Papers by Abdulkadir karakaş
European Journal of Science and Technology, 2021
In many physical systems such as ocean waves, nonlinear optics, plasma physics etc., extreme even... more In many physical systems such as ocean waves, nonlinear optics, plasma physics etc., extreme events and rare fluctuations of a wave field have been widely observed and discussed. In the field of oceanography and naval architecture, their understanding is fundamental for a correct design of platforms and ships, and for performing safe operations at sea. Here, we report a measurement of an impressive and unique wave packet recorded in the Bay of Biscay in the NorthEast of the Atlantic Ocean. An analysis of the spatial extension of the packet that includes three large waves reveals that it extents for more than 1 km, with individual crests moving faster than 100 km/h. The central and largest wave in the packet was 27.8 m high in a sea with significant wave height of 11 m. A detailed analysis of the data using the nonlinear Fourier analysis reveals that the wave packet is characterized by a non trivial nonlinear content. This observation opens a new paradigm which requires new understanding of the dynamics of ocean waves and, more in general, of nonlinear and dispersive waves. Ocean surface gravity waves are fascinating perturbations of the interface between the atmosphere and the sea: their oscillating properties are a direct consequence of gravity that acts as the restoring force. Apart from tsunamis, whose origin is a fast displacement of a large volume of water related to a telluric movement, ocean waves are generated by winds that slowly, but inexorably, transfer them energy. Randomness is a peculiarity of ocean wind waves; indeed, very seldom the wave dynamics under the effect of wind can be considered as a coherent process. The reasons is not unique: first of all wind forcing is in general turbulent and characterized by random fluctuations; moreover, surface gravity waves are dispersive, which inevitably imposes a finite life time of any localised coherent wave packet. This mechanism holds true unless nonlinearity, which is another intrinsic feature of finite amplitude ocean waves, enters into the game, balancing the dispersion. Such combination of effects leads eventually to the formation of localised structures which are known as solitons, i.e localised traveling waves solutions of integrable partial differential equations, the latter derived from a drastic reduction of the primitive fluid mechanical equations of motion. The existence of envelope solitons or breathers in the real ocean has been debated in the past literature 1-3 ; here we give evidence of the existence of a localized nonlinear structure on the sea surface which eventually will have a finite life time. Most of the times, if a time series of the surface elevation is recorded, its Fourier spectrum is characterized by some width which is inversely proportional to the local dispersion time scale and by some independent Fourier phases. Those are the prerequisite for a Gaussian probability density function of the surface elevation which indeed, with small deviations, is the one that mostly characterizes ocean waves 4. More rarely, in conditions that still needs to be understood, extreme events, known as rogue waves, may appear on the surface of the ocean 5-10. While this phenomenon is now well documented in the oceanographic literature 11 , its origin is still very much debated 12 : either a rogue wave is a rare event belonging to a quasi-Gaussian distribution or it is a more frequent (in some sea states) event pertaining to a different population. What one usually observes from time series recorded in the ocean is a large crest embedded in a random sea state characterized by a significant wave height that is smaller than half the height of the largest wave. The average shape (over different rogue waves measured in similar sea state conditions) can be predicted 13-16 .
In this work, we generalize the concepts of statistically convergent sequence of order α and stat... more In this work, we generalize the concepts of statistically convergent sequence of order α and statistical Cauchy sequence of order α by using the generalized difference operator ∆m. We prove that a sequence is ∆p −statistically convergent of order α if and only if it is ∆p −statistically Cauchy of order α.
Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 2020
We extented v by using difference operator v q . We generated the difference sequence space ()... more We extented v by using difference operator v q . We generated the difference sequence space () v pq l and investigated some of their properties. We showed that, if () v pq l is supplied with an proper norm ,. q v p then it will be a Banach space. We further more showed that, the sequence spaces () ,
Filomat, 2018
In this work, we generalize the concepts of statistically convergent sequence of order ? and stat... more In this work, we generalize the concepts of statistically convergent sequence of order ? and statistical Cauchy sequence of order ? by using the generalized difference operator ?m. We prove that a sequence is ?mp-statistically convergent of order ? if and only if it is ?mp-statistically Cauchy of order ?.
On generalized statistical convergence of order β of sequences of fuzzy numbers
Journal of Intelligent & Fuzzy Systems, 2014
In this article we introduce the concepts of $\Delta_{\lambda}^{m}-$statistical convergence of or... more In this article we introduce the concepts of $\Delta_{\lambda}^{m}-$statistical convergence of order β and strong $\Delta_{\lambda_{p}}^{m}-$summability of order β for sequences of fuzzy numbers. Also, we establish some relations between the $\Delta_{\lambda}^{m}-$statistical convergence of order β and strong $\Delta_{\lambda_{p}}^{m}-$summability of order β and we define $w_{\lambda}^{\beta}\left\Delta^{m},\mathcal{F},f,p\right$, where $f$ is a modulus function and give some inclusion relations.
Generalized statistical convergence of order β for sequences of fuzzy numbers
AIP Conference Proceedings, 2018
In the present paper, we introduce the concepts of Δm–statistical convergence of order β for sequ... more In the present paper, we introduce the concepts of Δm–statistical convergence of order β for sequences of fuzzy numbers and strongly Δm–summable of order β for sequences of fuzzy numbers by using a modulus function f and taking supremum on metric d for 0 < β ≤ 1 and give some inclusion relations between them.
Almost statistical convergence of order $$\beta $$ β of sequences of fuzzy numbers
Soft Computing, 2015
In this article, we introduce the concepts of almost $$\lambda $$λ-statistical convergence of ord... more In this article, we introduce the concepts of almost $$\lambda $$λ-statistical convergence of order $$\beta $$β and strongly almost $$\lambda _{p}$$λp-summability of order $$\beta $$β for sequences of fuzzy numbers. Also, we establish some relations between the almost $$\lambda $$λ-statistical convergence of order $$\beta $$β and strongly almost $$\lambda _{p}$$λp-summability of order $$\beta $$β and we define $$\hat{w}_{\lambda }^{\beta }\left( \mathcal {F},f,p\right) $$w^λβF,f,p, where $$f$$f is a modulus function and give some inclusion relations.
Δpm–Statistical Convergence of Order Α
AIP Conference Proceedings, 2017
In this study using the generalized difference operator Δm, we generalize the concepts of statist... more In this study using the generalized difference operator Δm, we generalize the concepts of statistical convergence sequences of order α and statistical Cauchy sequences of order α. It is shown that, Δpm-statistically convergent sequences of order α and Δpm-statistical Cauchy sequences of order α are equivalent.
On some topological properties of a new type difference sequence spaces
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Papers by Abdulkadir karakaş