Scaling Definition and 130 Threads

I am reading that diffusive scaling in one dimension means that "increasing the size of a cell by a factor of 20 increases average diffusion time by a factor of 400". I can't find anything on diffusive scaling. Can anyone give me an explanation of this? Thanks

Differential geometry (which includes general relativity) often introduces the length differential, expressed as ds2=gabdxadxb, to introduce the covariant form of the metric tensor gab. However, this formulation scales ds2 incorrectly. The appearance of an index as a superscript, as in dxa...

Homework Statement A statue is to be 'scaled down.' It will have its size changed without changing its shape. It starts with an initial volume of 4.25 m^3 and ends up with a final volume of 0.250 m^3. If the height of the original statue was 215 cm, calculate the height of the smaller...

Let's say I have a vector x in \mathcal{R}^3. Let's also suppose that any vector x undergoes the transformation x' = kx (where k is a positive real). Obviously, normalizing the vector will give us a quantity which is invariant to uniform scaling. In fact, \frac{\mathbf{x'}}{|\mathbf{x'}|} =...

Hi everybody, I'm trying to reproduce daubechies basic building graph and daubechies wavelet function graph (φ(r)=0 if r≦0 or 3≦r). And i found this algorithm. I would appreciate if there is anybody could help me to understand the function defined below as function [s,w] = cascade(n,cs,cw)...

Hi, suppose i have various graphs which each have many nodes. In one graph the nodes x and y values may be within the range 0-1000, in another the x values may range from 100-500 and the y values from 300-800. Basically, the ranges always vary and there is no consistency. I need a way to...

Homework Statement Many undamped mechanical vibrations are described by the Differential Equation x′′ + Kx = 0 that describes a position x(t) with t being time and K a positive constant. a) What are the MKS units for K? b) Introduce s=t/T for some characteristic...

Hi all! I am just wondering why scaling in DIS is approximately realized for the middle (Bjorken-) x-values and not e.g. for the high or low x-values? Is there any depicitive reason? Thanks for the ideas! Blue2script

Hi I understand most of the steps in the determination of the time scale. But i don't really understand the step in equation 6.96. The first attachment is the full details of the time scale, and the second attachment is the part which I am stuck on. I just want to know, how they get...

How does Wien's scaling law \frac{u(\lambda)}{T^5} = \frac{f(\lambda T)}{\lambda^5T^5} imply that if \frac{u(\lambda)}{T^5} is plotted as a function of \lambda T, all experimental data will lie on a single curve?

Geometrically, matrix multiplication of an nxn matrix is the scaling, and rotation of a vector in n dimensions true? So when you find the inverse of a matrix, what you're actually doing is finding a transformation such that in the 'transformed space' the vector is a unit vector. If the inverse...

I don't understand where to even start with this problem. This book has ZERO examples. I would appreciate some help. Show that by a suitable scaling of the space coordinates, the heat equation u_{t}=\kappa\left(u_{xx}+u_{yy}+u_{zz}\right) can be reduced to the standard form v_{t} = \Delta...

Homework Statement Derive the scaling law for static buoyancy force of a solid sphere in a liquid with a density of γ. Assume the sphere is made of a material with a density of γs (γs< γ). Homework Equations The Attempt at a Solution I calculated the the buoyancy force of the...

Homework Statement a system has the following property: Its response to a sum of inputs is the sum of its responses to the inputs. (a) Prove that the scaling property holds for any integer scaling factor (b) Prove that the scaling property holds for any rational scaling factor...

Hi all. To me, scaling means adopting properly scales in nondimensionalization. However, as I see in the book "A modern introduction to the mathematical theory of water waves" by R.S.Johnson, the author distinguish the two processes in a way that confuses me much. (Sec. 1.3.1 and 1.3.2) Can...

Hello All, I'm doing some fun at home experiments with my 1:6 scale RC car and I wanted do some camparisons with its full scale counter part. Mainly how jumping the two off a ramp (Duke's of Hazzard style). I wanted to know if you can help me with confirming some of my scaling...

i am taking a +/-5 voltage signal is supposed coming from a torque sensor. this is supposed to be equal to 100 N*m. However, -5.04 volts is actually equal to 100 N*m and 4.85 volts is actually equal to 100 N*m. I need to scale this signal to a maximum input of 200 mV for display on a panel...

Hi guys, I'm a high school student at a private high school in the LA county called Bishop Amat Memorial. I'm currently in Honors Physics, so far I've been have a smooth and fine time until my teacher hit us with a project concerning scaling... His philsophy of teaching for this project is...

Hi all! I always come across "scaling" in various subjects. Like in Fluid mechanics, I am confused about why there is a need to choose some characteristic scales and non-dimensionalize the differential equation? I am confused about this...can anyone expain me the rationale behind this...

http://arxiv.org/abs/astro-ph/0606048 About universes with scale-related total masses and their abolition of presently outstanding cosmological problems Authors: H.J. Fahr, M. Heyl Comments: Submitted to AN. 7 pages Cosmological consequences of a strictly valid total energy conservation...

http://arxiv.org/abs/astro-ph/0605488 Challenges for scaling cosmologies Authors: Luca Amendola, Miguel Quartin, Shinji Tsujikawa, Ioav Waga Comments: 14 pages, 3 figures A cosmological model that aims at solving the coincidence problem should show that dark energy and dark matter follow...

Hi all! I am having problems with understanding the scaling process of the N-S equations in fluid dynamics. From textbooks, I see that each quantity say velocity, time, length...etc are all divided some some reference values in order to obtain some dimensionaless quantity V*, t*, p*, g* etc...

Using Mathematica, does anyone know how to scale the axis equally in 2D graphs so that the grid formes perfect squares?

A particle of mass M moves along a straight line with initial speed v_i. A force of magnitude Fpushes the particle a distance D along the direction of its motion. assume that the particle's mass is increased to 3M. B.)By what multiplicative factor R_k does the initial kinetic energy...

Hi all, I am not sure if I'm posting on the right place. I am currently working on a computational project. It's about simulating a system with two non-test masses and a bunch of test masses. The instruction sheet says that we should "scale the problem carefully by setting the units such that...

physics 40s scaling and proportions ...please help the physics of a wire supporting a sphere... A wire of .2cm in diameter is just strong enough to support a steel sphere. What must the diameter of the wire be if the following changes are made to the sphere? A. new sphere has 4x the...

I am having dificulty with this homework problem. It doesn't seem to give me enough information. I am asked to find the volume and surface area of an object of unknown volume and shape. Here is the problem: A sculptor builds a model for a statue of a terrapin to replace Testudo (go UMD!)...

I am presently taking my first course in signals and systems and I have been charged with proving the scaling property of the impulse function; that: delta(a(t-to)) = 1/abs(a)*delta(t-to) I am seriously miffed and need some help.

Hi to all, my problem is the following: I have different different quality metrics which are able to assess image quality by investigating several parameters in an image. The problem with those metrics is their scale. Some of them range from 1 to 10 (10-highest quality) some of them from 0...

In critical phenomena, we can enlarge the block size(momenta fluctuation) by Kadanoff transformation, say k \rightarrow bk (b<=1) , and scale the new Hamiltonian by k' = k/b, x'=bx to recover to the original block size. In QFT, similarly integrating out the high momenta produces the effective...