Scaling Definition and 151 Threads

According to this article, it is beneficial to scale down heat exchangers due to the decreased distance the heat has to travel, and therefore the decreased thermal resistance and increased heat flow. "the best way to remove heat from a CPU is to minimize the distance heat must travel from a...

Hi guys, So I have the following Lagrangian: \mathcal{L}=\bar{\psi}(i\partial_{\mu}\gamma^{\mu}-m)\psi+\frac{1}{2}(\partial_{\mu}\phi)(\partial^{\mu}\phi)-\frac{M^{2}}{2}\phi^{2}-\lambda\bar{\psi}\psi\phi where m is the is the mass of the spin-half Dirac field and M is the mass of the spin-0...

I am looking for some advice. I am not a physicist but I have a problem that I am unsure of how to solve. This is the scenario; I have an object that is ploughing through mud on the sea floor at a constant speed of 0.02 m per second. Prior to the contact with the sea mud it was freely moving at...

Hello I don't quiet understand how the integration in the picture works... I must have forgotten something... Can anyone explain what is used?

Homework Statement Take the action S = \int d^4x \frac{1}{2} \left( \partial_{\mu}\phi(x)\partial^{\mu}\phi(x) - m^2\phi^2(x) - g\phi(x)^p \right) , and consider the following transformations: x^{\mu} \rightarrow x^{'\mu} = \lambda x^{\mu} \phi(x) \rightarrow \phi^{'}(x) =...

I need to create scales for a test before running t-tests / ANOVA. Instrument: One attitude survey test with 37 questions. Each question is a Likert type question with 1 to 5 points. Data Set: The set of data includes pre-test and post-test scores. There was a 6 month delay between the...

I need to build a table saw miter gauge at about 1/4/-1/8 scale. The center axis of rotation seems pretty straightforward - I have many old rollerblade bearings - but I have no idea how to do the handle assembly (the cylindrical screw arrangement that locks and unlocks the angle) and the sliding...

First I want to mention that I am not super good at maths and that I wasn't even sure if this was the right sub forum to post in (please move this to another one if that's the case). I am working on a 2D game in python where the player plays on an infinite map. Of course that means that the...

I've made mistakes where scaling was used but I just assumed that I didn't need it. e.g. a bug walking towards <1,1,1> is scaled to <1/sqrt(3), etc>. Under what kind of conditions/in what kind of problems should vectors be scaled? I know that v/|v| is the unit vector but how do I relate this to...

Hi everyone, I have the following problem in my hands, which I don't know how exactly to address. Let's assume that from any CAD(Solidworks, Catia), I obtain the inertia tensor of my model (impossible to calculate by hand btw). I_full=[Ixx Ixy Ixz Ixy Iyy Iyz Ixz Iyz Izz] I...

This is a hypothetical question. What would happen if everything in the Universe was scaled up (or down) in size by a constant factor? Starting from the nuclei in atoms, ending with galaxies; assume that all proportions would be kept intact, i.e. all distances are scaled up by the same factor...

Hi, I'm studying about Renormalization group. I have a question about mass beta-function. Usually, when we perform one-loop calculation to get counter-term coefficients, resulting RG coefficient for mass scaling is given by \mu \frac{d m}{d \mu} = a_1 (e ) m and a_1(e) is come from...

I had the concept of scaling up Maxwells' demon experiment to a marco scale. Replacing molecules of gas with light, rigid, balls. Perhaps coated in magnets with varying poles so they never touch (non-interacting). Would suspend them in a thin fluid with neutral buoyancy.

Let's say that we have a guy who is 6 feet tall and weighs 190 lb. If we were to make him 60 feet tall with the same proportions as before, how much would the man weigh? How much would he weigh if we make him 50 feet tall?

So I am still confused about how to applying scaling of parameters to a general optimization problem. Let's say I am trying to do maximum likelihood estimation. I understand how to find the scaling matrix (assuming we restrict it to diagonal form) and that the Hessian should be close to the...

Hi, I'm following the proof of the "Scaling Property of the Fourier Transform" from here: http://www.thefouriertransform.com/transform/properties.php ...but don't understand how they went from the integral to the right hand term here: The definition of the Fourier Trasform they...

Hello, if I think of the harmonic oscillator action S = ∫L dt, L = 1/2 (dx/dt)^2 - 1/2 x^2, and then of the "scaling transformation" x -> x' = 1/a x (a>0, const), then x = a x', and in new coordinates x', S' has the same form as in x except for multiplication by the constant a, formally...

Building a RC Lancaster 1/10 Scale Planning on putting in 4 x 4stroke glow fuel enjins on it Expected weight is 10-20 kg - but have no real idea yet Any sugestions? Real Lanc is as follows - from Wikipedia of coarse Wingspan: 102*ft 0 in (31.09*m) Height: 20*ft 6 in (6.25*m) Wing...

I'm working on an assignment that is due in roughly two weeks and I'm stuck on a problem. I have what I believe may be a solution but am unsure whether or not it is 'complete'. Here is the problem: "Let C be a circle or a straight line. Show that the same is true of the locus of points...

Homework Statement Consider the nonlinnear diffusion problem u_t - (u_x)^2 + uu_{xx} = 0, x \in \mathbb{R} , t >0 with the constraint and boundary conditions \int_{\mathbb{R}} u(x,t)=1, u(\pm \inf, t)=0 Investigate the existence of scaling invariant solutions for the equation...

Hi, I have tried to solve eigenvalue problem of the Helmholtz equation ∇×1/μ∇×E-k2E=0 in 2D, where k2=k20-β2 is the eigenvalue and k0=2*π/λ0 is the wavenumber in vacuum. Also β=neff*2*π/λ0 where λ0 is the wavelength in vacuum. Because constants ε=εrε0 and μ=μrμ0 are not very convinient...

Homework Statement Find the Fourier transform of (1/p)e^{[(-pi*x^2)/p^2]} for any p > 0 Homework Equations The Fourier transform of e^{-pi*x^2} is e^{-pi*u^2}. The scaling property is given to be f(px) ----> (1/p)f(u/p) The Attempt at a Solution Using the information above, I got...

the system alternates between ON and OFF states. Whenever the system is in ON state, packet transmission mechanism happens. whenever OFF state comes in between the system is frozen and resumes from the point where it left at the end of ON state. Now the packet transmissions are renewals...

Hello everyone, I have a question that is bothering me a bit. I would be happy if you could give an idea or tell me a specific point to look at. Lets say that we have an arbitrary function that obeys diffusion equation: f = f(η), here η is the scaling parameter for pde which equals to...

Hi. I am reading this chapter about dimensionless ratios and scaling law. and it says like this: \alphaF = \frac{Fp}{Fm} = \frac{ρp . Vp^2 . Lp^2}{ρm . Vm^2 . Lm^2} (1) From this, it is obvious one can write for these forces: Fp = C\frac{1}{2} ρp Vp^2 . Lp^2 (2)...

Homework Statement Your task is to determine: a.the length and bore of cannon that is required to accommodate an 80 kg Clown with an over-arm measurement of 48 inches b.the amount of fuel that is required to launch the Clown at the same angle as you did with your model...

Hi there. I am having trouble interpreting the Kolmogorov K41 scaling relation for homogeneous and isotropic turbulence: S_{p}(l) = <\delta u(l)^{p}> = <|u(r+l) - u(r)|^{p}> \propto (\epsilon l)^{p/3} where l is the length of displacement between two points under consideration in the...

Homework Statement A mass spring system carries a mass of 0.4kg. When the point of suspension is made to vibrate verticaly at a frequency of 15Hz resonance occurs. What mass should be added to the 0.4kg in order to reduce the resonant frequency to 10Hz. a) 0.20kg b) 0.40kg c) 0.50kg d)...

Homework Statement AQA Section A Q18 Jun 11 Homework Equations The answer should be C E=.5QV and C=Q/V The Attempt at a Solution So the original Q has increased by 1.5 times If C is constant than the voltage must also increase by 1.5 times Now the energy E is E=.5QV V...

The electric potential at a distance r from a positive point charge is 45V. The potential increases to 50 V when the distance from the charge decreases by 1.5 m. What is the value of r? A 1.3m B 1.5m C 7.9m D 15m Homework Statement the answer is D Homework Equations V=(1/4∏ε)...

Homework Statement The time period of a simple pendulum is doubled when the length of the pendulum is increased by 3.0m. What is the original length of the pendulum? Homework Equations T= 2∏√(l/g) also l is original length and l+3 is the new length The Attempt at a Solution So...

Homework Statement I'm confused on whether or not two functions would be equivalent or not. Let's say x(t) is a triangle with height 1, width 1. The hypotenuse of it is the function t (with a slope of 1). I'm told that x((t+2) / 4) then is making it 4 times as wide and left-shifting the...

Homework Statement http://puu.sh/1rcsO I got the first one from a simple scaling, but I can not figure out the second one. Homework Equations Det(cA) = cDet(A) Scaling a row scales the determinant Adding rows/columns to each other does not affect the determinant Det(AT) = Det A...

Homework Statement Let's say I've got the typical triangular waveform with function x(t) = t, goes from 0 to 1 on the x and y axes. How would I manipulate x(t) and the given X(ω) to, say, 1)Stretch the function on the x-axis from 0 to 2, but keep the slope as 1? 2)Flip the function...

Hi everyone, I'm new to quantum mechanics, so bear with me o:) Homework Statement I'm not sure if scaling is the right word here, but my problem is about the absolut value of a quantum mechanics state to be one. I have the state | \phi> which is a linear combination of the states |+>...

Let's say I have a precisely designed axial compressor, comprising of stages of rotor and stator wheels, that resembles something like this: Such a compressor, driven by a certain torque at a certain RPM, will deliver a certain air mass per time at a certain pressure. Now, what happens...

Hi all, I have a homework assignment related to the conservation of energy in a fluid. This is given in terms of the density ρ, specific heat c_{p}, thermal conductivity k, bulk viscosity μ, dissipation function \widetilde{\phi}_{v}, velocity function \widetilde{u}, spatial derivative of the...

Hi, I have a relatively small system. It takes 10 minutes to perform a CCSDT calculation. I know scaling is notoriously bad, but does anyone have a rough idea of how long a CCSDTQ calculation would take on the same system? Are we talking days or months? Thomas

I'm very surprised no one (that I know of) has plotted the score distribution of the Physics GRE form GR0877. The data comes from the table in http://www.ets.org/Media/Tests/GRE/pdf/Physics.pdf. Sample size = 14,395 exams between July 1, 2007, and July 30, 2010. Score Scaling Cummulative...

Hope this is in the right forum. I apologize in advance for my ignorance and imprecise discussion as I am at a major disadvantage, lacking rich mathematical educational background enjoyed by most here. Background is that I'm curious about calibrating for soft-iron distortion calibration for a...

Hi, Am plotting a graph and need to scale the axes so that i can take my range of 'x'-axis values from -1 to infinity. I shall provide script, but i am using the ParametricPlot command. ParametricPlot[tab2, {up, -1 + 10^-7, 10}, AxesLabel -> {"\[Rho]", "u'"}, PlotRange -> {{-1, 2}...

Hello everyone, I am currently studying the renorm. group in Stat. physics, more precisely how a rescaling (of space) leaves the partition function unchanged, at the price of having an infinite space of parameters due to the interaction proliferation at each rescaling. Let K be our...

Hi all, I have a question about Daubechies Wavelets. I've recently been trying to teach them to myself from the pdf here...

An augmented matrix scaled by a number also means the solutions set is scaled by that same number. I believe this is true due to it basically being the same as elementary row operations preformed on each row. Unless it is a zero scalar in which case you lose all conditions. Is my method of...

I have read at a lot of places that in 2D transformations rotation is a combination of scaling and simultaneous shear? What exactly does this mean & what's the proof for this?

Scaling and Proportion Physics problem. Please Help!? 1. A flea is able to jump straight up about 0.44 m. It has been said that if a flea were as big as a human, it would be able to jump over a 100-story building! When an animal jumps, it converts work done in contracting muscles into...

Homework Statement Not exactly a problem, more an example that has me confused :s \frac{dN}{dt}=\kappa N-(\kappa/a^{2})N This describes a population model where N is the population, \kappa is the net births (ie: births less deaths) and it doesn't tell you what a is (this in all the...

i am making a wind tunnel in order to test aerodynamics of 1/24 scale cars. i am having two problem: 1. i am not sure what wind speed at that scale to represent 100mph. 2. i am using a fan that has an outlet wind speed of 19.4 mph. i tried to increase wind speed by decreasing the outlet...

Homework Statement The problem is from Mathematical Methods in the Physical Sciences, 3rd Ed. Ch10, Sec. 10, Q4. My question is a bit subtle as I have actually figured out the problem, just that I don't understand my solution. The problem reads: 4) What are the physical components...

I have a feeling this question has a very simple answer, yet I cannot find it anywhere online. Let's say that I have a data set that represents and evenly-spaced sample of a function, taken uniformly over the interval (a,b) \qquad a,b \in \mathbb{Z} I perform a discrete Fourier transform to...