---
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:

1. A ← A + 1  
2. Compute B(A, Z)  
3. Compute BE/A  
4. Evaluate stability S  
5. Estimate half-life T  
6. 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:

```bash
python app.py