#Radial Magnets

[jdengineeringworksdelhi]

Powerful Performance: Testing a 5KW 500RPM 220VAC Single Phase PMG by J.D. Engineering Works

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[ellenhenryart]

(via "Carnival Red Pink Blue Symmetrical Flower" Magnet for Sale by ellenhenry)

[mpcomagnetics]

Radiation Ring Magnet

Radiation Ring Magnet Sintered NdFeB magnetic ring is a new product developed in recent years. It is mainly used in high-performance permanent magnet motors and sensors. In the application of permanent magnet motors, sintered NdFeB magnetic tiles are usually bonded into a ring, which has natural disadvantages: Since the processing of the tile-shaped magnet belongs to special-shaped processing,…

[chromaticflare]

Thank you for attending today’s Spell Seminar. This will be the first of many lessons explaining the spells and magic of WHA, ranging from the simplest of wall breakers to the wildest of windowways.

Today, we will be discussing one of my personal favorite spells, wall bend.

Spell Seminar Lesson One: The Wall Bend Spell

First seen on pg 27 of chap 14, wall bend is a spell capable of bending and pulling solid walls as if they were cloth. Remarkably, after the spell was first revealed in chapter 14, we wouldn’t see the glyph until chapter 65.

Experienced spell makers may recognize the earth sigil this glyph’s center, as well as the pull signs (the funky arrows) along the glyph’s sides. However, the signs at the top and bottom of thus glyph (highlighted in gold and purple) are unusual. They will be the focus of today’s lesson.

To understand the sign at the top of the spell (furthest away from Qifrey, highlighted in purple), you must first understand the one at the bottom (highlighted in gold)

Compound Signs

The sign drawn in gold is what we call a compound sign. Compound signs are signs composed of several other signs mixed together.

This one consists of three parts: a ribbon sign as the core, a bend sign on each end of the ribbon, and part of an inverted radial sign (strengthen).

Whereas a ribbon sign on it’s own just stretches things into long, soft ribbons, by combining it with bend (and inverted radial to boost its power), it is able to do one of two things; make a single portion of a wall bendable like a sheet of fabric, or allow the portion of wall near the spell to be bent and stretched.

Both of these interpretations are equally valid, but each has different implications as to the function of the bind (purple) sign. I only mentioned one of these interpretations in the twitter version of this lesson, but today, I’ll be going over both of them.

Interpretation One: Unify

Assuming the partial bending interpretation of the compound sign, bind has an important role in holding the wall together.

In this interpretation, bind functions to “bind” the entire wall together into a single cohesive object. This makes it so that, instead of stretching out just a single portion of wall, the spell instead stretches the wall in its entirety as a single cohesive unit.

In this version of the spell, the pull signs function to keep the wall connected to the spell, making use of the wall’s elasticity and stretchiness to do so. Imagine it like a magnet pulling the wall along rather than a direct connection between the spell and the wall.

Bind Interpretation Two: Glue

Assuming that the compound sign already effects the entire wall, then it makes much more sense for the bind sign to function like a glue between the wall and the spell.

In this interpretation, bind physically connects the part of the wall the spell is touching to the spell itself, allowing it to be dragged along with the spell to stretch the wall.

In this version, the pull signs serve simply as aids, helping to make it easier to drag the wall into the desired position and shape rather than just pulling it along as was the case in the other interpretation.

Conclusion

Regardless of which interpretation of bind one day proves to be the right one, this spell is unique for the lessons it can teach us about spell design and for the insights it can give us into magic as a whole. I’ve already designed 2 spells with bind, so it’s safe to say that it has a lot of uses both in universe and for us spell makers. I hope you enjoyed this lesson, and I’ll see you in the next one.

-Chromatic Flare

[covid-safer-hotties]

Reference archived on our website

Highlights • Long-COVID is heterogeneous in its symptoms, severity, and illness duration. • There was no association between long-COVID and cognitive performance. • Cognitive symptoms may represent functional cognitive disorders. • Long-COVID had lower mean diffusivity on diffusion imaging than normal recovery. • Diffusion imaging differences may suggest gliosis as a mechanism of long-COVID.

To be clear: There was no cognitive difference between people post infection. I can see some people misunderstanding what this says. It says there is some form of brain damage from covid across the board, even if you don't have long covid symptoms or diagnosis.

Abstract

Background

The pathophysiology of protracted symptoms after COVID-19 is unclear. This study aimed to determine if long-COVID is associated with differences in baseline characteristics, markers of white matter diffusivity in the brain, and lower scores on objective cognitive testing.

Methods

Individuals who experienced COVID-19 symptoms for more than 60 days post-infection (long-COVID) (n = 56) were compared to individuals who recovered from COVID-19 within 60 days of infection (normal recovery) (n = 35). Information regarding physical and mental health, and COVID-19 illness was collected. The National Institute of Health Toolbox Cognition Battery was administered. Participants underwent magnetic resonance imaging (MRI) with diffusion tensor imaging (DTI). Tract-based spatial statistics were used to perform a whole-brain voxel-wise analysis on standard DTI metrics (fractional anisotropy, axial diffusivity, mean diffusivity, radial diffusivity), controlling for age and sex. NIH Toolbox Age-Adjusted Fluid Cognition Scores were used to compare long-COVID and normal recovery groups, covarying for Age-Adjusted Crystallized Cognition Scores and years of education. False discovery rate correction was applied for multiple comparisons.

Results

There were no significant differences in age, sex, or history of neurovascular risk factors between the groups. The long-COVID group had significantly (p < 0.05) lower mean diffusivity than the normal recovery group across multiple white matter regions, including the internal capsule, anterior and superior corona radiata, corpus callosum, superior fronto-occiptal fasciculus, and posterior thalamic radiation. However, the effect sizes of these differences were small (all <|0.3|) and no significant differences were found for the other DTI metrics. Fluid cognition composite scores did not differ significantly between the long-COVID and normal recovery groups (p > 0.05).

Conclusions

Differences in diffusivity between long-COVID and normal recovery groups were found on only one DTI metric. This could represent subtle areas of pathology such as gliosis or edema, but the small effect sizes and non-specific nature of the diffusion indices make pathological inference difficult. Although long-COVID patients reported many neuropsychiatric symptoms, significant differences in objective cognitive performance were not found.

[radioactiveradley]

Hi! I have a question: can broken or fractured bones be seen in MRI scans and CT scans?

Also, when and how do doctors determine whether an MRI or CT scan is needed after an x-ray (in case they didn’t see a problem in the x-ray or unsure if there’s a pathology or not on the x-ray scan)?

Thank you!

Hello!

You can absolutely see broken/fractured bones on both MRI and CT. If we're specifically looking for bony damage, we're more likely to use CT - MRI is the best modality for looking at soft tissue injury, but is far more expensive than CT, so we're not going to use it for any old break!

We use CT to look at complex, 'comminuted' fractures, where the bone has split into multiple fragments, or in other cases where surgeons really need a clear three-dimensional view of the break.

If it's a clean transverse fracture (horizontal snap of a long bone) you probably won't need CT.

However, if you have this shit going on...

(unstable comminuted fracture of left femur due to gunshot wound, courtesy of radiopedia)

Yeah, it's probably CT time.

Similarly, some fractures can be hidden when using X-ray - particularly intra-articular fractures (breaks within a joint).

Intercondylar fractures of the humerus or fractures of the radial head are a classic example. In these cases, we look at the plain radiograph for other markers - particularly signs of haemarthrosis (bleeding into a joint).

Fat pad sign, on a non-displaced radial head fracture that is otherwise invisible on this elbow radiograph - courtesy of wiki

Can you see the slightly darker, raised areas that the red arrows are pointing to? Those are pads of fat around your elbow joint, which usually aren't nearly so obvious on a radiograph. They've been pushed outwards by soft-tissue swelling and bleeding around the break. If we see these two little 'dark flags', it means there's an injury hidden within the elbow joint itself, which we can't see. So, away to CT the patient goes!

Then we have the fabulous lipohaemarthrosis (the word every first-year student dreads having to say out loud in front of qualified staff). Check this baby out!

Lipohaemarthrosis of the left knee due to a hidden tibial plateau fracture, courtesy of radiopaedia

Look on either side of the patella. See those dark blobs? They're fat. As shown on the elbow image, fat is radiolucent (appears dark on X-ray) in comparison to other soft tissue. Fat also floats on top of blood.

This means, if we lay you down with your knee pointing up, and you happen to have free-floating fat and blood around your joint... the fat bloops up to the top, and you get a clear line between the fat and the blood. This is a very clear sign of intra-articular damage - and, again, you'll be heading to CT to get a three-dimensional look at that hidden fracture.

As for when we would use MRI... If we suspect that you have a serious soft-tissue injury that requires surgery (tears to the anterior cruciate ligament in the knee being the classic example!) that's when you'll get a trip to my favourite magnetic man, Big Boomy Chungus. I can go more into that if you want, but it would probably need its own separate post!

Hope that helps! x

[astraiox]

The radial magnetic field around NGC 4631 (Golla and Hummel 1994)

[dat-physics-gal]

Explain to me dipole selection rules please I beg

Okay, so for a transition between energy eigenstates, there needs to be an exchange of a photon with the correct energy. I'm assuming you know that.

Since photons are waves of the electromagnetic field, they impose an electric moment on charged particles, which in a vast majority of cases can be modeled as a simple dipole moment.

Now here's where the quantum mechanics starts: The dipole moment is expressed as a linear operator, which when applied to the wave function of a particular state gives you back the eigenvalue for the dipole moment of that state. However, since we want to describe the transition between states, and the operator only applies to the ket of the wave function, the bra and the ket which it is nestled in between are of the different states, aka the starting and the final electron state.

The operator applies to the starting state ket, which can then be completed on the left with the final state bra, and then integrated over to obtain the transition dipole moment integral.

This integral will tell you the expectation value for the transition. For the selection rules, you don't actually have to precisely calculate this integral, you just have to find out whether or not it is zero, because if it is, that means you have an impossible transition on your hands.

Depending on your representation, the dipole operator as well as the wave functions will look different, as will the space you integrate over.

So first, find which representation (spatial, spherical, momentum space, etc.) you are working with, how the dipole operator looks for that representation, and then pick the two states you want to see if a dipole transition exists between them.

The tricky part is usually to get the wave function representation right, and then to leverage the symmetries of that function to determine if the value of the integral is zero or not. The representation that i find most common for tasks like this is this one, which separates the wave function into a radial and two angular parts. It is also already conveniently expressed in terms of 3 quantum numbers, that being the main quantum number n, the orbital angular momentum number l, and the magnetic quantum number m.

I am afraid you'll have to learn the quirks and symmetries of the generalized Laguerre polynomials as well as the spherical harmonics, in order to make statements about the transition dipole moment integral. However, once you get a feel for their symmetries and remember in what special cases integrals vanish (like integrating an odd function over a symmetric interval, etc.) you will be able to derive the selection rules.

I know this wasn't a simple and easy answer, but, well, this is quantum mechanics, to be fair. Hope that helped anyway.

[oliviax727]

Physics Friday: Electricity and Magnetism - why are they together?

Introduction - WTF is this?

So this is the first post which is pretty different to what I've done before on Tumblr, Reddit, etc. But given the fact that I have a bunch of knowledge on the subjects of physics, astronomy, mathematics, and computer science, I might as well ramble about it somewhere ... and what's a better place then a blog format on Tumblr!

So my idea is basically to do a weekly thing where I wax lyrically about some random topic within the realm of STEM, and let the internet people see it ... or not. I'm more interested in just getting the neat and cool ideas out there. So if you're seeing this and you're interested - neat! If you're not ... well I'm still going to do what I normally do and shitpost.

The topics will also vary in education level from primary all the way to university level. I'll try and highlight that in each post!

Some pre-info

Education level: High School (Y11/12) Topic: Electromagnetism (Physics)

Ok it's Physics time

At some point in your long life, maybe in class, maybe perusing the internet, you might've come across the term 'Electromagnetism' and gotten confused. Not because it's a complex word and it's 3 am but more that it's strange to see such an emphasis on a combination of Electricity (circuits, lightning, etc.) and Magnetism (Bar Magnets, etc.) and well, why is that? Why don't we focus on something like gravity and electricity or some other physical phenomenon? This is a question I often came across in high school. I saw all of the equations that related electricity and magnetism with eachother: Ampere's law, Faraday's law, the motor effect, Electromagnetic waves. But what intrinsically ties these two phenomenon together? After all, we know magnetism comes from electrons, and electricity comes. But still - this doesn't seem to complete the gap.

This was a question that a lot of people were concerned with, until Maxwell, Lorentz, and Einstein came along and changed our understanding of electricity, magnetism, and motion.

To figure this out, we won't actually need special relativity, because we can just imagine scenarios in a low-speed limit. But we still require relativity of a more classical variety.

So how does it work?

Consider a wire with a current running through the wire. Electrons are moving through the wire, causing the flow of current.

Now, because of Ampere's law, we know the wire produces a circular magnetic field around it.

Given what we currently know, the act of having a current - an electricity thing, producing a magnetic field, is really odd. But what if we were to introduce some velocity into the equation?

Say we now place an electric charge next to the wire, and it's stationary. Ignoring gravity for a moment, nothing happens. Why? Well because of the lorentz force F = qE + qvB there's nothing to move it. But now let's move this charged object at some speed along the wire, and let's say it's moving at exactly the same speed as the electrons in the wire. Now we have force! The charge begins to move perpendicular to the field and the charge starts flying towards the wire.

But this is a kinda boring explanation from the perspective of someone standing still, looking at the wire and seeing this happen. What if we were to look at things from the perspective of the charged object?

Well, given the rules of relativity, in the charge's perspective, the electrons are actually stationary, so from here - there IS no magnetic field!

So what happens now? Well because we have a straight line of electrons, and these electrons are still, we now have radially pointing electric field emanating from the wire. Because of this electric field - the charge will begin to move towards the wire, coincidentally at the same rate as what we see the observer.

Now look at what we have here. From the perspective of the stationary wire, a magnetic field is produced. From the perspective of the charge, we have an electric field.

The fact of the matter is that the electric and magnetic fields are the same thing - just from different perspectives. A pure magnetic field is just an electric field viewed from a different velocity, and what you may see as an electric field is just a magnetic field but because we're moving relative to it, it now affects us.

How Special Relativity Comes into this

We can represent this effect using another equation:

E' = γ (E+vB)

Where γ is the lorentz factor. This is where the lorentz invariance - special relativity comes into this. This is a direct solution of Maxwell's Equations.

Let's simplify this by removing the γ in a low-velocity limit, and also multiply both sides by an electric charge term q:

qE' = qE + qvB

E' is the electric field in a frame moving at a particular velocity, whereas E and B are the electric and magnetic fields in a different frame of reference.

Notice how both expressions represent the force applied to a charge. This is a representation of the relativistic interpretation of electric and magnetic fields.

Image Credit: Wikipedia

This image from Wikipedia, it shows the effect I've been talking about but visually. In the top section we have a man standing stationary to an electric charge, which emanates an electric field. From the perspective of the moving woman, the charge produces both a magnetic and electric field.

On the bottom we see the opposite. A stationary man sees a moving charge as having both an electric and magnetic field. But when we move at the same velocity as the charge, the magnetic field disappears and it appears entirely as an electric field.

Conclusion

In conclusion, why electricity and magnetism can be unified is because they are quite literally the same field, but from a different perspective.

Technically speaking, magnetic fields don't exist, they're just electric fields moving at a particular speed. We could also say the exact same about electric fields.

This revelation is what allowed Einstein to simplify Maxwell's equation into just one - using the power of tensors. Because really, the two forces are one in the same!

I very much hope you enjoyed reading this post. I'm going to be doing this every Friday. It's a bit rusty - and you probably had a hard time reading it. Feedback (both positive and negative) is appreciated!

[spacetimewithstuartgary]

NOAA releases imagery from world's first operational space-based coronagraph

NOAA today shared the first images from the Compact Coronagraph (CCOR-1), a powerful solar telescope onboard the new GOES-19 satellite. CCOR-1, the world's first operational, space-based coronagraph, began observing the sun's corona, the faint outermost layer of the solar atmosphere, on September 19, 2024.

CCOR-1 monitors the corona to forecast coronal mass ejections (CMEs), which are large expulsions of plasma and magnetic fields from the sun that can produce space weather impacts on Earth.

When directed toward Earth, CMEs can cause geomagnetic storms and other types of space weather that can impact satellites, navigation systems like GPS/GNSS, astronaut safety, aviation communications and electric power grids. On Earth, the familiar aurora displays are the visible manifestations of these storms interacting with Earth's upper atmosphere.

CCOR-1 delivers uninterrupted coverage of the corona with a new image every 15 minutes. CCOR-1 uses an occulting disk (the dark blue circle at the center of the video) to eclipse the sun (depicted as the smaller white circle) so we can view the extremely faint corona.

The sun also dazzles with its small and large streamers, bright radial structures along which the solar plasma travels steadily outward. The CME explosions bend and sometimes disrupt the streaming plasma, buzzing past it at speeds of hundreds to thousands of miles per second.

CCOR-1 is the first in a series of NOAA coronagraphs. Similar instruments will be placed on the sun-Earth line and around the sun, as part of NOAA's Space Weather Follow-On and Space Weather Next programs, respectively.

GOES-19 is currently undergoing post-launch testing and checkout of its instruments and systems. After GOES-19 is assigned the operational role as NOAA's GOES East satellite in spring 2025, NOAA's Space Weather Prediction Center will begin using CCOR-1 observations to inform and improve its forecasts and warnings of impending space weather.

[jdengineeringworksdelhi]

Testing Video of 11KW 1500RPM 5000VAC Three Phase Permanent Magnet Generator (PMG) In this video, we are testing this Three Phase Permanent Magnet Generator (PMG) step by step according to RPM from 100RPM to 1500RPM.

For any queries, please Call or WhatsApp at +919289311243, +919582345931, +918826634990, or +919999467601. Email:- sales@pmsgen.com

[styllwaters]

What are most sea crawler meals like?

Every culture has their own distinct dishes, but they mostly look something like this! Radial symmetry is an extremely common motif for sea crawlers, and this extends to their food. Shown here is a popular Daihrut dish: Qhuavan 'nudibranchs' and roe. The spikes are magnetic at the tips, attached to magnetic points on a table. The translucent lid keeps unattended food from floating away.

They're also very decorative! Crawlers are all about extravagancy.

More about food and crawler diets in this older post.

[theterribletenno]

Wasp, the Anti-Grineer Warframe

Wasp is going to be the most ordinary of the three Anti-Warframes. I'm actually kind of surprised how much love the Grineer receive as a faction but that's beside the point. Wasp is acquired by defeating Captain Visak Shuuk at Kaentake.

Health: 550 (750 at rank 30) Shields: 100 (150 at rank 30) Armor: 575 (675 at rank 30) Energy: 150 (200 at rank 30) Sprint Speed: 0.95

Passive: Activating any ability increases Wasp's armor by 30% for as long as the ability is active plus an extra 6 seconds after the ability terminates. Successive casts refresh this effect.

Ability 1: Nailgun, 25 energy. Wasp fires a massive iron spike from the barrels on his gauntlets at the enemy closest to his crosshairs within a 90 degree 45 meter cone centered on his aiming reticle, dealing 1,000 times 1+X (where X is equal to the enemy's level divided by 10) puncture damage with 100% status chance to the target enemy. Using Nailgun again within a 1 second window of its last use increases its damage by 250 and status chance by 25% stacking up to six times. If the target enemy is within 15 meters the spike will be aimed perfectly at the victim's head (or similarly vulnerable body part) applying relevant damage multipliers.

Ability 2: Solvent Spray, toggled ability, drains 3 energy per second. While active the mechanical pumps and tubes on Wasp's back and arms activate, spraying flammable caustic fluids from his gauntlets in a 10 meter 90 degree cone. The Solvent Spray deals 400 corrosive damage with 100% status chance per second. Holding the ability key for Solvent Spray ignites the fluid, changing its damage to heat. Damage change can be triggered while Solvent Spray is active or inactive. Wasp moves at full speed and can use all movement techniques while Solvent Spray is active, but all weapon attacks, gear items, and abilities other than Nailgun cannot be used.

Ability 3: Flash Weld, 75 energy. A fluctuating pulse of magnetized plasma blooms out from Cain and then retracts, stripping the defenses from all enemies it touches and adding the stolen armor to Wasp as overguard. Flash Weld emits a radial pulse with an initial radius of 5 meters, which follows him as an aura and rapidly expands outward by 15 meters per second over a duration of 2 seconds. Enemies in direct line of sight of Wasp and within range of Flash Weld's aura have 25% of their current shields or total armor stripped. When Flash Weld expires or when the ability key is pressed again while the ability is active the pulse instantly retracts to Wasp granting overguard based on the amount of shields and/or armor stolen from all affected enemies. Flash Weld cannot grant overguard exceeding a value of 10,000.

Ability 4: Attrition, 100 energy. If there's one thing the Grineer know it's their brutally effective military weapons. When Wasp activates Attrition he becomes a force of pure destruction. For the next 8 seconds Wasp gains infinite ammo, 100% heavy attack combo efficiency, and +30% fire rate and attack speed. When Attrition expires Wasp releases an explosion that deals 100 blast damage in a 12 meter radius with 100% status chance. For every enemy killed by Wasp's weapons while Attrition was active this explosion gains an additional 100 damage, 0.5 meters, and 10% status chance.

Subsumed ability: Nailgun.

Signature Weapon Akgoblins: The Akgoblins are the Tenno answer to some of the Grineer's iconic weaponry. Ironically, the Tenno-made Akgoblins are closer to the original Orokin weapons used by the Grineer of the imperial era than the mass-produced bastardizations seen in their hands today. For players the Akgoblins blueprint is acquired for 25,000 credits from the orbiter market and is crafted using Twin Gremlins and Twin Grakatas plus 5 Morphics to meld them together. Akgoblins are nearly full-sized rifles, with their weight and recoil only a warframe could use them akimbo. The Akgoblins have a full-auto trigger and fire spike-like projectiles with a travel time and arc. Akgoblins capture the strengths of both of the weapons they are based on, having the superior reload speed & damage inherited from the Gremlins and the magazine size, max ammo capacity, accuracy, fire rate, and critical affinity of the Grakatas. Directly improving on both of its predecessors the Akgoblins have an innate 2 meters of punch-through. As Wasp's signature weapon the Akgoblins deal 30% bonus damage when they score a multi-hit with punch-through.

Closing Notes: I was a little nervous about Wasp at first but I've really come around on him. I certainly don't think he's breaking any molds but his combination of damage and tankiness surely leads to easy use.

[enetarch-quantum-physics]

Topics to study for Quantum Physics

Calculus

Taylor Series

Sequences of Functions

Transcendental Equations

Differential Equations

Linear Algebra

Separation of Variables

Scalars

Vectors

Matrixes

Operators

Basis

Vector Operators

Inner Products

Identity Matrix

Unitary Matrix

Unitary Operators

Evolution Operator

Transformation

Rotational Matrix

Eigen Values

Coefficients

Linear Combinations

Matrix Elements

Delta Sequences

Vectors

Basics

Derivatives

Cartesian

Polar Coordinates

Cylindrical

Spherical

LaPlacian

Generalized Coordinate Systems

Waves

Components of Equations

Versions of the equation

Amplitudes

Time Dependent

Time Independent

Position Dependent

Complex Waves

Standing Waves

Nodes

AntiNodes

Traveling Waves

Plane Waves

Incident

Transmission

Reflection

Boundary Conditions

Probability

Probability

Probability Densities

Statistical Interpretation

Discrete Variables

Continuous Variables

Normalization

Probability Distribution

Conservation of Probability

Continuum Limit

Classical Mechanics

Position

Momentum

Center of Mass

Reduce Mass

Action Principle

Elastic and Inelastic Collisions

Physical State

Waves vs Particles

Probability Waves

Quantum Physics

Schroedinger Equation

Uncertainty Principle

Complex Conjugates

Continuity Equation

Quantization Rules

Heisenburg's Uncertianty Principle

Schroedinger Equation

TISE

Seperation from Time

Stationary States

Infinite Square Well

Harmonic Oscillator

Free Particle

Kronecker Delta Functions

Delta Function Potentials

Bound States

Finite Square Well

Scattering States

Incident Particles

Reflected Particles

Transmitted Particles

Motion

Quantum States

Group Velocity

Phase Velocity

Probabilities from Inner Products

Born Interpretation

Hilbert Space

Observables

Operators

Hermitian Operators

Determinate States

Degenerate States

Non-Degenerate States

n-Fold Degenerate States

Symetric States

State Function

State of the System

Eigen States

Eigen States of Position

Eigen States of Momentum

Eigen States of Zero Uncertainty

Eigen Energies

Eigen Energy Values

Eigen Energy States

Eigen Functions

Required properties

Eigen Energy States

Quantification

Negative Energy

Eigen Value Equations

Energy Gaps

Band Gaps

Atomic Spectra

Discrete Spectra

Continuous Spectra

Generalized Statistical Interpretation

Atomic Energy States

Sommerfels Model

The correspondence Principle

Wave Packet

Minimum Uncertainty

Energy Time Uncertainty

Bases of Hilbert Space

Fermi Dirac Notation

Changing Bases

Coordinate Systems

Cartesian

Cylindrical

Spherical - radii, azmithal, angle

Angular Equation

Radial Equation

Hydrogen Atom

Radial Wave Equation

Spectrum of Hydrogen

Angular Momentum

Total Angular Momentum

Orbital Angular Momentum

Angular Momentum Cones

Spin

Spin 1/2

Spin Orbital Interaction Energy

Electron in a Magnetic Field

ElectroMagnetic Interactions

Minimal Coupling

Orbital magnetic dipole moments

Two particle systems

Bosons

Fermions

Exchange Forces

Symmetry

Atoms

Helium

Periodic Table

Solids

Free Electron Gas

Band Structure

Transformations

Transformation in Space

Translation Operator

Translational Symmetry

Conservation Laws

Conservation of Probability

Parity

Parity In 1D

Parity In 2D

Parity In 3D

Even Parity

Odd Parity

Parity selection rules

Rotational Symmetry

Rotations about the z-axis

Rotations in 3D

Degeneracy

Selection rules for Scalars

Translations in time

Time Dependent Equations

Time Translation Invariance

Reflection Symmetry

Periodicity

Stern Gerlach experiment

Dynamic Variables

Kets, Bras and Operators

Multiplication

Measurements

Simultaneous measurements

Compatible Observable

Incompatible Observable

Transformation Matrix

Unitary Equivalent Observable

Position and Momentum Measurements

Wave Functions in Position and Momentum Space

Position space wave functions

momentum operator in position basis

Momentum Space wave functions

Wave Packets

Localized Wave Packets

Gaussian Wave Packets

Motion of Wave Packets

Potentials

Zero Potential

Potential Wells

Potentials in 1D

Potentials in 2D

Potentials in 3D

Linear Potential

Rectangular Potentials

Step Potentials

Central Potential

Bound States

UnBound States

Scattering States

Tunneling

Double Well

Square Barrier

Infinite Square Well Potential

Simple Harmonic Oscillator Potential

Binding Potentials

Non Binding Potentials

Forbidden domains

Forbidden regions

Quantum corral

Classically Allowed Regions

Classically Forbidden Regions

Regions

Landau Levels

Quantum Hall Effect

Molecular Binding

Quantum Numbers

Magnetic

Withal

Principle

Transformations

Gauge Transformations

Commutators

Commuting Operators

Non-Commuting Operators

Commutator Relations of Angular Momentum

Pauli Exclusion Principle

Orbitals

Multiplets

Excited States

Ground State

Spherical Bessel equations

Spherical Bessel Functions

Orthonormal

Orthogonal

Orthogonality

Polarized and UnPolarized Beams

Ladder Operators

Raising and Lowering Operators

Spherical harmonics

Isotropic Harmonic Oscillator

Coulomb Potential

Identical particles

Distinguishable particles

Expectation Values

Ehrenfests Theorem

Simple Harmonic Oscillator

Euler Lagrange Equations

Principle of Least Time

Principle of Least Action

Hamilton's Equation

Hamiltonian Equation

Classical Mechanics

Transition States

Selection Rules

Coherent State

Hydrogen Atom

Electron orbital velocity

principal quantum number

Spectroscopic Notation

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Common Equations

Energy (E) .. KE + V

Kinetic Energy (KE) .. KE = 1/2 m v^2

Potential Energy (V)

Momentum (p) is mass times velocity

Force equals mass times acceleration (f = m a)

Newtons' Law of Motion

Wave Length (λ) .. λ = h / p

Wave number (k) ..

k = 2 PI / λ

= p / h-bar

Frequency (f) .. f = 1 / period

Period (T) .. T = 1 / frequency

Density (λ) .. mass / volume

Reduced Mass (m) .. m = (m1 m2) / (m1 + m2)

Angular momentum (L)

Waves (w) ..

w = A sin (kx - wt + o)

w = A exp (i (kx - wt) ) + B exp (-i (kx - wt) )

Angular Frequency (w) ..

w = 2 PI f

= E / h-bar

Schroedinger's Equation

-p^2 [d/dx]^2 w (x, t) + V (x) w (x, t) = i h-bar [d/dt] w(x, t)

-p^2 [d/dx]^2 w (x) T (t) + V (x) w (x) T (t) = i h-bar [d/dt] w(x) T (t)

Time Dependent Schroedinger Equation

[ -p^2 [d/dx]^2 w (x) + V (x) w (x) ] / w (x) = i h-bar [d/dt] T (t) / T (t)

E w (x) = -p^2 [d/dx]^2 w (x) + V (x) w (x)

E i h-bar T (t) = [d/dt] T (t)

TISE - Time Independent

H w = E w

H w = -p^2 [d/dx]^2 w (x) + V (x) w (x)

H = -p^2 [d/dx]^2 + V (x)

-p^2 [d/dx]^2 w (x) + V (x) w (x) = E w (x)

Conversions

Energy / wave length ..

E = h f

E [n] = n h f

= (h-bar k[n])^2 / 2m

= (h-bar n PI)^2 / 2m

= sqr (p^2 c^2 + m^2 c^4)

Kinetic Energy (KE)

KE = 1/2 m v^2

= p^2 / 2m

Momentum (p)

p = h / λ

= sqr (2 m K)

= E / c

= h f / c

Angular momentum ..

p = n h / r, n = [1 .. oo] integers

Wave Length ..

λ = h / p

= h r / n (h / 2 PI)

= 2 PI r / n

= h / sqr (2 m K)

Constants

Planks constant (h)

Rydberg's constant (R)

Avogadro's number (Na)

Planks reduced constant (h-bar) .. h-bar = h / 2 PI

Speed of light (c)

electron mass (me)

proton mass (mp)

Boltzmann's constant (K)

Coulomb's constant

Bohr radius

Electron Volts to Jules

Meter Scale

Gravitational Constant is 6.7e-11 m^3 / kg s^2

History of Experiments

Light

Interference

Diffraction

Diffraction Gratings

Black body radiation

Planks formula

Compton Effect

Photo Electric Effect

Heisenberg's Microscope

Rutherford Planetary Model

Bohr Atom

de Broglie Waves

Double slit experiment

Light

Electrons

Casmir Effect

Pair Production

Superposition

Schroedinger's Cat

EPR Paradox

Examples

Tossing a ball into the air

Stability of the Atom

2 Beads on a wire

Plane Pendulum

Wave Like Behavior of Electrons

Constrained movement between two concentric impermeable spheres

Rigid Rod

Rigid Rotator

Spring Oscillator

Balls rolling down Hill

Balls Tossed in Air

Multiple Pullys and Weights

Particle in a Box

Particle in a Circle

Experiments

Particle in a Tube

Particle in a 2D Box

Particle in a 3D Box

Simple Harmonic Oscillator

Scattering Experiments

Diffraction Experiments

Stern Gerlach Experiment

Rayleigh Scattering

Ramsauer Effect

Davisson–Germer experiment

Theorems

Cauchy Schwarz inequality

Fourier Transformation

Inverse Fourier Transformation

Integration by Parts

Terminology

Levi Civita symbol

Laplace Runge Lenz vector

[covid-safer-hotties]

Reference Archived on our website

Introduction: There is a growing interest in the effect of Long-COVID (LC) on cognition, and neuroimaging allows us to gain insight into the structural and functional changes underlying cognitive impairment in LC. We used multimodal neuroimaging data in combination with neuropsychological evaluations to study cognitive complaints in a cohort of LC patients with mild to moderate severity symptoms.

Methods: We conducted a 3T brain magnetic resonance imaging (MRI) study with diffusion tensor imaging (DTI) and functional MRI (fMRI) sequences on 53 LC patients 1.8 years after acute COVID-19 onset. We administered neuropsychological tests to evaluate cognitive domains and examined correlations with Tract-Based Spatial Statistics (TBSS) and resting state.

Results: We included 53 participants with LC (mean age, 48.23 years; 88.7% females). According to the Frascati criteria, more than half of the participants had deficits in the executive (59%) and attentional (55%) domains, while 40% had impairments in the memory domain. Only one participant (1.89%) showed problems in the visuospatial and visuoconstructive domain. We observed that increased radial diffusivity in different white matter tracts was negatively correlated with the memory domain. Our results showed that higher resting state activity in the fronto-parietal network was associated with lower memory performance. Moreover, we detected increased functional connectivity among the bilateral hippocampus, the right hippocampus and the left amygdala, and the right hippocampus and the left middle temporal gyrus. These connectivity patterns were inversely related to memory and did not survive false discovery rate (FDR) correction.

Discussion: People with LC exhibit cognitive impairments linked to long-lasting changes in brain structure and function, which justify the cognitive alterations detected.

[unknownsoldiers]

Outlier Ability;

General Info;

★ - Common knowledge Outlier abilities come in three types: Physical, Mental, or External*.

- Mental Abilities are those that come from the mind like Soundwave’s Hearing, Skid’s super learning, or Mindwipe’s telepathy. - Physical abilities are ones that affect the mech themselves, such as Tailgate’s strength or Mirage’s invisibility. - External abilities are usually projected from the outlier in some way, such as Skywarp’s teleportation, Trailbreaker’s force fields, Windcharger’s magnetic arms, Damus’ glitch touch, Hupcap’s Electromagnetic manipulation, Thundercracker’s sonic booms, etc etc.

(*External also has it's own subcategories of Physical and Mental, but for the sake of simplicity, they are filed as one.)

—— ◆ - Acquired knowledge

Outlier: Lieutenant

Ability: Seismic Sense

Category: Physical

—— ✖ - No knowledge

How it works:

Seismic Sense is an acute sensation of anything touching the ground. So long as Lieutenant is touching the ground, he can sense any movement up to an undisclosed radial distance from himself. He can even feel things on the walls when in rooms or hallways. That is if they're at a certain height. This means usual forms of stealth from sight are ineffective. He is nearly impossible to sneak up on as long as his opponent is touching the ground. Lieutenant has also worked to allow his frame to move instinctively if he senses anything too close to him. This was especially helpful during the war as his hand-to-hand combat excelled, although he preferred to avoid it if possible. Due to this ability, particularly when it was fully honed he would be selected to be part of Prowl's 'Diplomatic Corps.' early in the war. [See Bio for more info]

Info:

The primary source of this ability comes from his pedes, and more specifically, the sensory pads on the bottoms of his pedes. They aren't metal but rather a silicone rubber that allows him to traverse various terrains without damaging or scuffing the sensors. While they can take a beating, Lieutenant would prefer to avoid injury as it is still a part of him and he can feel everything quite intimately.

Drawbacks:

The seismic sense is a glass cannon. It’s incredibly intuitive, but if not kept secret it can be easily used against Lieutenant. One of the biggest issues is the heightened sense can cause overwhelming pain or sensory overload (not the fun kind). This can come from various sources such as being hit/injured, reverberating foundations, or anything physical. This is due to the ability affecting his entire nervous system, his pain tolerance is significantly lower than even the civilian class. Fortunately, this is not the biggest Achilles heel as it once was. With significant training over many years, Lieutenant can still fight without being paralyzed by the pain. However, he still tries to avoid it, opting for infiltration, tricks, and quick kills to get the job done without interacting with the enemy if possible, to lower the risk of overwhelming agony.

——

At a glance - Pros & Cons:

Pros:

Able to sense surroundings/persons acutely

Reflexes are instinctive

Blinded allows heightened senses to 'see' things more in-depth/further

The lower his other senses are, the higher his seismic sense becomes

Cons:

Sensitivity is very high

Pain hurts significantly more than it should

Universe Note: While Outliers are already rare, fliers that are outliers are even more abnormal in this circle. No one quite knows why this is, however, the speculation is that it’s likely due to the spark naturally having to compensate for the ability to fly. It’s not as near impossible as those with .01% sparks or triple-changers, but it is the running theory.