Usual pair obliteration reaction dynamic, taken from kinetic theory, allows describing the siege and fall of Constantinople (1453 AD) when Ottoman and Byzantine troops confronted each other. Most of the model parameters are based on historical, certainly debatable, assumptions. Ottoman cannons systematically destroyed the city's walls and, consequently, Byzantine disadvantage is considered through time-dependent parameters. Daily estimates for the relative number of warriors among both factions are presented. At the start of the war, the numerical simulation predicts an equilibrium status. But after weeks, systematic destruction of the city's walls eroded the equilibrium and the odds turned in the Ottomans' favor. The growing rapport among victims of both sides is also computed as a function of war days, also the number of victims. This work supports the pair obliteration reaction model for historical wars.
IntroductionQuantitative models devoted to historical, archaeological or biological problems have been persistent interdisciplinary topics [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19]. These models have helped to count the number of individuals, troops, or antique structures' evolution. This work starts from this point and assesses the dynamic of the siege and collapse of Constantinople, caused by the Ottoman Empire, using tolerable historical considerations. The main focus is the comparative evolution of the number of both sides' warriors.Constantinople, today Istanbul, was part of the Byzantine Empire for centuries until it came under siege in 1453 AD and was conquered by the Ottoman Empire. The Byzantine Empire was an alliance mostly of the Roman Republics. A vast literature has been devoted to this historical empire and its inflection point in 1453 AD [20][21][22][23][24][25][26][27][28][29].Constantinople's walls essentially formed a triangle, the external Theodosian walls enclosed some 14 [km 2 ] and were constructed around 410 AD. Geographically, in the south, the so-called Golden Horn was on the shores of the Sea of Marmara. Constantinople's towers rose on the inner (Constantinian) and outer (Theodosian) walls. The walls have a history of about 1,000 years. To conquer the city [20][21][22][23][24][25][26][27][28][29] the Ottomans needed around 90,000 soldiers and almost two months of severe artillery attack to destroy the fortifications. When the city sieged, its total population was around 50,000 including soldiers [25][26][27][28][29].Mehmed II led the Ottoman troops and Constantine XI the Byzantine ones, while Genovese warrior Giovanni Giustiniani Longo played a main role in defending the city. Unfortunately, a precise number of warriors related to Constantinople's siege and fall do not exist. Exaggerations cannot be ruled out for historical and dogmatic reasons. put the number of Ottoman soldiers between 50,000 and 90,000 (not excluding 120,000 [27]), and between 6,000 and 10,000 Byzantine soldiers. Therefore, the number of combatants could vary considerably, depending on th...