Dissipative Particle Dynamics Calculator

• Conservative force: F_C(r) = a (1 - r/rc) for r < rc, otherwise zero.
• Dissipative force scale: controlled by γ, with a characteristic time τ = m/γ.
• Random force (thermostat) constraint: σ² = 2 γ kB T. Here kB = 1.
• Box and density: V = L³ and ρ = N/V. If you choose density mode, L = (N/ρ)^(1/3).
• Heuristic timestep guidance: dt_max ≈ min(0.10τ, 0.05 sqrt(m rc / a)) for a conservative safety margin.

1. Pick a particle count and choose a box definition mode.
2. Set rc and a to match compressibility targets.
3. Enter γ and T, then enable auto σ for consistency.
4. Choose dt and steps; keep dt below the guideline.
5. Press Compute to see derived scales and checks.
6. Use the export buttons to download a CSV or a PDF report.

Dissipative particle dynamics in practice

1) What this calculator represents

Dissipative particle dynamics models hydrodynamic fluids with soft, short-range interactions and a built-in thermostat. Each bead follows Newton’s law in reduced units, while pair forces exchange momentum so that mesoscale flow and transport emerge without resolving atomistic detail.

2) Reduced units and common ranges

This tool assumes kB = 1 and reports dimensionless scales. In many practical setups, densities near ρ ≈ 3 beads per cutoff volume and cutoffs rc = 1 are used. Conservative amplitudes around a = 15–35 often produce liquid-like compressibility, while still allowing large timesteps compared with atomistic methods.

3) Conservative interaction and pressure control

The conservative term F_C(r)=a(1-r/rc) sets how strongly beads repel at short separation. Increasing a typically raises pressure and reduces density fluctuations. When you change a, keep an eye on the conservative timescale estimate tc≈sqrt(m rc / a) and tighten dt if tc becomes small.

4) Thermostat consistency from γ and σ

DPD uses paired dissipative and random forces to maintain temperature while conserving momentum. For a consistent thermostat, the fluctuation–dissipation relation requires σ² = 2 γ T (with kB=1). The calculator shows the target σ and the temperature implied by your chosen σ, flagging mismatches beyond a small tolerance.

5) Density, box size, and neighbor sampling

Neighbor statistics control both accuracy and noise. With a fixed cutoff, higher ρ increases the average number of interacting neighbors and typically smooths stress fluctuations. If you choose “Target density,” the tool computes L=(N/ρ)^{1/3} and reports the actual density N/L^3 so you can verify packing consistency.

6) Timestep guidance and stability

The calculator provides a conservative maximum timestep using two constraints: a friction time τ=m/γ and a conservative time estimate tc. A safe rule is dt well below both, often in the range 0.005–0.03 for typical reduced parameters. If the check warns, reduce dt before increasing total steps.

7) Reading the derived transport indicators

Thermal speed is estimated as vth=sqrt(T/m), while an order-of-magnitude diffusion estimate is shown as D≈T/(mγ). The reported Peclet estimate Pe≈vth rc / D helps you gauge whether dynamics are more ballistic-like or diffusion-dominated under your chosen friction.

8) Practical setup example

As a baseline, try N=2000, ρ=3, rc=1, a=25, γ=4.5, and T=1, with auto σ enabled. If the guideline suggests dt<0.02, set dt=0.01–0.015 and run 5000–20000 steps to cover a simulated time of 50–300 in reduced units.

FAQs