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Aeroelasticity

2014-02-27T09:12:45Z

5.150.69.5: Changed "the forcing exerted" to "the force exerted" in the first sentence.

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Saturation arithmetic

2013-11-04T09:14:16Z

5.150.199.17:

:''For the drug see [[PEPA (drug)]]''

'''Performance Evaluation Process Algebra''' ('''PEPA''') is a [[stochastic]] [[process algebra]] designed for modelling computer and communication systems introduced by [[Jane Hillston]] in the 1990s.<ref>{{cite book|last=Hillston|first=Jane|authorlink=Jane Hillston|title=A Compositional Approach to Performance Modelling|year=1996|publisher=Cambridge University Press|isbn=0-521-57189-8|url=http://www.dcs.ed.ac.uk/pepa/book.pdf|accessdate=2009-04-21}}</ref> The language extends classical process algebras such as [[Robin Milner|Milner]]'s [[Calculus of Communicating Systems|CCS]] and [[C.A.R. Hoare|Hoare]]'s [[Communicating Sequential Processes|CSP]] by introducing probabilistic branching and timing of transitions.

Rates are drawn from the [[exponential distribution]] and PEPA models are finite-state and so give rise to a [[stochastic process]], specifically a [[continuous-time Markov process]] (CTMC). Thus the language can be used to study quantitative properties of models of computer and communication systems such as [[throughput]], [[utilisation]] and [[Response time (technology)|response time]] as well as qualitative properties such as freedom from [[deadlock]]. The language is formally defined using a structured [[operational semantics]] in the style invented by [[Gordon Plotkin]].

As with most process algebras, PEPA is a parsimonious language. It has only four combinators, ''prefix'', ''choice'', ''co-operation'' and ''hiding''. Prefix is the basic building block of a sequential component: the process (''a'', ''r'').''P'' performs activity ''a'' at rate ''r'' before evolving to behave as component ''P''. Choice sets up a competition between two possible alternatives: in the process (''a'', ''r'').''P'' + (''b'', ''s'').''Q'' either ''a'' wins the race (and the process subsequently behaves as ''P'') or ''b'' wins the race (and the process subsequently behaves as ''Q'').

The co-operation operator requires the two "co-operands" to join for those activities which are specified in the co-operation set: in the process ''P'' < ''a'', ''b''> ''Q'' the processes ''P'' and ''Q'' must co-operate on activities ''a'' and ''b'', but any other activities may be performed independently. The [[reversed compound agent theorem]] gives a set of sufficient conditions for a co-operation to have a [[product form stationary distribution]].

Finally, the process ''P''/{''a''} hides the activity ''a'' from view (and prevents other processes from joining with it).

==Syntax==

Given a set of action names, the set of CCS processes is defined by the following [[BNF grammar]]:

:<math>P ::= (a,\lambda).P\,\,\, | \,\,\,P + Q\,\,\, | \,\,\,P\stackrel{\triangleright \!\! \triangleleft}{\scriptstyle{L}}Q\,\,\, | \,\,\,P/L\,\,\,|\,\,\,A</math>

The parts of the syntax are, in the order given above

; action : the process <math>(a,\lambda).P</math> can perform an action ''a'' at rate <math>\lambda</math> and continue as the process ''P''.
; choice : the process ''P+Q'' may behave as either the process ''P'' or the process ''Q''.
; cooperation : processes ''P'' and ''Q'' exist simultaneously and behave indepdendently for actions whose names do not appear in ''L''. For actions whose names appear in ''L'', the action must be carried out jointly and a race condition determines the time this takes.
; hiding : the process ''P'' behaves as usual for action names not in ''L'', and performs a silent action <math>\tau</math> for action names that appear in ''L''.
; process identifier : write <math>A \overset{\underset{\mathrm{def}}{}}{=} P</math> to use the identifier ''A'' to refer to the process ''P''.

==Tools==

* [http://www.dcs.ed.ac.uk/pepa/tools/plugin/index.html PEPA Plug-in] for [[Eclipse (software)|Eclipse]]<ref>{{cite doi|10.1145/1530873.1530880}}</ref>
* [http://www.doc.ic.ac.uk/ipc/ ipc: the imperial PEPA compiler]<ref>{{cite doi|10.1109/MASCOT.2003.1240679}}</ref>
* [http://code.google.com/p/gpanalyser/ GPAnalyser] for fluid analysis of massively parallel systems<ref>{{cite doi|10.1109/QEST.2011.26}}</ref>

==External links==

* [http://www.dcs.ed.ac.uk/pepa PEPA: Performance Evaluation Process Algebra]

==References==

{{Reflist}}

[[Category:Process calculi]]

Pharmacode

2013-05-16T19:13:11Z

5.150.218.51:

{{Refimprove|date=August 2008}}

[[File:FourIVcurves.svg|thumb|450px|The current–voltage characteristics of four devices: a [[resistor]] with large [[electric resistance|resistance]], a resistor with small resistance, a P–N junction [[Diode#Semiconductor diodes|diode]], and a [[Battery (electricity)|battery]] with nonzero internal resistance. The horizontal axis is [[voltage drop]], the vertical axis is [[electric current|current]].]]

A '''current–voltage characteristic''' or '''I–V curve''' (current–voltage curve) is a relationship, typically represented as a [[chart]] or graph, between the [[electric current]] through a circuit, device, or material, and the corresponding [[voltage]], or [[potential difference]] across it.

==In electronics==

[[Image:IvsV mosfet.svg|thumbnail|400px|MOSFET drain current vs. drain-to-source voltage for several values of the ''overdrive voltage'', <math>V_{GS}-V_{th}</math>; the boundary between '''linear''' ('''Ohmic''') and '''saturation''' ('''active''') modes is indicated by the upward curving parabola.]]

In [[electronics]], the relationship between the direct [[electric current|current]] ([[direct current|DC]]) through an [[electronic device]] and the DC [[voltage]] across its terminals is called a current–voltage characteristic of the device. [[Electronic engineers]] use these charts to determine basic parameters of a device and to model its behavior in an [[electrical circuit]]. These characteristics are also known as IV curves, referring to the standard symbols for current and voltage.

A more general form of current–voltage characteristic is one that describes the dependence of a terminal current on more than one terminal voltage difference; electronic devices such as [[vacuum tube]]s and [[transistor]]s are described by such characteristics.<ref>{{cite journal | journal = Proceedings of the IRE | publisher = Institute of Radio Engineers | volume = 7 | year = 1919 | issue = 2 | title = Theory and Operating Characteristics of the Themionic Amplifier | author = H. J. van der Bijl | pages = 97–126 | url = http://books.google.com/?id=p14AAAAAMAAJ&pg=PA105&dq=current-voltage-characteristic | doi = 10.1109/JRPROC.1919.217425}}</ref>

The figure to the right shows a family of IV curves for a [[MOSFET#Modes of operation|MOSFET]] as a function of drain voltage with overvoltage (''VGS − Vth'') as a parameter.

The simplest IV characteristic involves a [[resistor]], which according to [[Ohm's Law]] exhibits a [[linear]] relationship between the applied voltage and the resulting [[electric current]]. However, even in this case environmental factors such as temperature or material characteristics of the resistor can produce a non-linear curve.

The [[transconductance]] and [[Early voltage]] of a [[transistor]] are examples of parameters traditionally measured with the assistance of an I–V chart, or laboratory equipment that traces the charts in real time on an [[oscilloscope]].

==In solar cells==

[[Photovoltaic cell]]s are electronic devices that use P-N junctions to directly convert sunlight into electrical power. Like the electronics covered in the section above, the P-N junction in the solar cell has a complex relationship between voltage and current. As both the voltage and current is a function of the light falling on the cell, the relationship between insolation (sunlight)and output power is complex.

In particular, solar cells have a number of mechanisms that will capture slow-moving electrons of low energy (voltage). Under normal conditions in bright sunlight, these effects are saturated and represent a fixed loss in energy terms. However, at lower insolation levels, say on an overcast day, these mechanisms represent an increasing percentage of the total power being generated. It is also common for cells to be saturated if there is too much insolation, and the number of free electrons or their mobility is too small. For instance, in silicon the holes left by the photoelectrons take some time to be neutralized, and during this time they can absorb a photoelectron from another atom within the cell. This leads to maximum production rates as well as minimum.

If a cell was free of these effects, the graph between voltage, current and output power would form a rectangle on a graph of current vs. voltage. In practice, the actual output is non-linear. The [[fill factor (solar cell)|fill factor]], more commonly known by its abbreviation ''FF'', is a parameter which characterizes the non-linear electrical behavior of the solar cell. Fill factor is defined as the ratio of the maximum power from the solar cell to the product of Voc and Isc, and in tabulated data it is often used to estimate the power that a cell can provide with an optimal load under given conditions, ''P=FF*Voc*Isc''. For most purposes, FF, Voc, and Isc are enough information to give a useful approximate model of the electrical behavior of a photovoltaic cell under typical conditions.

==In electrophysiology==

[[Image:Whole cell IV.jpg|thumb|300px|An approximation of the potassium and sodium ion components of a so-called "whole cell" I–V curve of a neuron.]]

While I–V curves are applicable to any electrical system, they find wide use in the field of biological electricity, particularly in the sub-field of [[electrophysiology]]. In this case, the voltage refers to the voltage across a biological membrane, a [[membrane potential]], and the current is the flow of charged ions through [[ion channel|channels]] in this membrane. The current is determined by the conductances of these channels.

In the case of ionic current across biological membranes, currents are measured from inside to outside. That is, positive currents, known as "outward current", corresponding to positively charged ions crossing a cell membrane from the inside to the outside, or a negatively charged ion crossing from the outside to the inside. Similarly, currents with a negative value are referred to as "inward current", corresponding to positively charged ions crossing a cell membrane from the outside to the inside, or a negatively charged ion crossing from inside to outside.

The figure to the right shows an I–V curve that is more relevant to the currents in excitable biological membranes (such as a neuronal [[axon]]).
The blue line shows the I–V relationship for the potassium ion. Note that it is linear, indicating no voltage-dependent gating of the potassium ion channel. The yellow line shows the I–V relationship for the sodium ion. Note that it is not linear, indicating that the sodium ion channel is voltage-dependent. The green line indicates the I–V relationship derived from summing the sodium and potassium currents. This approximates the actual membrane potential and current relationship of a cell containing both types of channel.

==References==

{{commons category|Device current-voltage characteristics}}
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[[Category:Electronic engineering]]