Time-dependent calculations

Time-dependent calculations often result in obtaining a wave function that oscillates between the ground and first excited states. From this solution, it is possible to extract both these states. 

Time-dependent calculations have been completed with a number of different methods. There are three formulations giving equivalent results TDFIF,... 

Time-dependent calculations with highly correlated methods... 

The air and wall temperatures and the concentrations in both zones are solved by iteration toward a steady-state situation or by simulating the time-dependent development. In the time-dependent calculation the heat capacity of the walls should be included. 

Kulander KC, Schafer KJ (1996) Time-Dependent Calculations of Electron and Photon Emission from an Atom in an Intense Laser Field 86 149-172 Kiinzel FM, see Buchler JW (1995) 84 1-70 Kurad D, see also Tytko KH (1999) 93 1-64 Kustin K, see Epstein IR (1984) 56 1-33... 

Figure 3. Time-dependent calculations of kobB(t) vs. AG° for various observation times. Key - 1 ps - 5 ps and , kobsft) for formation of an excited-...

Figure 6. Frequency shift w /wl, Eq. (11), as a function of the relativistic parameter rf = ((jFuu)f(incwii), with - // = 10a.w.. The circles indicate the shift deduced from the full time-dependent calculation.

Let us summarize the essential steps of the time-dependent calculation ... 

Hartke, B. (1991). Continuum resonance Raman scattering in bromine comparison of time-dependent calculations with time-independent and experimental results, J. Raman Spec. 22, 131-140. 

Jiang, X-.P., Heather, R., and Metiu H. (1989). Time dependent calculation of the absorption spectrum of a photodissociating system with two interacting excited electroni states, J. Chem. Phys. 90, 2555-2569. 

Kulander, K.C., Cerjan, C., and Orel, A.E. (1991). Time-dependent calculations of molecular photodissociation resonances, J. Chem. Phys. 94, 2571-2577. 

The simulation of non-Newtonian fluid flow is significantly more complex in comparison with the simulation of Newtonian fluid flow due to the possible occurrence of sharp stress gradients which necessitates the use of (local) mesh refinement techniques. Also the coupling between momentum and constitutive equations makes the problem extremely stiff and often time-dependent calculations have to be performed due to memory effects and also due to the possible occurrence of bifurcations. These requirements explain the existence of specialized (often FEM-based) CFD packages for non-Newtonian flow such as POLYFLOW. 

When studying the stability of the steady-state, time-dependent calculations are needed (see [7]). It can also be used as a simple method to compute the steady-state solution. A time-dependent approach using the Lesaint-Ravian technique for the normal stress components and the Baba-Tabata scheme for the shear stress component is developed by Saramito and Piau ([34]). This method allows one to obtain rapidly stationary solutions of the PTT models. Convergence with mesh refinement is obtained as well as oscillation-free solutions. 

A few examples may demonstrate this. The approximation has been used to treat the photodissociation processes of NOHCl [33] and NO2 [34] which include three internal modes. Five dimensional time dependent calculations were performed on the photodissociation of CH3I [35, 36]. The state-to-state chemistry has been investigated for the reactive scattering of H-1-H2 (v=0,l) —> H2 (v=0,l) -1- H collinear system [37]. The MCTDSCF approach has also been applied to surface chemistry, in particular H2 dissociation on a transition metal surface [38] the photodissociation of CH3I on MgO surface [39, 40] and to inelastic molecule-surface scattering [41, 42]. Recently, the MCTDSCF method has been used to investigate multimode effects in the absorption spectrum of pyrazine taking into account 14 vibrational modes [43]. 

Time-Dependent Calculations of Electron and Photon Emission from an Atom in an Intense Laser Field... 

Time-Dependent Calculations of Electron and Photon Emission... 

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