Constant Definition and 1000 Threads

Every two semi-Riemannian manifolds of the same dimension, index and constant curvature are locally isometric. If they are also diffeomorphic, are they also isometric?

Setup: Let ##\hat{\mathbf{e}}_1,\hat{\mathbf{e}}_2,\hat{\mathbf{e}}_3## be the basis of the fixed frame and ##\hat{\mathbf{e}}'_1,\hat{\mathbf{e}}'_2,\hat{\mathbf{e}}'_3## be the basis of the body frame. Furthermore, let ##\phi## be the angle of rotation about the ##\hat{\mathbf{e}}_3## axis...

In a book that I am reading it stated that, the constant curvature implies curvature is homogeneous and isotropic, hence only three ##κ## values are possible for our universe $$κ = -1, 0, +1$$ as we all know these values represent negative, flat and positive curvature respectively. Now if...

Interpolating a straight line with a trigonometric function. In Matlab I ended up with this expression. fplot(@(x)(.0000001*cos(x*2*pi)+10), [0 1]) Would anyone like to discuss what this could be used in?

I encountered a weird conflict between my thought process and that of author's solution in book: The common viewpoint of both of us were invoking conservation of energy of this SHM system But the author proceeds to solve it using conservation of momentum, taking the new mass added to system as...

I'd be interested to hear comments from the forum on this paper. Is it a significant step forward? I haven't been able to make up my mind.

I wanted to re-do Egan's results for relativistic hoops with a different model, one with a relativistic hoop with a constant circumference. The idea is that by having the circumference not change as we spin up the hoop, we shouldn't be storing energy by "stretching" the material of the hoop...

Hi, I have been exploring Newtons Law of Cooling. What relationship should i expect to see from the cooling constant "k". I have plotted the "k" values for each equation that i have developed (based off of different volumes of water in the same sized beaker). So, when the "k" vs volume graph is...

Suppose we are driving on moon (I mean there is not air resistance) at a constant velocity. Suddenly the car goes on an icy land (the friction is zero). What happens? In other words, if we drive at constant velocity and there isn't air resistance, Is there any friction force between tires and...

If so, do we have estimates of what that is. Also, if we have estimates of that, what will the final entropy of the universe be, in J/K?

2.3.16 A car is traveling at $45 \, km/h$ at time $t=0$ It accelerates at a constant rate of $10 \, km/h\, s$ (a) How fast is the care going at $t=1\, s$? $$v_t=v_0+at=45+10(1)=55\,\dfrac{km}{h}$$ at $t=2\,s$ $$v_t=v_0+at=45+10(2)=45+20=60\,\dfrac{km}{h}$$ (b) What is its speed at a...

Doesn't volume of ideal gas include volume of the molecules? What I was taught in school is that, when two molecules collide, no other molecule can come around it (inside the green part in the figure) and that volume is excluded volume? Is it correct? If yes, why?

I was reviewing physics stuff and I've managed to confuse myself. I was reading about work (principles of ohysics, serway&jewtt): -work is an energy transfer -if work is done on a system and W is positive, energy is transferred to the system; if W us negative, energy is transferred from the...

We say the unit of gravitational costant is m3/kg.s2, but what does it mean? I mean, I think we define units when we need to measure a quantity and thereby compare it with other same kind of quantities. So what does it mean to define a unit for a constant, when it doesn't change?

Hi, I could you explain me what is the density of a constant (particurarly the spring constant, or should I say "stiffness" constant)? I guess it's a probabilty function but would like more details. I would like an answer that at first describe the concept and later refine the mathematical...

Hi there, I have modeled with MAXSURF a few variations of a prehistoric logboat in order to test a few theories. Now, I am trying to look at resistance-performance over a range of speed. To do so, I need to include a constant drag coefficient without knowing the drag force and velocity (both...

Recently I was thinking about the Hubble's constant (which, actually, is not Hubble's and not constant...) and wondering: if the universe is expanding at 70 km/s each Mpc, then there's possible to calculate some expansion of space, say from me to a person 1 meter away from me (theoretically)...

If the Hubble's constant is greater now (to the best of our estimates) than it was in the early universe, doesn't it just imply that the universe's expansion rate is increasing, which was shown by the High-Z Supernova Search team in 1998 that discovered dark energy? Wouldn't this Hubble...

Hubble constants (HCs) have been estimated based on the CMB, on Cepheid variables, gravitationally lensed quasars, Type 1 supernovae, and red giant luminosity. Not all agree within their estimated error bounds. This has been represented by some as a conundrum. Is it? The mean age of the...

I have to find pμ(τ) of a particle of mass m and charge q with v(0) = (vx(0), vy(0), vz(0)) in a electric field E parallel to the y-axis and a magnetic field B parallel to z axis, both constant and uniform, with E = B. Here follows what I have done (see pictures below): I wrote 4 differential...

The collaboration with the questionable acronym improved their measurement with a joint analysis of the whole dataset of six gravitationally lensed quasars. Measurements based on supernovae (measuring the Hubble constant "now") and measurements based on the cosmic microwave background (needing...

I’ve been trying to design a counterbalance system using a constant torque motor spring assembly. The spring I’m looking at has 25.4kg cm torque on the shaft from the output drum. So if I put a 100mm diameter cable drum on this shaft I should be able to counterbalance 5kg over the given...

I am hoping someone can explain to me why the constant Λ has units 1/m2. In the article https://en.wikipedia.org/wiki/Cosmological_constant In the Equations section, the following equation is presented. Do tensors have dimensions? If so, can someone tell me what the dimensions are for these...

The solar constant is only on one side of the Earth, however it moves around and the Sun gives out it's energy/heat all over the Earth in 24 hours. And the seas and land have heated up over time. However I got told this, No its not. By definition the solar constant is referring to a 2...

It is unclear from my text. Can you use the gamma constant to find the absorbed dose for a point source of photons?

Now, ## \displaystyle dQ=\left(\frac{\partial Q}{\partial p}\right)_V dp+\left(\frac{\partial Q}{\partial V}\right)_p dV## In an adiabatic change, ##dQ=0##. So, ## \displaystyle\left(\frac{\partial Q}{\partial p}\right)_V dp+\left(\frac{\partial Q}{\partial V}\right)_p dV=0## Using (3) and...

"It should be able to accelerate from rest to 20 m/s at least 50 times before the spring needs winding" -So F = -kd = -k(2.1) - d is 2.1 because it is the compression length Now, since we know the d, divide it by 50, 2.1/50 = 0.042m Basically, the spring unwinds 0.042 m 50 times for a total...

I need some clarification on how the Higgs field work. The popular science explanation explains the effect on moving particles the way an object would be impacted by moving through a medium of maple syrup. I understand this is a very bad, inaccurate analogy. What I want to understand is does...

I want to make a small mechanical calculator with no electric parts, nothing too advanced but a few binary gates capable of some basic functions. All the examples I were able to find were amazing but were still dependent on electricity to drive the mechanism. One possibility is a spring but I...

Dear Experts, We compute Cv for gases using the idea of equipartition principle and degrees of freedom. In case of a diatomic molecule, there are minimum 3 degrees of freedom (at very low temperatures) and maximum 6 degrees of freedom one of them being vibrational (at high temperatures. Does it...

How much impact does the presence of the cosmological constant have on the formation of structures in the universe? On a larger scale, is there less structure formation because of the presence of the cosmological constant?

I'm just having trouble understanding 1) how to plug in the formulas correctly and 2) the correct manner of attacking this. I feel like I'm missing something basic/simple. Any help is greatly appreciated! So far I've got: D = (0) + .5(2.2m/s^2 x 2.4s)^2 Enrique

I've set up a simple experiment to look at the ideal gas laws. My experiment is relatively simple in that I have a metal tube which is capped on one side. I am then pressurising the tube with air to 100 psi and locking it off. My thought is that as the pressure increased, with volume held...

I assumed that i had to take 5 time constants which would give the time taken to charge fully i assume then divide by 10 giving me a total number of readings of 34 , the answer is 6 yet they only used a single time constant to determine the number of readings? as this give me an answer of 68 or...

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My only question is what the εo symbol represents.

Using the fact that Pa ∝ |α|^2 and Pb ∝ |β|^2, we get: Pa = k|α|^2 and Pb = k|β|^2 Since the probability of measuring the two states must add up to 1, we have Pa + Pb = 1 => k = 1/(|α|^2 + |β|^2). Substituting this in Pa and Pb, we get: Pa = |α|^2/(|α|^2 + |β|^2) and Pb = |β|^2/(|α|^2 + |β|^2)...

Hello, I have a mass of 110 kg and I want to move it with a speed of 14 m/s by using springs. how can I determine the constant of the spring and design it? thank you!

Summary: Question about the Rydberg Constant. The Rydberg constant is essentially a 'relic' of a now obsolete model (the Bohr model) of the Hydrogen atom. So my question is why do scientists keep trying to measure it to greater and greater degrees of precision? Also I thought that the...

We need to prove that a3(t)= ρo/2Λ [cosh(sqrt(24πGΛ)*t) -1] by changing into a variable of u, where u=2Λa3/ρo From Friedmann's second equation we know that Λ= ρm/ 2 Also ρm= ρo/ a3 [First attempt] I begin from Friedmann's equation where (for here), ρtotal= ρm + Λ and k=0; a'2/a2 = 8πG(ρm +...

ρο/a4 ρο/a3 k Λ Βig Bang Big Crunch Polynomial Expansion Exponential Expansion x 0 x 0 >0 x +1 x +1 x 0 <0 x -1 x -1 >0...

Hi, I'm trying to make a realistic scene, in which water is kept under constant electrical charge. If the power is around 75 milliamps, and it's in a stream about twenty feet across by ten feet deep, would this affect water temperature? Thanks!

Hi all, Given that the question: From what i know , I am not sure how this equation can help me estimate the von-klitzing constant? Or is there another way? Thanks!

Is my solution reasonable? What I got from my first attempt is that the time constant won't change. WHY? Because when we double the number of loops (N) we're going to have new values for both the self inductance and the resistance of the solenoid and so the ratio (L/R) stays the same. Here is a...

I am confused about the cosmological constant and dark energy. In the most accepted theory, energy is created as the vacuum of space expands. This contravenes the conservation of energy. The law of conservation of energy does not hold in curved spacetime but isn't our universe flat spacetime ...

Hello, I'm trying to find the general solution of this homog. system w/ constant coefficients. I can't even get past the first step, which is to find the eigenvalues. As far as I know, there are a few approaches: 1) solve det(A-λI) = 0 2) solve the trace determinant plane equation (which is...

Hi everyone, When an electromagnetic wave passes through a material, then depending upon the atomic structure of that material it polarizes that material. There is another definition of polarization in physics which says that polarization is the direction of oscillating electric field in EM...

Is a constant vector field like F = kj conservative? Since the work of F for any closed path is null it seems that F is conservative but for a force to be conservative two conditions must be satisfied: a) The force must be a function of the position. b) The circulation of force is zero. My...

Some thoughts that I've had on the question are saying the volume flow rate (##Q##) in, must equal the volume flow rate out. If that's the case, then: ##Q_{in} = Q_{out}## ##A_1V_1=A_2V_2## But... no areas have been given. And height doesn't enter this equation at all. Then I thought it...

Hello! It says that the Time Constant of an RC circuit is equal to 100 ms. What is the energy that remains in the circuit after 300 ms? "Nothing mentioned about whether it is in falling or rising edge". The formulas that I have been using are : W = 0,5 (C* V^2) V = V0 ( e^-t/rc ) since I don't...