Neutron activator optimal configuration calculation

Foreword

This article is based on the mechanisms of 0.5.6-beta and attempts to calculate the optimal configuration for a Neutron Activator to operate stably (neutron kinetic energy will not empty) for a specific recipe. The mechanisms of both Neutron Vortex modes are different from the activator and are not applicable to Neutron Vortex.

Mechanism

The configuration of the neutron activator mainly includes the following content:

• Neutron Accelerator: Neutron Activators can be equipped with up to two Neutron Accelerators. Each will attempt to consume the maximum EU consumption per tick and convert it into 10-20 times neutron kinetic energy, with the random number following a uniform distribution. Therefore, the expected increase in kinetic energy = 15 * actual EU consumed, referred to as the original kinetic energy increase amount. Neutron Accelerators have a minimal internal energy buffer and require a Wireless Energy Receiver to maintain power.

• Height: Height determines the efficiency attribute of the Neutron Activator. Efficiency = 0.95^(Height - 4). The minimum height for an Activator is 4, and the maximum is 100.

• Max Parallel: Max Parallel increases the consumption of neutron kinetic energy but allows for parallel processing of recipes without affecting recipe duration.

The stable operation of a neutron activator depends on the following two properties:

• Neutron kinetic energy increase = Original kinetic energy increase × Efficiency

• Neutron kinetic energy consumption = Neutron kinetic energy consumption in formula × max(1, Parallel^1.2 × Efficiency)

When the neutron kinetic energy increase amount ≥ the neutron kinetic energy consumption amount, we believe it can operate stably.

The operating speed of the neutron activator depends on the recipe time and maximum parallelism, where Recipe Time = Original Recipe Time × Efficiency.

Conclusion

• Due to the different neutron kinetic energy consumption rates of each formula, in order to maximize operating speed and improve robustness, it is recommended to adopt a strategy of one formula and one activator for high-frequency formulas. The following calculations will be based on this scenario.

• The original kinetic energy increase has been significantly improved, and it is recommended to directly use dual highest-level neutron accelerators to avoid frequent replacements later.

• The height of the neutron activator should be prioritized, and the optimal parallelism should be calculated based on the height (proof omitted).

• If the original kinetic energy increase is less than the formula's neutron kinetic energy consumption, it is impossible to run the formula without losing neutron kinetic energy, regardless of other factors. The following assumes this situation does not occur.

Calculation

Since the minimum neutron kinetic energy consumption is Formula neutron kinetic energy consumption × 1, it is necessary to ensure that the increase in neutron kinetic energy is greater than or equal to the consumption of neutron kinetic energy in the formula. The optimal height can be determined based on this inequality.

Neutron kinetic energy consumption in the formula ≤ initial kinetic energy increase × 0.95^(height - 4)
height ≤ lg(Neutron kinetic energy consumption in the formula / initial kinetic energy increase) / lg(0.95) + 4

Due to the aforementioned principle of prioritizing maximum height, the optimal height = min(⌊lg(Kinetic energy consumption of the recipe / Original kinetic energy increase) / lg(0.95) + 4⌋, 100).

The increase in kinetic energy is now determined, and all that needs to be determined is the maximum parallelism:

Original kinetic energy increase × efficiency ≥ Neutron kinetic energy consumption in formula × max(1, parallel^1.2 × efficiency)
parallel^1.2 ≤ (Original kinetic energy increase / Neutron kinetic energy consumption in formula)^(1/1.2)
parallel ≤ (Original kinetic energy increase / Neutron kinetic energy consumption in formula)^(1/1.2)

Obviously, the higher the parallelism, the better. Therefore, max_parallelism = ⌊(original kinetic energy increase / kinetic energy consumption in recipe)^(1/1.2)⌋

Summary

Under the given recipe and initial kinetic energy increase (only considering when initial kinetic energy increase ≥ neutron kinetic energy consumption in the recipe):

• Optimal Height = min(⌊lg(Neutron Kinetic Energy Consumption in Formula / Original Kinetic Energy Increase) / lg(0.95) + 4⌋, 100)

• Maximum Parallel = ⌊(Original Kinetic Energy Increase / Neutron Kinetic Energy Consumption in Formula)^(1/1.2)⌋

Signature

Mio Mikoshi