3 via Optomechanics

Antiferroelectric (AFE) materials have attracted a great deal of attention owing to their high energy conversion efficiency and good tunability. Recently, an exotic two-dimensional AFE material, a β'-In2Se3 monolayer that could host atomically thin AFE nanostripe domains, has been experimentally synthesized and theoretically examined. In this work, we apply first-principles calculations and theoretical estimations to predict that light irradiation can control the nanostripe width of such a system. We suggest that an intermediate near-infrared light (below the bandgap) could effectively harness the thermodynamic Gibbs free energy and thermodynamic stability, and the AFE nanostripe width will gradually decrease. We also propose to use linearly polarized light above the bandgap to generate an AFE nanostripe-specific photocurrent, providing an all-optical pump-probe setup for such AFE nanostripe width phase transitions.

STUDY OF THE VISCOELASTIC PROBLEMS WITH SHORT MEMORY IN A THIN DOMAIN WITH TRESCA BOUNDARY CONDITIONS

In this paper, we are interested in the study of the asymptotic behavior of non linear problem in a quasistatic regime in a thin domain with Tresca boundary conditions. In the first step, we derive a variational formulation of the mechanical problem and prove the existence and uniqueness of the weak solution. We study the limit when the ε tends to zero, we prove the convergence of the unknowns which are the displacement and the velocity and we obtain the limit problem and the specific Reynolds equation.

Asymptotic properties in non-autonomous stochastic parabolic problems dominated by <inline-formula><tex-math id="M1">$ p $</tex-math></inline-formula>-Laplacian operator on thin domains

<p style='text-indent:20px;'>This paper is concerned with upper semicontinuity of the family of random attractors associated with non-autonomous stochastic parabolic problems dominated by <inline-formula><tex-math id="M8">\begin{document}$ p $\end{document}</tex-math></inline-formula>-Laplacian operator on thin domains in which the domain collapses onto lower dimensional domain. The existence and uniqueness of random attractors for the equations are strictly proved on an <inline-formula><tex-math id="M9">\begin{document}$ (n+1) $\end{document}</tex-math></inline-formula>-dimensional thin domain, and the upper semicontinuity of these attractors are established when an <inline-formula><tex-math id="M10">\begin{document}$ (n+1) $\end{document}</tex-math></inline-formula>-dimensional thin domain collapses onto an <inline-formula><tex-math id="M11">\begin{document}$ n $\end{document}</tex-math></inline-formula>-dimensional domain.</p>

Behavior of the isothermal Elasticity operator with non-linear friction in a thin domain

This paper deals with the asymptotic behavior of a boundary value problem in a three dimensional thin domain Ω ε with non-linear friction of Coulomb type. We will establish a variational formulation for the problem and prove the existence and uniqueness of the weak solution. We then study the asymptotic behavior when one dimension of the domain tends to zero. In which case, the uniqueness result of the displacement for the limit problem is also proved.

Non-Ising domain walls in c -phase ferroelectric lead titanate thin films

Ferroelectrics are technologically important, with wide application in micromechanical systems, nonlinear optics, and information storage. Recent discoveries of exotic polarization textures in these materials, which can strongly influence their properties, have brought to the forefront questions about the nature of their domain walls: long believed to be primarily Ising, with locally null polarization. Here, combining three complementary techniques---second-harmonic generation microscopy, piezoresponse force microscopy, and transmission electron microscopy---to cover all the relevant length scales, we reveal the N\'eel character (non-Ising polarization oriented perpendicular to the wall) of ${180}^{\ensuremath{\circ}}$ domain walls in $c$-phase tetragonal ferroelectric lead titanate epitaxial thin films, for both artificial and intrinsic domains at room temperature. Furthermore, we show that variations in the domain density---detected both optically and via local piezoresponse and then quantified by radial autocorrelation analysis---can give us insight into the underlying defect potential present in these materials.

Evolution of epitaxial BaTiO3 on SrTiO3-buffered Si: Phase field analysis

Barium titanate (BaTiO3) is a promising candidate for electro-optical modulators in Si photonics. The BaTiO3 ferroelectric domain morphology is strongly affected by thermal, electrical, and mechanical conditions and, in turn, profoundly influences the film's optical properties. Because BaTiO3 film growth takes place at a relatively high temperature, upon cooling, the film is subject to complex thermal effects that involve changes in the crystal phase, the emergence of ferroelectricity, and variations in the strain level. We use a phase field model to describe the evolution of the BaTiO3 thin film domain morphology upon cooling from growth to room temperature. We demonstrate that cooling under different cooling scenarios results in different domain morphologies. Our simulations provide a clear temperature–strain map and thermal strategy for controllable BaTiO3 epitaxy on the SrTiO3-buffered Si substrate.

Unsteady flow of Bingham fluid in a thin layer with mixed boundary conditions

"In this paper we consider the dynamic system for Bingham fluid in a three-dimensional thin domain with Fourier and Tresca boundary condition. We study the existence and uniqueness results for the weak solution, then we establish its asymptotic behavior, when the depth of the thin domain tends to zero. This study yields a mechanical laws that give a new description of the behavior this system."

Determination of the dielectric constant of non-planar nanostructures and single nanoparticles by electrostatic force microscopy

Electrostatic Force Microscopy has been proven to be a precise and versatile tool to perform quantitative measurements of the dielectric constant of thin film domains in the nanometer range. However, it is difficult to measure non-planar nanostructures because topographic crosstalk significantly contributes to the measured signal. This topographic crosstalk due to distance changes between tip and substrate measuring non-planar surface structures is still an ongoing issue in literature and falsifies measurements of the dielectric constant of nanostructures and nanoparticles. Tip and substrate form a capacitor based on the contact potential difference between the tip and substrate material. An increase of the distance between tip and substrate causes a repulsive force while a decrease causes an attractive force. Thus, measuring in the so-called lift mode scanning the surface in a second scan following the topography determined by a first scan leads to a mirroring of the non-planar surface structure in the electrostatic signal superimposing the signal from dielectric contrast. In this work we demonstrate that the topographic crosstalk can be avoided by using the linear mode instead of the lift mode. The use of the linear mode now allows the determination of the dielectric constant of single nanoparticles.

Hybrid 3D-plane finite element modeling for elastodynamics

The coupling of three-dimensional (3D) and plane (2D) finite element (FE) models to form a single hybrid 3D–2D model is considered for linear elastodynamic problems. The 2D model is used to represent a large thin 3D computational domain where the solution behaves approximately in a 2D (plane-elasticity) way. Problems where the normal displacement is important in the thin region (bending) are excluded. The hybrid model, if designed properly, is a more efficient way to solve the full 3D model over the entire problem. This paper focuses on the way the 3D–2D coupling is performed, and on the coupling error generated. The Panasenko technique is used to couple the 3D and 2D models. This method has been used previously for mixed-dimensional coupling in steady-state problems, as well as for 2D–1D coupling of acoustic waves. Here it is being used for the first time for the 3D–2D coupling of time-dependent elastic problems. The hybrid formulation is derived, and is shown to be well-posed. It is shown that the Panasenko method is extremely simple to implement in the framework of FE analysis, yet the resulting coupling yields a rather small error level, provided the 3D–2D interface is sensibly placed. The numerical accuracy and efficiency of the method are explored for a couple of example problems. In particular, it is shown that spurious reflections from the interface back into the 3D region are negligible. • A hybrid 3D–2D model is constructed for elastodynamics. • The 3D–2D coupling is performed using the Panasenko technique. • The hybrid formulation is shown to be well posed. • Numerical experimentation is performed with a few configurations. • Excellent agreement is obtained between the proposed and reference models.

Asymptotic analysis for the elasticity system with Tresca and maximal monotone graph conditions

In this paper, we consider the stationary problem in three dimensional thin domain \(\Omega ^{\varepsilon }\) with maximal monotone graph and Tresca conditions. In the first step, we present the problem statement and give the variational formulation. We then study the asymptotic behavior when one dimension of the domain tends to zero. In the latter case a specific Reynolds limit equation is obtained and the uniqueness of the displacement of the limit problem are proved.

Variational and asymptotic analysis of a static electro-elastic problem with Coulomb’s law

The electro-elastic problem in a three-dimensional thin domain Ωɛ is considered. In modeling the contact the Coulomb free boundary friction condition is used. First, we show the variational formulation of the problem and give the existence and the uniqueness of the solution. Then, we study the asymptotic analysis when then the small parameter ɛ tends to zero. A limit problem, the uniqueness result of the limit displacement and electric potential are obtained.

First-principles investigation of ferroelectric and piezoelectric properties in one-dimensional transition metal oxytetrahalides

We perform first-principles density functional theory calculations to systematically investigate electronic structures of a quasi-one-dimensional $M\mathrm{O}{X}_{4}$ ($M=\mathrm{Cr},\mathrm{Mo},\mathrm{W}$, and $X=\mathrm{F},\mathrm{Cl},\mathrm{Br}$) materials consisting of weakly coupled one-dimensional chains. The compositional dependence on the ferroelectric and piezoelectric properties such as switching polarization, energy barriers, Born effective charges, and piezoelectric coefficients are investigated. We find that the majority of the $M\mathrm{O}{X}_{4}$ systems exhibit sizable polarization and large piezoelectric coefficients comparable to conventional ferroelectrics. More importantly, we find that the energy cost of forming a ${180}^{\ensuremath{\circ}}$ domain walls is negligibly small due to the weak interchain coupling, having an atomically thin domain wall with almost no reduction in the local polarization. The robust ferroelectric switching, atomically thin ferroelectric domain wall, and large piezoelectric coefficients make the $M\mathrm{O}{X}_{4}$ family of materials potential candidates for applications for efficient electronic devices such as high-density ferroelectric memories and high-resolution pressure sensors.

Coupled local/nonlocal models in thin domains

In this paper, we analyze a model composed by coupled local and nonlocal diffusion equations acting in different subdomains. We consider the limit case when one of the subdomains is thin in one direction (it is concentrated to a domain of smaller dimension) and as a limit problem we obtain coupling between local and nonlocal equations acting in domains of different dimension. We find existence and uniqueness of solutions and we prove several qualitative properties (like conservation of mass and convergence to the mean value of the initial condition as time goes to infinity).

Source term model for elasticity system with nonlinear dissipative term in a thin domain

Abstract This article establishes an asymptotic behavior for the elasticity systems with nonlinear source and dissipative terms in a three-dimensional thin domain, which generalizes some previous works. We consider the limit when the thickness tends to zero, and we prove that the limit solution u ∗ {u}^{\ast } is a solution of a two-dimensional boundary value problem with lower Tresca’s free-boundary conditions. Moreover, we obtain the weak Reynolds-type equation.

Increasing stable time-step sizes of the free-surface problem arising in ice-sheet simulations

Numerical models for predicting future ice mass loss of the Antarctic and Greenland ice sheets require accurately representing their dynamics. Unfortunately, ice-sheet models suffer from a very strict time-step size constraint, which for higher-order models constitutes a severe bottleneck; in each time step a nonlinear and computationally demanding system of equations has to be solved. In this study, stable time-step sizes are increased for a full-Stokes model by implementing a so-called free-surface stabilization algorithm (FSSA). Previously this stabilization has been used successfully in mantle-convection simulations where a similar viscous-flow problem is solved. By numerical investigation it is demonstrated that instabilities on the very thin domains required for ice-sheet modeling behave differently than on the equal-aspect-ratio domains the stabilization has previously been used on. Despite this, and despite the different material properties of ice, it is shown that it is possible to adapt FSSA to work on idealized ice-sheet domains and increase stable time-step sizes by at least one order of magnitude. The FSSA method presented is deemed accurate, efficient and straightforward to implement into existing ice-sheet solvers.