arXiv subjects

Namik Ciblak

Publications and source records attributed to Namik Ciblak.

3 recordsLinked to original sources

arXiv2021

Kinematic Condition For Soliton Motions of an $n$-dimensional Continuum in $R^{n+m}$

A new kinematic condition for soliton motions of an $n$-dimensional continuum in $R^{n+m}$, independent of the underlying physics, is proven. The condition and its consequences for different cases are demonstrated. A soliton in a 1D string that rocks back and forth, a rotating soliton in a 2D membrane, and various other cases are presented as examples. It is shown that traveling knots based on classical wave equation are plausible. Cases in which all the motions are solitons are also presented. Compatibility of equations of motion with the kinematic constraint is explored and demonstrated.

physics.gen-ph↗

arXiv2018

Resolution of the 300-Year-Old Vibrating String Controversy

The dispute about the well-known 1D vibrating string model and its solutions, known as The Vibrating String Controversy, spanned the whole of 1700s and involved a group of the most eminent scientists of the time. After that, the model stood undisputed for over two centuries. In this study, it is shown that not only this 300-year-old model cannot correspond to reality, but it is theoretically not quite plausible, either. A new 2D model is developed removing all the assumptions of the classical model. The result is a pair of non-linear partial differential equations modeling 2D motions of a finite 1D string. A theorem that can be used to determine the initial displacement functions from the initial shape of the string is proven. The new model is capable of representing initial conditions that cannot be handled in the classical model. It also allows initially non-taut/non-slack strings and self-intersecting shapes. The classical model and the non-taut strings emerge as special limit cases. It is proven that pure transverse motions of a 1D string are possible only in very rare cases. A theorem that sets the conditions for pure transverse motions is also presented. Numerical studies of interesting cases are presented in support of the new model. High-speed camera experiments are also conducted, the results of which also support the new theory.

physics.gen-ph↗

arXiv2013

Variable Tension, Large Deflection Ideal String Model For Transverse Motions

In this study a new approach to the problem of transverse vibrations of an ideal string is presented. Unlike previous studies, assumptions such as constant tension, inextensibility, constant crosssectional area, small deformations and slopes are all removed. The main result is that, despite such relaxations in the model, not only does the final equation remain linear, but, it is exactly the same equation obtained in classical treatments. First, an "infinitesimals" based analysis, similar to historical methods, is given. However, an alternative and much stronger approach, solely based on finite quantities, is also presented. Furthermore, it is shown that the same result can also be obtained by Lagrangian mechanics, which indicates the compatibility of the original method with those based on energy and variational principles. Another interesting result is the relation between the force distribution and string displacement in static cases, which states that the force distribution per length is proportional to the second spatial derivative of the displacement. Finally, an equation of motion pertaining to variable initial density and area is presented.

physics.gen-ph↗