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Questions tagged [optimization]

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

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38 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 ...
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0answers
35 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 ...
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29 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 ...
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1answer
61 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. ...
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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 ...
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29 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 ...
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Optimizing interatomic potentials for lattice dynamics calculations

Context: I'm trying to calculate the $\mathbf{q}=0$ vibrational modes of a crystal given the experimentally determined structure in the framework of a rather simplified model. Background: DFT methods ...
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77 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 ...
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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 ...
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1answer
61 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 ...
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2answers
35 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 ...
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1answer
106 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 ...
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1answer
995 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 ...
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2answers
151 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 ...
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187 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 (...
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68 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. ...
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1answer
109 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 ...
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74 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 ...
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159 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 ...
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2answers
320 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. ...
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1answer
72 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 ...
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0answers
142 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 ...
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1answer
699 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 ...
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1answer
94 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 ...
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1answer
129 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, $r$. ...
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1answer
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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0answers
53 views

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 ...
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1answer
72 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 ...
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5answers
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 ...
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0answers
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 ...
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2answers
206 views

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 $(v_x, v_y)$. It also has a maximum acceleration $a_{max}$. Its goal is to be at position $(x', y')$ with a velocity of $...
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1answer
127 views

Optimal Airplane trajectory

The last time I took a plane the following problem crossed my mind. Setting: take the Earth and neglect its rotation around the Sun. It then only rotates on itself with angular velocity $\Omega$. ...
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460 views

Is it possible to work out the shortest time in which a body can travel a certain distance if all that is provided is the max a, max -a, v1, v2 and s?

Is it possible to calculate the shortest time it takes a body to travel a certain distance if the only information provided is its maximum acceleration, its maximum retardation and the distance it ...
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1answer
414 views

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 ...
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1answer
125 views

what's the world record in finding the ground state of the 3D Ising model

Finding the ground state of the 3D ising model (with no magnetization) is known to be NP-complete. Just wondering what is the biggest size cubic lattice someone has found the ground state of for this ...
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5answers
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Number of blades in a helicopter rotor

I was wondering how it is possible to determine what is the optimal number of blades in a helicopter rotor. I think that the length of the blade is involved as a longer blades would have to spin ...
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1answer
9k views

Help finding Delta T for a known position displacement with known accel/decel, etc

I'm looking for an equation to find the time it will take for a position displacement to happen, given known $V_{max}$, a (known) constant acceleration, deceleration, jerk, and displacement... and an ...
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4answers
694 views

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 ...
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1answer
260 views

What lifting mechanism is likely to have the best energy recovery ratio? [closed]

Suppose I was designing an apparatus which needed to lift 250kg 5cm high, hold it there for a few seconds, and then lower the object back to the original height. Such a process would need to be ...
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2answers
1k views

Utilizing maximum acceleration $a$ for displacement $d$ with initial velocity $v_0$ and final velocity $v_1$

Problem My goal is to move an object from point a to b (displacement $d$) as fast as possible utilizing the maximum available acceleration $a_{max}$, taking into account the initial velocity $v_0$ ...
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2answers
125 views

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

Given an Ising model, we have the energy formula: $E= - \sum_i h_i S_i - \sum_{i \neq j} J_{ij} S_i S_j$ and we have the probability of a given state, given the energy of that state and the ...
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113 views

Pareto efficiency and Standard Model parameters

Pareto Efficiency is a well understood concept in economics, which basically is a condition where no one actor could be made better off without some one being made worse off. This condition allows ...
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Dual methods in structure optimization

I am studying Structure Optimization, and the teacher took a few weeks to detail dual methods, but I don't get why it is useful. From an optimization problem with n...
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1answer
2k views

What are the optimal shapes, if any, for fractal antennae?

A DIY fractal antenna project is described at http://www.htpc-diy.com/2012/04/diy-flexible-fractal-window-hdtv.html Mainly idle curiosity, but I was wondering what the principles behind these might ...
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1answer
151 views

Good algorithm for in-experiment 1-D optimization?

I'm running an experiment -- for the question, it doesn't matter which one, but I'm measuring an optical intensity $I$ as a function of two parameters: reflection angle $\theta$ and wavelength $\...
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3answers
1k views

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 ...
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2answers
852 views

The Double Integrator: Matching velocity and position as quickly as possible with only a limited amount of force available

If a body with mass $m$ begins at position $x_0$ with velocity $v_0$ and experiences a force that varies as a function of time $f(t)$ (and we ignore gravity, friction, and everything else that might ...
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5answers
1k views

Maximal Gravity

I found this interesting problem in Introduction to Classical Mechanics with Problems and Solutions by David Morin: Given a point $P$ in space, and given a piece of malleable material of constant ...