Featured Science Threads - Page 3

Estimate the quiescent voltages at the inputs and outputs of the two op-amps and the overall voltage gain (in decibels) of the circuit at the frequency of operation. State any assumptions made.

Summary: Diffusion Equation, Sequence Space, Banach Space, Linear Algebra, Quadratic Forms, Population Distribution, Sylow Subgroups, Lotka-Volterra, Ring Theory, Field Extension.

A survey of attempts to connect the octonions to the Standard Model - mainly explaining the math and having fun, not advocating any particular theory. I've slowly been writing a thread on octonions and particle physics, just to explain some facts in a self-contained way, with all the proofs. I don't know where this will lead. I'm certainly not presenting a theory of physics, much less advocating one. Mainly it's just fun.

Tesla’s Autopilot a ‘distant second’ to GM’s Super Cruise system in Consumer Reports testing. I think this is very interesting because of Consumer Report's reason for their evaluation. The GM autopilot aggressively monitors the driver to make sure he/she is alert and paying attention. The GM autopilot can be used only on preplanned roads and not on residential suites.

"NASA’s Stratospheric Observatory for Infrared Astronomy (SOFIA) has confirmed, for the first time, water on the sunlit surface of the Moon. This discovery indicates that water may be distributed across the lunar surface, and not limited to cold, shadowed places."

A discussion of whether or not it is a good idea to modify the U.S. K-12 educational system with the new "Equitable Grading System" now being implemented in, for example, San Diego, CA ?

We find asteroids faster than ever before. By 1921 astronomers knew 1000, then it took almost 70 years to extend that to 10,000 (1989). Just 16 years later we reached 100,000 (in 2005), and 15 more years later we reached 1 million. Early discoveries were people looking at analog photos, but now most discoveries are done by computers analyzing giant datasets...

Like many others, I have been seeking new and fun things to do during a pandemic. I decided on the new Microsoft Flight Simulator 2020, but the Condor 2 Soaring Simulator is my intermediate step. I am certified as a pilot, including gliders, but I have not flown for many years because of the expense. These simulators will allow me to join much of the fun and to greatly increase my skills, while semi-quarantined...

The Nobel Prize in Physics 2020 was divided, one half awarded to Roger Penrose "for the discovery that black hole formation is a robust prediction of the general theory of relativity", the other half jointly to Reinhard Genzel and Andrea Ghez "for the discovery of a supermassive compact object at the centre of our galaxy."

Summary:: Functional Analysis, Algebras, Measure Theory, Differential Geometry, Calculus, Optimization, Algorithm, Integration. Lie Algebras.

Good story about hunting for an interfering RF source, where you are trying to track down an interfering signal. We do them frequently for practice (as HAM radio operators), and have used the skills a few times for real. I haven't done it in the rain yet, though...

When humanity finally detected the collision between two neutron stars in 2017, we confirmed a long-held theory - in the energetic fires of these incredible explosions, elements heavier than iron are forged. But a new analysis has revealed a problem...

Interesting article. At first I thought the article was saying that for many parents, helping their kids with their math homework was the hardest because maybe they weren't all that great at math themselves.

Summary: group theory, number theory, commutative algebra, topology, calculus, linear algebra

A recent study measures a transition frequency in positronium higher than predicted. They produce very slow positronium excited by a laser, that suppresses uncertainties previous measurements had and improves the statistics. They also have ideas how to reduce the uncertainties that are still relevant. No indication of the measurement time that went into the study, but taking data for a longer time will certainly help even if they don't make larger upgrades.

What was your favorite proof or Eureka moment you remember? Mine was about normal subgroups.. You learn the definition and prove a few properties and go to the next subject. I remember that I once tried to teach the concept to someone and in the middle of my explanations I all of a sudden realized...

What is the mathematical definition of a "wave" and the quantities associated with a wave, such as group velocity, phase velocity etc.? Is there a standard mathematical definition for "wave"? What is the definition? Assuming that there is a definition, what are the mathematical definitions of the properties of waves? For example, how is the "group" of a wave defined? ( as in the "group" that has a "group velocity").

A computer language is not a clear example of a formal language, a formal system, or a formal logic. Can we modify the rules for a computer language to create clear examples?

A magic square is a NxN array of numbers from 1 to N² such that the sum of elements of each row, column and diagonal adds up to the same number, 65 in the case of 5x5's. An example would be...

Suppose I took a pile of measures of length: 18, 19, 20, 21, 22, 23, 24, 25 giving a mean of 172/8 = 21.5 on my calculator. If I have to give the mean to the lowest number of significant figures then that would give an answer of 20 - which feels wrong. I think I should work to 2 sig fig so 22 - which makes sense. So I guess my question is how how many sig fig does 20 have? Can it depend on the context?

The Higgs boson couples to mass, muons are relatively light, that makes a decay to a pair of muons (muon+antimuon) very rare. In addition there are many other processes that produce pairs of muons, making this decay mode challenging to find. For a long time it was expected that the experiments would need the high luminosity upgrade for a clear signal...

functional analysis, operator theory, topology, measure theory, calculus
Authors: Math_QED (MQ), Infrared (IR), Wrobel (WR), fresh_42 (FR).

Our forums are full of physics and mathematics. One cannot talk about the former without getting into calculations and mathematics sooner or later: Hilbert spaces, differential operators and linear algebra all over the place. Students of both faculties have normally a similar motivation, foundation and interests in both - more or less...

Face shield or respirators are getting to be as common as masks in public. What kind of bleach in basin can theoretically kill the covid-19 virus? What should be the concentration of bleach and now does it kill it?

There is a dizzying array of editors and IDE's out there. What is a good option to get started? I've never programmed (or done anything technical) on Windows. Is there any general advice about using the Windows environment for programming? I don't want to get into installing Linux at this stage. Do I need to be able to find my way around the Windows O/S, or does an IDE make that unnecessary?

As a layman I also have conceptual difficulties with the twin paradox. It would allow me to move on if some one could quickly answer the rather obvious question: would there be any time dilation if the earth was removed entirely from the thought experiment so that the twins are in a symmetrical relationship of inertia or relative motion. I cannot see how there could be but would then have to look to gravity to explain it.

This paper was published in Nature, and it presented a rather fascinating result if it is true. The researcher used far-UVC light (222 nm wavelength) to kill the viruses in airborne aerosol with a claim based on the current guidelines that far-UVC is not as harmful as UVA and UVB.

In a recent paper submitted by the LHCb collaboration at arXiv, they have reported a tetraquark state composed of charm quarks and antiquarks. The statistical significance of the data is more than 5σ...

Functional Analysis, Topology, Differential Geometry, Analysis, Physics
Authors: Math_QED (MQ), Infrared (IR), Wrobel (WR), fresh_42 (FR).

What is the meaning of the mass assigned to an individual quark?
A hydrogen atom is less massive than the sum of an unbound proton and an unbound electron. If I add energy to the atom the system becomes more massive, and when I add enough then I have an unbound electron and proton, each of which has the usual mass...

XENON1T sees an excess of events at low energies that doesn't have a good explanation at the moment.

A alternative to the Drake Equation for thinking about how likely intelligent life on other planets has been recently published. The Astrobiological Copernican Weak and Strong Limits for Intelligent Life proposes a different way to think about the possibility of intelligent life other places than earth.

In honor of Juneteenth , PF has donated $50 to Black Girls Code and $50 to The National Society of Black Engineers. See what you can do today and beyond to further the support for african-americans in STEM!

There are a few different textbooks out there on differential geometry geared towards physics applications and also theoretical physics books which use a geometric approach. Yet they use different approaches sometimes. What are the advantages of one over the other? Do theoretical physicists today tend to prefer one over the other and is it field specific?

Normed, Banach and Hilbert spaces, topology, geometry, linear algebra, integration, flux.
Authors: Math_QED (MQ), Infrared (IR), Wrobel (WR), fresh_42 (FR).

Elevators are a problem in this post COVID world. It is impossible to maintain social distancing while also meeting the passengers-per-hour needs of the building. Skyscrapers without efficient elevators are not practical.

Watch history unfold on Saturday, May 30, as NASA and SpaceX launch astronauts Robert Behnken and Douglas Hurley to the International Space Station. Here we go again! Set for 3:22PM EST. Lots of analysis in this live video already!

Project Loon is a network of stratospheric balloons designed to bring Internet connectivity to rural and remote communities worldwide. There is one being tracked, between Reunion and Mauritius in the Indian Ocean. Another one over Equador, 6 over Peru, 1 over Puerto Rico, 3 over Kenya and 1 near the Seychelles.

It doesn't happen every day decade that people are being launched to orbit in a new spacecraft. The last time it happened was 2003 (Shenzhou), and the last time before that was the Space Shuttle in 1981. The next time will be in 12 hours, if the weather stays good. And for the first time it is a private spacecraft. Going to orbit is no longer the exclusive domain of governments. You can call SpaceX if you want a ride (and have maybe 100 million dollars).

Test your skills in this month's math challenge thread! Topological spaces and metrics, integrals, abstract algebra (groups and rings), heat equation, geometry .

I'm normally among those who think that renewable advocates lack realism when they advocate 100% wind+solar grid. This article is the first I've seen that comes close to being plausible. I do doubt the article's numbers for storage and for wind, but the basic idea of massively overbuilding solar is in the right direction...

The cumulative experience with distance learning must have soared in the past 2 months.

• What has been learned?
• What works? What doesn't work?
• Are there new distance learning methods or strategies for the coming fall term?

Previous measurements already hinted at this, now we have a relatively strong single measurement. CP violation is linked to matter/antimatter asymmetries. They are small for quarks, but it looks like they are larger in the neutrino sector. The measurement favors the maximal CP violation that was still within the range set by other parameters. DUNE will measure this parameter more precisely in the future.

A (displacement) boat hull has a design goal of making as little water resistance as possible with the required volume for load carrying capability. To achieve this the hull is given the shape similar to a vertical symetrical airfoil. But as the leading edge of a boat (it's bow) seems to be made as sharp as possible, the leading edge of airfoils are round. Why aren't boats bow round as the airfoil?

Can solve solve one of these 3 physics challenge problems? This is an experiment if we could establish a little physics competition. Topics include, Classical Physics, Special Relativity Theory

I have been reading some papers on accelerator physics recently, especially those on the LHC and the upcoming FCC-hh. As a beginner, I am not supposed to know everything, but there are a few terms that I feel I have to know in order to penetrate further into this field...

How can I measure the terrestrial tide on my place? Since i don't have a MEMS gravimeter or a laser spectometer what will be the simplest method to measure the local earth tide variations?

Calculus (Polynomials, Series and Functions), Differential Equations, Operators, Normal Distribution, Number Theory (Authors: Infrared - IR; QuantumQuest - QQ; fresh_42 - FR)

This is more of a "housekeeping" question (i.e. it's not particularly interesting), though I haven't studied much in the way of infinitesimals so apologies in advance for my lack of rigour! As far as I'm aware, an infinitesimal can be thought of as a small change in some quantity. Changes can be either positive or negative, so subsequently it also seems reasonable for ##dx## to potentially represent a negative change...

So Alice and Bob are hanging out near a really large black hole. It's quiet. Nothing has entered the BH is a while. Alice tosses Bob in and then waits long enough for him to collide with the singularity. Of course, Bob is keeping time differently than Alice - so I rather doubt that the time period Alice calculates for Bob to reach the "center" has any real meaning to Bob. But Alice's real goal is to enter the BH herself and to never seen Bob again...