69 citations · 101 across the 13 of their papers we have counts for
14 papers
Rational linear forms of linearizable ordinary differential equations
Dmitry Lyakhov
Every scalar ordinary differential equation of order at least three with rational right-hand side that is locally linearizable by a point transformation admits a linear form with r…
Flexible Kokotsakis Meshes with Skew Faces: Generalization of the Orthodiagonal Involutive Type
Alisher Aikyn, Yang Liu, Dmitry A. Lyakhov +3
In this paper, we introduce and study a remarkable class of mechanisms formed by a arrangement of rigid quadrilateral faces with revolute joints at the common edges. I…
Simulation of indirect 13C-13C J-coupling tensors in diamond clusters hosting the NV center
A. Nizovtsev, A. Pushkarchuk, S. Kuten +4
Using the ORCA 5.0.2 software package we have simulated for a first time the full tensors nJKL (K,L=X,Y,Z), describing n-bond J-coupling of nuclear spins 13C in H-terminated diamon…
Lost photon enhances superresolution
A. Mikhalychev, P. Novik, I. Karuseichyk +3
Quantum imaging can beat classical resolution limits, imposed by diffraction of light. In particular, it is known that one can reduce the image blurring and increase the achievable…
Controlling wave-front shape and propagation time with tunable disordered non-Hermitian multilayers
Denis Novitsky, Dmitry Lyakhov, Dominik Michels +3
Unique and flexible properties of non-Hermitian photonic systems attract ever-increasing attention via delivering a whole bunch of novel optical effects and allowing for efficient…
Optimal correlation order in super-resolution optical fluctuation microscopy
S. Vlasenko, A. B. Mikhalychev, I. L. Karuseichyk +3
Here, we show that, contrary to the common opinion, the super-resolution optical fluctuation microscopy might not lead to ideally infinite super-resolution enhancement with increas…
Unambiguous scattering matrix for non-Hermitian systems
Andrey Novitsky, Dmitry Lyakhov, Dominik Michels +3
symmetry is a unique platform for light manipulation and versatile use in unidirectional invisibility, lasing, sensing, etc. Broken and unbroken -symme…
A Strongly Consistent Finite Difference Scheme for Steady Stokes Flow and its Modified Equations
Yury A. Blinkov, Vladimir P. Gerdt, Dmitry A. Lyakhov +1
We construct and analyze a strongly consistent second-order finite difference scheme for the steady two-dimensional Stokes flow. The pressure Poisson equation is explicitly incorpo…
Symbolic-Numeric Integration of the Dynamical Cosserat Equations
Dmitry Lyakhov, Vladimir Gerdt, Andreas Weber +1
We devise a symbolic-numeric approach to the integration of the dynamical part of the Cosserat equations, a system of nonlinear partial differential equations describing the mechan…
Algorithmic Verification of Linearizability for Ordinary Differential Equations
Dmitry Lyakhov, Vladimir Gerdt, Dominik Michels
For a nonlinear ordinary differential equation solved with respect to the highest order derivative and rational in the other derivatives and in the independent variable, we devise…
On the General Analytical Solution of the Kinematic Cosserat Equations
Dominik Michels, Dmitry Lyakhov, Vladimir Gerdt +3
Based on a Lie symmetry analysis, we construct a closed form solution to the kinematic part of the (partial differential) Cosserat equations describing the mechanical behavior of e…
On the Partial Analytical Solution of the Kirchhoff Equation
Dominik L. Michels, Dmitry A. Lyakhov, Vladimir P. Gerdt +2
We derive a combined analytical and numerical scheme to solve the (1+1)-dimensional differential Kirchhoff system. Here the object is to obtain an accurate as well as an efficient…
Linearization of ODEs: algorithmic approach
Vladimir Gerdt, Dmitry Lyakhov
Algorithmic approach to the problem of linearization by point transformation of ordinary differential equation of arbitrary order is presented. Test-linearization is purely algorit…
Lie Symmetry Analysis for Cosserat Rods
Dominik L. Michels, Dmitry A. Lyakhov, Vladimir P. Gerdt +2
We consider a subsystem of the Special Cosserat Theory of Rods and construct an explicit form of its solution that depends on three arbitrary functions in (s,t) and three arbitrary…