Dimensional Domain Research Articles

Global space-time Trefftz DG schemes for the time-dependent linear wave equation

In this paper we are concerned with Trefftz discretizations of the time-dependent linear wave equation in anisotropic media in arbitrary space dimensional domains $\Omega \subset \mathbb{R}^d~ (d\in \mathbb{N})$. We propose two variants of the Trefftz DG method, define novel plane wave basis functions based on rigorous choices of scaling transformations and coordinate transformations, and prove that the corresponding approximate solutions possess optimal-order error estimates with respect to the meshwidth $h$ and the condition number of the coefficient matrices, respectively. Besides, we propose the global Trefftz DG method combined with local DG methods to solve the time-dependent linear nonhomogeneous wave equation in anisotropic media. In particular, the error analysis holds for the (nonhomogeneous) Dirichlet, Neumann, and mixed boundary conditions from the original PDEs. Furthermore, a strategy to discretize the model in heterogeneous media is proposed. The numerical results verify the validity of the theoretical results, and show that the resulting approximate solutions possess high accuracy.

A Fast Temporal Second Order Difference Scheme for the Fractional Sub-Diffusion Equations on One Dimensional Space Unbounded Domain

A Fast Temporal Second Order Difference Scheme for the Fractional Sub-Diffusion Equations on One Dimensional Space Unbounded Domain

On the convergence of the Crank-Nicolson method for the logarithmic Schrödinger equation

<p style='text-indent:20px;'>We consider an initial and Dirichlet boundary value problem for a logarithmic Schrödinger equation over a two dimensional rectangular domain. We construct approximations of the solution to the problem using a standard second order finite difference method for space discretization and the Crank-Nicolson method for time discretization, with or without regularizing the logarithmic term. We develop a convergence analysis yielding a new almost second order a priori error estimates in the discrete <inline-formula><tex-math id="M1">\begin{document}$ L_t^{\infty}(L_x^2) $\end{document}</tex-math></inline-formula> norm, and we show results from numerical experiments exposing the efficiency of the method proposed. It is the first time in the literature where an error estimate for a numerical method applied to the logarithmic Schrödinger equation is provided, without regularizing its nonlinear term.</p>

The Hadwiger theorem on convex functions, IV: The Klain approach

New proofs of the Hadwiger theorem for smooth and for continuous valuations on convex functions are obtained, and the Klain–Schneider theorem on convex functions is established. In addition, an extension theorem for valuations defined on functions with lower dimensional domain is proved, and its connection to the Abel transform is explained.

Global strong solutions to the viscous liquid–gas two-phase flow model with slip boundary conditions in 3D exterior domains

This paper is concerned with the viscous liquid–gas two-phase flow model in a three-dimensional exterior domain with the slip boundary conditions. We are able to prove the existence of a global strong solution when the initial total energy is suitably small. The initial masses of liquid and gas are allowed to contain a vacuum, with no extra restriction between the initial masses of liquid and gas. It should be noted here that we consider the slip boundary condition in a three dimensional (3D) exterior domain which is in sharp contrast to result of Yu (2021) where they consider the Cauchy problem.

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.

Polluted aquifer inverse problem solution using artificial neural networks

The problem of identifying an unknown pollution source in polluted aquifers, based on known contaminant concentrations measurement in the studied areas, is part of the broader group of issues, called inverse problems. This paper investigates the feasibility of using Artificial Neural Networks (ANNs) for solving the inverse problem of locating in time and space the source of a contamination event in a homogeneous and isotropic two dimensional domain. ANNs are trained in order to implement an input-output relationship which associates the position. Once the output of the system is known, the input is reconstructed by inverting the trained ANNs. The approach is applied for studying a theoretical test case where the inverse problem is solved on the basis of measurements of contaminant concentrations in monitoring wells located in the studied area. Groundwater pollution sources are characterized by varying spatial location and duration of activity. To identify these unknown pollution sources, concentration measurements data of monitoring wells are used. If concentration observations are missing over a length of time after an unknown source has become active, it is more difficult to correctly identify the unknown pollution source. In this work, a missing data scenario has been taken into consideration. In particular, a case where only one measurement has been made after the pollutant source interrupted its activity has been considered.

Computational study of the Transmission pole during downburst using ANSYS, considering fluid-structure interactions

A downburst is described as a strong downdraft that causes a devastating wind outburst on or near the earth surface. Such occurrences are more common during thunderstorms. Downbursts generally impinge on the ground and convect radially in all directions from the point of contact. Downbursts have been widely documented as a regular cause of high voltage electrical transmission tower and pole failures in numerous nations. The flow dynamics of impinging jets are investigated using numerical models, with applicability to downburst-related high intensity winds. The downburst is simulated using three primary viscous models (, , and RANS). These three viscous models are used to simulate downburst in two dimensions. The RANS viscous model is used for further investigation. To determine the temporal variant characteristics of a downburst, both steady and transient state simulations are performed. The flow is quasi-periodic, with vortex rings formed by the initial jet instability impinging on the surface, where they find an unstable separation reattachment of the boundary layer. Fluid-structure interactions (FSI) are multiphysics problems that cannot be handled using single physics equations. To determine the impacts of downburst on transmission poles, a 2-D steel pole 8 metres high with a fixed base is put near the downburst. Downburst pressure is measured on a transmission pole. The stresses and deflections caused by the pressure distribution on the tower due to varying fluid domain dimensions and jet velocities on the transmission poles are determined using one way coupling, from 2-D transmission pole geometry to 3-D transmission pole geometry.

Neural-signature methods for structured EHR prediction

Models that can effectively represent structured Electronic Healthcare Records (EHR) are central to an increasing range of applications in healthcare. Due to the sequential nature of health data, Recurrent Neural Networks have emerged as the dominant component within state-of-the-art architectures. The signature transform represents an alternative modelling paradigm for sequential data. This transform provides a non-learnt approach to creating a fixed vector representation of temporal features and has shown strong performances across an increasing number of domains, including medical data. However, the signature method has not yet been applied to structured EHR data. To this end, we follow recent work that enables the signature to be used as a differentiable layer within a neural architecture enabling application in high dimensional domains where calculation would have previously been intractable. Using a heart failure prediction task as an exemplar, we provide an empirical evaluation of different variations of the signature method and compare against state-of-the-art baselines. This first application of neural-signature methods in real-world healthcare data shows a competitive performance when compared to strong baselines and thus warrants further investigation within the health domain.

Dual-analgesic loaded UHMWPE exhibits synergistic antibacterial effects against Staphylococci.

Total joint arthroplasty is one of the most common surgeries in the United States, with almost a million procedures performed annually. Periprosthetic joint infections (PJI) remain the most devastating complications associated with total joint replacement. Effective antibacterial prophylaxis after primary arthroplasty could substantially reduce incidence rate of PJI. In the present study we propose to provide post-arthroplasty prophylaxis via dual-analgesic loaded ultra-high molecular weight polyethylene (UHMWPE). Our approach is based on previous studies that showed pronounced antibacterial activity of analgesic- and NSAID-loaded UHMWPE against Staphylococci. Here, we prepared bupivacaine/tolfenamic acid-loaded UHMWPE and assessed its antibacterial activity against Staphylococcus aureus and Staphylococcus epidermidis. Dual-drug loaded UHMWPE yielded an additional 1-2 log reduction of bacteria, when compared with single-drug loaded UHMWPE. Analysis of the drug elution kinetics suggested that the observed increase in antibacterial activity is due to the increased tolfenamic acid elution from dual-drug loaded UHMWPE. We showed that the increased fractal dimension of the drug domains in UHMWPE could be associated with increased drug elution, leading to higher antibacterial activity. Dual-analgesic loaded UHMWPE proposed here can be used as part of multi-modal antibacterial prophylaxis and promises substantial reduction in post-arthroplasty mortality and morbidity.

Bayesian fixed-domain asymptotics for covariance parameters in a Gaussian process model

Gaussian process models typically contain finite-dimensional parameters in the covariance function that need to be estimated from the data. We study the Bayesian fixed-domain asymptotics for the covariance parameters in a universal kriging model with an isotropic Matérn covariance function, which has many applications in spatial statistics. We show that when the dimension of domain is less than or equal to three, the joint posterior distribution of the microergodic parameter and the range parameter can be factored independently into the product of their marginal posteriors under fixed-domain asymptotics. The posterior of the microergodic parameter is asymptotically close in total variation distance to a normal distribution with shrinking variance, while the posterior distribution of the range parameter does not converge to any point mass distribution in general. Our theory allows an unbounded prior support for the range parameter and flexible designs of sampling points. We further study the asymptotic efficiency and convergence rates in posterior prediction for the Bayesian kriging predictor with covariance parameters randomly drawn from their posterior distribution. In the special case of one-dimensional Ornstein–Uhlenbeck process, we derive explicitly the limiting posterior of the range parameter and the posterior convergence rate for asymptotic efficiency in posterior prediction. We verify these asymptotic results in numerical experiments.

Forward and inverse modeling of fault transmissibility in subsurface flows

Characterizing physical properties of faults, such as their transmissibility, is crucial for performing predictive numerical simulation of subsurface flows, such as those encountered in petroleum engineering and remediation of subsurface contamination. This paper provides a complete investigation of the inverse problem for fault transmissibility in subsurface flow models, under appropriate assumptions on fault structure. In particular, the following aspects are considered: 1) fault modeling and well-posedness of the forward problem; 2) finite element (FEM) discretizations of the forward problem and their rigorous a priori convergence analysis; 3) Well-posedness of the Bayesian inverse problem, FEM discretization of the infinite dimensional Bayesian inverse formulation, and its rigorous a priori analysis. Moreover, computation of the maximum a posteriori (MAP) point via fast inexact Newton-conjugate gradient optimization and a Laplace approximation of the Bayesian posterior are also presented. Numerical results illustrate the use of the proposed fault model in forward and inverse problems for subsurface flows in two dimensional domains with multiple faults.

On the vanishing rigid body problem in a viscous compressible fluid

In this paper we study the interaction of a small rigid body in a viscous compressible fluid. The system occupies a bounded three dimensional domain. The object it allowed to freely move and its dynamics follows the Newton's laws. We show that as the size of the object converges to zero the system fluid plus rigid body converges to the compressible Navier-Stokes system under some mild lower bound on the mass and the inertia momentum. It is a first result of homogenization in the case of fluid-structure interaction in the compressible situation. As a corollary we slightly improved the result on the influence of a vanishing obstacle in a compressible fluid for γ≥6.

Homogenization of Evolutionary Incompressible Navier–Stokes System in Perforated Domains

In this paper, we consider the homogenization problems for evolutionary incompressible Navier-Stokes system in three dimensional domains perforated with a large number of small holes which are periodically located. We first establish certain uniform estimates for the weak solutions. To overcome the extra difficulties coming from the time derivative, we use the idea of Temam and consider the equations by integrating in time variable. After suitably extending the weak solutions to the whole domain, we employ the generalized cell problem to study the limit process.

Spectral Structure of the Neumann--Poincaré Operator on Thin Ellipsoids and Flat Domains

We investigate the spectral structure of the Neumann-Poincar\'e operator on thin ellipsoids. Two types of thin ellipsoids are considered: long prolate ellipsoids and flat oblate ellipsoids. We show that the totality of eigenvalues of the Neumann-Poincar\'e operators on a sequence of the prolate spheroids is densely distributed in the interval [0,1/2] as their eccentricities tend to 1, namely, as they become longer. We then prove that eigenvalues of the Neumann-Poincar\'e operators on the oblate ellipsoids are densely distributed in the interval [-1/2, 1/2] as the ellipsoids become flatter. In particular, this shows that even if there are at most finitely many negative eigenvalues on the oblate ellipsoids, more and more negative eigenvalues appear as the ellipsoids become flatter. We also show a similar spectral property for flat three dimensional domains.

Vanishing dispersion limit for Schrödinger-improved Boussinesq system in two space dimensions

We study the vanishing dispersion limit of strong solutions to the Cauchy problem for the Schrödinger-improved Boussinesq system in a two dimensional domain. We show an explicit representation of limiting profile in terms of the initial data. Moreover, the first approximation is also represented as a pair of solutions of a linear system with coefficients and forcing term given by the limiting profile.

Silane‐Mediated Expansion of Domains in Si‐Doped κ‐Ga2O3 Epitaxy and its Impact on the In‐Plane Electronic Conduction

AbstractUnintentionally doped (001)‐oriented orthorhombic κ‐Ga2O3 epitaxial films on c‐plane sapphire substrates are characterized by the presence of ≈ 10 nm wide columnar rotational domains that can severely inhibit in‐plane electronic conduction. Comparing the in‐ and out‐of‐plane resistance on well‐defined sample geometries, it is experimentally proved that the in‐plane resistivity is at least ten times higher than the out‐of‐plane one. The introduction of silane during metal‐organic vapor phase epitaxial growth not only allows for n‐type Si extrinsic doping, but also results in the increase of more than one order of magnitude in the domain size (up to ≈ 300 nm) and mobility (highest µ ≈ 10 cm2V−1s−1, with corresponding lowest ρ ≈ 0.2 Ωcm). To qualitatively compare the mean domain dimension in κ‐Ga2O3 epitaxial films, non‐destructive experimental procedures are provided based on X‐ray diffraction and Raman spectroscopy. The results of this study pave the way to significantly improved in‐plane conduction in κ‐Ga2O3 and its possible breakthrough in new generation electronics. The set of cross‐linked experimental techniques and corresponding interpretation here proposed can apply to a wide range of material systems that suffer/benefit from domain‐related functional properties.

Concavity of solutions to semilinear equations in dimension two

AbstractWe consider the Dirichlet problem for a class of semilinear equations on two‐ dimensional convex domains. We give a sufficient condition for the solution to be concave. Our condition uses comparison with ellipses, and is motivated by an idea of Kosmodem'yanskii. We also prove a result on propagation of concavity of solutions from the boundary, which holds in all dimensions.

Electrical Gating of the Charge-Density-Wave Phases in Two-Dimensional h-BN/1T-TaS2 Devices.

We report on the electrical gating of the charge-density-wave phases and current in h-BN-capped three-terminal 1T-TaS2 heterostructure devices. It is demonstrated that the application of a gate bias can shift the source-drain current-voltage hysteresis associated with the transition between the nearly commensurate and incommensurate charge-density-wave phases. The evolution of the hysteresis and the presence of abrupt spikes in the current while sweeping the gate voltage suggest that the effect is electrical rather than self-heating. We attribute the gating to an electric-field effect on the commensurate charge-density-wave domains in the atomic planes near the gate dielectric. The transition between the nearly commensurate and incommensurate charge-density-wave phases can be induced by both the source-drain current and the electrostatic gate. Since the charge-density-wave phases are persistent in 1T-TaS2 at room temperature, one can envision memory applications of such devices when scaled down to the dimensions of individual commensurate domains and few-atomic plane thicknesses.

Thermal transitions in domain wall AdS/QCD

We study thermal transitions in a Domain Wall AdS/QCD model. The model is based on the D5/probe D7 system with a discontinuous mass profile which restricts chiral fermions to 3+1 dimensional domain walls. Fluctuations on the domain wall are dual to the quark mass and condensate and reveal the relation between domain wall separation and the quark mass. The massive quarks exhibit a second order thermal, meson melting transition. Witten's multi-trace prescription can be used to interpret these configurations as having a dynamical mass from a Nambu-Jona-Lasinio interaction - here the transition is first order. Confinement can be introduced into the gauge sector by compactifying one direction of the D5. Compactification induces chiral symmetry breaking and there is a first order thermal restoration transition. If an NJL interaction is also introduced then the confinement and chiral symmetry breaking scales can be separated.