Showing posts with label physics. Show all posts
Showing posts with label physics. Show all posts

Overview: Study of magnetization temperature in ferromagnetic crystals


EuO and EuS Materials are used in study. As per Weiss mean field approximation (MFA), below certain critical temperature(Tc) ferromagnetic materials have spontaneous magnetization — i.e., a sizable macroscopic magnetic moment even in the absence of an external magnetic field. The effective field acting on a magnet in a ferromagnetic medium is H+gM(T), term gM(T) is called self-consistent molecular field.

Magnetization M is given by,

 

Langevin function describes the average alignment of magnetic moments with an applied magnetic field at a given temperature.

x=uB/kT

For very large T, x becomes small and Langevin function becomes

For H = 0 and T slightly below TC , The equation  becomes

Brillouin function is a quantum mechanical function that describes the magnetization of a system of spins in response to an applied magnetic field at a given temperature.

The study shows that M(T) exhibits anomalous scaling near Tc, with a scaling index β≈1/3, consistent with experimental data for EuO and EuS.

This result differs from the classical MFA prediction of β=1/2


The Weiss-Heisenberg MFA value of the Curie Temperature Tc wh ≈ 86.6K in EuO was observed.(about 20 % larger than its experimental value Tc exp≈ 69.8 K). spin-wave included  MFA equations match with experimental data across all temperature ranges. 


Source: https://arxiv.org/abs/2412.10124







Overview: Magnetic Field for Jupiter and Neptune Class exoplanets

Dynamo is the process by which a planetary magnetic field is generated through the movement of electrically conductive materials within the planet's interior. The dynamo region is identified based on the magnetic Reynolds number.


At the top of this region, the maximum magnetic field is 

 where 𝑞0 is the reference convective flux, ⟨𝜌⟩ is the average density,

𝐹 is an efficiency factor that accounts for all radially varying features of the dynamo region, and is calculated as 

where 𝐻T(𝑟) is the temperature length scale given by

 𝑃(𝑟) is the pressure, 𝑔(𝑟) the gravitational acceleration, and ∇adv the adiabatic, logarithmic gradient of temperature over pressure.

The convective flux 𝑞c is

𝑣conv the velocity of convective motions, and 𝛿 is the derivative of ln 𝜌 with respect to lnT.

Re mag is a non-dimensional quantity that measures the effects of convection against magnetic diffusion. 


As per study, for Jupiter and Neptune class planets, Magnetic field decay occurs because as planets age, they cool down and their luminosities and their convective flux become gradually weaker. Higher atmospheric envelope fractions cause more material available for convection, which yields stronger magnetic fields and extends the dynamo region.


 The field strength reduces for extremely irradiated planets because they have lower average density. The surface magnetic field decreases past the threshold value as orbital separation (distance between the exoplanet and its host star) further increases.


The magnetic fields could be observable in the radio wavelengths via auroral emission using ground based observations.


Jupiter-class planets have magnetic fields large enough to generate radiation whose peak frequency exceeds the Earth’s ionospheric cutoff. The same occurs for the Neptune-class planets  if they have  𝑀 > 15 𝑀⊕ and 𝑓env> 4%.


For hot jupiter class planets, atmospheric evaporation does not affect magnetic field generation. For hot Neptunes, atmospheric evaporation leads to greater mass loss and causes less material for convection, so they produce weaker magnetic fields. 



Source: https://arxiv.org/html/2411.00674v1


Summary of Article about Tests of the Hard X-ray Imager


The objective of HXI is to investigate how energy from the sun is released in solar flares.

The relative displacement and rotation were tested from assembly to on-orbit operation and must be maintained under 36 μm and 10 arcsecs.

When HXI reaches a thermal balanced state, further deformation measurements are done and collimator alignment is tested which is essential for accurate imaging.


Deformation of the equipment was mainly influenced by vibration during launch and temperature differences in orbit.


Differential Nonlinearity (DNL) Effect Correction is a calibration technique used to address inaccuracies in data from analog-to-digital converters. It ensures that the energy levels of X-rays from solar flares are accurately represented in the digital data.


The energy calibration is done to calibrate the corresponding energy (keV) for each of the ADC channels of each detector. Mixed calibration sources of Barium and Americium are housed inside every detector module.


Detector response matrix describes how an Hard XRay detector records count flux from incident photon flux. It converts count spectra and images back to photon spectra and images of the X-ray source.

Four-Quadrant Method (FQM) and Least Square Method (LSM)—have been used to determine the position of the Sun’s center in the image. 

source:https://link.springer.com/article/10.1007/s11207-024-02392-x


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


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




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 


Summary of Article: The topological aberrations of twisted light

 

  • Topology describes the study of properties of spaces that are invariant under any continuous deformation.

  • Topological aberration: It contains a high-order optical vortex which experiences not only geometrical shifts, but an additional splitting of its high-order vortex into a constellation of unit-charge vortices.

  • Multiple optical vortices indicate  the presence of more than one optical vortex in a light beam. Each optical vortex is a point or region where the intensity of light is zero, and the phase of the light waves spirals around this point, creating a "twisted" or helical wavefront. These beams are characterized by their helical wavefronts.

  • Goos-Hänchen (GH) Shift: The GH shift is a lateral displacement of a reflected light beam along the plane of incidence. Instead of reflecting exactly along the predicted path, the beam's central position shifts slightly parallel to the interface. GH shift arises from changes in the reflection coefficient of the interface, which vary with the incidence angle. These changes affect the beam's overall phase, leading to a shift.

  • ΔGH​ is the lateral shift (Goos-Hänchen shift), λ is the wavelength of the light. ϕr​ is the phase of the reflection coefficient, θi​ is the angle of incidence.

  • Imbert-Fedorov (IF) Shift : It is a transverse displacement of a reflected  beam that occurs perpendicular to the plane of incidence.

  • In the context of vortex constellations, the coordinates of the vortices can be represented as complex numbers. The authors use Elementary Symmetric Polynomials(ESP)  to summarize these coordinates and understand how they change under reflection.

  • vectors eI and eR contain the ESPs of the input and aberrated constellations, respectively.

  • Wirtinger Derivative: It helps how a complex function (or light beam) changes, especially when dealing with distortions or shifts in the beam's structure.

  • Above equations applying for this experiment,

  • R’ and R” are first and second Wirtinger derivatives of R(χ) at χ = χ* = 0.

  • Aberrations usually change the elementary symmetric polynomials (ESP), which describe the positions of the vortices in a group (constellation). From these changes, we can directly figure out the angular Wirtinger derivatives related to the aberration.




https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10305470/

https://www.nature.com/articles/s41467-024-52529-6


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