# Questions tagged [optimization]

The process of determining the best solution among all possible solutions given a set of constraints.

93 questions
Filter by
Sorted by
Tagged with
50 views

### Can anyone explain convergence of parallel rays on the focus of a parabolic reflector using Fermat's Principle?

Can anyone explain convergence of parallel rays on the focus of a parabolic reflector using Fermat's Principle? using optimization techniques from calculus?
73 views

### Find shape of minimum resistance between two points given a fixed volume of conductor

I am given a homogenous volume $F$ of isotropic conductor with resistivity $\rho$. I need to allow current to flow from Point A to B which are a distance $L$ away from each other. I can shape the ...
• 132
1 vote
40 views

### Defining the Problem Hamiltonian for Quantum Annealing in Solving the Shortest Path Problem [closed]

I’m currently studying quantum annealing and its application to solving the shortest path problem. However, I’m facing challenges in defining the problem Hamiltonian, whose ground state should encode ...
• 11
1 vote
35 views

### What is the physical explanation for $cm(h_{min})= h_{min}$ when minimising the centre of mass of a can of coke?

There's an undergraduate statics problem that is about finding the lowest centre of mass of a coke can as it is emptied out (say through a weightless straw). The problem itself is not difficult and ...
• 11
112 views

### Optimal position of negative charge to "neutralise" a positive distribution

This question stems from trying to understand the notion of center of charge and if the analytical definition of this center depends on what exactly is minimized (the dipole moment or the total ...
• 5,078
24 views

### Procedure to accurately extract the instantaneous velocity and spin information from experimental position data?

I have the time information of 3D position data (discrete) of a sports ball in flight, and I'm attempting to extract the velocity and spin information just using that data as I believe every ...
1 vote
100 views

### Reformulating problem into form of Ising Hamiltonian

The Ising Hamiltonian has the following form: $$H= -\sum_{j<k}J_{j,j+1}\sigma_j\sigma_{j+1}-\sum_{j} h_j\sigma_j + \varepsilon,$$ Where $\sigma$ are the spins that take values of $\pm$ 1 I have a ...
111 views

### Tipping a cylinder [closed]

A horizontal force is applied to the top of a cylinder, creating a torque on it trying to tip it over. Now I have wondered to what height should the cylinder be filled with water to render it most ...
• 25
68 views

### Rocket propulsion energy efficiency

What ratio of final to initial mass of a rocket to achieves the highest energy efficiency - the highest ratio of final mass kinetic energy to chemical energy expended? And more generally the relation ...
• 39
1 vote
85 views

### Mapping an arbitrary spin graph to one with nearest neighbour interactions

I remember having heard once that generic spin-graphs e.g. Ising, or at least 2-local ones (defined as the Hamiltonian contains pairwise interactions at most), can always be mapped to one another one (...
• 1,620
1 vote
123 views

### Difficulty solving conformal-bootstrap-like crossing equations using semidefinite-programming (SDP) via SDPB software

My question involves semidefinite programming (SDP) in the sense of attempting to find some vector $\alpha^{\mu}$ that satisfies the following conditions: Normalisation: $\alpha^{\mu}n_{\mu} = 1$ ...
1 vote
68 views

• 286
48 views

### Can the energy of a physical system be described as an unconstrained optimisation problem?

Sorry if this is something that is well known, not really familiar with modern physics beyond high school / introductory undergrad level. I largely work in deep learning and broadly speaking, you can ...
• 103
273 views

### Brachistochrone to a vertical line [closed]

Just for fun, I am working through some problems in Mathematics of Classical and Quantum Physics by Byron and Fuller. Problem 2.13 reads: Prove that a particle moving under gravity in a plane from a ...
89 views

### Application of KT?

I am not familiar with physics and I am lost about how should I actually apply this to the result from the computer simulation. I would like to apply 𝑘𝐵𝑇 to the results of the computational ...
• 101
1 vote
36 views

### Convex optimisation for holomorphic functions [closed]

Convexity/concavity are useful properties of a function when performing optimisation, as one can rest assured that the found solution is the global minimum/maximum. For a real function of one or two ...
1 vote