Metadata-Version: 2.1
Name: PySDM
Version: 2.72
Summary: Pythonic particle-based (super-droplet) warm-rain/aqueous-chemistry cloud microphysics package with box, parcel & 1D/2D prescribed-flow examples in Python, Julia and Matlab
Home-page: https://github.com/open-atmos/PySDM
Author: https://github.com/open-atmos/PySDM/graphs/contributors
Author-email: sylwester.arabas@agh.edu.pl
License: GPL-3.0
Project-URL: Tracker, https://github.com/open-atmos/PySDM/issues
Project-URL: Documentation, https://open-atmos.github.io/PySDM
Project-URL: Source, https://github.com/open-atmos/PySDM
Description: # PySDM
        
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        PySDM is a package for simulating the dynamics of population of particles. 
        It is intended to serve as a building block for simulation systems modelling
          fluid flows involving a dispersed phase,
          with PySDM being responsible for representation of the dispersed phase.
        Currently, the development is focused on atmospheric cloud physics
          applications, in particular on modelling the dynamics of particles immersed in moist air 
          using the particle-based (a.k.a. super-droplet) approach 
          to represent aerosol/cloud/rain microphysics.
        The package features a Pythonic high-performance implementation of the 
          Super-Droplet Method (SDM) Monte-Carlo algorithm for representing collisional growth 
          ([Shima et al. 2009](https://rmets.onlinelibrary.wiley.com/doi/abs/10.1002/qj.441)), hence the name. 
        
        There is a growing set of example Jupyter notebooks exemplifying how to perform 
          various types of calculations and simulations using PySDM.
        Most of the example notebooks reproduce results and plot from literature, see below for 
          a list of examples and links to the notebooks (which can be either executed or viewed 
          "in the cloud").
        
        There are also a growing set of [tutorials](https://github.com/open-atmos/PySDM/tree/main/tutorials), also in the form of Jupyter notebooks.
        These tutorials are intended for teaching purposes and include short explanations of cloud microphysical 
          concepts paired with widgets for running interactive simulations using PySDM.
        Each tutorial also comes with a set of questions at the end that can be used as homework problems.
        Like the examples, these tutorials can be executed or viewed "in the cloud" making it an especially 
          easy way for students to get started.
        
        PySDM has two alternative parallel number-crunching backends 
          available: multi-threaded CPU backend based on [Numba](http://numba.pydata.org/) 
          and GPU-resident backend built on top of [ThrustRTC](https://pypi.org/project/ThrustRTC/).
        The [`Numba`](https://open-atmos.github.io/PySDM/PySDM/backends/numba.html) backend (aliased ``CPU``) features multi-threaded parallelism for 
          multi-core CPUs, it uses the just-in-time compilation technique based on the LLVM infrastructure.
        The [`ThrustRTC`](https://open-atmos.github.io/PySDM/PySDM/backends/thrust_rtc.html) backend (aliased ``GPU``) offers GPU-resident operation of PySDM
          leveraging the [SIMT](https://en.wikipedia.org/wiki/Single_instruction,_multiple_threads) 
          parallelisation model. 
        Using the ``GPU`` backend requires nVidia hardware and [CUDA driver](https://developer.nvidia.com/cuda-downloads).
        
        For an overview of PySDM features (and the preferred way to cite PySDM in papers), please refer to our JOSS papers:
        - [Bartman et al. 2022](https://doi.org/10.21105/joss.03219) (PySDM v1).
        - [de Jong, Singer et al. 2023](https://doi.org/10.21105/joss.04968) (PySDM v2).
          
        PySDM includes an extension of the SDM scheme to represent collisional breakup described in [de Jong, Mackay et al. 2023](10.5194/gmd-16-4193-2023).   
        For a list of talks and other materials on PySDM as well as a list of published papers featuring PySDM simulations, see the [project wiki](https://github.com/open-atmos/PySDM/wiki).
        
        A [pdoc-generated](https://pdoc.dev/) documentation of PySDM public API is maintained at: [https://open-atmos.github.io/PySDM](https://open-atmos.github.io/PySDM) 
        
        ## Example Jupyter notebooks (reproducing results from literature):
        
        See [PySDM-examples README](https://github.com/open-atmos/PySDM/blob/main/examples/README.md).
        
        ![animation](https://github.com/open-atmos/PySDM/wiki/files/kinematic_2D_example.gif)
        
        ## Dependencies and Installation
        
        PySDM dependencies are: [Numpy](https://numpy.org/), [Numba](http://numba.pydata.org/), [SciPy](https://scipy.org/), 
        [Pint](https://pint.readthedocs.io/), [chempy](https://pypi.org/project/chempy/), 
        [pyevtk](https://pypi.org/project/pyevtk/),
        [ThrustRTC](https://fynv.github.io/ThrustRTC/) and [CURandRTC](https://github.com/fynv/CURandRTC).
        
        To install PySDM using ``pip``, use: ``pip install PySDM`` 
        (or ``pip install git+https://github.com/open-atmos/PySDM.git`` to get updates
        beyond the latest release).
        
        Conda users may use ``pip`` as well, see the [Installing non-conda packages](https://docs.conda.io/projects/conda/en/latest/user-guide/tasks/manage-pkgs.html#installing-non-conda-packages) section in the conda docs. Dependencies of PySDM are available at the following conda channels:
        - numba: [numba](https://anaconda.org/numba/numba)
        - conda-forge: [pyevtk](https://anaconda.org/conda-forge/pyevtk), [pint](https://anaconda.org/conda-forge/pint) and []()
        - fyplus: [ThrustRTC](https://anaconda.org/fyplus/thrustrtc), [CURandRTC](https://anaconda.org/fyplus/curandrtc)
        - bjodah: [chempy](https://anaconda.org/bjodah/chempy)
        - nvidia: [cudatoolkit](https://anaconda.org/nvidia/cudatoolkit)
        
        For development purposes, we suggest cloning the repository and installing it using ``pip -e``.
        Test-time dependencies can be installed with ``pip -e .[tests]``.
        
        PySDM examples constitute the [``PySDM-examples``](https://github.com/open-atmos/PySDM-examples) package.
        The examples have additional dependencies listed in [``PySDM_examples`` package ``setup.py``](https://github.com/open-atmos/PySDM/blob/main/examples/setup.py) file.
        Running the example Jupyter notebooks requires the ``PySDM_examples`` package to be installed.
        The suggested install and launch steps are:
        ```
        git clone https://github.com/open-atmos/PySDM.git
        pip install -e PySDM
        pip install -e PySDM/examples
        jupyter-notebook PySDM/examples/PySDM_examples
        ```
        Alternatively, one can also install the examples package from pypi.org by 
        using ``pip install PySDM-examples`` (note that this does not apply to notebooks itself,
        only the supporting .py files).
        
        ## Submodule organization
        ```mermaid
        mindmap
          root((PySDM))
            Builder
            Formulae
            Particulator
            ((attributes))
              (physics)
                DryVolume: ExtensiveAttribute
                Kappa: DerivedAttribute
                ...
              (chemistry)
                Acidity
                ...
              (...)
            ((backends))
              CPU
              GPU
            ((dynamics))
              AqueousChemistry
              Collision
              Condensation
              ...
            ((environments))
              Box
              Parcel
              Kinematic2D
              ...
            ((initialisation))
              (spectra)
                Lognormal
                Exponential
                ...
              (sampling)
                (spectral_sampling)
                  ConstantMultiplicity
                  UniformRandom
                  Logarithmic
                  ...
                (...)  
              (...)
            ((physics))
              (hygroscopicity)
                KappaKoehler
                ...
              (condensation_coordinate)
                Volume
                VolumeLogarithm
              (...)
            ((products))
              (size_spectral)
                EffectiveRadius
                WaterMixingRatio
                ...
              (ambient_thermodynamics)
                AmbientRelativeHumidity
                ...
              (...)
        ```
        
        ## Hello-world coalescence example in Python, Julia and Matlab
        
        In order to depict the PySDM API with a practical example, the following
          listings provide sample code roughly reproducing the 
          Figure 2 from [Shima et al. 2009 paper](http://doi.org/10.1002/qj.441)
          using PySDM from Python, Julia and Matlab.
        It is a [`Coalescence`](https://open-atmos.github.io/PySDM/PySDM/dynamics/collisions/sollision.html#Coalescence)-only set-up in which the initial particle size 
          spectrum is [`Exponential`](https://open-atmos.github.io/PySDM/PySDM/initialisation/spectra/exponential.html#Exponential) and is deterministically sampled to match
          the condition of each super-droplet having equal initial multiplicity:
        <details>
        <summary>Julia (click to expand)</summary>
        
        ```Julia
        using Pkg
        Pkg.add("PyCall")
        Pkg.add("Plots")
        Pkg.add("PlotlyJS")
        
        using PyCall
        si = pyimport("PySDM.physics").si
        ConstantMultiplicity = pyimport("PySDM.initialisation.sampling.spectral_sampling").ConstantMultiplicity
        Exponential = pyimport("PySDM.initialisation.spectra").Exponential
        
        n_sd = 2^15
        initial_spectrum = Exponential(norm_factor=8.39e12, scale=1.19e5 * si.um^3)
        attributes = Dict()
        attributes["volume"], attributes["multiplicity"] = ConstantMultiplicity(spectrum=initial_spectrum).sample(n_sd)
        ```
        </details>
        <details>
        <summary>Matlab (click to expand)</summary>
        
        ```Matlab
        si = py.importlib.import_module('PySDM.physics').si;
        ConstantMultiplicity = py.importlib.import_module('PySDM.initialisation.sampling.spectral_sampling').ConstantMultiplicity;
        Exponential = py.importlib.import_module('PySDM.initialisation.spectra').Exponential;
        
        n_sd = 2^15;
        initial_spectrum = Exponential(pyargs(...
            'norm_factor', 8.39e12, ...
            'scale', 1.19e5 * si.um ^ 3 ...
        ));
        tmp = ConstantMultiplicity(initial_spectrum).sample(int32(n_sd));
        attributes = py.dict(pyargs('volume', tmp{1}, 'multiplicity', tmp{2}));
        ```
        </details>
        <details open>
        <summary>Python (click to expand)</summary>
        
        ```Python
        from PySDM.physics import si
        from PySDM.initialisation.sampling.spectral_sampling import ConstantMultiplicity
        from PySDM.initialisation.spectra.exponential import Exponential
        
        n_sd = 2 ** 15
        initial_spectrum = Exponential(norm_factor=8.39e12, scale=1.19e5 * si.um ** 3)
        attributes = {}
        attributes['volume'], attributes['multiplicity'] = ConstantMultiplicity(initial_spectrum).sample(n_sd)
        ```
        </details>
        
        The key element of the PySDM interface is the [``Particulator``](https://open-atmos.github.io/PySDM/PySDM/particulator.html#Particulator) 
          class instances of which are used to manage the system state and control the simulation.
        Instantiation of the [``Particulator``](https://open-atmos.github.io/PySDM/PySDM/particulator.html#Particulator) class is handled by the [``Builder``](https://open-atmos.github.io/PySDM/PySDM/builder.html#Builder)
          as exemplified below:
        <details>
        <summary>Julia (click to expand)</summary>
        
        ```Julia
        Builder = pyimport("PySDM").Builder
        Box = pyimport("PySDM.environments").Box
        Coalescence = pyimport("PySDM.dynamics").Coalescence
        Golovin = pyimport("PySDM.dynamics.collisions.collision_kernels").Golovin
        CPU = pyimport("PySDM.backends").CPU
        ParticleVolumeVersusRadiusLogarithmSpectrum = pyimport("PySDM.products").ParticleVolumeVersusRadiusLogarithmSpectrum
        
        radius_bins_edges = 10 .^ range(log10(10*si.um), log10(5e3*si.um), length=32) 
        
        env = Box(dt=1 * si.s, dv=1e6 * si.m^3)
        builder = Builder(n_sd=n_sd, backend=CPU(), environment=env)
        builder.add_dynamic(Coalescence(collision_kernel=Golovin(b=1.5e3 / si.s)))
        products = [ParticleVolumeVersusRadiusLogarithmSpectrum(radius_bins_edges=radius_bins_edges, name="dv/dlnr")] 
        particulator = builder.build(attributes, products)
        ```
        </details>
        <details>
        <summary>Matlab (click to expand)</summary>
        
        ```Matlab
        Builder = py.importlib.import_module('PySDM').Builder;
        Box = py.importlib.import_module('PySDM.environments').Box;
        Coalescence = py.importlib.import_module('PySDM.dynamics').Coalescence;
        Golovin = py.importlib.import_module('PySDM.dynamics.collisions.collision_kernels').Golovin;
        CPU = py.importlib.import_module('PySDM.backends').CPU;
        ParticleVolumeVersusRadiusLogarithmSpectrum = py.importlib.import_module('PySDM.products').ParticleVolumeVersusRadiusLogarithmSpectrum;
        
        radius_bins_edges = logspace(log10(10 * si.um), log10(5e3 * si.um), 32);
        
        env = Box(pyargs('dt', 1 * si.s, 'dv', 1e6 * si.m ^ 3));
        builder = Builder(pyargs('n_sd', int32(n_sd), 'backend', CPU(), 'environment', env));
        builder.add_dynamic(Coalescence(pyargs('collision_kernel', Golovin(1.5e3 / si.s))));
        products = py.list({ ParticleVolumeVersusRadiusLogarithmSpectrum(pyargs( ...
          'radius_bins_edges', py.numpy.array(radius_bins_edges), ...
          'name', 'dv/dlnr' ...
        )) });
        particulator = builder.build(attributes, products);
        ```
        </details>
        <details open>
        <summary>Python (click to expand)</summary>
        
        ```Python
        import numpy as np
        from PySDM import Builder
        from PySDM.environments import Box
        from PySDM.dynamics import Coalescence
        from PySDM.dynamics.collisions.collision_kernels import Golovin
        from PySDM.backends import CPU
        from PySDM.products import ParticleVolumeVersusRadiusLogarithmSpectrum
        
        radius_bins_edges = np.logspace(np.log10(10 * si.um), np.log10(5e3 * si.um), num=32)
        
        env = Box(dt=1 * si.s, dv=1e6 * si.m ** 3)
        builder = Builder(n_sd=n_sd, backend=CPU(), environment=env)
        builder.add_dynamic(Coalescence(collision_kernel=Golovin(b=1.5e3 / si.s)))
        products = [ParticleVolumeVersusRadiusLogarithmSpectrum(radius_bins_edges=radius_bins_edges, name='dv/dlnr')]
        particulator = builder.build(attributes, products)
        ```
        </details>
        
        The ``backend`` argument may be set to ``CPU`` or ``GPU``
          what translates to choosing the multi-threaded backend or the 
          GPU-resident computation mode, respectively.
        The employed [`Box`](https://open-atmos.github.io/PySDM/PySDM/environments/box.html#Box) environment corresponds to a zero-dimensional framework
          (particle positions are not considered).
        The vectors of particle multiplicities ``n`` and particle volumes ``v`` are
          used to initialise super-droplet attributes.
        The [`Coalescence`](https://open-atmos.github.io/PySDM/PySDM/dynamics/collisions/collision.html#Coalescence)
          Monte-Carlo algorithm (Super Droplet Method) is registered as the only
          dynamic in the system.
        Finally, the [`build()`](https://open-atmos.github.io/PySDM/PySDM/builder.html#Builder.build) method is used to obtain an instance
          of [`Particulator`](https://open-atmos.github.io/PySDM/PySDM/particulator.html#Particulator) which can then be used to control time-stepping and
          access simulation state.
        
        The [`run(nt)`](https://open-atmos.github.io/PySDM/PySDM/particulator.html#Particulator.run) method advances the simulation by ``nt`` timesteps.
        In the listing below, its usage is interleaved with plotting logic
          which displays a histogram of particle mass distribution 
          at selected timesteps:
        <details>
        <summary>Julia (click to expand)</summary>
        
        ```Julia
        using Plots; plotlyjs()
        
        for step = 0:1200:3600
            particulator.run(step - particulator.n_steps)
            plot!(
                radius_bins_edges[1:end-1] / si.um,
                particulator.formulae.particle_shape_and_density.volume_to_mass(
                    particulator.products["dv/dlnr"].get()[:]
                )/ si.g,
                linetype=:steppost,
                xaxis=:log,
                xlabel="particle radius [µm]",
                ylabel="dm/dlnr [g/m^3/(unit dr/r)]",
                label="t = $step s"
            )   
        end
        savefig("plot.svg")
        ```
        </details>
        <details>
        <summary>Matlab (click to expand)</summary>
        
        ```Matlab
        for step = 0:1200:3600
            particulator.run(int32(step - particulator.n_steps));
            x = radius_bins_edges / si.um;
            y = particulator.formulae.particle_shape_and_density.volume_to_mass( ...
                particulator.products{"dv/dlnr"}.get() ...
            ) / si.g;
            stairs(...
                x(1:end-1), ... 
                double(py.array.array('d',py.numpy.nditer(y))), ...
                'DisplayName', sprintf("t = %d s", step) ...
            );
            hold on
        end
        hold off
        set(gca,'XScale','log');
        xlabel('particle radius [µm]')
        ylabel("dm/dlnr [g/m^3/(unit dr/r)]")
        legend()
        ```
        </details>
        <details open>
        <summary>Python (click to expand)</summary>
        
        ```Python
        from matplotlib import pyplot
        
        for step in [0, 1200, 2400, 3600]:
            particulator.run(step - particulator.n_steps)
            pyplot.step(
                x=radius_bins_edges[:-1] / si.um,
                y=particulator.formulae.particle_shape_and_density.volume_to_mass(
                    particulator.products['dv/dlnr'].get()[0]
                ) / si.g,
                where='post', label=f"t = {step}s"
            )
        
        pyplot.xscale('log')
        pyplot.xlabel('particle radius [µm]')
        pyplot.ylabel("dm/dlnr [g/m$^3$/(unit dr/r)]")
        pyplot.legend()
        pyplot.savefig('readme.png')
        ```
        </details>
        
        The resultant plot (generated with the Python code) looks as follows:
        
        ![plot](https://github.com/open-atmos/PySDM/releases/download/tip/readme.png)
        
        The component submodules used to create this simulation are visualized below:
        ```mermaid
         graph
            COAL[":Coalescence"] --->|passed as arg to| BUILDER_ADD_DYN(["Builder.add_dynamic()"])
            BUILDER_INSTANCE["builder :Builder"] -...-|has a method| BUILDER_BUILD(["Builder.build()"])
            ATTRIBUTES[attributes: dict] -->|passed as arg to| BUILDER_BUILD
            N_SD["n_sd :int"] ---->|passed as arg to| BUILDER_INIT
            BUILDER_INIT(["Builder.__init__()"]) --->|instantiates| BUILDER_INSTANCE
            BUILDER_INSTANCE -..-|has a method| BUILDER_ADD_DYN(["Builder.add_dynamic()"])
            ENV_INIT(["Box.__init__()"]) -->|instantiates| ENV
            DT[dt :float] -->|passed as arg to| ENV_INIT
            DV[dv :float] -->|passed as arg to| ENV_INIT
            ENV[":Box"] -->|passed as arg to| BUILDER_INIT
            B["b: float"] --->|passed as arg to| KERNEL_INIT(["Golovin.__init__()"])
            KERNEL_INIT -->|instantiates| KERNEL
            KERNEL[collision_kernel: Golovin] -->|passed as arg to| COAL_INIT(["Coalesncence.__init__()"])
            COAL_INIT -->|instantiates| COAL
            PRODUCTS[products: list] ----->|passed as arg to| BUILDER_BUILD
            NORM_FACTOR[norm_factor: float]-->|passed as arg to| EXP_INIT
            SCALE[scale: float]-->|passed as arg to| EXP_INIT
            EXP_INIT(["Exponential.__init__()"]) -->|instantiates| IS
            IS["initial_spectrum :Exponential"] -->|passed as arg to| CM_INIT
            CM_INIT(["ConstantMultiplicity.__init__()"]) -->|instantiates| CM_INSTANCE
            CM_INSTANCE[":ConstantMultiplicity"] -.-|has a method| SAMPLE
            SAMPLE(["ConstantMultiplicity.sample()"]) -->|returns| n
            SAMPLE -->|returns| volume
            n -->|added as element of| ATTRIBUTES
            PARTICULATOR_INSTANCE -.-|has a method| PARTICULATOR_RUN(["Particulator.run()"])
            volume -->|added as element of| ATTRIBUTES
            BUILDER_BUILD -->|returns| PARTICULATOR_INSTANCE["particulator :Particulator"]
            PARTICULATOR_INSTANCE -.-|has a field| PARTICULATOR_PROD(["Particulator.products:dict"])
            BACKEND_INSTANCE["backend :CPU"] ---->|passed as arg to| BUILDER_INIT
            PRODUCTS -.-|accessible via| PARTICULATOR_PROD
            NP_LOGSPACE(["np.logspace()"]) -->|returns| EDGES 
            EDGES[radius_bins_edges: np.ndarray] -->|passed as arg to| SPECTRUM_INIT
            SPECTRUM_INIT["ParticleVolumeVersusRadiusLogarithmSpectrum.__init__()"] -->|instantiates| SPECTRUM
            SPECTRUM[":ParticleVolumeVersusRadiusLogarithmSpectrum"] -->|added as element of| PRODUCTS
        
            click COAL "https://open-atmos.github.io/PySDM/PySDM/dynamics/collisions/collision.html#Coalescence"
            click BUILDER_INSTANCE "https://open-atmos.github.io/PySDM/PySDM/builder.html"
            click BUILDER_INIT "https://open-atmos.github.io/PySDM/PySDM/builder.html"
            click BUILDER_ADD_DYN "https://open-atmos.github.io/PySDM/PySDM/builder.html"
            click ENV_INIT "https://open-atmos.github.io/PySDM/PySDM/environments.html"
            click ENV "https://open-atmos.github.io/PySDM/PySDM/environments.html"
            click KERNEL_INIT "https://open-atmos.github.io/PySDM/PySDM/dynamics/collisions/collision_kernels.html"
            click KERNEL "https://open-atmos.github.io/PySDM/PySDM/dynamics/collisions/collision_kernels.html"
            click EXP_INIT "https://open-atmos.github.io/PySDM/PySDM/initialisation/spectra.html"
            click IS "https://open-atmos.github.io/PySDM/PySDM/initialisation/spectra.html"
            click CM_INIT "https://open-atmos.github.io/PySDM/PySDM/initialisation/sampling/spectral_sampling.html"
            click CM_INSTANCE "https://open-atmos.github.io/PySDM/PySDM/initialisation/sampling/spectral_sampling.html"
            click SAMPLE "https://open-atmos.github.io/PySDM/PySDM/initialisation/sampling/spectral_sampling.html"
            click PARTICULATOR_INSTANCE "https://open-atmos.github.io/PySDM/PySDM/particulator.html"
            click BACKEND_INSTANCE "https://open-atmos.github.io/PySDM/PySDM/backends/numba.html"
            click BUILDER_BUILD "https://open-atmos.github.io/PySDM/PySDM/builder.html"
            click NP_LOGSPACE "https://numpy.org/doc/stable/reference/generated/numpy.logspace.html"
            click SPECTRUM_INIT "https://open-atmos.github.io/PySDM/PySDM/products/size_spectral/particle_volume_versus_radius_logarithm_spectrum.html"
            click SPECTRUM "https://open-atmos.github.io/PySDM/PySDM/products/size_spectral/particle_volume_versus_radius_logarithm_spectrum.html"
        ```
        
        ## Hello-world condensation example in Python, Julia and Matlab
        
        In the following example, a condensation-only setup is used with the adiabatic 
        [`Parcel`](https://open-atmos.github.io/PySDM/PySDM/environments/parcel.html) environment.
        An initial [`Lognormal`](https://open-atmos.github.io/PySDM/PySDM/initialisation/spectra/lognormal.html#Lognormal)
        spectrum of dry aerosol particles is first initialised to equilibrium wet size for the given
        initial humidity. 
        Subsequent particle growth due to [`Condensation`](https://open-atmos.github.io/PySDM/PySDM/dynamics/condensation.html) of water vapour (coupled with the release of latent heat)
        causes a subset of particles to activate into cloud droplets.
        Results of the simulation are plotted against vertical 
        [`ParcelDisplacement`](https://open-atmos.github.io/PySDM/PySDM/products/housekeeping/parcel_displacement.html)
        and depict the evolution of 
        [`PeakSupersaturation`](https://open-atmos.github.io/PySDM/PySDM/products/condensation/peak_supersaturation.html), 
        [`EffectiveRadius`](https://open-atmos.github.io/PySDM/PySDM/products/size_spectral/effective_radius.html), 
        [`ParticleConcentration`](https://open-atmos.github.io/PySDM/PySDM/products/size_spectral/particle_concentration.html#ParticleConcentration) 
        and the 
        [`WaterMixingRatio `](https://open-atmos.github.io/PySDM/PySDM/products/size_spectral/water_mixing_ratio.html).
        
        <details>
        <summary>Julia (click to expand)</summary>
        
        ```Julia
        using PyCall
        using Plots; plotlyjs()
        si = pyimport("PySDM.physics").si
        spectral_sampling = pyimport("PySDM.initialisation.sampling").spectral_sampling
        discretise_multiplicities = pyimport("PySDM.initialisation").discretise_multiplicities
        Lognormal = pyimport("PySDM.initialisation.spectra").Lognormal
        equilibrate_wet_radii = pyimport("PySDM.initialisation").equilibrate_wet_radii
        CPU = pyimport("PySDM.backends").CPU
        AmbientThermodynamics = pyimport("PySDM.dynamics").AmbientThermodynamics
        Condensation = pyimport("PySDM.dynamics").Condensation
        Parcel = pyimport("PySDM.environments").Parcel
        Builder = pyimport("PySDM").Builder
        Formulae = pyimport("PySDM").Formulae
        products = pyimport("PySDM.products")
        
        env = Parcel(
            dt=.25 * si.s,
            mass_of_dry_air=1e3 * si.kg,
            p0=1122 * si.hPa,
            initial_water_vapour_mixing_ratio=20 * si.g / si.kg,
            T0=300 * si.K,
            w= 2.5 * si.m / si.s
        )
        spectrum = Lognormal(norm_factor=1e4/si.mg, m_mode=50*si.nm, s_geom=1.4)
        kappa = .5 * si.dimensionless
        cloud_range = (.5 * si.um, 25 * si.um)
        output_interval = 4
        output_points = 40
        n_sd = 256
        
        formulae = Formulae()
        builder = Builder(backend=CPU(formulae), n_sd=n_sd, environment=env)
        builder.add_dynamic(AmbientThermodynamics())
        builder.add_dynamic(Condensation())
        
        r_dry, specific_concentration = spectral_sampling.Logarithmic(spectrum).sample(n_sd)
        v_dry = formulae.trivia.volume(radius=r_dry)
        r_wet = equilibrate_wet_radii(r_dry=r_dry, environment=env, kappa_times_dry_volume=kappa * v_dry)
        
        attributes = Dict()
        attributes["multiplicity"] = discretise_multiplicities(specific_concentration * env.mass_of_dry_air)
        attributes["dry volume"] = v_dry
        attributes["kappa times dry volume"] = kappa * v_dry
        attributes["volume"] = formulae.trivia.volume(radius=r_wet) 
        
        particulator = builder.build(attributes, products=[
            products.PeakSupersaturation(name="S_max", unit="%"),
            products.EffectiveRadius(name="r_eff", unit="um", radius_range=cloud_range),
            products.ParticleConcentration(name="n_c_cm3", unit="cm^-3", radius_range=cloud_range),
            products.WaterMixingRatio(name="liquid water mixing ratio", unit="g/kg", radius_range=cloud_range),
            products.ParcelDisplacement(name="z")
        ])
            
        cell_id=1
        output = Dict()
        for (_, product) in particulator.products
            output[product.name] = Array{Float32}(undef, output_points+1)
            output[product.name][1] = product.get()[cell_id]
        end 
            
        for step = 2:output_points+1
            particulator.run(steps=output_interval)
            for (_, product) in particulator.products
                output[product.name][step] = product.get()[cell_id]
            end 
        end 
        
        plots = []
        ylbl = particulator.products["z"].unit
        for (_, product) in particulator.products
            if product.name != "z"
                append!(plots, [plot(output[product.name], output["z"], ylabel=ylbl, xlabel=product.unit, title=product.name)])
            end
            global ylbl = ""
        end
        plot(plots..., layout=(1, length(output)-1))
        savefig("parcel.svg")
        ```
        </details>
        <details>
        <summary>Matlab (click to expand)</summary>
        
        ```Matlab
        si = py.importlib.import_module('PySDM.physics').si;
        spectral_sampling = py.importlib.import_module('PySDM.initialisation.sampling').spectral_sampling;
        discretise_multiplicities = py.importlib.import_module('PySDM.initialisation').discretise_multiplicities;
        Lognormal = py.importlib.import_module('PySDM.initialisation.spectra').Lognormal;
        equilibrate_wet_radii = py.importlib.import_module('PySDM.initialisation').equilibrate_wet_radii;
        CPU = py.importlib.import_module('PySDM.backends').CPU;
        AmbientThermodynamics = py.importlib.import_module('PySDM.dynamics').AmbientThermodynamics;
        Condensation = py.importlib.import_module('PySDM.dynamics').Condensation;
        Parcel = py.importlib.import_module('PySDM.environments').Parcel;
        Builder = py.importlib.import_module('PySDM').Builder;
        Formulae = py.importlib.import_module('PySDM').Formulae;
        products = py.importlib.import_module('PySDM.products');
        
        env = Parcel(pyargs( ...
            'dt', .25 * si.s, ...
            'mass_of_dry_air', 1e3 * si.kg, ...
            'p0', 1122 * si.hPa, ...
            'initial_water_vapour_mixing_ratio', 20 * si.g / si.kg, ...
            'T0', 300 * si.K, ...
            'w', 2.5 * si.m / si.s ...
        ));
        spectrum = Lognormal(pyargs('norm_factor', 1e4/si.mg, 'm_mode', 50 * si.nm, 's_geom', 1.4));
        kappa = .5;
        cloud_range = py.tuple({.5 * si.um, 25 * si.um});
        output_interval = 4;
        output_points = 40;
        n_sd = 256;
        
        formulae = Formulae();
        builder = Builder(pyargs('backend', CPU(formulae), 'n_sd', int32(n_sd), 'environment', env));
        builder.add_dynamic(AmbientThermodynamics());
        builder.add_dynamic(Condensation());
        
        tmp = spectral_sampling.Logarithmic(spectrum).sample(int32(n_sd));
        r_dry = tmp{1};
        v_dry = formulae.trivia.volume(pyargs('radius', r_dry));
        specific_concentration = tmp{2};
        r_wet = equilibrate_wet_radii(pyargs(...
            'r_dry', r_dry, ...
            'environment', env, ...
            'kappa_times_dry_volume', kappa * v_dry...
        ));
        
        attributes = py.dict(pyargs( ...
            'multiplicity', discretise_multiplicities(specific_concentration * env.mass_of_dry_air), ...
            'dry volume', v_dry, ...
            'kappa times dry volume', kappa * v_dry, ... 
            'volume', formulae.trivia.volume(pyargs('radius', r_wet)) ...
        ));
        
        particulator = builder.build(attributes, py.list({ ...
            products.PeakSupersaturation(pyargs('name', 'S_max', 'unit', '%')), ...
            products.EffectiveRadius(pyargs('name', 'r_eff', 'unit', 'um', 'radius_range', cloud_range)), ...
            products.ParticleConcentration(pyargs('name', 'n_c_cm3', 'unit', 'cm^-3', 'radius_range', cloud_range)), ...
            products.WaterMixingRatio(pyargs('name', 'liquid water mixing ratio', 'unit', 'g/kg', 'radius_range', cloud_range)) ...
            products.ParcelDisplacement(pyargs('name', 'z')) ...
        }));
        
        cell_id = int32(0);
        output_size = [output_points+1, length(py.list(particulator.products.keys()))];
        output_types = repelem({'double'}, output_size(2));
        output_names = [cellfun(@string, cell(py.list(particulator.products.keys())))];
        output = table(...
            'Size', output_size, ...
            'VariableTypes', output_types, ...
            'VariableNames', output_names ...
        );
        for pykey = py.list(keys(particulator.products))
            get = py.getattr(particulator.products{pykey{1}}.get(), '__getitem__');
            key = string(pykey{1});
            output{1, key} = get(cell_id);
        end
        
        for i=2:output_points+1
            particulator.run(pyargs('steps', int32(output_interval)));
            for pykey = py.list(keys(particulator.products))
                get = py.getattr(particulator.products{pykey{1}}.get(), '__getitem__');
                key = string(pykey{1});
                output{i, key} = get(cell_id);
            end
        end
        
        i=1;
        for pykey = py.list(keys(particulator.products))
            product = particulator.products{pykey{1}};
            if string(product.name) ~= "z"
                subplot(1, width(output)-1, i);
                plot(output{:, string(pykey{1})}, output.z, '-o');
                title(string(product.name), 'Interpreter', 'none');
                xlabel(string(product.unit));
            end
            if i == 1
                ylabel(string(particulator.products{"z"}.unit));
            end
            i=i+1;
        end
        saveas(gcf, "parcel.png");
        ```
        </details>
        <details open>
        <summary>Python (click to expand)</summary>
        
        ```Python
        from matplotlib import pyplot
        from PySDM.physics import si
        from PySDM.initialisation import discretise_multiplicities, equilibrate_wet_radii
        from PySDM.initialisation.spectra import Lognormal
        from PySDM.initialisation.sampling import spectral_sampling
        from PySDM.backends import CPU
        from PySDM.dynamics import AmbientThermodynamics, Condensation
        from PySDM.environments import Parcel
        from PySDM import Builder, Formulae, products
        
        env = Parcel(
          dt=.25 * si.s,
          mass_of_dry_air=1e3 * si.kg,
          p0=1122 * si.hPa,
          initial_water_vapour_mixing_ratio=20 * si.g / si.kg,
          T0=300 * si.K,
          w=2.5 * si.m / si.s
        )
        spectrum = Lognormal(norm_factor=1e4 / si.mg, m_mode=50 * si.nm, s_geom=1.5)
        kappa = .5 * si.dimensionless
        cloud_range = (.5 * si.um, 25 * si.um)
        output_interval = 4
        output_points = 40
        n_sd = 256
        
        formulae = Formulae()
        builder = Builder(backend=CPU(formulae), n_sd=n_sd, environment=env)
        builder.add_dynamic(AmbientThermodynamics())
        builder.add_dynamic(Condensation())
        
        r_dry, specific_concentration = spectral_sampling.Logarithmic(spectrum).sample(n_sd)
        v_dry = formulae.trivia.volume(radius=r_dry)
        r_wet = equilibrate_wet_radii(r_dry=r_dry, environment=env, kappa_times_dry_volume=kappa * v_dry)
        
        attributes = {
          'multiplicity': discretise_multiplicities(specific_concentration * env.mass_of_dry_air),
          'dry volume': v_dry,
          'kappa times dry volume': kappa * v_dry,
          'volume': formulae.trivia.volume(radius=r_wet)
        }
        
        particulator = builder.build(attributes, products=[
          products.PeakSupersaturation(name='S_max', unit='%'),
          products.EffectiveRadius(name='r_eff', unit='um', radius_range=cloud_range),
          products.ParticleConcentration(name='n_c_cm3', unit='cm^-3', radius_range=cloud_range),
          products.WaterMixingRatio(name='liquid water mixing ratio', unit='g/kg', radius_range=cloud_range),
          products.ParcelDisplacement(name='z')
        ])
        
        cell_id = 0
        output = {product.name: [product.get()[cell_id]] for product in particulator.products.values()}
        
        for step in range(output_points):
          particulator.run(steps=output_interval)
          for product in particulator.products.values():
            output[product.name].append(product.get()[cell_id])
        
        fig, axs = pyplot.subplots(1, len(particulator.products) - 1, sharey="all")
        for i, (key, product) in enumerate(particulator.products.items()):
          if key != 'z':
            axs[i].plot(output[key], output['z'], marker='.')
            axs[i].set_title(product.name)
            axs[i].set_xlabel(product.unit)
            axs[i].grid()
        axs[0].set_ylabel(particulator.products['z'].unit)
        pyplot.savefig('parcel.svg')
        ```
        </details>
        
        The resultant plot (generated with the Matlab code) looks as follows:
        
        ![plot](https://github.com/open-atmos/PySDM/releases/download/tip/parcel.png)
        
        ## Contributing, reporting issues, seeking support 
        
        #### Our technologicial stack:   
        [![Python 3](https://img.shields.io/static/v1?label=+&logo=Python&color=darkred&message=Python)](https://www.python.org/)
        [![Numba](https://img.shields.io/static/v1?label=+&logo=Numba&color=orange&message=Numba)](https://numba.pydata.org)
        [![LLVM](https://img.shields.io/static/v1?label=+&logo=LLVM&color=gold&message=LLVM)](https://llvm.org)
        [![CUDA](https://img.shields.io/static/v1?label=+&logo=nVidia&color=darkgreen&message=ThrustRTC/CUDA)](https://pypi.org/project/ThrustRTC/)
        [![NumPy](https://img.shields.io/static/v1?label=+&logo=numpy&color=blue&message=NumPy)](https://numpy.org/)
        [![pytest](https://img.shields.io/static/v1?label=+&logo=pytest&color=purple&message=pytest)](https://pytest.org/)   
        [![Colab](https://img.shields.io/static/v1?label=+&logo=googlecolab&color=darkred&message=Colab)](https://colab.research.google.com/)
        [![Codecov](https://img.shields.io/static/v1?label=+&logo=codecov&color=orange&message=Codecov)](https://codecov.io/)
        [![PyPI](https://img.shields.io/static/v1?label=+&logo=pypi&color=gold&message=PyPI)](https://pypi.org/)
        [![GithubActions](https://img.shields.io/static/v1?label=+&logo=github&color=darkgreen&message=GitHub&nbsp;Actions)](https://github.com/features/actions)
        [![Jupyter](https://img.shields.io/static/v1?label=+&logo=Jupyter&color=blue&message=Jupyter)](https://jupyter.org/)
        [![PyCharm](https://img.shields.io/static/v1?label=+&logo=pycharm&color=purple&message=PyCharm)](https:///)
        
        Submitting new code to the project, please preferably use [GitHub pull requests](https://github.com/open-atmos/PySDM/pulls) - it helps to keep record of code authorship, 
        track and archive the code review workflow and allows to benefit
        from the continuous integration setup which automates execution of tests 
        with the newly added code. 
        
        Code contributions are assumed to imply transfer of copyright.
        Should there be a need to make an exception, please indicate it when creating
        a pull request or contributing code in any other way. In any case, 
        the license of the contributed code must be compatible with GPL v3.
        
        Developing the code, we follow [The Way of Python](https://www.python.org/dev/peps/pep-0020/) and 
        the [KISS principle](https://en.wikipedia.org/wiki/KISS_principle).
        The codebase has greatly benefited from [PyCharm code inspections](https://www.jetbrains.com/help/pycharm/code-inspection.html)
        and [Pylint](https://pylint.org), [Black](https://black.readthedocs.io/en/stable/) and [isort](https://pycqa.github.io/isort/)
        code analysis (which are all part of the CI workflows).
        
        We also use [pre-commit hooks](https://pre-commit.com). 
        In our case, the hooks modify files and re-format them.
        The pre-commit hooks can be run locally, and then the resultant changes need to be staged before committing.
        To set up the hooks locally, install pre-commit via `pip install pre-commit` and
        set up the git hooks via `pre-commit install` (this needs to be done every time you clone the project).
        To run all pre-commit hooks, run `pre-commit run --all-files`.
        The `.pre-commit-config.yaml` file can be modified in case new hooks are to be added or
          existing ones need to be altered.  
        
        Further hints addressed at PySDM developers are maintained in the [open-atmos/python-dev-hints Wiki](https://github.com/open-atmos/python-dev-hints/wiki).
        
        Issues regarding any incorrect, unintuitive or undocumented bahaviour of
        PySDM are best to be reported on the [GitHub issue tracker](https://github.com/open-atmos/PySDM/issues/new).
        Feature requests are recorded in the "Ideas..." [PySDM wiki page](https://github.com/open-atmos/PySDM/wiki/Ideas-for-new-features-and-examples).
        
        We encourage to use the [GitHub Discussions](https://github.com/open-atmos/PySDM/discussions) feature
        (rather than the issue tracker) for seeking support in understanding, using and extending PySDM code.
        
        We look forward to your contributions and feedback.
        
        ## Credits:
        
        The development and maintenance of PySDM is led by [Sylwester Arabas](https://github.com/slayoo/).
        [Piotr Bartman](https://github.com/piotrbartman/) had been the architect and main developer 
        of technological solutions in PySDM. 
        PySDM includes contributions from researchers 
        from [Jagiellonian University](https://en.uj.edu.pl/en) departments of computer science, physics and chemistry;
        from [Caltech's Climate Modelling Alliance](https://clima.caltech.edu/),
        from [University of Warsaw](https://en.uw.edu.pl/) (dept. physics), and
        from [AGH University of Krakow](https://agh.edu.pl/en) (dept. physics \& applied computer science) where release maintenance takes place currently.
        
        Development of PySDM had been initially supported by the EU through a grant of the 
        [Foundation for Polish Science](https://www.fnp.org.pl/)) (grant no. POIR.04.04.00-00-5E1C/18) 
        realised at the [Jagiellonian University](https://en.uj.edu.pl/en).
        The immersion freezing support in PySDM was developed with support from the
        US Department of Energy [Atmospheric System Research](https://asr.science.energy.gov/) programme
        through a grant (no. DE-SC0021034) realised at the 
        [University of Illinois at Urbana-Champaign](https://illinois.edu/).
        Development of isotopic fractionation representation and mixed-phase support is carried out with support from
        the [Polish National Science Centre](https://ncn.gov.pl/en) (grant no. 2020/39/D/ST10/01220).
        
        copyright: [Jagiellonian University](https://en.uj.edu.pl/en) (2019-2023) & [AGH University of Krakow](https://agh.edu.pl/en) (2023-...)    
        licence: [GPL v3](https://www.gnu.org/licenses/gpl-3.0.html)
        
        ## Related resources and open-source projects
        
        ### SDM patents (some expired, some withdrawn):
        - https://patents.google.com/patent/US7756693B2
        - https://patents.google.com/patent/EP1847939A3
        - https://patents.google.com/patent/JP4742387B2
        - https://patents.google.com/patent/CN101059821B
        
        ### Other SDM implementations:
        - SCALE-SDM (Fortran):    
          https://github.com/Shima-Lab/SCALE-SDM_BOMEX_Sato2018/blob/master/contrib/SDM/sdm_coalescence.f90
        - Pencil Code (Fortran):    
          https://github.com/pencil-code/pencil-code/blob/master/src/particles_coagulation.f90
        - PALM LES (Fortran):    
          https://palm.muk.uni-hannover.de/trac/browser/palm/trunk/SOURCE/lagrangian_particle_model_mod.f90
        - libcloudph++ (C++):    
          https://github.com/igfuw/libcloudphxx/blob/master/src/impl/particles_impl_coal.ipp
        - LCM1D (Python)    
          https://github.com/SimonUnterstrasser/ColumnModel
        - superdroplet (Cython/Numba/C++11/Fortran 2008/Julia)   
          https://github.com/darothen/superdroplet
        - NTLP (FORTRAN)   
          https://github.com/Folca/NTLP/blob/SuperDroplet/les.F
        - CLEO (C++)    
          https://yoctoyotta1024.github.io/CLEO/
        - droplets.jl (Julia)   
          https://github.com/emmacware/droplets.jl
        - LacmoPy (Python/Numba)    
          https://github.com/JanKBohrer/LacmoPy/blob/master/collision/all_or_nothing.py
        - McSnow (FORTRAN):     
          https://gitlab.dkrz.de/mcsnow/mcsnow/-/blob/master/src/mo_coll.f90
        
        ### non-SDM probabilistic particle-based coagulation solvers
        
        - PartMC (Fortran):    
          https://github.com/compdyn/partmc
        
        ### Python models with discrete-particle (moving-sectional) representation of particle size spectrum
        
        - pyrcel: https://github.com/darothen/pyrcel
        - PyBox: https://github.com/loftytopping/PyBox
        - py-cloud-parcel-model: https://github.com/emmasimp/py-cloud-parcel-model
        
        ### non-Python cloud microphysics open-source software
        
        - CloudMicrophysics.jl: https://github.com/CliMA/CloudMicrophysics.jl
        - McSnow: https://gitlab.dkrz.de/mcsnow/mcsnow
          
        
Keywords: physics-simulation,monte-carlo-simulation,gpu-computing,atmospheric-modelling,particle-system,numba,thrust,nvrtc,pint,atmospheric-physics
Platform: UNKNOWN
Classifier: Development Status :: 4 - Beta
Classifier: Intended Audience :: Science/Research
Classifier: License :: OSI Approved :: GNU General Public License v3 (GPLv3)
Classifier: Operating System :: OS Independent
Classifier: Programming Language :: Python :: 3
Classifier: Topic :: Scientific/Engineering
Classifier: Topic :: Scientific/Engineering :: Atmospheric Science
Classifier: Topic :: Scientific/Engineering :: Mathematics
Classifier: Topic :: Scientific/Engineering :: Physics
Classifier: Topic :: Software Development :: Libraries
Description-Content-Type: text/markdown
Provides-Extra: tests
