Simple Analytical Model Research Articles

Lateral behaviour of steel plate shear wall with cold-formed steel strips reinforcing door opening

Holes in the walls of buildings are occasionally necessary to fulfil buildings’ functional requirements. When a steel plate shear wall (SPSW) is used as the primary lateral force-resistant structural member in a building, the effect of such openings on the mechanical properties of the SPSW is non-negligible. In this study, reinforcement of SPSWs with door openings using prefabricated cold-formed steel (CFS) strips is proposed. The proposed method can improve the mechanical properties of SPSWs with openings without inducing the residual deformation and stress caused by the typical welding reinforcement method. Cyclic loading tests were conducted to analyse the lateral resistance of two perforated SPSW structures reinforced using the proposed method: one SPSW with a door opening in the centre, and another with the door opening positioned at its edge. The test results showed that the openings reduced the lateral stiffness and strength of the structures. Specifically, a 30.84% decline in ultimate strength was observed for specimens with central door opening, while a 32.78% reduction was noted for specimens with edge door opening. Finite element models were derived and evaluated based on these results, and an SPSW with openings reinforced by CFS strips was modelled as equivalent to an SPSW without openings for analysis. The proposed simplified analysis model realises the weakening effect observed in a perforated SPSW by reducing the thickness of the equivalent unperforated SPSW. Finally, the equivalent analysis model (EAM) proposed herein was compared with experimental results, with the errors in yield strength and ultimate strength both within 5%. The results demonstrating that the proposed EAM is accurate and reasonable.

Experimental Analysis of the Leakage Characteristics of Three Types of Annular Segmented Seals

Abstract The present paper presents an experimental analysis of the leakage characteristics of three kinds of segmented seals. The segments of the first seal have smooth pads while the second seal has pads with pockets. The pads of the third seal are smooth but the rotor is textured with inclined grooves. The pockets or the textures lift the segments from the rotor and create a radial clearance. This is reflected by the leakage flow rate, the friction torque, and the seal's temperature. These characteristics are hereby measured on a dedicated test rig. The presented results are dimensionless, the measured values for the three types of seal types being divided by the same maximum value. This makes it possible to compare the performance of different segmented seal technologies and to evaluate the compromise between low leakage and enhanced lifespan. The assumptions made on the opening of the segmented seal with pockets during the tests are finally verified with a simple analytical model.

A Simple Analytical Model to Predict the Freeze Plug Opening Time in Molten Salt Reactors

Abstract The Freeze plug is an important passive safety system used in molten salt reactor (MSR). It enables automatic drainage of the liquid fuel from the core to the storage tanks in an emergency to stop the nuclear fission chain reaction without any operator's action or electric power supply. The opening time, that is the time taken for the freeze plug to open, is therefore of considerable importance to ensure passive safety of MSR. In our previous studies, systematic numerical simulations were carried out to understand how the fundamental design parameters such as the tube diameter and wall thickness of the freeze plug affected the opening time. In this work, a simple analytical model was developed for rough estimation of the opening time. It was shown that the opening time calculated by the present simple model was in fairly good agreement with that by the full simulation using the mass, momentum, and energy conservation equations for the salt and the heat conduction equation within the wall material. The present simple model was hence shown to be useful particularly for the schematic design of the improved MSR freeze plugs.

Photonic Artifacts in Ratiometric Luminescence Nanothermometry.

Ongoing developments in science and technology require temperature measurements at increasingly higher spatial resolutions. Nanocrystals with temperature-sensitive luminescence are a popular thermometer for these applications offering high precision and remote read-out. Here, we demonstrate that ratiometric luminescence thermometry experiments may suffer from systematic errors in nanostructured environments. We place lanthanide-based luminescent nanothermometers at controlled distances of up to 600 nm from a Au surface. Although this geometry supports no absorption or scattering resonances, distortion of the emission spectra of the thermometers due to the modified density of optical states results in temperature read-out errors of up to 250 K. Our simple analytical model explains the effects of thermometer emission frequencies, experimental equipment, and sample properties on the magnitude of the errors. We discuss the relevance of our findings in several experimental scenarios. Such errors do not always occur, but they are expected in measurements near reflecting interfaces or scattering objects.

Sustainable phase change materials (PCMs): waste fat from cooking pork meat confined in polypropylene fibrous mat from waste surgical mask and porous bio-silica

In this article, waste fat deriving from the cooking process of pork sausages has been studied as a sustainable phase change material (PCM). The waste fat is composed of saturated and unsaturated fatty acids and presents melting point and melting enthalpy values of 32 °C and 20 J/g respectively. The BioPCM was confined in two different hosts, namely (i) biosilica (diatomite) and (ii) polypropylene non-woven mat coming from surgical mask filter waste. Both hosts are effective in entrapping high quantity of BioPCM (i.e. 65-75%) maintaining its physical and thermal properties. A simplified analytical model has been developed to analyze the use of the BioPCM in building passive cooling application simulating the thermal behavior of a building wall containing the BioPCM confined in the hosts. A transmitted thermal power per unit area of 10.2 W/m2 was obtained. This value is 37% less of transmitted thermal power calculated for the wall without the BioPCM (16.2 W/m2), confirming that waste cooking fat can be an effective eco-sustainable solution in a good practice of circular economy.

Sensitivity and uncertainty propagation in buckling of spherical shells under external pressure

The simple analytical model of spherical shell buckling suggested in the previous publication in the TWS journal is applied to studying the response of the structure to different perturbations given as random variables. Among them probing radial force, energy barrier and geometrical imperfections are considered as factors decreasing uniform buckling pressure. The model is expanded to the case of imperfect shells. The propagation of uncertainty of perturbations is studied by estimation the standard deviation of the buckling load. Monte Carlo method and the propagation of error formula based on Tailor expansion are used. The application of the methods to design buckling pressure estimation is discussed.

Particle size effects on the axial pull-out and push-in behaviour of roots

For smaller plant roots in coarse-grained soils, large relative size of soil particles compared to roots can affect their axial resistance. Even for the larger roots of trees, particle size effects may be important, e.g. when testing 1:N scale models of tree uprooting in a geotechnical centrifuge. In this study the distinct element method (DEM) was used to investigate this problem. The sinker root of a centrifuge model tree root system under axial loading was analysed, with its simulated behaviour compared with finite element method (FEM) simulations, where the soil was modelled as a continuum and hence did not incorporate particle size effects. Both were validated against laboratory tests. Considering the same prototype size and soil particle size distribution, different scale factors/g-levels were applied to model roots, hence varying the ratio of root diameter (dr\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${d}_{\\rm r}$$\\end{document}) to mean particle size (D50\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${D}_{50}$$\\end{document}). Even at the lower dr/D50\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${d}_{\\rm r}/{D}_{50}$$\\end{document} values investigated (6–21), particle size effects on end-bearing capacity were negligible upon push-in of the root. In contrast, effects on shaft resistance (for pull-out) were significant and were interpreted by a simplified analytical model developed in this study using a combination of cavity expansion and root-particle size ratio. The absolute size of the root analogues considered was also representative of small diameter roots present in other plant species at 1:1 scale, making the analytical model also applicable to crop-lodging problems and for defining input parameters for analyses of nature-based solutions (NBS) using vegetation (e.g. for slope stabilisation).

Comparison of traditional district heating with low temperature district heating systems featuring organic Rankine cycle and heat pump

Paper presents a comparison between a traditional district heating system with conventional boilers as a source of heat and electricity purchases from power utilities and a low temperature DH system incorporating the CHP with organic Rankine Cycle providing electricity and local heat pump raising the temperature of the DH fluid to the required temperature in the dwelling, meaning that both heat and electricity are produced within the system. Additionally, such “island” system may feature or not the heat pump. Comparisons are made based on the results obtained using a developed simple analytical model enabling calculations of the efficiency of respective systems. The analyses have a general character and can be used in studies of complex networks however presented in the paper simple examples show merely the fundamental capabilities of the developed tool. The objective of the heat pump in the system is to increase temperature of hot water to the required level locally at the dwelling and provide the heating in such way, contrary to the traditional system, where water heating is considered by the use of electric heaters to increase parameters of water for central heating purposes and preparation of utility hot water. Presence of the heat pump in the system allows for significantly lower temperatures of distributed in the network heat carrier.

Spectroscopic Observation and Modeling of Photonic Modes in CeO2 Nanostructures.

Photonic modes in dielectric nanostructures, e.g., wide gap semiconductor like CeO2 (ceria), have the potential for various applications such as information transmission and sensing technology. To fully understand the properties of such phenomenon at the nanoscale, electron energy-loss spectroscopy (EELS) in a scanning transmission electron microscope was employed to detect and explore photonic modes in well-defined ceria nanocubes. To facilitate the interpretation of the observations, EELS simulations were performed with finite-element methods. The simulations allow the electric and magnetic field distributions associated with different modes to be determined. A simple analytical eigenfunction model was also used to estimate the energy of the photonic modes. In addition, by comparing various spectra taken at different location relative to the cube, the effect of the surrounding environment on the modes could be sensed. This work gives a high-resolution description of the photonic modes' properties in nanostructures, while demonstrating the advantage of EELS in characterizing optical phenomena locally.

Low-cost compact optical spectroscopy and novel spectroscopic algorithm for point-of-care real-time monitoring of nanoparticle delivery in biological tissue models.

Real-time monitoring of nanoparticle delivery in biological models is essential to optimize nanoparticle-mediated therapies. However, few techniques are available for convenient real-time monitoring of nanoparticle concentrations in tissue samples. This work reported novel optical spectroscopic approaches for low-cost point-of-care real-time quantification of nanoparticle concentrations in biological tissue samples. Fiber probe measured diffuse reflectance can be described with a simple analytical model by introducing an explicit dependence on the reduced scattering coefficient. Relying on this, the changes on the inverse of diffuse reflectance are proportional to absorption change when the scattering perturbation is negligible. We developed this model with proper wavelength pairs and implemented it with both a standard optical spectroscopy platform and a low-cost compact spectroscopy device for near real-time quantification of nanoparticle concentrations in biological tissue models. Both tissue-mimicking phantom and ex vivo tissue sample studies showed that our optical spectroscopic techniques could quantify nanoparticle concentrations in near real-time with high accuracies (less than 5% error) using only a pair of narrow wavelengths (530 nm and 630 nm). Novel low-cost point-of-care optical spectroscopic techniques were demonstrated for rapid accurate quantification of nanoparticle concentrations in tissue-mimicking medium and ex vivo tissue samples using optical signals measured at a pair of narrow wavelengths. Our methods will potentially facilitate real-time monitoring of nanoparticle delivery in biological models using low-cost point-of-care optical spectroscopy platforms, which will significantly advance nanomedicine in cancer research.

Rossby Waves and Zonal Flux Anomalies in Hadley and Ferrell Cell Analogs of the General Atmospheric Circulation: Model and Experiments

The circulation of the form of axysimmetrically flow with induced anomalies (disturbances) in closed rotating annular channel with conical bottom is generated by sources-sinks and MHD-method. The reducing of external forcing affects the changes of the anticyclones translation speed, but not the cyclones. The great part of moving anticyclones can disappear or stoped or new quasistationary cyclones may realized, whereas there are no change in the flow pattern in the sector where external anomalies take a place. But the variations in averaged parameters of the flow vortex are distinguished for the entire channel area and for their part. These anomalies physically are the weakness of subtropical Hadley cell with diminishing of passats in some sector of subequatorial atmospheric circulation and also the weakness the westerlies in the middle latitudes. The superposition of blocked and transported vortices are investigated with the help of simple analytical resonance interaction model for transient (with the maximum of velocity) modes in the shear flow. The amplitude of stationary background and the famous Sverdrup relation of the free surface streamfunction in the west oceanic shore intensification are affected in the same way from the beta-effect.

General assembly rules for metamaterials with scalable twist effects

Metamaterials with twist effects can exhibit remarkable rotational deformation under tension or compression, a behavior that is uncommonly observed in conventional materials. Despite its promise in achieving complex engineering functionalities, the twist effect is unscalable and will quickly diminish as the number of unit cells increases, which is the major restriction for practical applications. In this study, we use screw theory to rigorously analyze the relationship between microscale geometries and twist effects, unraveling the mechanism underlying the loss of scalability. We further propose a general assembly rule for metamaterial crystals to achieve scalable effects. A simplified analytical model is developed to characterize the scalability of the twist. Through simulation, analytical models, and physical experiments, we demonstrate the flexibility and superiority of the proposed assembly rules in enabling scalable twist effects for various unit-cell designs, different strain levels, and even twists around multiple axes. This constitutes an important step towards scaling up the twist effects for real applications.

Напружено-деформований стан клейового з’єднання, що має поздовжній дефект

In adhesive joints, one has to face the phenomenon of non-adhesive. It is known that non-adhesive reduces the strength of such joints. Analytical models known today for calculating the stress-strain state of adhesive joints have certain defects that appear as a result of simplification (one-dimensional models), and the realization of numerical methods requires a large resource of computing equipment. The subject of study in this article is a mathematical model of the stress-strain state of an adhesive joint of two plates. The purpose of this research is to study the stress-strain state of an adhesive joint with non-adhesives and to develop methods for studying the stress state of adhesive lap joints. Methods: a simplified two-dimensional analytical model of the stress state of the adhesive joint was used to construct an analytical solution to the problem of the stress state of the joint, which contains a defect in the adhesive layer along the side edge of the bonding area. The simplification of the model consists of the fact that the transverse displacements of the base layers are considered to be zero. This assumption can be interpreted as the presence of base layers of high stiffness in the transverse direction, and it allows reducing the problem of the stressed state of the joint to a system of two partial differential equations with respect to the longitudinal movements of the base layers and obtaining the solution of the problem in an analytical form. The obtained solution is written in the form of functional series. The eigenfunctions are not orthogonal. Using the least squares method, the solution of the problem is reduced to a system of linear equations. The model problem for joining two aluminum plates of the same size has been solved. The results showed that the presence of non-adhesive area can significantly increase the stress near the edge of the adhesive layer. Corner points in the adhesive layer are especially dangerous from the strength point of view. The results were compared with the results of finite element modeling. The comparison showed that the proposed mathematical model has high accuracy for engineering calculations. This model can be developed to solve similar problems, for example, to study the stress state of the joint of coaxial pipes, which has defects in the adhesive layer.

The effectiveness of D2 pellet injection in reducing intra-ELM and inter-ELM tungsten divertor erosion rates in DIII-D during the Metal Rings Campaign

Edge localized modes (ELMs) in H-mode plasmas erode plasma-facing components (PFCs) and lead to impurities in the core, reducing confinement. This study analyzes D2 pellet injection on the DIII-D fusion experiment used as an ELM mitigation technique applied during the 2016 tungsten Metal Rings Campaign to reduce W erosion during ELMs. The 400.9 nm photon wavelength line emission intensity of tungsten atoms (WI) filterscope channels and Langmuir probes were used to infer the gross erosion rate of tungsten-coated tiles installed in the divertor of DIII-D. D2 mass injection rates ranging from 34 to 41 arbitrary units (A.U.) and no D2 injection resulted in a similar total W erosion rate during ELMs (intra-ELM). On average, results show a 29% increase in the total gross W erosion rate with intermediate mass injection rates (∼13–23 A.U.) compared to the no pellets and the highest injection rate cases. On average, the fast D2 mass injection rate cases had 15% less erosion in the inter-ELM phase than the case with no pellets. Generally, higher D2 mass injection rates increased the ELM frequency, and the highest injection rates reduced the average erosion per ELM and fractional carbon impurities at the top of the pedestal by nearly 40% when compared to the no-pellet case. As expected, a higher D2 pellet injection rate led to a higher plasma density and lower plasma temperature in the divertor. Additionally, an increasing divertor inter-ELM plasma electron density directly correlated to more frequent pellet injection and a decrease in both the average gross intra-ELM W erosion and the total gross intra-ELM W erosion rate. Simulations of intra-ELM erosion using the ‘free-streaming plus recycling model’ (FSRM) underestimate W erosion during pellet injection by about 30% on average. The discrepancies between the experimental measurements and the FSRM intra-ELM W erosion predictions are postulated to be due to C/W material mixing. A simple analytic mixed-material model is presented and results in better agreement with the experimental data. These results highlight the importance of incorporating the effects of a mixed-material layer in the analysis of PFC erosion.

Timber-to-steel inclined screws connections with interlayers: Experimental investigation, analytical and finite element modelling

Thanks to the axial resisting contribution, inclined screw connections offer a mechanical advantage over connections with purely transversely loaded fasteners. However, the strong coupling between the axial and the transversal behaviour of the screw makes it challenging to predict the actual connection behaviour. Moreover, the presence of polyurethane interlayers for soundproofing or OSB interlayers of light-frame buildings between main members may increase the bending moment component interacting with the axial force in the screw, thus reducing the connection failure load. This paper experimentally assesses the behaviour of steel-to-timber connections, and a parametric finite element model of Winkler non-linear beam is presented and validated. Finally, a simplified analytical model for capacity prediction is presented. The results of the approach currently provided by the Eurocode 5, of an additive model and the proposed analytical model, are then compared with the results of 500 finite element analysis.

Locality of contacts determines the subdiffusion exponents in polymeric models of chromatin.

Loop extrusion by motor proteins mediates the attractive interactions in chromatin on the length scale of megabases, providing the polymer with a well-defined structure and at the same time determining its dynamics. The mean-square displacement of chromatin loci varies from a Rouse-like scaling to a more constrained subdiffusion, depending on cell type, genomic region, and time scale. With a simple polymeric model, we show that such a Rouse-like dynamics occurs when the parameters of the model are chosen so that contacts are local along the chain, while in the presence of nonlocal contacts we observe subdiffusion at short time scales with exponents smaller than 0.5. Such exponents are independent of the detailed choice of the parameters and build a master curve that depends only on the mean locality of the resulting contacts. We compare the loop-extrusion model with a polymeric model with static links, showing that also in this case only the presence of nonlocal contacts can produce low-exponent subdiffusion. We interpret these results in terms of a simple analytical model.

The role of volume effect on the transient behavior of a transonic compressor

Abstract The significance of the volume effect on the compressor performance during acceleration and deceleration has received limited attention, despite its demonstrated importance in compressor flow instabilities. To better understand this effect, the in-house simulation program CAM (a modular transient simulator) is used to investigate the volume effect on the compressor transient performance. The modeling procedure is derived from Greziter’s lumped parameter approach and the accuracy of the simulation model is verified by experimental data. This study presents a comprehensive comparison and explanation of variations in compressor transient behavior observed under different conditions, including different shaft speed change rates, compressor volume sizes, and operating speeds. The relative difference between the compressor inlet and outlet mass flow is identified as the key factor contributing to these discrepancies. In addition, a simplified analytical model is developed to provide a basic description of the compressor operating line during acceleration and deceleration, which also provides additional support for the validity of the numerical results. This study systematically establishes the dynamic dependencies between shaft speed change, pressure and mass flow change, offering critical information for ensuring the safety of compressors during transient operation.

Cooling-driven coagulation

ABSTRACT Astrophysical gases such as the interstellar-, circumgalactic-, or intracluster-medium are commonly multiphase, which poses the question of the structure of these systems. While there are many known processes leading to fragmentation of cold gas embedded in a (turbulent) hot medium, in this work, we focus on the reverse process: coagulation. This is often seen in wind-tunnel and shearing layer simulations, where cold gas fragments spontaneously coalesce. Using 2D and 3D hydrodynamical simulations, we find that sufficiently large (≫cstcool), perturbed cold gas clouds develop pulsations which ensure cold gas mass growth over an extended period of time (≫r/cs). This mass growth efficiently accelerates hot gas which in turn can entrain cold droplets, leading to coagulation. The attractive inverse square force between cold gas droplets has interesting parallels with gravity; the ‘monopole’ is surface area rather than mass. We develop a simple analytic model which reproduces our numerical findings.

Universal optical polarizability for plasmonic nanostructures

Optical spectra of small metal nanoparticles are dominated by surface plasmon resonance. In this Letter, a simple analytical model for optical polarizability of metal nanoparticles of arbitrary shape is presented.

Development of Ankle-Joint Rehabilitation Device for Bedridden Patient Using Fan-Shaped Pneumatic Soft Actuator Driven at Low Pressure

Recently, the number of older people and the reduction in infant birth rates in Japan have increased. Elderly against the younger increased to more than 28.9% in 2020. According to the Japanese aging society, a welfare pneumatic device to rehabilitate the temporally injured elderly and the disabled has been actively researched and developed. However, the developed rehabilitation device is almost always used for a patient who is not bedridden. Therefore, the joint of a bedridden patient is given only a passive exercise, by a physical therapist (PT). In this study, in order to reduce the burden of PTs, we aim to develop a rehabilitation device that can be used by anyone assisting the bedridden patient. The target joint was decided to be an ankle-joint because it is difficult for patients with contractions to walk. Therefore, a fan-shaped pneumatic soft actuator (FPSA) using a no-stretch hose with weaved bellows and silicone rubber string was proposed and tested. In addition, the characteristics of FPSA with different pitches and lengths are measured. To predict the bending angle of FPSA, a simplified shape analytical model of it is proposed. It can be confirmed that a calculated bending angle of FPSA using the model generally agrees with the experimental result. The proposed analytical model is a first-stage model that does not include the influence of external forces on FPSA. The ankle-joint rehabilitation device using FPSAs is proposed and tested, where an ankle-joint is changed from a plantarflexion to a dorsiflexion motion by pressurizing both FPSAs on the tested device. And it can be confirmed that a range of motion (“ROM” for short) is satisfied in an inversion and eversion driven by operating one or another FPSA on the device.