Boundary first type

The analytical solution to Equation 2 for a semi-infinite medium with first-type boundary conditions may be written in dimensionless form as (Powers et cil, 1991) ... 

Let us first discuss the properties of migration coupling in the first type of systems. Here, the solution of Laplace s equation for any homogeneous situation yields a linear dependence of on z, i.e. with boundary condition 14b and the origin of the z-axis, z = 0 at the CE,... 

In atomic physics we encounter one-electron bound states with different types of boundary condition. For the first type the electron is completely confined to a spherical box, near the boundary of which the potential is negligible. The second type involves a potential which falls to zero... 

Work done on or by a closed system is accomplished by movement of the system boundary against a resisting force or the passage of an electrical current or radiation across the system boundary. Examples of the first type of work are motion of a piston or rotation of a shaft that projects through the syste nr boundary. If there are no moving parts or electrical currents or radiation at the system boundary, then W = 0. 

Mammillary calcite is very dense, with porosities much less than 1%. Pore spaces are of two different types. The first type consists of irregularly shaped pore spaces with fluid inclusions that are commonly oriented parallel with the crystallite boundaries. In traditional speleothems, spindle-shaped inclusions mark the sites where columnar crystals have coalesced (Kendall and Broughton, 1978). In mammillary calcite, the irregular inclusions probably mark... 

By attention to Figures 4(b), 6(b) and 8(b), it is seen that the exit mass flux from the leakage location have an intense fluctuant behavior. The boundary conditions in upstream and downstream also affect the time average of the exit mass flux and the amplitude and frequency of the fluctuations. The average at the first type of boundary condition is about 118 kg/s, at the second state it is about 110 kg/s after 70 seconds and at the third boundary state this average reaches 350 kg/s. 

The macroscopic multi-phase models resulting from the local averaging procedures must be supplemented with state equations, constitutive equations, boundary and initial conditions. The constitutive equations specify how the phases interact with themselves and with each other. The closure laws or constitutive laws can thus be divided into three types [16] Topological, constitutive and transfer laws, where the first type describes the spatial distribution of phase-specific quantities, the second type describes physical properties of the phases and the third type describes different interactions between the phases. 

Sequence of experiment can be divided into two main types. In the first type, one of the boundary values of the independent variable is set, and then consecutive transfer from one experimental point to another takes place until the second boundary value will be achieved. A plan of such experiment is called a consecutive plan. 

At the bottom boundary there is a source of heat q(x, y, t) - thermal flow from the bottom boundary and the impermeability conditions for the groundwater flow. At the upper boundary, the first type condition is specified for pressure P ... 

The first type of boundary conditions (or Dirichlet type) is set by the concentration values at the boundaries ... 

Three types of phantom networks can be distinguished free phantom networks, fixed phantom networks, and localised phantom networks The first type is without any constraints and will consequently collapse. The second type is a phantom network with some junctions fixed in space. As a result, it is subjected to contraints that do not really exist. The most natural phantom network model is the last variant, in which the equilibrium positions of all segments are determined by suitable boundary conditions without any need for segments or junctions being fixed. 

A term describing the transport across the boundaries is called flux, and the creation of any extensive quantity within the system is called production. Immediately, one recognizes that the conservation laws of mass and energy, which is discussed in Sect. 2.1.2, forbid their production. A final set of new terms is also shown in Fig. 2.16. It is a classification of the types of systems. The first type is an open system, represented by an open container, for example, as used for the sample placement in thermogravimetry. In such a system mass and energy flux may occur... 

Two types of comer boundary functions appear near each of the vertices (0, b) and (a, b). Let us consider them, for example, for the vertex (0, b). Comer boundary functions of the first type [we will denote... 

The four dependent variables are substrate, 5 oxidized mediator, reduced mediator, and biofilm matrix potential, E. The following are all of the differential equations, initial conditions, and boundary conditions. Each boundary condition is specified as either a Dirichlet (first-type) or a Neumann (second-type) boundary condition. The electrode surface is at x = 0, and the top of the biofilm is at x = L. 

An electrode in contact with an electrolyte is called a half-cell, often also written half cell. Thus, a simple two-electrode electrochemical cell is composed of two half-cells that contain either the same electrolyte but different electrodes or different electrodes and electrolytes. The first type of chemical cell, where there is no phase boundary between different electrolytes, is a cell without transference. The other type, in which a liquid-liquid junction potential or diffusion potential is developed across the boundary between the two solutions, is a cell with transference. Commercially available reference electrodes can be considered half-cells. ... 

Processes of the first type include formation of the new phase nuclei in the contact zone as a result of heterophase fluctuations under chemical potential and concentration gradient. The description of solid-state reactions of the second and third types, namely those at the moving boundaries between phases that already exist in the diffusion zone, is reduced to the following consecutive stages ... 

There are three types of boundary conditions on the border of the design volume. The boundary condition of the first type ... 

The simplest method of approximation of boundary conditions of the first type for a surface perpendicular to the x-axis for the numerical scheme shown above is the following ... 

The boundary state is important conception in the reliability analysis. We consider the boundary states as states for which the change of one system component causes the change of the system performance level. But this system performance level change can be caused by any component or fixed component. Therefore, two types of boundary states are considered. The first type is a boundary state for which the system state change is caused by the change of the fixed component state. These types of states are named as exact boundary states. The second type is boundary state for which the change of any system component state results change in the system state. This type is known as Minimal Cut Set. 

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