Why is this “the” functional of Laplace’s equation?

Halfway through a discussion of the finite element method for solutions to Laplace’s equation, Sadiku (2000) drops in a formulation of the work functional for an electric field: Algebraically and physically, I buy this–it looks like a true statement to me. But why bring this in? It motivates the rest of the algebra, true, but … Read more

Control systems from a physicist’s perspective

Before answering, please see our policy on resource recommendation questions. Please write substantial answers that detail the style, content, and prerequisites of the book, paper or other resource. Explain the nature of the resource so that readers can decide which one is best suited for them rather than relying on the opinions of others. Answers … Read more

Determining the probability of a particular site having a particular spin in an Ising model

Given an Ising model, we have the energy formula: E=−∑ihiSi−∑i≠jJijSiSj and we have the probability of a given state, given the energy of that state and the temperature: P({S})∼e−E({S})/kT (where the normalization constant is the partition function). The question I am interested in is if there is a computationally efficient way to determine (or at … Read more

Physics problems requiring optimization? [closed]

Closed. This question is off-topic. It is not currently accepting answers. Want to improve this question? Update the question so it’s on-topic for Physics Stack Exchange. Closed 7 years ago. Improve this question I would like to know if there are simple benchmark physics problems to test a Genetic Algorithm C++ library I developed. The … Read more

How long does it take to optimally change position and velocity?

A spaceship moving in two dimensions is at position (x,y) and has a velocity (vx,vy). It also has a maximum acceleration amax. Its goal is to be at position (x′,y′) with a velocity of (v′x,y′x). What path takes the smallest amount of time? I see that the problem can be reduced to a spaceship at … Read more

Optimization of Bottle Rocket Water Level

My (entry-level) physics class is building bottle rockets, and we are competing to build the longest-flying bottle rocket. The rockets are filled partway (we get to decide how much to fill them) with water, placed on the launcher, and filled with compressed air to a certain arbitrary pressure, the value of which will be the … Read more

What are circles on broth (eating soup) surface?

Think about broth in the soup, usually it has circles on its surface. What are their properties? Why there are many of them (not a few big blobs)? Are they depended on liquid’s temperature? What needs to be added to water so these kind of circles appear? I can only guess that it is because … Read more

Is there a closed form solution to the Esdale river problem?

This is probably not well known problem but it looks like open problem. What kind of methods there are to find a closed form solution to the physical situation? Can you solve this problem? You’re passively flowing downstream in the middle of a river that has its fastest flow in the middle. Most places along … Read more

How does the shape (form; not cross-section) of a spring impact performance?

Cylindrical compression springs are everywhere and then some applications choose other forms like rectangular or unique polygonal form. What impact does the form of a compression spring have and how do you calculate an optimal solution? Answer I could find a site which describes about the variations in spring designs, mainly attributed to the usage … Read more