Parameter Definition and 352 Threads

For a flat universe, density parameter Ωuniverse=1. How does negative signage of a constituent density parameter, such as that of curvature index Ωk, which can be 0,1,-1 affect the signage of Ωuniverse? If Ωk were to be converted to its energy density, which is much less than the energy density...

Hello! If I have a measurement of a (dimensionless) parameter, ##a##, say 998 +/- 3 and the theoretical prediction of that parameter (assuming known physics) is 1000 +/- 4. Let's say that I want to set limits on a new parameter (not included in the theoretical calculations), call it ##\alpha##...

Hello! I have a matrix (about 20 x 20), which corresponds to a given Hamiltonian. I would like to write an optimization code that matches the eigenvalues of this matrix to some experimentally measured energies. I wanted to use gradient descent, but that seems to not work in a straightforward...

For Ω=1, κ=0. Does the value of κ simply follow from the value of Ω, or can its value have an independent existence? So if Ω>1, does κ have to be 1?

idk how to start after finding the second derivative

Hi, there. I am doing differentiation with respect to an affine parameter ##s##, I am not sure whether my idea is right or wrong. Let ##C## be a geodesic for light and the path length ##s## on it be the affine parameter. Now I need to calculate ##\frac {\partial f}{\partial s}##, with ##f##...

Hello, I am trying and failing to derive that the shear modulus ##G## is equal to the Lame parameter ##\mu##. I start with the linear, symmetric, isotropic stress-strain formula: $$\sigma = \lambda \mathrm{tr}(\epsilon) \mathrm{I} + 2\mu \epsilon$$ I then substitute a simple (symmetric) shear...

https://stackoverflow.com/questions/2685854/why-should-the-copy-constructor-accept-its-parameter-by-reference-in-c I've read these answers, but most of them aren't satisfactory. They just throw a big wall of text. I get they're trying to say something about infinite recursion, but I'm failing...

Referring to this link : https://qcdloop.fnal.gov/bubg.pdf Using Mathematica Integrate command to solve it does not give the result stated here but I am unclear as to how they got to the result in the 4th line. It is clear that the integrand (1st line) can diverge for certain values of the...

As I understand it, when the squeezing operator acts on an annihilation/creation operator, a function of sinh(r) and cosh(r) is produced, where r is the squeezing parameter. I've been reading some papers that say that up to '15 dB of squeezing' have been produced in a laboratory. Does this mean...

This graph shows ##H## as a function of time related to the L-CDM model. Do we (@Jorrie) have similar graphs e.g. for ##\Lambda=0##; ##k=-1## critical, ##\Lambda=0##; ##k=0## open, ##\Lambda=0##; ##k=+1## closed? That would be great, thanks in advance.

#include<stdio.h> void sort(int arr[]){ int n=sizeof(arr)/sizeof(arr[0]); printf("%d",n);} void main(){ int array[]={12,11,54,6,77}; sort(array);} But I'm getting the answer as 2. I searched it up and found out that array has decayed into pointer and hence its showing size of pointer...

This works: a=0.4 Select[ list, #[[2]] > a-0.025 && #[[2]] < a+0.025 & ] {{401803.,0.42485,3.33299,0.776904,0.277985},{402066.,0.40333,9.23462,0.381478,0.397121},{402872.,0.41899,3.47237,0.742789,0.27385}} But why doesn't this work? :- Select[ list, #[[2]] > b - 0.025 && #[[2]] < b +...

Hi PF! Given random time series data ##y_i##, we assume the data follows a EWMA (exponential weighted moving average) model: ##\sigma_t^2 = \lambda\sigma_{t-1}^2 + (1-\lambda)y_{t-1}^2## for ##t > 250##, where ##\sigma_t## is the standard deviation, and ##\sigma_{M=250}^2 =...

In the usual Schwarzschild coordinates the Lagrangian can be written: $$\mathcal{L}= \frac{\dot r^2}{1-\frac{2M}{r}} - \left( 1- \frac{2M}{r} \right) \dot t^2 + r^2 \dot \phi^2$$ where all derivatives are with respect to a (affine) parameter ##\lambda##, and where for convenience I have...

I'm reading an article about the order-chaos-order sequence of a spring pendulum [Ref 1], as I'm reading it I'm trying to reproduce the graphs and results through Mathematica. However, I am new to this software. I will list below some of the most important equations mentioned in the paper. "In...

Hi all, I am somewhat familiar the Landau Ginzburg paradigm for phase transition. My understanding is that it is a phenomological model of 2nd order phase transitions by "guessing" that the free energy can be expanded a configuration integral (path integral) of a functional of a local order...

(P.S! this is an open question, feel free to answer)

This problem is from David Morin's classical mechanics textbook: I am having trouble with Part b. Here is the textbook's answer: I do not understand why large particle energies lead to capture. I would think that smaller energies would lead to capture because the particle wouldn't have enough...

We are working on new software for one of our measurement systems (written in Python). The new system is capable of measuring more devices simultaneously than before so keeping track of what we are doing is important; it will also be more automated. One of the things we want to implement is...

Einstein famously derived his relation between the diffusion constant of Brownian motion, particle mobility in a disippative medium, and temperature by considering Brownian motion in a harmonic oscillator potential. The result, $D = \mu k_BT$, is derived assuming that the mobility $\mu$ is...

Hi,I'm reading about critical density and I'm a bit confused about it's derivation.Solving the Einstein equations using the cosmological principle we get the (second) Friedmann equation: $$ \bigg( \frac{\dot{a}}{a} \bigg)^2...

Suppose you have a smooth parametrized path through spacetime ##x^\mu(s)##. If the path is always spacelike or always timelike (meaning that ##g_{\mu \nu} \dfrac{dx^\mu}{ds} \dfrac{dx^\nu}{ds}## always has the same sign, and is never zero), then you can define a smooth function of ##s##...

I would like to be able to determine the current through a device for a given junction temperature. I am looking at a datasheet and notice that it gives the device power dissipation with different case temperatures. Since the maximum junction temperature is 175 C, I believe that means that lower...

It is clear that ##1-x^2## is equal to zero in both boundaries ##1## and ##-1##. So for me is interesting to think like this \frac{d^m}{dx^m}(1-x^2)^m=\frac{d}{dx}(1-x^2)\frac{d}{dx}(1-x^2)\frac{d}{dx}(1-x^2)... and...

The book is asking me to write my own unique_ptr template (after just covering a bit about templates). I called my template single_ptr, and I gave it two template parameters, T and D. T is supposed to be the type that the raw pointer points to. D is supposed to represent a function type so that...

Hi everyone! So, the problem I'm having has more to do with "how to pose the problem to solve it in some software as Matlab or similar". I have experimentally measured values ##\varepsilon_{exp}^i## with ##i=1,\cdots,6##, that is, I have 6 detectors. Then, I know (from a Monte Carlo...

In cosmology the deceleration parameter defined as the $$q_0 = \frac{1}{2}\sum_i\Omega_{i,0}(1+3w_i)$$ Is there a similar expression for the jerk parameter (##j_0##) ?

So, for this exercise I'm considering the removable singularity for ##x=2## to cause ##f(2)## to be different from ##\lim_{x \to 2}f(x)##. But as soon as I write everything down, I get stuck here: ##\lim_{x \to 2}f(x)\neq\frac{4(a-4)}{0}## How do I calculate ##a##?

Let ## \mathcal{S} ## be a family of probability distributions ## \mathcal{P} ## of random variable ## \beta ## which is smoothly parametrized by a finite number of real parameters, i.e., ## \mathcal{S}=\left\{\mathcal{P}_{\theta}=w(\beta;\theta);\theta \in \mathbb{R}^{n}...

Hello Forum, Limiting our discussion to 1D motion, it is clear that the concept of instantaneous velocity is defined as the covered displacement dx divided by the time interval elapsed dt: $$ v = \frac {dx}{dt}$$ However, mathematically, the velocity ##v## can be made to depend on any...

I am given the following matrix representation of a linear mapping $$L_{\alpha}^{\beta}= \begin{pmatrix} 1 & 0 & 1 & 0 & 1 & 0 \\ 0 & 1 & 0 & 1 & 0 & 1 \\ 0 & a & 0 & b & 0 & c \\ a & 0 & b & 0 & c & 0 \\ 0 & a^3 & 0 & b^3 & 0 & c^3 \\ a^3 & 0 & b^3 & 0 & c^3 & 0 \\...

I note the general Taylor series for ##a(t)## as: \begin{equation} \begin{split} a(t)&\approx a(t_0) + a'(t_0) (t-t_0) + \frac{1}{2!} a''(t_0) (t-t_0)^2 ... \end{split} \end{equation} which I rewrite as: \begin{equation} \begin{split} a(t)&\approx a(t_0)\left(1 +...

Hi guys, I am using ScikitLearn's Elastic Net implementation to perform regression on a data set where number of data points is larger than number of features. The routine uses crossvalidation to find the two hyperparameters: ElasticNetCV The elastic net minimizes ##\frac {1}{2N} ||y-Xw||^2 +...

I tried to derive this by myself but I'm stuck. What i did it to substitute a_{1} with a_{1} +\Delta a_{1} in the first equation, getting: (a_{1}+\Delta a_{1})\dot{y}(t)+y(t)=b_{0}u(t)+b_{1}\dot{u}(t) and trying to subtract a_{1}\dot{y}(t)+y(t)=b_{0}u(t)+b_{1}\dot{u}(t) to it. But it's not...

The strategy here would probably be to find a differential equation that ##f## satisfies, but differentiating with respect to ##x## using Leibniz rule yields ##f'=\int_x^{2x} (-te^{-t^2x}) \ dt + \frac{2e^{-4x^3}-e^{-x^3}}{x}## Continuing to differentiate will yield the integral term again...

Here were my assumptions: Energy and angular momentum are both conserved because the only force acting here is a central force. The initial angular momentum of this particle is ##L = mv_0b## and we can treat E as a constant in the homework equation given above. I solved for the KE (1/2 mv^2) in...

I just saw a new paper on measuring the Hubble Parameter : https://arxiv.org/pdf/1908.06060.pdf It seems they are agreeing with Planck which I understand would speak largely against the idea of new physics from the Hubble tension. However it says +14 and -7 next to the estimate. I presume...

Does ##w## = -1 by itself imply that spacetime is flat, or is it only due to ##\Omega##Matter + ##\Omega##Λ = 1 ?

Ashcroft & Mermin Chapter 25, the Gruneisen Parameters are defined as: $$\gamma_{ks}=-\frac V {\omega_{ks}} \frac {\partial {\omega_{ks}}} {\partial V}$$ where the normal mode frequencies are defined by the eigenvalue equation: $$ M \omega^2 \epsilon = D(k) \epsilon $$ The volume of the crystal...

How can I calculate the Hubble Parameter in time. I know that it decreases in time and approaches to some constant value but I am not sure to what value, Is there any graph for that ?

I have been studying primordial black hole formation through inflation for a while and I was curious to know how the parameters in an inflation model are determined such that they are consistent with CMB constraints. In my literature reviews, there are quite a few models that exhibit an...

The released products of a transmutation reaction (I say transmutation when 2 particles reacts to generate more than one) follows the conservation of kinetic energy law. Also particles moving in opposite direction can have equal speed one with respect the other than rather if one of them is...

Let's say you have a helix defined parametrically as r(t) =<sin(t), cos(t), t> Is it possible to eliminate t and write an equation for this helix just in terms of x, y, and z?

In the Ansatz : $$C(a,b)=\int A(a,s)B(b,s)ds$$, is $$s$$ not simply the mute summation index ? In this sense it is not hidden to the experiment. Then what about an "dummy" hidden variable that is not integrated over : $$C(a,b)(\phi)=\int A(a,s,\phi)B(b,s,\phi)ds$$ $$\phi$$ were tuned one and...

https://uploads.tapatalk-cdn.com/20180712/28a4bbb89e76d3478ae2fd0825562148.jpg Question 81

Interesting paper here: https://colala.bcs.rochester.edu/papers/piantadosi2018one.pdf which using a closed-form solution to the logistic map m(z) = 4z(1−z) of mk (θ) = sin2 [ 2k arcsin √ θ] with a finely tuned parameter θ (extending to hundreds of decimal places) can fit just about any 2...

As part of my work, I'm making use of the familiar properties of function minima/maxima in a way which I can't seem to find in the literature. I was hoping that by describing it here, someone else might recognise it and be able to point me to a citation. I think it's highly unlikely that I'm the...

Homework Statement I have E as a material parameter. It is a modulus of Elasticity It is given as: 109/E = 80/psi I want to write E as a value with units psi. Homework EquationsThe Attempt at a Solution Is this correct? 1/E = 80*109/psi So psi/E = 80*109 So E = 1.25*10^7 psi

Homework Statement Find the value of the parameter α for which the pencil of planes through the straight line AB has a common plane with the pencil of planes through the straight line CD, where A(1, 2α, α), B(3, 2, 1), C(−α, 0, α) and D(−1, 3, −3). Homework Equations Let Δ be a line given by...