Collective intelligence Collective action Self-organized criticality Herd mentality Phase transition Agent-based modelling Synchronization Ant colony optimization Particle swarm optimization Swarm behaviour. Evolutionary computation Genetic algorithms Genetic programming Artificial life Machine learning Evolutionary developmental biology Artificial intelligence Evolutionary robotics.

Reactionâ€”diffusion systems Partial differential equations Dissipative structures Percolation Cellular automata Spatial ecology Self-replication Spatial evolutionary biology. Rational choice theory Bounded rationality Irrational behaviour. In mathematics and sciencea nonlinear system is a system in which the change of the output is not proportional to the change of the input.

Typically, the behavior of a nonlinear system is described in mathematics by a nonlinear system of equationswhich is a set of simultaneous equations in which the unknowns or the unknown functions in the case of differential equations appear as variables of a polynomial of degree higher than one or in the argument of a function which is not a polynomial of degree one.

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In other words, in a nonlinear system of equations, the equation s to be solved cannot be written as a linear combination of the unknown variables or functions that appear in them.

Systems can be defined as nonlinear, regardless of whether known linear functions appear in the equations. In particular, a differential equation is linear if it is linear in terms of the unknown function and its derivatives, even if nonlinear in terms of the other variables appearing in it. As nonlinear dynamical equations are difficult to solve, nonlinear systems are commonly approximated by linear equations linearization.

This works well up to some accuracy and some range for the input values, but some interesting phenomena such as solitonschaos[9] and singularities are hidden by linearization. It follows that some aspects of the dynamic behavior of a nonlinear system can appear to be counterintuitive, unpredictable or even chaotic. Although such chaotic behavior may resemble random behavior, it is in fact not random. For example, some aspects of the weather are seen to be chaotic, where simple changes in one part of the system produce complex effects throughout.

This nonlinearity is one of the reasons why accurate long-term forecasts are impossible with current technology.

Some authors use the term nonlinear science for the study of nonlinear systems. This term is disputed by others:. Using a term like nonlinear science is like referring to the bulk of zoology as the study of non -elephant animals. For example, an antilinear map is additive but not homogeneous.

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The conditions of additivity and homogeneity are often combined in the superposition principle. Nonlinear algebraic equationswhich are also called polynomial equationsare defined by equating polynomials of degree greater than one to zero.V-I characteristics of diode and Zener diode.

Light spectrum of a LED. The measurement of electrical properties of linear or nonlinear components by V-I method is an important lab topic in college physics training. LEEI apparatus consists of a 5 VDC regulated power supply, a digital voltage meter, a digital current meter, variable resistors, a regular diode, a Zener diode, a light-emitting diode, a tungsten bulb and so on.

### Special Issue on Simulation versus Experiment in Non-linear Dynamical Systems

The following objectives can be achieved:. Master the method and the basic circuit of measuring V-I characteristics of nonlinear components. Master the basic characteristics of diodes, Zener diodes and light-emitting diodes.

Accurately measure their forward threshold voltages. The instruction manual contains experimental configurations, principles and step-by-step instructions.

Part List. Lab Equipment for Teaching Physics. Introduction The measurement of electrical properties of linear or nonlinear components by V-I method is an important lab topic in college physics training. The following objectives can be achieved: 1. Plot the graphs of V-I characteristic curves of the above three nonlinear components. All rights reserved. Power consumption.For most conductors, resistance is a rather stable property, largely unaffected by voltage or current.

For this reason, we can regard the resistance of many circuit components as a constant, with voltage and current being directly related to each other. However, reality is not always this simple. One of the phenomena explored in a later chapter is that of conductor resistance changing with temperature. In an incandescent lamp the kind employing the principle of electric current heating a thin filament of wire to the point that it glows white-hotthe resistance of the filament wire will increase dramatically as it warms from room temperature to operating temperature.

If we were to increase the supply voltage in a real lamp circuit, the resulting increase in current would cause the filament to increase temperature, which would, in turn, increase its resistance, thus preventing further increases in the current without further increases in battery voltage.

The phenomenon of resistance changing with variations in temperature is one shared by almost all metals, of which most wires are made. For most applications, these changes in resistance are small enough to be ignored.

In the application of metal lamp filaments, the change happens to be quite large. It is by no means the only example. The straight-line plot of current over voltage indicates that resistance is a stable, unchanging value for a wide range of circuit voltages and currents.

Resistors, which are manufactured to provide a definite, stable value of resistance, behave very much like the plot of values seen above. A more realistic analysis of a lamp circuit, however, over several different values of battery voltage would generate a plot of this shape:. The plot is no longer a straight line. It rises sharply on the left, as voltage increases from zero to a low level. As it progresses to the right we see the line flattening out, the circuit requiring greater and greater increases in voltage to achieve equal increases in current.

We could say that the resistance here is nonlinearincreasing with increasing current and voltage. The nonlinearity is caused by the effects of high temperature on the metal wire of the lamp filament.

Another example of nonlinear current conduction is through gases such as air. At standard temperatures and pressures, air is an effective insulator. Once ionized, air and other gases become good conductors of electricity, allowing electron flow where none could exist prior to ionization. If we were to plot current overvoltage on a graph as we did with the lamp circuit, the effect of ionization would be clearly seen as nonlinear:.The most common kind of enzyme kinetics experiment is to vary the concentration of substrate and measure enzyme velocity.

The goal is to determine the enzyme's Km substrate concentration that yield a half-maximal velocity and Vmax maximum velocity.

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If your goal is to determine the turnover number kcat, rather than the Vmax, use an alternative version of the equation. Create an XY data table. Enter substrate concentration into X, and enzyme velocity into Y.

If you have several experimental conditions, place the first into column A, the second into column B, etc. You can also choose Prism's sample data: Enzyme kinetics -- Michaelis-Menten. After entering data, click Analyze, choose nonlinear regression, choose the panel of enzyme kinetics equations, and choose Michaelis-Menten enzyme kinetics. Vmax is the maximum enzyme velocity in the same units as Y.

It is the velocity of the enzyme extrapolated to very high concentrations of substrate, so its value is almost always higher than any velocity measured in your experiment. Km is the Michaelis-Menten constant, in the same units as X. It is the substrate concentration needed to achieve a half-maximum enzyme velocity. Before nonlinear regression was available, investigators had to transform curved data into straight lines, so they could analyze with linear regression. One way to do this is with a Lineweaver-Burk plot, which plots the reciprocal of substrate concentration vs.

If you create a Lineweaver-Burk plot, use it only to display your data. Don't use the slope and intercept of a linear regression line to determine values for Vmax and Km. If you do this, you won't get the most accurate values for Vmax and Km. The problem is that the transformations reciprocals distort the experimental error, so the double-reciprocal plot does not obey the assumptions of linear regression.

Use nonlinear regression to obtain the most accurate values of Km and Vmax. To create a Lineweaver-Burk plot with Prism, use the Transform analysis, then choose the panel of biochemistry and pharmacology transforms.

To create a Lineweaver-Burke line corresponding to the nonlinear regression fit, follow these steps:. Create a new XY data table, with no subcolumns. Note the name of this data table. Perhaps rename it to something appropriate.Journal Articles M. Boiti, F. Pempinelli, A.

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Pogrebkov and B. Steklov Institute of Math. Prinari" On some nondecaying potentials and related Jost solutions for the heat conduction equation '', Inverse Problems 16, pp. Pempinelli, B.

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Prinari and A. Prinari" Inverse scattering transform for the perturbed 1-soliton potential of the heat equation '', Physics Letters App. Prinari, " Inverse scattering theory of the heat equation for the perturbed 1-soliton potential '', Journal of Math.

Spire, " Integrable discretization of the sine-Gordon equation '', Inverse Problems 18, pp. Boiti, M. Bruschi, F.

Pempinelli and B. Ablowitz, B.

PrinariA. Villarroel, M. Ablowitz, and B. J-P Francoise, F.

Naber, T. Tsun, pp. PrinariM. Ablowitz and G. Ablowitz, G. Biondini and B. Lo Schiavo, B.Hotel reservation form. Participants list. Abstracts and poster booklets. Talks downloadable from June Talks nonlinear4. The theory of solitons which began as an investigation of a very interesting but particular class of nonlinear phenomena in physics now involves a broad variety of mathematical methods that allow one to study a wide range of phenomena and problems that arise in physics, technology, biology and pure and applied mathematics.

The purpose of the Workshop is to bring together qualified scientists and young researchers who study nonlinear physics, mathematics or science.

A goal of the meeting is to offer researchers the opportunity to discuss recent developments and achievements, as well as to discuss future perspectives, in the fascinating natural environment of Southern Italy. As stated in the title of the Workshop, emphasis will be placed on both theory and experiment.

An objective is to offer to the nonlinear scientific community a truly interdisciplinary workshop as a privileged place for scientific interaction among theoreticians and experimentalists. The organizers of the Workshop have observed the increasing relevance of solitons and other nonlinear effects in laboratory experiments and applications. Applications to nonlinear optics, molecular dynamics, fluid dynamics, plasma waves, hydrodynamics, quantum electronics, solid state physics, string theory, gravity etc.

Mathematical approaches including continuous and discrete nonlinear systems, classical and quantum, will be considered. The list is to be considered open, especially to potentially new mathematical methods and applications. This Workshop is part of thirty years of active participation by the University of Lecce now University of Salento in developing international scientific cooperation in Nonlinear Science.

An all-inclusive fee of Euro will cover the cost of registration Euromeals and lodging during the Workshop in double occupancy rooms with private facilities and the transportation from Lecce terminal or Brindisi International Airport to Gallipoli and back for participants arriving on June 12 and leaving on June The all-inclusive rate for accompanying persons is Euro Co-organizers: Mark J.

Pobgrebkov, Steklov Mathematical Institute, Moscow, pogreb mi. Ablowitz, Boulder Andrei K.

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Pogrebkov, Moscow.Enter your login details below. If you do not already have an account you will need to register here. Due to migration of article submission systems, please check the status of your submitted manuscript in the relevant system below:. Once production of your article has started, you can track the status of your article via Track Your Accepted Article. Ever since the inception of computers, experimental measurement and numerical simulation have always been inherently complementary and never adversarial.

Setting aside the epistemological significance of experiments, a question nevertheless remains open: what is the exact contribution of physically realizing electronic, mechanical, optical, chemical and other non-linear systems, relative to only studying them in simulation? Experimental verification, at a minimum, is essential to confirm model validity, but its role appears to extend beyond that: for example, serendipitous discovery in the laboratory has often inspired numerical investigation.

Furthermore, there are potential issues with numerical simulations that appear worthy of more explicit and detailed consideration, particularly as regards networks comprising large numbers of units, especially if these are heterogeneous.

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First, system stiffness, sensitivity to finite step size and discretization effects. Second, the effect of noise, affecting not only the dynamical variables but also the system parameters. Third, the influence of often subtle non-ideal behaviors such as self-resonances in reactive electronic components, frequency-dependent responses of active devices etcetera.

Under what conditions and to what extent do these aspects impact the ability of simulations to properly capture emergent phenomena? Further still, what exactly are the contributions of simulations with stylized models and with more complex realistic ones, such as those embedded in the SPICE program? The papers collected in this Special Issue will cover these topics from diverse multi- and cross-disciplinary perspectives, including theory, numerical methods and experimental demonstrations.

We invite contributions from areas of non-linear science explicitly addressing the relationship between experiment and numerical simulation. We welcome both research papers and survey papers. The submitted papers will be peer-reviewed by experts in the field. Accepted papers will be immediately published online and on ScienceDirect.

Track accepted paper Once production of your article has started, you can track the status of your article via Track Your Accepted Article.

Order Journal. Journal Metrics CiteScore : 5. CiteScore values are based on citation counts in a range of four years e.

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