Related papers: Van Vleck Analysis of Angularly Distorted Octahedr…
In obstructed atomic insulators, fractionally quantized charges appear at the corners of the crystals in the shapes of vertex-transitive polyhedra, and are given by the filling anomaly divided by the number of corners. Recent studies reveal…
We define a regularized size-shape distortion (quality) measure for curved high-order elements on a Riemannian space. To this end, we measure the deviation of a given element, straight-sided or curved, from the stretching, alignment, and…
The tilt, rotation, or offset of each CCD with respect to the focal plane, as well as the distortion of the focal plane itself, cause shape distortions to the observed objects, an effect typically known as field distortion (FD). We point…
Understanding intraventricular hemodynamics requires compact and physically interpretable representations of the underlying flow structures, as characteristic flow patterns are closely associated with cardiovascular conditions and can…
In this study, an image-assisted Approximate Bayesian Computation (ABC) parameter inverse method is proposed to identify the design parameters. In the proposed method, the images are mapped to a low-dimensional latent space by Variational…
This study proposes an acceleration technique for the computational challenges in extending the variational deterministic-particle-based scheme (VDS) [Bao et al., Journal of Computational Physics 522 (2025) 113589] to 3D complex fluid…
Viscoelasticity and related phenomena are of great importance in the study of mechanical properties of material especially, biological materials. Certain materials show some complex effects in mechanical tests, which cannot be described by…
A VB-algebroid is a vector bundle object in the category of Lie algebroids. We attach to every VB-algebroid a differential graded Lie algebra and we show that it controls deformations of the VB-algebroid structure. Several examples and…
Volterra's definition of dislocations in crystals distinguishes edge and screw defects geometrically, according to whether the Burgers vector is perpendicular or parallel to the defect. Here, we demonstrate a distinction between screw and…
The wide adoption of thermoplastic composites to reduce weight in structural parts requires reliable numerical methods to account for debonding between overmolded parts. Although cohesive elements are effective for debonding, the need for…
In this paper, we study applications of the virtual element method (VEM) for simulating the deformation of multiphase composites. The VEM is a Galerkin approach that is applicable to meshes that consist of arbitrarily-shaped polygonal and…
The band-unfolding method is widely used to calculate the effective band structures of a disordered system from its supercell model. The unfolded band structures show the crystallographic symmetry of the underlying structure, where the…
The coherent structures in the turbulent wake of a disk at a moderately high Reynolds number ($\Rey$) of $50,000$ are examined using spectral proper orthogonal decomposition (SPOD) which considers all three velocity components in a…
Angular measurements is essential to make a resonable treatment for Hallux valgus (HV), a common forefoot deformity. However, it still depends on manual labeling and measurement, which is time-consuming and sometimes unreliable. Automating…
Since the turn of the millennium, capitalizing on modern advances in mathematics and computation, a slew of computational models have been proposed in the literature with the objective of describing the nucleation and propagation of…
The scattering of electromagnetic waves by three--dimensional periodic structures is important for many problems of crucial scientific and engineering interest. Due to the complexity and three-dimensional nature of these waves, the fast,…
In this article, discrete variants of several results from vector calculus are studied for classical finite difference summation by parts operators in two and three space dimensions. It is shown that existence theorems for scalar/vector…
The van Vleck determinant is an ubiquitous object, arising in many physically interesting situations such as: (1) WKB approximations to quantum time evolution operators and Green functions. (2) Adiabatic approximations to heat kernels. (3)…
A nonlocal relativistic variational principle (VP) has recently been proposed as an alternative to the Dirac wave equation of standard quantum mechanics. We apply that principle to the electron two-slit experiment. The detection system is…
Low-order virtual element methods (VEM) compute a consistent finite-strain contribution through polynomial projections and rely on stabilization to control the unresolved modes in the projector kernel. In current hyperelastic VEM practice,…