Solidarity in Hebrews - Embracing Shared Suffering and Redemption
The book of Hebrews illuminates the profound solidarity between God and humanity through Jesus Christ's suffering and redemption. It emphasizes how identifying with the shared human experience helps cultivate compassion and unity among individuals. The text emphasizes the transformative power of empathy and communal support in navigating life's challenges and finding healing. Discovering the beauty of solidarity in the face of suffering can lead to a deeper understanding of interconnectedness and shared grace.
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1 second v(t) 1700 1600 (millimeters/second) Wind speed 1500 1400 1300 1200 t 1100 0 512 1024 1536 2048
1 second v(t) 1700 (millimeters/second) 1600 Wind speed 1500 1400 1300 1200 t 1100 0 512 1024 1536 2048 v(t) v(t) 4 3 2 t 1 0.2 0.4 0.6 0.8 1 -1 -2 t
W(t) 4 3 2 1 t 0.2 0.4 0.6 0.8 1 -1 -2
-49 Temperature oC -50 -51 -52 16.7 -53 Distance (km) 500 1000 1500 2000 gradient 1
The Historical development of numerical atmospheric models and 23/9D dynamics Log10 (vertical levels) 2.0 12 10 11 13 8 1.5 7 9 5 6 1.0 4 23/9-D model 3 0.5 2 1 0.5 1.0 1.5 2.0 2.5 3.0 3.5 Log10 (horizontal points)
Log10 (number of vertical levels) 100 2.0 12 10 11 13 8 1.5 7 9 5 6 1.0 10 4 3 0.5 2 1 10 100 1000 0.5 1.0 1.5 2.0 2.5 3.0 3.5 Log10 (number of horizontal points)
Many particles: Statistical mechanics Particle scale scale Continuum mechanics scale: a single vortex Turbulence laws: the spaghetti picture Many vortices
Example: The emergence of Thermodynamics from Newton s laws Newton s laws: Thermodynamics: First law: dU = dq+dW (energy conservation) Second law: dS = dq/T 0 (increase in entropy) Large number of particles Ideal gas law: pV = nRT High level Low level, (difficult to handle for many particles) (Valid when many particles are present)
Example: The emergence of the laws of optics Laws of Electromagnetism (Maxwell s equations) Scales>>wavelength Laws of geometric optics
The emergence of turbulence dynamics (Classical) Vortices in strongly turbulent fluid (M. Wiczek, numerical simulation, 2010) Spaghetti Fluid mechanics Low level (fundamental) Strong stirring (nonlinearity) Laws of turbulence Classical: Richardson, Kolmogorov, Corrsin, Obukhov, Bolgiano High level
