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Metal additive manufacturing via laser-based powder bed fusion (PBF-LB/M) faces performance-critical challenges due to complex melt pool and vapor dynamics, often oversimplified by computational models that neglect crucial aspects, such as…
Fractional derivatives are a well-studied generalization of integer order derivatives. Naturally, for optimization, it is of interest to understand the convergence properties of gradient descent using fractional derivatives. Convergence…
A conformal flattening maps a curved surface to the plane without distorting angles---such maps have become a fundamental building block for problems in geometry processing, numerical simulation, and computational design. Yet existing…
Based on the radial basis function (RBF), non-singular general solution and dual reciprocity principle (DRM), this paper presents an inheretnly meshless, exponential convergence, integration-free, boundary-only collocation techniques for…
We propose the use of a Transformer to accurately predict normals from point clouds with noise and density variations. Previous learning-based methods utilize PointNet variants to explicitly extract multi-scale features at different input…
A class of quasi-distribution evaluation criteria based on piecewise Bezier curves is proposed to address the issue of the inability to objectively evaluate finite element models. During the optimization design of mechanical parts, finite…
The surface critical behavior of bcc binary alloys undergoing a continuous B2-A2 order-disorder transition is investigated in the mean-field (MF) approximation. Our main aim is to provide clear evidence for the fact that surfaces which…
We obtain analytical solutions for positive-to-negative transition materials with a smooth transition profile "$\tanh$". The fields are expressed in terms of hypergeometric functions. The final expressions for reflection and transmission…
We study a non-Anderson disorder driven quantum phase transition in a semi-infinite Dirac semimetal with a flat boundary. The conformally invariant boundary conditions, which include those that are time-reversal invariant, lead to…
Analysis-suitable T-splines (AST-splines) are a promising candidate to achieve a seamless integration between the design and the analysis of thin-walled structures in industrial settings. In this work, we generalize AST-splines to allow…
In this paper, we analyze and provide numerical illustrations for a moving finite element method applied to convection-dominated, time-dependent partial differential equations. We follow a method of lines approach and utilize an underlying…
In this note is presented a method, given nodal values on multidimensional nonconforming spectral elements, for calculating global Fourier-series coefficients. This method is ``exact'' in that given the approximation inherent in the…
Subdivision surfaces provide an elegant isogeometric analysis framework for geometric design and analysis of partial differential equations defined on surfaces. They are already a standard in high-end computer animation and graphics and are…
We use an accurate implementation of density functional theory (DFT) to calculate the zero-temperature generalized phase diagram of the 4$d$ series of transition metals from Y to Pd as a function of pressure $P$ and atomic number $Z$. The…
We provide a basis transformation that inverts the coordinate Bethe Ansatz. It is widely believed that the Bethe Ansatz is complete, based on numerical evidence and combinatorial arguments. We present a constructive and comprehensive…
Block copolymers provide a wonderful platform in studying the soft condensed matter systems. Many fascinating ordered structures have been discovered in bulk and confined systems. Among various theories, the self-consistent field theory…
We derive a full Bern-Kosower-type rule for scalar QED starting from quantum field theory: we derive a set of rules for calculating $S$-matrix elements for any processes at any order of the coupling constant. Gauge-invariant set of diagrams…
An equivalent circuit model for Frequency Selective Surfaces (FSS) comprising anisotropic elements is presented. The periodic surface is initially simulated with an arbitrary azimuthal incidence angle and its surface impedance matrix is…
We generalized the conventional concept of q-plate, allowing in its definition non linear functions of the azimuthal coordinate, and simulated the resulting fields of applying this kind of element to uniformly polarized input beams, both in…
A novel multi-scale finite element formulation for contact mechanics between nominally smooth but microscopically rough surfaces is herein proposed. The approach integrates the interface finite element method (FEM) for modelling interface…