Questions tagged [optimization]
The process of determining the best solution among all possible solutions given a set of constraints.
96 questions
2 votes
1 answer
60 views
How to minimise jettisoned mass spent for a body with continuous but variable thrust?
In general I would like to know how to minimise fuel mass spent for an orbiting body that continuously jettisons its mass (i.e. ion thruster) so as to perform efficient transfer maneuver in ...
- 31
0 votes
0 answers
55 views
What is the spin-glass analogue of random LinSAT over $\mathbb{F}_p$?
Boolean variables $\vec{x} \in \{0,1\}^n$ can be mapped to Ising spins $\vec{z} \in \{-1,+1\}^n$ via the relation $z_i = (-1)^{x_i}$. Under this mapping, a sparse XORSAT clause such as $$ x_1 \oplus ...
- 11
1 vote
1 answer
76 views
Method for minimising mass and maximising surface area of a parachute
I am participating in an Egg drop challenge, I want to design a parachute so that its impact force is less than $20 \, \text{N}$ to ensure the egg's survival. To do so I would need to balance mass and ...
- 11
4 votes
2 answers
1k views
How to solve self-consistent equations numerically?
I am working in condensed matter, where I'm required to solve an integral self consistently which is of the form, $$ \Delta = \int f(x,y,\Delta,\mu,h)dxdy $$ Basically I need to find value of $\mu,\,\...
- 51
2 votes
0 answers
137 views
Multilateration of a light source in a medium whose index of refraction varies with position
Background I have a set of $N$ receivers whose locations in $3D$ space are well-known. These receivers are immersed in a medium whose index of refraction (and thereby the velocity of light propagation)...
- 349
0 votes
2 answers
155 views
Find shape of minimum resistance between two points given a fixed volume of conductor
I am given a homogenous volume $F$ of isotropic conductor with resistivity $\rho$. I need to allow current to flow from Point A to B which are a distance $L$ away from each other. I can shape the ...
- 132
1 vote
0 answers
93 views
Defining the Problem Hamiltonian for Quantum Annealing in Solving the Shortest Path Problem [closed]
I’m currently studying quantum annealing and its application to solving the shortest path problem. However, I’m facing challenges in defining the problem Hamiltonian, whose ground state should encode ...
- 11
1 vote
1 answer
92 views
What is the physical explanation for $ cm(h_{min})= h_{min} $ when minimising the centre of mass of a can of coke?
There's an undergraduate statics problem that is about finding the lowest centre of mass of a coke can as it is emptied out (say through a weightless straw). The problem itself is not difficult and ...
- 11
2 votes
1 answer
213 views
Optimal position of negative charge to "neutralise" a positive distribution
This question stems from trying to understand the notion of center of charge and if the analytical definition of this center depends on what exactly is minimized (the dipole moment or the total ...
- 6,248
1 vote
1 answer
188 views
Reformulating problem into form of Ising Hamiltonian
The Ising Hamiltonian has the following form: $$H= -\sum_{j<k}J_{j,j+1}\sigma_j\sigma_{j+1}-\sum_{j} h_j\sigma_j + \varepsilon,$$ Where $\sigma$ are the spins that take values of $\pm$ 1 I have a ...
2 votes
0 answers
238 views
Tipping a cylinder [closed]
A horizontal force is applied to the top of a cylinder, creating a torque on it trying to tip it over. Now I have wondered to what height should the cylinder be filled with water to render it most ...
- 25
0 votes
1 answer
137 views
Rocket propulsion energy efficiency
What ratio of final to initial mass of a rocket to achieves the highest energy efficiency - the highest ratio of final mass kinetic energy to chemical energy expended? And more generally the relation ...
- 75
1 vote
1 answer
160 views
Mapping an arbitrary spin graph to one with nearest neighbour interactions
I remember having heard once that generic spin-graphs e.g. Ising, or at least 2-local ones (defined as the Hamiltonian contains pairwise interactions at most), can always be mapped to one another one (...
- 1,763
1 vote
1 answer
221 views
Difficulty solving conformal-bootstrap-like crossing equations using semidefinite-programming (SDP) via SDPB software
My question involves semidefinite programming (SDP) in the sense of attempting to find some vector $\alpha^{\mu}$ that satisfies the following conditions: Normalisation: $\alpha^{\mu}n_{\mu} = 1$ ...
- 31
1 vote
0 answers
140 views
How to obtain the goal function of DMRG by Lagrange multiplier method?
The goal of DMRG is to minimize the expectation value of energy, which can be written as $$ \frac{d}{d |\psi \rangle} \frac{\langle \psi | \hat{H} | \psi \rangle}{\langle \psi | \psi \rangle} = 0. \...
- 429