# Questions tagged [optimization]

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

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### Why does current arrange itself in such a way as to minimize power loss in resistors connected in parallel?

In problem 2 in Problem Set 6, it is said: "Electricity prefers to flow in the way that minimizes energy loss to resistance." Using Lagrange multipliers I was able to show that assuming the above ...
18 views

### Optimising equation with 3 or more changable variables

In order not to bother you with technical details I've laid my therms in plain math. The sets are experimentally obtained mechanical characteristics, and unknowns are some empirical parameters from ...
29 views

### How to position table legs to distribute weight optimally? [closed]

Background I'm building a table using 4 table legs and a table top. The table top, made out of wood, tends to be quite elastic. Yet, I want the table to be able to hold heavy objects without worrying ...
31 views

### Lagrangian Mechanics to solve arbitrary maximization problem

I've been thinking for some time about how to better find the optimal weights for neural networks and it struck me that when solving Lagrangian mechanics problem you are optimizing the action function....
55 views

### Optimal trajectory of rocket with variable specific impulse and constant power

I am trying to derive trajectory of rocket with variable specific impulse and given power of engines $P$ that minimizes the total time. The specific impulse is given as time-variable effective exhaust ...
29 views

### Attaining extrema when a stationarity condition has no solution

I was wondering if someone could shed some light on the following for me: If a stationarity (maximizing or minimizing) condition has no solution inside a particular domain, then how do we reason that ...
185 views

### Ising to QUBO mapping for quantum annealing

I'm trying to solve an optimisation problem by simulating quantum annealing using the path-integral Monte Carlo Metropolis approach. So far I have formulated the problem as an Ising model with the ...
37 views

### Why Euler-Lagrange Theorem gives the optimal control law? [closed]

Can anyone explain me in simple language why applying Euler-Lagrange Theorem on Hamiltonian equations gives the optimal control law? I am specifically talking about trajectory optimization problems ...
31 views

### Optimally cooling a cup of broth

Say I have a cup of broth with volume V1 and it's too hot to drink. I want to cool it down as quickly as possible. the current temp of the cup is T1 I want to drink the cup when it cools to T2 I have ...
103 views

### Control systems from a physicists perspective

I am highly interested in the study of control systems theory. However it seems that almost all books are written by electronics or mechanical engineers. Due to this they generally omit many things. ...
24 views

### Designing capacitor or resistor systems where capacitor or resistor can bear limited voltage

A capacitance of $2\ \mu F$ is required in an electrical circuit across a potential difference of $1.0\ kV$. A large number of $1\ \mu F$ capacitors are available which can withstand a potential ...
30 views

### Numerical optimisation over quantum states/measurements

Suppose we need to find a quantum state and set of measurement basis that optimise a given function of these parameters. This is quite common for e.g. in finding optimal violation of some bell ...
95 views

### Minimizing entropy generation in storing heat

I am working on a cogenerative PV (Photovoltaic) array. The idea is to generate electricity from the solar cells while cooling them to both increase solar conversion efficiency and extract waste heat ...
37 views

### Improving classical processors with simulation or optimization on a quantum computer?

Two classes of applications for quantum computers are (1) solving constrained optimization problems [example] and (2) ab initio simulation of quantum systems [review]. Have there been any concrete ...
73 views

### Maximising velocity at B when rolling down the curve between A and B

I would like to build a curve between two points A and B. A ball would roll down the curve in a gravitational uniform field (i.e., I'm actually going to build the thing here on Earth). My question ...
184 views

### Quantum Approximate Optimization Algorithm

I try to understand the 'Quantum Approximate Optimization Algorithm' (QAOA) by Farhi et al. - arXiv:1411.4028. I understand that the solution is hidden in the unitaries, but I do not understand how ...
42 views

### Optimization problem and measurements

This is more of math problem, but my doubt is about the measurement units of the final answer so I figured I'd post it here. Problem: A lighthouse is located on a small island 3 km away from a ...
117 views

### Rigidity of a material with respect to its structure

Suppose I have some material like graphene that I shaped in some structure (honeycomb, triangular lattice), then it would have a different rigidity according to the structure. My question is, how can ...
1k views

### Non-uniform Circular motion velocity optimization

Consider the following problem: A vehicle (modeled as a particle) enters into a circular arc trajectory at point $s_1$ (given), see figure below. If at $s_2$ the speed of the vehicle is not to ...
174 views

### 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 ...
192 views

### What trajectory minimizes the time traveling between two points under constant acceleration given initial and final position and velocity?

I have asked this question in the math SE but no one there knew an answer; there are similar questions here but they differ a bit from what I am trying to understand. I was wondering if there is an (...
75 views

### When does “solve and plugin” fail?

In Lagrangian mechanics, sometimes some symmetry is implicit, and we perform variation on the Lagrangian and find the conserved quantity, e.g. conservation of angular momentum in a central field. ...
116 views

### Optimal axis of rotation of a baseball for lateral movement

Suppose a baseball travels at $90\;\mathrm{mph}$; what is the ideal axis of rotation for lateral movement of the ball? (two-seamer or cutter). So far I think that the following factors play a ...
82 views

### Can you help me solve this using the current value Hamiltonian? [closed]

Okay, so I am getting a little stuck on this question, I will post it and then tell you how far I get. $$max - \int_0^2 (x^2 + u^2)e^{-0.03t}dt\,$$ $$x' = x-2u$$ $$x(0) = 3$$ $$x(2)free$$ ...
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### Maximize time of flight and range at the same time in projectile motion

Given the equations of projectile motion (no air resistance), it is easy to find the launching angle theta that produces the maximum range. That angle is 45 degrees. The maximum time of flight is ...
181 views

### What is the path taken by a “cable car”?

A well known result in variational calculus & Lagrangian Mechanics is the solution to the "brachistochrone" problem, where it is found the path connecting two points, A & B such that the time ...
367 views

### Optimal curve for a marble drop [closed]

I'm doing a marble roller coaster project for my physics class at school. The first part of our roller coaster involves a marble falling downwards into a curve that will drop then go up 12 inches. ...
74 views

### Optimizing the second, third,… eigenvalues - applications

I'm working on some topics related to spectral optimization as a function of the domain. For example it is known for almost a century (lord Rayleigh and Faber, Krahn) that the shape which minimizes ...
155 views

### Optimization of transfer matrix method for quarter wave stack

Does anyone have any tips for Matlab optimization algorithms to use with a 2x2 Transfer Matrix Method Program? I have written a Matlab function that takes a series of refractive index values and ...
753 views

### 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 ...
97 views

### Using differentials to optimize a function [closed]

I've read in a paper by Tevian Dray an alternative way to solve optimization problems manipulating "differentials". Here is an example of how it works (next I quote the paper). Consider the problem ...
251 views

### What is Optimal Control Theory and Controllability Theory?

I was exploring the methods to analyze the evolution of a system from one quantum state to another using a suitable Hamiltonian. Some searching led me to the keywords Controllability Theory and ...
131 views

### Optimal size of a windmill for a given windspeed

Here is the problem: Assume that you have some constant wind speed. I want to run a windmill but I need to decide how big a windmill I want. The size is characterized by the length of the blades, $r$. ...
1k views

### Physics problems requiring optimization? [closed]

I would like to know if there are simple benchmark physics problems to test a Genetic Algorithm C++ library I developed. The library supports single and multi-objective constrained optimization and I ...
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### Coefficients and Parameters for contracted Gaussian basis sets

This is a repost from Chemistry.stackexchange in the hopes that someone here will be able to help me. Any help at all would be greatly appreciated. As far as I understand, an STO-NG contracted ...
73 views

### Converting Point Gradients to Rotational Representation

I'm a PhD student in an unrelated field. It's been a very long time since I've done physics, and I've run into a problem in my research which I think is actually a physics problem. Basically, I have ...
2k views

### What is the best path for a given initial and final state?

I am trying to calculate an efficient acceleration curve given starting and final positions and velocities. I'm assuming no friction, and that the acceleration can be applied in any direction at any ...
166 views

### Particle Collision with Static System

I have a system of particles with equal distance with each other and another at random positions which is moving with time. What I want to know is : The method by which I can reduce the number of ...