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Elastic contact in hydrodynamic environments is a complex multiphysics phenomenon and can be found in applications ranging from engineering to biological systems. Understanding the intricacies of this coupled problem requires the development of a generalized framework capable of handling topological changes and transitioning implicitly from FSI conditions to solid-solid contact conditions. We propose a mono-field interface advancing method for handling multibody contact simulations in submerged environments. Given the physical demands of the problem, we adopt a phase-field based fully Eulerian approach to resolve the multiphase and multibody interactions in the system. We employ a stabilized finite element formulation and a partitioned iterative procedure to solve the unified momentum equation comprising solid and fluid dynamics coupled with the Allen-Cahn phase-field equation. We introduce a contact force approach to handle smooth elastic-elastic and elastic-rigid contact based on the overlap of the diffused interfaces of two colliding bodies. We propose a novel approach to extend the model for multibody contact simulations while using a single phase-field function for all the solids. The method is based on updating the solid boundaries at every time step and checking for collisions among them. The developed approach eliminates the need to solve multiple phase field equations and multiple strain equations at every time step. This reduces the overall computational time by nearly $16\%$ compared to a multi phase-field approach. The implemented model is verified for smooth dry contact and FSI contact scenarios. Using the proposed framework, we demonstrate the collision dynamics between multiple bodies submerged in an open liquid tank., Comment: 35 pages

Using a fixed Eulerian mesh, the phase-field method has been successfully utilized for a broad range of moving boundary problems involving multiphase fluids and single-phase fluid-structure interaction. Nevertheless, multiphase fluids interacting with multiple solids are rarely explored, especially for large-scale finite element simulations with contact dynamics. In this work, we introduce a novel parallelized three-dimensional fully Eulerian variational framework for simulating multiphase fluids interacting with multiple deformable solids subjected to contact dynamics. In the framework, each solid or fluid phase is identified by a standalone phase indicator. Moreover the phase indicators are initialized by the grid cell method, which restricts the calculation to several grid cells. A diffuse interface description is employed for a smooth interpolation of the physical properties across the phases, yielding unified mass and momentum conservation equations for the coupled dynamical interactions. For each solid object, temporal integration is carried out to track the strain evolution in an Eulerian frame of reference. The coupled differential equations are solved in a partitioned iterative manner. We first verify the framework against reference numerical data in a two-dimensional case of a rotational disk in a lid-driven cavity flow. The case is generalized to a rotational sphere in a lid-driven cavity flow to showcase large deformation and rotational motion of solids and examine the convergence in three dimensions. We then simulate the falling of an immersed solid sphere on an elastic block under gravitational force to demonstrate the translational motion and the solid-to-solid contact in a fluid environment. Finally, we demonstrate the framework for a ship-ice interaction problem involving multiphase fluids with an air-water interface and contact between a floating ship and ice floes., Comment: 32 pages, 18 figures

We present an interface and geometry preserving (IGP) method for the modeling of fully Eulerian fluid-structure interaction via phase-field formulation. While the hyperbolic tangent interface profile is preserved by the time-dependent mobility model, the proposed method maintains the geometry of the solid-fluid interface by reducing the volume-conserved mean curvature flow. To achieve the reduction in the curvature flow, we construct a gradient-minimizing velocity field (GMV) for the convection of the order parameter. The constructed velocity field enables the preservation of the solid velocity in the solid domain while extending the velocity in the normal direction throughout the diffuse interface region. With this treatment, the GMV reduces the normal velocity difference of the level sets of the order parameter which alleviates the undesired thickening or thinning of the diffuse interface region due to the convection. During this process, the time-dependent mobility coefficient is substantially reduced and there is a lesser curvature flow. The GMV ensures that the diffuse interface region moves with the solid bulk such that the fluid-solid interface conforms to the geometry of the solid. Using the unified momentum equation and the phase-dependent interpolation, we integrate the IGP method into a fully Eulerian variational FSI solver based on the incompressible viscous fluid and the neo-Hookean solid. We first demonstrate the ability of the phase-field-based IGP method for the convection of circular and square interfaces with a prescribed velocity field. The variational FSI framework with the IGP method is then examined for the flow passing a fixed deformable block in a channel domain. Finally, the vibration of a plate attached behind a stationary cylinder subjected to incoming flow is employed to assess the fully Eulerian framework for a large aspect ratio and sharp corners.

In this paper, we present a novel interface-driven adaptive variational procedure using a fully Eulerian description of fluid-structure interaction. The proposed fully-Eulerian procedure involves a fixed background unstructured mesh on which the fluid-structure interface is treated implicitly. We model the fluid-structure interaction by the phase-field finite element formulation relying on a partitioned staggered integration of the convective Allen-Cahn equation with the unified momentum equation for both solid and fluid dynamics. We employ the positivity preserving variational scheme for a bounded and stable solution of the Allen-Cahn phase-field equation. To evaluate the solid stresses, the left Cauchy-Green deformation tensor is convected at each time step to trace the evolution of the solid strain in the Eulerian reference frame. We utilize the residual based error indicators and the newest vertex bisection algorithm for the adaptive refinement/coarsening of the unstructured mesh. The proposed nonlinear adaptive partitioned procedure restricts the coarsening step to the last non-linear iteration while simultaneously ensuring convergence properties of the coupled governing equations. We perform a detailed convergence and accuracy analysis via two benchmark problems namely, the pure solid system and a coupled fluid-solid system with an interface in a rectangle domain. We next systematically assess the performance of the adaptive procedure in terms of conservation properties for the increasing complexity of problems. Finally, we demonstrate our fully-Eulerian interface-driven adaptive FSI model to simulate the contact and bouncing phenomenon between an elastic solid and a rigid wall.

We study the localization properties of generalized, two- and three-dimensional Lieb lattices, $\mathcal{L}_2(n)$ and $\mathcal{L}_3(n)$, $n= 1, 2, 3$ and $4$, at energies corresponding to flat and dispersive bands using the transfer matrix method (TMM) and finite size scaling (FSS). We find that the scaling properties of the flat bands are different from scaling in dispersive bands for all $\mathcal{L}_d(n)$. For the $d=3$ dimensional case, states are extended for disorders $W$ down to $W=0.01 t$ at the flat bands, indicating that the disorder can lift the degeneracy of the flat bands quickly. The phase diagram with periodic boundary condition for $\mathcal{L}_3(1)$ looks similar to the one for hard boundaries. We present the critical disorder $W_c$ at energy $E=0$ and find a decreasing $W_c$ for increasing $n$ for $\mathcal{L}_3(n)$, up to $n=3$. Last, we show a table of FSS parameters including so-called irrelevant variables; but the results indicate that the accuracy is too low to determine these reliably. \end{abstract}

We demonstrate a 2D ferroelectric heterostructure with monolayer MoSe$_2$ and CuInP$_2$S$_6$ (CIPS). In the heterostructure, the electric polarization of CIPS results in c electronic modulation in monolayer MoSe$_2$., Comment: 8 pages, 4 figures

We present a finite element based variational interface-preserving and conservative phase-field formulation for the modeling of incompressible two-phase flows with surface tension dynamics. The preservation of the hyperbolic tangent interface profile of the convective Allen-Cahn phase-field formulation relies on a novel time-dependent mobility model. The mobility coefficient is adjusted adaptively as a function of gradients of the velocity and the order parameter in the diffuse interface region in such a way that the free energy minimization properly opposes the convective distortion. The ratio of the convective distortion to the free energy minimization is termed as the convective distortion parameter, which characterizes the deviation from the hyperbolic tangent shape due to the convection effect. The mass conservation is achieved by enforcing a Lagrange multiplier with both temporal and spatial dependence on the phase-field function. We integrate the interface-preserving and conservative phase-field formulation with the incompressible Navier-Stokes equations and the continuum surface tension force model for the simulation of incompressible two-phase flows. A positivity preserving scheme designed for the boundedness and stability of the solution is employed for the variational discretization using unstructured finite elements. We examine the convergence and accuracy of the Allen-Cahn phase-field solver through a generic one-dimensional bistable diffusion-reaction system in a stretching flow. We quantify and systematically assess the relative interface thickness error and the relative surface tension force error with respect to the convective distortion parameter. Two- and three-dimensional rising bubble cases are further simulated to examine the effectiveness of the proposed model on the volume-preserving mean curvature flow and the interface-preserving capability.

Tuning the electric properties of crystalline solids is at the heart of material science and electronics. Generating the electric field-effect via an external voltage is a clean, continuous and systematic method. Here, utilizing the unique electric dipole locking in van der Waals (vdW) ferroelectric alpha-In2Se3, we report a new approach to establish the electric gating effect, where the electrostatic doping in the out-of-plane direction is induced and controlled by an in-plane voltage. With the vertical vdW heterostructure of ultrathin alpha-In2Se3 and MoS2, we validate an in-plane voltage gated coplanar field-effect transistor (CP-FET) with distinguished and retentive on/off ratio. Our results demonstrate unprecedented electric control of ferroelectricity, which paves the way for integrating two-dimensional (2D) ferroelectric into novel nanoelectronic devices with broad applications.

We study the localization properties and the Anderson transition in the 3D Lieb lattice $\mathcal{L}_3(1)$ and its extensions $\mathcal{L}_3(n)$ in the presence of disorder. We compute the positions of the flat bands, the disorder-broadened density of states and the energy-disorder phase diagrams for up to 4 different such Lieb lattices. Via finite-size scaling, we obtain the critical properties such as critical disorders and energies as well as the universal localization lengths exponent $\nu$. We find that the critical disorder $W_c$ decreases from $\sim 16.5$ for the cubic lattice, to $\sim 8.6$ for $\mathcal{L}_3(1)$, $\sim 5.9$ for $\mathcal{L}_3(2)$ and $\sim 4.8$ for $\mathcal{L}_3(3)$. Nevertheless, the value of the critical exponent $\nu$ for all Lieb lattices studied here and across disorder and energy transitions agrees within error bars with the generally accepted universal value $\nu=1.590 (1.579,1.602)$.

We study the localization properties of the two-dimensional Lieb lattice and its extensions in the presence of disorder using transfer matrix method and finite-size scaling. We find that all states in the Lieb lattice and its extensions are localized for $W \geq 1$. Clear differences in the localization properties between disordered flat band and disordered dispersive bands are identified. Our results complement previous experimental studies of clean photonic Lieb lattices and provide information about their stability with respect to disorder., Comment: 7 pages, 20 figures, 1 table

Recent experiments on layered {\alpha}-In2Se3 have confirmed its room-temperature ferroelectricity under ambient condition. This observation renders {\alpha}-In2Se3 an excellent platform for developing two-dimensional (2D) layered-material based electronics with nonvolatile functionality. In this letter, we demonstrate non-volatile memory effect in a hybrid 2D ferroelectric field effect transistor (FeFET) made of ultrathin {\alpha}-In2Se3 and graphene. The resistance of graphene channel in the FeFET is tunable and retentive due to the electrostatic doping, which stems from the electric polarization of the ferroelectric {\alpha}-In2Se3. The electronic logic bit can be represented and stored with different orientations of electric dipoles in the top-gate ferroelectric. The 2D FeFET can be randomly re-written over more than $10^5$ cycles without losing the non-volatility. Our approach demonstrates a protype of re-writable non-volatile memory with ferroelectricity in van de Waals 2D materials., Comment: 19 pages, 4 figures

Nanoscaled room-temperature ferroelectricity is ideal for developing advanced non-volatile high-density memories. However, reaching the thin film limit in conventional ferroelectrics is a long-standing challenge due to the possible critical thickness effect. Van der Waals materials, thanks to their stable layered structure, saturate interfacial chemistry and weak interlayer couplings, are promising for exploring ultra-thin two-dimensional (2D) ferroelectrics and device applications. Here, we demonstrate a switchable room-temperature ferroelectric diode built upon a 2D ferroelectric {\alpha}-In2Se3 layer as thin as 5 nm in the form of graphene/{\alpha}-In2Se3 heterojunction. The intrinsic out-of-plane ferroelectricity of the {\alpha}-In2Se3 thin layers is evidenced by the observation of reversible spontaneous electric polarization with a relative low coercive electric field of ~$2 X 10^5 V/cm$ and a typical ferroelectric domain size of around tens ${\mu}m^2$. Owing to the out-of-plane ferroelectricity of the {\alpha}-In2Se3 layer, the Schottky barrier at the graphene/{\alpha}-In2Se3 interface can be effectively tuned by switching the electric polarization with an applied voltage, leading to a pronounced switchable double diode effect with an on/off ratio of ~$10^4$. Our results offer a new way for developing novel nanoelectronic devices based on 2D ferroelectrics., Comment: 10 pages, 4 figures