Intermediate Velocity Research Articles

Design and Performance of a Planetary Gearbox with Two DOFs

The article aims to describe the design and operation of a fundamentally new self-regulating planetary transmission, which, without a control system, changes the gear ratio under the influence of a variable external load. A self-regulating transmission can be created based on a kinematic chain with two degrees of freedom, having only one input. According to the laws of mechanics, such a chain has no definability of motion, since the number of inputs must be equal to the number of degrees of freedom. The equilibrium of a two-movable chain with one input can obtained by creating an additional constraint that substitutes a reaction in the instantaneous center of the intermediate link velocities by the friction moment in the hinge of the intermediate link. The friction moment creates a force constraint, which is taken into account in the equilibrium condition. The obtained equilibrium conditions ensure the definiteness of motion and the ability of self-regulation in the form of an inversely proportional dependence of the speed of the output link on the variable external load. The described method makes it possible to create a fundamentally new class of self-regulating mechanisms in all branches of technology. The interaction of kinematic and force parameters and the construction of parameter graphs was performed using the SolidWorks 2021 program with certain additions. The experimental studies performed confirm the reliability of the theoretical developments.

Control of a Wind Turbine Working in the Intermediate Velocity Zone: A Model Free Discrete Time Approach

Control of a Wind Turbine Working in the Intermediate Velocity Zone: A Model Free Discrete Time Approach

Shocks in the warm neutral medium

Context. Atomic and molecular line emissions from shocks may provide valuable information on the injection of mechanical energy into the interstellar medium (ISM), the generation of turbulence, and the processes of phase transition between the warm neutral medium (WNM) and the cold neutral medium (CNM). Aims. In this series of papers, we investigate the properties of shocks propagating in the WNM. Our objective is to identify the tracers of these shocks, use them to interpret ancillary observations of the local diffuse matter, and provide predictions for future observations. Methods. Shocks propagating in the WNM are studied using the Paris-Durham shock code, a multi-fluid model built to follow the thermodynamical and chemical structures of shock waves at steady-state in a plane-parallel geometry. The code, designed to take into account the impact of an external radiation field, is updated to treat self-irradiated shocks at intermediate (30 < VS < 100 km s−1) and high velocity (VS ⩾ 100 km s−1), which emit ultraviolet (UV), extreme-ultraviolet (EUV), and X-ray photons. The couplings between the photons generated by the shock, the radiative precursor, and the shock structure are computed self-consistently using an exact radiative-transfer algorithm for line emission. The resulting code is explored over a wide range of parameters (0.1 ⩽ nH ⩽ 2 cm−3, 10 ⩽ VS ⩽ 500 km s−1, and 0.1 ⩽ B ⩽ 10 μG), which covers the typical conditions of the WNM in the solar neighborhood. Results. The explored physical conditions lead to the existence of a diversity of stationary magnetohydrodynamic solutions, including J-type, CJ-type, and C-type shocks. These shocks are found to naturally induce phase transition between the WNM and the CNM, provided that the postshock thermal pressure is higher than the maximum pressure of the WNM and that the maximum density allowed by magnetic compression is greater than the minimum density of the CNM. The input flux of mechanical energy is primarily reprocessed into line emissions from the X-ray to the submillimeter domain. Intermediate- and high-velocity shocks are found to generate a UV radiation field that scales as VS3 for VS < 100 km s−1 and as VS2 at higher velocities, and an X-ray radiation field that scales as VS3 for VS ⩾ 100 km s−1. Both radiation fields may extend over large distances in the preshock depending on the density of the surrounding medium and the hardness of the X-ray field, which is solely driven by the shock velocity. Conclusions. This first paper presents the thermochemical trajectories of shocks in the WNM and their associated spectra. It corresponds to a new milestone in the development of the Paris-Durham shock code and a stepping stone for the analysis of observations that will be carried out in forthcoming works.

Hydro‐Biogeochemical Controls on Nitrate Removal: Insights From Artificial Emergent Vegetation Experiments in a Recirculating Flume Mesocosm

AbstractEnvironments with aquatic vegetation can mitigate excess nitrogen (N) loads to downstream waters. However, complex interactions between multiple hydro‐biogeochemical processes control N removal within these environments and thus complicate implementation of aquatic vegetation as a management solution. Here, we conducted controlled experiments using a canopy of artificial rigid emergent vegetation in a recirculating flume mesocosm to quantify differences in rates of mass transport and nitrate (NO3−N) removal between the open channel‐canopy interface across a range in nominal water velocities. We found NO3−N removal rates were 86% greater with the canopy present compared to no canopy control experiments and were always greatest at intermediate velocity (6 cms−1). With the canopy present, a hydrodynamically distinct mixing layer formed at the open channel‐canopy interface, and resources, such as carbon (C), CN ratios, and dissolved oxygen, differed between open channel and vegetated canopy. The dimensionless Damköhler (Da) number indicated NO3−N removal rates were reaction limited (Da << 1) for all canopy experiments, yet across all velocities NO3−N removal was more reaction limited in the open channel than the canopy due to higher rates of mixing and less contact time with reactive surfaces. We found significant relationships between NO3−N removal rates and Da with hydrodynamic metrics (mixing zone width and Reynolds number, respectively), suggesting that NO3−N removal in the presence of rigid vegetation can be enhanced by manipulating flow conditions. These findings demonstrate that rigid emergent vegetation‐open channel interfaces create conditions conducive for NO3−N removal and with effective management can improve overall water quality.

First detection of the [CII] 158 µm line in the intermediate-velocity cloud Draco

High-latitude intermediate-velocity clouds (IVCs) are part of the Milky Way’s H I halo and originate from either a galactic fountain process or extragalactic gas infall. They are partly molecular and can most of the time be identified in CO. Some of these regions also exhibit high-velocity cloud gas, which is mostly atomic, and gas at local velocities (LVCs), which is partly atomic and partly molecular. We conducted a study on the IVCs Draco and Spider, both were exposed to a very weak UV field, using the spectroscopic receiver upGREAT on the Stratospheric Observatory for Infrared Astronomy (SOFIA). The 158 µm fine-structure line of ionized carbon ([C II]) was observed, and the results are as follows: In Draco, the [C II] line was detected at intermediate velocities (but not at local or high velocities) in four out of five positions. No [C II] emission was found at any velocity in the two observed positions in Spider. To understand the excitation conditions of the gas in Draco, we analyzed complementary CO and H I data as well as dust column density and temperature maps from Herschel. The observed [C II] intensities suggest the presence of shocks in Draco that heat the gas and subsequently emit in the [C II] cooling line. These shocks are likely caused by the fast cloud’s motion toward the Galactic plane that is accompanied by collisions between H I clouds. The nondetection of [C II] in the Spider IVC and LVC as well as in other low-density clouds at local velocities that we present in this paper (Polaris and Musca) supports the idea that highly dynamic processes are necessary for [C II] excitation in UV-faint low-density regions.

A non-hydrostatic numerical model for simulating regular wave breaking and surf-swash zone motions

In the present study, a non-hydrostatic two-dimensional vertical model has been developed to simulate the breaking of regular waves and surf-swash zone motions on a sloping beach. The objective of the present study was to estimate parameters at depth. The governing equations, based on the pressure-correction projection method, were solved in two main phases. In the initial phase, intermediate velocities were acquired through the resolution of advection–diffusion and explicit dynamic pressure gradient terms within the momentum equations, employing a time-splitting technique. To ensure local momentum conservation and solution monotonicity, modifications were made to the governing equations and the solution approach. In the second phase, through the substitution of intermediate velocities and the corrected pressure gradient term from the momentum equations into the continuity equation, with the elimination of velocities, a Poisson pressure-correction equation was derived. In the discretization stage, an innovation was proposed to compute horizontal velocities at the locations where vertical velocities are present, significantly reducing computational costs. The equation was then converted into a system of linear equations, which was solved implicitly. Comparisons between numerical results and experiments concerning plunging and spilling breakers reveal that the developed model satisfactorily simulates the outcomes.

Semi‐implicit material point method for simulating infiltration‐induced failure of unsaturated soil structures

AbstractThis study presents a semi‐implicit MPM to adequately characterize the mechanical behavior of unsaturated soil based on Biot's mixture theory. To represent the dependency of the degree of saturation on the suction, we employ the VG model along with a soil‐water characteristic curve, which determines a functional form of permeability called the Mualem model. Hencky's hyperelastic model and the Drucker‐Prager model assuming nonassociativity are adopted for elastic and plastic deformations, respectively. The novelty of this study is the incorporation of the fractional‐step method into the MPM framework so that the pore water pressure is obtained by implicitly solving the pressure Poisson's equation, which reduces numerical instability and improves computational efficiency. Also, because the drag force between solid and liquid phases is evaluated using the intermediate velocity of pore water relative to the intermediate velocity of solid skeleton, the time increment can be chosen without considering the magnitude of water permeability. In addition, to suppress “odd‐even” oscillation, we employ a sub‐grid method in which two grids with different spatial resolutions are used for the velocities and pore water pressure. Furthermore, considering the advantages and disadvantages of two different interpolation schemes for pore water pressure, we suggest switching the schemes depending on the model conditions. Several numerical examples are presented to demonstrate the performance of the proposed method. Specifically, unidirectional consolidation and leak flow analyses are performed for verification purposes, followed by validation analysis of a model experiment of infiltration‐induced landslides.

Cloud–Cloud Collision and Cluster Formation in the W5-NW Complex

We present a detailed structural and gas kinematic study of the star-forming complex W5-NW. A cloud–cloud collision scenario unravels with evidence of collision-induced star and cluster formation. Various signatures of cloud–cloud collision such as “complementary distribution” and “bridging features” are explored. At the colliding region, the two clouds have complementary morphologies, where W5-NWb has a filamentary key-like shape that fits into the U-shaped cavity in W5-NWa that behaves like a keyhole. The interaction region between the two clouds is characterized by bridging features with intermediate velocities connecting the two clouds. A skewed V-shaped bridging feature is also detected at the site of the collision. A robust picture of the molecular gas distribution highlighting the bridges is seen in the position–position–velocity diagram obtained using the SCOUSEPY algorithm. Star cluster formation with an overdensity of Class I and Class II young stellar objects is also seen towards this cloud complex, likely triggered by the cloud collision event.

Revealing Multiple Nested Molecular Outflows with Rotating Signatures in HH270mms1-A with ALMA

We present molecular line observations of the protostellar outflow associated with HH270mms1 in the Orion B molecular cloud with ALMA. The 12CO (J = 3−2) emissions show that the outflow velocity structure consists of four distinct components of low (≲10 km s−1), intermediate (∼10–25 km s−1) and high (≳40 km s−1) velocities in addition to the entrained gas velocity (∼25–40 km s−1). The high- and intermediate-velocity flows have well-collimated structures surrounded by the low-velocity flow. The chain of knots is embedded in the high-velocity flow or jet, which is the evidence of episodic mass ejections induced by time-variable mass accretion. We could detect the velocity gradients perpendicular to the outflow axis in both the low- and intermediate-velocity flows. We confirmed the rotation of the envelope and disk in the 13CO and C17O emission and found that their velocity gradients are the same as those of the outflow. Thus, we concluded that the velocity gradients in the low- and intermediate-velocity flows are due to the outflow rotation. Using observational outflow properties, we estimated the outflow launching radii to be 67.1–77.1 au for the low-velocity flow and 13.3–20.8 au for the intermediate-velocity flow. Although we could not detect the rotation in the jets due to the limited spatial resolution, we estimated the jet launching radii to be (2.36–3.14) × 10−2 au using the observed velocity of each knot. Thus, the jet is driven from the inner disk region. We could identify the launching radii of distinct velocity components within a single outflow with all the prototypical characteristics expected from recent theoretical works.

Spectroscopic identification of rapidly rotating red giant stars in APOKASC-3 and APOGEE DR16

ABSTRACT Rotationally enhanced red giant stars are astrophysically interesting but rare. In this paper, we present a catalogue of 3217 active red giant candidates in the APOGEE DR16 (Apache Point Observatory Galactic Evolution Experiment – Data Release 16) survey. We use a control sample in the well-studied Kepler fields to demonstrate a strong relationship between rotation and anomalies in the spectroscopic solution relative to typical giants. Stars in the full survey with similar solutions are identified as candidates. We use vsini measurements to confirm that 50 ± 1.2 per cent of our DR16 candidates are rotationally enhanced (vsini > 5 km s−1), compared to 4.9 ± 0.2 per cent in the Kepler control sample. In both, the Kepler control sample and a control sample from DR16, we find that there are 3–4 times as many giants rotating with intermediate velocities of 5 < vsini < 10 km s−1 compared to velocities of vsini > 10 km s−1, the traditional threshold for rapid rotation for red giants. The vast majority of intermediate rotators are not spectroscopically anomalous. We use binary diagnostics from APOGEE and Gaia to infer a binary fraction of 73 ± 2.4 per cent among the confirmed rotationally enhanced giants in DR16. We identify a significant bias in the reported metallicity for DR16 candidates with complete spectroscopic solutions, with a median offset of −0.37 dex in [M/H] from a control sample. As such, up to 10 per cent of stars with reported [M/H]<−1 are not truly metal poor. Finally, we use Gaia data to identify a subpopulation of main-sequence photometric binaries erroneously classified as giants.

The Peculiar Ejecta Rings in the O-Rich Supernova Remnant Puppis A: Evidence of a Binary Interaction?

Near the center of the Puppis A supernova remnant a series of nested, optically emitting rings of high-velocity ejecta (known as “the Swirl”) were identified several decades ago by Winkler et al. To date, no follow-up observations of these rings have been published, and their physical origin has remained a mystery. We present results of integral field spectroscopy of the Swirl using the Wide Field Integral Spectrograph on the 2.3 m telescope at Siding Spring Observatory in Australia. The outermost ring exhibits a nitrogen-rich spectrum blueshifted to 1350 km s−1, with smaller blueshifted rings within the first exhibiting mostly oxygen-rich spectra moving at 1000 and 750 km s−1. The structures are connected by material of intermediate velocity and variable composition, including sulfur-rich material. The Swirl is turbulent and shock-excited, and contains as much as 0.5 M ⊙ of metal-rich material. The chemical composition and exclusively blueshifted radial velocities of the Swirl are consistent with progressively deeper nucleosynthetic layers in a massive progenitor star. We suggest the possibility that the Swirl marks a “funnel” carved into the supernova ejecta by a close, massive binary companion at the moment of explosion.

Two-photon Production in Low-velocity Shocks

The Galactic interstellar medium abounds in shocks with low velocities v s ≲ 70 km s−1. Some are descendants of higher velocity shocks, while others start off at low velocity (e.g., stellar bow shocks, intermediate velocity clouds, spiral density waves). Low-velocity shocks cool primarily via Lyα and two-photon continuum, augmented by optical recombination lines (e.g., Hα), forbidden lines of metals and free-bound emission, free–free emission. The dark far-ultraviolet (FUV) sky, aided by the fact that the two-photon continuum peaks at 1400 Å, makes the FUV band an ideal tracer of low-velocity shocks. GALEX FUV images reaffirm this expectation, discovering faint and large interstellar structure in old supernova remnants and thin arcs stretching across the sky. Interstellar bow shocks are expected from fast stars from the Galactic disk passing through the numerous gas clouds in the local interstellar medium within 15 pc of the Sun. Using the bests atomic data available to date, we present convenient fitting formulae for yields of Lyα, two-photon continuum, and Hα for pure hydrogen plasma in the temperature range of 104–105 K. The formulae presented here can be readily incorporated into time-dependent cooling models as well as collisional ionization equilibrium models.

Numerical simulations of two-dimensional incompressible Navier-Stokes equations by the backward substitution projection method

The backward substitution method is a newly developed meshless method that has been used for the simulation of many problems in science and engineering with high accuracy and efficiency. In this paper, we explore the feasibility of employing the backward substitution method for simulating two-dimensional incompressible flows. Two non-increment pressure correction projection methods are considered to decompose the original velocity and pressure coupling system into two boundary value problems of intermediate velocity and pressure. Then, two boundary value problems are solved by the backward substitution method in each time iteration step. Five numerical examples are provided to demonstrate the accuracy, computational efficiency and convergence of the method. Comparisons with some existing meshless methods verify the method's advantages and potential applications to engineering.

How to make giant planets via pebble accretion

Planet formation is directly linked to the birthing environment that protoplanetary disks provide. The disk properties determine whether a giant planet will form and how it evolves. The number of exoplanet and disk observations is consistently rising, however, it is not yet possible to directly link these two populations. Therefore, a deep theoretical understanding of how planets form is crucial. Giant planets are not the most common exoplanets, but their presence in a disk can have significant consequences for the evolution of the disk itself and the planetary system undergoing formation. Their presence also offers more chances of spotting observational features in the disk structure. We performed numerical simulations of planet formation via pebble and gas accretion, while including migration, in a viscously evolving protoplanetary disk, with dust growing, drifting, and evaporating at the ice lines. In our investigation of the most favorable conditions for giant planet formation, we find that these are high disk masses, early formation, and a large enough disk to host a long-lasting pebble flux, so that efficient core growth can take place before the pebble flux decays over time. Specifically, core growth needs to start before 0.9 Myr to form a giant, with an initial disk mass of 0.04 M⊙ (or higher) and the disk radius needs to be larger than 50 AU. However, small disks with the same mass allow more efficient gas accretion onto already formed planetary cores, leading to more massive gas giants. Given the right conditions, high viscosity (α = 10−3) leads to more massive cores (compared to α = 10−4) and it also enhances gas accretion. At the same time, it causes faster type II migration rates, so the giants have a decreasing final position for increasing viscosity. Intermediate dust fragmentation velocities, between 4 and 7 m s−1, provide the necessary pebble sizes and radial drift velocities for maximized pebble accretion with optimal pebble flux. The starting location of a planetary embryo defines whether a giant planet will form, with the highest fraction of giants originating between 5 and 25 AU. Finally, a dust-to-gas ratio of 0.03 can compensate for lower disk masses with fDG ≤ 0.015, but early formation is still important in order to form giant planets. We conclude that there is no specific initial parameter that leads to giant planet formation; rather, it is the outcome of a combination of complementary factors. This also implies that the diversity of the exoplanet systems is the product of the intrinsic diversity of the protoplanetary disks and it is crucial to take advantage of the increasing number and quality of observations to constrain the disk population properties and ultimately devise planet formation theories.

The kinematic structure of magnetically aligned H i filaments

ABSTRACT We characterize the kinematic and magnetic properties of H i filaments located in a high Galactic latitude region (165° < α < 195° and 12° < δ < 24°). We extract three-dimensional filamentary structures using fil3d from the Galactic Arecibo L-Band Feed Array H i (GALFA-H i) survey 21-cm emission data. Our algorithm identifies coherent emission structures in neighbouring velocity channels. Based on the mean velocity, we identify a population of local and intermediate velocity cloud (IVC) filaments. We find the orientations of the local (but not the IVC) H i filaments are aligned with the magnetic field orientations inferred from Planck 353 GHz polarized dust emission. We analyse position–velocity diagrams of the velocity-coherent filaments, and find that only 15 per cent of filaments demonstrate significant major-axis velocity gradients with a median magnitude of 0.5 km s−1 pc−1, assuming a fiducial filament distance of 100 pc. We conclude that the typical diffuse H i filament does not exhibit a simple velocity gradient. The reported filament properties constrain future theoretical models of filament formation.

Exploring the dynamics of viscoelastic adhesion in rough line contacts

Modeling the adhesion of viscoelastic rough surfaces is a recent challenge in contact mechanics. Existing models have primarily focused on simple systems with smooth topography or single roughness scale due to the co-action of roughness and viscoelasticity leading to elastic instabilities and rate-dependent behavior, resulting in complex adhesion dynamics. In this study, we propose a numerical model based on a finite element methodology to investigate the adhesion between a randomly rough profile and a viscoelastic half-plane. Approach-retraction simulations are performed under controlled displacement conditions of the rough indenter. The results demonstrate that viscous effects dampen the roughness-induced instabilities in both the approach and retraction phases. Interestingly, even when viscous effects are negligible, the pull-off stress, i.e., the maximum tensile stress required to detach the surfaces, is found to depend on the stiffness modulus and maximum load reached during the approach. Furthermore, when unloading is performed from a relaxed state of the viscoelastic half-plane, both adhesion hysteresis and pull-off stress are monotonic increasing functions of the speed. Conversely, when retraction begins from an unrelaxed state of the material, the maximum pull-off stress and hysteretic loss are obtained at intermediate velocities.

Magnetic resonance velocity imaging of turbulent gas flow in a packed bed of catalyst support pellets

Compressed sensing magnetic resonance methods have been used to image the time-averaged velocity and turbulent kinetic energy in 3D for turbulent gas flowing through a bed of porous, hollow cylindrical catalyst support pellets. Velocity and turbulent kinetic energy images were acquired at a spatial resolution of 0.70 mm (x) × 0.70 mm (y) × 1.0 mm (z) for particle Reynolds numbers, Rep, of 500, 2500 and 6500 in a bed with a tube-to-particle diameter ratio of 4.7. These data represent the first full-field measurements of turbulent gas flow in packed beds of non-spherical pellets. The resulting images reveal several interesting features of the hydrodynamics in this system. A large degree of flow heterogeneity is observed in the bed, with regions of high-speed fluid observed near the walls and in large voids, and regions of backflow observed in the wake of pellets, between pellets, and within the pellet holes. For increasing Rep, the normalized axial velocity at the wall is found to increase, and the normalized turbulent kinetic energy becomes more homogeneous throughout the bed. The correlation between the turbulent kinetic energy and time-averaged velocity shows that the highest turbulent kinetic energy occurs in regions of intermediate time-averaged velocity. Further, the turbulent kinetic energy profile at the pellet-scale is substantially different from the case of simple channel flow for Rep≥ 2500. Overall, these measurements clearly demonstrate the ability of magnetic resonance methods for acquiring full-field flow data in packed bed systems using commercially-relevant pellets and flow conditions.

Potential Role of Volcanic Glass‐Smectite Mixtures in Slow Earthquakes in Shallow Subduction Zones: Insights From Low‐ to High‐Velocity Friction Experiments

AbstractVolcanic glass and its mixture with smectite are commonly observed in shallow parts of subduction zones. As volcanic glass layers often act as glide planes in submarine landslides, and because its alteration product, smectite, is one of the frictionally weakest geological materials, the frictional characteristics of volcanic glass‐smectite mixtures are important for fault slip behavior in shallow parts of subduction zones. We performed a series of friction experiments on volcanic glass‐smectite mixtures with different smectite contents from 0% to 100% at various velocity conditions from 10 μm/s to 1 m/s under an effective normal stress of 5 MPa and pore pressure of 10 MPa. In general, apparent friction coefficients negatively depend on the smectite content at any velocity tested. We found that samples with smectite contents of 15%–30% showed a drastic slip‐weakening behavior at intermediate velocities of 1–3 mm/s. Finite element method modeling shows that thermal pressurization does not contribute to the observed weakening behavior. The critical nucleation length estimated from the slip‐weakening behavior is approximately 1–10 km, which is large enough to prevent the slip to accelerate to seismic slip velocity. Therefore, gouges with minor amount of clay, such as subducting volcanic ash layers, may contribute to the occurrence of the slow earthquakes at shallow depths in subduction zones.

Fragmentation of a molten metal droplet in an ambient water flow

The influence of an ambient fluid flow on the fragmentation of hot molten tin droplets (initially at 800°C) and cold low melting point alloy droplets (initially at 70°C) in water is investigated with high-speed photography and flash radiography. The water is accelerated using a converging nozzle to a constant speed of up to 30 m/s using a double piston arrangement designed to eliminate the formation of a shock wave that is present in most earlier studies. At low flow velocities, the fragmentation of hot droplets is governed by thermal effects and vapour formation, growth, and collapse. At high flow velocities, vapour formation is suppressed and the droplet fragmentation is determined by hydrodynamic effects in which hydrodynamic instabilities (Rayleigh-Taylor and Kelvin-Helmholtz) and wavecrest stripping all play a role in the droplet breakup. At intermediate flow velocities, both thermal and hydrodynamic effects play a role. Quantitative image analysis of the radiographs is used to determine the spatial distribution of the droplet mass during the fragmentation process. Comparison with earlier work in which the ambient flow is preceded by a strong shock wave indicates that the transition from thermal to hydrodynamic breakup is strongly dependent on the pressure field.

Human blood circulation model based on flow laws of intensity and continuity in relation to earth’s surface gravity

With the help of the physical laws of flow, it is possible to describe the entire human blood circulation. However, this requires precise knowledge of the individual parameters. Within this, the determination of the flow rate included in the law of continuity is essential. Together with the data of the heart and circulation examination procedures, in order to establish the average human blood circulation, an intermediate velocity value must be selected, which is located in the middle between the two extreme velocities of the blood circulation. Another important factor from the point of view of the structure and operation of the model is the value of the earth's surface gravity. By finding the average flow speed value and using ‘g’, a torus-shaped circulation can be created, which can actually reflect the circulation conditions. By further refining the model, the pulmonary and systemic circulations can be separated and a ‘folded figure eight’ model can be formed. This realistically reflects the different sizes, flow and pressure conditions of the two blood circulations, as well as the work of the left and right sides of the heart.