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'''Dissipative solitons''' (DSs) are stable solitary localized
{{marketing}}
structures that arise in nonlinear spatially extended
{{wikibookspar||Marketing}}
[[dissipative system]]s because of [[self-organization]].
'''Product placement''' advertisements are [[Promotion (marketing)|promotion]]al ads placed by [[marketing|marketers]] using real commercial products and services in media, where the presence of a particular brand is the result of an economic exchange. When featuring a product is not part of an economic exchange, it is called a '''product plug'''. Product placement appears in plays, film, television series, music videos, [[video games]] and books. It became more common starting in the 1980s, but can be traced back to at least 1949. Product placement occurs with the inclusion of a brand's [[logo]] in shot, or a favorable mention or appearance of a product in shot. This is done without disclosure, and under the premise that it is a natural part of the work. Most major movie releases today contain product placements.<ref name="cons">Solomon. Zaichkowsky, Polegato.'''Consumer Behaviour''' Pearson, Toronto. 2005</ref> The most common form is movie and television placements and more recently [[in-game advertising|computer and video games]]. Recently, [[Web 2.0]] sites have experimented with in-site product placement as a revenue model.
They can be considered as an extension of the classical
[[soliton]] concept in conservative systems. An alternative
terminology includes autosolitons, spots and pulses.
Apart from
== Manifestations of product placement ==
aspects similar to the behavior of classical particles like the
=== Early examples ===
formation of bound states, DSs exhibit entirely
[[Image:NASA shuttle astronaut drinks from a specially designed Coke beverage can.jpg|right|thumb|A [[Coca Cola]] product placement on the [[space shuttle]] is a form of [[space advertising]].]]
''nonclassical'' behavior – e.g. scattering, generation and
One of the best-known instances of product placement appeared in 1982 movie ''[[E.T. the Extra-Terrestrial]]'', which increased sales of [[Reese's Pieces]] 80 percent.<ref name="http://www.itvx.com/SpecialReport.asp" />
annihilation – all without the constraints of energy or momentum
conservation. The excitation of internal
[[degrees of freedom (physics and chemistry)|degrees of
freedom]] may result in a dynamically stabilized intrinsic
speed, or periodic oscillations of the shape.
== Historical development ==
A very early example of product placement in film occurs in the [[1946 in film|1946 film]] ''[[It's a Wonderful Life]]'' by [[Frank Capra]] where a young boy with aspirations to be an explorer displays a prominent copy of [[National Geographic]]. Another is in the [[1949 in film|1949 film]] ''[[Love Happy]]'', in which [[Harpo Marx]] cavorts on a rooftop among various billboards and at one point escapes from the villains on the old [[Mobil]] logo, the "Flying Red Horse".
=== Origin of the soliton concept ===
Another very early example potentially occurs in Jules Verne's ''[[Around the World in Eighty Days]]'' in which transport and shipping companies lobbied to be mentioned as it was initially published in serial form.
DSs have been experimentally observed for a long time. In 1831,
Still another example is the conspicuous display of [[Studebaker]] motor vehicles in the television show ''[[Mr. Ed]]'', which was sponsored by the Studebaker Corporation from [[1961]] to [[1963]].
[[Michael Faraday|Faraday]] <ref>M. Faraday, Phil. Transact.
Roy. Soc. 121 (1831): 319</ref> saw solitary localized
structures in a vibrating layer of fine powder.
[[Helmholtz]]<ref>H. Helmholtz, Arch. Anat. Physiol. 57 (1850):
276</ref> measured the propagation velocity of nerve pulses in
1850. In 1902, [[Otto Lehmann|Lehmann]]<ref>O. Lehmann, Ann.
Phys. 4 (1902): 1</ref> found the formation of localized anode
spots in long gas-discharge tubes. Nevertheless, the term
"soliton" was originally developed in a different context. The
starting point was the experimental detection of "solitary
water waves" by [[John Scott Russell|Russell]] in 1834.<ref>J.
S. Russell, Report of the fourteenth meeting of the British
Association for the Advancement of Science (1845): 311</ref>
These observations initiated the theoretical work of
[[John Strutt%2C 3rd Baron Rayleigh|Rayleigh]]<ref>J. W. Rayleigh, Phil. Mag. 1 (1876): 257
</ref> and [[Joseph Valentin Boussinesq|Boussinesq]]<ref>J.
Boussinesq, Compt. Rend. Acad. Sc. 72 (1871): 755</ref> around
1870, which finally led to the approximate description of such
waves by Korteweg and de Vries in 1895; that description is known today as the (conservative)
[[Korteweg-de Vries Equation|KdV]] equation.<ref>D. J. Korteweg and H. de Vries, Phil. Mag. 39 (1895):
422</ref>
On this background the term "soliton" was
The earliest example of product placement in a computer or video game occurs in the [[1984 in video gaming|1984]] game [[Action Biker]] for [[KP Snacks|KP]]'s [[Skips (snack)|Skips]] [[Potato chip|crisps]].
coined by Zabusky and Kruskal<ref>N. J. Zabusky and M. D.
Kruskal, Phys. Rev. Lett. 15 (1965): 240</ref> in 1965. These
authors investigated certain well localised solitary solutions
of the KdV equation and named these objects solitons. Among
other things they demonstrated that in 1-dimensional space
solitons exist, e.g. in the form of two unidirectionally
propagating pulses with different size and speed and exhibiting the
remarkable property that number, shape and size are the same
before and after collision.
Gardner at al.<ref>C. S. Gardner et al., Phys. Rev. Lett. 19
The earliest example of product placement in a [[cartoon]] occurs in the [[Comedy Central]] show: [[Shorties Watchin' Shorties]].[http://www.commercialalert.org/issues/culture/product-placement/in-another-conquest-for-product-placement-the-new-comedy-central-cartoon-for-adults-joins-the-trend]
(1967): 1095</ref> introduced the inverse scattering technique
for solving the KdV equation and proved that this equation is
completely [[Integrability|integrable]]. In 1972 Zakharov and
Shabat<ref>V. E. Zakharov and A. B. Shabat, Funct. Anal. Appl.
8 (1974): 226</ref> found another integrable equation and
finally it turned out that the inverse scattering technique can
be applied successfully to a whole class of equations (e.g. the
[[Nonlinear Schrödinger equation|nonlinear Schrödinger]] and
[[Sine-Gordon equation|Sine-Gordon]] equations). From 1965
up to about 1975, a common agreement was reached: to reserve the term ''soliton'' to
pulse-like solitary solutions of conservative nonlinear partial
differential equations that can be solved by using the inverse
scattering technique.
=== Weakly and strongly dissipative systems ===
Other times, product usage is negotiated rather than paid for. Some placements provide productions with below-the-line savings, with products such as props, clothes and cars being loaned for the production's use, thereby saving them purchase or rental fees. Barter systems (the director/actor/producer wants one for himself) and service deals (cellular phones provided for crew use, for instance) are also common practices. Producers may also seek out companies for product placements as another savings or revenue stream for the movie, with, for example, products used in exchange for help funding advertisements tied-in with a film's release, a show's new season or other event.
With increasing knowledge of classical solitons, possible
The most common [[product (business)|product]]s to be promoted in this way are automobiles. Frequently, all the important vehicles in a movie or television serial will be supplied by one manufacturer. For example, ''[[The X-Files]]'' used [[Ford Motor Company|Ford]]s, as do leading characters on ''[[24 (television)|24]]''. The [[James Bond]] films pioneered such placement.<ref name="ntata">Nadja Tata: "Product Placement in James-Bond-Filmen". Saarbrücken 2006 - ISBN 3-86550-440-X</ref> The [[1974]] film ''[[The Man with the Golden Gun (film)|The Man with the Golden Gun]]'' featured extensive use of [[American Motors Corporation|AMC]] cars, even in scenes in [[Thailand]], where AMC cars were not sold, and had the steering wheel on the wrong side of the vehicle for the country's roads. Other times, vehicles or other products take on such key roles in the film it is as if they are another character. Examples of this practice include ''[[Bad Boys 2]]'', in which every car was made by [[General Motors Corporation|General Motors]]. In ''[[Desperate Housewives]]'' three of the characters drive [[Nissan]]s, and the camera view often focuses on the Nissan symbol on someone's car. Also the character Gabrielle Solis can also be seen driving an Aston Martin DB9 Volante prominently. In ''[[The Matrix Reloaded]]'', a key chase scene is conducted between a brand new [[Cadillac CTS]] and a [[Cadillac Escalade EXT]]. The chase scene also features a [[Ducati]] motorcycle in the getaway.
technical applicability came into perspective, with the most
promising one at present being the transmission of optical
solitons via [[Fiberglass|glass fibers]] for the purpose of
[[data transmission]]. In contrast to systems with purely
classical behavior, solitons in fibers dissipate energy and
this cannot be neglected on an intermediate and long time
scale. Nevertheless the concept of a classical soliton can
still be used in the sense that on a short time scale
dissipation of energy can be neglected. On an intermediate time
scale one has to take small energy losses into account as a
perturbation, and on a long scale the amplitude of the soliton
will decay and finally vanish.<ref>Y. S. Kivshar and G. P.
Agrawal, ''Optical Solitons. From Fibers to Photonic Crystals'',
Academic press (2003)</ref>
There are however various types of systems which are capable of
More recently, [[Apple Computer]] frequently places its products in films and on television, where they therefore seem much more common than in most real-world offices and homes. Apple has stated that it does not pay for product placement, though executives will not say how their products get into movies and onto TV. The most plausible argument may be that Apple computers appear to be more visually appealing than ordinary PCs. (Notably, recognizable Apple products have appeared in newspaper [[comic strips]], including [[Opus]], [[Baby Blues]], [[Non Sequitur (comic strip)|Non Sequitur]], and [[FoxTrot]], even though paid placement in comics is all but unknown.) In a twist on traditional product placement, [[Hewlett-Packard]] computers now appear exclusively as part of photo layouts in the [[IKEA]] catalog in addition to placing plastic models of its computers in IKEA stores, having taken over Apple's position in the Swedish furniture retailer's promotional materials several years ago. [[Hewlett-Packard]] also put their computers in the US production of ''[[The Office (US TV series)|The Office]]'', though it is likely that this was a purposeful choice, since offices rarely have Macintosh computers.
producing solitary structures and in which dissipation plays an
essential role for their formation and stabilization. Although
research on certain types of these DSs has been carried out for
a long time (for example, see the research on nerve pulses culminating
in the work of [[Hodgkin and Huxley]]<ref>A. L. Hodgkin and A.
F. Huxley, J. Physiol. 117 (1952): 500</ref> in 1952), since
1990 the amount of research has significantly increased.
Possible reasons are improved experimental devices and
analytical techniques, as well as the availability of more
powerful computers for numerical computations. Nowadays, it is
common to use the term ''dissipative solitons'' for solitary structures in
strongly dissipative systems.
== Experimental observations of DSs ==
A variant of product placement is ''advertisement placement''. In this case an [[advertisement]] for the product (rather than the product itself) is seen in the movie or television series. Examples include a [[Lucky Strike]] cigarette advertisement on a [[Billboard (advertising)|billboard]] or a truck with a milk advertisement on its trailer.
Today, DSs can be found in various types of different
Product placement is also used in books (particularly novels) and [[video games]], such as [[Crazy Taxi]], which featured numerous real retail stores as game destinations. However, sometimes the economics are reversed, and video game makers pay for the rights to use real sports teams and players.
experimental set-ups. Examples include
- [[Gas-discharge lamp|Gas-discharge systems]]:
Quantification methods track brand integrations, with both basic quantitative and more demonstrative qualitative systems used to determine the cost and effective media value of a placement. Rating systems measure the type of placement and on-screen exposure is gauged by audience recall rates. Products might be featured but hardly identifiable, clearly identifiable, long or recurrent in exposure, associated with a main character, verbally mentioned and/or they may play a key role in the storyline. Media values are also weighed over time, depending on a specific product's degree of presence in the market.
[[Plasma_(physics)|plasmas]] confined in a discharge space
which often has a lateral extension large compared to the main
discharge length. DSs arise as current filaments between the
electrodes and were found in dc systems with high-ohmic
barrier<ref>C. Radehaus et al., Phys. Lett. A 125 (1987):
92</ref> , ac systems with dielectric barrier<ref> I. Brauer et
al., Phys. Rev. Lett. 84 (2000): 4104</ref>, as anode
spots<ref>S. M. Rubens and J. E. Henderson, Phys. Rev. 58
(1940): 446</ref> as well as in an obstructed discharge with
metallic electrodes<ref>S. Nasuno, Chaos 13 (2003): 1010</ref>.
Product placement can be seen as a modern version of the exhibit displays seen at world's fairs, concerts, sporting events, or anywhere that large numbers of potential customers gathered.
<gallery caption="DSs experimentally observed in planar dc gas-discharge systems with high-ohmic barrier" widths="320" heights="269" perrow="2">
Virtual product placement uses computer graphics to insert the product into the program after the program is complete.[http://www.nytimes.com/glogin?URI=http://www.nytimes.com/2006/01/02/business/media/02digital.html&OQ=_rQ3D1&OP=295c0536Q2FQ5B6ZQ3DQ5BamQ2BpemmbtQ5BtQ3FQ3FQ3AQ5BQ3FqQ5BQ3FtQ5BQ3DQ24p.Q5DZppQ5BIZa.Q2FQ5BQ3Fta.d.bQ2FyPibIy][http://www.ecommercetimes.com/story/48956.html]
Image:Isoldissol1_en.gif| Without oscillatory tails
Image:Isoldissol2_en.gif| With oscillatory tails
</gallery>
- [[Semiconductor]] systems: similar to gas-discharges, however
The [[Pilot (30 Rock episode)|pilot episode]] of the [[NBC]] [[sitcom]] ''[[30 Rock]]'' prominently featured [[General Electric]]'s [[Trivection oven]], which many people believed was an example of product placement.[http://www.kitchencontraptions.com/archives/007881.php] However, [[Tina Fey]], the show's creator, stated in an interview that the oven was included purely as a joke,[http://www.accesshollywood.com/news/ah1969.shtml] although this didn't stop GE from running ads for the oven during the commercial break. Allison Eckelkamp, a spokesperson for GE, said that GE chose to do this to make sure viewers knew it was a real product.[http://www.twice.com/article/CA6396950.html?industryid=23104]
instead of a gas semiconductor material is sandwiched between
two planar or spherical electrodes. Set-ups include Si and GaAs
[[PIN_diode|pin diodes]]<ref>D. Jäger et al., Phys. Lett. A 117
(1986): 141</ref>, n-GaAs<ref>K. M. Mayer et al., Z. Phys. B 71
(1988): 171</ref>, Si
p<sup>+</sup>-n<sup>+</sup>-p-n<sup>-</sup><ref>F.-J.
Niedernostheide et al., Phys. stat. sol. (b) 172 (1992):
249</ref> and ZnS:Mn structures<ref>M. Beale, Phil. Mag. B 68
(1993): 573</ref> .
- [[Nonlinear_optics|Nonlinear optical systems]]: a light beam
== Controversy ==
of high intensity interacts with a nonlinear medium, typically
The James Bond film ''[[Licence to Kill]]'' featured use of the Lark brand of [[cigarette]], and the producers accepted payment for that product placement. The studio's executives apparently believed that the placement triggered the American warning notice requirement for cigarette advertisements and thus the picture carried the [[Tobacco packaging warning signs|Surgeon General's Warning]] at the end credits of the film. This brought forth calls for banning such cigarette advertisements in future films.
the medium reacts on rather slow time scales compared to the
beam propagation time. Often, the output is [[Feedback|fed
back]] into the input system via single-mirror feedback or a
feedback loop. DSs may arise as bright spots in two-dimensional
plane orthogonal to the beam propagation direction, one may
however also exploit other effects like [[polarization]]. DSs
have been observed for [[Saturable_absorption|saturable
absorbers]]<ref>V. B. Tarananko et al., Phys. Rev. A 56 (1997):
1582</ref>, degenerate [[Optical_parametric_oscillator|optical
parametric oscillators]] (DOPOs)<ref> V. B. Tarananko et al.,
Phys. Rev. Lett. 81 (1998): 2236</ref>, liquid crystal light
valves (LCLVs)<ref>A. Schreiber et al., Opt. Comm. 136 (1997):
415</ref>, alkali vapor systems <ref>B. Schäpers et al., Phys.
Rev. Lett. 85 (2000): 748</ref>,
[[Photorefractive_effect|photorefractive media]]<ref>C. Denz et
al., ''Transverse-Pattern Formation in Photorefractive Optics'',
Springer Tracts in Modern Physics (2003): 188</ref>
and semiconductor microresonators<ref>S. Barland et al., Nature
419 (2002), 699</ref> .
Chemical systems: realized either as one- and two-dimensional
Some consumer groups such as [[Commercial Alert]] object to product placement as "an affront to basic honesty",[http://www.commercialalert.org/issues/culture/product-placement] which they claim is too common in today's society. Commercial Alert asks for full disclosure of all product placement arrangements, arguing that most product placements are deceptive and not clearly disclosed. They advocate notification before and during television programs with embedded advertisements. One justification for this is to allow greater parental control for children, whom they claim are easily influenced by product placement.
reactors or via catalytic surfaces, DSs appear as (often as
propagating) pulses of increased concentration or temperature.
Typical reactions are the
[[Belousov-Zhabotinsky_reaction]]<ref>C. T. Hamik et al., J.
Phys. Chem. A 105 (2001): 6144</ref>, the
ferrocyanide-iodate-sulphite as well as the oxidation of
hydrogen<ref>S. L. Lane and D. Luss, Phys. Rev. Lett. 70
(1993): 830</ref>, CO<ref>H. H. Rotermund et al., Phys. Rev.
Lett. 66 (1991): 3083</ref> or iron<ref>R. Suzuki, Adv.
Biophys. 9 (1976): 115</ref>. [[Action_potential|Nerve
pulses]]<ref>A. L. Hodgkin and A. F. Huxley, J. Physiol. 117
(1952): 500</ref> also belong to this class of systems.
- Vibrated media: vertically shaken granular media<ref>P. B.
The film ''[[Minority Report (film)|Minority Report]]'', loosely based on the [[Philip K. Dick]] [[Minority Report|short story of the same name]], makes heavy use of product placement, including [[Coca-Cola]], [[Gap (clothing retailer)|Gap]], and [[Lexus]]. Director [[Steven Spielberg]] also uses one scene to criticize advertising: the main character ([[Tom Cruise]]) is harassed by personalised advertisements calling out his own name. The film ''[[Fight Club (film)|Fight Club]]'', directed by [[David Fincher]], bit the hand that fed it by depicting acts of violence against most of the products that paid to be placed in the film. Examples include the scene where the [[Apple Store (retail) | Apple Store]] is broken into, and the scene in which [[Brad Pitt]] and [[Edward Norton]] smash the headlights of a [[Volkswagen New Beetle|new Volkswagen Beetle]]. The comedy film ''[[Kung Pow! Enter the Fist]]'' also attempted to spoof its product placements, clearly pointing out the anachronistic inclusion of a [[Taco Bell]] in the film. In a similar vein, in ''[[Looney Tunes: Back In Action]]'' the main characters stumble across a [[Wal-Mart]] while stranded in the middle of [[Death Valley]] and get all necessary supplies for their endorsement of the company.
Umbanhowar et al., Nature 382 (1996): 793</ref>,
[[Colloid|colloidal suspensions]]<ref>O. Lioubashevski et al.,
Phys. Rev. Lett. 83 (1999): 3190</ref> or
[[Newtonian_fluid|Newtonian fluids]]<ref> O. Lioubashevski et
al., Phys. Rev. Lett. 76 (1996): 3959</ref> produce
harmonically or sub-harmonically oscillating heaps of material,
which are usually called [[Oscillon|oscillons]].
- [[Hydrodynamics|Hydrodynamic systems]]: the most prominent
2004's ''[[Harold & Kumar Go to White Castle]]'' was one of the first films to be completely centered around a product or product retail store. The [[White Castle]] [[fast food]] chain, though very regional, enjoyed a high rise in exposure when the film was released.{{Fact|date=April 2007}} The story centers around two stoners who attempt to track down a White Castle.
realization of DSs are domains of
[[Horizontal_convective_rolls|convection]] rolls on a
conducting background state in binary liquids<ref>G. Ahlers,
Physica D 51 (1991): 421</ref>. Another example is film
dragging in a rotating cylindric pipe filled with oil<ref>F.
Melo and S. Douady, Phys. Rev. Lett. 71 (1993): 3283</ref>.
- Electrical networks: large one- or two-dimensional arrays of
The film ''[[I, Robot (film)|I, Robot]]'', loosely based on the story collection by [[Isaac Asimov]], makes heavy use of product placements for sports shoes, automobile, and hi-fi companies among others One particularly infamous scene borderlines into actual advertisement territory in which a character compliments Will Smith's character's shoes to which he replies "[[Converse]]. Vintage 2004" (the year of the movie's release). The film was subject to negative criticism[http://www.thebestpageintheuniverse.net/c.cgi?u=i_robot] as a result, being ranked as the #1 worst film for product placement on one site.[http://www.theshiznit.co.uk/review.php?id=144]
coupled cells with a nonlinear
[[current-voltage_characteristic|current-voltage
characteristic]]<ref>J. Nagumo et al., Proc. Inst. Radio Engin.
Electr. 50 (1962): 2061</ref>, DSs are characterized by a
locally increased current through the cells.
Remarkably enough, phenomenologically the dynamics of the DSs
The film ''[[The Island]]'', directed by [[Michael Bay]], features at least 21 individual products or brands, including cars, [[bottled water]], shoes, credit cards, beer, and ice cream.<ref>[http://numsum.com/spreadsheet/show/7807l ''Numsum.com''] Partial list of product placements in ''The Island''. Retrieved March 8, 2007.</ref> The film was highly criticized for this.<ref>[http://advertisingindustrynewswire.com/2006/04/03/13_005916 ''Advertisingindustrynewswire.com''] Criticism of product placements in ''The Island''. Retrieved March 8, 2007.</ref>. In movie's DVD Commentary track, Michael Bay claims he added the advertisements for realism purposes. <ref>[http://www.agonybooth.com/agonizer/article.asp?Id=0000004#bay ''Agony Booth''] Discussion of ''The Island'' DVD Commentary Track. Retrieved April 26, 2007.</ref>
in many of the above systems is similar in spite of the
microscopic differences. Typical observations are (intrinsic)
propagation, [[scattering]], formation of [[Bound_state|bound
states]] and clusters, drift in gradients, interpenetration,
generation and annihilation as well as higher instabilities.
The film ''[[Talladega Nights: The Ballad of Ricky Bobby]]'', directed by [[Adam McKay]], also contained a high amount of product placement. Characters repeatedly mention brands under the disguise of [[NASCAR]] sponsorship. The movie contains possibly the first instance of an actual television commercial in a movie.<ref>[http://www.themoviespoiler.com/Spoilers/talladega.html ''Themoviespoiler.com''] Plot, product placements. Retrieved March 23, 2007.</ref>
== Theoretical description of DSs ==
The television show ''[[South Park]]'' has also used product placements during episodes in its tenth season. Franchise restaurant [[P.F. Chang's]] was featured prominently in the episode "[[A Million Little Fibers]]" without being mocked in any fashion. "[[Cartoon Wars Part I]]" showed the character [[Eric Cartman]] packing [[Dr Pepper]] alongside the fictional [[Cheesy Poofs]] in a methodical fashion. The [[Nintendo]] [[Wii]] played a pivotal role in a [[Go God Go|two part episode]] in 2006. Finally, the episode "Make Love, not Warcraft" revolves entirely around the popular [[MMORPG]], [[World of Warcraft]].
Most systems showing DSs are described by nonlinear
== Size of Product Placement Market ==
[[partial_differential_equations|partial differential
equations]], sometimes also discrete equations or
[[Cellular_automaton|cellular automata]] are used. Up to now,
modeling from first principles followed by a quantitative
comparison of experiment and theory as been performed only
rarely and sometimes also poses severe problems due to to large
discrepancies between microscopic and macroscopic time and
space scales. Often simplified prototype models are
investigated which reflect the essential physical processes in
a larger class of experimental systems. Among these are
- [[Reaction–diffusion_system|Reaction-diffusion systems]],
According to PQMedia, a consulting firm that tracks the product placement market, 2006 product placement was estimated at $3.07B rising to $5.6B in 2010. However, these figures are somewhat misleading in PQMedia's view in that today, many product placement and brand integration deals are a combination of advertising and product placement. In these deals, the product placement is often contingent upon the purchase of advertising revenues. When the product placement that is bundled with advertising is allocated to part of the spending, PDMedia estimates that product placement is closer to $7B in value, rising to $10B by 2010.
used for chemical systems, gas-discharges and
semiconductors<ref>H.-G. Purwins et al., Dissipative Solitons
in Reaction-Diffusion Systems, in ''Dissipative Solitons'',
Lectures Notes in Physics, Springer (2005)</ref>. The evolution
of the state vector
<math>\boldsymbol{q}(\boldsymbol{x},t)</math> describing the
concentration of the different reagents is determined by
diffusion as well as local reactions:
:<math>\partial_t \boldsymbol{q} = \underline{\boldsymbol{D}}
A major driver of growth for the use of product placement is the increasing use of digital video recorders (DVR) such as TIVO which enable viewers to skip advertisements. This ad skipping behavior increases in frequency the longer a household has owned a DVR.
\Delta \boldsymbol{q} + \boldsymbol{R}(\boldsymbol{q}).</math>
A frequently encountered example is the two-component
== Definitions ==
Fitzhugh-Nagumo-type activator-inhibitor system
:<math> \left( \begin{array}{c} \tau_u \partial_t u\\\tau_v
Because products play a broad role in society and in media, it's sometimes useful to distinguish between different types of product appearances in video material. Key categories are sponsorship, brand integration, cost reduction oriented product placement and fee based product placement.
\partial_t v
\end{array} \right) =
\left(\begin{array}{cc} d_u^2 &0\\0&d_v^2
\end{array}\right)
\left( \begin{array}{c} \Delta u\\ \Delta v
\end{array} \right) + \left(\begin{array}{c} \lambda u -u^3 - \kappa_3 v +\kappa_1\\u-v
\end{array}\right)
.</math>
Stationary DSs are generated by production of material in the
In early media, e.g. radio in the 1930s and 1940s and early TV in the 1950s , programs were often underwritten by companies. "Soap operas" are called such because they were initially underwritten by consumer packaged goods companies such as P&G or Unilever. Sponsorship still exists today with programs being sponsored by major vendors such as Hallmark. Incorporation of products into the actual plot of a TV show is generally called "brand integration". A recent example is HBO's Sex In The City, where the plot revolved around an attractive male model dated by one of the protagonists, Absolut Vodka, a campaign upon which she was working, and a billboard in Time Square where the bottle prevented an image of the model from being X-rated. Knight Rider, a TV series featuring a talking [[Chevrolet Camaro]] is another example of brand integration.
center of the DSs, diffusive transport into the tails and
depletion of material in the tails. A propagating pulse arises
from production in the leading and depletion in the trailing
end<ref>E. Meron, Phys. Rep. 218 (1992):1</ref>. Among others,
one finds also periodic oscillations of DSs<ref
name="gurevich">S. V. Gurevich et al., Phys. Rev. E 74 (2006),
066201</ref>, bound states<ref>M. Or-Guil et al., Physica D 135
(2000): 154</ref>, collisions, merging, generation and
annihilation<ref>C. P. Schenk et al., Phys. Rev. Lett. 78
(1997): 3781</ref>.
- [[Ginzburg-Landau_theory|Ginzburg-Landau type systems]] for a complex scalar
Actual product placement, according to ERMA.org, a Hollywood product placement association falls into two categories: products or locations that are obtained from manufacturers or owners to reduce the cost of production, and products that deliberately placed into productions in exchange for fees.
<math>q(\boldsymbol{x},t)</math> used to describe e.g.
nonlinear optical systems, plasmas, Bose-Einstein condensation,
liquid crystals and granular media<ref>I. S. Aranson and L.
Kramer, Rev. Mod. Phys. 74 (2002): 99</ref>. A frequently found
example is the cubic-quintic subcritical Ginzburg-Landau
equation
:<math> \partial_t q = (d_r+ i d_i) \Delta q + l_r A + (c_r + i
== Faux Product Placement ==
c_i)|q|^2 q + (q_r + i q_i) |q|^4 q.</math>
Some filmmakers have responded to product placement by creating fictional products that frequently appear in the movies they make. Some examples:
* [[Kevin Smith]] - Nails Cigarettes, Mooby Corporation, Chewlees Gum, Discreeto Burritos
* [[Quentin Tarantino]] - Red Apple Cigarettes, Big Kahuna Burger, Jack Rabbit Slim's Restaurants
* [[Robert Rodriguez]] - Chango Beer
* [[Pixar Animation Studios]] - Pizza Planet
An alternative formulation is given by considering the energy
This practice is also fairly common in certain [[comics]], such as [[Svetlana Chmakova]]'s ''[[Dramacon]]'', which makes several product-placement-esque usages of "Pawky", (a modification of the name of the Japanese snack "[[Pocky]]", popular among the [[anime]] and [[manga]] fan community in which the story is set) or [[Naoko Takeuchi]]'s ''[[Sailor Moon]]'', which includes numerous references to the series ''[[Codename: Sailor V]]'' which ''Sailor Moon'' was spun off of; the anime makes further use of this [[meta-reference|meta-referential]] gag, going so far as having an animator on a ''Codename: Sailor V'' feature film be a victim in one episode.
<math>\rho = q^2</math> for which one may derive the continuity
equation
:<math> \partial_t \rho + \nabla \cdot \boldsymbol{m} = S = d_r
This practice is also common in certain "reality-based" video games such as the [[Grand Theft Auto (series)|Grand Theft Auto series]] which feature fictitious stores such as Ammu-Nation, Vinyl Countdown, Gash (spoofing [[Gap (clothing retailer)|Gap]]. Another spoof was made in [[GTA:San Andreas]] with Zip), Pizza Boy, etc.
(q \Delta q^{\ast} + q^{\ast} \Delta q) + 2 l_r \rho + 2 c_r
\rho^2 + 2 q_r \rho^3 \quad\text{with} \quad\boldsymbol{m} = 2
d_i \text{Im}(q^{\ast}\nabla q).</math>
One can thereby show that energy is produced in the flanks of the DSs
In the [[1984]] [[cult film]] ''[[Repo Man]]'', a reverse form of product placement is used, with an exaggerated form of 1980's era [[Generic brand|generic]] packaging used on products prominently shown on-screen (these include "Beer", "Drink", "Dry Gin" and "Food - Meat Flavored"). Reportedly, this was done out on necessity after an intended advertiser, who was to have used product placement, backed out in mid-production.
and transported to the center and potentially to the tails
where it is depleted. Dynamical phenomena include propagating
DSs in 1d<ref>V. V. Afanasjev et al., Phys. Rev. E 53 (1996):
1931</ref>, propagating clusters in 2d<ref>N. N. Rosanov et
al., J. Exp. Theor. Phys. 102 (2006): 547</ref>, bound states,
vortex solitons<ref>L.-C. Crasovan et al., Phys. Rev. E 63
(2000): 016605</ref> as well as "exploding DSs"<ref>J. M.
Soto-Crespo et al., Phys. Rev. Lett. 85 (2000), 2937</ref>.
- Swift-Hohenberg equation: Used e.g. in nonlinear optics, granular
== Emerging Technologies ==
media dynamics of flames or electroconvection, the Swift-Hohenberg
can be considered as an extension of the Ginzburg-Landau equation.
It can be written as
:<math>\partial_t q = (s_r+ i s_i) \Delta^2 q + (d_r+ i d_i)
As of 2007, a new trend is emerging in product placement, the development of capabilities that permit dynamic or switchable product placement. Previously post production tools have permitted one time insertion of new product placement images and billboard advertising, e.g. at baseball or hockey games. As of 2007, new startups are offering or developing the ability to switch product placement. First generation virtual product placement has tended to be based upon sports arenas where the geometrical relationships of camera and the surface of the flat area onto which the billboard is projected, can be easily calculated. Second generation product placement or dynamic product placement is more focused upon commercial products. Third generation virtual or dynamic product placement allows targeting of customers with different products that can be dynamically switched based upon e.g. demographics, pyschographics or behavioral information about the consumer.
\Delta q + l_r q + (c_r + i c_i)|q|^2 q + (q_r + i q_i) |q|^4
q.</math>
For <math>d_r > 0</math> one essentially has the same
==See also==
mechanisms as in the Ginzburg-Landau equation<ref>J. M.
* [[Morley (cigarette)|Morley]], a fictional brand of cigarettes used in movies and TV
Soto-Crespo and N. Akhmediev, Phys. Rev. E 66 (2002):
* [[Kmart realism]] - product placement for cultural familiarity
066610</ref>. For <math>d_r < 0</math>, in the real Swift-Hohenberg
* [[Parody advertisement]]
equation one finds bistability between homogeneous states and
* [[Publicity]]
Turing patterns. DSs are stationary localized Turing domains on
* [[Undercover marketing]]
the homogeneous background<ref>H. Sakaguchi and H. R. Brandt,
* [[Cross media marketing]]
Physica D 97 (1996): 274</ref>. This also holds for the complex
* [[Advertising]]
Swift-Hohenberg equations, however here also propagating DSs as
* [[False advertising]]
well as interaction phenomena are possible, observations
* [[Advertiser funded programming]]
include merging and interpenetration<ref>H. Sakaguchi and H. R.
* [[Namechecking]]
Brandt, Physica D 117 (1998): 95</ref>.
* [[Ad creep]]
== Particle properties and universality ==
==References==
<references />
[[Category:Film and video terminology]]
[[Category:Marketing]]
[[Category:Promotion and marketing communications]]
[[Category:Television terminology]]
DSs in many different systems show universal particle-like
[[da:Product placement]]
properties. To understand and describe the latter, one may try
[[de:Schleichwerbung]]
to derive "particle equations" for slowly varying order
[[es:Publicidad por emplazamiento]]
parameters like position, velocity or amplitude of the DSs by
[[hr:Product placement]]
adiabatically eliminating all fast variables in the field
[[it:Pubblicità occulta]]
description. This technique is known from linear systems,
[[he:פרסומת סמויה]]
however mathematical problems arise from the nonlinear models
[[nl:Sluikreclame]]
due to a coupling of fast and slow modes<ref>R. Friedrich,
[[no:Produktplassering]]
Group Theoretic Methods in the Theory of Pattern Formation, in
[[pl:Product placement]]
''Collective dynamics of nonlinear and disordered systems'',
[[ro:Poziţionare]]
Springer (2004)</ref>.
[[ru:Продакт-плейсмент]]
[[fi:Tuotesijoittelu]]
Similar to low-dimensional dynamic systems, for supercritical
[[sv:Produktplacering]]
bifurcations of stationary DSs one finds characteristic normal
[[zh:置入性行銷]]
forms essentially depending on the symmetries of the system.
E.g., for a transition from a symmetric stationary to an
intrinsically propagating DS one finds the Pitchfork normal
form
:<math> \dot{\boldsymbol{v}} = (\sigma - \sigma_0)
\boldsymbol{v} - |\boldsymbol{v}|^2 \boldsymbol{v}</math>
for the velocity <math>\boldsymbol{v}</math> of the DS<ref>M.
Bode, Physica D 106 (1997): 270</ref>, here <math>\sigma</math>
represents the bifurcation parameter and <math>\sigma_0</math>
the bifurcation point. For a bifurcation to a "breathing" DS,
one finds the Hopf normal form
:<math> \dot{A} = (\sigma - \sigma_0) A - |A|^2
A</math>
for the amplitude <math>A</math> of the oscillation<ref
name="gurevich">. It is also possible to treat "weak interaction"
as long as the overlap of the DSs is not too large<ref>M. Bode
et al., Physica D 161 (2002): 45</ref>. In this way, a
comparison between experiment and theory is facilitated<ref>H.
U. Bödeker et al., Phys. Rev. E 67 (2003): 056220</ref>,
<ref>H. U. Bödeker et al., New J. Phys. 6 (2004): 62</ref>.
Note that the above problems do not arise for classical
solitons as inverse scattering theory yields complete
analytical solutions.
== References ==
<references/>
[[Category:Solitons]]
[[Category:Self-organization| ]]
[[Category:Systems theory]]
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