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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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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?
Sachin Kalakoti's user avatar
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2 answers
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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 ...
Milind R's user avatar
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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 ...
CBM's user avatar
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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 ...
capstain's user avatar
2 votes
1 answer
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 ...
Quillo's user avatar
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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 ...
PASUNURU SAI VINEETH's user avatar
1 vote
1 answer
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 ...
LieAlgebraGuy1999's user avatar
2 votes
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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 ...
Ahdriam's user avatar
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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 ...
ddddmmmm's user avatar
1 vote
1 answer
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 (...
Wouter's user avatar
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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: $\alpha^{\mu}n_{\mu} = 1$ ...
user8675309's user avatar
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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. \...
brzepkowski's user avatar
3 votes
1 answer
207 views

Lagrange multipliers $\lambda$ in Nonholonomic systems and Costates $\lambda$ in Optimal control theory

In Structure and Interpretation of Classical Mechanics, Section 1.10.3 by Sussman & Wisdom, talking about systems with non-holonomic constraints, it says the following about the Lagrange equations ...
Thomas Antony's user avatar
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How to mathematically express and then optimize my photon emitter? [closed]

A laser shoots photons directly at a flat disk with a fixed linear rate f(t) on the interval [t0=a,tn=b] with a horizontal path. E.x. f(t)=100 photons per second The laser is controlled by robotic ...
nsc9's user avatar
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2 votes
2 answers
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Shape of fastest spinning rod

A one-meter steel rod of variable thickness is attached at one end to a spinning hub. The cross-sectional area of the rod is a function $f(x)$ of the distance $x$ in meters from the hub, x ranging ...
causative's user avatar
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Does nature perform optimal linear quadratic control?

Given any linear quadratic control problem $$\min \sum_t c_x(x_t, t) + c_u(u_t, t)$$ where $u_t$ is a "control variable" (think of it as an adjustable velocity) and $x_t$ is a "state ...
MaudPieTheRocktorate's user avatar
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Minimum time passed for stationary observer at destination in relativistic physics

While my friend and I were discussing about relativistic physics, we came up with the following question. Suppose a person $P$ wanted to travel from point $A$ to point $B$ in one-dimensional space. ...
Prajith Velicheti's user avatar
1 vote
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79 views

How to calculate degrees of freedom?

Background I am trying to run optimizations on a multilink (car-) suspension. That is each link is defined by two points, one on the vehicles body, one on the wheel mount. There are 5 links in total, ...
fho's user avatar
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2 votes
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How are conjugate variables in mechanics and stat mech related to duality in convex optimization?

I recently studied duality in optimization where a primal optimization problem can be casted as a dual problem which provides meaningful lower bounds on the primal. There is also a notion of conjugate ...
Kevin's user avatar
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Why do we maximize according to the values of Lagrange multipliers?

In some Lagrangian problems, when we use the lagrange multipliers to minimize a function $f(x)$ they write: \begin{equation} \max_{\lambda,\mu} \min_{x}\mathcal{L} = \max_{\lambda,\mu}\min_{x} \Big( ...
Remember's user avatar
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2 votes
1 answer
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Given a path and maximum acceleration, what is the minimum time to reach the end?

As stated in the title, I want to find an expression or a way to calculate the minimum time to go from one point of a path to another when the path is given and acceleration is restricted. Thus far, I ...
110112345's user avatar
1 vote
0 answers
32 views

2D boundary value problem for planetary lander [closed]

I'm solving a 2D lander guidance problem where a planetary lander must be guided to a safe landing spot on an arbitrary terrain. The specific method I'm coding use methods similar to RRT/RRT* motion ...
Kevin Charls's user avatar
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1 answer
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Optimizing a Capacitance function

I am trying to find the optimum values, in order to maximize the following equation: $$ C (L, (b/a)) =\frac{L 2\pi k\epsilon_0}{\ln(b/a)} $$ where $$ \frac{dC}{d(b/a)} = -\frac{L2\pi k\epsilon_0 \ln(b/...
STOI's user avatar
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1 answer
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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 ...
ashenoy's user avatar
  • 103
2 votes
2 answers
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 ...
OmnipotentEntity's user avatar
0 votes
1 answer
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 ...
DGKang's user avatar
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0 answers
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 ...
user avatar
1 vote
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71 views

Optimal control of a damped harmonic oscillator through a lossy, dispersive medium

Say a damped harmonic oscillator is at the far end of a dispersive, lossy medium governed by, say, Debye relaxation. I would like to determine what the optimal arbitrary input waveform is to obtain ...
0xDBFB7's user avatar
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3 votes
3 answers
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Maximum horizontal distance of a freefalling ball with one allowed bounce anywhere along its initial path?

I was washing a spoon in the sink and this question popped into my mind: If a ball is dropped from height H and is allowed a single deflection of any angle $0 < \theta < 180$ at any height $ 0 \...
JS_Riddler's user avatar
2 votes
0 answers
116 views

For discrete optimization problems, why does continuous approximation - solving - discretization work?

I was wondering about the following question. In maths/computer science, many optimization problems ask for integer optimizations. A prominent example would be spin-glass (Ising) systems for simulated ...
edan9891's user avatar
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2 answers
185 views

Variational method: Why do parameters differ for two trial functions (optimization)?

Below the potential and trial functions: $$V(x)=(x^2-1)^2-x^2$$ Use the variational method with the two trial wave functions: $$\psi_{\pm}(x)=A\left(e^{-\frac{(x-x_0)^2}{2\sigma^2}}\pm e^{-\frac{(x+...
Sant Man's user avatar
5 votes
1 answer
426 views

Could two concatenated cycloids be an optimal solution to the Brachistochrone problem?

The following is a specific instance of the brachistochrone problem, which I first encountered in grad school, and I have occasionally used as hw problem in teaching CM. A particle is started from ...
Thomas's user avatar
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1 vote
1 answer
61 views

Optimizing engines to produce a certain torque and net force

Say we have $n$ engines sitting on a rigid body. Each engine has position $R_i$ and points in a certain direction and generates a force in that direction, $F_i$. The magnitude of that force ($k_i$) ...
Rubydesic's user avatar
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1 vote
0 answers
28 views

What methods can I use to find the minimum of a tranverse field Ising model?

I am trying to solve for the minimum of the hamiltonian of the form: $$ H = \sum_{i,j} J_{ij}q(i)q(j) + g_i\sum_i x(i) $$ where q(i) is the operator (I + z(i))/2 and z(i) and x(i) are pauli operators ...
rosaniline's user avatar
1 vote
0 answers
60 views

Black Hole Coin curve

I've seen a toy at my local pharmacy called The Black Hole that lets you insert a quarter into a vertical slot. The quarter starts rolling around a curved funnel's circumference and slowly winds its ...
Michael 's user avatar
1 vote
0 answers
350 views

Minimizing a Line Integral of a Vector Field Using Euler-Lagrange---Problem with Boundary Conditions

Let $F:\mathbb{R}^2\rightarrow\mathbb{R}^2$ be the following vector field: $$F(x,y)=\left< x\cdot p(x,y(x)), y(x)\cdot p(x,y(x))\right>$$ where $$p(x,y(x)) = \frac{5x}{6} + \frac{7 x^2}{4} + \...
Jason Konek's user avatar
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1 answer
72 views

How to minimise sum potential of the system?

Given $m$ number of immobile electric charges at some points of the plane. We want to place $n$ number of further charged particles (not including the fixed charges) along a circle centered at the ...
Joe Rakhimov's user avatar
3 votes
0 answers
420 views

Can quantum computing solve the curse of dimensionality?

The curse of dimensionality is ubiquitous in machine learning (ML) modeling, stochastic control and reinforcement learning, arising in a probabilistic sense, with strong connections to quantum ...
kbakshi314's user avatar
  • 2,402
0 votes
0 answers
135 views

How to maximize overlap integral

my question is on finding the function $p(x)$ that maximizes the overlap integral $\int_{-\infty}^{+\infty} f(x)p(x) dx$, where the site condition $\int_{\infty}^{+\infty} p(x)dx=1$ holds (of course ...
Roy's user avatar
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3 votes
1 answer
155 views

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 ...
Andrew Paul's user avatar
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0 answers
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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 ...
barefoot_fiki's user avatar
3 votes
0 answers
4k 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 ...
Eti's user avatar
  • 131
2 votes
0 answers
87 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....
Beacon of Wierd's user avatar
1 vote
1 answer
120 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 ...
Irigi's user avatar
  • 444
1 vote
1 answer
39 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 ...
J. Emilio's user avatar
2 votes
1 answer
649 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 ...
AlexAbrahams's user avatar
1 vote
0 answers
61 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 ...
Esi's user avatar
  • 11
0 votes
0 answers
47 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 ...
Alexander Mills's user avatar
5 votes
3 answers
1k views

Control systems from a physicist's 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. ...
1 vote
0 answers
34 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 ...
ghosts_in_the_code's user avatar