arXiv subjects

Ruslan A. Sharipov

Publications and source records attributed to Ruslan A. Sharipov.

4 recordsLinked to original sources

arXiv2004

Separation of plastic deformations in polymers based on elements of general nonlinear theory

We report a method for describing plasticity in a broad class of amorphous materials. The method is based on nonlinear (geometric) deformation theory allowing the separation of the plastic deformation from the general deformation tensor. This separation allows an adequate pattern of thermodynamical phenomena for plastic deformations in polymers to be constructed. A parameter describing the stress relaxation rate of the material is introduced within the frame of this approach. Additionally, several experimental configurations to measure this parameter are discussed.

cond-mat.soft↗

arXiv2004

Exact analytical solution for electrostatic field produced by biased atomic force microscope tip dwelling above dielectric-conductor bi-layer

An exact analytical solution based on the method of images has been obtained for the description of the electrostatic field in the system comrising of atomic force microscope (AFM)tip, dielectric, and conductor. The solution provides a step towards quantitative modelling of AFM-assisted electrostatic nanolithography in polymers.

cond-mat.mtrl-sci↗

arXiv2000

Orthogonal matrices with rational components in composing tests for High School students

Fermat Last Theorem, which inspired mathematicians during 300 years, is proved by Andrew Wiles. Even among mathematicians there is a narrow circle of specialists, who can read this proof and understand all details. Is it a reason for pessimism? No, since arithmetics if entire numbers contains broad variety of problems with a simple statement, which might be not less intricate. One of them arises in elementary geometry.

math.GM↗

arXiv1996

On the solution of normality equations for the dimension $n\geq 3$

The normality equations for the Newtonian dynamical systems on an arbitrary Riemannian manifold of the dimension $n \geq 3$ are considered. Locally the solution of such equations reduces to three possible cases: in two of them the solution is written out explicitly, and in the third case the equations of normality are reduced to an ordinary differential equation of the second order. Some new examples of explicit solutions of normality equations are constructed.

solv-int↗