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1 May 2019: ē(Nsp,L) =1. M. Mj=1. e(Nsp,L)(tj), (79). where the M time steps tj are equidistant. ... ēsts (t) =. 1. M. Mj=1. ests (tj), (83). where the M time steps tj are equidistant.

1 May 2019: T. Define function ρi(n) such that:. ρi(n) =φi(n)Tj=1 φi(j). (24). 2 Start with any initial state (x(0),T (0)).

1 May 2019: aposteriori). Specifically, we employ. ctot :=1. M 1. M. j=0. x(tj) x̃(tj), (2). ... tj := j tstopM. For the numerical study M = 29 = 512 has been used.

1 May 2019: Finish. Loop over reactors. Loop over timesteps. Solve gas-phase over[tj , tj ts2. ]. ... Solve particle-phase over[tj , tj ts. ]. Solve gas-phase over[tj ts2 , tj ts. ].

1 May 2019: a posteriori) we employ. c(n,L)tot :=. 1. M 1. Mj=0. η(n,L)1 (tj) ξ(tj), (4.3). ... c(n,L)stat := max. j{0,.,M}. {c(n,L)p (tj). }, (4.6). again applying splitting (4.4).

1 May 2019: ctot =1. M 1. Mj=0. f (tj) f̃ (tj), (4.1). where f denotes some function of the exact solution (e.g. ... M subintervals of equal length via. tj = j tstopM. 4.1 Performance of the new algorithm.

1 May 2019: junction temper-ature Tj. ... Tg = Tj ε j σ(T 4j T 4w)d. k Nu(1).

1 May 2019: Qconv,i = j. hconv,i jAconv,i j (Tj Ti). (5). 5. The heat of conduction between volume element i and j is calculated according to eq. ... Qcond,i = j. λViL2cond,i j. (Tj Ti). (6). The contribution to the energy balance due to gas flow is governed by:.

1 May 2019: A stochastic approximation scheme and convergencetheorem for particle interactions with. perfectly reflecting boundary conditions. Clive G. Wells. Department of Chemical Engineering, University of Cambridge, New Museum Site,. Pembroke Street,

1 May 2019: Ntto σt as N in reases we have plotted in Figure 4 the quantitydvar(N ) =. j. i>1. (σ̄L ; Ntj σ. tj. )(i),where σ̄tL ; N (i) and σt (i) represent ... These results empiri ally onrm Theorem 2 (in this ase where it10For Figure 4, the times points {tj