Boundary controllability and source reconstruction in a viscoelastic string under external traction

Treatises on vibrations devote large space to study the dynamical behavior of an elastic system subject to known external tractions. In fact, usually a "system" is not an isolated body but it is part of a chain of mechanisms which disturb the "system" for example due to the periodic rotation of shafts. This kind of problem has been rarely studied in control theory. In the specific case we shall study, the case of a viscoelastic string, the effect of such external action is on the horizontal component of the traction, and so it affects the coefficients of the corresponding wave type equation, which will be time dependent. The usual methods used in controllability are not naturally adapted to this case. For example at first sight it might seem that moment methods can only be used in case of coefficients which are constant in time. Instead, we shall see that moment methods can be extended to study controllability of a viscoelastic string subject to external traction and in particular we shall study a controllability problem which is encountered in the solution of the inverse problem consisting in the identification of a distributed disturbance source

Boundary controllability problems for the wave equation in a parallelepiped

AbstractThe wave equation in an N-dimensional parallelepiped with boundary control equal zero everywhere except of an edge of dimension N − 2 is considered. The other case which is investigated is the boundary control acting on a face of dimension N − 1 and depending on N − 1 independent variables (including t). It is proved that, in both cases, the system is not approximately controllable for any T > 0

Rational in silico design of aptamers for organophosphates based on the example of paraoxon

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.Poisoning by organophosphates (OPs) takes one of the leading places in the total number of exotoxicoses. Detoxication of OPs at the first stage of the poison entering the body could be achieved with the help of DNA- or RNA-aptamers, which are able to bind poisons in the bloodstream. The aim of the research was to develop an approach to rational in silico design of aptamers for OPs based on the example of paraoxon. From the published sequence of an aptamer binding organophosphorus pesticides, its threedimensional model has been constructed. The most probable binding site for paraoxon was determined by molecular docking and molecular dynamics (MD) methods. Then the nucleotides of the binding site were mutated consequently and the values of free binding energy have been calculated using MD trajectories and MM-PBSA approach. On the basis of the energy values, two sequences that bind paraoxon most efficiently have been selected. The value of free binding energy of paraoxon with peripheral anionic site of acetylcholinesterase (AChE) has been calculated as well. It has been revealed that the aptamers found bind paraoxon more effectively than AChE. The peculiarities of paraoxon interaction with the aptamers nucleotides have been analyzed. The possibility of improving in silico approach for aptamer selection is discussed

Shape, Velocity, and Exact Controllability for the Wave Equation on a Graph with Cycle

Exact controllability is proven on a graph with cycle. The controls can be a mix of controls applied at the boundary and interior vertices. The method of proof first uses a dynamical argument to prove shape controllability and velocity controllability, thereby solving their associated moment problems. This enables one to solve the moment problem associated to exact controllability. In the case of a single control, either boundary or interior, it is shown that exact controllability fails

Exact controllability for wave equation on general quantum graphs with non-smooth controls

In this paper we study the exact controllability problem for the wave equation on a finite metric graph with the Kirchhoff-Neumann matching conditions. Among all vertices and edges we choose certain active vertices and edges, and give a constructive proof that the wave equation on the graph is exactly controllable if $H^1(0,T)'$ Neumann controllers are placed at the active vertices and $L^2(0,T)$ Dirichlet controllers are placed at the active edges. The proofs for the shape and velocity controllability are purely dynamical, while the proof for the exact controllability utilizes both dynamical and moment method approaches. The control time for this construction is determined by the chosen orientation and path decomposition of the graph