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# Topic: Nonlinearity

 Nonlinearity - Wikipedia, the free encyclopedia Since nonlinear systems are not equal to the sum of their parts, they are often difficult (or impossible) to model, and their behavior with respect to a given variable (for example, time) is extremely difficult to predict. Nonlinear equations and functions are of interest to physicists and mathematicians because most physical systems are inherently nonlinear in nature. For nonlinear equations the solutions to the equations do not in general form a vector space and cannot (in general) be superposed (added together) to produce new solutions. en.wikipedia.org /wiki/Nonlinearity   (720 words)

 Nonlinear Dynamics and Complex Systems Theory (Glossary)   (Site not responding. Last check: 2007-11-07) Deterministic chaos refers to irregular or chaotic motion that is generated by nonlinear systems evolving according to dynamical laws that uniquely determine the state of the system at all times from a knowledge of the system's previous history. The logistic map is one of the simplest (continuous and differentiable) nonlinear systems that captures most of the key mechanisms responsible for producing deterministic chaos. If f is a nonlinear function or an operator, and x is a system input (either a function or variable), then the effect of adding two inputs, x1 and x2, first and then operating on their sum is, in general, not equivalent to operating on two inputs separately and then adding the outputs together; i.e. www.cna.org /isaac/Glossb.htm   (8566 words)

 Reference.com/Encyclopedia/Nonlinearity Nonlinear systems are mathematically represented systems whose behavior is not expressible as a linear function of its descriptors; that is, such systems are not linear. As such, the behavior of nonlinear systems is not subject to the principle of superposition, when the system equations can be split into "sum of its parts" and which can make certain kind of assumptions, approximations and mathematical approaches possible. Nonlinear equations and functions are of interest to physicists and mathematicians because they are hard to solve and give rise to interesting phenomena such as chaos. www.reference.com /browse/wiki/Non-linear   (647 words)

 Nonlinearity   (Site not responding. Last check: 2007-11-07) Nonsensical values of both the nonlinearity and the transformation parameters are the usual result, accompanied by a misleadingly ``good'' fit (small residuals, and small standard errors on the coupled parameters). To determine nonlinearity accurately, a neutral attenuator should be used to observe a considerable number (say, 15 or 20) of the brightest stars. A less precise determination of nonlinearity is possible by using the atmospheric extinction as the attenuator; unfortunately, this is not neutral, so the coupling between nonlinearity, extinction, and bandwidth parameters can produce systematic reduction errors. www.eso.org /projects/esomidas/doc/user/98NOV/vol2_html/node295.html   (335 words)

 Measured Boolean Function Nonlinearity in Mixing Cipher Constructions   (Site not responding. Last check: 2007-11-07) Nonlinearity is the number of bits which must change in the truth table of a Boolean function to reach the closest affine function. That is, nonlinearity measures one form of cipher "strength." For cryptographic purposes, it is desired to take the nonlinearity of a substitution table to be the *minimum* of the nonlinearity values for each output bit in that table. Nonlinearity is measured by forming the (one-bit-wide) truth table for a particular output bit, then performing a Fast Walsh-Hadamard Transform (FWT) on that array. www.ciphersbyritter.com /ARTS/MIXNONLI.HTM   (2186 words)

 Poynton's Gamma FAQ   (Site not responding. Last check: 2007-11-07) By the way, the nonlinearity of a CRT is a function of the electrostatics of the cathode and the grid of an electron gun; it has nothing to do with the phosphor. Nonlinearities from these sources are often categorized as gamma and attributed to the display. But when a nonlinear transform lies between the two systems, as in video, a linear transformation performed in one domain is not linear in the other. people.ee.ethz.ch /~buc/brechbuehler/mirror/color/GammaFAQ.html   (3189 words)

 Define nonlinearity - a Whatis.com definition   (Site not responding. Last check: 2007-11-07) Nonlinearity is the behavior of a circuit, particularly an amplifier, in which the output signal strength does not vary in direct proportion to the input signal strength. Nonlinearity can be tolerated in devices and systems that use digital modulation, and also in frequency modulation (FM) wireless transmitters. Nonlinear circuits generally cause distortion in applications such as amplitude-modulation (AM) wireless transmission and hi-fi audio. whatis.techtarget.com /definition/0,,sid9_gci530501,00.html   (225 words)

 Temporal Contrast Adaptation in the Input and Output Signals of Salamander Retinal Ganglion Cells -- Kim and Rieke 21 ... The thick trace is the predicted response from the static nonlinearity model using the linear filter and static nonlinearity shown in B and C. In 28 of 32 cells, the shape of the static nonlinearity was independent of the contrast of the light input, and hence the effect of contrast on the sensitivity was restricted to changes in the linear filter. The static nonlinearities overlapped, and hence the effect of changes in variance in the response of the cell were confined to the linear filter. www.jneurosci.org /cgi/content/full/21/1/287   (9335 words)

 Journal of Research of the National Institute of Standards and Technology: Nonlinearity measurements of high-power ...   (Site not responding. Last check: 2007-11-07) We specifically discuss the attenuation method for optical nonlinearity measurement that the NIST system is based upon, and we review the possible sources of nonlinearity inherent to thermal detectors used with high-power lasers. We also describe, in detail, the NIST nonlinearity measurement system, in which detector responsivity can be measured at wavelengths of 1.06 [micro]m and 10.6 [micro]m, over a power range from 1 W to 1000 W. We present the data processing method used and show measurement results depicting both positive and negative nonlinear behavior. The nonlinearity source (3) is a function of the exposure time, and for short exposure times (customary operating condition for most detectors) this nonlinearity contribution will be quite small. www.findarticles.com /p/articles/mi_m0IKZ/is_4_109/ai_n8706937   (1268 words)

 Control-Relevant Process Nonlinearity Characterization   (Site not responding. Last check: 2007-11-07) While the process nonlinearity and operating region are considered when one is assessing the nonlinearity of the process itself, consideration of the closed-loop performance objective is also a critical component of assessing control-relevant nonlinearity. For example, in the case of a significantly nonlinear process, if the performance specification is mild (e.g., purely stabilization) it may be shown that linear control is adequate. It is presumed that the control-relevant nonlinearity analysis will provide insight to these questions as a spectrum of controllers is considered, ranging from linear through varying degrees of nonlinearity. www.chemengr.ucsb.edu /~hernjak/research.html   (703 words)

 NICMOS Data Handbook Chapter 4.3: Detector Nonlinearity Issues Early nonlinearity calibrations, used for all Cycle 7 and 7N data processed retrieved from the HST Archive before 26 September 2001, used a low-order correction, which worked well for most purposes. However, NICMOS data are actually nonlinear at all levels, and in the new reference files the linearity correction will be calibrated and applied at all count levels. The simplest cure is to modify the nonlinearity reference file to reduce the threshold where saturation flagging is triggered, and then to reprocess the data. www.stsci.edu:8082 /hst/nicmos/documents/handbooks/DataHandbookv5/nic_ch44.html?printable=1   (802 words)

 Active Boolean Function Nonlinearity Measurement in JavaScript Nonlinearity measurement is particularly useful to quantify the strength of invertible So the nonlinearity value is half the length of the function, less the maximum absolute value of the unexpected distance to each affine function. For nonlinearity measures, the input data are {0,1} or {1,-1}; the results are potentially bipolar in either case. www.ciphersbyritter.com /JAVASCRP/NONLMEAS.HTM   (2482 words)

 Ideas in Nonlinearity The microwave nonlinearity of superconductors was well known before the discovery of HTS, and shortly after its discovery, nonlinearity was already a subject of research These intrinsic nonlinearities, in particular the nonlinear Meissner effect, are currently the subject of study in an NSF funded program headed by Prof. However, an affordable nonlinear device could serve calibration purposes, and could be used as a primary reference for the phase and amplitude of the fundamental and higher harmonics. home.earthlink.net /~steveremillard/id2.html   (1197 words)

 LoBue: Enterprise Evolution: Concepts: Nonlinearity Hence, nonlinear seems the better term for our purposes in business.) In a nonlinear system, under certain conditions, a small action may have a very large effect. It has been determined that when El Nino occurs, the probability is much greater for increased amounts of rainfall across the southern tier of the US and in Peru, which may lead to destructive flooding, and for there to be drought conditions in the West Pacific that could contribute to devastating brush fires in Australia. But nonlinearity is all around us, from the weather to the global economy. www.lobue.com /enterprise_evolution/knowledge_nonline.html   (459 words)

 Memoryless Nonlinearity (Communications Blockset) Apply a memoryless nonlinearity to a complex baseband signal. The Memoryless Nonlinearity block applies a memoryless nonlinearity to a complex, baseband signal. The Memoryless Nonlinearity block provides five different methods for modeling the nonlinearity, which you specify by the Method parameter in the block's mask. www-rohan.sdsu.edu /doc/matlab/toolbox/commblks/ref/memorylessnonlinearity.html   (879 words)

 Relating Nonlinearity to Propagation Characteristics (ResearchIndex)   (Site not responding. Last check: 2007-11-07) Abstract: The connections among the various nonlinearity criteria is currently an important topic in the area of designing and analyzing cryptographic functions. In this paper we show a quantitative relationship between propagation characteristics and nonlinearity, two critical indicators of the cryptographic strength of a Boolean function. We also present a tight lower bound on the nonlinearity of a cryptographic function that has propagation characteristics. citeseer.ist.psu.edu /43151.html   (461 words)

 More Simple Chaotic Flows with ABS nonlinearity A system of first-order ordinary differential equations with at least three variables and one nonlinearity are the necessary conditions for chaos. Systems with the absolute value as the nonlinearity are arguably the simplest cases and provide interesting examples of chaos in almost linear systems. Sprott provided a list of 19 systems with quadratic nonlinearities in which all the systems that involve only a squaring nonlinearity were replaced by an absolute value. sprott.physics.wisc.edu /chaos/finco/abs.html   (479 words)

 Archer's Compound Bow--smart use of Nonlinearity Some historically important examples include the anharmonic potential [1]-ultimately responsible for thermal expansion and nonlinear acoustics [2], parametric phenomena [3], subharmonic response in forced oscillations [4], plasma waves and instabilities [5], gravitational surface waves in water [6], fluid drag [7], and solitons [8]. Unlike earlier work, where nonlinear terms resulted in small corrections to otherwise linear equations; nonlinearity has in recent years become quintessential. Observe that the ordinate scale for all the nonlinear cases has been expanded by a factor of 20, as compared to the Hookeian case. physics.mercer.edu /petepag/combow.html   (2454 words)

 DOCTRINAL COMPLEXITY It is essentially an easily readable distillation of Carl von Clausewitz's famous philosophical treatise On War,*2 heavily flavored by the ideas of the ancient Chinese military sage Sun Tzu and written to encourage a maneuverist orientation. The use of nonlinear concepts and imagery in the MCDPs is severely constrained by problems of space and the target audience: Doctrine is not the ideal arena in which to introduce a new world view. The definitive treatment of Clausewitz as a nonlinear thinker is Alan D. Beyerchen, "Clausewitz, Nonlinearity and the Unpredictability of War," International Security, 17:3 (Winter, 1992), pp. www.clausewitz.com /CWZHOME/Complex/DOCTNEW.htm   (2611 words)

 Neural Mechanisms for Processing Binocular Information I. Simple Cells -- Anzai et al. 82 (2): 891 -- Journal of ... Correlation coefficient (r) is 0.70, which suggests that a model of a linear binocular filter followed by a static nonlinearity does not provide an accurate description of the data for this cell. Static nonlinearity of this cell is approximately a half-squaring function. The results of this study show that the static nonlinearity of simple cells is a half-power function with an exponent of ~2. jn.physiology.org /cgi/content/full/82/2/891   (8403 words)

 Simple Chaotic Flow with ABS nonlinearity Here we report the result of a search for simple chaotic flows in which the single nonlinearity has the form of the absolute value of one of the variables. Several other simple systems with the absolute value nonlinearity are also known. The virtue of this one is that all components are linear except for the diodes, and their nonlinearity is entirely in their I-V characteristic and not in some subtle and hard-to-model property such as junction capacitance. sprott.physics.wisc.edu /chaos/abschaos.htm   (913 words)

 Nonlinearity at opensource encyclopedia   (Site not responding. Last check: 2007-11-07) de:Nichtlinearität A nonlinear system is one that cannot be described by a system of linear equations. Nonlinear systems are more complex, and much harder to understand because of their lack of simple superposed solutions. In nonlinear systems the solutions to the equations do not form a vector space and cannot be superposed (added together) to produce new solutions. www.wiki.tatet.com /Non-linear.html   (161 words)

 EconPapers: Nonlinearity in the Term Structure The paper reports clear evidence of nonlinearity, in contrast to the affine term structure model and consistent with recent claims in the literature. The quadratic term structure model recently proposed performs better for capturing the nonlinearity than the threshold model but the former model seems to miss some aspect of nonlinearity for short-term rates. However, our flexible nonlinear model which incorporates the threshold effect and the convexity of volatility into the quadratic model, generally performs well for all interest rates. econpapers.repec.org /paper/ecmfeam04/440.htm   (270 words)

 INL/DNL Measurements for High-Speed Analog-to-Digital Converters (ADCs) - Maxim/Dallas Although integral and differential nonlinearity may not be the most important parameters for high-speed, high dynamic performance data converters, they gain significance when it comes to high-resolution imaging applications. Although INL and DNL are not among the most important electrical characteristics that specify the high-performance data converters used in communications and fast data-acquisition applications, they gain significance in the higher-resolution imaging applications. Embedded in this figure of merit are the effects of glitches, integral nonlinearity, and sampling-time uncertainty. www.maxim-ic.com /appnotes.cfm/appnote_number/283   (2389 words)

 Relationships Among Nonlinearity Criteria - Seberry, Zhang, Zheng (ResearchIndex)   (Site not responding. Last check: 2007-11-07) Abstract: An important question in designing cryptographic functions including substitution boxes (S-boxes) is the relationships among the various nonlinearity criteria each of which indicates the strength or weakness of a cryptographic function against a particular type of cryptanalytic attacks. In this paper we reveal, for the first time, interesting connections among the strict avalanche characteristics, differential characteristics, linear structures and nonlinearity of quadratic S-boxes. 13: Nonlinearity and propagation characteristics of balanced boolean functions - Seberry, Zhang et al. citeseer.ist.psu.edu /13153.html   (577 words)

 Abstract: Beyerchen, Clausewitz, Nonlinearity, and the Unpredictability of War, from International Security My suggestion is more radical: in a profoundly unconfused way, he understands that seeking exact analytical solutions does not fit the nonlinear reality of the problems posed by war, and hence that our ability to predict the course and outcome of any given conflict is severely limited. The correctness of Clausewitz's perception has both kept his work relevant and made it less accessible, for war's analytically unpredictable nature is extremely discomfiting to those searching for a predictive theory. If Beyerchen's discussion of nonlinearity intrigues you, you can pursue the topic by visiting the homepage of the Santa Fe Institute, a major center for the study of Complexity. www.clausewitz.com /CWZHOME/BEYRABST.html   (661 words)

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