The influence of the first integrals and the rolling resistance model on tippe top inversion

Nonlinear Dynamics - In this paper, we analyze the effect which the choice of a friction model has on tippe top inversion in the case where the resulting action of all dissipative forces is...     

Experimental investigations of the controlled motion of a screwless underwater robot

In this paper we describe the results of experimental investigations of the motion of a screwless underwater robot controlled by rotating internal rotors. We present the results of comparison of the trajectories obtained with the results of numerical simulation using the model of an ideal fluid.     

Qudit-type entanglement of continuous variables via weak cross-Kerr non linearity

We propose a protocol for creating arbitrary qudit state (including entangled states) with arbitrary dimensionality in continuous variable system using weak cross-Kerr nonlinearity, linear beamsplitters, detectors not resolving photon numbers, and sources of coherent states. The equation for unique determination of the used coherent states amplitudes is found. The protocol is applicable for creating entangled states at distances of 100 km using cross-Kerr nonlinearity χ ≥ χ _min ≃ 0.01 and optical fiber quantum channel.     

Creation of an entangled state between two NV centers in a single-photon interferometric scheme

We study a method for creating an entangled state between two NV centers in diamond that do not directly interact with each other. The method is based on excitation of centers with a single photon via a half divider with subsequent coherent inversion of the spin of the excited center by a microwave pulse and on the detection of a photon that was emitted by the excited center and that passed through the divider. We consider the general case in which the transition frequencies of the centers are shifted with respect to each other and the control pulses are detuned with respect to these transitions. We find the probability of creating an entangled state and its fidelity in relation to the parameters of the method and transition frequencies of the centers. Optimal values of these parameters are determined.     

Quantum anonymous voting with anonymity check

We propose a new protocol for quantum anonymous voting having serious advantages over the existing protocols: it protects both the voters from a curious tallyman and all the participants from a dishonest voter in unconditional way. The central idea of the protocol is that the ballots are given back to the voters after the voting process, which gives a possibility for two voters to check the anonymity of the vote counting process by preparing a special entangled state of two ballots. Any attempt of cheating from the side of the tallyman results in destroying the entanglement, which can be detected by the voters.     

Lipase biosensor for tributyrin and pesticide detection

Potentiometric biosensors based on Candida rugosa lipase was described for the detection of organophosphorus pesticide; methyl-parathion and tributyrin. Lipase was immobilized on the glass electrode by means of a gelatin membrane, which is then cross-linked with glutaraldehyde. The principle of the biosensor is based on the measurement of pH variation which was recorded in millivolts due to the enzymatic hydrolysis of tributyrin to butyric acid. For the inhibitor detection, biosensor responses were measured after pesticide treatment, which caused a drop in enzyme activity because of the irreversible inhibition. Reactivation conditions of the reused enzyme electrodes were also investigated by pyridine-2-aldoxime methiodide (2-PAM). The limit of detection for tributyrin was estimated as 93?µM for lipase sensor within the linear range of 65–455?µM.     

On the model of non-holonomic billiard

In this paper we develop a new model of non-holonomic billiard that accounts for the intrinsic rotation of the billiard ball. This model is a limit case of the problem of rolling without slipping of a ball without slipping over a quadric surface. The billiards between two parallel walls and inside a circle are studied in detail. Using the three-dimensional-point-map technique, the non-integrability of the non-holonomic billiard within an ellipse is shown.     

Hamilton’s principle and the rolling motion of a symmetric ball

In this paper, we show that the trajectories of a dynamical system with nonholonomic constraints can satisfy Hamilton’s principle. As the simplest illustration, we consider the problem of a homogeneous ball rolling without slipping on a plane. However, Hamilton’s principle is formulated either for a reduced system or for a system defined in an extended phase space. It is shown that the dynamics of a nonholonomic homogeneous ball can be embedded in a higher-dimensional Hamiltonian phase flow. We give two examples of such an embedding: embedding in the phase flow of a free system and embedding in the phase flow of the corresponding vakonomic system.