Spaces:
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title: Soundless Soundscapes
emoji: 🔊
colorFrom: purple
colorTo: purple
sdk: gradio
sdk_version: 6.14.0
app_file: app.py
pinned: false
license: apache-2.0
short_description: nuclear physics sandbox
thumbnail: >-
https://cdn-uploads.huggingface.co/production/uploads/64628a722a83863b97beed5e/CPWwdvn_OwLukmsjvm2jw.png
Soundless Soundscapes
“What is the sound of one hand clapping?”
Supplementary Material
Moscovium Neutron Expansion Simulator
Abstract
This app presents a computational sim framework for exploring nuclear stability trends under incremental neutron loading in superheavy nuclei, specifically Moscovium (Z = 115). The model employs the semi-empirical mass formula (SEMF) to approximate binding energy and derives secondary metrics including stability probability, half-life estimates, and transition indicators.
An optional speculative extension introduces a parameterized coupling between nuclear density and a gravitational proxy derived from mass-energy scaling. This extension is not physically validated and is included strictly for exploratory analysis.
1. System Overview
The simulator models the evolution of a nucleus as neutrons are added sequentially:
A₀ → A₀ + n
At each step, the system computes:
- Total binding energy
- Binding energy per nucleon (BE/A)
- Stability probability
- Half-life estimate (stochastic)
- Gravitational proxy (optional)
Simulation terminates when the nucleus crosses an energetic instability threshold.
2. Nuclear Model
2.1 Semi-Empirical Mass Formula
Binding energy is computed using the Weizsäcker formulation:
B(A, Z) = a_v A − a_s A^(2/3) − a_c Z(Z−1)/A^(1/3) − a_a (A−2Z)^2/A + δ(A, Z)
Where:
- a_v = 15.8 MeV (volume term)
- a_s = 18.3 MeV (surface term)
- a_c = 0.714 MeV (Coulomb term)
- a_a = 23.2 MeV (asymmetry term)
- δ(A, Z) = pairing correction
2.2 Pairing Term
The pairing term distinguishes nuclear parity:
- δ > 0 for even-even nuclei
- δ < 0 for odd-odd nuclei
- δ = 0 for odd-A nuclei
This correction captures nucleon pairing effects on stability.
2.3 Stability Metric
Primary stability is defined using:
BE/A = B(A, Z) / A
Empirically:
- Stable nuclei cluster near 7–8 MeV/A
- Instability emerges below ~6.5 MeV/A
A sigmoid transform maps BE/A to a normalized stability score:
S = 1 / (1 + exp(−k(BE/A − μ)))
Where μ ≈ 7.5 MeV/A.
3. Decay Approximation
Half-life is modeled as an exponential function of stability:
T ∝ exp(αS + ε)
Where:
- α is a scaling constant
- ε is Gaussian noise
This introduces stochastic variability to approximate chaotic decay behavior observed in unstable nuclei.
4. Speculative Extension
4.1 Gravitational Proxy
A baseline gravitational proxy is defined as:
G ∝ A
This reflects mass-energy scaling in arbitrary units.
4.2 Coupled Resonance Model (Speculative)
When enabled, the model introduces:
G' = G · (1 + c · sin(ωA) / A^(1/3))
Where:
- c = coupling coefficient
- ω = frequency scaling constant
This formulation loosely couples:
- nuclear size (A^(1/3), radius scaling)
- oscillatory perturbation (resonance term)
4.3 Interpretation
This extension does not represent accepted physics.
It is a structured hypothetical framework intended to explore:
- nonlinear coupling behavior
- emergent oscillatory patterns
- sensitivity of derived fields to nuclear scaling
5. Simulation Dynamics
5.1 Iterative Process
For each neutron increment:
- A ← A + 1
- Compute B(A, Z)
- Compute BE/A
- Evaluate stability S
- Estimate half-life T
- Compute gravitational proxy G
5.2 Termination Condition
Simulation halts when:
BE/A < 6.5 MeV
AND
S < 0.2
This defines a soft instability boundary.
6. Derived Quantities
6.1 Second Derivative of Binding Energy
d²E/dn² is computed numerically:
d²E ≈ ∇(∇B)
This serves as a transition indicator, highlighting:
- curvature shifts in the energy landscape
- potential phase-like transitions
- regions of structural instability
7. Outputs
7.1 Tabular Data
Each simulation produces:
- Neutron count
- Mass number
- Binding energy
- BE/A
- Stability
- Half-life (arb. units)
- Gravitational proxy
7.2 Visualization
Generated plots include:
- Binding energy vs neutron count
- BE/A vs neutron count
- Stability vs neutron count
- Gravitational proxy vs neutron count
8. Limitations
This model is a simplified approximation with known constraints:
- No shell corrections or magic number modeling
- No quantum mechanical treatment
- No explicit decay channel simulation
- Gravitational modeling is speculative
- Constants are fixed and not fitted dynamically
9. Conceptual Framing
The system can be interpreted as a discrete phase transition model:
- Control parameter: neutron number
- Energy landscape: binding energy
- Order parameter: stability
- Perturbation: resonance coupling
This framing enables connections to:
- nonlinear dynamical systems
- energy landscape theory
- resonance-based modeling approaches
10. Reproducibility
Dependencies
- gradio
- numpy
- pandas
- matplotlib
Execution
Run locally:
python app.py