In statistics, a power law is a functional relationship between two quantities, where a relative change in one quantity results in a proportional relative change in the other quantity, independent of the initial size of those quantities: one quantity varies as a power of another. For instance, considering the area of a square in terms of the length of its side, if the length is doubled, the area is multiplied by a factor of four.
Dear colleagues,
I am dealing with rope friction and the so-called Capstan equation.
Situation: A rope wraps around a cylinder with a wrap angle. It depends on the input force.
There are very comprehensive approaches by other colleagues, where the friction value depends on the normal force or...
I am reading Planck 2015 results. In particular, I focused on "Power law potentials" subsection.
The issues I have are
1. I do not understand why the validity of the model can be determined by the value of the ##B## mode.
2. Why the ##B## mode values ##\ln B = −11.6## and ##\ln B = −23.3## for...
Hi everyone! Awesome forum!
I'm doubting myself on a problem about inverse square law.
I'll change the actual values from my homework problem as I want to check that I have the right idea rather than the specific numeric answer.
If I am using an inverse 2.5 power law and know the power at 100m...
Hello, as part of the study of fields with central forces, I came across with fields called power law, defined by F = - K/r ^ n u
(u is radial vector passing through the origin O)
I would like to dismiss case n = 2, which refers to the Newtonian fields whose study was exhaustively conducted in...
Homework Statement
For a power spectrum density fluctuations ##P(k) \propto k^n##, I need to find the scaling (with respect to ##a##) of the horizon wavenumber ##\frac{2\pi}{\chi_H}## in a matter dominated universe in terms of ##n##. ##\chi_H(a)## is the evolving particle horizon, in a flat...
Hello everybody,
I have a problem with the logarithmic binning of some data (which are expected to be distributed as a power law). I found this https://www.physicsforums.com/threads/exponential-binning.691834/
What "mute" says is exactly what I need: equally spaced bins on a logscale to...
When, in wireless communications, does the inverse fourth power-law become relevant? My understanding is that is that what cause the average signal power to degrade to the forth power is cancellation from self reflections. So by my way of thinking, an LOS point to point system, like a...
Homework Statement
need to solve for v? I also know the value of x=0.02
Homework Equations
v(x)= 47.8 ⋅ (0.451/x)^(5.39)
The Attempt at a Solution
how do I take the log of both sides, is that the right approach to solve for v?
1. Problem statement
A steel rod supporting a stress of 8000 psi at 1000 ◦ F is not to exceed 5 % creep strain. Knowing that the steady-state creep rate can be expressed by an equation of the form
##\dot{\epsilon}_{s}^{C}=B|\sigma |^{n} exp \left(\frac{-Q}{kT} \right)##
ε⋅, strain rate
B...
Just a quick question. Let A and B be two points. Electrical work is defined as the amount of energy it takes to move an amount of charge Q through a potential difference VB-VA (for our purposes here, we will assume that the voltage values are measured with respect to an Earth ground) and is...
Homework Statement
The Black Mesa pipeline transports 660 tons / hr of solid coal ground to 8 mesh (2.4 mm) as a 50 wt % slurry in water with an estimated sg of 1.26 for 273 miles across northern Arizona. The pipeline ID is 18 inches and the slurry flow rate (coal and water) is 4200 gal/min...
So I have a series of 5 data points let's say that they are (1,1),(2,3),(3,4),(4,4.5),(5,4.75) that create a power function that has the equation y=1.2x^.97. Let's also say that the error uncertainty for every number is 0.1. I know that for a linear line you can take the uncertainty of the...
Hi All,
After reading some books on how stock market returns are better modeled by a power law distribution, I wanted to play with some data based on this.
When using some software and or doing it myself on excel, I can generate one tail, but not two.
This is what I would like my data...
Many natural hazards or geological phenomena satisfy power-law (fractal) frequency-size statistics to a good approximation for medium and large events. Examples include earthquakes, volcanic eruptions, asteroid impacts, landslides, and forest ﬁres. So my questions is that, Why geological...
I'm trying to find a power law relationship between mass and metabolic rate, given that each of these quantities is defined by a differential equation.
Assuming dM/dt=a*M(t) and dR/dt=b*R(t), where M(t) is mass and R(t) is metabolic rate, I know that I can solve each of these equations to...
Looking at the known masses of the elementary particles, they appear at first sight to be on some kind of exponential curve. It is certainly attractive for there to be such a simplicity - however, and interestingly ...nothing really lines up exactly. Is there any explanation for this or for the...
Problem Statement:
Blood is a pseudoplastic fluid that has a variable viscosity at 37 °C that depends on the percent composition of hematocrit and plasma. It will usually range between 3 x 10^-3 to 4 x 10^-3 Pa s. A small sample of blood is tested in a viscometer and the following results are...
y_i=A{x_i}^b
When I solve for A two different ways I am getting different answers..so somewhere I'm doing something wrong. If someone could point out where I would be grateful :).
Using logs:
y_i=A{x_i}^b
ln(y_i)=ln(A)+b*ln(x_i)
ln(y_i)-(ln(A)+b*ln(x_i))=r_i for least squares we want...
Hi! Iam doing metal sheet forming simulations and I want to find a material for AA6082 and I wanted to use a power law description of the form sigma = K*(strain)^n
where K is the strength coefficient and n is the strain hardening index. But I can not find the value for K. Anyone know any...
I'm not a mathematician, but I want to understand how a mathematician would view this issue.
I'm working primarily with degree distributions for finite graphs, and when I make a log log plot of the frequency distribution the data points form a nice straight line (at least for low degree...
Please teach me this:
In QTF theory of Schroeder,chapter 13.1 saying:
Just at t=0(t=\frac{T-T_{c}}{T_{c}}),the correlation should decay as power law.
Define the exponent \eta by the formula:
G(x)=\frac{1}{x^{d-2+\eta}}
where d is Euclidien space dimension.
I do not understand why at...
Homework Statement
A particle of mass m is bound in a one-dimensional power law potential V(x)=K*x^B, where B is an even positive integer. Show that the allowed energy levels are proportional to m^[-B/(2+B)].Homework Equations
Using Schrodinger Eq (one-dimensional) The Attempt at a Solution...
Hello, world :)
My first post here.
I have to choose a topic for a project in astrophysics. I intend to major in astronomy and it's my first year of studies, so I don't have much knowledge so far, though I don't mind picking a 'heavy' topic for this assignment - I know I'll benefit from...
As the title, I want to know details of the following integrations
\int |x|^a * exp[i*k*x] * dx = k^{-1-a} * Gamma[1+a] * sin[a*pi/2] -------(1)
by variable changes, k*x -> z, it's easy to get the factor k^{-1-a}, i.e.
l.h.s -> (\int z^a * exp[i*z] * dz) / k^{1+a}...
In prices's theorem, the power law damping of the radiative tail can take the asymptotic form of-
\delta m(v_1) \sim hv_1^{\ -p}
where \delta m is the mass-energy of the radiation flux, v_1 is the null coordinate and p determines the decay rate of the radiation (≥11 for gravitational...
Homework Statement
is the potential in the center of a solid 3d sphere having uniform mass density and a total mass of m (which is constant), which is gravitating according to an inverse 10th power law, inversly proportional to the square of its radius? this isn't really homework but I...
Is it true that the existence of extra dimensions can lower the unification scale to the GeV scale? Does this mean that the LHC would be in range to detect a unification of couplings if this were true?
some have suggested that gravity can be unified with the nuclear force by introducing extra dimensions so that gravity doesn't follow an inverse square law at short distances. it seems like it should be rather easy to determine whether the nuclear force follows an inverse cube or 4th or 5th...
Is it correct to say that independent random events (additively) lead to a normal distribution, and dependent random events (multiplicatively) lead to a power law distribution?
The following might be trivial, but it was quite interesting to find for me, someone with a very limited knowledge...
Homework Statement
I have no idea how to solve this differential equasion:(d^2y/ds^2)=L^2/(y^3)
where L is constant. It looks like a inhomogenius DE but what should I do with y^3?
I am trying to write some code to produce a model of a star. I've done loads of research and come to the conclusion that for ease i want to represent the opacity in my model with the power law.
k=k(0)*(rho^alpha)*(T^beta)
this seems very straight forward apart from the fact that in every...