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This paper presents a fast implementation of the Graham scan on the GPU. The proposed algorithm is composed of two stages: (1) two rounds of preprocessing performed on the GPU and (2) the finalization of finding the convex hull on the CPU. |
Delaunay has shown that the Delaunay complex of a finite set of points $P$ of Euclidean space $\mathbb{R}^m$ triangulates the convex hull of $P$, provided that $P$ satisfies a mild genericity property. Voronoi diagrams and Delaunay complexes can be defined for arbitrary Riemannian manifolds. |
We describe how to approximate, in quasi-polynomial time, the largest independent set of polygons, in a given set of polygons. Our algorithm works by extending the result of Adamaszek and Wiese \cite{aw-asmwi-13, aw-qmwis-14} to polygons of arbitrary complexity. |
Planar graph drawings tend to be aesthetically pleasing. In this poster we explore a Neural Network's capability of learning various planar graph classes. |
We show that for every n > 0 there is a planar topological disk A_0 and n translates A_1, A_2, ..., A_n of A_0 such that the interiors of A_0, ... A_n are pairwise disjoint, but with each A_i touching A_0 for 1 <= i <= n. |
An ortho-radial grid is described by concentric circles and straight-line spokes emanating from the circles' center. An ortho-radial drawing is the analog of an orthogonal drawing on an ortho-radial grid. |
Every graph $G$ can be represented by a collection of equi-radii spheres in a $d$-dimensional metric $\Delta$ such that there is an edge $uv$ in $G$ if and only if the spheres corresponding to $u$ and $v$ intersect. The smallest integer $d$ such that $G$ can be represented by a collection of spheres (all of the same r... |
Edit distances between merge trees of scalar fields have many applications in scientific visualization, such as ensemble analysis, feature tracking or symmetry detection. In this paper, we propose branch mappings, a novel approach to the construction of edit mappings for merge trees. |
We show that the greedy spanner algorithm constructs a $(1+\epsilon)$-spanner of weight $\epsilon^{-O(d)}w(\mathrm{MST})$ for a point set in metrics of doubling dimension $d$, resolving an open problem posed by Gottlieb. Our result generalizes the result by Narasimhan and Smid who showed that a point set in $d$-dimens... |
The local search framework for obtaining PTASs for NP-hard geometric optimization problems was introduced, independently, by Chan and Har-Peled (2009) and Mustafa and Ray (2010). In this paper, we generalize the framework by extending its analysis to additional families of graphs, beyond the family of planar graphs. |
We introduce staged self-assembly of Wang tiles, where tiles can be added dynamically in sequence and where intermediate constructions can be stored for later mixing. This model and its various constraints and performance measures are motivated by a practical nanofabrication scenario through protein-based bioengineeri... |
(I) We exhibit a set of 23 points in the plane that has dilation at least $1.4308$, improving the previously best lower bound of $1.4161$ for the worst-case dilation of plane spanners. <br>(II) For every integer $n\geq13$, there exists an $n$-element point set $S$ such that the degree 3 dilation of $S$ denoted by $\de... |
We introduce tools from numerical analysis and high dimensional probability for precision control and complexity analysis of subdivision-based algorithms in computational geometry. We combine these tools with the continuous amortization framework from exact computation. |
Let $S$ and $D$ each be a set of orthogonal line segments in the plane. A line segment $s\in S$ \emph{stabs} a line segment $s'\in D$ if $s\cap s'\neq\emptyset$. |
Based on a newly proposed spatial data model - spatial chromatic model (SCM), we developed a spatial coding scheme, called full-coded ordinary arranged chromatic diagram (full-OACD). Full-OACD is a type of spatial tessellation, where space is partitioned into a number of subspaces such as cells, edges, and vertexes. |
We present approximation algorithms for maximum independent set of pseudo-disks in the plane, both in the weighted and unweighted cases. For the unweighted case, we prove that a local search algorithm yields a \PTAS. |
An emanation graph of grade $k$ on a set of points is a plane spanner made by shooting $2^{k+1}$ equally spaced rays from each point, where the shorter rays stop the longer ones upon collision. The collision points are the Steiner points of the spanner. |
There is an old conjecture by Shermer \cite{sher} that in a polygon with $n$ vertices and $h$ holes, $\lfloor \dfrac{n+h}{3} \rfloor$ vertex guards are sufficient to guard the entire polygon. The conjecture is proved for $h=1$ by Shermer \cite{sher} and Aggarwal \cite{aga} seperately. |
We study metrics that assess how close a triangulation is to being a Delaunay triangulation, for use in contexts where a good triangulation is desired but constraints (e.g., maximum degree) prevent the use of the Delaunay triangulation itself. Our near-Delaunay metrics derive from common Delaunay properties and satisf... |
Sharing the spectrum among mobile network operators (MNOs) is a promising approach to improve the spectrum utilization and to increase the monetary income of MNOs. In this paper, we model a nonorthogonal spectrum sharing system for a large-scale cellular network where multiple seller MNOs lease their licensed sub-band... |
One of the challenges in single particle reconstruction in cryo-electron microscopy is to find a three-dimensional model of a molecule using its two-dimensional noisy projection-images. In this paper, we propose a robust "angular reconstitution" algorithm for molecules with $n$-fold cyclic symmetry, that estim... |
The interference at a wireless node s can be modelled by the number of wireless nodes whose transmission ranges cover s. Given a set of positions for wireless nodes, the interference minimization problem is to assign a transmission radius (equivalently, a power level) to each node such that the resulting communication... |
We propose and study a generalization to the well-known problem of polyline simplification. Instead of a single polyline, we are given a set of $\ell$ polylines possibly sharing some line segments and bend points. |
Given a convex polygon $P$ with $n$ vertices, the two-center problem is to find two congruent closed disks of minimum radius such that they completely cover $P$. We propose an algorithm for this problem in the streaming setup, where the input stream is the vertices of the polygon in clockwise order. |
In the companion paper, we measured homology classes and computed the optimal homology basis. This paper addresses two related problems, namely, localization and stability. |
The use of realistic input models has gained popularity in the theory community. Assuming a realistic input model often precludes complicated hypothetical inputs, and the analysis yields bounds that better reflect the behaviour of algorithms in practice. |
We study range spaces, where the ground set consists of either polygonal curves in $\mathbb{R}^d$ or polygonal regions in the plane that may contain holes and the ranges are balls defined by an elastic distance measure, such as the Hausdorff distance, the Fréchet distance and the dynamic time warping distance. The ran... |
We investigate two optimization problems on area-proportional rectangle contact representations for layered, embedded planar graphs. The vertices are represented as interior-disjoint unit-height rectangles of prescribed widths, grouped in one row per layer, and each edge is ideally realized as a rectangle contact of p... |
We present an extension of Voronoi diagrams where when considering which site a client is going to use, in addition to the site distances, other site attributes are also considered (for example, prices or weights). A cell in this diagram is then the locus of all clients that consider the same set of sites to be releva... |
Given a periodic placement of copies of a tromino (either L or I), we prove co-RE-completeness (and hence undecidability) of deciding whether it can be completed to a plane tiling. By contrast, the problem becomes decidable if the initial placement is finite, or if the tile is a domino instead of a tromino (in any dim... |
The morphometric approach [HRC13,RHK06] writes the solvation free energy as a linear combination of weighted versions of the volume, area, mean curvature, and Gaussian curvature of the space-filling diagram. We give a formula for the derivative of the weighted Gaussian curvature. |
The Art Gallery Problem (AGP) is one of the classical problems in computational geometry. It asks for the minimum number of guards required to achieve visibility coverage of a given polygon. |
Subtrajectory clustering is an important variant of the trajectory clustering problem, where the start and endpoints of trajectory patterns within the collected trajectory data are not known in advance. We study this problem in the form of a set cover problem for a given polygonal curve: find the smallest number $k$ o... |
We study the problem of determining coordinated motions, of minimum total length, for two arbitrary convex centrally-symmetric (CCS) robots in an otherwise obstacle-free plane. Using the total path length traced by the two robot centres as a measure of distance, we give an exact characterization of a (not necessarily ... |
This paper defines a theory of conformal parametrization of digital surfaces made of surfels equipped with a normal vector. The main idea is to locally project each surfel to the tangent plane, therefore deforming its aspect-ratio. |
In 1967, Whitham proposed a simplified surface water-wave model which combined the full linear dispersion relation of the full Euler equations with a weakly linear approximation. The equation he postulated which is now called the Whitham equation has recently been extended to a system of equations allowing for bi-dire... |
We propose a metasurface antenna capable of real time holographic beam steering. An array of reconfigurable dipoeles can generate on demand far field patterns of radiation through the specific encoding of meta atomic states. |
Two finite difference schemes for the numerical treatment of the von Neumann equation for the (2+1)D Dirac Hamiltonian are presented. Both utilize a single-cone staggered space-time grid which ensures a single-cone energy dispersion to formulate a numerical treatment of the mixed-state dynamics within the von Neumann ... |
Adjoint variable method in combination with gradient descent optimization has been widely used for the inverse design of nanophotonic devices. In many of such optimizations, the design region is only a small fraction of the total computational domain. |
A problem of considerable importance within the field of uncertainty quantification (UQ) is the development of efficient methods for the construction of accurate surrogate models. Such efforts are particularly important to applications constrained by high-dimensional uncertain parameter spaces. |
A multiphysics finite volume method (FVM) solver, coupling neutronics and shock physics, is under development at Politecnico di Milano for the analysis of shock imploding fissile materials [1]. The proposed solver can be a useful tool to make preliminary safety assessment of subcritical plutonium experiments [2] and, ... |
The influence of defect dipoles on the electrocaloric effect (ECE) in acceptor doped BaTiO$_3$ is studied by means of lattice-based Monte-Carlo simulations. A Ginzburg-Landau type effective Hamiltonian is used. |
Simulating wave propagation on discrete grid in time domain requires the description of both the parameters of the media and the values of the wave field at two different time steps within the simulated domain. For most practical cases this operation is very demanding on the system's memory and runtime. |
We turn `the' Church-Turing Hypothesis from an ambiguous source of sensational speculations into a (collection of) sound and well-defined scientific problem(s): <br>Examining recent controversies, and causes for misunderstanding, concerning the state of the Church-Turing Hypothesis (CTH), suggests to study the CTH ... |
We present a particle method for estimating the curvature of interfaces in volume-of-fluid simulations of multiphase flows. The method is well suited for under-resolved interfaces, and it is shown to be more accurate than the parabolic fitting that is employed in such cases. |
We investigate the switching field distribution and the resulting bit error rate of exchange coupled ferri-/ferromagnetic bilayer island arrays by micromagnetic simulations. Using islands with varying microstructure and anisotropic properties, the intrinsic switching field distribution is computed. |
Computer simulation with Monte Carlo is an important tool to investigate the function and equilibrium properties of many systems with biological and soft matter materials solvable in solvents. The appropriate treatment of long-range electrostatic interaction is essential for these charged systems, but remains a challe... |
We implement a full nonlinear optimization method to fit continuum states with complex Gaussians. The application to a set of regular scattering Coulomb functions allows us to validate the numerical feasibility, to explore the range of convergence of the approach, and to demonstrate the relative superiority of complex... |
Local grid refinement aims to optimise the relationship between accuracy of the results and number of grid nodes. In the context of the finite volume method no single local refinement criterion has been globally established as optimum for the selection of the control volumes to subdivide, since it is not easy to assoc... |
In this work, we develop Non-Intrusive Reduced Order Models (NIROMs) that combine Proper Orthogonal Decomposition (POD) with a Radial Basis Function (RBF) interpolation method to construct efficient reduced order models for time-dependent problems arising in large scale environmental flow applications. The performance... |
In this paper, a third-order compact gas-kinetic scheme is firstly proposed for three-dimensional computation for the compressible Euler and Navier-Stokes solutions. The scheme achieves its compactness due to the time-dependent gas distribution function in GKS, which provides not only the fluxes but also the time accu... |
We present the Tucker tensor DFT (TTDFT) code which uses a tensor-structured algorithm with graphic processing unit (GPU) acceleration for conducting ground-state DFT calculations on large-scale systems. The Tucker tensor DFT algorithm uses a localized Tucker tensor basis computed from an additive separable approximat... |
Local neural operator (LNO) conception has provided a feasible way for scientific computations. The LNO learns transient partial differential equations from random field samples, and then the pre-trained LNO solves practical problems on specific computational domains. |
This new version of TaylUR is based on a completely new core, which now is able to compute the numerical values of all of a complex-valued function's partial derivatives up to an arbitrary order, including mixed partial derivatives. |
In this work, a lattice Boltzmann scheme is developed for numerical solution of the phonon Boltzmann equation under Callaway's dual relaxation model in the hydrodynamic limit. Through a Chapman-Enskog expansion to the lattice Boltzmann equation with the resistive scattering term as an equivalent source term, we re... |
A logical explanation as to why the choice of the Pian-Sumihara basis (as a linear basis to approximate stress) leads to greater efficiency in enhanced strain problems, is presented. An Airy stress function and the consequent selective simplification resulting from the differentiation of an implied, single, parent app... |
Infrared thermography is a powerful tool for studying liquid-to-vapor phase change processes. However, its application has been limited in the study of vapor-to-liquid phase transitions due to the presence of complex liquid dynamics, multiple phases within the same field of view, and experimental difficulty. |
Features of the angular distributions of accelerated atomic projectiles at grazing angles of incidence on the crystal surface are studied by using the computer simulation. The interaction between the projectiles and the crystal-lattice atoms and atomic structure of the crystal surface are calculated by means of the el... |
We present a numerical exercise in which classical and non-classical electrostatic potentials were calculated. The non-classical fields take into account effects due to a possible non-zero photon rest mass. |
We demonstrate a heuristic optimization algorithm based on the game tree search for multi-component materials design. The algorithm searches for the largest spin polarization of seven-component Heusler alloys. |
The most tight conformation of the trefoil knot found by the SONO algorithm is presented. Structure of the set of its self-contact points is analyzed. |
We propose a novel dual physics-informed neural network for topology optimization (DPNN-TO), which merges physics-informed neural networks (PINNs) with the traditional SIMP-based topology optimization (TO) algorithm. This approach leverages two interlinked neural networks-a displacement network and an implicit density... |
In conventional molecular simulation, metastable structures often survive over considerable computational time, resulting in difficulties in simulating equilibrium states. In order to overcome this difficulty, here we propose a newly devised method, molecular Monte Carlo simulation of systems connected to three reserv... |
An efficient solver for the three dimensional free-space Poisson equation is presented. The underlying numerical method is based on finite Fourier series approximation. |
The properties of a one space-dimension, one particle dynamical system under the influence of a purely dissipative force are investigated. Assuming this force depends only on the velocity, it is demonstrated, in contrast to the case of linear damping, that there exist dissipative forces for which the particle \textquo... |
As a multi-purpose Particle-In-Cell (PIC) code, Smilei gathers many different features in a single software. Combining some of them is challenging. |
Particle transport through a duct by Lambertian reflection from duct walls is again considered. This popular transport example has been solved by most numerical transport methods except notably one- the method of doubling. |
The mechanical properties of periodic microstructures are pivotal in various engineering applications. Homogenization theory is a powerful tool for predicting these properties by averaging the behavior of complex microstructures over a representative volume element. |
Runaway electrons (RE) generated during magnetic disruptions present a major threat to the safe operation of plasma nuclear fusion reactors. A critical aspect of understanding RE dynamics is to calculate the runaway probability, i.e., the probability that an electron in the phase space will runaway on, or before, a pr... |
The accuracy and efficiency of a coarse-grained (CG) force field are pivotal for high-precision molecular simulations of large systems with complex molecules. We present an automated mapping and optimization framework for molecular simulation (AMOFMS), which is designed to streamline and improve the force field optimi... |
The advanced ENZ-theory of diffraction integrals, as published recently in J. Europ. Opt. |
Accurately predicting key combustion phenomena in reactive-flow simulations, e.g., lean blow-out, extinction/ignition limits and pollutant formation, necessitates the use of detailed chemical kinetics. The large size and high levels of numerical stiffness typically present in chemical kinetic models relevant to transp... |
Lattice Boltzmann models provide better understanding with mesoscopic eyesight on multi-component diffusion than macroscopic models. Based on the kinetic theory and starting from the He-Luo model, the state-of-the-art multi-component diffusion Lattice Boltzmann models have defects of the compressible error and the lim... |
The numerical simulation of acoustic waves in complex 3D media is a key topic in many branches of science, from exploration geophysics to non-destructive testing and medical imaging. With the drastic increase in computing capabilities this field has dramatically grown in the last twenty years. |
In the present letter a method to find a proper expression for the force distribution inside a granular sample in static equilibrium is proposed. The method is based in statistical mechanics and the force distribution is obtained by studying how the potential elastic energy is divided among the different contacts betw... |
Multiboson production provides a unique way to probe Electroweak Symmetry Breaking (EWSB) and physics beyond the Standard Model (SM). With the discovery of the Higgs boson, the default model is that EWSB occurs according to the Higgs mechanism. |
Modeling multimetallic systems efficiently enables faster prediction of desirable chemical properties and design of new materials. This work describes an initial implementation for performing multireference wave function method localized active space self-consistent field (LASSCF) calculations through the use of multi... |
We used density-functional theory based first principles simulations to study the effects of uniaxial strain and quantum confinement on the electronic properties of germanium nanowires along the [110] direction, such as the energy gap and the effective masses of the electron and hole. The diameters of the nanowires be... |
In this work, a stochastic, physics-based model for Lithium-ion batteries (LIBs) is presented in order to study the effects of parametric model uncertainties on the cell capacity, voltage, and concentrations. To this end, the proposed uncertainty quantification (UQ) approach, based on sparse polynomial chaos expansion... |
Engineered biomedical nanoparticles (NP) administered via intravenous routes are prone to associate to serum proteins. The protein corona can mask the NP surface functionalization and hamper the delivery of the NP to its biological target. |
A locking-free rectangular Mindlin plate element with a new multi-resolution analysis (MRA) is proposed and a new finite element method is hence presented. The MRA framework is formulated out of a mutually nesting displacement subspace sequence whose basis functions are constructed of scaling and shifting on the eleme... |
A quasi one-dimensional layered material, CuTe undergoes a charge density wave (CDW) transition in Te chains with a modulation vector of $q_{CDW}=(0.4, 0.0, 0.5)$. Despite the clear experimental evidence for the CDW, the theoretical understanding especially the role of the electron-electron correlation in the CDW has ... |
This paper presents a detailed evaluation of the envelope-tracking adaptive integral method (ET-AIM), an FFT-accelerated algorithm for analyzing electromagnetic scattering. ET-AIM is used to solve progressively more complex benchmark scattering problems and key parameters of the method (the auxiliary grid size, near-z... |
The performance of discrete general purpose graphics processing units (GPGPUs) has been improving at a rapid pace. The PCIe interconnect that controls the communication of data between the system host memory and the GPU has not improved as quickly, leaving a gap in performance due to GPU downtime while waiting for PCI... |
In this first part of two papers, we extend the C-method developed in [40] for adding localized, space-time smooth artificial viscosity to nonlinear systems of conservation laws that propagate shock waves, rarefaction waves, and contact discontinuities in one space dimension. For gas dynamics, the C-method couples the... |
Even more interesting than the intricate organization of complex networks are the dynamical behavior of systems which such structures underly. Among the many types of dynamics, one particularly interesting category involves the evolution of trails left by moving agents progressing through random walks and dilating pro... |
The accuracy of the many-body perturbation theory GW formalism to calculate electron-phonon coupling matrix elements has been recently demonstrated in the case of a few important systems. However, the related computational costs are high and thus represent strong limitations to its widespread application. |
Many biological systems and artificial structures are ramified, and present a high geometric complexity. In this work, we propose a space-averaged model of branched systems for conservation laws. |
The Geant4 reference paper published in Nuclear Instruments and Methods A in 2003 has become the most cited publication in the whole Nuclear Science and Technology category of Thomson-Reuter's Journal Citation Reports. It is currently the second most cited article among the publications authored by two major resea... |
This paper presents a general positivity-preserving algorithm for implicit high-order finite volume schemes solving Euler and Navier-Stokes equations. Previous positivity-preserving algorithms are mainly based on mathematical analyses, being highly dependent on the existence of low-order positivity-preserving numerica... |
Great progress has been made in quantum computing in recent years, providing opportunities to overcome computation resource poverty in many scientific computations like computational fluid dynamics (CFD). In this work, efforts are made to exploit quantum potentialities in CFD, and a hybrid classical and quantum comput... |
For over a decade now, physical and energy constraints have limited clock speed improvements in commodity microprocessors. Instead, chipmakers have been pushed into producing lower-power, multi-core processors such as GPGPU, ARM and Intel MIC. |
A crucial step in constructing a Lattice Boltzmann model is the definition of a suitable set of lattice velocities, and the correct assignment of the associated weights. For high-order models, the solution of this problem requires a non-trivial effort. |
A variational method is used to derive a self-consistent macro-particle model for relativistic electromagnetic kinetic plasma simulations. Extending earlier work [E. G. Evstatiev and B. A. Shadwick, J. Comput. Phys., vol. 245, pp. 376-398, 2013], the discretization of the electromagnetic Low Lagrangian is performed vi... |
We present a novel methodology based on Physics-Informed Neural Networks (PINNs) for solving systems of partial differential equations admitting discontinuous solutions. Our method, called Gradient-Annihilated PINNs (GA-PINNs), introduces a modified loss function that requires the model to partially ignore high-gradie... |
A perturbation method for computing quick estimates of the echo decay in pulsed spin echo gradient NMR diffusion experiments in the short gradient pulse limit is presented. The perturbation basis involves (relatively few) dipole distributions on the boundaries generating a small perturbation matrix in O(s^2) time, whe... |
We present a new stabilised and efficient high-order nodal spectral element method based on the Mixed Eulerian Lagrangian (MEL) method for general-purpose simulation of fully nonlinear water waves and wave-body interactions. In this MEL formulation a standard Laplace formulation is used to handle arbitrary body shapes... |
Bubble chambers and droplet detectors used in dosimetry and dark matter particle search experiments use a superheated metastable liquid in which nuclear recoils trigger bubble nucleation. This process is described by the classical heat spike model of F. Seitz [Phys. Fluids (1958-1988) 1, 2 (1958)], which uses classica... |
Restricted Boltzmann machine (RBM) provide a general framework for modeling physical systems, but their behavior is dependent on hyperparameters such as the learning rate, the number of hidden nodes and the form of the threshold function. This article accordingly examines in detail the influence of these parameters on... |
Structure-preserving integrators are in the focus of ongoing research because of their distinguished features of robustness and long time stability. In particular, their formulation for coupled problems that include dissipative mechanisms is still an active topic. |
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