Questions tagged [scaling]
Questions involving the laws which are scale invariant, i.e. that apply to different scales equally. Also laws that involve exponential behavior, expressed in terms of certain magnitudes to the power of certain exponents.
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Scaling equation for the external field H in an Ising like system [closed]
i want to show that the following relation is true for the external field H, starting from the scaling form of the free energy. It is an Ising like System close to a critical point with $M \geq 0$ and ...
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Scaling Magnetic Fields Properties
Do magnetic fields of magnets of different mass differ in scale rationally or do the fields change in size and shape exponentially. In other words, would a microscopic magnet magnetic field look the ...
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Using the RG equations to find the free energy scaling form of the 2D Ising Model
i am trying to calculate the scaling form of the free energy of the 2D Ising model, starting from it's RG equations:
$$\frac{d u_I}{dl} = 2 u_I + u_t^2$$
$$\frac{d u_t}{dl} = u_t$$
$$\frac{d u_h}{dl} =...
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Why do we rescale momenta after integrating out high momenta in Wilsonian renormalization?
In Section 12.1 of Peskin & Schroeder they motivate Wilson's approach to renormalization by asking how a quantum field theory changes after changing the momentum scale. To answer this they start ...
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Change of scaling due to a perturbation
I am looking for known examples of models where the introduction of a perturbation changes the scaling law of one or more observables.
I would appreciate suggestions relevant to any branch of Physics, ...
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Is there a reason why $\det(g)$ is a scalar density of weight 2 and not 1, 3 or 4?
$\det(g)$ is not coordinate-independent - it is a scalar density of weight +2 (or −2 depending on convention) which generally changes across spacetime. In Minkowski space equipped with spherical polar ...
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Connectivity of random geometric graph with open boundary conditions
I have a question regarding the existence of a closed-form solution of the connectivity in terms of the radius of vertices (disks) in a two-dimensional ($d=2$) random geometric graph (RGG) with open ...
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Could a human-sized flea really jump over the Eiffel Tower?
I am puzzled why so many people think such a large flea could jump as high as the Eiffel Tower. We know that a 3mm long flea can jump 150mm, which is 50 times its own length. So I suppose it's ...
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Landau/Lifshitz "Mechanics" Mechanical Similarity
In Landau/Lifshitz "Mechanics", 3e, subsection 10, a question asks to "find the ratio of the times in the same path for particles having the same mass but potential energies differing ...
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Is there a relatively quick way to obtain the scale factor on the metric as a response to special conformal transformation on spacetime?
For a special conformal transformation on spacetime positions $$x'^\mu=\frac{x^\mu-x^2b^\mu}{1-2b\cdot x+b^2x^2}$$
I was able to derive the scale factor $$\eta'_{\mu\nu}=\Omega(x)\eta_{\mu\nu}$$by ...
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How does safe fall distance scale with the size of an animal?
An animal has a maximum safe fall distance, the distance it can fall without getting hurt.
If you take an animal and a similar animal twice as large, what would we expect to hold about the maximum ...
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Time scale of earthquake simulations on scaled building models
The effect of earthquakes on a building can be investigated by creating a scaled down model of the building, and simulate an earthquake on a shake table.
A recording of a natural earthquake can be ...
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A Problem in Scaling
Question: - If the size of the nucleus (in the range of $10^{-15} m$ to $10^{-11} m $) is scaled up to the tip of a sharp pin, what roughly is the size of an atom? (Assume the tip of the pin to be in ...
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Dependence of phase transition on scale factors
In a numerical experiment, I have obtained a phase diagram of the system under study. The phase diagram is obtained between two scaled quantities say, $P^{\prime}$ and $Q^{\prime}$ of the system. I ...
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Normalized units versus dimensionless units
In a molecular dynamics code, suppose, the distances are expressed in units of a characteristic length of the simulated system, $R_0$. In some papers it is written as, " distances are normalized ...
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