Simple Algebraic Approach Research Articles

A conservative level set method for liquid-gas flows with application in liquid jet atomisation

In this paper, a methodology for modelling two-phase flows based on a conservative level set method in the framework of finite volume method is presented. The novelty of the interface capturing method used here lies on the advection of level set which is solved with a WENO scheme and corrected with a novel re-initialisation method for retaining its signed distance function character. The coupling with the volume of fluid method is done with a simple algebraic approach, and with the new algorithm the accumulated mass conservation errors remain reasonably low. The paper presents a unique coupling between the level set method and the Eulerian-Lagrangian Spray Atomisation approach for modelling spray dispersion in liquid atomisation systems. The method is shown to have good accuracy providing similar results to other numerical codes for the classical tests presented. Preliminary results are also shown for three-dimensional simulations of the primary break-up of a turbulent liquid jet obtaining results comparable to direct numerical simulations. Consequently, the coupled method can be used for simulating various two-phase flow applications offering an accurate representation of the interface dynamics.

Spectral curve duality beyond the two-matrix model

We describe a simple algebraic approach to several spectral duality results for integrable systems and illustrate the method for two types of examples: the Bertola–Eynard–Harnad spectral duality of the two-matrix model and the various dual descriptions of minimal model conformal field theories coupled to gravity.

A $$C^*$$ C ∗ -algebraic approach to the principal symbol II

We introduce an abstract theory of the principal symbol mapping for pseudodifferential operators extending the results of Sukochev and Zanin (J Oper Theory, 2019) and providing a simple algebraic approach to the theory of pseudodifferential operators in settings important in noncommutative geometry. We provide a variant of Connes’ trace theorem which applies to certain noncommutative settings, with a minimum of technical preliminaries. Our approach allows us to consider operators with non-smooth symbols, and we demonstrate the power of our approach by extending Connes’ trace theorem to operators with non-smooth symbols in three examples: the Lie group $$\mathrm {SU}(2)$$ , noncommutative tori and Moyal planes.

A simple approach to solve the time independent Schröedinger equation for 1D systems

A simple algebraic approach based on the well known angular momentum SU(2) algebra is presented to describe 1D systems for arbitrary potentials. The approach is based on the dimension increase of the 1D harmonic oscillator space through the addition of a scalar boson, keeping constant the total number of bosons. In this new space the realization of the coordinate and momentum correspond to components of the angular momentum algebra, which in turn define the coordinate and momentum representation bases. This remarkable result allows the Hamiltonian matrix representationto be expressed in terms of a diagonal matrix characterizing the potential we are considering. The solutions are obtained as an expansion of harmonic oscillator functions by purely algebraic means. As an example of our approach the Morse and asymmetric double Morse potentials are considered.

Gas–Liquid Flow Rate Measurement Using a Twin-Plane Capacitive Sensor and a Venturi Meter

We introduce a flow meter to monitor the flow rate of individual phases in gas-liquid flows. The meter combines pressure data from a Venturi tube and void fraction data from a twin-plane capacitive sensor. By the twin geometry of the capacitive sensor it is possible to cross-correlate the two signals and estimate gas flow rate. A simple algebraic approach, which considers no-slip condition between phases and disregards influence of gas phase, combines pressure fluctuations of the Venturi meter with the measured phase fraction to estimate liquid flow rate. The proposed meter has been tested in horizontal air-water flow loops, 1-inch and 2-inches internal pipe diameter, in permanent and transient regimes. Calculated values were compared to reference measurements. The proposed meter performs well determining liquid flow rate, independent of the flow pattern, in the whole measured range with some more discrepancies at lower values of liquid flow rate. Gas flow rate presented good agreement with reference measures whereas here mainly slug flow pattern has been investigated. RMSD% in steady-state condition was 6.5% for liquid and 20.6% for gas, being satisfactory for many applications, considering the fact the introduced flow rate meter operates without the need for any adjustment based on reference measurements or previous knowledge/assumption of the gas/vapor quality parameter, as has been usual for other similar recent developments.

On a realization of {\u03b2}-expansion in QCD

We suggest a simple algebraic approach to fix the elements of the {β}-expansion for renormalization group invariant quantities, which uses additional degrees of freedom. The approach is discussed in detail for N2LO calculations in QCD with the MSSM gluino — an additional degree of freedom. We derive the formulae of the {β}-expansion for the nonsinglet Adler D-function and Bjorken polarized sum rules in the actual N3LO within this quantum field theory scheme with the MSSM gluino and the scheme with the second additional degree of freedom. We discuss the properties of the {β}-expansion for higher orders considering the N4LO as an example.

Colloquium: An algebraic model of localized surface plasmons and their interactions

Although localized surface plasmons in metal nanoparticles can be modelled by Maxwell's equations, the difficulty in solving them forces many researchers to use numerical methods. Such methods give accurate results but rarely provide much insight into the complex behaviors of the surface plasmons, nor do they provide a means to choose a configuration of metal nanoparticles to achieve a desired optical response. This Colloquium presents a simple algebraic approach for modelling localized surface plasmons, their excitation by light and their interactions with one another. Although the method is not numerically accurate it yields useful insights into plasmon behavior and provides a basis for the design of complex plasmonic devices. The approach relies on a description of the surface plasmons in terms of a set of eigenmodes. However, the functional form of these modes is not usually required and the entire problem is reduced to a simple algebra involving the plasmon amplitudes, resonance terms and their mutual coupling. The algebraic method is derived from an electrostatic formalism, appropriate for near-field interactions at optical frequencies, which is then used to demonstrate a variety of optical effects associated with localized surface plasmons, such as plasmon hybridization, induced transparency, Fano resonances, optical phase detection and all-optical modulation, among others.

A process fault estimation strategy for non-linear dynamic systems

The paper deals with the problem of simultaneous state and process fault estimation for non-linear dynamic systems. Instead of estimating the fault directly, its product with state and the state itself are estimated. To derive the fault from the product, a simple algebraic approach is proposed. The estimation strategy is based on the quadratic boundedness approach. The final part of the paper presents an illustrative example concerning a laboratory multi-tank system. The real data experiments clearly exhibit the performance of the proposed approach.

Global stability of a class of futile cycles

In this paper, we prove the global asymptotic stability of a class of mass action futile cycle networks which includes a model of processive multisite phosphorylation networks. The proof consists of two parts. In the first part, we prove that there is a unique equilibrium in every positive compatibility class. In the second part, we make use of a piecewise linear in rates Lyapunov function in order to prove the global asymptotic stability of the unique equilibrium corresponding to a given initial concentration vector. The main novelty of the paper is the use of a simple algebraic approach based on the intermediate value property of continuous functions in order to prove the uniqueness of equilibrium in every positive compatibility class.

X-ray tube spectra measurement and correction using a CdTe detector and an analytic response matrix for photon energies up to 160 keV

The aims of our work were: i) to measure selected normalized X-ray beam spectra with the commercially available cadmium telluride detector based spectrometry system; ii) to construct the approximate response matrix of the detector using a simple algebraic model approach; iii) to reconstruct the physical energy spectra from the measured instrumental spectra using the detector response matrix; iv) to compare the obtained spectra parameters with the published and reference data in order to verify the model and to optimize the measurement setup if necessary. In particular, the spectra of five “narrow-spectrum series” beams, namely N60 to N150, were measured with a spectrometry system consisting of the Amptek XR-100T X-ray semiconductor detector and the PX5 multichannel analyser. Two different measuring geometries were used. The response matrix R(E, E′) of the detector was constructed which quantifies the energy dependence of the relative detection efficiency of the detector, the probabilities of the escape effects, and the probability of the Compton effect. A single matrix operation was applied to recover the physical energy spectra from the measured instrumental ones. The parameters of the corrected spectra were compared with the published and reference data. Despite the fact that the effect of incomplete charge collection was not implemented in the detector model, a fully satisfying quantitative correspondence was observed between the measured corrected spectra and the available reference data.

PI-PD controllers for controlling stable processes with inverse response and dead time

Many tuning methods for controlling stable processes with dead time can be found in the literature. Usually, proportional-integral-derivative (PID) controllers are used for this purpose. In practice, stable processes with inverse response characteristics can also be encountered. Addition of inverse response characteristic makes the control of a process more troublesome. Therefore, the use of PID controllers for tuning inverse response processes may lead to unsatisfactory closed loop responses. On the other hand, PI-PD controllers have been shown to perform in very good closed loop responses where PID controllers cannot result in satisfactory closed loop responses. Therefore, this paper adopts the structure previously suggested by the author for controlling processes without inverse response. This adaptation, in conjunction with a simple but powerful factorization, eliminates the affect of the inverse response term in the closed loop transfer function, hence resulting in a simplified design procedure. Tuning parameters of the PI-PD controller used in the control structure are found using standard forms, which is a simple algebraic approach and proven to be resulting in very satisfactory closed loop responses. Simulation examples are provided to illustrate the superiority of the proposed method over some existing ones.

Linear-algebraic bath transformation for simulating complex open quantum systems

In studying open quantum systems, the environment is often approximated as a collection of non-interacting harmonic oscillators, a configuration also known as the star-bath model. It is also well known that the star-bath can be transformed into a nearest-neighbor interacting chain of oscillators. The chain-bath model has been widely used in renormalization group approaches. The transformation can be obtained by recursion relations or orthogonal polynomials. Based on a simple linear algebraic approach, we propose a bath partition strategy to reduce the system-bath coupling strength. As a result, the non-interacting star-bath is transformed into a set of weakly coupled multiple parallel chains. The transformed bath model allows complex problems to be practically implemented on quantum simulators, and it can also be employed in various numerical simulations of open quantum dynamics.

Multiphase Fibonacci Switched Capacitor Converters

A simple algebraic approach to synthesize Fibonacci switched capacitor converters (SCC) is analyzed and the expected losses are estimated. The proposed approach reduces the power losses by increasing the number of target voltages. The synthesized Fibonacci SCC is compatible with the binary SCC and uses the same switch network. This feature is exceptionally beneficial as it provides the option to switch between the binary and Fibonacci target voltages, increasing thereby the resolution of attainable conversion ratios. The theoretical results were verified by experiments.

An algebraic approach to the study of multipartite entanglement

We introduce a simple algebraic approach to the study of multipartite entanglement for pure states together with a class of suitable functionals able to detect the entanglement. On this basis, we reproduce some known results. Indeed, by investigating the properties of the introduced functionals, we show that a subset of such class is strictly connected to the purity. Moreover, we provide a direct and basic solution to the problem of simultaneous maximization of three appropriate functionals for three-qubit states, confirming that the simultaneous maximization of the entanglement for all possible bipartitions is compatible only with the structure of the GHZ states.

An Algebraic Approach for Determining the Optimal Lot Size for EPQ Model with Rework Process

This paper presents a simple algebraic approach for deriving the optimal lot size for economic production quantity (EPQ) model with rework process. Conventional methods for solving lot size problems are by using differential calculus on the long-run average production-inventory cost function with the need to prove optimality first. A few recent articles proposed the algebraic approach to the solution of classic economic order quantity (EOQ) and EPQ model without reference to the use of derivatives. This paper extends it to an EPQ model with reworking of defective items. We demonstrate that optimal lot size and optimal production-inventory cost for such an imperfect EPQ model can be derived without derivatives. As a result, it may enable the practitioners or students who with little knowledge of calculus to understand or handle with ease the realistic production systems.

Internal axioms for domain semirings

New axioms for domain operations on semirings and Kleene algebras are proposed. They generalise the relational notion of domain–the set of all states that are related to some other state–to a wide range of models. They are internal since the algebras of state spaces are induced by the domain axioms. They are simpler and conceptually more appealing than previous two-sorted external approaches in which the domain algebra is determined through typing. They lead to a simple and natural algebraic approach to modal logics based on equational reasoning. The axiomatisations have been developed in a new style of computer-enhanced mathematics by automated theorem proving, and the approach itself is suitable for automated systems analysis and verification. This is demonstrated by a fully automated proof of a modal correspondence result for Löb’s formula that has applications in termination analysis.

A generalized algebraic model for optimizing inventory decisions in a centralized or decentralized multi-stage multi-firm supply chain

First of all, a number of integrated models with/without lot streaming under the integer multiplier coordination mechanism is generalized by allowing lot streaming and three types of inspection for some/all upstream firms. Secondly, the optimal solutions to the three- and four-stage models are individually derived, both using the perfect squares method, which is a simple algebraic approach so that ordinary readers unfamiliar with differential calculus can easily understand how to obtain the optimal solution procedures. Thirdly, optimal expressions for some well-known models are deduced. Fourthly, expressions for sharing the coordination benefits based on Goyal’s (1976) scheme are derived, and a further sharing scheme is introduced. Fifthly, two numerical examples for illustrative purposes are presented. Finally, some future research works involving extension or modification of the generalized model are suggested.

ALGEBRAIC APPROACH TO SPIN SYMMETRY FOR THE DIRAC EQUATION WITH THE TRIGONOMETRIC SCARF POTENTIAL

By a simple algebraic approach we study the exact solution to the Dirac equation with scalar and vector trigonometric Scarf potentials in the case of spin symmetry. The transcendental energy equation and spinor wave functions are presented. It is found that there exist only positive energy bound states in the case of spin symmetry. Also, the energy eigenvalue approaches a constant when the potential parameter α goes to zero. The equally scalar and vector case is studied briefly.

Balance point characterization of interstitial fluid volume regulation

The individual processes involved in interstitial fluid volume and protein regulation (microvascular filtration, lymphatic return, and interstitial storage) are relatively simple, yet their interaction is exceedingly complex. There is a notable lack of a first-order, algebraic formula that relates interstitial fluid pressure and protein to critical parameters commonly used to characterize the movement of interstitial fluid and protein. Therefore, the purpose of the present study is to develop a simple, transparent, and general algebraic approach that predicts interstitial fluid pressure (P(i)) and protein concentrations (C(i)) that takes into consideration all three processes. Eight standard equations characterizing fluid and protein flux were solved simultaneously to yield algebraic equations for P(i) and C(i) as functions of parameters characterizing microvascular, interstitial, and lymphatic function. Equilibrium values of P(i) and C(i) arise as balance points from the graphical intersection of transmicrovascular and lymph flows (analogous to Guyton's classical cardiac output-venous return curves). This approach goes beyond describing interstitial fluid balance in terms of conservation of mass by introducing the concept of inflow and outflow resistances. Algebraic solutions demonstrate that P(i) and C(i) result from a ratio of the microvascular filtration coefficient (1/inflow resistance) and effective lymphatic resistance (outflow resistance), and P(i) is unaffected by interstitial compliance. These simple algebraic solutions predict P(i) and C(i) that are consistent with reported measurements. The present work therefore presents a simple, transparent, and general balance point characterization of interstitial fluid balance resulting from the interaction of microvascular, interstitial, and lymphatic function.

A technical note on “Optimizing inventory decisions in a multi-stage multi-customer supply chain”

We first generalize Khouja [Khouja, M., 2003. Optimizing inventory decisions in a multi-stage multi-customer supply chain. Transportation Research Part E: Logistics and Transportation Review 39 (3), 193–208] integrated model considering the integer multipliers mechanism and next individually derive the optimal solution to the three- and four-stage model using the perfect squares method, which is a simple algebraic approach so that ordinary readers unfamiliar with differential calculus can understand the optimal solution procedure with ease. We subsequently deduce the optimal expressions for Khouja (2003) and Cárdenas-Barrón [Cárdenas-Barrón, L.E., 2007. Optimal inventory decisions in a multi-stage multi-customer supply chain: a note. Transportation Research Part E: Logistics and Transportation Review 43 (5), 647–654] model, and identify the associated errors in Khouja (2003). We present two numerical examples for illustrative purposes. We finally shed light on some future research by extending or modifying the generalized model.