Current and fluctuation in a two-state stochastic system under non-adiabatic periodic perturbation

We calculate a current and its fluctuation in a two-state stochastic system under a periodic perturbation. The system could be interpreted as a channel on a cell surface or a single Michaelis-Menten catalyzing enzyme. It has been shown that the periodic perturbation induces so-called pump current, and the pump current and its fluctuation are calculated with the aid of the geometrical phase interpretation. We give a simple calculation recipe for the statistics of the current, especially in a non-adiabatic case. The calculation scheme is based on the non-adiabatic geometrical phase interpretation. Using the Floquet theory, the total current and its fluctuation are calculated, and it is revealed that the average of the current shows a stochastic-resonance-like behavior. In contrast, the fluctuation of the current does not show such behavior.Comment: 7 pages, 1 figur

The stochastic pump current and the non-adiabatic geometrical phase

We calculate a pump current in a classical two-state stochastic chemical kinetics by means of the non-adiabatic geometrical phase interpretation. The two-state system is attached to two particle reservoirs, and under a periodic perturbation of the kinetic rates, it gives rise to a pump current between the two-state system and the absorbing states. In order to calculate the pump current, the Floquet theory for the non-adiabatic geometrical phase is extended from a Hermitian case to a non-Hermitian case. The dependence of the pump current on the frequency of the perturbative kinetic rates is explicitly derived, and a stochastic resonance-like behavior is obtained.Comment: 11 page

Fermionic coherent states for pseudo-Hermitian two-level systems

We introduce creation and annihilation operators of pseudo-Hermitian fermions for two-level systems described by pseudo-Hermitian Hamiltonian with real eigenvalues. This allows the generalization of the fermionic coherent states approach to such systems. Pseudo-fermionic coherent states are constructed as eigenstates of two pseudo-fermion annihilation operators. These coherent states form a bi-normal and bi-overcomplete system, and their evolution governed by the pseudo-Hermitian Hamiltonian is temporally stable. In terms of the introduced pseudo-fermion operators the two-level system' Hamiltonian takes a factorized form similar to that of a harmonic oscillator.Comment: 13 pages (Latex, article class), no figures; v2: some amendments in section 2, seven new refs adde

Stochastic pump effect and geometric phases in dissipative and stochastic systems

The success of Berry phases in quantum mechanics stimulated the study of similar phenomena in other areas of physics, including the theory of living cell locomotion and motion of patterns in nonlinear media. More recently, geometric phases have been applied to systems operating in a strongly stochastic environment, such as molecular motors. We discuss such geometric effects in purely classical dissipative stochastic systems and their role in the theory of the stochastic pump effect (SPE).Comment: Review. 35 pages. J. Phys. A: Math, Theor. (in press

ANALYSIS OF INTERFACE REACTION BETWEEN CELL AND GRAIN BOUNDARY DURING CELLULAR PRECIPITATION

La précipitation discontinue dans l'alliage Cu-15% en poids In se fait essentiellement par décomposition cellulaire. Il a été établi que la réaction de précipitation discontinue peut avoir lieu en un joint de grain pré-existant (statique) seulement si la structure de ce joint est convertie en une structure de haute mobilité par une transformation structurale. Il est connu que la déformation plastique provoque le déplacement du joint de grain sous l'effet d'une force motrice en plus de la force chimique. Suivant le taux de déformation plastique la vitesse de précipitation cellulaire peut croître ou décroître. L'analyse de l'intéraction joint de grain-lamelles dans les cellules peut expliquer ces résultats.Discontinuous precipitation in Cu-15 wt% In is found to occur predominatly by cellular decomposition. It has been established that a discontinuous precipitation reaction can occur only at pre-existing (static) grain boundary if the structure of the static boundary is converted into a structure of high mobility by a structural transformation. It is known that plastic deformation causes grain boundary motion due to a driving force in addition to the chemical force. It depends on the amount of plastic deformation whether the reaction rate is incrensed or decreased. The analysis of the interaction between grain boundary and lamella in the cells interface can explain these results

Earthquake Ground Motion Matching on a Small Electric Shaking Table Using a Combined NN-PDFF Controller

Replicating acceleration time histories with high accuracy on shaking table platforms is still a challenging task. The complex interference between the components of the system, the inherent nonlinearities, and the coupling effect between the specimen and the shaking table are among other reasons that most affect the control performance. In this paper, a neural network- (NN-) based controller has been developed and experimentally implemented to improve the acceleration tracking performance of an electric shaking table. The latter is a biaxial shaking table driven by linear motors and controlled by a proportional-derivative-feedforward (PDFF) controller that is very efficient in reproducing displacement waveforms on the detriment of the simulation of the prescribed acceleration ground motions. In order to bypass this shortcoming, a control scheme combining the PDFF as a basic control function with a NN controller which filters the shaking table feedback signal and acts on the drive signal by compensating for acceleration distortions is proposed in this study. Several experimental tests have been carried out to build a database for offline training, validating, and testing of the proposed NN control model. Subsequently, the well-trained NN is implemented in the inner control loop of the shaking table to compensate, in parallel with the PDFF controller, the distortions during the replication of acceleration signals. Results of tests using earthquake records showed an enhancement in signal matching when integrating the NN model for both bare and loaded conditions of the shaking table. The tracking errors, estimated using the relative root-mean-square error, between the measured and the desired signal, are significantly reduced in time and frequency domains with the additional NN online controller