Algebraic Model Research Articles

Accurate computing paradigm for decoupled harmonic load flow analysis with CONOPT solvers for non-sinusoidal radial distribution systems

In this article, a novel method for performing Decoupled Harmonic Load Flow (DHLF) analysis in radial distribution systems is presented. The proposed method involves solving load flow equations for both fundamental and higher frequencies as constrained minimization problems utilizing a nonlinear programming (NLP) CONOPT solver integrated into the General Algebraic Modeling Systems (GAMS) environment. The effectiveness of the proposed method is assessed across three IEEE test systems: 18-bus, 33-bus, and 69-bus. Five cases of DHLF analysis are taken into consideration. DHLF was performed on standard test systems with incorporated non-linear loads in the first case. Cases two through five examine the DHLF in the presence of distributed generators (DGs), shunt capacitors (SCs), simultaneous DGs and SCs, and electric vehicles (EVs). Comparing the obtained results to those of DHLF analysis tools ETAP and DigSilent, as well as to those found in the literature, proved that the proposed CONOPT solver provides precise solutions.

Coupling of Eddy-Viscosity-Scale Reynolds-Stress Model with an Algebraic Transition Model

Attempts to extend a Reynolds-stress model (RSM) for transition flow simulations have begun to cause concern in recent years based on the fact that the RSM has more potential than an eddy viscosity model when applied to complex three-dimensional flowfields. In terms of the RSM, however, coupling more transport equations will further increase its complexity (may worsen robustness and convergence rate). In this paper, a γ-based algebraic transition model originating from the SA-BC model is coupled with an νt-scale RSM (EV-RSM) to form a new transition/turbulence model, called tEV-RSM. Some numerical tests are conducted with a fifth-order scheme, WCNS, including the well-known T3 flat plate series, a two-dimensional airfoil (S809), a two-dimensional three-element airfoil (30P-30N), a three-dimensional prolate-spheroid, and a three-dimensional circular cylinder. The proposed model is compared with the SA-BC and γ-Reθt SST models, which indicates that it can predict the flows primarily governed by Tollmien–Schlichting transition or bypass transition well and has an advantage in predicting the flows with detached separation. Meanwhile, the iteration convergence rate of the tEV-RSM is fast enough considering it as a seven-equation model.

A Concrete Model for the Quantum Permutation Group on 4 Points

In 2019, Jung–Weber gave an example of a concrete magic unitary M, which defines a C * -algebraic model of the quantum permutation group S 4 + . We show with the help of a computer that there exist no polynomials up to degree 50 separating the entries of M from the generators of C ( S 4 + ) . This indicates that the magic unitary M might already define a faithful model of S 4 + .

Simple Two-Message OT in the Explicit Isogeny Model

In this work we study algebraic and generic models for group actions, and extend them to the universal composability (UC) framework of Canetti (FOCS 2001). We revisit the constructions of Duman et al. (PKC 2023) integrating the type-safe model by Zhandry (Crypto 2022), adapted to the group action setting, and formally define an algebraic action model (AAM). This model restricts the power of the adversary in a similar fashion to the algebraic group model (AGM). By imposing algebraic behaviour to the adversary and environment of the UC framework, we construct the UC-AAM. Finally, we instantiate UC-AAM with isogeny-based assumptions, in particular the CSIDH action with twists, obtaining the explicit isogeny model, UC-EI; we observe that, under certain assumptions, this model is "closer" to standard UC than the UC-AGM, even though there still exists an important separation. We demonstrate the utility of our definitions by proving UC-EI security for the passive-secure oblivious transfer protocol described by Lai et al. (Eurocrypt 2021), hence providing the first concretely efficient two-message isogeny-based OT protocol in the random oracle model against malicious adversaries.

Economic impact of government health expenditure: An application of the computable general equilibrium model to the Iran.

Considering the increase in health expenses and the government's role in health financing, this study investigated the economic impact of increases in the share of the health sector in the government budget while taxes remain unchanged and government spending is fixed. The economic model used in this study was a macroeconomic Computable General Equilibrium (CGE) model. This model was calibrated using a 2011 Social Accounting Matrix (SAM) Of Iran. The CGE model was solved with non-linear programming using the General Algebraic Modeling System package, version 2.50. The effect of this simulation on the government budget deficit, the production of different sectors of the economy, and the employment rate was investigated. Based on our fundings the elasticity of substitution in the agricultural and industrial sectors is higher than in the health and service sector. Also, the biggest decrease in production occurred in the industry, agriculture, and service sectors, respectively. With the doubling of the share of government spending in the health sector, the employment rate of this sector has increased by 40.9%, but the highest decrease in the ignition rate is related to the service sectors (-2.7%), agriculture (-0.23%), and industry (-0.14%). Increasing the share of government spending in the health sector in comparison with other sectors of the economy, provided that government spending is maintained in general, leads to a decrease in production and economic welfare. It seems that the Iranian government should seek to increase the sources of health financing and the share of government expenditures in the health sector with other ways in order to improve the health level of the society and have a positive effect on other economic sectors.

ALGEBRAIC MODELS FOR DATA AND KNOWLEDGE REPRESENTATION IN MODERN DATABASE MANAGEMENT SYSTEMS

The article discusses algebraic data and knowledge representation models in modern database management systems. It is shown that despite the effectiveness of the relational model in storing large volumes of structured information, its capabilities are limited for expressing machine learning algorithms. In this regard, new approaches are proposed based on advanced algebraic models that allow formalizing the architecture and operations of neural networks in SQL. Methods of hybridization of SQL and GPU computations, application of specialized operators, combining data processing and analysis stages are considered. The results confirm the high efficiency of the developed solutions for intelligent analytics.

Asymptotic behaviour of a conservative reaction-diffusion system associated with a Markovian process algebra model

This paper demonstrates a framework using lower and upper solutions approximation to investigate the asymptotic behaviour of conservative reaction-diffusion systems associated with Markovian process algebra models. In a case study, we proved the uniform convergence of the solution to its constant equilibrium as time tends to infinity, which is further illustrated by numerical experiments.

On state monadic MV-algebras

Monadic MV-algebras are an algebraic model of the predicate calculus of the Łukasiewicz infinite valued logic in which only a single individual variable occurs. In this paper, we extend monadic MV-algebras with a state operator that describes algebraic properties of states. The resulting variety of algebras will be called state monadic MV-algebras. First, we introduce state monadic MV-algebras and establish a natural equivalence between the category of state monadic MV-algebras and the category of state monadic ℓ-groups with strong units. Moreover, we prove that the class of all state monadic ideals in state monadic MV-algebras is a complete Heyting algebra. In particular, by studying extended state monadic ideals, we prove that the set of all stable state monadic ideals in state monadic MV-algebras is a complete Heyting algebra. Also, the class of all involutory state monadic ideals in state monadic MV-algebras is a complete Boolean algebra. Finally, we introduce and characterize some members in the variety of state monadic MV-algebras, which are subdirectly irreducible, simple, semisimple, local and semilocal, respectively.

Input-Output Analysis on Pia Saronde Production Process Scheduling with Invariant Max-Plus Linear System

Max-plus algebra is one of the analysis methods of discrete event systems which has many applications on systems theory and graph theory. Max-plus algebra is a set of real numbers R combined with =-∞ equipped with operations max (⊕) and plus (⊗), can be denoted [(R]_ε,⊕,⊗) with [(R]_ε=R⋃{ε}) . The production process of pia saronde is one of the problems that can be analyzed using max-plus algebra. The production process of this product is sequentially carried out by making skin dough, filling, baking, cooling, and packaging the pia. The max-plus algebra theory was used in this research to determine the optimal time in the production scheduling of pia saronde. Meanwhile, the Invarian Max-plus Linear System (IMLS), max-plus algebraic theory, and the Discrete Event System (DES) were used to solve the production-related problems. IMLS analysis produces eigenvalues that represent the optimum production time. The results obtained the max-plus algebra model of x(k+1)=A x(k), where A =A⊕B⊗C and y=K⊗x_0⊕H⊗u for input-output IMLS analysis. From the matrix A, eigenvalue λ= 226 and eigenvector v=[278 278 278 279 299 302 324 356 488] were obtained. Furthermore, the value of λ describes the pia production schedule at a time span of 226 minutes.
 Keywords: input-output analysis, pia saronde, scheduling, max-plus linear system

Revisiting the modelling framework for the unresolved scalar variance

The unresolved scalar variance in large-eddy simulations of turbulent flows is a fundamental physical and modelling parameter. Despite its importance, relatively few algebraic models have been developed for this important variable with the most prominent models to date being the classic scale-similarity and gradient models. In this work a new generalized modelling framework based on reconstruction has been developed, which in contrast to classic modelling approaches allows the construction of base static variance models of arbitrary accuracy. It is demonstrated that higher-order reconstructions naturally lead to base static variance models of increased accuracy, and that the classic scale-similarity and gradient models are subsets of more general and higher-order models. The classic scale-similarity assumption for developing dynamic models is also revisited, and it is demonstrated that this can essentially be reinterpreted as a two-level reconstruction approach. Based on this result, a new general methodology is proposed that allows the construction of dynamic models for any given base static model, and a corresponding general reconstruction operator, algebraic or iterative. Consequently, improved static and dynamic models for the scalar variance are developed. The newly developed models are then thoroughly tested a priori using two high-fidelity direct numerical simulation databases corresponding to two substantially different flame and flow configurations, and are shown to outperform classic algebraic models for the variance.

A simple analytical model for turbulent kinetic energy dissipation for self-similar round turbulent jets

This work presents a simple analytical model for the streamwise and radial variations of turbulent kinetic energy dissipation in an incompressible round turbulent jet. The key assumptions in the model are: similarity in the axial velocity profile with a Gaussian shape, axisymmetric flow and the dominance of radial derivatives of the mean velocity over axial direction derivatives (similar to boundary layer theory). Initially, a simplified eddy-viscosity relation for turbulent stresses is derived using the algebraic stress model by Gatski & Speziale (J. Fluid Mech., vol. 254, 1993, pp. 59–78). Subsequently, with this eddy-viscosity relation, the relation for variations of turbulent kinetic energy dissipation is formulated using the conservation of turbulent kinetic energy. To extract the necessary constants of the model, experimental velocity statistics for round jets are obtained through particle image velocimetry measurements. The experimental results of the mean entrainment coefficient for turbulent jets are also analysed. When comparing the radial variation of turbulent kinetic energy dissipation from the model with experimental results at Reynolds number $1.4\times 10^5$ and numerical results at Reynolds number $1200$ from the available literature, we observe a maximum error of $10\,\%$ and $15\,\%$ , respectively. Finally, using the validated model, we analyse the impact of mean velocity evolution parameters on the behaviour of turbulent kinetic energy dissipation and discuss its potential significance in future studies.

Optimal scheduling of a microgrid based on renewable resources and demand response program using stochastic and IGDT-based approach

Optimal economic scheduling of microgrids with photovoltaic (PV) and wind generation has gained increased attention during recent years. Integration of renewable energy resources in microgrids requires increasingly active control and management of energy storages and demand response (DR). In this paper, a risk-based stochastic optimal energy management model is developed for microgrid with renewables, energy storage and load control by time-of-use-based DR programs. Microgrid includes PV system, wind system, micro-turbine, fuel cell, electric vehicle (EV), and energy storage. Information-gap decision theory (IGDT) is employed to address the uncertainty of loads and to provide the operating strategies for the microgrid controllable energy resources. This proposed model has been solved as a mixed-integer non-linear programming (MINLP) in General Algebraic Modeling System (GAMS) software and simulation results in different conditions are studied and discussed. Three different risk management strategies have been studied such as risk-averse, risk-neutral and risk-seeker mode. The simulation results indicate that the impacts of risk-averseness or risk-seeker of the decision maker affect the system operation. For instance, the results showed the DR program's role in risk-averse and risk-taking strategies, impacting consumption and costs. The proposed model ensures the risk-averse decision-maker that if the uncertain parameter deviates within the optimum robustness region, the final cost will not exceed the critical cost. On the other hand, the risk-seeking decision-maker can reach lower final costs by accepting the risks if the uncertain parameter deviates favorably within the opportunity region. Decision-makers can manage risks by adjusting consumption. Thus, considering the cost of risk management is crucial, as it increases with robust or opportunistic approaches.

Inference and Learning in Dynamic Decision Networks Using Knowledge Compilation

Decision making under uncertainty in dynamic environments is a fundamental AI problem in which agents need to determine which decisions (or actions) to make at each time step to maximise their expected utility. Dynamic decision networks (DDNs) are an extension of dynamic Bayesian networks with decisions and utilities. DDNs can be used to compactly represent Markov decision processes (MDPs). We propose a novel algorithm called mapl-cirup that leverages knowledge compilation techniques developed for (dynamic) Bayesian networks to perform inference and gradient-based learning in DDNs. Specifically, we knowledge-compile the Bellman update present in DDNs into dynamic decision circuits and evaluate them within an (algebraic) model counting framework. In contrast to other exact symbolic MDP approaches, we obtain differentiable circuits that enable gradient-based parameter learning.

Replicating transition with modified Spalart–Allmaras model

An algebraic transition model has been developed to preserve the “flow-structure-adaptive” characteristics in “Reynolds-Averaged Navier–Stokes” (RANS) computations for multiple transition mechanisms. The formulation is convenient and plausible in a sense that it relies on the local flow information to trigger transition employing an algebraic intermittency parameter γ rather than a γ-transport equation. The turbulence intensity Tu appearing in γ has been evaluated locally using an empirical relation for the turbulent kinetic energy k, resolving the interaction between local and free-stream turbulence intensities. Splitting γ into low and elevated Tu regimes assists in calibrating the model coefficients as well as minimizing the “trial-and-error” inconsistency, involved in most of the correlation-based transition models for initiating proper simulations. The γ function is directly fed into the production term of a modified Spalart–Allmaras (MSA) turbulence model. The artifact is pivotal to precisely representing the relevant physical aspects of the flow, such as the bypass, natural and separation-induced transitions, and boundary layer (BL) separation and shock BL interactions. Numerical results demonstrate that the MSA transition model maintains decent agreement with other transition and non-transition models available in the literature.

Costs and benefits of the LIFO‐FIFO choice

AbstractThe choice of inventory cost flow assumption is a key financial reporting decision. The resurgence of inflation has renewed interest in this option. We derive algebraic models of the LIFO‐FIFO difference in cost of goods sold and the LIFO tax savings as a function of inflation, turnover, inventory increments, and tax rates. Managers and researchers can use these models to estimate the likely financial and tax impacts of LIFO adoption. Historic trends in public company LIFO usage since 1971 are consistent with the changing impacts estimated by our model. We infer an approximate cost level of using LIFO based on historic public company behavior. In the 1971–2022 period, LIFO adoptions were only common when the tax benefit in our model exceeded about 0.35% of COGS. Even when inflation rose in 2021 and 2022, the tax savings remained below this threshold, and there were far more LIFO abandonments than adoptions.

Algebraic cluster model calculations for shape phase transitions of boson-fermion systems

The Algebraic Cluster Model (ACM) is an interacting boson model that gives the relative motion of the cluster configurations in which all vibrational and rotational degrees of freedom are present from the outset. We schemed a solvable extended transitional Hamiltonian based on affine [Formula: see text] Lie algebra within the framework for two-, three- and four-body algebraic cluster models that explains both regions [Formula: see text], [Formula: see text] and [Formula: see text], respectively. We offer that this method can be used to study [Formula: see text] nucleon structures with [Formula: see text] and [Formula: see text] in specific [Formula: see text] such as structures [Formula: see text], [Formula: see text], [Formula: see text]; [Formula: see text], [Formula: see text], [Formula: see text]; [Formula: see text], [Formula: see text]. Numerical extraction to the energy levels, the expectation value of the boson number operator, and the behavior of the overlap of the ground state wave function within the control parameters of this evaluated Hamiltonian are presented. The effect of the coupling of the odd particle to an even–even boson core is discussed along the shape transition and, in particular, at the critical point.

Comparison of Eddy Viscosity Models for High Turbulence Nozzle Guide Vane Flows

Abstract In this paper we investigate the performance of eddy viscosity turbulence models for high-pressure nozzle guide vane (NGV) flows with engine-realistic turbulence. Using metrics such as integrated kinetic energy (KE) loss and mixing rate, we compare simulation results using turbulence models with high-fidelity experimental data from fully-cooled NGVs, operating at engine-matched conditions of Reynolds number and Mach. For the widely-used k–ω shear stress transport (SST) model, the aerodynamic and thermal wakes of the NGVs were undermixed. We compare simulation results with those using other common turbulence models including the standard k–ω, baseline k–ω, Spalart–Allmaras, and baseline explicit algebraic Reynolds stress model. Alternative turbulence models formulations are explored, with an emphasis on modifications to the implementation of the shear stress limiter. We also investigate the sensitivity of models to the specified inlet turbulence intensity. We demonstrate that predictions of integrated KE loss, as well as the decay trends of the aerodynamic and thermal wakes are a closer match to experimental data for the baseline algebraic Reynolds stress model than for other turbulence models in more common use for NGV predictions.

Development of a modified thermal phase change model based on the interfacial area concentration determined by an interface reconstruction algorithm

In order to enhance the physical basis of the mass transfer model in numerical simulation of gas-liquid direct contact condensation and improve the fidelity, a set of methods and models are developed. Based on the concept of the piecewise-linear interface calculation (PLIC), an interface reconstruction algorithm is proposed to calculate the interfacial area concentration in three-dimensional non-orthogonal structured grids. The actual interface in the cell is replaced by a plane, whose position is determined iteratively to satisfy the local volume fraction and orientation of the actual interface. The area of the polygonal cut by the plane is taken as the interfacial area in the cell. The proposed algorithm is validated by calculating the surface area of a series of basic geometries. Obvious superiority of the proposed algorithm over the traditional models (gradient model and algebraic model) is seen. Then, the reconstructed area is used to determine the interfacial area concentration in the thermal phase change model. The process is implemented by ANSYS Fluent user-defined functions. The Stefan problem and steam bubble condensation experiment are used to test the performance of the developed methods and models. The simulation results agree well with the theoretical and experimental results with the quantitative relative errors no more than 4.3 % and 15 %, respectively. The oxygen jets condensation experiments are also used as test cases. The primary dominant frequencies predicted by the simulations are 163.01 Hz and 131.65 Hz, which agree well with the 139.72 Hz and 125.75 Hz in the experiments. The relative errors are only 17 % and 4.7 %. The unstable flow pattern of oxygen jet in liquid oxygen crossflow is explained based on the dynamic characteristics of turbulence, heat and mass transfer. The periodic variation of mass transfer rate is considered as the cause of condensation oscillation. The method for calculating the interfacial area proposed in this paper can serve as an optional and practical improvement to the numerical simulation of direct contact condensation.

Multi-resolution analysis of partially-stirred reactor models for subgrid turbulence / chemistry interactions

A multi-resolution analysis (MRA) technique in which coupled sequences of LES simulations are solved on successively coarsened meshes is used to analyze the relative performance of several algebraic partially-stirred reactor (PaSR) subgrid models for turbulent combustion. The test case is a methane-hydrogen bluff-body flame, and the ‘truth solution’ is obtained from a fine-mesh LES that resolves the flow into the dissipative scales. The velocity field from this solution drives the solutions obtained on the underlying coarser meshes, enabling a tight correlation of eddy structures. Conditional distributions of chemical production rate norms and local heat release over a subgrid Reynolds-number / Damköhler sample space are extracted from each coarse-mesh level. The results show that none of the tested PaSR methods accurately predicts the combustion characteristics evidenced from the finest mesh; results improve when coupling with an ‘outer environment’ is included. Optimal forms for the characteristic PaSR time scale and fine-scale volume fraction are regressed from the data and can be modeled effectively using resolved scale information. The use of these forms provides improved results and yields a level of mesh-independence that is not found in the original algebraic PaSR models.

Hydrodynamic Performance Analysis of Camber Ratio Variations on B-series Propeller Types

The hydrodynamic performance of the B-series propeller can be determined by calculating the polynomial equation published by MARIN. Furthermore, analysis and evaluation of B-series propeller modifications can be done by varying the camber ratio of the foil. The camber ratio affects the lift force on the propeller foil, directly affecting the propeller thrust and torque. Numerical calculations were carried out using Computational Fluids Dynamics (CFD), based on Reynolds Averaged Navier Stokes Equations (RANSE) and turbulence model in the form of explicit algebraic stress models (EASM). The overall results of this study show an increase in efficiency of 4.182 on the foil with a camber ratio of 2.2% when compared to the foil camber ratio of 0%.