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1
Content available remote

Alfvén-Magnetosonic Waves Interaction

100%
Murawski K.
Acta Physica Polonica A
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1992
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vol. 81
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issue 3
335-351
EN
The nonlinear propagation of the Alfvén and magnetosonic waves in the solar corona is investigated in terms of model equations. Due to viscous effects taken into account the propagation of the Alfvén wave itself is governed by a Burgers-type equation. The Alfvén waves exhibit a tendency to drive both the slow and fast magnetosonic waves. For this process model equations are a generalization of the Zakharov equations. The propagation of the magnetosonic waves is described by linearized Boussinesq-type equations with ponderomotive terms due to the Alfvén wave. Both long and short Alfvén waves are considered. Also the limits of the slow and fast modes are investigated. An approximate shock wave solution has been found for a vertically propagating slow mode. Numerical results for the fast mode propagating perpendicular to the magnetic field show the effect of inhomogeneity and pumping on a shock as the solution of the homogeneous Burgers equation.
2
Content available remote

Gaussian Beam Diffraction and Self-Focusing in Weakly Anisotropic and Dissipative Nonlinear Plasma

80%
Berczynski P., Berczynski S., Kravtsov Y.
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vol. 125
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issue 1
39-45
EN
The paper presents a simple and effective method to calculate polarization and diffraction of the Gaussian beam in nonlinear and weakly dissipative plasma. The presented approach is a combination of quasi-isotropic approximation of geometric optics with complex geometrical optics. Quasi-isotropic approximation describes the evolution of polarization vector reducing the Maxwell equations to coupled ordinary differential equations of the first order for the transverse components of the electromagnetic field. Complex geometrical optics describes the Gaussian beam diffraction and self-focusing and deals with ordinary differential equations for Gaussian beam width, wave front curvature, and amplitude evolution. As a result, the quasi-isotropic approximation + complex geometrical optics combination reduces the problem of diffraction and polarization evolution of an electromagnetic beam to the solution of the ordinary differential equations, which enable to prepare fast and effective numerical algorithms. Using combined complex geometrical optics/quasi-isotropic approximation for weakly anisotropic plasma, we assume that nonlinearity of anisotropy tensor is small and we restrict ourselves to considering only isotropic nonlinearity. The quasi-isotropic approximation effectively describes the evolution of microwave and IR electromagnetic beams in polarimetric and interferometric measurements in thermonuclear reactors and the complex geometrical optics method can be applied for modeling of electron cyclotron absorption and current drive in tokamaks.
3
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On Darboux-Bäcklund Transformation and Positon Type Solution of Coupled Nonlinear Optical Waves

80%
Sen D. C., Chowdhury A. R.
Acta Physica Polonica A
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2000
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vol. 98
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issue 1-2
3-10
EN
A Darboux-Bäcklund transformation is used to obtain a positon type solution of the nonlinear equations describing the propagation of coupled nonlinear optical pulses.This form of the positon solution is then compared with that obtained by the special limiting procedure applied to a two-soliton solution. It is observed that though the algebraic form of the two solutions is different yet both of these have singularities and the position of the singularities remains on the similar curve in the (x,t) plane. We also depict the form of these solutions graphically. Finally, it may be added that the method of Darboux-Bäcklund transformation is convenient for generating more than one-positon solution.
4
Content available remote

Modified Nonlinear Schrödinger Equation for Nonlinear Waves in Optical Fibres

80%
Murawski K.
Acta Physica Polonica A
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1991
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vol. 80
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issue 4
485-493
EN
A new model equation governing the propagation of nonlinear pulses in optical fibres has been derived on the assumption of a saturated nonlinearity of the refractive index. This equation is a combination of the exponential nonlinear Schrödinger equation and the derivative one. It is valid for the long fibres. A modulational stability has been calculated to find out a cut-off in an angular frequency of a carrier wave. Moreover, it has been shown that the equation possesses family of stationary solutions. An initial value problem has been discussed on the basis of the implicit pseudo-spectral scheme.
5
Content available remote

Modulational Instability of Nonlinear Exponential Schrödinger Waves

80%
Murawski K.
Acta Physica Polonica A
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1991
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vol. 80
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issue 4
495-501
EN
Modulational instability of a plane wave of the nonlinear Schrödinger equation is discussed numerically on the basis of the pseudo-spectral method. The linear theory is verified and influence of the attenuation is considered.
6
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Content available

Amplitude Modulation and Demodulation in Strain Dependent Diffusive Semiconductors

80%
Ghosh S., Yadav N.
Acta Physica Polonica A
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2007
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vol. 112
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issue 1
29-40
EN
In communication processes, amplitude modulation is very helpful to save power by using a single band transmission. Thus in this paper authors have explored the possibility of amplitude modulation as well as demodulation of an electromagnetic wave in a transversely magnetized electrostrictive semiconductor. The inclusion of carrier diffusion and phenomenological damping coefficient in the nonlinear laser-semiconductor plasma interaction adds a new dimension to the analysis present in this paper. This problem is analyzed in different wave number regimes over a wide range of cyclotron frequencies. It is found that the complete absorption of the waves takes place in all the possible wavelength regimes when the cyclotron frequency (ω_c) becomes exactly equal to (ν^2+ω_0^2)^{1/2} in absence of damping parameter. It has also been seen that diffusion of charge carriers modifies amplitude modulation and demodulation processes significantly. The damping parameter plays a very important role in deciding the parameter range and selecting the side band mode that will be modulated by the above-mentioned interaction.
7
Content available remote

Current Log-Periodic View on Future World Market Development

80%
Drożdż S., Kwapień J., Oświęcimka P., Speth J.
Acta Physica Polonica A
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2008
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vol. 114
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issue 3
539-546
EN
Applicability of the concept of financial log-periodicity is discussed and encouragingly verified for various phases of the world stock markets development in the period 2000-2010. In particular, a speculative forecasting scenario designed in the end of 2004, that properly predicted the world stock market increases in 2007, is updated by setting some more precise constraints on the time of duration of the present long-term equity market bullish phase. A termination of this phase is evaluated to occur in around November 2009. In particular, on the way towards this dead-line, a Spring-Summer 2008 increase is expected. On the precious metals market a forthcoming critical time signal is detected at the turn of March/April 2008 which marks a tendency for at least a serious correction to begin.
8
Content available remote

Criticality Characteristics of Current Oil Price Dynamics

80%
Drożdż S., Kwapień J., Oświęcimka P.
Acta Physica Polonica A
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2008
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vol. 114
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issue 4
699-702
EN
Methodology that recently leads us to predict to an amazing accuracy the date (July 11, 2008) of reverse of the oil price up trend is briefly summarized and some further aspects of the related oil price dynamics elaborated. This methodology is based on the concept of discrete scale invariance whose finance-prediction-oriented variant involves such elements as log-periodic self-similarity, the universal preferred scaling factor λ≈2, and allows a phenomenon of the "super-bubble". From this perspective the present (as of August 22, 2008) violent - but still log-periodically decelerating - decrease of the oil prices is associated with the decay of such a "super-bubble" that has started developing about one year ago on top of the longer-term oil price increasing phase (normal bubble) whose ultimate termination is evaluated to occur in around mid 2010.
9
Content available remote

Fractals, Log-Periodicity and Financial Crashes

80%
Oświęcimka P., Drożdż S., Kwapień J., Górski A.
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EN
Presence of self-similar patterns in the financial dynamics is by now well established and even convincingly quantified within the multifractal formalism. Here we focus attention on one particular aspect of this self-similarity which potentially is related to the discrete-scale invariance underlying the system composition and manifests itself by the log-periodic oscillations cascading self-similarly through various time scales. Such oscillations accumulate at the turning (critical) points that in the financial dynamics are often identified as crashes. This property thus allows us to develop a methodology that may be useful also for prediction. A model Weierstrass-type function is used to illustrate the relevant effects and several examples demonstrating that such effects in the real financial markets take place indeed, are reviewed.
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