enhanced_metamaterial_amplification_uq.py

"""
Enhanced Metamaterial Amplification UQ Resolution Framework
==========================================================

Implements enhanced mathematical frameworks for metamaterial amplification limits
using golden ratio resonance enhancement and repository-validated physics.

Key Features:
- φⁿ golden ratio metamaterial resonance (n→100+)
- 1.2×10¹⁰× amplification factor validation
- T⁻⁴ temporal stability scaling
- Schwinger critical field analysis
- Cross-repository integration
"""

import numpy as np
import matplotlib.pyplot as plt
from scipy import constants
from scipy.special import gamma, factorial
import json
from datetime import datetime

class EnhancedMetamaterialAmplificationUQ:
    """Enhanced UQ framework for metamaterial amplification limits with golden ratio enhancement."""
    
    def __init__(self):
        """Initialize enhanced metamaterial amplification UQ framework."""
        # Physical constants
        self.m_e = constants.m_e  # Electron mass
        self.c = constants.c      # Speed of light
        self.e = constants.e      # Elementary charge
        self.hbar = constants.hbar # Reduced Planck constant
        self.epsilon_0 = constants.epsilon_0  # Vacuum permittivity
        
        # Golden ratio for metamaterial resonance
        self.phi = (1 + np.sqrt(5)) / 2  # φ = 1.618034...
        
        # Repository-validated parameters
        self.amplification_factor = 1.2e10  # From warp-spacetime-stability-controller
        self.max_n_golden = 100  # Maximum φⁿ terms
        self.temporal_scaling_power = -4  # T⁻⁴ scaling
        
        # Schwinger critical field
        self.E_schwinger = (self.m_e * self.c**3) / (self.e * self.hbar)
        
        print(f"Enhanced Metamaterial Amplification UQ Framework Initialized")
        print(f"Schwinger Critical Field: {self.E_schwinger:.2e} V/m")
        print(f"Golden Ratio φ: {self.phi:.10f}")
        print(f"Maximum Amplification Factor: {self.amplification_factor:.2e}")
    
    def calculate_critical_field_enhancement(self, n_max=100):
        """
        Calculate enhanced critical field with golden ratio metamaterial resonance.
        
        Φ_critical = Φ_schwinger × (1 + Σ_{n=1}^{100} α_n φⁿ ΔM_n / M_planck)
        """
        # Planck mass
        M_planck = np.sqrt(self.hbar * self.c / constants.G)
        
        # Calculate golden ratio enhancement series
        enhancement_sum = 0
        alpha_coefficients = []
        
        for n in range(1, n_max + 1):
            # Coupling coefficient (decreases with n for convergence)
            alpha_n = 1.0 / (n**2 * factorial(min(n, 20)))  # Factorial cutoff for numerical stability
            
            # Mass correction term (polymer-like corrections)
            delta_M_n = (self.hbar * self.c) / (constants.G * (n * self.phi)**2)
            
            # Golden ratio term
            phi_n = self.phi**n
            
            # Enhancement contribution
            enhancement_term = alpha_n * phi_n * (delta_M_n / M_planck)
            enhancement_sum += enhancement_term
            
            alpha_coefficients.append({
                'n': n,
                'alpha_n': alpha_n,
                'phi_n': phi_n,
                'delta_M_n': delta_M_n,
                'enhancement_term': enhancement_term
            })
        
        # Enhanced critical field
        E_critical_enhanced = self.E_schwinger * (1 + enhancement_sum)
        
        return {
            'E_critical_enhanced': E_critical_enhanced,
            'enhancement_factor': 1 + enhancement_sum,
            'enhancement_sum': enhancement_sum,
            'alpha_coefficients': alpha_coefficients,
            'convergence_check': enhancement_sum < 1.0  # Should converge
        }
    
    def validate_amplification_limits(self, E_local_array):
        """
        Validate metamaterial amplification against enhanced critical field limits.
        
        A_metamaterial ≤ E_critical_enhanced / E_local
        """
        enhancement_results = self.calculate_critical_field_enhancement()
        E_critical = enhancement_results['E_critical_enhanced']
        
        validation_results = []
        
        for E_local in E_local_array:
            # Maximum allowed amplification
            A_max = E_critical / E_local
            
            # Safety factor (10× safety margin)
            A_safe = A_max / 10
            
            # Validation against repository amplification factor
            is_safe = self.amplification_factor <= A_safe
            
            validation_results.append({
                'E_local': E_local,
                'A_max_theoretical': A_max,
                'A_safe_practical': A_safe,
                'A_repository': self.amplification_factor,
                'is_safe': is_safe,
                'safety_margin': A_safe / self.amplification_factor if is_safe else 0
            })
        
        return validation_results
    
    def calculate_temporal_stability(self, time_array):
        """
        Calculate temporal stability using T⁻⁴ scaling from repository frameworks.
        
        Stability_factor(t) = (t₀/t)⁴ where t₀ is characteristic time
        """
        # Characteristic time scale (Planck time scaled)
        t_planck = np.sqrt(self.hbar * constants.G / self.c**5)
        t_0 = 1e6 * t_planck  # Scaled characteristic time
        
        stability_factors = []
        
        for t in time_array:
            if t <= 0:
                stability_factor = np.inf
            else:
                stability_factor = (t_0 / t)**4
            
            stability_factors.append({
                'time': t,
                'stability_factor': stability_factor,
                'is_stable': stability_factor >= 0.01  # 1% minimum stability
            })
        
        return stability_factors
    
    def plasma_frequency_analysis(self, n_e_array, omega_drive):
        """
        Analyze plasma frequency stability for metamaterial operation.
        
        ω_plasma = sqrt((n_e e²)/(ε₀ m_e))
        Stability: ω_drive < ω_plasma/A_metamaterial
        """
        analysis_results = []
        
        for n_e in n_e_array:
            # Plasma frequency
            omega_plasma = np.sqrt((n_e * self.e**2) / (self.epsilon_0 * self.m_e))
            
            # Critical drive frequency
            omega_critical = omega_plasma / self.amplification_factor
            
            # Stability check
            is_stable = omega_drive < omega_critical
            
            # Critical density for given drive frequency
            n_e_critical = (self.epsilon_0 * self.m_e * omega_drive**2 * self.amplification_factor**2) / self.e**2
            
            analysis_results.append({
                'n_e': n_e,
                'omega_plasma': omega_plasma,
                'omega_critical': omega_critical,
                'omega_drive': omega_drive,
                'is_stable': is_stable,
                'stability_margin': omega_critical / omega_drive if is_stable else 0,
                'n_e_critical': n_e_critical
            })
        
        return analysis_results
    
    def comprehensive_uq_analysis(self):
        """
        Perform comprehensive UQ analysis for metamaterial amplification limits.
        """
        print("\n" + "="*60)
        print("COMPREHENSIVE METAMATERIAL AMPLIFICATION UQ ANALYSIS")
        print("="*60)
        
        # 1. Enhanced critical field analysis
        print("\n1. Enhanced Critical Field Analysis")
        print("-" * 40)
        enhancement = self.calculate_critical_field_enhancement()
        print(f"Schwinger Critical Field: {self.E_schwinger:.2e} V/m")
        print(f"Enhanced Critical Field: {enhancement['E_critical_enhanced']:.2e} V/m")
        print(f"Enhancement Factor: {enhancement['enhancement_factor']:.6f}")
        print(f"Series Convergence: {'✓ PASS' if enhancement['convergence_check'] else '✗ FAIL'}")
        
        # 2. Amplification validation
        print("\n2. Amplification Validation Analysis")
        print("-" * 40)
        E_local_test = np.logspace(6, 10, 5)  # 10⁶ to 10¹⁰ V/m
        validations = self.validate_amplification_limits(E_local_test)
        
        for val in validations:
            status = "✓ SAFE" if val['is_safe'] else "✗ UNSAFE"
            margin = val['safety_margin'] if val['is_safe'] else 0
            print(f"E_local: {val['E_local']:.1e} V/m | A_max: {val['A_max_theoretical']:.1e} | {status} (margin: {margin:.1f}×)")
        
        # 3. Temporal stability analysis
        print("\n3. Temporal Stability Analysis")
        print("-" * 40)
        time_scales = np.logspace(-15, -9, 7)  # Femtosecond to nanosecond
        temporal_stability = self.calculate_temporal_stability(time_scales)
        
        for ts in temporal_stability[:5]:  # Show first 5
            status = "✓ STABLE" if ts['is_stable'] else "✗ UNSTABLE"
            print(f"t: {ts['time']:.1e} s | Stability: {ts['stability_factor']:.2e} | {status}")
        
        # Plasma frequency analysis
        print("\n4. Plasma Frequency Stability Analysis")
        print("-" * 40)
        n_e_array = np.logspace(20, 26, 5)  # Electron densities
        omega_drive = 2*np.pi * 1e12  # 1 THz drive frequency
        plasma_analysis = self.plasma_frequency_analysis(n_e_array, omega_drive)
        
        for pa in plasma_analysis:
            status = "✓ STABLE" if pa['is_stable'] else "✗ UNSTABLE"
            margin = pa['stability_margin'] if pa['is_stable'] else 0
            print(f"n_e: {pa['n_e']:.1e} m⁻³ | ω_p: {pa['omega_plasma']:.1e} rad/s | {status} (margin: {margin:.1f}×)")
        
        # 5. UQ Summary
        print("\n5. UQ RESOLUTION SUMMARY")
        print("-" * 40)
        safe_amplifications = sum(1 for val in validations if val['is_safe'])
        stable_temporal = sum(1 for ts in temporal_stability if ts['is_stable'])
        stable_plasma = sum(1 for pa in plasma_analysis if pa['is_stable'])
        
        print(f"Safe Amplification Regimes: {safe_amplifications}/{len(validations)}")
        print(f"Stable Temporal Regimes: {stable_temporal}/{len(temporal_stability)}")
        print(f"Stable Plasma Regimes: {stable_plasma}/{len(plasma_analysis)}")
        
        overall_status = "✓ RESOLVED" if all([
            enhancement['convergence_check'],
            safe_amplifications > 0,
            stable_temporal > len(temporal_stability)//2,
            stable_plasma > 0
        ]) else "✗ UNRESOLVED"
        
        print(f"\nOVERALL UQ STATUS: {overall_status}")
        
        return {
            'enhancement_analysis': enhancement,
            'amplification_validation': validations,
            'temporal_stability': temporal_stability,
            'plasma_analysis': plasma_analysis,
            'uq_status': overall_status,
            'timestamp': datetime.now().isoformat()
        }
    
    def save_uq_results(self, results, filename='metamaterial_amplification_uq_results.json'):
        """Save UQ analysis results to JSON file."""
        # Convert numpy arrays to lists for JSON serialization
        def convert_numpy(obj):
            if isinstance(obj, np.ndarray):
                return obj.tolist()
            elif isinstance(obj, np.float64):
                return float(obj)
            elif isinstance(obj, np.int64):
                return int(obj)
            return obj
        
        # Recursive conversion
        def deep_convert(data):
            if isinstance(data, dict):
                return {k: deep_convert(v) for k, v in data.items()}
            elif isinstance(data, list):
                return [deep_convert(item) for item in data]
            else:
                return convert_numpy(data)
        
        converted_results = deep_convert(results)
        
        with open(filename, 'w') as f:
            json.dump(converted_results, f, indent=2)
        
        print(f"\nUQ results saved to: {filename}")

def main():
    """Main execution function for enhanced metamaterial amplification UQ."""
    print("Enhanced Metamaterial Amplification UQ Resolution")
    print("=" * 55)
    
    # Initialize UQ framework
    uq_framework = EnhancedMetamaterialAmplificationUQ()
    
    # Perform comprehensive analysis
    results = uq_framework.comprehensive_uq_analysis()
    
    # Save results
    uq_framework.save_uq_results(results)
    
    print("\n" + "="*60)
    print("ENHANCED METAMATERIAL AMPLIFICATION UQ RESOLUTION COMPLETE")
    print("="*60)
    
    return results

if __name__ == "__main__":
    results = main()