Using the methods originally developed for Random Matrix Theory we derive an exact mathematical formula for number variance ∆N(L) (introduced in [4]) describing a rigidity of particle ensembles with power-law repulsion. The resulting relation is consequently compared with the relevant statistics of the single-vehicle data measured on the Dutch freeway A9. The detected value of an inverse temper...

In this paper, with the aid of symbolic computation we improve the extended F-expansion method described in Chaos, Solitons and Fractals 22, 111 (2004) to solve the (2 +1)-dimensional Korteweg de Vries equation. Using this method, we derive many exact non-travelling wave solutions. These are more general than the previous solutions derived with the extended F-expansion method. They include the ...

Accurate detection of weak periodic signals within noise and possibility of secure messaging have made Duffing oscillator (DO) highly important in the field of communication. Investigation on the properties of DO is thus ardently sought for. An elegant approach to accomplish the same is to fabricate electronic circuit simulating DO non-linear equation and to study the effect of input signal amp...

Exact numerical minimization of interface energies is used to test the functional renormalization group analysis for interfaces pinned by quenched disorder. The fixed-point function R(u) (the correlator of the coarse-grained disorder) is computed. In dimensions D=d+1, a linear cusp in R''(u) is confirmed for random bond (d=1, 2, 3), random field (d=0, 2, 3), and periodic (d=2, 3) disorders. The...

A well known description of superradiance from pointlike collections of many atoms involves the dissipative motion of a large spin. The pertinent \superradiance master equation" allows for a formally exact solution which we subject to a semiclassical evaluation. The clue is a saddle-point approximation for an inverse Laplace transform. All previous approximate treatments, disparate as they may ...

We consider backward error analysis of numerical approximations to ordinary diie-rential equations, i.e., the numerical solution is formally interpreted as the exact solution of a modiied diierential equation. A simple recursive deenition of the modiied equation is stated. This recursion is used to give a new proof of the exponentially closeness of the numerical solutions and the solutions to a...

The time-reversal imaging with multiple signal classification method for the location of point targets developed within the framework of the Born approximation in Lehman and Devaney @‘‘Transmission mode time-reversal super-resolution imaging,’’ J. Acoust. Soc. Am. 113, 2742–2753 ~2003!# is generalized to incorporate multiple scattering between the targets. It is shown how the same method can be...

Some economic models like the cash-in-advance model of money or overlapping generations model have the property that the dynamics are ill-defined going forward in time, but well-defined going backward in time. In such instances, what does it mean for an ill-defined dynamical system to be chaotic? Furthermore, under what conditions are such dynamical systems chaotic? In this paper, we provide a ...

chaos theory discusses unstable and non-periodic behavior of non-linear fluctuating dynamicsystems. since evaporation level variations of lakes have a dynamic identity, chaos theory can have a uniquerole in collecting data of these variations. therefore it is an important and challenging problem in the field ofplanning and qualitative and quantitative management of urmia lake to verify whether ...

In this paper, the dynamics of elementary cellular automaton (ECA) rule 73 is investigated under the framework of the bi-infinite symbolic sequence space. This paper provides a rigorous mathematical analysis for the evolution of symbol sequences in some subsystems of rule 73. ECA rule 73, a member of Wolfram’s class III and Chua’s complex Bernoulli-shift rules, defines many more subsystems with...