Dimensionless Quantities Research Articles

Equation of State of Quark–Gluon Matter in the Clustering-of-Color-Sources Approach

In the first few microseconds after the Big Bang, the hot dense matter was in the form of quark–gluon plasma consisting of free quarks and gluons. By colliding heavy nuclei at RHIC and LHC at a velocity close to the speed of light, we were able to recreate primordial matter and observe that matter after expansion and cooling. In the present work, we have analyzed the transverse-momentum spectra of charged particles in high-multiplicity pp collisions at LHC energies s= 5.02 and 13 TeV, published by the ALICE Collaboration, using the Color-String Percolation Model. For heavy ions, Pb–Pb at sNN= 2.76 and 5.02 TeV along with Xe–Xe at sNN= 5.44 TeV have been analyzed. The initial temperature was extracted both in low- and high-multiplicity events in pp collisions. For A−A collisions, the temperature was obtained as a function of centrality. A universal scaling in the temperature from pp and A−A collisions was obtained when multiplicity was scaled by the transverse interaction area. For the higher-multiplicity events in pp collisions at s= 5.02 and 13 TeV, the initial temperature was above the universal hadronization temperature and was consistent with the creation of deconfined matter. From the measured energy density ε and the temperature, the dimensionless quantity ε/T4 was obtained, to obtain the degree of freedom of the deconfined matter.

Quantum backflow for a free-particle hermite wavepacket

Abstract Quantum backflow is the unexpected effect that wavepackets consisting of only positive momentum components can apparently move in the negative direction. This is usually described in terms of the backflow constant, which is a dimensionless quantity describing least upper bound on the amount of probability that can flow backwards during a given time interval. Backflow is usually calculated for wavepackets that can be written as a sum of positive momentum plane waves. Here we present a calculation of the backflow constant using the localised free particle hermite wavefunctions where equal weights of positive and negative momentum eigenfunctions occur. The resulting backflow constant is substantially smaller than the accepted value. The reasons for this are discussed and finally we draw conclusions about the calculation of backflow more generally.

Flow and heat transfer of nanofluids in a cylindrical permeable wavy channel embedded in porous medium using Buongiorno’s model

This investigation deals with the flow of Al2O3–water nanofluid in a wavy porous channel embedded in porous rocks. Fluid exchange takes place uniformly between porous rocks and the wavy channel. In this analysis, cylindrical and parallel plate wavy porous channels are considered. Consequences of Brownian motion and thermophoresis on the flow inside a wavy porous channel are elucidated. The modeled equations are made dimensionless by using dimensionless quantities. Impacts of flow parameters on the velocity, temperature, Nusselt number and friction factor are depicted through graphs. The numerical results with respect to parallel plate wavy porous channel are validated by comparing with the published results. The effectiveness of the cylindrical wavy porous channel as a heat transfer enhancement device in comparison to the parallel plate wavy porous channel is confirmed in this study. Designing devices at microlevels and understanding the heat transfer enhancement mechanism in wavy channels using the nanoparticle addition are the major outcomes from the results of this numerical investigation. The heat and mass transfer rate enhancements in the wavy porous channels are due to the higher Brownian motion in the boundary layer region and accelerated thermophoresis through thermal and concentration boundary layer thicknesses.

Semi-Analytical Approach and Green's Function Method: A Comparison in the Analysis of the Interaction of a Moving Mass on an Infinite Beam on a Three-Layer Viscoelastic Foundation at the Stability Limit-The Effect of Damping of Foundation Materials.

In this paper, the interaction of a mass moving uniformly on an infinite beam on a three-layer viscoelastic foundation is analyzed with the objective of determining the lowest velocity at the stability limit, called, in this context, the critical velocity. This issue is important for rail transport and, in particular, for the high-speed train, because the moving mass is the basic model of a vehicle, and the infinite beam on a three-layer viscoelastic foundation is the usual mechanical representation of the railway track. In addition to this, the advantages and disadvantages of the two implemented methods, namely, the semi-analytical approach and the Green's function method, are summarized in terms of computational time, the precision of the obtained results, limitations, and the feasibility of implementation. All results are presented in a dimensionless form to cover a wide range of possible scenarios. Some results may be considered academic, however, results related to a particular railway track are also included. Particular attention is paid to the influence of the damping of materials in the foundation upon the critical velocity of the moving mass. Regarding the semi-analytical approach, it is demonstrated that the critical velocities can be obtained in an exact manner by tracing the branches of the so-called instability lines in the velocity-moving-mass plane. This analysis can be maintained within the real domain. As for the time series, they can be determined by a numerical inverse Laplace transform. Moreover, thanks to the analytical form of the final result in the Fourier domain, each value corresponding to a specific time instant can be obtained directly, that is, without the previous time history. Regarding the Green's function method, this is used to verify a few points delimiting the stable and unstable regions of the moving mass with the help of the D-decomposition approach. Additionally, a numerical algorithm based on the Green's function and convolution integral written for dimensionless quantities is used to calculate the time series of the moving mass. In addition to identifying the critical velocity of the moving mass, its connection with the critical velocity of the moving force is emphasized, and the possibility of validating the results on long finite beams using modal expansion is presented and described.

Irrotational flow analysis of Rayleigh-Taylor instability in nanofluid layer with tangential magnetic field

The application of nanofluids in the presence of a magnetic field holds promise for advanced drug delivery systems, where controlled manipulation of magnetic nanoparticles within nanofluids can enhance targeted and localized drug delivery. This study explores the instability of a viscous fluid-nanofluid interface arranged in a planar configuration influenced by a tangential magnetic field using the irrotational flow theory. When the nanofluid is positioned above a viscous fluid, the interface is susceptible to the Rayleigh-Taylor instability. Employing linear stability theory, an explicit relationship connecting the perturbation growth parameter with the wavenumber is derived. Different dimensionless quantities such as the Atwood number, Weber number, Froude number, and Reynolds number are analyzed using stability plots. These plots provide valuable information about the behavior of interfaces. Increased magnetic field strength is observed to delay instability onset. Surface tension is found to stabilize the interface, whereas inertial forces destabilize it. This investigation contributes to understanding and controlling the interface dynamics in nanofluid systems.

A Baseline‐Free Electromechanical Impedance Resonance Method for Measuring the Modulus of Elasticity of Concrete Cubes Using Surface‐Bonded PZT Patches

The modulus of elasticity of concrete (Ec) is an essential parameter commonly used in concrete design, concrete curing monitoring, and deterioration evaluation and damage detection of concrete structures. A quick and reliable in situ determination of Ec helps in accurate decision‐making for construction and maintenance. The electromechanical impedance (EMI) technique using surface‐bonded lead zirconate titanate (PZT) patches (referred to as SBP) has become a popular nondestructive method for monitoring concrete structures due to ease of operations. The existing research mainly utilized baseline‐dependent approaches to monitor the changes (e.g., hardening or damage evolution) of concrete structures. However, relevant baselines are greatly influenced by the status of PZT sensors and bonding layers, limiting the practical applications of this technique. This paper presents a baseline‐free EMI resonance method for measuring Ec of concrete without using prior baseline data for the first time. Numerical and experimental studies on standard concrete cubes (100 mm in width) with SBP were conducted to examine the proposed method. A dimensionless physical quantity was first proposed to view the EMI signals. Then, resonance peaks highly related to concrete properties but insensitive to the status of the sensor system were selected, physically described, and correlated to the concrete parameters through numerical analyses. Finally, experimental validations, covering the measurement of Ec, repeatability of the chosen resonance peaks, and temperature effects, were conducted to illustrate the proposed method’s stability, accuracy, and sensitivity.

Numerical and physical modeling of the aerodynamic process in a direct-flow coil-type boiler using a laboratory stand

The article examines the modes of gas passage through the chimney of a direct-acting steam generator set using a laboratory stand made of a cylindrical coil. The criterion for determining the gas flow regime is a dimensionless quantity called the Reynolds number. The air flow velocities and temperatures were determined experimentally. Based on these results, the Reynolds number was calculated and the flow regimes at each measurement point were determined, and the dependence of the Reynolds number on temperature and velocity was obtained, and the experiment was analyzed. With the help of the ANSYS program, a model of air movement on the stand was built. When deciphering the geometric model, the ANSYS SpaceClaim program was used. The model made it possible to estimate the distribution of the air flow velocity in the boiler model based on experimental values. Further, after constructing a geometric model using the ANSYS Icem CFD program, a dispersion model was cre-ated that showed the temperature distribution of flue gases in the external gas flow of the basic model of a direct-flow steam boiler. The processing of experimental data showed a further prospect of intensification of the heat exchange process in a direct-flow steam boiler of the coil type.

EDL Induced Electro-magnetized Modified Hybrid Nano-blood Circulation in an Endoscopic Fatty Charged Arterial Indented Tract.

The electrokinetic process for streaming fluids in magnetic environments is emerging due to its immense applications in medical and biochemical industrial domains. In this context, our proposed model seeks to inquire into the hemodynamic characteristics of electro-magnetized blood blended with trihybrid nanoparticles circulation induced by electro-osmotic forces in an endoscopic charged arterial annular indented tract. This steaming model also invokes the consequences of variable Lorentz attractive force, buoyancy force, heat source, viscous and Joule warming, arterial wall properties, and sliding phenomena for featuring more realistic problems in blood flows. Different shapes of suspended trihybrid nanoparticles, such as spheres, bricks, cylinders, and platelets, are included in the model formation. Electro-magnetized modified hybrid nano-blood is an electro-conductive solution comprising blood as base fluid and magnetized trihybrid nanoparticles (copper, gold, and alumina). Closed-form solution in terms of Bessel's functions is gotten for electro-osmotic potential due to the electric double layer (EDL). The homotopy perturbation methodology is implemented in order to track down the convergent series solutions of non-linear coupled flow equations being elicited. The physical attributes of distinct evolving parameters on the different dimensionless hemodynamic profiles and quantities of interest are elucidated evocatively via a sort of graphs and charts. The ancillary outcomes proved that the Debye-Hückel parameter and Helmholtz-Smoluchowski velocity have a dual impact on the ionized bloodstream. The bloodstream rapidity is alleviated/boosted for the assisting/opposing electroosmosis process. Cooling of ionized blood in the endoscopic arterial conduit is achieved with lower Hartmann numbers. Copper-gold-alumina/blood exhibits a superior heat transmission rate across the arterial wall than copper-gold-blood, copper-blood, and pure blood. Additionally, the contour topology for the bloodstream in the flow domain is briefly elaborated. The contour distribution is significantly amended due to the variant of the Debye-Hückel parameter. The model's new findings may be invaluable in electro-magneto-endoscopic operation, electro-magneto-treatment for cancer, surgical process, etc.

Critical heat flux for downward flows in vertical round pipes

Pressurized thermal shock (PTS) is one of the causes of pressure vessel failure during nuclear reactor accidents. Critical heat flux (CHF) for downward flow is an essential thermohydraulic parameter for predicting PTS using nuclear reactor system codes. While many experimental data have been accumulated and many correlations have been proposed for CHF for upward flow, only a few studies exist on downward flow. This study reviewed the literature that measured CHF for downward flow in round pipes and arranged the proposed correlations. Then, we extracted the parameter values that determine experimental conditions and CHF values from the literature and compared the CHF values predicted from the correlation in each study and the measured CHF values under those conditions across the literature. Each correlation shows relatively good prediction accuracy (average prediction accuracy of 10%–30%) for experimental data from their literature, but the accuracies sometimes decrease for experimental data from other literature. No correlation accurately predicts all the experimental data of the literature, indicating an issue in extrapolating existing correlations. Therefore, we developed a correlation that can accurately predict the experimental data of the collected literature. First, we used a neural network to select the essential dimensionless quantities that comprise the correlation. Then, we regarded the prediction accuracy when all candidate dimensionless quantities extracted from the literature were used for the input variables of the network as the achievable limit prediction accuracy and searched for the minimum combination of dimensionless quantities required to achieve it. The results showed that only the dimensionless mass flux (G*) and the ratio of the heating length to the channel diameter (L/D) are the essential parameters to achieve it. We developed a correlation equation using these two dimensionless quantities and achieved 17.6% of the average prediction accuracy. This result considerably improved existing correlation equations with 25%–40% average prediction accuracy for the same experimental data. Furthermore, unlike many existing correlations, it has excellent practical features, such as applicability over wide parameter ranges and no need to separate cases.

Study of Quality and Damping Factor at First and Second Resonance of Closed Organ Pipe

The quality factor is a dimensionless physical quantity related to the damping factor present in the medium. The sound is recorded from the resonance tube experiment at the first and second resonating lengths. It is analyzed by PRAAT software to calculate the quality and damping factor. The quality factor varies from 12.50 to 146.70 and 6.32 to 130.95 at first and second resonant length respectively. In case of damping factor, it varies from 3.50x10−3 to 40.00x10−3 and 3.82 x10−3 to 79.11x10−3 at respective first and second resonating length. The ratio of the quality factor of the second resonance to that first resonance varies from 0.49 to 0.97 and for the damping factor that ratio varies from 1.02 to 2.02. The quality factor is higher at the first resonating length than at the second resonating length. The damping factor is lower in the first resonating length than in the second resonating length. From the experiment on the closed organ pipe, it was found that the system is under-damped due to the damping factor of less than one. At the first and second resonating lengths the relation between quality and damping factor is inversely nature.

The absorbing boundary conditions of Newtonian fluid flowing across a semi-infinite plate with different velocities and pressures

Abstract The Newtonian fluid flowing across a semi-infinite plate with variable velocity and pressure is considered in this work. The dimensionless governing equation is obtained by introducing the dimensionless quantities. For infinite region, the artificial boundary approach by using the Laplace transform is applied to gain the absorbing boundary condition (ABC) in a finite region which we call the inner region. The approach differs from the traditional approximation method for infinite boundaries with large values and is first applied to the research. And the stability of the ABC is verified by considering the same point of the outer region and inner region. The numerical difference scheme by using the L1-scheme to approximate the fractional derivative is used to get solutions, and the feasibility assessments, such as stability and convergence, are developed. Three numerical examples are given. In the first example, the exact solution is gained by importing a source term. Through the comparison of numerical solution with exact solution verifies the accuracy of difference method. A comparison between the velocity distribution of the ABC and the infinite boundary approximated by a large value is also discussed and graphically analyzed. In the following two examples, by analyzing the fluid flow over the plate with assorted speeds or pressure gradient, the impact of correlative parameters on the velocity distribution and the flow mechanism are thoroughly analyzed.

FRACTAL SPACE BASED DIMENSIONLESS ANALYSIS OF THE SURFACE SETTLEMENT INDUCED BY THE SHIELD TUNNELING

The surface settlement during the tunneling process is becoming increasingly difficult to forecast as its surroundings become more and more erratic, and the maximal surface settlement raises risks posed suddenly by various uncertain factors. This paper proposes a novel approach to prediction of the surface settlement and analyzes the stability of tunnel construction. The dimensionless analysis and Buckingham’s π-theorem are adopted for this purpose, and some useful dimensionless quantities are found, which can be used to determine the surface settlement’s main properties. In this manner, the paper offers new ways of predicting surface settlement in various cases, and it sheds a new light on the tunnel’s design and safety monitoring.

Effect of Heat and Mass Transfer over Mixed Convective Hybrid Nanofluids past an Exponentially Stretching Sheet

The presented study investigates the heat and mass transfer characteristics of hybrid nanofluid flow past an exponentially enlarging sheet, featuring both heat source and sink effects. A distinctive aspect of this work lies in its examination of slip conditions to understand the flow behavior of hybrid nanofluids. The nanofluid itself consists of a blend of copper (Cu) and metal oxide (Al2O3) nanoparticles suspended in blood, which serves as the base fluid. This choice of nanofluid composition is noteworthy due to its potential impact on enhancing heat and mass transfer processes. Similarity conversion technique is applied that effectively transforms the partial differential equations (PDEs) governing the system into a set of ordinary differential equations (ODEs). The utilization of tables and graphs aids in conveying the influence of various embedded parameters on the obtained results. This graphical representation of parameter effects is a distinctive feature of the study, facilitating a clearer understanding of the relationships between different variables. In the concluding remarks, the study's outcomes highlight several distinctive findings. Firstly, an increase in the heat-generating parameter leads to elevated temperature distribution along the expanding sheet. Secondly, the introduction of a magnetic parameter is found to dampen the velocity of the nanofluids, which presents an interesting avenue for exploration in terms of flow control. Thirdly, the concentration profile of the nanofluids experiences a decline as the Schmidt number, a dimensionless quantity representing the ratio of momentum diffusivity to mass diffusivity, increases. It concluded that the heat and mass transfer rate is greatly enhanced by the addition of copper and aluminium oxide. This observation is a unique contribution to the understanding of heat and mass transfer behavior in such systems. The significance of this research extends to various applications, particularly in the realms of chemical engineering, environmental remediation processes, and solar thermal systems.

Investigating the effect of structural changes of two stretching disks on the dynamics of the MHD model

The purpose of this theoretical study is to explore the behavior of an electrically conducting micropolar fluid when subjected to a uniform magnetic field along the vertical axis between two stretching disks as the structure of the problem changes. In this context, structural changes refer to alterations in the distance between the two discs or the stretching rate of the two discs. The governing equations of this problem are a set of nonlinear coupled partial differential equations, which are transformed into a nonlinear coupled ordinary differential equation set by a similarity transformation. The transformation results in four dimensionless quantities and their derivatives that appear in the equations. Nine dimensionless parameters are derived via similarity variables, including stretching Reynolds number, magnetic parameter, radiation parameter, Prandtl number, Eckert number, Schmidt number, and three micropolar parameters. Previous similarity solutions focused on analyzing the effect of changes in each parameter on the four dimensionless quantities. However, this type of analysis is mainly mathematical and does not provide practical results. This study’s primary novelty is to redefine the magnetic parameter, Eckert number, stretching Reynolds number, and two micropolar parameters to analyze physical parameters that depend on the stretching rate of the two discs or the distance between them. The semi-analytical hybrid analytical and numerical method (HAN-method) is used to solve the equations. The results demonstrate that structural changes affect all five quantities of radial velocity, axial velocity, microrotation, temperature, and concentration. The study’s most significant finding is that an increase in the stretching rate of the two disks causes a sharp increase in temperature and Nusselt number. Conversely, increasing the distance between the two disks causes a sharp decrease in micro-rotation and wall couple stress. They were compared to a previous study in a specific case to validate the results’ accuracy.

Study on the effectiveness of impact factor in underwater explosion model test

The dimensionless quantity is the invariant under the unit conversion, and the only choice to characterize the laws of physics. Aiming at the similarity law of underwater explosion model test, the deficiency of traditional impact factor and the similarity condition of single value of model test are analyzed by using dimensional analysis method and combining with domestic and foreign research. In view of the shortcomings of traditional impact factors, a new impact factor is derived from the perspective of single-value similarity based on the impact dynamic response characteristics of underwater explosion structures. Taking the midship cabin structure of a certain frigate as the prototype, the scale model tests are designed based on the traditional and new impact factors respectively. The effectiveness of the impact factors is evaluated from the aspects of structural damage characteristics, dimensionless deformation deflection, dimensionless velocity and dimensionless acceleration at the center of the structure. To account for the impact of structural characteristics, scale ratio, and proportional distance on the impact factor's effectiveness, various grillage, cabin, and hull girder model tests are conducted using ships of different tonnages as prototypes. The results of the model test, guided by the new impact factor, align well with the prototype test data. In contrast to the traditional impact factor, the model test exhibits greater precision for predicting structural responses, with a broad spectrum of potential applications.

Upgrades of Genetic Programming for Data-Driven Modeling of Time Series.

In many engineering fields and scientific disciplines, the results of experiments are in the form of time series, which can be quite problematic to interpret and model. Genetic programming tools are quite powerful in extracting knowledge from data. In this work, several upgrades and refinements are proposed and tested to improve the explorative capabilities of symbolic regression (SR) via genetic programming (GP) for the investigation of time series, with the objective of extracting mathematical models directly from the available signals. The main task is not simply prediction but consists of identifying interpretable equations, reflecting the nature of the mechanisms generating the signals. The implemented improvements involve almost all aspects of GP, from the knowledge representation and the genetic operators to the fitness function. The unique capabilities of genetic programming, to accommodate prior information and knowledge, are also leveraged effectively. The proposed upgrades cover the most important applications of empirical modeling of time series, ranging from the identification of autoregressive systems and partial differential equations to the search of models in terms of dimensionless quantities and appropriate physical units. Particularly delicate systems to identify, such as those showing hysteretic behavior or governed by delayed differential equations, are also addressed. The potential of the developed tools is substantiated with both a battery of systematic numerical tests with synthetic signals and with applications to experimental data.

Optimization of Reynolds numbers effects on aerodynamic drag and automotive performance

With the automotive industry continually striving to achieve greater fuel efficiency and heightened performance, understanding the intricacies of aerodynamics becomes paramount. Central to this research is the Reynolds number, a dimensionless quantity capturing the essence of fluid flow regimes and its implications for air drag and vehicular performance. This paper explores aerodynamic optimization in automotive design, specifically focusing on techniques that leverage the effects of the Reynolds number. Delving deep into diverse car designs, the study sheds light on how shape modifications, surface roughness, ground effects, and active aerodynamics are intertwined with Reynolds number variations, subsequently influencing a vehicles overall performance. Through a blend of experimental data, numerical simulations, and case studies, this research presents an integrated analysis that holds profound implications for the future of automotive design. This research paves the way for next-generation vehicles that meld efficiency with top-tier performance by unraveling the synergies between Reynolds number dynamics and innovative design strategies.

Experimental investigation on hydrodynamic characteristics of 1,1,1,2-tetrafluoroethane (R134a) in a horizontal tube at supercritical pressures

In this study, we experimentally assessed the hydrodynamic characteristics of supercritical-pressure R134a in a horizontal circular tube at pressure, inlet temperature, and heat flux ranges of p = 4.2 – 5.4 MPa, Tin = 20 – 50 °C, and q = 60 – 300 kW/m2, respectively. The hydrodynamic curves of R134a were plotted under various working conditions to assess the underlying mechanisms. The hydrodynamic characteristic curve of supercritical-pressure R134a does not possesses a negative-slope region but has a transition region compared with that under subcritical pressure. The transition region becomes more evident with increasing heat flux, while it weakens with increasing pressure and inlet temperature. Moreover, the onset of the transition region shifts in the direction of high mass flow rate with increasing heat flux. The transition region, generated by the relative changes in viscosity and density, is indicated by a dimensionless heat quantity Qratio, whose boundary is 1.8–2.2.

The construction of an index system for measuring photography teaching literacy in universities based on grey correlation analysis in cross-cultural teaching

Abstract This paper proposes a model of photography teaching literacy based on cross-cultural teaching by designing and implementing a photography curriculum based on “recording the fading colors of Suzhou” and combining it with cross-cultural teaching. Then, we set the gray correlation factor series, transformed the gray correlation factor series into a dimensionless pure quantity through mathematical transformation, calculated the correlation coefficients between the comparison series and the reference series, and applied the gray correlation analysis to analyze the intercultural photography teaching literacy index system. The results showed that teachers of different genders showed significant differences in intercultural photography teaching ability (F=2.774, p=0007<0.05) and no significant differences in intercultural photography teaching knowledge and intercultural photography teaching emotion. In terms of correlation, the correlation coefficient between research hard work and autonomous cooperation was 0.523 (**), and its correlation exists, indicating that teachers in colleges and universities at the prefecture level have a stronger awareness of the degree of correlation between research spirit and teaching spirit than those in colleges and universities at the county level. This study explores the good relationship between research literacy and photography teaching literacy so that it can be adapted to the development of teachers and students in the context of the new curriculum.

Mathematical analysis of nonlinear models and their role in dynamics

Micropolar fluids provide a more accurate description of fluid behavior at small scales, where classical continuum models may fail to capture complicated microscale interactions. These interactions become significant in situations involving non-Newtonian fluids, complex geometries, and materials with internal structures. Unlike traditional fluids, micropolar fluids consider the effects of micro-rotations and micro-deformations. The objective of this exploration is to investigate the characteristics of flow in a micropolar-Casson fluid that is doubly stratified, and is induced by a stretching sheet. Additionally, the study investigates the transfer of both thermal energy and mass species over a two-dimensional porous medium. By utilizing suitable similarity transformations, a system of nonlinear ordinary differential equations (ODEs) is derived by transforming the governing partial differential equations (PDEs) that describe the physics of the problem. The combination of a fourth-order Runge–Kutta integration scheme and the Shooting method is utilized to solve these equations. Various graphs and tables are utilized to illustrate the impact of physical parameters on the dimensionless quantities. Our findings exhibit strong conformity with the existing results in literature for specific scenarios. Furthermore, the outcomes highlight that the velocity and micro-rotation are enhanced by the material parameter.