Wide Applications In Physics Research Articles

Burgers-Korteweg-de Vries equation and its traveling solitary waves

The Burgers-Korteweg-de Vries equation has wide applications in physics, engineering and fluid mechanics. The Poincare phase plane analysis reveals that the Burgers-Korteweg-de Vries equation has neither nontrivial bell-profile traveling solitary waves, nor periodic waves. In the present paper, we show two approaches for the study of traveling solitary waves of the Burgers-Korteweg-de Vries equation: one is a direct method which involves a few coordinate transformations, and the other is the Lie group method. Our study indicates that the Burgers-Korteweg-de Vries equation indirectly admits one-parameter Lie groups of transformations with certain parametric conditions and a traveling solitary wave solution with an arbitrary velocity is obtained accordingly. Some incorrect statements in the recent literature are clarified.

Boosted decision trees as an alternative to artificial neural networks for particle identification

The efficacy of particle identification is compared using artificial neutral networks and boosted decision trees. The comparison is performed in the context of the MiniBooNE, an experiment at Fermilab searching for neutrino oscillations. Based on studies of Monte Carlo samples of simulated data, particle identification with boosting algorithms has better performance than that with artificial neural networks for the MiniBooNE experiment. Although the tests in this paper were for one experiment, it is expected that boosting algorithms will find wide application in physics.

Stability and long time evolution of the periodic solutions to the two coupled nonlinear Schrödinger equations

The system of two coupled nonlinear Schrödinger equations has wide applications in physics. In the past, the main attention has been their solitary waves. Here we turn our attention to their periodic wave solutions. In this paper, the stability of the periodic solutions is studied analytically and the criteria for the stability are obtained. The long time evolution of the solutions to the coupled system is studied numerically for the unstable case emphasizing wave–wave interactions in nonlinear optics. Different kinds of evolution are observed depending on the coefficients of the system and the parameters of the unperturbed waves and perturbation. For certain ranges of parameters, the evolution appears to be periodic, while for some other ranges of parameters, solitary wave or solitary wave pairs can be excited among the irregular background although often the evolution is completely chaotic.

MULTIFRACTAL DIMENSION SPECTRA IN POLYMER PHYSICS

The notion of non-integer dimension although developed by mathematicians in late 19th – early 20th centuries has found its wide application in physics only in the last few decades. This application was mainly initiated by the pioneering work of B. Mandelbrot who attracted attention to the fact that “fractal” geometry provides an appropriate framework for the description of a whole range of complex structures that are formed from smaller subunits [1]. Whereas such structures are characterized by appropriate fractal dimensions, their growth and spatial correlations [2] are described by a (non-trivial) spectrum of multifractal (MF) dimensions [3,4]. In this paper, we study the properties of diffusion phenomena in the presence of an absorbing polymer. This provides another example of a multifractal phenomenon in condensed matter physics. To this end we use the model proposed by Cates and Witten [5] and derive the MF spectrum in the frames of a field theoretical formalism using the renormalization group [6,7] method. The MF spectrum is related to the spectrum of exponents governing scaling properties of copolymer stars [8]. We calculate this spectrum to the third order of perturbation

SCIENTIFIC AND TECHNICAL INFORMATION AS ONE OF THE PROBLEMS OF CYBERNETICS

Mechanized methods of information storage and processing have recently gained wide application in physics, in its technical applications, and in fields associated with physics. We therefore consider it advisable to examine both the theoretical and technical aspects of this problem in a physics journal.