Overview : Non newtonian fluid flow rate, viscosity, pressure drop

 

In non-monotonic flow, the graph of flow rate versus shear stress or pressure often forms an S-shaped curve. Initially, the flow rate increases with stress. At a certain threshold, further increases in stress cause the flow rate to drop. fluid can exhibit two different shear rates at the same shear stress, causing a separation or banding in shear rates.

In vorticity banding different regions have distinct shear stresses but the same shear rate. 

Weienberg-Rabinowitsch allows for calculating the shear rate at the tube wall, even when a fluid’s viscosity changes with shear rate.

Wyart and Cates rheological model is used in this study. It explains the behavior of shear-thickening fluids—specifically, how their viscosity increases abruptly under certain conditions. 

ηr​ is the viscosity when all contacts are frictional, ns is for frictionless contacts. Q is flowrate, delta P is pressure drop

At low concentrations the curve is smooth and almost linear, indicate a continuous shear-thickening (CST) behavior. As concentration increases fluid exhibits discontinuous shear thickening (DST), where viscosity increases abruptly. At very high concentrations  the curve forms an S-shape, indicating non-monotonic behavior. Here, the shear rate can decrease with increased shear stress, leading to instabilities like shear banding.

When this type of fluid flows in a tube, streamwise banding occurs, here the pressure gradient can be inhomogeneous, dividing into regions of high viscosity and low viscosity along the tube.

In study, experiment was done at homogeneous and heterogeneous initial conditions. Initially, the flow rate is high. The dispersion of the pressure gradient is a result of the initial distribution of friction and viscosity. With time, the flow rate decreases and the different pressure gradients diverge. Some locations converge to a low gradient, while others converge to a higher pressure gradient.

source:

https://universite-paris-saclay.hal.science/hal-04743748

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Key Points of Article about Measuring gravitational waves by graphene

Current detectors can only capture low-frequency gravitational waves.

By using graphene, higher frequency gravitational waves can be detected and size of detector also reduced. Here relative intensity varies when gravitational waves are measured.

As a gravitational wave propagates through a crystal lattice, it causes directional stretching and compression of the lattice, it causes shifts in the electronic energy band and density of energy states also changes.

Changes occur in graphene under gravitational wave,

Where,  yAB is the overlapping integral of the nearest neighbors, E is Graphene  energy

As per equations, gravitational waves alter the distances between carbon atoms in graphene, changing its lattice structure and causing a slight shift in the electron wave vectors. This affects the electronic transport behavior.

As gravitational wave radiation intensity hGW increases, the relative change in wave vector and wavelength increases.  

When the polarization direction of the gravitational wave is along the z-axis, the

the y-direction lattice of the photonic-like interferometer is stretched while the x-direction lattice is compressed. 

The change in Fermi energy is related to the shift of the energy band and the corresponding change in the density of energy states, which  affects gravitational waves on electrons in k-space. When the Fermi energy increases, the relative changes in the wave vector and wavelength decreases.

The relative intensity change (delta I/I )caused by arm length change in the photonic-like interferometer is about 2782 times larger than that in the laser interferometer because of the shorter electron wavelength.

Gravitational wave detection can be conducted by graphene at extremely low temperatures.

Source: https://arxiv.org/abs/2410.18711

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Equations Used for measuring Exoplanet parameters

In recent article, brightness (flux) of the target star and the reference stars has been measured as analog digital units (ADU). 

The duration of a planetary orbit

𝑅𝑠 is the star radius, 𝑅𝑝 is the planet radius, 𝑀𝑠 is the star mass, 𝑀𝑝 is the planet mass, 𝐺 is the gravitational constant, a is the planetary orbital semi-major axis, e is the planetary orbital eccentricity, i is the planet inclination.

Depth of a planetary transit is the amount by which the light from a star dims when a planet passes in front of it. It is measured as a percentage or fraction of the total light blocked by the planet during the transit. 

L is luminosity, Depth of transit is obtained by 

If the radius of the star is known (from the spectral classification), 𝑅𝑝 can be obtained from Equation

If the orbital period 𝑃 and the mass of the star 𝑀⊙ are also known, the orbital semi-major axis a can be obtained from Kepler’s third law, and therefore the duration of the transit can be obtained.

From above equation latitude of the transit on the star, 𝛿, is calculated.

Traditional radial velocity is measured based on shifts of wavelength at which a star moves toward or away from Earth, which indirectly gives information about an orbiting planet's mass and orbit. But Synthetic radial velocity is  used to calculate mass from the radius using the forecaster model. In this model, Monte Carlo simulation is used to determine radius and mass.

Source: https://arxiv.org/abs/2410.07425

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Overview of Article about Random illumination Microscopy (EDF-RIM)

 

The objective of RIM is to compute the variance (the spread or difference) in the intensity of the images.

Intensity at camera plane depends on ρ sample fluorescence density, h the Point spread function(PSF) of the optical system and S the illumination intensity and distance of the focal plane.

As the light passes through the modulator, it gets scattered in random directions, creating interference, which produces a random, grainy pattern of bright and dark spots known as the speckle pattern. 

Each speckle illumination creates a different intensity pattern on the sample. Electrically tunable lens  made of a shape-changing polymer, is used here.

 Bessel speckle is created by a bessel beam to maintain focus over extended distances which  helps to capture fine details across different depths.

Image reconstruction is done by Wiener filter which enhance high frequencies and remove noise

where h bar is the Fourier transform of the extended depth PSF.

Here, to achieve super-resolved reconstruction, Tikhonov regularization method is used. The equation for Fluorescence density is

  

μ is the Tikhonov regularization parameter.

For simulation, lateral distribution follows the equation  ρ(r,θ) = 1 + cos(40θ), which generates a pattern of higher spatial frequencies towards the center of the patter.

Application: EDF- RIM is used in microscope to image larger, thicker biological samples with super-resolution.

https://www.nature.com/articles/s41377-024-01612-0

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Summary of Article related to Use of Free-form dual-comb spectroscopy

Free-form DCS allows control of the timing between the light pulses from two lasers and compressive sensing factor up to 155.

Here Comb is a special kind of laser that emits light at many equally spaced frequencies. 

Traditional DCS Sampling is a method where the sampling occurs at evenly spaced time intervals. Free-form DCS provides control over the temporal offset between pulses, which allows user-selected sampling. 

The Compressive Sensing method uses random, non-uniform sampling to capture the important parts of the signal, drastically reducing the number of measurements needed.

When gas like Methane absorbs light, it creates a specific pattern in the signal, which repeats at regular intervals (called "recurrences").

Instead of measuring everything, recurrence sampling skips the unnecessary parts and only looks at these important repeating signals.

Ax=b

A = ΦΨ

Heterodyne signal is the result of two laser light sources (called frequency combs) interfering with each other. This creates a new signal that shifts the high-frequency information to a much lower frequency. 

The light passes through the gas plume,  methane absorption pattern creates a signal that can be detected at specific recurrence times.

The Power Spectral Density (PSD) is used to analyze the noise levels in the system. PSD measures how the power of the signal is distributed across different frequencies and helps to identify noise sources that could affect the measurement.

For each pixel, the time-domain signal is converted to the frequency domain using the Fourier transform. This allows the analysis of how the signal's power is distributed over different frequencies.

The Fourier transform of the time-domain signal gives the spectrum of the signal, which shows both the useful methane signal and any noise present.

https://www.researchgate.net/publication/371495210_Free-form_dual-comb_spectroscopy_for_compressive_sensing_and_imaging

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Key Points Of Article: Use of Multi-focus laser sculpting for microstructured glass

 

Multi-focus laser sculpting is a technique used to shape materials using a laser beam. Instead of focusing on just one point, the laser is split into multiple focal points, so it can focus on several areas at the same time, making the process faster and more efficient.

Here, the Gaussian beam is manipulated using optical components Fresnel lenses and blaze gratings to create multiple laser spots.

For a Gaussian beam, the intensity is highest at the center (the beam's axis) and decreases as you move away from the center.

Gratings are made up of a microscopic, repeating structure of grooves. When light hits the grating, the structure causes the light to split into multiple beams that travel in different directions. 

A blaze grating is a type of diffraction grating that is designed to direct most of the light energy into a specific diffraction order, It enhances the brightness of wavelength or direction. 

Fresnel lenses consist of a series of concentric grooves.

.

The equation for calculating the laser spot position, considering the refractive index of the glass, is given by:

zj is the target coordinate.

Equation for Correction of Blaze Grating and Fresnel Lens Deviations

where m is x or y denoting sectional displacement, zj is the z-direction displacement, the λ is the wavelength fOB is the focal length of objective, and pj is the period of blaze grating.

 f0 is the focal length of Fresnel lens for light modulation.

Low surface roughness is important for great application performance, which can be achieved by improving laser spot intensity uniformity and especially decreasing the point-to-point distance.

The energy at each laser point is adjusted by modifying the transmission function of the light as follows:

T is the transmission function for the light modulation( Light modulation is the process of controlling the intensity of light, or changing its wave features, such as its frequency, polarization, phase, or intensity)

A is the amplitude constant, j is the point number, ϕ is the phase forming the phase diagram for light modulation, Ij is normalized energy adjustment coefficient for each point,

px,j and py,j are the blaze grating period .Multi focus laser is used for precisely shaping glass microstructures and in fiber packaging devices.

Reference

https://www.oejournal.org//article/doi/10.29026/oea.2025.240082

https://en.wikipedia.org/wiki/Blazed_grating

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Overview of Article about Magnetic helium-rich hot star found

 

Here the magnetic field was detected 200kG which is detected based on the zeeman effect. 

Zeeman effect: In zeeman effect, magnetic field distorts electron orbitals, which affects atomic energy levels and the transitions between them. This results in the splitting of atomic energy levels in a molecule, which in turn splits the spectral lines.

The splitting of a spectral line in the presence of a magnetic field is given by

Surface gravity is given by

Effective temperature is calculated based on 

The radial velocity is calculated using the Doppler effect equation:

Δλ = observed wavelength shift .

λ0 = rest wavelength of the spectral line

Galactic space velocities for the confirmed magnetic He-sdOs are calculated from their radial velocity.

Magnetic fields can cause dark or bright spots on a star’s surface, resulting in variations in brightness as the star rotates

Here the Hertzsprung-Russell diagram is used to compare the magnetic He-sdO stars with non-magnetic hot subdwarfs and other stars based on their temperature, luminosity, and mass.  

In the article, the mass of the magnetic He-sdO stars is estimated based on their location relative to the helium main sequence. The mass is interpolated from their position on the diagram.

When stars plot the same region of the H-R diagram, it indicates that they likely formed through a specific and same process.

Reference: https://arxiv.org/abs/2410.02737 

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