Dimensional Analysis Research Articles

Mass Transfer Resistance and Reaction Rate Kinetics for Carbohydrate Digestion with Cell Wall Degradation by Cellulase.

This paper introduces an enzymatic approach to estimate internal mass-transfer resistances during food digestion studies. Cellulase has been used to degrade starch cell walls (where cellulose is a significant component) and reduce the internal mass-transfer resistance, so that the starch granules are released and hydrolysed by amylase, increasing the starch hydrolysis rates, as a technique for measuring the internal mass-transfer resistance of cell walls. The estimated internal mass-transfer resistances for granular starch hydrolysis in a beaker and stirrer system for simulating the food digestion range from 2.2 × 107 m-1 s at a stirrer speed of 100 rpm to 6.6 × 107 m-1 s at 200 rpm. The reaction rate constants for cellulase-treated starch are about three to eight times as great as those for starch powder. The beaker and stirrer system provides an in vitro model to quantitatively understand external mass-transfer resistance and compare mass-transfer and reaction rate kinetics in starch hydrolysis during food digestion. Particle size analysis indicates that starch cell wall degradation reduces starch granule adhesion (compared with soaked starch samples), though the primary particle sizes are similar, and increases the interfacial surface area, reducing internal mass-transfer resistance and overall mass-transfer resistance. Dimensional analysis (such as the Damköhler numbers, Da, 0.3-0.5) from this in vitro system shows that mass-transfer rates are greater than reaction rates. At the same time, SEM (scanning electron microscopy) images of starch particles indicate significant morphology changes due to the cell wall degradation.

Numerical and experimental investigation of the effect of interstitial liquid viscosity on the collapse of wet granular columns

The collapse of wet granular columns with high- and low-viscosity interstitial liquid is investigated through experiments and numerical simulations. By incorporating both capillary and viscous force models of interstitial liquid in the Discrete Element Method (DEM), simulations have been conducted and reproduced consistent collapse processes with the experiment. The influence of water content, contact angle, particle diameter, liquid surface tension, and viscosity is explored over a large parameter space using DEM. For wet granular columns with low-viscosity interstitial liquid of water, the final profile of the collapsed column can be predicted by Bond number (Bo), a ratio of particle gravity to capillary force. For wet granular columns where the inertial effect dominates and both capillary and viscous forces are significant, dimensional analysis is employed to characterize the collapse, indicating that the collapsed profile can be predicted by Bo and Galileo number (Ga). Using water and silicone oils with different viscosities as interstitial liquids, simulations show that the collapsed profile depends on Bo with a low capillary number (Ca ∼ 10−3), Bo and Ga when Ca is intermediate (Ca ∼ 10−1). When Ca is high (Ca > 100), the final profile is solely controlled by Bo and a rolling-collapsed regime is observed.

Theory and Measurement of Heat Transport in Solids: How Rigidity and Spectral Properties Govern Behavior.

Models of heat transport in solids, being based on idealized elastic collisions of gas molecules, are flawed because heat and mass diffuse independently in solids but together in gas. To better understand heat transfer, an analytical, theoretical approach is combined with data from laser flash analysis, which is the most accurate method available. Dimensional analysis of Fourier's heat equation shows that thermal diffusivity (D) depends on length-scale, which has been confirmed experimentally for metallic, semiconducting, and electrically insulating solids. A radiative diffusion model reproduces measured thermal conductivity (K = DρcP = D × density × specific heat) for thick solids from ~0 to >1200 K using idealized spectra represented by 2-4 parameters. Heat diffusion at laboratory temperatures (conduction) proceeds by absorption and re-emission of infrared light, which explains why heat flows into, through, and out of a material. Because heat added to matter performs work, thermal expansivity is proportional to ρcP/Young's modulus (i.e., rigidity or strength), which is confirmed experimentally over wide temperature ranges. Greater uptake of applied heat (e.g., cP generally increasing with T or at certain phase transitions) reduces the amount of heat that can flow through the solid, but because K = DρcP, the rate (D) must decrease to compensate. Laser flash analysis data confirm this proposal. Transport properties thus depend on heat uptake, which is controlled by the interaction of light with the material under the conditions of interest. This new finding supports a radiative diffusion mechanism for heat transport and explains behavior from ~0 K to above melting.

Free energy and extension of stiff polymer chains confined in nanotubes with diverse cross-sectional shapes

The statistical mechanics of stiff polymer chains confined within narrow tubes is a foundational topic in polymer physics, extensively analyzed in prior research. For cylindrical, rectangular, and slit-like confinements, the chains’ free energy and extension adhere to a scaling law consistent with the Odijk theory. While this scaling law may not apply to tubes with different cross-sectional geometries, there is a lack of research examining the behavior of stiff chains in tubes with intricate cross-sectional shapes. In this study, we investigate the partition function of a stiff chain confined within an elliptic tube using the path integral approach, deriving a deflection length in a concise closed form through dimensional analysis. This length scale facilitates straightforward expressions for the chain's free energy and extension. Notably, we discover a shape-independent property of these expressions applicable to tubes with a wide variety of cross-sectional geometries. Extensive numerical simulations are conducted using a biased chain-growth Monte Carlo method, incorporating the Pruned and Enriched Rosenbluth algorithm, to validate the theoretical predictions on the confinement free energy and extension of chains in tubes with differing shapes.

A strain-based J-integral formulation for an internal circumferential surface crack of pipeline under inner pressure and large axial deformation

The presence of cracks on pipelines poses a potential threat to their operational status, and it is critical to assess the permissibility of pipelines containing cracks. The dimensional analysis combined with the finite element method is applied to investigate the fracture behavior of circumferential crack on the internal surface of pipe under internal pressure and large axial deformation. Dimensionless parameters are determined to represent the effects of crack size, pipe geometry, pipe material, and external load on the crack front driving force, and a strain-based J-integral formulation is obtained by a stepwise coefficient fitting approach rather than a polynomial fitting method. This J-integral formula can be used to quickly assess the crack front driving force of a pipe in service condition and subjected to axial displacement. The diameter-to-thickness ratio of the pipe and the dimensionless pressure of the pipe are found to act together in a combined form on the crack front driving force. Increases in dimensionless crack depth, dimensionless crack length, the ratio of circumferential stress to yield strength of the pipe, and strain hardening exponent cause an increase in the crack front driving force. The effect of dimensionless crack depth on crack front driving force is more significant than other dimensionless parameters. Changes in the other dimensionless parameters do not significantly change the crack front driving force when the dimensionless crack depth is small. Other dimensionless parameters have a progressively greater influence on the crack front driving force as the crack dimensionless crack depth increases. Large deformations in the ligament zone and increasing axial stress are the main reasons for the high crack front driving force. The J-integral formula has a similar form to that of the J-integral in the Electric Power Research Institute (EPRI) method when the effect of internal pressure is not considered. It can be reduced to predict the crack front driving force of a surface cracked plate subjected to uniaxial tensile loading. For the interaction between an internal surface crack and an embedded crack, re-characterizing the crack size using BS 7910 will overestimate the equivalent crack depth, and a more accurate equivalent crack size can be obtained using the J-integral formula proposed.

Recipient tissue microenvironment determines developmental path of intestinal innate lymphoid progenitors

Innate lymphoid cells (ILCs) are critical in maintaining tissue homeostasis, and during infection and inflammation. Here we identify, by using combinatorial reporter mice, a rare ILC progenitor (ILCP) population, resident to the small intestinal lamina propria (siLP) in adult mice. Transfer of siLP-ILCP into recipients generates group 1 ILCs (including ILC1 and NK cells), ILC2s and ILC3s within the intestinal microenvironment, but almost exclusively group 1 ILCs in the liver, lung and spleen. Single cell gene expression analysis and high dimensional spectral cytometry analysis of the siLP-ILCPs and ILC progeny indicate that the phenotype of the group 1 ILC progeny is also influenced by the tissue microenvironment. Thus, a local pool of siLP-ILCP can contribute to pan-ILC generation in the intestinal microenvironment but has more restricted potential in other tissues, with a greater propensity than bone marrow-derived ILCPs to favour ILC1 and ILC3 production. Therefore, ILCP potential is influenced by both tissue of origin and the microenvironment during development. This may provide additional flexibility during the tuning of immune reactions.

Study of the hydraulic characteristics of an airfoil‐shaped weir trough measurement and control integrated facility combined with numerical simulation

AbstractIn this study, an integrated measurement and control facility with an airfoil weir as the primary overcurrent structure is proposed by considering the flow characteristics over different shapes of weir trough facilities as well as the approach of merging measurement and control functions. The incomplete self‐similarity theory and dimensional analysis are used to derive the stage‐discharge relationship. The hydraulic characteristics of the facility under different shape‐related parameters, weir crest heights (rotation angles), and flows are studied by combining model testing and numerical simulation. The findings demonstrate that changes in shape‐ related parameters and rotation angle do not affect the linear relationship between the water depths in the critical and reference sections. The mean error in the discharge formula derived by dimensional analysis is 2%. The Froude number is less than 0.25 under all the working conditions. From the backwater height and head loss, it can be seen that the larger the P/C (the maximum airfoil thickness P to the chord length C ratio) value of the facility under the premise of unifying the weir crest height, the better the overflow capacity. When the height of the weir crest is 0.3778 m, the negative pressure on the surface of the airfoil weir increases with increasing P/C value.

Modelling and Analysis of Evacuated Tube Solar Collector Working with Hybrid Nanofluid

This research study is concerned with developing a mathematical model for an Evacuated Tube Solar Collector (ETSC) that utilizes a Hybrid Nanofluid flow in a manifold. The model consists of a set of the partial differential equations that, using the dimensional analysis approach, are reduced to a dimensionless system. The exact solution method, assisted by the Mathematica program, is used to solve the system. The study examines the impact of certain factors on flow and heat transmission, including horizontal velocity, temperature variation, heat source, magnetic field, Prandtl Number, and Eckert Number, and provides a detailed analysis of the results. The key findings of the analysis revealed that an increase in hybrid nanoparticle volume effects in a reduce in velocity and heat transfer coefficient. Additionally, elevated heat source and Prandtl number correspond to an increased heat transfer coefficient.

Dynamic response mechanisms of thin UHMWPE under high-speed impact

This study systematically explores the dynamic response mechanisms and energy dissipation mechanisms of ultra-high-molecular-weight polyethylene (UHMWPE) fiber laminated plates with thicknesses of 1.1 mm, 2.8 mm, and 5.4 mm under high-speed steel ball impacts through experimental, theoretical analysis, and dimensional analysis. By analyzing the damage mechanisms from experimental results, the main modes of energy absorption were identified, and a relatively accurate predictive model for ballistic limit speed was established. The results show that under high-speed steel ball impacts, the primary failure modes of UHMWPE fiber laminated plates are localized permanent bulging plastic deformation and perforation failure caused by compressive shear. The ballistic limit speeds for UHMWPE with thicknesses of 1.1 mm, 2.8 mm, and 5.4 mm are respectively 233.5 m/s, 415.7 m/s, and 602.9 m/s. The theoretical calculations of the energy model align well with the experimental results, indicating that as the speed increases, the proportion of tensile energy absorption gradually decreases, consistent with the observed phenomena. Near the ballistic limit, there are significant turning points in the level of energy absorption and the height of the rear bulge. The ballistic limit increases linearly with target thickness, and the unit area density energy absorption also increases continuously. Finally, this study established a dimensionless ballistic limit model considering the mechanical properties of fibers and the matrix, which through regression analysis, can accurately describe the ballistic limits of various strengths and types of fiber laminated plates, suitable for predicting the ballistic performance of various composite materials.

Automated Feedback on Student Attempts to Produce a Set of Dimensionless Power Products from a Set of Physical Quantities that Describe a Physical Problem

Formative feedback is important in learning. Automating the provision of specific, objective, constructive feedback to large cohorts requires complex algorithms that most teachers do not have time to develop, suggesting that a community effort is needed to create a library of specialised algorithms. We present an exemplar algorithm for a class of tasks in ‘dimensional analysis’ relating to the Buckingham Pi theorem. The challenge arises because there are infinitely many valid and invalid answers, but any valid answer is sufficient to complete a task. We present an algorithm that, given one valid reference answer, can evaluate any response to a task. The algorithm uses a vector-space formulation of the Pi theorem. Deployment across seven tasks for 380 students provided feedback 3,090 times, including stating why a response is invalid. The most common reason was that a student-proposed set was not dimensionless, but other educationally relevant reasons were also identified.

Deflection characteristics and influencing factors of projectile oblique impact on concrete targets

The projectile deflects and even ricochets after an oblique impact on the concrete. However, research on the oblique impact of projectiles on concrete targets mainly focuses on oblique penetration and the critical ricochet angle, and there are few experimental studies on ricochets. Deflection and its influencing factors remain undefined. This study conducted experiments and LS-DYNA numerical simulations on projectiles obliquely impacting C60 concrete targets. The experimental research visually revealed deflection and ricochet phenomena after the oblique impact. The ricochet caused by large-angle impacts can effectively reduce the damaged area of concrete targets. Subsequently, the main governing parameters affecting the deflection angle of the projectile were identified through dimensional analysis, and a sensitivity analysis was performed on these parameters using an orthogonal experimental design. On this basis, the influence of the incident angle, impact velocity, and projectile length-to-diameter ratio on the projectile deflection was further clarified. The results showed that the maximum deflection angle was achieved when a 30 mm caliber projectile obliquely impacted a C60 concrete at an incident angle of ∼45°. In the case of ricochets, the deflection angle increased with an increase in the impact velocity and decreased with an increase in the length-to-diameter ratio. This study aids in predicting and controlling projectile deflection and provides a reference for the innovative design of concrete protective structures.

Experimental and modelling studies on static sag of solid weighting powders in Polysulfonate workover fluids at high temperature and high pressure

The solid weighting material in a high-density workover fluid is prone to static sag. Existing experimental methods cannot predict the parameters of the settling stability of workover fluids at high temperature and high pressure (HTHP). Therefore, in this study, static settlement experiments were carried out using a novel experimental setup. The experimental setup enables the measurement of the density profile of heavy workover fluids at HTHP. A multi-parameter correlation equation between the sag factor and particle diameter, particle density, base fluid density, workover fluid density and rheological parameters, aging time, temperature, and pressure was obtained using dimensional analysis and multivariate nonlinear regression methods. The results reveal that the settlement stability of the workover fluid decreases with the increase in temperature and pressure. Based on the multi-parameter correlation, the predicted and the measured values were compared and verified. The error between the predicted value and the measured value was within 5%. The average prediction error was 1.68%, and the maximum prediction error was 3.8%. These results reveal that the model proposed in this study can effectively predict the static sedimentation stability of the solid weighted Polysulfonate workover fluids. Furthermore, the proposed correlation can guide the properties adjustment of the workover fluids to achieve the required sag stability. This work provides a new approach to predict and control the sag stability of the solid weighted workover fluids.

Enhancing Hydraulic Performance and Discharge Efficiency of a Type-C Piano Key Weir Through Stage Incorporation

Weirs are hydraulic constructions typically employed in dam spillways and channel control structures. The shape and size of the crest will determine whether the weir is linear or non-linear. Of the two types, non-linear weirs are often selected due to their ability to allow different discharge levels at the minimal heads. A recently introduced variation of the non-linear kind is the piano key weir. This research undertakes a comprehensive analysis of the hydraulic functionality of the type-C piano key weir under conditions of free flow. The research methodology involved modifying the models by adding stages to the sides and monitoring the effect on the efficacy of discharge, represented by the discharge coefficient. The study further extrapolated formulae linking critical variables to the discharge coefficient, using dimensional analysis and SPSS software. The findings of this study revealed that the introduction of stages significantly bolstered the discharge coefficient in the altered models compared to the standard model. This enhancement was reflected in a 6% and 11% ascent with length expansion of the stages and a 6% and 8% rise with height increase of the stages. Additionally, the model's performance was augmented with a drop in the total head ratio

Psychometric evaluation of the Clinical Interview for Externalizing Disorders (ILF-EXTERNAL) in an online setting - Results from the consortium project INTEGRATE-ADHD.

The study examines the psychometric properties of the ADHD section of the semi-structured diagnostic interview ILF-EXTERNAL, which was conducted online via video chat. As part of the INTEGRATE-ADHD research project, 202 children and adolescents (age M = 12.87 years, SD = 3.04, 28.2 % female) with an administrative diagnosis of ADHD registered with their health insurance company were clinically assessed for the presence of ADHD according to the German ADHD S3 guideline. Using the ILF-EXTERNAL, one parent and, from the age of eight, also the children themselves were interviewed. A proxy rating by a parent was made using the German FBB-ADHS rating scale. In a subsample (n = 65), an independent blind interviewer rated the videorecordings of the ILF-EXTERNAL parent interview to determine the interrater reliability of the ILF-EXTERNAL. All ADHD symptom scales of the ILF-EXTERNAL showed good to excellent internal consistency (α = 0.89 to 0.93). Interrater reliability was high for both categorical and dimensional analyses (κ = 0.78 and κ = 0.81; ICC(1,1) = 0.97 and 0.98). High correlations of the ILF-EXTERNAL parent interview with the FBB-ADHS (r = 0.79 to r = 0.85) and with the ILF-EXTERNAL child interview (r = 0.60 to r = 0.71) demonstrated convergent validity. Sound psychometric properties of the ILF-EXTERNAL were also confirmed for its use in an online setting. High interrater reliabilities demonstrate the quality of the ADHD diagnostics carried out in the consortium project INTEGRATE-ADHD.

Level of implementation of digital transformation in dental radiology centers in Metropolitan Lima: A cross-sectional study.

Digital transformation (DT) involves introducing digital technologies into business models in all areas. This research aimed to evaluate the level of implementation of DT using the digital health indicator in private radiology centers in Lima, Perú. Forty-five randomly selected radiology centers included in a database of 50 registered centers were evaluated. The inclusion criteria were having a web domain and institutional email address. They were digitally surveyed using a digital survey (HIMSS DHI Rapid) measuring four dimensions: interoperability, governance and workforce, predictive analytics, and person-enabled health. These indicators allowed determination of the digital transformation level of a radiological company. The level of implementation was measured quantitatively on a scale from 0 to 400, and the Kruskal Wallis test (p>0.05) was used to compare DT according to the geographical location of the centers. The digital health indicator obtained was 60.24 ± 43.14 out of 400 achievable points. The dimensional analysis in terms of interoperability was 24 ± 18.09, followed by governance and workforce at 23.44 ± 18.58, person-enabled health at 18.73 ± 15.63, and finally, predictive analysis at 16.18 ± 13.51. No significant differences were found in health indicator dimensions according to the geographical location (p>0.05). DT in maxillofacial radiology centers in Lima is at an initial level. Radiology centers should take this situation into account to have relevant information for making diagnostic and treatment decisions and to provide better preventive health policies to benefit the population. Key words:Digital transformation, digital health indicator, dental radiology.

Isopycnal Eddy Stirring Dominates Thermohaline Mixing in the Upper Subpolar North Atlantic

AbstractThe Atlantic Meridional Overturning Circulation entails vigorous thermohaline transformations in the subpolar North Atlantic Ocean (SPNA). There, warm and saline waters originating in the (sub)tropics are converted into cooler and fresher waters by a combination of surface fluxes and sub‐surface mixing. Using microstructure measurements and a small‐scale variance conservation framework, we quantify the diapycnal and isopycnal contributions –by microscale turbulence and mesoscale eddies, respectively– to thermohaline mixing within the eastern SPNA. Isopycnal stirring is found to account for the majority of thermal (65%) and haline (84%) variance dissipation in the upper 400 m of the eastern SPNA. A simple dimensional analysis suggests that isopycnal stirring could account for (5–10) Sv of diahaline volume flux, suggesting an important role of such stirring in regional water‐mass transformations. Our mixing measurements are thus consistent with recent indirect estimates in highlighting the importance of isopycnal stirring for North Atlantic overturning.

Simple methods for converting equations between the SI, Heaviside–Lorentz and Gaussian systems

School and undergraduate students are almost always taught the equations of electromagnetism using a set of conventions that are described as the SI. More advanced students are often introduced to different conventions that produce different equations for the same relationships, using either the Gaussian or Heaviside–Lorentz systems. In general, the connection between these equations is not simple. However, if the basis of each system is understood, conversion from SI equations to either Gaussian or Heaviside–Lorentz ones is very straightforward. The reverse processes are less straightforward, but more comprehensible when the fundamental differences are understood. Simple methods for these processes are presented, using a novel application of dimensional analysis, without factors of ε 0 1/2 or (4πε 0)1/2 appearing. It is also shown that when different physical quantities are given different symbols, and these are used consistently, the SI can be seen to provide general equations, with the Gaussian and Heaviside–Lorentz ones being simplifications of them. This removes any need for ‘system-independent’ versions of electromagnetic equations, with additional parameters that take different values in the different systems, which have been proposed in various forms over many decades.

Structural strength and fatigue analyses of large-scale underwater compressed hydrogen energy storage accumulator

Underwater compressed hydrogen energy storage (UWCHES) is a potential solution for offshore energy storage. By taking advantage of the hydrostatic pressure of deep seawater, the compressed hydrogen can be isobarically stored in underwater artificial energy storage accumulators. The accumulator should withstand high pressure and large buoyancy and possess reliable anchoring to the seabed. In this study, the structural strength analysis and fatigue life of the large-scale accumulator is conducted employing the finite element method (FEM). The dimensionless stress prediction model and dimensionless fatigue life prediction model are developed through dimensional analysis and multivariate regression analysis. The performance of the accumulator with operating water depth of 100∼300 m, gas storage volume of 1081∼10128 m³, and concrete wall thickness of 0.1∼0.63 m is investigated. The results show that with an operating water depth of 100 m, gas storage capacity of 10,128 m3, and concrete wall thickness of 0.63 m, the maximum compressive stress is 1.43 MPa (yield strength is 60 MPa) and the maximum tensile stress of the accumulator is 2.55 MPa (yield strength is 6 MPa). The design fatigue life is 106 cycles which is larger than the expected service life of 104 cycles. Therefore, the accumulator structure meets the static strength and fatigue life. As the operating water depth increases with a consistent gas storage capacity, a transition in the stress state shifts from primarily tensile stress to predominantly compressive stress. The accuracy of the dimensionless stress prediction model and the dimensionless fatigue life prediction model were verified, with maximum deviations of 10.3 % and 13.7 %, respectively. Furthermore, the anchoring factor of safety of 1.12 is achieved.

Probabilistic solution of non-linear random ship roll motion by data-driven method

In this paper, a data-driven method is employed to investigate the probability density function (PDF) of nonlinear stochastic ship roll motion. The mathematical model of ship roll motion comprises a linear term with cubic damping and a nonlinear restoring moment represented as an odd-degree polynomial up to the fifth order. The data-driven method integrates maximum entropy, the pseudo-inverse algorithm, and a backpropagation (BP) neural network to obtain the PDF. The process begins with simulating data for the nonlinear stochastic system, followed by dimensional analysis to identify dimensionless parameter clusters. Optimization algorithms are then employed to solve for the coefficients, leading to the development of a BP neural network model trained to predict the PDF across various system characteristics and excitation intensities. The method's effectiveness is validated with Monte Carlo simulations, demonstrating high accuracy and reduced sensitivity to parameter variations.

Metaphysics and Convention in Dimensional Analysis, 1914–1917

Metaphysics and Convention in Dimensional Analysis, 1914–1917