This paper presents a novel shooting method for solving two-point boundary value problems for second order ordinary differential equations. The method works as follows: first, a guess for the initial condition is made and an integration of the differential equation is performed to obtain an initial value problem solution; then, the end value of the solution is used in a simple iteration formula...

The velocity and mixing field of two coaxial jet configurations has been experimentally characterized by means of hotand cold-wire anemometry to investigate the effect of the initial conditions on the flow development, and to determine the leading processes in the “mixing transition” of the two streams. Amongst the possible operating conditions, four configurations with different inner and oute...

We study the production of η′ from hadronizing thermal gluons using recently proposed η′ − g − g effective vertex. The η′ yield is found to be sensitive to the initial condition. At RHIC and LHC, the enhancement is large enough to be easily detected.

This paper deals with continuous-time opinion dynamics that feature the interplay of continuous opinions and discrete behaviours. In our model, the opinion of one individual is only influenced by the behaviours of fellow individuals. The key technical difficulty in the study of these dynamics is that the right-hand sides of the equations are discontinuous and thus their solutions must be intend...

and Applied Analysis 3 Subject to the initial condition D α−k 0 U (x, 0) = f k (x) , (k = 0, . . . , n − 1) , D α−n 0 U (x, 0) = 0, n = [α] , D k 0 U (x, 0) = g k (x) , (k = 0, . . . , n − 1) , D n 0 U (x, 0) = 0, n = [α] , (11) where ∂α/∂tα denotes the Caputo or Riemann-Liouville fraction derivative operator, f is a known function, N is the general nonlinear fractional differential operator, a...

The so-called renormalization group (RG) method is applied to derive Boltzmann equation in classical mechanics and Fokker-Planck equation from the respective microscopic equations. Utilizing the formulation of the RG method which elucidates the important role played by the choice of the initial conditions, the general structure and the underlying assumptions in the derivation of kinetic equatio...

We propose a new definition of geodesic completeness, based on analytical continuation in the complex domain: we apply this idea to Clifton-Pohl torus, relating, for each geodesic, completeness to the value of a function of initial conditions, called ’impulse’.

A fundamental ingredient that controls the kinetics of the two-species annihilation process, A + B → 0, is the rate of reaction in the interfacial region between a domain of A’s and a domain of B’s. A natural way to study this interface is to prepare a system with initially separated components and then monitor the reaction rate as a function of time, as first studied by Gálfi and Rácz [1]. Thi...

A new proof of a pathwise uniqueness result of Krylov and Röckner is given. It concerns SDEs with drift having only certain integrability properties. In spite of the poor regularity of the drift, pathwise continuous dependence on initial conditions may be obtained, by means of this new proof. The proof is formulated in such a way to show that the only major tool is a good regularity theory for ...

We consider a simple two strategy game in which each pure strategy is an evolutionarily stable strategy (ESS). Under the usual dynamical equations, • the large-time behaviour of the system will depend upon the initial conditions and the pay-off matrix. If spatial effects are included to give a reaction-diffusion system, we prove that travelling wavefronts can occur which in effect replace one E...