Dimensional Grid Research Articles

Monitoring tendon breaks in concrete structures at different depths using distributed fiber optical sensors

Unannounced tendon breaks are a dreaded failure mechanism in concrete bridges. The failure of single wires or tendons does not necessarily cause cracking of the concrete. Thus, the damage cannot be detected by visual inspection. But, in the case of tendons bonded in concrete, re-anchoring causes characteristic local strain fields: tensile strains occur between the crack edges while three-dimensional compressive strains develop in the area around. On the surface, these strains are small and depend, e.g., on the concrete stiffness, the depth of the tendon inside the member and the anchorage length. Such strain fields can be measured by fiber optical sensors on the surface in two dimensional grids. By evaluating the backscatter of emitted light beams, minimal strain changes (uncertainty: ±1 µm/m) can be detected in quasi-continuous resolution (0.65 mm pitch). An experimental investigation on a prestressed concrete beam with bonded tendons is presented. Gradually, three tendons of 10.5 mm diameter were mechanically cut to simulate failure, while longitudinal strains were measured on a 2D grid at the surface. With a prestressing force of 64.5 kN and up to a depth of 25 cm breaks of the tendons could be detected. They caused strains about 10-15 µm/m at the surface at maximum. For varying tendon positions, the effect of depth on the strain is investigated by two sided measurements. As the distance between the break and the concrete surface increases, the strain significantly decreases but remains detectable. In the future, the results enable deeper analyses of the most influential parameters. The final aim remains to precisely detect the position and number of failed wires or tendons just from the strain signal at the surface.

What Goes Around Comes Around: Covering Tours and Cycle Covers with Turn Costs

We investigate several geometric problems of finding tours and cycle covers with minimum turn cost, which have been studied in the past, with complexity, approximation results, and open problems dating back to work by Arkin et al. in 2001. Many new practical applications have spawned variants: For full coverage, all points have to be covered, for subset coverage, specific points have to be covered, and for penalty coverage, points may be left uncovered by incurring a penalty. We show that finding a minimum-turn (full) cycle cover is NP-hard even in 2-dimensional grid graphs, solving the long-standing open Problem 53 in The Open Problems Project edited by Demaine, Mitchell and O’Rourke. We also prove NP-hardness of finding a subset cycle cover of minimum turn cost in thin grid graphs, for which Arkin et al. gave a polynomial-time algorithm for full coverage; this shows that their boundary techniques cannot be applied to compute exact solutions for subset and penalty variants. We also provide a number of positive results. In particular, we establish the first constant-factor approximation algorithms for all considered subset and penalty problem variants for grid-based instances, based on LP/IP techniques. These geometric versions allow many possible edge directions (and thus, turn angles, such as in hexagonal grids or higher-dimensional variants); our approximation factors improve the combinatorial ones of Arkin et al.

Minimum Congestion and Wirelength of Embedding the nth Cartesian Product of K4 into Various Kinds of Grid Networks

Embedding an interconnection network into another network is one of the main problems in parallel processing and computing systems. Interconnection networks in multiprocessing systems facilitate effective communication among various system components. Obtaining the minimum cutwidth, congestion, and wirelength in graph embedding problems is of great significance for network design and architecture, where the minimum is taken over all embedding of guest graphs into host graphs, and addressing these issues can reduce time and cost in embedded design. This work aims to accurately calculate the minimum congestion and wirelength for the [Formula: see text] (the [Formula: see text]th Cartesian product of [Formula: see text]) layout into [Formula: see text]-dimensional, [Formula: see text]-dimensional, and [Formula: see text]-dimensional grids by the optimal solution of edge isoperimetric problem on [Formula: see text].

Effective Data Distillation for Tabular Datasets (Student Abstract)

Data distillation is a technique of reducing a large dataset into a smaller dataset. The smaller dataset can then be used to train a model which can perform comparably to a model trained on the full dataset. Past works have examined this approach for image datasets, focusing on neural networks as target models. However, tabular datasets pose new challenges not seen in images. A sample in tabular dataset is a one dimensional vector unlike the two (or three) dimensional pixel grid of images, and Non-NN models such as XGBoost can often outperform neural network (NN) based models. Our contribution in this work is two-fold: 1) We show in our work that data distillation methods from images do not translate directly to tabular data; 2) We propose a new distillation method that consistently outperforms the baseline for multiple different models, including non-NN models such as XGBoost.

Wireless Power Transfer for Variable Load, Distance, and Power Division Ratio in a Loosely-Coupled Multiple-Receiver Relay System

This paper proposes a wireless power transfer (WPT) system for variant receiver (Rx) configuration, power distribution ratio, load and distance with multiple relays, each of which is connected to a resistive load. Each Rx relay transfers power to an adjacent Rx and acts as a relay while its local load consumes power. We develop a methodology for the design of wireless power transfer resonators that achieve optimum efficiency for multiple receivers with power distribution ratios, loads, and distances. The WPT configuration is extended to a general m×n, 2-dimensional grid for a large area coverage. A mathematical model of the proposed WPT system is provided, and a multiple-Rx wireless power network using a power inverter serves as a proof-of-concept. Following the design guidelines provided in this paper, experimental examples with variable parameters while delivering a total power of 100 W are discussed. To illustrate the practical applicability of this approach, a demonstration on a consumer display and speaker device is performed.

Two Birds One Stone: Graphene Assisted Reaction Kinetics and Ionic Conductivity in Phthalocyanine-Based Covalent Organic Framework Anodes for Lithium-ion Batteries.

This work reports a covalent organic framework composite structure (PMDA-NiPc-G), incorporating multiple-active carbonyls and graphene on the basis of the combination of phthalocyanine (NiPc(NH2 )4 ) containing a large π-conjugated system and pyromellitic dianhydride (PMDA) as the anode of lithium-ion batteries. Meanwhile, graphene is used as a dispersion medium to reduce the accumulation of bulk covalent organic frameworks (COFs) to obtain COFs with small-volume and few-layers, shortening the ion migration path and improving the diffusion rate of lithium ions in the two dimensional (2D) grid layered structure. PMDA-NiPc-G showed a lithium-ion diffusion coefficient (DLi + ) of 3.04 × 10-10 cm2 s-1 which is 3.6 times to that of its bulk form (0.84 × 10-10 cm2 s-1 ). Remarkably, this enables a large reversible capacity of 1290 mAhg-1 can be achieved after 300 cycles and almost no capacity fading in the next 300 cycles at 100mAg-1 . At a high areal capacity loading of ≈3 mAhcm-2 , full batteries assembled with LiNi0.8 Co0.1 Mn0.1 O2 (NCM-811) and LiFePO4 (LFP) cathodes showed 60.2% and 74.7% capacity retention at 1 C for 200 cycles. Astonishingly, the PMDA-NiPc-G/NCM-811 full battery exhibits ≈100% capacity retention after cycling at 0.2 C. Aided by the analysis of kinetic behavior of lithium storage and theoretical calculations, the capacity-enhancing mechanism and lithium storage mechanism of covalent organic frameworks are revealed. This work may lead to more research on designable, multifunctional COFs for electrochemical energy storage.

Anterior and posterior imaging with hyperparallel OCT.

Hyperparallel OCT (HP-OCT) is a parallel spectral domain imaging technology particularly well-suited to the anterior segment. It uses a 2-dimensional grid of 1008 beams to simultaneously image across a wide area of the eye. In this paper we demonstrate that sparsely sampled volumes captured at 300 Hz can be registered without the need for active eye tracking to produce 3-dimensional (3D) volumes free from motion artefacts. The anterior volume provides complete 3D biometric information, including lens position, curvature, epithelial thickness, tilt, and axial length. We further demonstrate that, with the change of a detachable lens, we can capture high resolution anterior volumes and importantly, posterior volume images for preoperative assessment of the posterior segment. Advantageously, the retinal volumes have the same 11.2 mm Nyquist range as the anterior imaging mode.

Flamelet LES of a turbulent non-premixed cool flame

Turbulence, low-temperature reactivity, and their couplings as turbulent cool flames are crucial to modern engine designing and low-carbon fuel development. While the flamelet method is a promising solution to turbulent combustion, its applicability and accuracy to cool flames have not been thoroughly comprehended. The objective of the present study is to explore the capability of the steady flamelet method in large eddy simulation (LES) of turbulent cool flames. A laminar counterflow non-premixed cool flame configuration is first simulated on a 2-dimensional grid, showing the good validity of flamelet library setup and table interpolation of the method. Then the application to full-scale turbulent cases of cool combustion is presented with the comparison to the experimental measurements and the referenced direct numerical simulation (DNS) data. This is the first LES of a turbulent cool flame, and the result demonstrates the ability of the method in capturing the mean and variance trends for the temperature, mixture fraction and formaldehyde with good quantitative agreement. Meanwhile, conditional result analysis also shows that this approach in a two-stream flamelet form can describe the three-stream experimental system reasonably well. On this basis, three well-documented reaction mechanisms are employed to examine their performances in flamelet LES of turbulent cool flames. The result reveals that the choice of the chemistry scheme does alter the time-averaged prediction of temperature and formaldehyde, whereas the variance profiles of formaldehyde and mixture fraction are not significantly influenced.

Simulations of External Multi-Particle DLA on the Plane and Connections to the Super-Cooled Stefan Problem

We consider the external multi-particle difusion-limited aggregation (MDLA) process on the 2-dimensional integer grid. In this random growth process, particles are distributed uniformly at random on the grid and undergo a simple symmetric random walk with exclusion. They walk until they contact a collection of particles centered at the origin, at which point they attach. Iterating this process, a cluster forms. Since its inception, DLA models in the plane have resisted rigorous mathematical treatment. Whereas mathematicians have succeeded in establishing scaling limits for other stochastic growth models, this result for DLA process remains elusive. Recent findings in (1) establish a connection between the 1-dimensional MDLA process and solutions to a partial differential equation known as the super-cooled Stefan problem in space dimension (1SSP0. By fully characterizing the solutions to 1SSP, scaling limits for the 1-dimensional MDLA process were proven. It is natural to conjecture that a similar connection holds between 2-dimensional MDLA and SSP in two space dimensions. To address the conjecture, we take a numerical approach. We simulate the 2-dimensional MDLA process by decreasing the grid mesh towards 0. By studying the regularity of the cluster's interior and the statistical properties of its boundary, we show that the 2-dimensinoal MDLA process does not converge to solutions of 2SSP. We discuss why this process fails and propose possible resolutions.

BubbleHeatmap: an R package for visualization of nightingale health metabolomics datasets.

We present bubbleHeatmap, an R plotting package which combines elements of a bubble plot and heatmap to conveniently display two numerical variables for each data point across a categorical two dimensional grid. This has particular advantages for visualizing the 251 metabolomic measures produced by the automated, high-throughput, 1H-NMR-based platform provided by Nightingale Health, which includes 12 measures repeated across each of 14 lipoprotein subclasses. As these metabolomic profiles are currently available for large biobanks, we provide a figure template to aid the use of bubbleHeatmap in displaying results from analyses using these data. https://cran.r-project.org/web/packages/bubbleHeatmap.

Universal scaling of extinction time in stochastic evolutionary dynamics

Evolutionary dynamics is well captured by the replicator equations when the population is infinite and well-mixed. However, the extinction dynamics is modified with finite and structured populations. Experiments on the non-transitive ecosystem containing three populations of bacteria found that the ecological stability sensitively depends on the spatial structure of the populations. Based on the Reference–Gamble–Birth algorithm, we use agent-based Monte Carlo simulations to investigate the extinction dynamics in the rock-paper-scissors ecosystem with finite and structured populations. On the fully-connected network, the extinction time in stable and unstable regimes falls into two universal functions when plotted with the rescaled variables. On the two dimensional grid, the spatial structure changes the transition boundary between stable and unstable regimes but doesn’t change its extinction trend. The finding of universal scaling in extinction dynamics is unexpected, and may provide a powerful method to classify different evolutionary dynamics into universal classes.

Transitions in Computational Complexity of Continuous-Time Local Open Quantum Dynamics.

We analyze the complexity of classically simulating continuous-time dynamics of locally interacting quantum spin systems with a constant rate of entanglement breaking noise. We prove that a polynomial time classical algorithm can be used to sample from the state of the spins when the rate of noise is higher than a threshold determined by the strength of the local interactions. Furthermore, by encoding a 1D fault tolerant quantum computation into the dynamics of spin systems arranged on two or higher dimensional grids, we show that for several noise channels, the problem of weakly simulating the output state of both purely Hamiltonian and purely dissipative dynamics is expected to be hard in the low-noise regime.

Spatial relationships between interaural differences in a room

The interaural ratio, as it occurs for a human head in a room, can be represented by a filter with a complex transfer function of the spatial location of the head. The log of this transfer function has real and imaginary parts, respectively, the interaural level difference (ILD) and the interaural phase difference (IPD). Because the filter is causal, the ILD and IPD spatial functions are Hilbert transforms of each other if the interaural filter is a minimum phase function of the head location. Interaural differences for a spherical “head” with tiny probe microphones, separated by a head diameter of 17.5 cm, were measured by Mr. Zane Crawford in an empty room having a volume of 63 $m∧3$ and a reverberation time of 0.4 s. The head was moved in increments of 2.54 cm over a two dimensional grid 102 cm by 23 cm. Measurements at 250 Hz showed that the ILD and IPD were almost perfectly related by Hilbert transforms. Measurements at 500 and 1000 Hz showed increasing deviations. Because a function is orthogonal to its Hilbert transform, the ideal ILD is orthogonal to the IPD. Therefore, at locations where the ILD is the most stable function of space, the IPD is the most unstable and vice versa.

Centralised connectivity-preserving transformations for programmable matter: A minimal seed approach

We study a model of programmable matter systems consisting of n devices lying on a 2-dimensional square grid which are able to perform the minimal mechanical operation of rotating around each other. The goal is to transform an initial shape A into a target shape B. We investigate the class of shapes which can be constructed in such a scenario under the additional constraint of maintaining global connectivity at all times. We focus on the scenario of transforming nice shapes, a class of shapes consisting of a central line L where for all nodes u in S either u∈L or u is connected to L by a line of nodes perpendicular to L. We prove that by introducing a minimal 3-node seed it is possible for the canonical shape of a line of n nodes to be transformed into a nice shape of n−1 nodes. We use this to show that a 4-node seed enables the transformation of nice shapes of size n into any other nice shape of size n in O(n2) time. We leave as an open problem the expansion of the class of shapes which can be constructed using such a seed to include those derived from nice shapes.

Angle-incremental range estimation for FDA-MIMO radar via hybrid sparse learning

In this paper, a target parameter estimation problem is addressed for the recently emerging frequency diverse array multiple-input multiple-output (FDA-MIMO) radar system, utilizing sparse learning. The scene is modeled as a two dimensional (2D) angle-incremental range grid. To solve the resulting sparse problem, the recently proposed user-parameter free algorithms including block sparse learning via iterative minimization (BSLIM), iterative adaptive approach (IAA), sparse iterative covariance-based estimation (SPICE), likelihood-based estimation of sparse parameters (LIKES), and orthogonal matching pursuit (OMP) are applied which achieve excellent parameter estimation performance. However, these algorithms do not exhibit a uniform performance under different scenarios such as the number of available snapshots and the number of present targets. In this paper, we propose a hybrid estimation approach which utilizes the model order selection (MOS), and automatically selects the best algorithm for the scenario under test. The performance analyses show that the proposed hybrid algorithm presents higher accuracy in terms of root mean square error (RMSE), as compared with the discussed sparse algorithms, and converges to the Cramér-Rao lower bound (CRLB).

Extending FEniCS to work in higher dimensions using tensor product finite elements

We present a method to extend the finite element library FEniCS to solve problems with domains in dimensions above three by constructing tensor product finite elements. This methodology only requires that the high dimensional domain is structured as a Cartesian product of two lower dimensional subdomains. In this study we consider Dirichlet problems for scalar linear partial differential equations, though the methodology can be extended to non-linear problems. The utilization of tensor product finite elements allows us to construct a global system of linear algebraic equations that only relies on the finite element infrastructure of the lower dimensional subdomains contained in FEniCS. We demonstrate the effectiveness of our methodology in four distinctive test cases. The first test case is a Poisson equation posed in a four dimensional domain which is a Cartesian product of two unit squares solved using the classical Galerkin finite element method. The second test case is the wave equation in space–time, where the computational domain is a Cartesian product of a two dimensional space grid and a one dimensional time interval. In this second case we also employ the Galerkin method. The third test case is an advection dominated advection–diffusion equation where the global domain is a Cartesian product of two one dimensional intervals in which the streamline upwind Petrov–Galerkin method is applied to ensure discrete stability. The final test case uses the Galerkin approach to solve a Poisson problem on a Cartesian product of two intervals with a spatially varying, non-separable diffusivity term In all cases, a p=1 basis is used and optimal L2 convergence rates of order hp+1 of the errors are achieved with respect to h refinement.

Cylindrical wave excitation of a chiral cylindrical object covered with a metasurface

Cylindrical wave scattering characteristics of an infinite chiral cylindrical object of circular cross section and covered with a metasurface has been studied numerically. The field expressions inside a chiral cylindrical object have been derived using the wave field decomposition approach. Analytic expressions of expansion coefficients inside chiral cylinder and scattering coefficients outside chiral cylinder have also been derived in the simplest forms. The influences of chirality parameter, surface reactance of metasurface and locations of cylindrical wave source upon scattering gain have been investigated. It is studied that by varying the chirality and surface reactance, one can significantly control the scattering gain. The proposed theory is also extended to the two dimensional strip grid metasurface covered frequency dispersive chiral cylinder. It is found that the specifically designed two dimensional strip grid metasurface can be used to significantly reduce the back scattering gain from a chiral cylinder at a certain frequency of interest.

The multicolored graph realization problem

We introduce the multicolored graph realization problem (MGR). The input to this problem is a colored graph (G,φ), i.e., a graph G together with a coloring φ on its vertices. We associate each colored graph (G,φ) with a cluster graph (Gφ) in which, after collapsing all vertices with the same color to a node, we remove multiple edges and self-loops. A set of vertices S is multicolored when S has exactly one vertex from each color class. The MGR problem is to decide whether there is a multicolored set S so that, after identifying each vertex in S with its color class, G[S] coincides with Gφ.The MGR problem is related to the well-known class of generalized network problems, most of which are NP-hard, like the generalized Minimum Spanning Tree problem. The MGR is a generalization of the multicolored clique problem, which is known to be W[1]-hard when parameterized by the number of colors. Thus, MGR remains W[1]-hard, when parameterized by the size of the cluster graph. These results imply that the MGR problem is W[1]-hard when parameterized by any graph parameter on Gφ, among which lies treewidth. Consequently, we look at the instances of the problem in which both the number of color classes and the treewidth of Gφ are unbounded. We consider three natural such graph classes: chordal graphs, convex bipartite graphs and 2-dimensional grid graphs. We show that MGR is NP-complete when Gφ is either chordal, biconvex bipartite, complete bipartite or a 2-dimensional grid. Our reductions show that the problem remains hard even when the maximum number of vertices in a color class is 3. In the case of the grid, the hardness holds even for graphs with bounded degree. We provide a complexity dichotomy with respect to cluster size.

The Number of $k$-Dimensional Corner-Free Subsets of Grids

A subset $A$ of the $k$-dimensional grid $\{1,2, \dots, N\}^k$ is said to be $k$-dimensional corner-free if it does not contain a set of points of the form $\{ \textbf{a} \} \cup \{ \textbf{a} + de_i : 1 \leq i \leq k \}$ for some $\textbf{a} \in \{1,2, \dots, N\}^k$ and $d > 0$, where $e_1,e_2, \ldots, e_k$ is the standard basis of $\mathbb{R}^k$. We define the maximum size of a $k$-dimensional corner-free subset of $\{1,2, \ldots, N\}^k$ as $c_k(N)$. In this paper, we show that the number of $k$-dimensional corner-free subsets of the $k$-dimensional grid $\{1,2, \dots, N\}^k$ is at most $2^{O(c_k(N))}$ for infinitely many values of $N$. Our main tools for proof are the hypergraph container method and the supersaturation result for $k$-dimensional corners in sets of size $\Theta(c_k(N))$.

Stochastic approximation of lamplighter metrics

We observe that embeddings into random metrics can be fruitfully used to study the L 1 $L_1$ -embeddability of lamplighter graphs or groups, and more generally lamplighter metric spaces. Once this connection has been established, several new upper bound estimates on the L 1 $L_1$ -distortion of lamplighter metrics follow from known related estimates about stochastic embeddings into dominating tree-metrics. For instance, every lamplighter metric on an n $n$ -point metric space embeds bi-Lipschitzly into L 1 $L_1$ with distortion O ( log n ) $O(\log n)$ . In particular, for every finite group G $G$ the lamplighter group H = Z 2 ≀ G $H=\mathbb {Z}_2\wr G$ bi-Lipschitzly embeds into L 1 $L_1$ with distortion O ( log log | H | ) $O(\log \log |H|)$ . In the case where the ground space in the lamplighter construction is a graph with some topological restrictions, better distortion estimates can be achieved. Finally, we discuss how a coarse embedding into L 1 $L_1$ of the lamplighter group over the d $d$ -dimensional infinite lattice Z d $\mathbb {Z}^d$ can be constructed from bi-Lipschitz embeddings of the lamplighter graphs over finite d $d$ -dimensional grids, and we include a remark on Lipschitz free spaces over finite metric spaces.