Biomedical subjects

Dmitrii N Maksimov

Publications and source records attributed to Dmitrii N Maksimov.

2 recordsLinked to original sources

PubMed2006

Bound states in elastic waveguides.

We consider numerically the L-, T-, and X-shaped elastic waveguides with the Dirichlet boundary conditions for in-plane deformations (displacements) which obey the vectorial Navier-Cauchy equation. In the X-shaped waveguide we show the existence of a doubly degenerate bound state with frequency below the first symmetrical cutoff frequency, which belongs to the two-dimensional irreducible representation E of symmetry group C(4upsilon). Moreover the next bound state is below the next antisymmetric cutoff frequency. This bound state belongs to the irreducible representation A2. The T-shaped waveguide has only one bound state while the L-shaped one has no bound states.

Journal Article↗

PubMed2005

Electric circuit networks equivalent to chaotic quantum billiards.

We consider two electric RLC resonance networks that are equivalent to quantum billiards. In a network of inductors grounded by capacitors, the eigenvalues of the quantum billiard correspond to the squared resonant frequencies. In a network of capacitors grounded by inductors, the eigenvalues of the billiard are given by the inverse of the squared resonant frequencies. In both cases, the local voltages play the role of the wave function of the quantum billiard. However, unlike for quantum billiards, there is a heat power because of the resistance of the inductors. In the equivalent chaotic billiards, we derive a distribution of the heat power which describes well the numerical statistics.

Journal Article↗