Factorization Formula Research Articles

GENERALIZED DEFINITION OF THE APPARENT POWER AND ENERGY-EFFICIENT STRATEGIES OF ACTIVE FILTRATION IN THE REDUCED COORDINATE BASIS OF A MULTIPHASE POWER SUPPLY SYSTEM

The paper substantiates the equivalence of determining the apparent power of a multiphase power supply system with different transmission line impedances using the Fryze-Buchholz-Deppenbrock method and on a reduced coordinate basis. Two energy-efficient control strategies for shunt active filtering in the reduced coordinate basis are proposed. The first strategy provides a unit value of the power factor, and the second strategy minimizes power losses in the transmission line while maintaining symmetry and the quasi-sinusoidal shape of the consumed currents. The advantages of using a reduced coordinate basis are a reduction in the number of sensors and key active filter regulators as well as the absence of the problem to organize the artificial grounding point for phase voltage measurements. A correction factor for the apparent power and power factor formulas was determined and verified in the presence of restrictions on the symmetrical and sinusoidal shape of the consumed currents. References 22, figures 5, tables 2.

ALGORITHM FOR CALCULATING RELIABILITY OF ON-SITE POWER SUPPLY SCHEMES USING CONNECTION COEFFICIENTS

The article deals with the method of simplifying the forecasting of reliability parameters and assessing the technical condition of the most critical nodes of the power supply system by means of connection coefficients. The aim of the study is to develop a methodology to determine the probability of failure-free operation of the power supply scheme using connection coefficients. Materials and methods. The scheme of 10/0,4 kV power supply within the workshop is presented. Probabilistic methods of reliability determination and mathematical statistics were used. Research results. The probability of failure-free operation in time using the exponential distribution law has been calculated. Graphs of dependences of probability of system uptime on the number of load connections, as well as graphs of changes in the values of connection coefficients in time are presented. The formulas for the load connection factors depending on the number of connections are derived. The received analytical expressions allow to model values at possible additional load connections. The obtained dependences allow to determine the probability of failure-free operation time of low-voltage electrical equipment, as well as the schemes of the in-house power supply. Conclusions. The proposed methodology simplifies the forecasting of reliability parameters of the scheme of the internal shop power supply and the assessment of the technical condition of the most important and critical nodes. The modeled values of the load connection coefficients can be used in technical and economic calculations, namely for further increase of the number of outgoing lines from the switchboard and distribution point or increase of the load on the line taking into account the permissible probability of failure-free operation of the scheme. The results of the study are recommended to evaluate technical performance and determination of the main reliability parameters of the operating systems of in-plant power supply.

Dynamic compressive properties and constitutive model of waste crumb rubber (CR) modified ultra-high performance engineered cementitious composites (UHP-ECC)

Ultra-high-performance engineered cementitious composites (UHP-ECC) are well-known for their outstanding mechanical properties under static and dynamic loads. However, the effect of modifying UHP-ECC with crumb rubber (CR) on its performance, especially under high strain rates, remains poorly understood. This study systematically examined the dynamic compressive behavior and characteristic failure patterns of CR-modified UHP-ECC under high strain rates using a split Hopkinson pressure bar (SHPB) system. The study focused on evaluating the dynamic compressive strength, stress-strain response, and strain energy density (SED). A dynamic increase factor (DIF) formula was developed based on experimental data, and a nonlinear viscoelastic constitutive model was proposed to predict compressive behavior across various strain rates. Results indicate that while the addition of 10% CR slightly reduces the quasi-static compressive and flexural strength, it significantly enhances tensile ductility. Under high strain rates, CR-modified UHP-ECC shows no substantial effect on peak compressive stress but a marked increase in peak compressive strain. The SED also increased by 20.2%, outperforming other high-performance materials such as UHPC and normal ECC. These findings demonstrate that incorporating 10% CR into UHP-ECC offers considerable advantages, particularly in enhancing structural resilience under dynamic loading conditions. The proposed nonlinear viscoelastic model accurately predicts the compressive behavior of CR-modified UHP-ECC, presenting significant implications for practical engineering applications where high strain rate performance is crucial.

There and Back Again: Mapping and Factorizing Cosmological Observables.

Cosmological correlators encode invaluable information about the wave function of the primordial Universe. In this Letter we present a duality between correlators and wave function coefficients that is valid to all orders in the loop expansion and manifests itself as a Z_{4} symmetry. To demonstrate the power of the duality, we derive a correlator-to-correlator factorization formula for the parity-odd part of cosmological correlators that relates n-point observables to lower-point ones via a series of diagrammatic cuts. These relations serve as the first example of physically testable cutting rules as they involve observables defined for arbitrary physical kinematics. We further show how the duality allows us to translate the cosmological optical theorem for wave function coefficients into statements about cosmological correlators.

Factorization of rational six vertex model partition functions

We show factorization formulas for a class of partition functions of rational six vertex model. First we show factorization formulas for partition functions under triangular boundary. Further, by combining the factorization formulas with the explicit forms of the generalized domain wall boundary partition functions by Belliard-Pimenta-Slavnov, we derive factorization formulas for partition functions under trapezoid boundary which can be viewed as a generalization of triangular boundary. We also discuss an application to emptiness formation probabilities under trapezoid boundary which admit determinant representations.

Cold nuclear matter effects on azimuthal decorrelation in heavy-ion collisions

The assumption of factorization lies at the core of calculations of medium effects on observables computable in perturbative Quantum Chromodynamics. In this work we examine this assumption, for which we propose a setup to study hard processes and bulk nuclear matter in heavy-ion collisions on the same footing using the Glauber modelling of heavy nuclei. To exemplify this approach, we calculate the leading-order corrections to azimuthal decorrelation in Drell-Yan and boson-jet processes due to cold nuclear matter effects, not considering radiation. At leading order in both the hard momentum scale and the nuclear size, the impact-parameter dependent cross section is found to factorize for both processes. The factorization formula involves a convolution of the hard cross section with the medium-modified parton distributions, and, for boson-jet production, the medium-modified jet function.

Development of Friction Factor-Generalized Equation for Multi-Shapes Microchannel

The major goal of this research is to use computational fluid dynamics, CFD to derive a generalized friction factor formula for a smooth micro-size channel in a laminar flow regime. Based on the number of channel sides and the Reynolds number value, this generated formula can be used to precisely calculate the friction factor. The microchannel shapes are correlated to the friction factor constant as a function of the number of channel sides, N, starting from infinity for a circular microchannel, down to 3 numbers of N, for a triangular microchannel. The following microchannel shapes with a constant hydraulic diameter of 104 µm are selected, which are triangle, square, pentagon, hexagonal, octagonal, decagon, and circle. The developed equation works for a fully developed laminar flow range up to Reynolds number of 2000. Moreover, the current work results are further compared with the previous results of microchannels for verification within acceptable value of 0.07% to 0.48%.

Response and seismic resilience of metro tunnels under normal fault dislocation evaluated based on the quantitative method of concrete damage state

The damage to tunnels crossing active fault zones caused by earthquakes can be of a severe and irreversible nature. The paper defines the quantification of the concrete damage state based on the uniaxial compression equation and the tensile-compression curve equation. Furthermore, the paper refines the concrete damage level in conjunction with the damage factor and crack width formulas, which is one of the most significant factors affecting the durability of concrete. A three-dimensional refinement model, constructed using ABAQUS software, was employed to analyse the mechanical response and seismic resilience of the tunnel structure under normal fault displacement with variable section mitigation measures. The model incorporated a number of key parameters, including fortification length, joint location and thickness. The following conclusions were obtained: the tunnel structure is susceptible to tensile damage and the damage is widely distributed under normal fault d; the use of variable section measures can help improve and reduce the overall damage of the cross-fault metro tunnel structure; the use of tensile damage state classification to assess the damage of the tunnel structure can determine the location and extent of the damage; an appropriate protection length is required, too long/short does not maximise the mitigation effect of setting variable section measures; an appropriate lining length is required; and the lining structure is not suitable for the tunnel structure. An appropriate location and thickness of the lining structure will help to reduce the overall damage to the structure. The application of localised reinforcement to the structure, in conjunction with variable section, serves to minimise the probability of collapse of the tunnel as a whole and to enhance the seismic resilience of the underground structure across the active fault zone.

Hard-scattering approach to strongly hindered electric dipole transitions between heavy quarkonia

The conventional wisdom in dealing with electromagnetic transition between heavy quarkonia is the multipole expansion, when the emitted photon has a typical energy of order quarkonium binding energy. Nevertheless, in the case when the energy carried by the photon is of order typical heavy quark momentum, the multipole expansion doctrine is expected to break down. In this work, we apply the “hard-scattering” approach originally developed to tackle the strongly hindered magnetic dipole (M1) transition [Y. Jia , ] to the strongly hindered electric dipole (E1) transition between heavy quarkonia. We derive the factorization formula for the strongly hindered E1 transition rates at the lowest order in velocity and αs in the context of the nonrelativistic QCD, and conduct a detailed numerical comparison with the standard predictions for various bottomonia and charmonia E1 transition processes. Published by the American Physical Society 2024

Several kinds of integral factors for first order nonlinear ODEs and some parts of their solutions

Abstract For the first-ordered nonlinear ordinary differential equations, we explore several kinds of integral factors in this paper, where the concrete formulas of the integral factors are acquired, and some of them are applied to solve corresponding nonlinear ordinary differential equations. At first, the sufficient and necessary condition of linearity for ordinary differential equations is proved that the ordinary differential equations are linear if and only if their integral factors only have a unique independent variable. Secondly, for several types of nonlinear ordinary differential equations, their corresponding integral factors formulas are discussed with not the same methods according to their special characters and different structures. Finally, among some of the integral factors, they are applied to complete to solve their matching first-ordered nonlinear ordinary differential equations.

Low and moderate x gluon contribution to exclusive Compton scattering processes

We revisit the high energy semi-classical description of the exclusive processes DVCS, TCS, and Double DVCS by explicitly keeping track of the Feynman x dependence in both the hard and the hadronic matrix elements. This is achieved by a modification of the standard shock wave approximation to derive the effective Feynman rules, which leads to a generic expression on which we then perform a partial twist expansion to get rid of quantities suppressed by the proper physical scales. We obtain a compact factorized master formula that can be used to investigate the Bjorken limit at leading twist. In particular, we recover the full one-loop result in the collinear limit for pure gluon exchange with the target. Finally, we discuss the subtleties in taking the simultaneous collinear and small x limit.

Investigation of the Fitness for Service (FFS) of Cracks in API 5L X70 Pipeline Steel using Failure Assessment Diagram (FAD)

In this study, the fitness for service of crack propagation in API 5L X-70 stee1 was investigated using a model called Failure Assessment Diagram (FAD) to determine how fit a crack can be under certain operational pressure. It is a known fact that during the production of pipes, there are tendencies for flaws such as inclusions and cracks to occur in the pipes. When these flaws are subjected to stresses, there are tendencies for failures to occur starting from where the cracks or flaws are located. The failure due to the propagation of the cracks leads to oil spillage causing pollution to the environment which had negatively impacted livelihood of the host communities and aquatic lives. This had resulted in Government spending huge amount of money maintaining the pipelines and remediation. The purpose of this paper is to investigate the fitness for service of crack lengths 12 mm, 17 mm, 22 mm and 27 mm using the Failure Assessment Diagram (FAD) mode1. The material used in this paper is API 5L X 70 steel in the form of a Compact Tension (CT) specimen machined according to ASTM E1820 – 13. API 5L X-70 stee1 is a low-carbon stee1 with a carbon content of as low as 0.04 %. It is used in the production of pipelines for conveying crude oil and natural gas from the place of production to the place of refining or export. In the investigation of the fitness for service of the cracks, a charpy V-notch impact test was carried out to determine the energy required to fracture the steel, which was later inputted numerically into a critical stress intensity factor formula in accordance with BS 7910 – 13 standards to obtain the critical stress intensity factor (KIC or KQ). The stress intensity factor (KI) was obtained from formula also according to BS 7910 – 13 standards. The ratio of KI to KQ was used in the FAD analysis. Subsequently, a monotonic tensile test was conducted to obtain the yield stress ( ys) and the reference stress ( ref) was obtained numerically according to BS 7910 – 13. The ratio of ref) to ys) was also used in the FAD analysis. The FAD analysis was used to determine the fitness for services and fracture behaviour of each crack. Scanning electron microscopy (SEM) was used to confirm the fracture behaviour obtained from the FAD. The results obtained show that the energy from the charpy V-notch impact test was 302.9 J and the critical stress intensity factor (KQ) correlated numerically according to BS 7910 – 13 was determine as 246.73 MPa . The yield stresses obtained from the monotonic test for crack lengths of 12 mm, 17 mm, 22 mm and 27 mm were 132.51 MPa, 109.10 MPa, 114.36 MPa and 118.21 MPa, respectively. In the FAD analysis, it was observed that the safe operational stress to ensure fitness for service decreases with an increase in crack length. The fracture behaviour shows a ductile fracture behaviour since the FAD lies within the plastic collapse region. This fracture behaviour was confirmed by the image obtained from the scanning electron microscopy (SEM), which showed a cup and cone image suggesting ductile fracture behaviour. This FAD method will ensure that safe operational stresses are maintained for various crack length to prolong the life span of the pipeline. It is a novel method that can also be used to properly schedule the rate of inspection in pipelines alongside Ultrasonic sound, Liquid penetrant, Magnetic particle and radiographic methods of inspection.

The transverse energy-energy correlator at next-to-next-to-next-to-leading logarithm

We present an operator based factorization formula for the transverse energy-energy correlator in the back-to-back (dijet) region, and uncover its remarkable perturbative simplicity and relation to transverse momentum dynamics. This simplicity enables us to achieve next-to-next-to-next-to leading logarithmic (N3LL) accuracy for a hadron collider dijet event shape for the first time. Our factorization formula applies to W/Z/γ + jet, and dijet production, providing a natural generalization of transverse momentum observables to one- and two-jet final states. This provides a laboratory for precision studies of QCD and transverse momentum dynamics at hadron colliders, as well as an opportunity for understanding factorization and its violation in a perturbatively well controlled setting.

Revisiting wave friction factors for rough turbulent flow

The wave friction factor 𝑓𝑤 and the phase lead of the seabed shear stress over the free stream velocity 𝜑 for rough turbulent flow are revisited by utilizing the similarity theory used by Myrhaug (1989). Results are obtained for 𝑓𝑤 and 𝜑 by determining the similarity coefficients using the Dixen et al. (2008) data for large bed roughness. Comparisons are made with other experimental data and wave friction factor formulae. As a result, an approximation for 𝑓𝑤 by disregarding the phase 𝜑 is recommended covering a wide range of amplitude-to-roughness ratios.

Analysis on slope stability by anchorage based on soil creep with flood effect

In order to analyze the adverse effect of flood affection on slope stability, the analytical expressions of buoyancy force and capillary force, hydrodynamic pressure and impact force, and scour erosion were proposed based on the aging characteristics of soil shear strength and limit equilibrium theory. According to the load combination and flood action, shear failure occurs preferentially at the foot of slope. Then, the plastic zone continues to extend upward to produce traction landslide disaster mode. Furthermore, the power function relation between shear strength index and time was established. The nonlinear accelerated creep model was also obtained. At the same time, the safety factor formula for flood loading effect slope aging stability, the time-varying characteristic value of anchor force and the compensation value of anchor force were also obtained and used to research sliding mechanism. In addition, the numerical calculation example shows that the slope safety factor decreases by more than 20 % considering the effect of flood ascending scour and impact, and the compensation value of anchorage force increases obviously with time increasing. Simultaneously, the change rate of compensation value of anchorage force increases nonlinearly with the increase of design safety factor.

Expressions for Stress Concentration Factors for T-Joints of Hollow and Concrete-Filled Square Cross-Sections for In-Plane Axial and Bending Loads

In recent years, square hollow section (SHS) joints with concrete-filled square hollow section (CFSHS) chords have increasingly been used in truss bridges where the fatigue life reliability is a critical issue. In this paper, a finite element analysis was performed to investigate the SCFs in SHS-CFSHS T-joints under in-plane bending in the brace, axial force in the chord and in-plane bending in the chord. The finite element models were developed and validated with experimental results. Then a parametric study was conducted with a reasonable range of three key non-dimensional parameters, i.e., β (width ratio between brace and chord), 2γ (width–to–wall thickness ratio of the chord) and τ (wall thickness ratio between brace and chord). Consequently, the stress concentration factor formulae for the fatigue design of SHS-CFSHS T-joints were proposed through multiple regression analysis. For in-plane bending in the brace, the maximum stress concentration factors were found at lines B and C for thick-walled chords (2γ = 25.0), while the stress concentration factors at all the lines need to be checked for thin-walled chords (2γ < 16.0). Under axial force in the chord and in-plane bending in the chord, only stress concentration factors at lines C and D needed to be considered. A comparison of stress concentration factors between SHS-SHS and SHS-CFSHS joints showed reductions of 10~26% and 14~31% in stress concentration factors in SHS-CFSHS joints under axial force in the brace and in-plane bending in the brace, respectively. In addition, it showed a general increase in stress concentration factors in SHS-CFSHS joints under axial force and in-plane bending in the chord. This reduction is attributed to the reduction in chord face deformation benefiting from the in-filled concrete. Meanwhile, the stress concentration factors caused by loads in the chord are much lower than those caused by loads in the brace. This work complements earlier studies on SHS-CFSHS T-joints under axial force.

Pendeteksian Kerusakan Komputer Editing Sinetron Pada Sistem Pakar Dengan Metode Certainty Factor

An expert system is a device designed with the thought processes of one or more experts in specific or complex fields of knowledge. This system is built on instructional elements that identify and analyze data to address unstructured problems or conduct mathematical analyses of particular issues. With the advancement of web-based information technology, computer damage detection becomes easier for users. Therefore, a web-based expert system application using the certainty factor method is needed to detect computer damage. The certainty factor method works based on symptoms and diagnoses weighted by experts and user input. These weights are then calculated using the certainty factor formula to produce a confidence level in the given diagnosis. The end result is the creation of an expert system application capable of detecting computer damage for users using the web-based certainty factor method. This application not only enhances efficiency in detecting damage but also facilitates maintenance processes by providing a history of damage detection, thereby reducing the time required for repairs. Thus, this application offers an effective and efficient solution for computer damage detection. Additionally, this application can be continually developed and adapted to user needs, making it a highly useful tool in computer maintenance across various environments.

Power counting to saturation

We present a description of saturation in small x deep inelastic scattering from power counting in a top-down effective theory derived from quantum chromodynamics (QCD). A factorization formula isolates the universal physics of the nucleus at leading power in x. The onset of saturation is then understood as a breakdown in the expansion in an emergent power counting parameter, which is defined by the matrix element of a gauge invariant operator. We identify a new radiation mode, which enables us to extend previous literature by distinguishing the appearance of the saturation scale from the transition to nonlinear evolution. Published by the American Physical Society 2024

Small field measurements using electronic portal imaging device

Purpose/Objective. Small-field measurement poses challenges. Although many high-resolution detectors are commercially available, the EPID for small-field dosimetry remains underexplored. This study aimed to evaluate the performance of EPID for small-field measurements and to derive tailored correction factors for precise small-field dosimetry verification. Material/Methods. Six high-resolution radiation detectors, including W2 and W1 plastic scintillators, Edge-detector, microSilicon, microDiamond and EPID were utilized. The output factors, depth doses and profiles, were measured for various beam energies (6 MV-FF, 6 MV-FFF, 10 MV-FF, and 10 MV-FFF) and field sizes (10 × 10 cm2, 5 × 5 cm2, 4 × 4 cm2, 3 × 3 cm2, 2 × 2 cm2, 1 × 1 cm2, 0.5 × 0.5 cm2) using a Varian Truebeam linear accelerator. During measurements, acrylic plates of appropriate depth were placed on the EPID, while a 3D water tank was used with five-point detectors. EPID measured data were compared with W2 plastic scintillator and measurements from other high-resolution detectors. The analysis included percentage deviations in output factors, differences in percentage for PDD and for the profiles, FWHM, maximum difference in the flat region, penumbra, and 1D gamma were analyzed. The output factor and depth dose ratios were fitted using exponential functions and fractional polynomial fitting in STATA 16.2, with W2 scintillator as reference, and corresponding formulae were obtained. The established correction factors were validated using two Truebeam machines. Results. When comparing EPID and W2-PSD across all field-sizes and energies, the deviation for output factors ranged from 1% to 15%. Depth doses, the percentage difference beyond dmax ranged from 1% to 19%. For profiles, maximum of 4% was observed in the 100%–80% region. The correction factor formulae were validated with two independent EPIDs and closely matched within 3%. Conclusion. EPID can effectively serve as small-field dosimetry verification tool with appropriate correction factors.

Field Theory of the Fermi Function.

The Fermi function F(Z,E) accounts for QED corrections to beta decays that are enhanced at either small electron velocity β or large nuclear charge Z. For precision applications, the Fermi function must be combined with other radiative corrections and with scale- and scheme-dependent hadronic matrix elements. We formulate the Fermi function as a field theory object and present a new factorization formula for QED radiative corrections to beta decays. We provide new results for the anomalous dimension of the corresponding effective operator complete through three loops, and resum perturbative logarithms and π enhancements with renormalization-group methods. Our results are important for tests of fundamental physics with precision beta decay and related processes.