General Notation Research Articles

Experimental validation of an inverse method for defect reconstruction in a two-dimensional waveguide model.

Defect reconstruction is essential in non-destructive testing and structural health monitoring with guided ultrasonic waves. This paper presents an algorithm for reconstructing notches in steel plates, which can be seen as artificial defects representing cracks by comparing measured results with those from a simulation model. The model contains a parameterized notch, and its geometrical parameters are to be reconstructed. While the algorithm is formulated and presented in a general notation, a special case of guided wave propagation is used to investigate one of the simplest possible simulation models that discretizes only the cross section of the steel plate. An efficient simulation model of the plate cross section is obtained by the semi-analytical scaled boundary finite element method. The reconstruction algorithm applied is gradient-based, and algorithmic differentiation calculates the gradient. The dedicated experimental setup excites nearly plane wave fronts propagating orthogonal to the notch. A scanning laser Doppler vibrometer records the velocity field at certain points on the plate surface as input to the reconstruction algorithm. Using two plates with notches of different depths, it is demonstrated that accurate geometry reconstruction is possible.

Biot-consistent framework for wave propagation with macroscopic fluid and thermal effects

SUMMARY In principle, wave propagation in porous media can simultaneously trigger macroscopic fluid flow and thermal flow, which can be described by Biot's poroelasticity and Lord–Shulman thermoelasticity, respectively. The physical processes of those effects are significantly different, but phenomenologically, they can lead to identical wave attenuation and dispersion and are hard to be distinguished. By using Biot's virtual concept entropy flow, the Biot-consistent General Linear Solid (the GLS) framework and matrix notation, a rigorous and convenient tool is provided to reveal the similarities and disparities between poroelasticity and thermoelasticity. By using the same framework, a Biot-consistent thermo-poroelastic model is proposed to consider macroscopic effects of fluid and thermal flows simultaneously in an elegant way. These similarities allow us to directly translate many of the available results in poroelasticity to thermoelasticity and vice versa by a simple change of notation. The disparities indicate a fundamental difference in physical mechanisms. Plane-wave analysis shows that the primary P-wave modes of thermoelasticity and poroelasticity are all GSLS-equivalent (Generalized Standard Linear Solid) and can be identical if the model parameters are selected properly. However, the corresponding slow-wave modes have significantly different phase velocity dispersion although the attenuation spectra of which are identical. Such a surprising result can be explained by the GSLS non-equivalence of the slow-wave modes and the fundamentally different mechanisms. As expected, the thermo-poroelastic model predicts four wave modes, which are the fast- and slow-P, temperature (T wave) and S waves. Two attenuation peaks due to, respectively, the thermal- and fluid-flow effects are predicted for the fast-P wave. The slow-P wave mode due to fluid flow is influenced by the thermal effects, but the T wave seems unaffected by the fluid flow. The thermo-poroelastic model is then applied to laboratory observations at 200–106 Hz for the brine-saturated tight sandstone under 35 MPa effective pressure. The unified model provides a convenient framework for studying geothermal exploration, thermal-enhanced oil recovery and other applications involving temperature variations within the porous rock.

Evaluating cancer screening programs using survival analysis.

The main purpose of cancer screening programs is to provide early treatment to patients that are diagnosed with cancer on a screening test, thus increasing their chances of survival. To test this hypothesis directly, one should compare the survival of screen-detected cases to the survival of their counterparts not included to the program. In this study, we develop a general notation and use it to formally define the comparison of interest. We explain why the naive comparison between screen-detected and interval cases is biased and show that the total bias that arises in this case can be decomposed as a sum of lead time bias, length time bias, and bias due to overdetection. With respect to the estimation, we show what can be estimated using existing methods. To fill in the missing gap, we develop a new nonparametric estimator that allows us to estimate the survival of the control group, that is, the survival of cancer cases that would be screen-detected among those not included to the program. By joining the proposed estimator with existing methods, we show that the contrast of interest can be estimated without neglecting any of the biases. Our approach is illustrated using simulations and empiricaldata.

What is This Thing Called Adat Logic?

The notion of adat (or custom) law does not encourage people in philosophy to reveal its logic. This article aims to investigate the possibility of adat logic, its variety, and a possible common ground or thesis among its own kinds. In general, the adat logic means the true contradiction between the rigidity and the reflexibility of custom. In other words, it resembles the idea of dialetheia in modern logic, but it does not mean that the adat logic is a subdivision of the former. To seek a thesis of adat logic is to discuss the Javanese and Minangkabaunese adat logics, and I transform both logics into some notations for the sake of avoiding unnecessary linguistic challenges and hurdles. Thus, I insert each notation of a particular adat logic into the general notation of adat logic. By doing so, I wish to discover a common ground between some different adat logics.

Temporal Models for Demographic and Global Health Outcomes in Multiple Populations: Introducing a New Framework to Review and Standardise Documentation of Model Assumptions and Facilitate Model Comparison.

There is growing interest in producing estimates of demographic and global health indicators in populations with limited data. Statistical models are needed to combine data from multiple data sources into estimates and projections with uncertainty. Diverse modelling approaches have been applied to this problem, making comparisons between models difficult. We propose a model class, Temporal Models for Multiple Populations (TMMPs), to facilitate both documentation of model assumptions in a standardised way and comparison across models. The class makes a distinction between the process model, which describes latent trends in the indicator interest, and the data model, which describes the data generating process of the observed data. We provide a general notation for the process model that encompasses many popular temporal modelling techniques, and we show how existing models for a variety of indicators can be written using this notation. We end with a discussion of outstanding questions and future directions.

The mid‐point Green‐Gauss gradient method and its efficient implementation in a 3D unstructured finite volume solver

AbstractTo achieve consistent second‐order spatial accuracy in cell‐centered finite volume methods using the divergence theorem, the gradient computation at the cell‐centers should at least be first‐order accurate, which is not assured by the Traditional Green‐Gauss (TGG) method on irregular meshes. The Circle Green‐Gauss (CGG) method, however, achieves this by constructing a new auxiliary volume (AV) around the cell of interest using a circle and then employs linear interpolation to obtain estimates of the solution at the face centers of this AV, which are then used to compute the cell‐center gradients. We propose a modified method, which we call the mid‐point Green‐Gauss method (mpGG), that alleviates the complexity in the implementation while maintaining the same accuracy as the CGG method. We offer detailed construction of the three‐dimensional AV for the most commonly used multi‐hydral elements in unstructured meshes, that is, hexahedral, pyramidal, prism, and tetrahedral cells, using an in‐house finite volume solver that reads and writes data based on the computational fluid dynamics (CFD) General Notation System (CGNS). Accuracy analysis of the proposed method is carried out in comparison with the TGG, CGG, and weighted least squares methods. The proposed method is further validated using the case of laminar flow over a sphere at a Reynolds number of 100. An inviscid vortex dissipation study is performed to compare the level of numerical dissipation produced by these methods. Further, we study the performance of these methods in a problem that involves turbulent shock‐wave boundary layer interaction.

ParTransgrid: A scalable parallel preprocessing tool for unstructured‐grid cell‐centered computational fluid dynamics applications

AbstractThe development of a basic scalable preprocessing tool is the key routine to accelerate the entire computational fluid dynamics (CFD) workflow toward the exascale computing era. In this work, a parallel preprocessing tool, called ParTransgrid, is developed to translate the general grid format like CFD General Notation System into an efficient distributed mesh data format for large‐scale parallel computing. Through ParTransgrid, a flexible face‐based parallel unstructured mesh data structure designed in Hierarchical Data Format can be obtained to support various cell‐centered unstructured CFD solvers. The whole parallel preprocessing operations include parallel grid I/O, parallel mesh partition, and parallel mesh migration, which are linked together to resolve the run‐time and memory consumption bottlenecks for increasingly large grid size problems. An inverted index search strategy combined with a multi‐master‐slave communication paradigm is proposed to improve the pairwise face matching efficiency and reduce the communication overhead when constructing the distributed sparse graph in the phase of parallel mesh partition. And we present a simplified owner update rule to fast the procedure of raw partition boundaries migration and the building of shared faces/nodes communication mapping list between new sub‐meshes with an order of magnitude of speed‐up. Experiment results reveal that ParTransgrid can be easily scaled to billion‐level grid CFD applications, the preparation time for parallel computing with hundreds of thousands of cores is reduced to a few minutes.

Performance comparison among the variants of curved serpentine coil

In the present work, two variants of the novel curved serpentine coil formed by relaxing the switching angle at the junctions are explored and compared with the original design for the same mean radius Rm of concentric tubes. With α as the semi-cone angle and θ as the subtended angle of concentric tubes, the general notation given to different variants of the curved serpentine coil is CS-α-θ. The three variants are named as a cylindrical curved serpentine coil (α = 0°), conical curved serpentine coil (0° < α < 90°), and spiral curved serpentine coil (α = 90°). The fluid experiences a switching angle of 90° − α and 90° + α at the entrance and exit of every U-bend, respectively. The laminar flow of water in CS-α-θ coils (45° ≤ θ ≤ 270°, 0° ≤ α ≤ 90°) is simulated using ANSYS FLUENT version 20.2 for the range 500 ≤ Re ≤ 2000. The length-averaged Nu and f are found to decrease with an increase in either α or θ for the same mean radius Rm of concentric tubes. Secondary flow intensity is quantified using the parameter Se and is correlated with the flow and geometric parameters. Generalized correlations for predicting the average Nusselt number and friction factor for CS-α-θ coils are expressed as the sum of corresponding straight tube values and as a function of Se with a maximum deviation of ±8.5% and ±7%, respectively.

Signal estimation in on/off measurements including event-by-event variables

Signal estimation in the presence of background noise is a common problem in several scientific disciplines. An ``on/off'' measurement is performed when the background itself is not known, being estimated from a background control sample. The ``frequentist'' and Bayesian approaches for signal estimation in on/off measurements are reviewed and compared, focusing on the weakness of the former and on the advantages of the latter in correctly addressing the Poissonian nature of the problem. In this work, we devise a novel reconstruction method, Bayesian analysis including single-event likelihoods (dubbed BASiL), for estimating the signal rate based on the Bayesian formalism. It uses information on event-by-event individual parameters and their distribution for the signal and background population. Events are thereby weighted according to their likelihood of being a signal or a background event and background suppression can be achieved without performing fixed fiducial cuts. Throughout the work, we maintain a general notation that allows us to apply the method generically and provides a performance test using real data and simulations of observations with the MAGIC telescopes, as a demonstration of the performance for Cherenkov telescopes. BASiL allows one to estimate the signal more precisely, avoiding loss of exposure due to signal extraction cuts. We expect its applicability to be straightforward in similar cases.

A Survey of Moving Target Defenses for Network Security

Network defenses based on traditional tools, techniques, and procedures (TTP) fail to account for the attacker’s inherent advantage present due to the static nature of network services and configurations. To take away this asymmetric advantage, Moving Target Defense (MTD) continuously shifts the configuration of the underlying system, in turn reducing the success rate of cyberattacks. In this survey, we analyze the recent advancements made in the development of MTDs and highlight (1) how these defenses can be defined using common terminology, (2) can be made more effective with the use of artificial intelligence techniques for decision making, (3) be implemented in practice and (4) evaluated. We first define an MTD using a simple and yet general notation that captures the key aspects of such defenses. We then categorize these defenses into different sub-classes depending on what they move, when they move and how they move. In trying to answer the latter question, we showcase the use of domain knowledge and game-theoretic modeling can help the defender come up with effective and efficient movement strategies. Second, to understand the practicality of these defense methods, we discuss how various MTDs have been implemented and find that networking technologies such as Software Defined Networking and Network Function Virtualization act as key enablers for implementing these dynamic defenses. We then briefly highlight MTD test-beds and case-studies to aid readers who want to examine or deploy existing MTD techniques. Third, our survey categorizes proposed MTDs based on the qualitative and quantitative metrics they utilize to evaluate their effectiveness in terms of security and performance. We use well-defined metrics such as risk analysis and performance costs for qualitative evaluation and metrics based on Confidentiality, Integrity, Availability (CIA), attack representation, QoS impact, and targeted threat models for quantitative evaluation. Finally, we show that our categorization of MTDs is effective in identifying novel research areas and highlight directions for future research.

Systematic use of velocity and acceleration coefficients in the kinematic analysis of single-DOF planar mechanisms

In single-degree-of-freedom (DOF) mechanisms, velocity coefficients (VCs) and their 1st derivative with respect to the generalized coordinate (acceleration coefficients (ACs)) only depend on the mechanism configuration. In addition, if the mechanism is a planar linkage (i.e., a mechanism containing only lower pairs), complex numbers are an easy-to-use tool for writing linkage's loop equations that are formally differentiable and are the only constraint equations of linkages. Actually, the use of complex numbers for systematically writing the constraint equations of planar mechanisms is often limited to linkages. The possible presence of higher pairs in these mechanisms is usually managed through either equivalent linkages or apparent velocity/acceleration equations. Both these methods are simple to implement for a single mechanism configuration, but become cumbersome when continuous motion has to be analyzed. Other approaches use ad hoc auxiliary equations. Here, first, a general notation that brings to select particular auxiliary equations is proposed; then, such notation is adopted to propose an algorithm that systematically uses VCs and ACs for solving the kinematic-analysis problems of single-DOF planar mechanisms. The proposed notation and algorithm, over being efficient enough for constituting the kinematic block of any dynamic model of these mechanisms, are easy to present planar kinematics, with the complex-number method extended to higher pairs, in graduate and/or undergraduate courses.

Nonuniform (h,k,μ,ν)-dichotomy with applications to nonautonomous dynamical systems

The paper develops a more general notion of dichotomy, referred to as “nonuniform (h,k,μ,ν)-dichotomy”. The new notion unifies most versions of existing dichotomy in the literature, includes them in one comprehensive mathematics, and reveals more dichotomic behaviors of dynamical systems. Then we show that any linear nonautonomous system admits a nonuniform (h,k,μ,ν)-dichotomy if it has an (h,k) Lyapunov exponent with different signs or a Lyapunov function with different growth rates in the stable and unstable subspaces of solutions. This implies that the nonuniform (h,k,μ,ν)-dichotomy arises naturally and exists widely in the linear systems. Using the general notation, new versions of robustness, Hartman–Grobman theorem, and stable invariant manifold theorem for nonautonomous dynamical systems in Banach spaces will be presented. Especially, these new results not only generalize the corresponding ones in the literature, but also characterize the influences of different growth functions in the stable and unstable subspaces and in the uniform and nonuniform parts of a linear system for solving the above problems. This improves the application range of dichotomy in the nonautonomous systems.

Description grammars: A general notation

A description grammar, in conjunction with a shape grammar, serves to generate verbal descriptions of designs, next to the spatial descriptions. These verbal descriptions can also assist in guiding the generative process. This paper presents a general notation for descriptions and description rules that accounts, extensively if not entirely, for many of the applications of description grammars found in literature. Specifically, a review of the notation with respect to these description schemes supports the explication of its strengths and limitations and the identification of future work. A follow-up paper revisits selected applications of description grammars and demonstrates the applicability of this general notation to these case studies.

Description grammars: Precedents revisited

A description grammar, in conjunction with a shape grammar, serves to generate verbal descriptions of designs, next to the spatial descriptions. These verbal descriptions can also assist in guiding the generative process. This paper revisits applications of description grammars found in literature and demonstrates how they can be recast and redeveloped to make use of a general notation and implementation for description grammars. The review of this notation was the topic of a previous paper; this paper is both meant as an illustration and as a confirmation of those review analysis results.

On a Simple and Efficient Approach to Probability Distribution Function Aggregation

In group decision making, it is inevitable that the individual decision maker’s subjectivity is involved, which causes difficulty in reaching a group decision. One of the difficulties is to aggregate a small set of expert opinions with the individual subjectivity or uncertainty modeled with probability theory. This difficult problem is called probability distribution function aggregation (DFA). This paper presents a simple and efficient approach to the DFA problem. The main idea of the proposed approach is that the DFA problem is modeled as a nonlinear function of a set of probability distribution functions, and then a linear feedback iteration scheme is proposed to solve the nonlinear function, leading to a group judgment or decision. Illustration of this new approach is given by a well-known DFA example which was solved with the Delphi method. The DFA problem is a part of the group decision problem. Therefore, the proposed algorithm is also useful to the decision making problem in general. Another contribution of the this paper is the proposed notation of systematically representing the imprecise group decision problem with the classification of imprecise information into three classes, namely incomplete information, vague information, and uncertain information. The particular DFA problem dealt with in this paper is then characterized with this general notation.

A direction sensitive detonation model for granular to continuum scale for shock initiation of pentaerythritol tetranitrate single crystal in multi-dimensions

Experiments have shown that the shock sensitivity of a single crystal pentaerythritol tetranitrate (PETN) has a strong dependence on the crystal orientation. The ignition and growth (I & G) model has been widely used in studies of the shock initiation of energetic materials while the model is independent of the direction of compression, and thus it is impossible to address anisotropic sensitivity of such material. In this paper, we base our new model in the recently proposed reactive flow concept that incorporates an anisotropic ignition mechanism that depends on both strain and strain rate which are given in the general tensor notation. A multi-dimensional simulation is performed in order to illustrate the strain dependence of the initiation of a PETN pellet. The model is applicable to any anisotropic energetic material subjected to a shock impact, not limited to single crystal PETN.

Modeling and analysis of dynamics for spacecraft relative motion actuated by inter-satellite non-contacting force

With the recent flurry of research on spacecraft relative motion actuated by inter-satellite non-contacting force, i.e., electrostatic force, electromagnetic force and magnetic flux-pinned force, the need has become apparent for dynamic modeling and dynamics analysis that capture the characteristics of this generic force. Based on the basic derivation of electrostatic force model and some theorems, the actuations of electrostatic force, electromagnetic force/torque and magnetic flux-pinned force/torque are unified and the corresponding mathematic models are derived. And then, with a general notation of this inter-satellite non-contacting force, the dynamic models are developed with respect to several assumptions of circular orbit, elliptical orbit and general Keplerian orbit pertaining to the motion of center of mass of the spacecraft cluster. A detailed dynamics analysis based on these derived models are carried out, including constraints of the relative motion dynamics, the special characteristics of applications to the near-Earth relative orbit motion and the deep space relative motion, and then a case with co-rotating pair of satellites subject to the previously mentioned inter-satellite non-contacting forces was simulated to validate the dynamic modeling and dynamics analysis. At last, some useful conclusions follow.

Multiobjective optimization: When objectives exhibit non-uniform latencies

Abstract Building on recent work by the authors, we consider the problem of performing multiobjective optimization when the objective functions of a problem have differing evaluation times (or latencies). This has general relevance to applications since objective functions do vary greatly in their latency, and there is no reason to expect equal latencies for the objectives in a single problem. To deal with this issue, we provide a general problem definition and suitable notation for describing algorithm schemes that can use different evaluation budgets for each objective. We propose three schemes for the bi-objective version of the problem, including methods that interleave the evaluations of different objectives. All of these can be instantiated with existing multiobjective evolutionary algorithms (MOEAs). In an empirical study we use an indicator-based evolutionary algorithm (IBEA) as the MOEA platform to study performance on several benchmark test functions. Our findings generally show that the default approach of going at the rate of the slow objective is not competitive with our more advanced ones (interleaving evaluations) for most scenarios.

Decrypting gauge-Yukawa cookbooks

For many years, theorists have calculated formulas for useful quantities in general gauge-Yukawa theories. However, these cookbooks are often very difficult to use since the general notation is far removed from practical model building. In this paper, we present the structure delta, which allows us to use a surprisingly convenient notation that bridges the gap between general gauge-Yukawa theories and specific models. This is particularly useful for the computation of beta functions, but can also be extended to handle spontaneous symmetry breaking, the effective potential and a variety of other quantities. We will introduce it using the standard model of particle physics and a toy model with an SU(N c ) gauge symmetry.

Joining and splitting the quantum states of photons

A photonic process named as "quantum state joining" has been recently experimentally demonstrated [C. Vitelli et al., Nature Photon. 7, 521 (2013)] that corresponds to the transfer of the internal two-dimensional quantum states of two input photons, i.e., two photonic qubits, into the four-dimensional quantum state of a single photon, i.e., a photonic ququart. A scheme for the inverse process, namely "quantum state splitting", has also been theoretically proposed. Both processes can be iterated in a cascaded layout, to obtain the joining and/or splitting of more than two qubits, thus leading to a general scheme for varying the number of photons in the system while preserving its total quantum state, or quantum information content. Here, we revisit these processes from a theoretical point of view. After casting the theory of the joining and splitting processes in the more general photon occupation number notation, we introduce some modified schemes that are in principle unitary (not considering the implementation of the CNOT gates) and do not require projection and feed-forward steps. This can be particularly important in the quantum state splitting case, to obtain a scheme that does not rely on postselection. Moreover, we formally prove that the quantum joining of two photon states with linear optics requires the use of at least one ancilla photon. This is somewhat unexpected, given that the demonstrated joining scheme involves the sequential application of two CNOT quantum gates, for which a linear optical scheme with just two photons and postselection is known to exist. Finally we explore the relationship between the joining scheme and the generation of clusters of multi-particle entangled states involving more than one qubit per particle.