Exact Representation Research Articles

Sequential topology and shape optimization framework to design compliant mechanisms with boundary stress constraints

We present a sequential topology and shape optimization framework to design compliant mechanisms with boundary stress constraints. In our approach, a density-based topology optimization method is used to generate the configuration of the mechanisms. Afterwards, a node-based shape optimization is invoked to obtain an exact boundary representation. A specialized, optimality criteria-based design update is formulated for the shape optimization. To avoid impractical hinges with point connections, stress constraints are imposed. The stress constraints are imposed using two strategies: Local stress constraints on the nodes of the boundary or global P-norm stress constraints in the domain. Further, an adaptive shape refinement strategy is adopted to increase the design space of shape optimization and to capture the fine-scale details of the geometry. Finally, numerical experiments are presented, showing that the proposed approach can be effectively applied to the design of compliant mechanisms with stress constraints.

Learning the Rules of the Game: An Interpretable AI for Learning How to Play

In this article, we present an interpretable artificial intelligence, and its associated machine learning algorithm, that is capable of automatically learning the rules of a game whenever the rules&#x2014;the relationship between a player&#x2019;s current state and their corresponding set of legal moves&#x2014;can be represented as a set of low degree Zhegalkin polynomials, a special class of Boolean functions. This is true for many popular games including <i>Spanish Domin&#x00F3;</i> and the card game <i>President</i>. Our method takes advantage of such low polynomial degree to compute an exact representation of the rules in polynomial time instead of the required exponential time for generic Boolean functions. The rules can also be represented using significantly less storage than in the generic case which, for many games, leads to a representation that is easy to interpret.

A Second Look at the Illustration of Matthew 2:11 in Selected Ghanaian Bibles

One of the ways to make the word of God become relevant in a new culture is through Bible translation and illustration. Some Ghanaian Bibles with illustrations enable local indigenes to understand the word of God in their language and give them a pictorial view of the written text. However, there seem to be some illustrations that do not give a precise description of the corresponding texts. One of such is the illustration of Matthew 2:11. Using exegesis and Erwin Panofsky’s iconographic analysis approaches, it was identified that the illustration does not give an exact representation of the text. Hence, the Bible Society of Ghana must either drop the current illustration on Matthew 2:11 or come out with a new illustration that meets the religio-cultural settings and the text of the author. For illustrations to meet both the text of the author and the religio-cultural background of the local indigenes, proposals were outlined for consideration.

On the analytically-improved running coupling in QCD

In this paper, we examine, in the ’t Hooft renormalization scheme, the analytic running coupling [Formula: see text] in QCD, using the two-loop [Formula: see text]-function with positive expansion parameters [Formula: see text] and [Formula: see text]. An exact integral representation is derived for this causal coupling, which is fully expressed in terms of the imaginary part of the Lambert function [Formula: see text]. This integral form manifestly accounts for the universal value of the infrared limit [Formula: see text].

Specters of the Colony

SUMMARYThis story is a wander—walking through conversation, histories, and the beach‐side city of Swakopmund, Namibia—guided by Daniel, a young man I spent much time with while in Swakopmund conducting fieldwork. Written from memory but aided by one particularly evocative recording, photographs, and a field diary, the story points to different experiences and histories that lie beyond the surface of the everyday: ghosts hidden in buildings, people, and the spaces and gaps between them. Even if they are not exact representations of the events being told, all stories are grounded in truth.

Quantum features of nonlinear coupler with competing nonlinearity

In this work, we examine the quantum features of a multi-waveguide nonlinear coupler exploiting the second-and third-order nonlinearities. The considered system contains four identical channels, each with a single fundamental transverse mode. The essence of this type of nonlinear coupler is to examine the effect of two or more competing nonlinearities on the generated nonclassical features in this class of devices. Here, we consider the case of second harmonic generation, wherein the fundamental harmonic (FH) fields are up-converted in pairs to double-frequency second harmonic (SH) fields, which are then evanescently coupled with the fields from other Kerr nonlinear waveguides. Using the positive P representation of the phase space, the time-evolution of the density matrix could be mapped to the corresponding Fokker–Planck equation of a classical quasiprobability distribution. Using Langevin stochastic equation, an exact representation of the system in phase space led to the demonstration of sub-Poissonian property, squeezing, and entanglement. With more effective squeezing achieved in all channel waveguides, the present system with χ(2)–χ(3) interaction can be a more efficient alternative to other versions of nonlinear couplers such as the quantum optical dimer (QOD) and Kerr nonlinear coupler (KNC). Furthermore, such a structure offers more flexibility in coupled-mode interactions in the form of correlation between the modes in different waveguides. This provides a better mechanism for the generation of enhanced nonclassical effects.

Bifurcations and Exact Traveling Wave Solutions in the Generalized Sasa–Satsuma Equation

This paper studies traveling wave solutions of a generalized Sasa–Satsuma equation introduced in [Adem et al., 2020]. For the cases of [Formula: see text], under given parameter conditions, the bifurcations of traveling wave solutions in the parameter space are investigated for the corresponding traveling systems. All possible explicit exact parametric representations of various solutions are obtained.

An Analytic Element Model for Intersecting and Heterogeneous Fractures in Groundwater Flow

AbstractIntersecting fractures often dominate the rock though which groundwater flows and they represent a crucial feature in groundwater models. In this paper, limitless analytic elements were used to model intersecting and heterogeneous fractures with either high or low transmissivity relative to that of the surrounding medium. To handle the singular behavior at the intersections, fractures were modeled as multiple elements, the tips of which meet at the point of intersection. The same approach was used to model heterogeneous fractures where the transmissivity is discontinuous along a fracture. Representing the fractures analytically in the continuum allows for an exact representation of the groundwater exchange between the fractures and the continuum. Thereby producing an accurate model of flow through a network of fractures in a continuum. This solution is capable of accurately computing the groundwater flow for both a network of fractures with a high transmissivity and an assembly of heterogeneous fractures near a tunnel.

Exact matrix product state representation and convergence of a fully correlated electronic wavefunction in the infinite-basis limit

In this paper we present the exact representation of a fully correlated electronic wavefunction as the single-particle basis approaches completeness. It consists of a half-infinite chain of matrices of exponentially increasing size. The complete basis limit is illustrated numerically using the density-matrix renormalization-group method by computing the core-valence entanglement in the ${\mathrm{C}}_{2}$ ground state in increasing subsets of cc-pVTZ and pVQZ bases until convergence is reached.

Discrete analysis of Schwarz waveform relaxation for a diffusion reaction problem with discontinuous coefficients

In this paper, we investigate the effect of the space and time discretisation on the convergence properties of Schwarz Waveform Relaxation (SWR) algorithms. We consider a reaction-diffusion problem with discontinuous coefficients discretised on two non-overlapping domains with several numerical schemes (in space and time). A methodology to determine the rate of convergence of the classical SWR method with standard interface conditions (Dirichlet-Neumann or Robin-Robin) accounting for discretisation errors is presented. We discuss how such convergence rates differ from the ones derived at a continuous level (i.e. assuming an exact discrete representation of the continuous problem). In this work we consider a second-order finite difference scheme and a finite volume scheme based on quadratic spline reconstruction in space, combined with either a simple backward Euler scheme or a two-step “Padé” scheme (resembling a Diagonally Implicit Runge Kutta scheme) in time. We prove those combinations of space-time schemes to be unconditionally stable on bounded domains. We illustrate the relevance of our analysis with specifically designed numerical experiments.

Modular Arithmetic CPM for SDR Platforms

This brief presents a new Continuous Phase Modulation (CPM) module for multi- <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$h$ </tex-math></inline-formula> transmission based on modular arithmetic processing. It is well known that CPM systems are sensitive to changes in the modulation index, which is implied when fixed-point format is used in the hardware implementation. In this scenario, modular arithmetic allows a more accurate signal processing regarding SQNR performance. This proposal has been shown to improve performance compared to other state-of-the-art methods, even when the modulation indices do not have an exact representation in a given fixed-point format. Due to its highly reconfigurable architecture, this hardware block is suitable for Software Defined Radio (SDR) platforms. A complete digital architecture is also provided. Implementation results show that the new proposal have clear advantages in terms of hardware resources and operating frequency against other CPM transmitters in open-literature.

Bifurcations, Exact Peakon, Periodic Peakons and Solitary Wave Solutions of the Modified Camassa–Holm Equation

For the modified Camassa–Holm equation, by using the methodologies of dynamical systems and singular traveling wave theory developed by Li and Chen [2007] to its corresponding traveling wave system, under different parameter conditions, all possible exact explicit bounded solutions (solitary wave solutions, periodic wave solutions, peakon, periodic peakons, as well as compactons) are obtained. More than 23 explicit exact parametric representations of the above-mentioned traveling wave system are presented.

High order local farfield expansions absorbing boundary conditions for multiple scattering

In this paper, we derive high order and local absorbing boundary conditions (ABC) for two- and three-dimensional multiple acoustic scattering problems. For this purpose, we employ Karp and Wilcox farfield expansions, which are exact representations of purely outgoing waves in two- and three-dimensions, respectively. We seek solutions of multiple scattering problems for scatterers of arbitrary shape in both homogeneous and locally inhomogeneous media by assuming that each scatterer and its surrounding inhomogeneity (if any) can be well-separated by artificial boundaries from the other scatterers. As a consequence, the computational domain is reduced to the union of relatively small disjoint subdomains bounded in the interior by a scatterer boundary and in the exterior by a circular (2D) or spherical (3D) artificial boundary. The novel ABC is defined at these artificial boundaries by considering continuities of the scattered field and its derivatives at the artificial boundaries and by representing the scattered wave as a superposition of outgoing waves from each subdomain. Finally, we numerically solve the new bounded boundary value problem for numerous examples including complexly shaped obstacles, such as prototype submarines and aircrafts. Accurate results are obtained at relatively low computational cost for problems in both homogeneous and inhomogeneous media.

Ultrasound evaluation of interstitial lung disease in rheumatoid arthritis and autoimmune diseases.

The interpretation of lung ultrasound (US) is the result of the analysis of artifacts, rather than exact representations of anatomical structures, which appear when changes in the physical properties of the lung occur. Its application to the study of interstitial lung disease (ILD) associated with autoimmune diseases has aroused great interest in the last 10 years, as evidenced by a growing number of publications studying its usefulness in the diagnostic process, as a prognostic marker, and as an aid in monitoring of patients. The main elements in lung US interpretation in ILD are the B lines and the changes in the pleural line. B lines are vertical artifacts that are generated when there is a partial decrease in the air content of the lung parenchyma and/or the volume of the interstitial area expands. Pleural line alterations that can be seen are irregularities, thickening, fragmentation, or subpleural nodules. Both the B lines and the changes in the pleural line have shown a significant positive correlation with the evidence on chest computed tomography (high-resolution computed tomography [HRCT]) of ILD associated with autoimmune diseases, with sensitivity and negative predictive values of up to 100%. These results, together with the safety, accessibility, and low cost of lung US, support this imaging technique as a promising screening method for optimizing the indication for HRCT. The role of lung US regarding sensitivity to change needs further investigation with multicenter prospective studies.

Effective persistency evaluation via exact excursion distributions for random processes and fields

Finding the probability that a stochastic system stays in a certain region of its state space over a specified time—a long-standing problem both in computational physics and in applied and theoretical mathematics—is approached through the extended and multivariate Rice formula. In principle, it applies to any smooth process multivariate both in argument and in value given that efficient numerical implementations of the high-dimensional integration are available. The computational method offers an exact integral representation yielding remarkably accurate results and provides an alternative method of computing persistency probability and exponent for a physical system. It can be viewed as an implementation of path integration for a smooth Gaussian process with an arbitrary covariance. Its high accuracy is due to efficient computation of expectations with respect to high-dimensional nearly singular Gaussian distributions. For Gaussian processes, the computations are effective and more precise than those based on the Rice series expansions and the independent interval approximation. For the benchmark diffusion process, it produces the persistency exponent that is essentially the same as the recently obtained analytical value and surpasses accuracy, interpretability as well as control of the error, previous methods including the independent or Markovian approximation. The method solves the two-step excursion dependence for a stationary differentiable Gaussian process, in both theoretical and numerical sense. The solution is based on exact expressions for the probability density for one and two successive excursion lengths. The numerical routine RIND computes the densities using recent advances in scientific computing and is easily accessible for a general covariance function, via a simple numerical interface. The work offers also analytical results that explain the effectiveness of the implemented methodology and elaborates its utilization for non-Gaussian processes.

A Branch and Bound Algorithm to Solve Travelling Salesman Problem (TSP) with Uncertain Parameters

The core of the theoretical Computing science and mathematics is computational complexity theory. It is usually concerned with the classification of computational problems in to P and NP problems by using their inherent challenges. There is no efficient algorithms for these problems. Travelling Salesman Problem is one of the most discussed problems in Combinatorial Mathematics. To deduct a Hamiltonian cycle in which the cost or time is minimum is the main objective of the TSP. There exist many algorithms to solve it. Since all the existing algorithms are not efficient to solve it, still many researchers are working to produce efficient algorithms. If the description of the parameters is vague, then fuzzy notions which include membership value are applied to model the parameters. Still the modeling does not give the exact representation of the vagueness. The Intuitionistic fuzzy set which includes non-membership value along with membership values in its domain is applied to model the parameters. The decision variables in the TSP, the cost, time or distance are modeled as intuitionistic fuzzy numbers, then the TSP is named as Intuitionistic fuzzy TSP (InFTSP). We develop the intuitionistic fuzzified version of littlewood's formula or branch and bound method to solve the Intuitionistic fuzzy TSP. This method is effective because it involves the simple arithmetic operation of Intuitionistic fuzzy numbers and ranking of intuitionistic fuzzy numbers. Ordering of intuitionistic fuzzy numbers is vital in optimization problems since it is equivalent to the ordering of alternatives. In this article, we used weighted arithmetic mean method to order the fuzzy numbers. Weighted arithmetic mean method satisfies linear property which is a very important characteristic of ranking function. Numerical examples are solved to validate the given algorithm and the results are discussed.

Isogeometric semi-Lagrangian analysis for transport problems

Isogeometric analysis (IGA) is combined with the semi-Lagrangian scheme to develop a stable and highly accurate method for the numerical solution of transport problems. An L2 projection using the non-uniform rational B-splines (NURBS) is proposed for the approximation of the solution at the departure points. The proposed method maintains the advantages of the semi-Lagrangian scheme in reducing the truncation errors and allowing for large CFL numbers in the simulations while the IGA guarantees the exact representation of the geometry of the computational domain. The performance of the isogeometric semi-Lagrangian analysis is demonstrated for a deformational flow problem and the benchmark of a single vortex flow.

Magnitude and sources of proactive interference in visual memory

ABSTRACT Proactive interference – the disruptive effect of old memories on new learning – is a long-established forgetting mechanism, yet there are doubts about its impact on visual working memory and uncertainty about the kinds of information that cause proactive interference. The present study aimed to assess these issues in three experiments using a modified recent probes task. Participants encoded four target images on each trial and determined whether a probe matched one of those targets. In Experiment 1, probes matching targets from trial N-1 or N-3 damaged responding in relation to a novel probe. Proactive interference was also produced by probes differing in state to a previously experienced target. This was further assessed in Experiments 2 and 3. Here, probes differing in colour to a previous target, or matching the general target category only, produced little proactive interference. Conversely, probes directly matching a prior target, or differing in state information, hindered task performance. This study found robust proactive interference in visual working memory that could endure over multiple trials, but it was also produced by stimuli closely resembling an old target. This challenges the notion that proactive interference is produced by an exact representation of a previously encoded image.

Analytical Design of Conventional and Electrical Aircraft Environmental Control Systems

Environmental control systems hold vital importance as they are responsible for aircraft cabin air ventilation and passenger comfort. This paper presents an analytical design of both Conventional & Electrical environmental control systems. The result of the estimated design is represented in a geometrical model that gives freedom to visualize various options in the conceptual design process, using Knowledge-based engineering application as a base for the design and methodology. Flexibility in the model enables the user to control the size and positioning of the system and sub-systems associated with it. The number of passengers serves as the driving input and the three-dimensional model gives the exact representation concerning the volume occupied and dependencies on the number of passengers. It also provides a faster method to alter the system to user needs with respect to the number of air supply pipes, number of ducts, and pipe length.

Scattering of surface waves by a vertical truncated structured cylinder.

This paper describes the solution to the problem of scattering of plane incident waves on water of constant depth by a bottom mounted circular cylinder, extending partially through the depth, which has an internal structure comprised of closely spaced thin vertical barriers between which fluid is allowed to flow. The problem is solved under full depth-dependent linearized water wave theory using an effective medium equation to describe the fluid motion in cylinder and effective boundary conditions to match that flow to the fluid region outside the cylinder. The interest in this problem lies in the development of novel solution methods for fully three-dimensional water wave interaction with bathymetric plate arrays. Results computed using this theory are compared with a shallow water approximation based on the recent work of Marangos & Porter (2021 Shallow water theory for structured bathymetry. Proc. R. Soc. A 477, 20210421.) and with accurate computations of an exact representation of the geometry using a discrete set of plates. Other results highlight the resonant directional lensing effects of this type of cylindrical plate array device.