Superposition Rule Research Articles

An AC Z-bus-based distribution factors for contingency analysis of AC–DC networks

The AC–DC networks are susceptible to deliberate and unforeseen contingencies, much like any other traditional power network. Due to the complex form of the unified impedance matrix derived for the provided network, the classic Z-bus-based contingency analysis approach cannot comprehend the AC–DC network. The distribution factors thus obtained from a unified complex Z-bus lead to an indication of the flow of complex current for DC lines. Therefore, an alternative method to discover post-contingency consequences is looked for. A streamlined approach for visualizing an equivalent AC network for the given AC–DC network has been proposed in this work. The AC-equivalent network takes the original AC–DC network and recreates it using two parallel AC networks to get the requisite distribution factors. The ultimate current/power distributions of the original AC–DC network can be determined by applying the superposition rule to the parallel networks, by the linear characteristics of the suggested technique. With this, the standard AC-contingency analysis method to complete the steady-state contingency analysis for the AC–DC network can be utilized. The proposed approach has been validated by the encouraging outcomes achieved for AC–DC networks with 10, 13, and 66 buses.

A nonlinear analytical model for consolidated geotextile-encased sand columns

A nonlinear model for consolidated geotextile-encased sand columns (GESACs) was formulated in this study. The model is based on the power law and predicts the stress-strain curve of a consolidated GESAC based on the superposition rule, wherein the stress-strain curve of the unconsolidated GESAC is superposed by the stress-strain curve of the soil alone in a consolidated triaxial test. A uniaxial compression test was conducted to study the failure mechanism of the GESAC. In addition, unconsolidated and consolidated triaxial tests on loose GESACs were conducted to investigate the effect of initial stresses on the shear behavior of GESACs. To further investigate the interaction between the soil and geotextile, and to assess the GESAC model, finite element method simulations were conducted. Based on the results, internal lateral stresses developed in the GESAC due to the confining effect of the geotextile, which increases the circumferential tension force on the geotextile while the p-q path of the GESAC approaches the critical state line, and follows the line when the shear strength of the soil is mobilized. The model was verified based on data on dense consolidated GESACs found in the literature, and results have shown good agreement between the measured and predicted data.

Influence of the superposition and flow rule assumptions on the bearing capacity of shallow strip footings

Influence of the superposition and flow rule assumptions on the bearing capacity of shallow strip footings

Microstructure-Informed Prediction of Hardening in Ion-Irradiated Reactor Pressure Vessel Steels

Ion irradiation combined with nanoindentation is a promising tool for studying irradiation-induced hardening of nuclear materials, including reactor pressure vessel (RPV) steels. For RPV steels, the major sources of hardening are nm-sized irradiation-induced dislocation loops and solute atom clusters, both representing barriers for dislocation glide. The dispersed barrier hardening (DBH) model provides a link between the irradiation-induced nanofeatures and hardening. However, a number of details of the DBH model still require consideration. These include the role of the unirradiated microstructure, the proper treatment of the indentation size effect (ISE), and the appropriate superposition rule of individual hardening contributions. In the present study, two well-characterized RPV steels, each ion-irradiated up to two different levels of displacement damage, were investigated. Dislocation loops and solute atom clusters were characterized by transmission electron microscopy and atom probe tomography, respectively. Nanoindentation with a Berkovich indenter was used to measure indentation hardness as a function of the contact depth. In the present paper, the measured hardening profiles are compared with predictions based on different DBH models. Conclusions about the appropriate superposition rule and the consideration of the ISE (in terms of geometrically necessary dislocations) are drawn.

Contact Lie systems: theory and applications

A Lie system is a time-dependent system of differential equations describing the integral curves of a time-dependent vector field that can be considered as a curve in a finite-dimensional Lie algebra of vector fields V. We call V a Vessiot–Guldberg Lie algebra. We define and analyse contact Lie systems, namely Lie systems admitting a Vessiot–Guldberg Lie algebra of Hamiltonian vector fields relative to a contact manifold. We also study contact Lie systems of Liouville type, which are invariant relative to the flow of a Reeb vector field. Liouville theorems, contact Marsden–Weinstein reductions, and Gromov non-squeezing theorems are developed and applied to contact Lie systems. Contact Lie systems on three-dimensional Lie groups with Vessiot–Guldberg Lie algebras of right-invariant vector fields and associated with left-invariant contact forms are classified. Our results are illustrated with examples having relevant physical and mathematical applications, e.g. Schwarz equations, Brockett systems, quantum mechanical systems, etc. Finally, a Poisson coalgebra method to derive superposition rules for contact Lie systems of Liouville type is developed.

Geometric Numerical Methods for Lie Systems and Their Application in Optimal Control

A Lie system is a nonautonomous system of first-order ordinary differential equations whose general solution can be written via an autonomous function, the so-called (nonlinear) superposition rule of a finite number of particular solutions and some parameters to be related to initial conditions. This superposition rule can be obtained using the geometric features of the Lie system, its symmetries, and the symmetric properties of certain morphisms involved. Even if a superposition rule for a Lie system is known, the explicit analytic expression of its solutions frequently is not. This is why this article focuses on a novel geometric attempt to integrate Lie systems analytically and numerically. We focus on two families of methods based on Magnus expansions and on Runge–Kutta–Munthe–Kaas methods, which are here adapted, in a geometric manner, to Lie systems. To illustrate the accuracy of our techniques we analyze Lie systems related to Lie groups of the form SL(n,R), which play a very relevant role in mechanics. In particular, we depict an optimal control problem for a vehicle with quadratic cost function. Particular numerical solutions of the studied examples are given.

Evaluation model of shale-adsorbed gas considering clay and water saturation

Shale adsorption capacity is affected by many factors including temperature, pressure, geochemical characteristics of organic matter, clay, and water saturation. The traditional calculation model of adsorbed gas content only considers the influence of temperature, pressure, and organic geochemical characteristics. The influence of clay and water saturation on adsorption capacity is seldom considered. Isotherm adsorption experiments were conducted on synthetic specimens and natural specimens with varying clay types, clay contents, and water saturations. Then, the influences of clay and water saturation on the adsorption capacity were systematically studied. The experimental results found that the order of clay adsorption capacities was smectite > kaolinite > chlorite > illite. The multicomponent superposition rule was applicable in evaluating shale-adsorbed gas content. The total adsorption capacity was equal to the accumulation of the adsorption capacities of all types of clay and organic matter. Moisture will significantly reduce the adsorption capacity of shale. The adsorption capacities of synthetic specimens and natural specimens after being fully saturated with water were 9%–14% and 42%–61% of those in dry states, respectively. Then, a new shale-adsorbed gas evaluation model was established based on the Langmuir equation considering clay and water saturation. The calculation error of this new model was approximately 11%, which provides a new method for evaluating the adsorbed gas content of shale.

Exact solutions and superposition rules for Hamiltonian systems generalizing time-dependent SIS epidemic models with stochastic fluctuations

<abstract><p>Using the theory of Lie-Hamilton systems, formal generalized time-dependent Hamiltonian systems that extend a recently proposed SIS epidemic model with a variable infection rate are considered. It is shown that, independently on the particular interpretation of the time-dependent coefficients, these systems generally admit an exact solution, up to the case of the maximal extension within the classification of Lie-Hamilton systems, for which a superposition rule is constructed. The method provides the algebraic frame to which any SIS epidemic model that preserves the above-mentioned properties is subjected. In particular, we obtain exact solutions for generalized SIS Hamiltonian models based on the book and oscillator algebras, denoted by $ \mathfrak{b}_2 $ and $ \mathfrak{h}_4 $, respectively. The last generalization corresponds to an SIS system possessing the so-called two-photon algebra symmetry $ \mathfrak{h}_6 $, according to the embedding chain $ \mathfrak{b}_2\subset \mathfrak{h}_4\subset \mathfrak{h}_6 $, for which an exact solution cannot generally be found but a nonlinear superposition rule is explicitly given.</p></abstract>

Simulating random optical fields: tutorial.

Numerous applications-including optical communications, directed energy, remote sensing, and optical tweezing-utilize the principles of statistical optics and optical coherence theory. Simulation of these phenomena is, therefore, critical in the design of new technologies for these and other such applications. For this reason, this tutorial describes how to generate random electromagnetic field instances or realizations consistent with a given or desired cross-spectral density matrix for use in wave optics simulations. This tutorial assumes that the reader has knowledge of the fundamental principles of statistical optics and optical coherence theory. An extensive reference list is provided where the necessary background information can be found. We begin this tutorial with a brief summary of the coherent-mode representation and the superposition rule of stochastic electromagnetic fields as these foundational ideas form the basis of all known synthesis techniques. We then present optical field expressions that apply these concepts before discussing proper sampling and discretization. We finally compare and contrast coherent-mode- and superposition-rule-based synthesis approaches, discussing the pros and cons of each. As an example, we simulate the synthesis and propagation of an electromagnetic partially coherent field from the literature. We compare simulated or sample statistics to theory to verify that we have successfully produced the desired field and are capturing its propagation behaviors. All computer programs, including detailed explanations of the source code, are provided with this tutorial. We conclude with a brief summary.

Low Complexity Majority-Logic Decoding for LDPC-Coded PNC Systems

In this letter, we propose majority-logic decoding (MLGD) algorithms of low complexity for low-density parity-check (LDPC) coded physical-layer network coding (PNC) in a two-way relay channel (TWRC). In particular, we decode the transmit combination of two-user messages from the superimposed signal and then map the XOR message of two users. By exploiting the superposition rules of PNC, we develop hard decision-based and reliability-based decoding algorithms, i.e., modified one-step MLGD (M-OSMLGD) and iterative soft reliability-based decoding (M-ISRB), to iteratively update the combination of two-user messages. Moreover, we propose an improved M-ISRB (IM-ISRB) decoding to update the external reliability of the combination of two-user messages in each iteration. Simulation results show that the proposed decoding algorithms can achieve effective an trade-off between complexity and decoding performance for LDPC-coded PNC systems.

Characterizing the subsea Pleistocene fluvial system of the Sunda shelf, offshore Malaysia, using multiattribute corendering and self-organizing maps

The advancement of multiattribute analysis techniques has significantly improved the ability to capture subtle geologic information that is not easily detected on the original seismic. The use of corendering and automated facies clustering/classification techniques with an appropriate set of seismic attributes increases the reliability and accelerates the interpretation process. We have proved the effectiveness of multiattribute corendering and self-organizing maps (SOMs) in characterizing the late Pleistocene fluvial system of the Sunda shelf that was previously studied using the original seismic only. The work aims to document the attribute expression and capture subtle depositional patterns of the fluvial system. We find that amplitude, texture, and spectral attributes delineate the lithology contrast among different depositional features, whereas geometric attributes reveal channel morphology. The red-green-blue and alpha blends significantly increased the data interpretability by manipulating up to four attributes in the same display. In addition, the SOM clustering aids in distinguishing among different sand-prone depositional elements and muddy facies. We use the cross-cutting relation and superposition rules to understand the stratigraphic evolution of the interval. We observe several fluvial depositional elements through a closely spaced time slicing, including straight channel, meander channel, point bar, crevasse splay, and levee. We recognize that the straight and low-sinuosity channels were developed along preexisting faults and find a deeper incision and thicker sediment fill than the other channel types. The widely variable fluvial style in the middle of the interval is attributed to a rapid change in the accommodation space and climate conditions. The small meanders that find a prominent dendritic pattern indicate a marine influence on the less channelized uppermost part of the interval. The well-imaged and documented shallow fluvial system in the area represents an excellent analogous that helps to understand and accurately predict the reservoir distribution in the deeper productive stratigraphic units.

A generalization of a SIS epidemic model with fluctuations

In a recent paper (Nakamura and Martinez, 2019), the classical epidemic compartmental susceptible‐infectious‐susceptible (SIS) model has been upgraded to a form which permits fluctuations in terms of the mean and the variance of infected individuals. This novel model happens to admit a Hamiltonian realization involving a constant ρ0 that is related to the reproduction number R0. In this work, we generalize ρ0 as a t‐dependent function to arrive at a non‐autonomous system of differential equations that we call SISt model. We make use of the theory of Lie systems to provide a (nonlinear) superposition rule for the general solution of SISt model. To conclude, we present a quantum version of the same model, giving rise to a parametric family of SISt systems. We provide a superposition rule for the general solution of the quantum extension as well.

Microstructure-informed prediction and measurement of nanoindentation hardness of an Fe-9Cr alloy irradiated with Fe-ions of 1 and 5 MeV energy

Hardening of Fe-9%Cr alloys exposed to irradiation with Fe2+ ions of two different energies, 1 and 5 MeV, is investigated using nanoindentation. The limited penetration depth of the ions causes steep damage gradients in the near-surface volumes of the irradiated samples. This damage gives rise to graded microstructures resulting in depth-dependent irradiation hardening. Nanoindentation integrates the depth-dependent hardness over the indentation plastic zone. Our study combines quantitative analysis of the ion-irradiated microstructures with the determination of the full depth dependence of irradiation hardening. The microstructure-informed model incorporates direct experimental evidence revealed by a former investigation using cross-sectional scanning transmission electron microscopy. For both ion energies, the observed microstructures consist of dislocation loops with band-like distributions and are concluded to be the dominant source of the measured irradiation-induced hardening. The model predictions are found to be in reasonable agreement with the as-measured nanoindentation response. The comparison of hardening predictions with different kinds of superposition rules of hardening contributions suggests linear superposition as the most appropriate selection under the present conditions. The possible transferability of these results to neutron irradiation is also discussed.

Microstructural evolution, mechanical behaviors and strengthening mechanism of 300 M steel subjected to multi-pass laser shock peening

300 M steel was treated by multi-pass laser shock peening (LSP). The microstructures were characterized by transmission electron microscopy (TEM), electron backscattered diffraction (EBSD) and X-ray diffraction (XRD). In addition, the surface roughness, microhardness, residual stress, impact toughness and mechanical properties after LSP were measured. The results showed that high-density dislocations were generated after multi-pass LSP and the dislocation motion dominated the deformation process. The intensity of texture decreased while low-angle grain boundaries increased, and the grain refinement was not achieved after LSP. The residual stress transformed from tensile stress (+20 MPa) to compressive stress (−556 MPa) and the microhardness was 24.8% higher than the unpeened sample after LSP. Based on the linear superposition rule, a strengthening model was established to predict the contribution of dislocation and grain boundary strengthening on microhardness. Additionally, the fatigue life of peened samples increased by 165% compared with the unpeened ones. The improvement of high-cycle fatigue (HCF) properties was attributed to the rewarding compressive residual stress and microstructural evolution.

Modelling of Phase Formation in Solid–Solid and Solid–Liquid Interactions: New Developments

Recent developments (after 2016) in modelling of phase formation during solid–solid and solid–liquid reactions by SKMF (Stochastic Kinetic Mean-Field) method, Monte Carlo simulation and phenomenological modelling are reviewed. Reasonable results of multiphase reactive diffusion modelling demonstrating distinct concentration plateau for each intermediate ordered compound and distinct concentration steps between these phases are obtained by the SKMF and Monte Carlo methods, if one takes into account interatomic interactions within two coordination shells and if the signs of mixing energies are ‘minus’ for the first coordination shell and ‘plus’ for the second one. Second possibility for reasonable modelling results is consideration of interatomic interactions depending on local concentration with maxima around stoichiometric composition. In phenomenological modelling, the generalization of Wagner diffusivity concept and respective superposition rule are introduced. New mechanism of the lateral grain growth in the growing phase layers during reactive diffusion is suggested. Anomalously fast grain growth at the final stages of soldering in sandwich-like Cu–Sn–Cu contacts is reported and explained. Simple model of Zn-additions’ influence on the Cu–Sn reaction is described.

An Atomic Insight into the Chemical Origin and Variation of the Dielectric Constant in Liquid Electrolytes

AbstractThe dielectric constant is a crucial physicochemical property of liquids in tuning solute–solvent interactions and solvation microstructures. Herein the dielectric constant variation of liquid electrolytes regarding to temperatures and electrolyte compositions is probed by molecular dynamics simulations. Dielectric constants of solvents reduce as temperatures increase due to accelerated mobility of molecules. For solvent mixtures with different mixing ratios, their dielectric constants either follow a linear superposition rule or satisfy a polynomial function, depending on weak or strong intermolecular interactions. Dielectric constants of electrolytes exhibit a volcano trend with increasing salt concentrations, which can be attributed to dielectric contributions from salts and formation of solvation structures. This work affords an atomic insight into the dielectric constant variation and its chemical origin, which can deepen the fundamental understanding of solution chemistry.

An Atomic Insight into the Chemical Origin and Variation of the Dielectric Constant in Liquid Electrolytes.

The dielectric constant is a crucial physicochemical property of liquids in tuning solute-solvent interactions and solvation microstructures. Herein the dielectric constant variation of liquid electrolytes regarding to temperatures and electrolyte compositions is probed by molecular dynamics simulations. Dielectric constants of solvents reduce as temperatures increase due to accelerated mobility of molecules. For solvent mixtures with different mixing ratios, their dielectric constants either follow a linear superposition rule or satisfy a polynomial function, depending on weak or strong intermolecular interactions. Dielectric constants of electrolytes exhibit a volcano trend with increasing salt concentrations, which can be attributed to dielectric contributions from salts and formation of solvation structures. This work affords an atomic insight into the dielectric constant variation and its chemical origin, which can deepen the fundamental understanding of solution chemistry.

Rotary gate: Submerged flow condition

The rotary gate is a recently proposed gate for application in semicircular elevated irrigation networks. In this study, the hydraulics of rotary gate submerged flow was theoretically and experimentally investigated. Two approaches for estimating the submerged flowrate were considered, namely the stage-discharge based on the superposition rule and the dimensional analysis principles. The results revealed that the gate opening angle and the submergence ratio affect the submerged discharge the most. Based on the compiled experimental data relationships for estimating the discharge in such flow conditions were presented. Statistical analysis indicated that both approaches yielded satisfactory results for discharge estimation. Also, the submerged threshold condition of the rotary gate was investigated and a relationship was proposed whose results concurred with the observed data. In addition, the gate discharge coefficient and its head loss were studied and relationships for determining the discharge coefficient and the relative head loss in submerged flow condition were proposed.

A study on earthquake performances of reinforced concrete buildings with various number of stories

Seismic codes generally require that the Equivalent Seismic Load Method or the Modal Response Spectrum Method is adopted in the design of buildings. In the equivalent seismic load method, the equivalent seismic static force applied to the building is determined depending on the seismicity of the region where the building is located, the usage class of the building, the fundamental period of the building and the building mass. Later, this equivalent seismic load is reduced by the seismic load reduction factor to take into account the increase in the capacity of the system and the decrease in the seismic demand due to the nonlinear and inelastic behavior of the system, i.e., by accepting limited inelastic deformations in the building subjected to the design earthquake. Then, structural system of the building is analyzed under the reduced seismic forces in addition to the vertical loads by using the load combinations given in the design codes. The process is completed by designing the sections and the structural elements of the building. Similar processes can be implemented by using the modal response spectrum method. The difference between these two methods is consideration of the higher modes of the building instead of the first mode only and the use of the modal masses of the building for each mode, instead of the total mass of the building. In the latter method, the contributions of the higher mode are combined by using specific superposition rules. The codes assume that the structural systems designed in this way will exhibit the almost same level of inelastic deformation, i.e., the controlled damage state, regardless of the building parameters, such as the number of stories. In this study, an attempt is made to investigate the validity of this implicit acceptance. For this purpose, the buildings with a various number of stories are designed by satisfying the bare minimum requirements of the code only, as much as possible. The seismic behavior and the lateral load capacity of these buildings are examined by the static and dynamic nonlinear analyses. The ratio of the nonlinear load capacity to the reduced equivalent seismic load is evaluated depending on the number of the stories of the buildings. The results which are presented in detail yield that the buildings with a low number of stories have relatively larger nonlinear lateral load capacity-to-the reduced elastic seismic load ratio, which is not compatible with the general implicit assumption made in the seismic codes.

Poisson–Hopf deformations of Lie–Hamilton systems revisited: deformed superposition rules and applications to the oscillator algebra

The formalism for Poisson–Hopf (PH) deformations of Lie–Hamilton (LH) systems, recently proposed in Ballesteros Á et al (2018 J. Phys. A: Math. Theor. 51 065202), is refined in one of its crucial points concerning applications, namely the obtention of effective and computationally feasible PH deformed superposition rules for prolonged PH deformations of LH systems. The two new notions here proposed are a generalization of the standard superposition rules and the concept of diagonal prolongations for Lie systems, which are consistently recovered under the non-deformed limit. Using a technique from superintegrability theory, we obtain a maximal number of functionally independent constants of the motion for a generic prolonged PH deformation of a LH system, from which a simplified deformed superposition rule can be derived. As an application, explicit deformed superposition rules for prolonged PH deformations of LH systems based on the oscillator Lie algebra are computed. Moreover, by making use that the main structural properties of the book subalgebra of are preserved under the PH deformation, we consider prolonged PH deformations based on as restrictions of those for -LH systems, thus allowing the study of prolonged PH deformations of the complex Bernoulli equations, for which both the constants of the motion and the deformed superposition rules are explicitly presented.