The disc brake rotors are designed to withstand both, Maximum possible deceleration (emergency braking) and a series of frequent braking cycles. A effective rotor design and superior heat dissipating material provide better performance during the braking mechanism. In this experiment, modified ventilated disk brake rotors are developed with holes and slots and the stress, deformation, heat flux and temperature distribution has been analysed. Designing of the Finite element models of the rotor are created with SolidWorks and simulated using ANSYS. Structural and thermal characteristics are compared with a reference disk brake rotor of the motorcycle (TVS Apache RTR180). It is found that the modified rotors outperform the conventional one in terms of stress generation, temperature distribution and deformation. Furthermore, this Analysis helps us to find out the best suited material for one of the proposed designs. This experiment provides us an insight of the structural and thermal characteristics of the geometrically modified rotor that can be used to upgrade and outperform the current disc brake rotor used in the motorcycle (TVS Apache RTR180).

In this paper, closed and semi-closed form solutions are presented for the self - and mutual inductance of ordinary and Better disk coils which lie concentrically in a plane. The solutions are given as the combination of the elliptic integral of the first kind and a simple integral or only as the second elliptic integral of the second kind. All formulas or obtained in remarkably simple form and give extremely accurate results with significantly neglectable computational time. All cases either regular or singular (disks in contact or overlap) are covered. The formulas for the mutual inductances can be directly used to calculating the self-inductance of the ordinary disk coil or the Bitter disk coil, respectively. Many presented examples show the excellent numerical agreement with previous publish methods.

With over 5,000 exoplanets discovered since the advent of planetary science, understanding protoplanetary disk evolution remains critical. Although existing models have offered insights, the intricacies regarding the disk's structure and the impact of the host star's parameters on planet formation persist. Utilizing FARGO3D, we simulated the evolution of protoplanetary disks. Critical factors like surface density and the disk-to-host star mass ratio were primarily considered in terms of the host star's mass. After introducing necessary parameters into FARGO3D and integrating test particles for simulation, we assessed the protoplanetary disk's planetary formation capability. Our findings indicate that protoplanetary disks can form planets for host star masses below a certain threshold. However, as the host star's mass augments, its potential for planet formation diminishes, with a notable transition zone observed. Our research elucidates why most exoplanet-hosting stars have masses below this threshold, suggesting it's potentially more related to the intrinsic properties of the protoplanetary disk as determined by the host star rather than observational limitations.

Pollution by heavy metals is one of the most severe environmental issues that threaten global sustainability. This review presents a recent advance in electrochemical sensors for heavy metal detection Rotating Disk Platinum Electrode are discussed. This study on the production of a modern natural water electrochemical antimony (II) and cupper (II) test include the use of platinum electrode. Antimony and cupper were pre-concentrated on the modified electrode surface and adsorbed to the surface, oxidizing at E = 540 mV and E = 85 mV, respectively. After 20 min of accumulation, time the best-defined anodic peak was obtained of surface. The precision was tested by carrying out chronoamperometric measurements at a concentration of Sb⁺² and Cu⁺² 8.5x10^-8 M and 9.5x10^-7 M, respectively.

Highly-doped graphene samples show the conductance reduced and the shot-noise power enhanced compared to standard ballistic systems in two-dimensional electron gas. These features can be understood within a model assuming incoherent scattering of Dirac electrons between two interfaces separating the sample and the leads. Here we find, by adopting the above-mentioned model for the edge-free (Corbino) geometry and by means of the computer simulation of quantum transport, that another graphene-specific feature should be observable when the current flow through a doped disk is blocked by high magnetic field. In case the conductance drops to zero, the Fano factor approaches the value of $F\approx{}0.56$, with a very weak dependence on the disk radii ratio. The role of finite source-drain voltages and the system behavior upon tuning the electrostatic potential barrier from a rectangular to parabolic shape are also discussed.

Fluorescence-linked immunosorbent assay (FLISA) is a commonly used, quantitative technique for detecting biochemical based on antigen–antibody binding reactions using a well-plate platform. With the developments in the manufacturing technology of microfluidic systems, FLISA can be implemented onto microfluidic disk platforms, which allows the detection of trace biochemical with high resolutions. Apart from requiring a lower proportion of reagent (1/10), this method also reduces the time required for the entire process to less than an hour. The incubation process involves antigen–antibody binding reactions as well as the binding of fluorogenic substrates to target proteins. The protocol for FLISA on a microfluidic platform necessitates the appropriate execution of liquid reagent movements during each step in order to ensure sufficient binding reactions. Herein, we propose a novel microfluidic disk comprising a 3D incubation chamber. Vascular endothelial growth factor as concentration with ng mL-1 is detected sequentially using a benchtop process employing this 3D microfluidic disk. The 3D microfluidic disk is implemented without requiring manual intervention or additional procedures for liquid control. During the incubation process, microbead movement is controlled through centrifugal force, generated due to disk rotation, and gravitational force via bead sedimentation on the sloped floor of the chamber.

Atmospheric stability affects wind turbine wakes significantly. High-fidelity approaches such as large eddy simulations (LES) with the actuator line (AL) model which predicts detailed wake structures, fail to be applied in wind farm engineering applications due to its expensive cost. In order to make wind farm simulations computationally affordable, this paper proposes a new actuator disk model (AD) based on the blade element method (BEM) and combined with Reynolds-averaged Navier–Stokes equations (RANS) to model turbine wakes under different atmospheric stability conditions. In the proposed model, the upstream reference velocity is firstly estimated from the disk averaged velocity based on the one-dimensional momentum theory, and then is used to evaluate the rotor speed to calculate blade element forces. Flow similarity functions based on field measurement are applied to limit wind shear under strongly stable conditions, and turbulence source terms are added to take the buoyant-driven effects into consideration. Results from the new AD model are compared with field measurements and results from the AD model based on the thrust coefficient, the BEM-AD model with classical similarity functions and a high-fidelity LES approach. The results show that the proposed method is better in simulating wakes under various atmospheric stability conditions than the other AD models and has a similar performance to the high-fidelity LES approach however in much lower computational cost.

Lactococcus spp. has emerged as a pathogen that is affecting global aquaculture, with L. garvieae, L. petauri, and L. formosensis causing piscine lactococcosis. While antimicrobials are commonly used to treat diseases in aquaculture, reports of antimicrobial resistance in fish isolates are increasing. However, little is known about the susceptibility patterns of Lactococcus spp. strains isolated from native fish species in Brazil. This study aimed to assess the antimicrobial susceptibility of these strains and establish a provisional epidemiological cut-off value for L. garvieae using the normalized resistance interpretation approach. A total of 47 isolates were tested: 17 L. garvieae, 24 L. petauri, and 6 L. formosensis. The isolates were classified as wild-type or non-wild-type (NWT) based on inhibition zone diameters. Isolates classified as NWT for three or more antimicrobial classes were considered multidrug-resistant, and the multiple antibiotic resistance (MAR) index was calculated. The results revealed heterogeneity in antimicrobial resistance profiles, with higher resistance to trimethoprim/sulfamethoxazole and norfloxacin. Resistance to other antimicrobials, including florfenicol and oxytetracycline (approved for use in Brazil), varied according to the bacterial species. Lactococcus petauri (87.5%) and L. formosensis (66.7%) showed the highest multidrug resistance, compared to L. garvieae (11.7%), along with higher MAR index values. These findings suggest that multidrug-resistant strains could pose future challenges in the production of native species, underscoring the need for ongoing monitoring of antimicrobial resistance and responsible use of antimicrobials in aquaculture.

On a rotating disk, two particles bounce at the vertices of a regular polygon in opposite directions. On the return to the entry point, a clock measures the time difference, called Sagnac effect. Due to Coriolis effects, the counterclockwise and clockwise paths are different. The particular case of the slow disk where the two trajectories are very close and almost polygonal is studied. The existence of a transition between a classical and a relativistic regime is proved. An experimental verification is proposed. Although the two Sagnac effects seem analogous, in detail their behavior is quite different.

Manufacturing of grinding wheels is continuously adapting to new industrial requirements. New abrasives and new wheel configurations, together with wheel wear control allow for grinding process optimization. However, the wear behavior of the new abrasive materials is not usually studied from a scientific point of view due to the difficulty to control and monitor all the variables affecting the tribochemical wear mechanisms. In this work an original design of pin on disk tribometer is developed in a CNC grinding machine. An Alumina grinding wheel with special characteristics is employed and two types of abrasive are compared: White Fused Alumina (WFA) and Sol-Gel Alumina (SG). The implemented tribometer reaches sliding speeds of between 20 and 30 m/s and real contact pressures up to 190 MPa. The results show that the wear behavior of the abrasive grains is strongly influenced by their crystallographic structure and the tribometer appears to be a very good tool for characterizing the wear mechanisms of grinding wheels, depending on the abrasive grains.

Sunflower is one of the oil crops and its planting areas was listed behind Soybean, peanut and rapeseeds in China. It will encounter different kind of diseases during planting, thus limited the seeds yield. Fusarium species are the major threat to different crops nowadays, it is very important to identify the species caused diseases on different hosts, so that the potential control measures may be explored. In Inner mongolia, Sunflower Disk Rot (SDR) was found in different sunflower planting field, the average infection ratio around 8.50%, typically in some verieties, its infection ratio reach to 11.67%. The diseased receptacle were collected from different locations and Koch’s postulate was conducted. The results showed that Fusarium verticillioides was the main causal agent caused SDR. Fungicide toxicity tests shown that Fludioxonil and Flutolanil were screened out from six fungicides for controlling F. verticillioides, with EC50 values of 0.05 µg/mL (R = 0.9825) and 0.96 µg/mL (R = 0.9964) , respectively. This is the first report of SDR caused by F. verticillioides, and it will alert sunflower reseachers to include SDR in the disease list, so as to control sunflower diseases with integrated management strategy successfully.

The reference method for cefiderocol antimicrobial susceptibility testing is broth microdilution (BMD) with iron-depleted-Mueller-Hinton (ID-MH) medium, whereas breakpoints recommended for disk diffusion (DD) are based on MH-agar plates. We aimed to compare the performance of the commercial BMD tests ComASP (Liofilchem) and UMIC (Bruker), DD and E-test using MH- and ID-MH-agar plates with the reference BMD method using 100 carbapenem-resistant-A. baumannii isolates. Standard BMD was performed according to the EUCAST guidelines, DD and E-test were carried out using two commercial MH-agar plates (bioMérieux and Liofilchem) and an in-house ID-MH-agar plate, while ComASP and UMIC were performed according to the manufacturer’s guidelines. DD performed with the ID-MH-agar plates led to a higher categorical agreement (CA, 95.1%) with standard BMD and fewer categorization errors compared to the commercial MH-agar plates (CA bioMérieux 91.1%, Liofilchem 89.2%). E-test on ID-MH-agar plates exhibited a significantly higher essential agreement (EA, 75%) with standard BMD compared to the two MH-agar plates (EA bioMérieux 57%, Liofilchem 44%), and showed a higher performance in detecting high-level resistance than ComASP and UMIC (mean log2 difference with standard BMD for resistant isolates of 0.5, 2.83 and 2.08, respectively). In conclusion, DD and E-test on ID-MH-agar plates exhibit a higher diagnostic performance than on MH-agar plates and the commercial BMD methods. Therefore, we recommend using ID-MH-agar plates for cefiderocol susceptibility testing of A. baumannii.

We measured the ring collection coefficient of bromide anion oxidation products in a neutral and slightly alkaline medium on a rotating ring-disk electrode (glassy carbon disk, platinum ring) varying the following parameters: disk electrode rotation velocity, sodium bromide concentration, pH of the medium (in the range of 6 – 12), anode current on the disk and the electroreduction potential of the bromide anion oxidation products on the ring. The data obtained is presented via dependences of the cathode ring current to the disk current ratio vs the ring electrode potential. The analysis of the results was carried out by comparing the experimental polarization curves of the ring electrode with the data of cyclic voltammetry in model solutions to determine the electrical activities of various bromine compounds in positive oxidation states. We claim that RRDE method could be used to obtain quantitative and qualitative data on the electrooxidation of bromide ion in neutral and alkaline solutions. For the most effective regeneration of the spent oxidizer the values of pH > 10 and moderate concentrations of NaBr should be used.

In this paper we give the new formulas for calculating the self-inductance for the circular coils of the rectangular cross sections with the radial and the azimuthal current densities. These formulas are given by the single integration of the elementary functions which are integrable on the interval of the integration. From these new expressions we can obtain the special cases for the self-inductance of the thin disk pancake and the thin wall solenoid that confirm the validity of this approach. For the asymptotic cases, the new formula for the self-inductance of the thin wall solenoid is obtained for the first time in the literature. In this paper we do not use special functions such as the elliptical integrals of the first, second and third kind, Struve, and Bessel functions because that is very tedious work. The results of this work are compared with already different known methods and all results are in the excellent agreement. This is way we consider this approach as the novelty because of its simplicity in the self -inductance calculation of the previously mentioned configurations.

In our recent experimental study we found that variability in sarcomere lengths (SLs) is lower if we get them from A-band centers (visualized by Second Harmonic Generation microscopy, SHG) vs. Z-disks (ANEPPS-staining of t-tubules). In the present study we demonstrate, using a simulation approach, that the extent of variability and “randomness” in SL are directly affected by what “sarcomeric structure” is used to calculate the SL. We simulated randomly dispersed positions of Z-disks and calculated the center points between two Z-disks as A-band centers. We found that variance in SL, if calculated from A-band centers (A-SL), was twice lower vs. variance in Z-disk-based SL (Z-SL), regardless the predefined dispersion of Z-disks. Furthermore, A-SLs were “non-randomly” interrelated – each next A-SL tended to be longer if the preceding one was longer – in contrast to Z-SLs which were truly random. Next, we demonstrated the presence and prevalence of this “non-random” effect for A-SL vs. Z-SL in our previously acquired experimental records. The rationale for this artifact is the “mathematical dependence” of sarcomere center on its edges, and it must always be taken into account in the interpretation of smaller variability of the distance between sarcomeric A-band centers vs. the distance between Z-disks.

Low-energy cosmic rays (LECRs) play a crucial role in the formation of planetary systems, and detecting and reconstructing the properties of early LECRs is essential for understanding the mechanisms of planetary system formation. Given that LECRs interact with the surrounding medium to produce nuclear de-excitation line emissions with energy mainly within 0.1–10 MeV, which are unaffected by stellar wind modulation, these gamma-ray emissions can accurately reflect the properties of LECRs. This study introduces an innovative method for using gamma-ray emissions to infer LECR properties. We employed the Parker transport equation to simulate the propagation and spectral evolution of LECRs in a protoplanetary disk and calculated the characteristic gamma-ray emissions resulting from interactions between LECRs and disk material. These gamma-ray emissions encapsulate the spectral information of LECRs, providing a powerful tool to reconstruct the cosmic ray environment at that time. This method, supported by further theoretical developments and observations, will fundamentally enhance our understanding of the impact of CRs on the origin and evolution of planetary systems and address significant scientific questions regarding the cosmic ray environment at the origin of life.

: This study focuses on optimizing chlorophyll extraction techniques and strategically placing leaf disks to enhance chlorophyll concentration in sesame (Sesamum indicum L.) leaves. Thirty sesame genotypes, categorized into light green (LG), middle green (MG), and deep green (DG) pigment groups based on leaf coloration, were selected from a larger pool of field-grown accessions. The investigation involved determining optimal SPAD value index measurements, quantifying pigment concentrations, exploring extraction solvents, and selecting suitable leaf disk positions. Significant variations in chlorophyll content were observed across genotypes, greenness categories, and leaf disk positions. The categorization of genotypes into DG, MG, and LG groups revealed a correlation between leaf appearance and chlorophyll content. The study highlighted a consistent relationship between carotenoids and chlorophyll, indicating their role in adaptation to warm environments. Examination of leaf disk positions revealed a significant chlorophyll gradient along the leaf blade, emphasizing the need for standardized protocols. Chlorophyll extraction experiments identified DMSO and 96% ethanol, particularly the later incubated for 10 minutes at 85°C, as effective choices. This recommendation considers factors like cost-effectiveness, time efficiency, safety, and environmental regulations, ensuring consistent and simplified extraction processes. For higher chlorophyll extraction, focusing on leaf tips and the 75% position along the sesame leaf blade is suggested, consistently yielding higher chlorophyll content. Our findings therefore, underscores insightful knowledge on chlorophyll gradients and encouraging for standardized protocols, that enabling researchers to refine experimental designs for precise and comparable chlorophyll measurements. Recommended solvent choices ensure reliable outcomes in plant physiology, ecology, and environmental studies.

The present article investigates the threshold analysis of yielding in a variable thickness rotating disk based on the Tresca criterion. The analysis is conducted on a Functionally Graded Material (FGM) constructed from tailored materials, following the theory of small deformations and for the case of plane stress. The elasticity modulus, density, and yield stress are assumed to be power functions of the radial coordinate. Poisson’s ratio is considered constant due to small variations in different materials. Additionally, the governing equation for the rotating disk is solved analytically. Besides the material type, another factor affecting the distribution of effective stress magnitudes is the cross-sectional shape (profile) of the disk. The thickness of the cross-sectional disk varies radially as a power function. In the current analysis, different conditions for the onset of yielding and the evolution of plastic flow are considered. For evaluation and validation, the obtained results are compared and validated against similar results for specific cases (homogeneous disk and constant thickness graded disk) available in previous references. The results indicate that considering variable thickness for the disk section significantly affects the stresses and the location of the initiation of yielding

In this study, we investigated water transparency estimation models in the hypertrophic lagoon of the Albufera of Valencia using Sentinel-2 images. Water transparency, a crucial environmental indicator, was assessed via Secchi disk depth (ZSD) measurements. Three optical models (R490/R560, R490/R705, R560/R705) were explored to establish a robust algorithm for ZSD estimation. Through extensive field sampling and laboratory analyses, weekly data spanning 2018 to 2023 were collected, including water transparency, temperature, conductivity, and chlorophyll-a concentration. Remote sensing imagery from the Sentinel-2 mission was employed, and images were processed using SNAP software. The R560/R705 model, calibrated for turbid lakes, emerged as the most suitable. The algorithm's calibration was validated with high correlation coefficients (R2) in both calibration (0.6149) and validation (0.916) phases, demonstrating the model's accuracy in estimating ZSD. This new algorithm significantly outperformed a previous approach, highlighting the importance of tailoring algorithms to specific water body characteristics. The study contributes to improved water quality assessment and resource management, underscoring the value of remote sensing in environmental research.

Distributed electric propulsion technology has great potential and advantage in the development of drones. In this paper, to study the slipstream effect of distributed propeller, the actuator disk method was used to verify a single propeller, and the calculated thrust was in good agreement with the test results. Then, based on the actuator disk method, the influence of different installation positions on the slipstream effect was studied, and the distributed propeller layout was optimized by genetic algorithm. The analysis results showed that lift of the wing will be larger when the propellers are higher than the wing. When the relative height between the propeller and the wing is zero, the drag is the lowest. The influence of disk diameter on the slipstream is that the larger the diameter is, the higher the lift force and the drag force are. The slipstream effect of the optimized propeller distribution improves the lift-drag ratio of the wing, by 108.5% in the initial lift-drag ratio.

The geometry of Poincare disk itself is interpreted without any mapping to dierent spaces. Our approach might be one of the shortest and is intended for educational contribution.

This paper presents a new approach of eddy current methods for determining the size of the co-axial hole in the metallic circular disk. In recent decades, for the air-cored sensor probe, the impedance change due to the presence of an infinite metal plate can be calculated by the Dodd-Deeds model. However, in practical measurements, the sample cannot match with the condition required - ‘infinite’, thus the Dodd-Deeds model could not be applied to the disk with finite size and certainly not a co-axial hole in the center. In this paper, a dual-constraint analytical method is proposed. That is, the upper and lower limits of the integration are substituted with specific values instead of the original 0 and . Besides, it is found that, once the outer radius of the disk is fixed (i.e. the lower limit of integration is fixed), the upper limit reduces linearly as the size of the coaxial hole increases. Both the FEM simulation and experiments have been carried out to validate this method. The radius of the hole can be estimated based on the dual-constraint integration feature.

Glaucoma is a disease associated with retina of eye. Presently, millions of human being is suffering from this disease. Early detection of these diseases can save the people from blindness. Therefore, various methods have been developed for its detection. In this paper, we have studied the reported methods and summarized their performance in terms of accuracy of detection.

The goal of this paper is to investigate the aerodynamic and aerothermodynamic behaviour of the Schiaparelli capsule after the deployment of the supersonic disk-gap-band (DGB) parachute during its re-entry phase into the Martian atmosphere. Large-Eddy Simulations of compressible flows have been performed over the capsule and the flexible DGB parachute to analyse the behaviour of the turbulent wake behind the capsule and its interaction with the parachute flow-field. The simulations are performed at an altitude of 10 km and a Mach number around 2, i.e., a regime in which large canopy-area oscillations are observed. These simulations have shown a strong interaction between the bow shock, the recompression and expansion waves, high pressure, density and temperature gradients, heat flux towards the airstream and the body implying turbulence generation, ingestion, and amplification through the shock waves. This nonlinear turbulence flowfield explains the non-axisymmetric behaviour around and behind the parachute that caused the uncontrolled capsule oscillation and the mission failure.

The most cited evidence for (nonbaryonic) dark matter has been an apparent lack of visible mass to gravitationally support the observed orbital velocity of matters in rotating disk galaxies. Yet measurement of the mass of celestial objects cannot be straightforward, requiring theories derived from the known physical laws along with some empirically established semi-quantitative relationship. The most reliable means for determining the mass distribution in rotating disk galaxies is to solve a force balance equation according to Newton’s laws from measured rotation curves, similar to calculating the Sun’s mass from the Earth’s orbital velocity. Another common method to estimate galactic mass distribution is to convert measured brightness from surface photometry based on empirically established mass-to-light ratio. For convenience, most astronomers commonly assumed a constant mass-to-light ratio for estimation of the so-called “luminous” or “visible” mass, which should not be expected accurate. The mass determined from rotation curve typically exhibit an exponential-like decline with galactrocentric distance, qualitatively consistent with observed surface brightness. This fact scientifically suggests variable mass-to-light ratio of baryonic matter in galaxies without the need for dark matter.

In this work we study the intersection properties of a finite disk system in the euclidean space. We accomplish this by utilizing subsets of spheres with varying dimensions and analyze specific points within them, referred to as poles. Additionally, we introduce two applications: estimating the common scale factor for the radii that makes the re-scaled disks intersects in a single point, this is the \v{C}ech scale, and constructing the minimal Axis-Aligned Bounding Box (AABB) that encloses the intersection of all disks in the system.

In the field of computational fluid dynamics (CFD) for rotorcraft, two significant challenges are resolving the complex vortex structures in rotor wakes, and representing the moving rotor blades in the ambient airflow. This study addresses the first challenge by using a third-order unstructured finite volume solver, which, compared to its second-order counterpart, has substantially lower dissipation. Consequently, even relatively coarse meshes are capable of resolving small vortices. With this background flow field solver, the second challenge is addressed by modeling each rotor as an Actuator Disk Model (ADM), or describing individual rotor blades as actuator lines, designated as the Actuator Line Model (ALM). Both of these models are equipped with an improved correction for aerodynamic losses at blade tips, which is thoroughly presented in the methodology section. The numerical experiments section centers on analyzing errors linked to various sampling approaches. Additionally, the article discusses comparisons between vortex theory and ALM, specifically regarding calculations for fixed-wing aircraft. Furthermore, high-order precision and parallel efficiency are exemplified in scenarios encompassing rotors engaged in both hovering and forward flight rotors. The results in this paper demonstrate that the combination of the ALM/ADM with the improved tip loss correction and the third-order finite volume solver presents a new way of developing efficient tools for the aerodynamic analysis of helicopter rotors.

Black hole X-ray binary systems consist of a black hole accreting mass from its binary companion, forming an accretion disk. As a result, twin relativistic plasma ejections (jets) are launched towards opposite and perpendicular directions. Moreover, multiple broadband emission observations from X-ray binary systems range from radio to high-energy gamma-rays. The emission mechanisms exhibit thermal origins from the disk, stellar companion, and non-thermal jet-related components (i.e., synchrotron emission, inverse comptonization of less energetic photons, etc.). In many attempts at fitting the emitted spectra, a static black hole is often assumed regarding the accretion disk modeling, ignoring the Kerr metric properties that significantly impact the geometry around the usually rotating black hole. In this work, we study the possible implications of the spin inclusion in predictions of the X-ray binary spectrum. We mainly focus on the most significant aspect inserted by the Kerr geometry, the innermost stable circular orbit radius dictating the disk’s inner boundary. The outcome suggests a higher-peaked and hardened X-ray spectrum from the accretion disk and a substantial increase in the inverse compton component of disk-originated photons. Jet-photon absorption is also heavily affected at higher energy regimes dominated by hadron-induced emission mechanisms. Nevertheless, a complete investigation requires the full examination of the spin contribution and the resulting relativistic effects beyond the disk truncation.

The famous singlet correlations of a composite quantum system consisting of two spatially separated components exhibit notable features of two kinds. The first kind consists of striking certainty relations: perfect correlation and perfect anti-correlation in certain settings. The second kind consists of a number of symmetries, in particular, invariance under rotation, as well as invariance under exchange of components, parity, or chirality. In this note, I investigate the class of correlation functions that can be generated by classical composite physical systems when we restrict attention to systems which reproduce the certainty relations exactly, and for which the rotational invariance of the correlation function is the manifestation of rotational invariance of the underlying classical physics. I call such correlation functions classical EPR-B correlations. It turns out that the other three (binary) symmetries can then be obtained "for free": they are exhibited by the correlation function, and can be imposed on the underlying physics by adding an underlying randomisation level. We end up with a simple probabilistic description of all possible classical EPR-B correlations in terms of a "spinning coloured disk" model, and a research programme: describe these functions in a concise analytic way.