Deterministic models boundary conditions

From the scientific point of view, however, all approaches in the sense of the Kd concept (Henry, Freundlich or Langmuir isotherm) are unsatisfactory, since the complex processes on surfaces cannot be described by empirical fitting parameters. Boundary conditions like pH value, redox potential, ionic strength, competition reactions for binding sites are not considered. Thus results from laboratory and field experiments are not transferable to real systems. They are only advisable to provide a suitable prognosis model, if no changes concerning boundary conditions are to be expected and if no parameters for deterministic or mechanistic approach can be determined. 

All methods described above can be categorized as automated case-by-case simulations based on accidents. There are two more aspects which are of importance for a sound system evaluation during the pre-crash phase. Many processes involved are deterministic, e.g., the participants dynamics, the technical functions implemented, as well as many physical boundary conditions. However, some of the key processes do have a stochastic nature for example, the driver action and reaction as well as some characteristics, e.g., of the sensors modeled. Due to the sensitivity of the results to those processes, stochastic elements are an important feature of any representative evaluation (see also Sect. 3.4). 

Deterministic methods ° are based on the use of models to describe the system these models may be empirical or based on physical relationships. For a given input or set of initial and boundary conditions, the model will generate a single value or a set of values to describe the state of the system. To obtain conservative estimates, appropriate extreme or conservative values of the input parameters should be used. 

Execution of the method requires the physical domain to be divided into a distribution of conqiutational cells. The cells provide geometric boundaries and volumes, which are used to sample macroscopic properties. Also, only molecules located within the same cell, at a given time, are allowed to collide. The DSMC simulation proceeds from a set of prescribed initial condition. The molecules randomly populate the computational domain. These simulated molecules are assigned random velocities, usually based on the equilibrium distribution. The simulated representative particles move for a certain time step. This molecule motion is modeled deterministically. This process enforces the boundary conditions. With the simulated particles being appropriately indexed, the molecular collision process can be performed. The collision process is modeled statistically, which is different from deterministic simulation methods such as the molecular dynamics methods. In general, only particles within the same computational cell are considered to be possible collision partners. Mthin each cell, collision pairs are selected randomly and a representative set of collisions is performed. The post-collision velocities are determined. There are several... 

Prediction models Prediction models provide data on flow, subsidence, and mass transport of pollutants. They utilize data on aquifer parameters such as direction of flow, rate of flow, changes in water level, stream-aquifer interactions, and effects of wells. The mass transport models may be conservative in which reactions are considered or nonconservative Most effort to date has been in this area Predictions are deterministic rather than probabilistic Spatially these models may be two-dimensional or multilayered Chemical reactions can be considered Most flow models do not consider interactions at boundaries with steam or seawater Few models can handle both ground and surface water Difficult to model highly variable flow conditions Computer support required Few models couple flow and quality... 

Most recently Jiang et al [12] published a deterministic EHL solution that handled hydrodynamic luhrication and asperity contacts (up to 12% of Hertzian contact area in presented cases) simultaneously. Shortly after that Zhu and Hu [13,14] presented a unified approach that is capable of simulating the entire transition fi-om the full-film, mixed, down to boundary lubrication. The contact load and area ratios could vary finm zero up to 100%, while the film thickness ratio, X, could be reduced from infinity down to zero. The numerical model has been proven to be robust under severe operating conditions (see [13-16]). Based on this model, a systematic study has been conducted by the present author for the effects of load and speed on the EHL film thickness in extended parameter ranges [17]. 

Similarly, the state and auxiliary data are also described by vectors or functions with the same possibilities of space or time dependence. The auxiliary data which models control parameters such as flow rates in wells, boundary and initial conditions, can be deterministic or stochastic. The state is deterministic if both the properties and the auxiliary data are deterministic. 

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