Klas Modin PRO
Mathematician at Chalmers University of Technology and the University of Gothenburg
Installation
git clone https://github.com/klasmodin/quflow.git
cd quflow
pip install .Basic concepts
Classical
function \(\omega:S^2\to\mathbb{R}\)
spherical harmonics \(\omega = \sum_{l=0}^\infty\sum_{m=-l}^l\omega^{lm}Y_{lm}\)
Quantized
complex matrix \(W\in\mathfrak{u}(N)\)
matrix harmonics \(W = \sum_{l=0}^N\sum_{m=-l}^l\omega^{lm}T_{lm}\)
import quflow as qf
omega = np.random.randn(10)
N = 512
W = qf.shr2mat(omega, N)
qf.plot(W)Units of time
Classical time: seconds
Quantum time: qtime
1 second = \(\displaystyle\frac{1}{\sqrt{16\pi}}N^{3/2}\) qtime
General rule:
- numerical parameters use qtime (e.g. stepsize)
- physical parameters use second (e.g. total simulation time)
import quflow as qf
N = 512
print(qf.seconds2qtime(1.0, N))
print(qf.qtime2seconds(1.0, N))Running simulations
High-level solve function:
- initial data \(W_0\in\mathfrak{u}(N)\)
- simulation step-size (qtime)
- total simulation time (seconds)
- inner simulation time (seconds)
(how often callback) - callback function (typically QuData object)
import quflow as qf
N = 128
W0 = qf.shr2mat(np.random.randn(10), N)
h = 0.1
mysim = qf.QuData("mysim.hdf5")
mysim(W0, 0.0) # Save first output
qf.solve(W0, qstepsize=h, time=3.0, inner_time=0.2, callback=mysim)
mysim.flush()Generic smooth initial data
Generic vanishing momentum smooth initial data
Brief demo of QUFLOW
By Klas Modin
Brief demo of QUFLOW
Demonstration of the Python software QUFLOW for simulation of Euler's equations on the sphere.
