arXiv subjects

Georgii Koniukov

Publications and source records attributed to Georgii Koniukov.

3 recordsLinked to original sources

arXiv2026

The principle of stationary action and Lagrangian for dissipative dynamics with velocity-proportional frictional force

It has been known for a long time that the equation of motion for dissipative linear dynamical systems with constant coefficients cannot be derived from the classical principle of stationary action because the term proportional to velocity in the equation of motion leads to the time derivative of order one half in the Lagrangian. Thus, approaches utilising fractional calculus have been used; however, they suffer from deficiencies both from mathematical and physical points of view. We here present our version of such fractional calculus based approach that provides correct Euler-Lagrange and, ultimately, the Hamilton equations, energy change of the moving body, and an attempt for a geometric interpretation of how energy dissipates.

cond-mat.mes-hall↗

arXiv2024

Deriving friction force using fractional calculus

The friction force is derived using fractional calculus by considering the non-uniform flow of time in dissipative processes. The approach incorporates inhomogeneous velocity without unphysical approximations, resulting in a Lagrangian where the order of fractional derivatives measures time intervals. The fractional term in the Lagrangian provides correct Euler-Lagrange, and ultimately, the Hamilton equations, and vanishes during energy change measurements, like a ghost.

cond-mat.mes-hall↗

arXiv2024

Protein atom traps as seeing by neutron scattering

The expression for the higher temperature dependence of the mean squared displacement in proteins is obtained. The quantum multi-well model explains the dynamic transitions of the proteins and minimizes the amount of parameters to a single one leading to the few-state harmonic system at low-temperatures, and, thus, justifying the possibility of using proteins as atom traps to control qubits at a bit higher temperatures.

q-bio.BM↗