Physics
Boundary Conditions for Circuits
Boundary conditions for circuits refer to the conditions that must be met at the interface between two different materials or regions in a circuit. These conditions include continuity of current and voltage, as well as the absence of any abrupt changes in these quantities. Boundary conditions are important for understanding the behavior of circuits and designing them for specific applications.
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4 Key excerpts on "Boundary Conditions for Circuits"
eBook - PDFEngineering Electromagnetics
Pergamon Unified Engineering Series
- David T. Thomas, Thomas F. Irvine, James P. Hartnett, William F. Hughes(Authors)
- 2013(Publication Date)
- Pergamon(Publisher)
150 Boundary Value Problems tant fields calculated. The boundary condition would state that far from the body, the fields must equal the original uniform field. A similar example is the assumed incident plane wave used for calculating reflection, transmission or scattering from a body. These idealized source fields yield the simplest possible solution and valuable information with only slight (often negligible) errors. A different example occurs in our sample diode problem. There the exterior battery causes a potential difference, V 0 , to exist between the plates of the diode. This is the most common type of exterior source condition you will encounter. One final type of source condition occurs within the region. This is where we assume a point charge (source) or current carrying filament wire creates mathe-matical unbounded (infinite) fields. This is despite our imposed bounded fields constraint, again for simplification and maximum information gain with minimum effort and time. The boundary condition in cases such as this requires the fields near the point or line source to be identical to those which would exist were the source in an unbounded medium (infinite size). Returning to our diode problem, we now apply the above four categories of boundary conditions, and upon completion the idealized mathematical boundary value problem will be stated. By category then, the boundary values are: 1. Geometrical Considerations. Rectangular coordinates will be used, oriented as shown in Fig. 5-4. (The orientation is not really critical in this problem.) Our assumption that both plates may be con-sidered of infinite size leads to the assumption of no y or z variation. The voltage and fields will be functions of x only. 2. Fundamental Physical Conditions. No useful conditions are available here since although finiteness restraints are necessary, they do not simplify the solution. 3. Boundary Conditions. The boundaries between media occur at x = 0, and x = d.
eBook - PDF- James S. Vrentas, Christine M. Vrentas(Authors)
- 2016(Publication Date)
- CRC Press(Publisher)
55 3 Boundary Conditions Boundary conditions relate the interactions of a system of interest with its physical surroundings. This chapter deals primarily with the formulation of boundary conditions at phase interfaces for multicomponent mixtures. Appropriate jump balances for mass and linear momentum conservation are derived. Various aspects of the formulation of valid boundary conditions at phase interfaces in the presence as well as in the absence of mass transfer are discussed. 3.1 Definitions For partial differential equations, initial conditions and boundary conditions at infi-nite distances can usually be formulated in a straightforward manner although, in cer-tain cases, care must be exercised in the formulation of conditions at infinite distances (Stakgold 1968b, p. 297). It proves somewhat more difficult to formulate proper conditions at phase interfaces because phase interfaces are dividing surfaces which are singular. Certain quantities such as mass density and velocity can be discontinuous at the phase boundary. For example, there is usually a significant change of density that takes place at a gas–liquid interface. In general, three basic models are used to describe phase interfaces: 1. The phase interface is a mathematical surface between phases which has no prop-erties of its own. 2. The phase interface is a mathematical surface between phases which has its own properties such as surface tension, surface viscosity, and surface reactions. 3. The phase interface is a transition region between phases, and this transition region has special properties. In this text, a variation of the second model is adopted. It is assumed that a phase interface is a mathematical surface with only one surface property, namely the ability to carry out surface reactions. Other surface properties such as surface tension and surface viscosity are not considered here. There are two types of boundary conditions which can be formulated at phase interfaces: 1.
eBook - ePubPersonal Reality, Volume 1
The Emergentist Concept of Science, Evolution, and Culture
- Daniel Paksi(Author)
- 2019(Publication Date)
- Pickwick Publications(Publisher)
This means that for fundamental physics, the higher-level boundary conditions are only instrumental tools which have no role in the final results, but for physical sciences, the basic principles, laws, and results of fundamental physics are fundamental; this is the reason, actually, we call it fundamental physics. Ontologically speaking: the laws of fundamental physics and the fundamental properties of matter determine the conditions among which any higher-level boundary condition can emerge. However, as Galilei rightly observed, these fundamental conditions are usually constant (e.g., on Earth), and for physical sciences, the third factor—that is, the actual initial conditions—become the most important one to explain the origin of different higher-level, comprehensive phenomena called structural boundary conditions. 7.5 Boundary Conditions in Life Sciences and Engineering The exploration of boundary conditions becomes more fascinating when we arrive at the territories of engineering and the life sciences. As we have seen in subchapter 7. 2, the structures of living beings control and harness the lower-level processes in the same way as the structures of machines—in both cases, we are speaking of control boundary conditions. The two main differences are that the structures of living beings are determined by the principles of biology, life, and evolution—and not by that of engineering—and the aims of the former are not determined by man but rather by nature. The two main goals of living beings are self-preservation and reproduction because this is the way that living beings preserve their unique structures and can persist in time (9. 5). Contrary to this, the aims of machines are entirely subordinate to man, and they cannot preserve their unique structures in themselves (8. 5)
eBook - PDF- Jens-Dominik Mueller(Author)
- 2015(Publication Date)
- CRC Press(Publisher)
5 Boundary conditions and flow physics Boundary conditions (BCs) allow the user to choose the flow conditions once the domain of the simulation is fixed. Clearly, only the assignment of specific boundary conditions make a simulation unique and applicable to the problem that is being simulated. The correct selection of BCs for a particular boundary needs to consider the combination of all BCs around the domain. Sec 5.3 will have a more mathematical look at what combinations can work and which ones can’t. This requires the understanding of how information travels in the flow field which is discusssed in Sec. 5.2. Let us start with some considerations based on the flow physics to get started. 5.1 Selection of boundary conditions 5.1.1 Some simple examples In some cases the assignment of boundary conditions is very straightforward. Consider e.g., the flow near a solid wall, the wall condition . Depending on what type of mathematical model is being used, and what behaviour we want to impose there, we need to choose an appropriate condition. In a viscous Navier-Stokes model a no-slip condition is imposed on a fixed wall; the flow has zero velocity at the wall. 1 If the wall is moving, e.g., a rotat-ing tyre, the no-slip condition means that the the velocity is zero with respect to the moving surface, i.e., the fluid at the wall moves with the rotational speed of the tyre. If an Euler model is used for the flow where viscous effects are neglected, a slip-wall condition needs to be chosen which imposes tangency of the flow at the wall: the velocity at the wall has to be parallel to the wall, but cannot penetrate it. It may also be appropriate to choose a slip-wall condition in viscous flow, e.g., when simulating a vehicle in a wind-tunnel where the viscous effects on the tunnel wall are not of interest and we don’t want to refine the grid there to represent these effects. For inflow and exit boundaries, the conditions have to be considered more carefully and in conjunction.
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