생명공학

List of variables dt = timestep tau = decay time spring constant = 1, mass = 1, omega = 1, period = 2 Pi, nPeriod = 16, dt = 2 Pi/nPeriod, tau = 4 (2Pi) Simulation tutorial 1) Generate new position newP[p0_] := RandomReal[NormalDistribution[p0 Exp[-dt/tau], Sqrt[1 - Exp[-2 dt/tau]]]] 2) Verlet step simulation for a noisy harmonic oscillator verletStep[p_, q_] := Module[{}, nextQ = q + p dt - q/2..

Modeling/Mathematica 2020. 12. 6. 02:18

List of variables Config = list of particle positions boxL = system linear dimension nTot = total number of particles bete = beta epsilon rMax = truncation range nCell = number of cells in one direction wid = width of a cell cellist = 2d lists of particles in cells eTotal = total energy pExcess = excess pressure iSave = index into eValues and pValues eValues = list of stored energy values pValue..

Modeling/Mathematica 2020. 12. 6. 02:09

List of initial constants Pe = 1.0; Peh = 1.0; Da = 10.0; Da0 = 10.0; Dah0 = 10.0; EA = 1.0; b = 2.0; φ a = 1.0; tmax = 20; List of functions 1) Isothermal reactor 1-a) Set up mole balance equation with boundary-initial conditions eqns = [0==(1/Pe)D[ψ[λ], λ, λ]- D[ψ[λ], λ]- Da ψ[λ], (D[ψ[λ], λ]/. λ → 0.0) ==Pe((ψ[λ]/. λ → 0.0)- 1.0), (D[ψ[λ], λ]/. λ → 1.0) == 0.0]; sol = NDsolveValue[eqns, ψ,{λ,..

Modeling/Mathematica 2020. 12. 6. 00:45

Multiple reactions in a gas phase A + B -> D (1) desired reaction 2A -> U (2) byproduct List of initial constants k1 = 0.7; k2 = 0.6; P0 = 10; T0 = 373.15; CT0 = P0/(0.082 T0); v0 = 100.0; FT0 = CT0 v0; FA0 = 1/2 FT0; FB0 = 1/2 FT0; List of functions 1) NDSolve nonlinear equations for molar flow rate of each species sol = NDSolve[{ FA'[V] == -k1((CT0^2 FA[V]FB[V])/FT[V]^2)-k2 CT0^2 (FA[V]/FT[V])..

Modeling/Mathematica 2020. 12. 6. 00:34

Multiple reactions in a gas phase A + B -> D (1) desired reaction 2A -> U (2) byproduct List of initial constants k1 = 0.7; k2 = 0.6; P0 = 10; T0 = 373.15; CT0 = P0/(0.082 T0); v0 = 100.0; FT0 = CT0 v0; FA0 = 1/2 FT0; FB0 = 1/2 FT0; V = 500.0; List of functions 1) Solve nonlinear equations for molar flow rate of each species sol = FindRoot [{ FA0 - FA - (k1 ((CT0^2 FA FB)/FT^2) + k2 (CT0^2 (FA/F..

Modeling/Mathematica 2020. 12. 6. 00:32

Multiple reactions in constant volume Batch Reactor A + B -> D (1) desired reaction 2A -> U (2) byproduct List of initial constants k1 = 0.7; k2 = 0.6; CA0 = 5.0; CB0 = 5.0; Liston of functions 1) NDSolve the molar concentration of each species sol = NDSolve[{CA'[t] == -k1 CA[t] - k2 CA[t]^2, CB'[t] == -k1 CA[t] , CD'[t]==k1 CA[t], CU'[t]== (k2/2) CA[t]^2, CA[0] == CA0, CB[0] == CB0, CD[0]== CU[..

Modeling/Mathematica 2020. 12. 6. 00:29

As mentioned in the previous part, all accessible microstates are equally likely in equilibrium. We can obtain the properties by averaging over the ensembles. We don’t have to evolve the exact configurations in time. Link down here, https://synbio.tistory.com/entry/Phase-space In this section, four ensembles are introduced as a useful framework for describing the average properties. Moreover, we..

Other studies/Thermodynamics and statistical mechanics 2020. 11. 29. 18:47

In statistical thermodynamics, phase space represents all possible states of momentum and position variables. All the variables obey the same physical law but behave in unpredicted way. If we can solve Newton’s second law numerically, we would figure out every momentum (q) and position (p). Unfortunately, it is well known that it is nearly impossible to know both the exact momentum and position...

Other studies/Thermodynamics and statistical mechanics 2020. 11. 29. 18:36

Other studies/Thermodynamics and statistical mechanics 2020. 11. 29. 12:40

The real reactors are often far from the ideal reactors in the book so the chemical engineers must handle the real chemical reactor with diagnosing problems of operating reactors and predicting effluent conversion. To achieve this goal, three factors are considered to describe the characteristics of the real reactors; the residence time distribution (RTD), the quality of mixing, and the model fo..

Other studies/Reaction engineering 2020. 11. 29. 12:37