Localization in a one-dimensional disordered model

Numerical investigation of a random, one dimensional Kronig-Penny-like model is performed using long chains and large ensembles. Dependence of the inverse localization length α on randomness, irreproducibility of resistance measurements and the dependence of the standard deviation of α on α and the length of the chain were studied. For energies, E=k² close to the zone boundary k=π, we have found α～(π-k).     

Field statistics in a one-dimensional Reverberation Chamber model

This work focuses on building a fairly simple yet physically appropriate 1D model for a Reverberation Chamber which claims to be able to analytically predict the statistical behavior of such a chamber, without forsaking to the benefits of deterministic models. The statistical properties are introduced by varying the size of a 1D stirrer or the cavity size itself. A validation analysis shows agreement with other theories and measured results on real RCs. Field statistics in undermoded regime is examined. A radiated emission test is defined and shows reliable matching with reality. The field performance near the conducting walls is investigated. To cite this article: R. Serra, F. Canavero, C. R. Physique 10 (2009).     

Equilibrium statistics of the one-dimensional Ising model for a solid solution of limited size

We treat the one-dimensional Ising model of a binary solution closed in a ring. We analyze the criteria for two-phase behavior of the model system. Bimodality of the distribution function of the atoms over clusters was used as one of the criteria. The effect of the size and dimensionality of the model on the form of the thermodynamic functions is traced. It is shown that in the one-dimensional Ising model of limited size there is a configurational change which can be treated as a smeared phase transition. The results of the present work obtained for a small one-dimensional model agree well with the results for two-dimensional small systems and are analogous to the behavior of three-dimensional systems. Khakassk State University. Tomsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 3–8, January, 1997.     

Localization in one-dimensional Soukoulis-Economou model with incommensurate potentials

The localization of one-dimensional Soukoulis- Economou model with incommensurate potentials ε_n=1.9 [cos(2πωn)+1/3cos(4πωn)], where ω=σ≡(√5?1)/2 is studied by the use of two methods: the scaling analysis of bandwidth in successively periodic approximation, and the mutlifractal analysis of wave functions. A mobility edge is found in a gap of the fifth subband. We found that all the states at higher energies are localized while all those at lower energies are extended. These results are different from those given in previous works.     

A model of structure periodically modulated in three dimensions

A model of structure periodically modulated in three dimensions is calculated in the presented paper and applied to the alloy Cu₈₀Au₂₀. The existence and intensity of the side-bands of the Bragg lines appearing with hyperstructural lines on films of this alloy after heating to temperature on the border of the order-disorder transformation are explained by means of the given model and the value of the period of sinusoidal variation of the lattice parameter and scattering power is calculated.ikova 22, Brno, Czechoslovakia.The author thanks Mrs. V. Gregor and Mr. M. Jelínek who prepared the necessary pictures.     

Photothermal waves in a periodically modulated structure

The generation of thermal waves in a one-dimensional structure with a sinusoidal variation in thermal diffusivity can be described by an inhomogeneous Mathieu equation. An exact solution to the frequency-domain Mathieu equation can be found by using a variation of parameters method to give the alternating component of the temperature along the structure. From the theory of Mathieu functions a dispersion relation for the thermal waves is found, which does not display band gaps, but which shows damping that departs from that for thermal waves in a uniform medium.     

Magnetoresistance calculations for a quantum wire with periodically modulated width

We present numerical calculations of the magnetoresistance in a ballistic quantum wire with periodically modulated width. Surprisingly, the negative magnetoresistance peak is found to persist to a field strength which is two orders of magnitude larger than in single quantum dots. In the weakB-field regime, our results are in good agreement with recent experiments. We argue that the wide peak is due to multiple backscattering among the segments of the wire, leading to a novel weak localization effect.     

Self-localization of excitons in a periodically modulated molecular medium

Electromagnetic field propagation is analyzed in a one-dimensional Bragg grating consisting of periodically arranged linear molecules making up a resonant medium. Dye J-aggregates and conjugated polymers are considered as examples of the medium. Both adiabatic and nonadiabatic dynamics of the acoustic waves generated by electromagnetic field in the system are examined. The effects of exciton-phonon and exciton-phonon-photon interactions on the band structure and formation of self-localized excitations are examined on various time scales. A new mechanism for controlling bandgap parameters in a bistable regime is described. Some effects of electromagnetic-field nonuniformity on generation of phonons in molecules and exciton self-localization are investigated.     

Delay-induced state transition and resonance in periodically driven tumor model with immune surveillance

The phenomenon of stochastic resonance (SR) in a tumor growth model under the presence of immune surveillance is investigated. Time delay and cross-correlation between multiplicative and additive noises are considered in the system. The signal-to-noise ratio (SNR) is calculated when periodic signal is introduced multiplicatively. Our results show that: (i) the time delay can accelerate the transition from the state of stable tumor to that of extinction, however the correlation between two noises can accelerate the transition from the state of extinction to that of stable tumor; (ii) the time delay and correlation between two noises can lead to a transition between SR and double SR in the curve of SNR as a function of additive noise intensity, however for the curve of SNR as a function of multiplicative noise intensity, the time delay can cause the SR phenomenon to disappear, and the cross-correlation between two noises can lead to a transition from SR to stochastic reverse-resonance. Finally, we compare the SR phenomenon for the multiplicative periodic signal with that for additive periodic signal in the tumor growth model with immune surveillance.     

Practical time-delay synchronization of a periodically modulated self-excited oscillators with uncertainties

This paper studies time-delay synchronization of a periodically modulated Duffing Van der Pol (DVP) oscillator subjected to uncertainties with emphasis on complete synchronization. A robust adaptive response system is designed to synchronize with the uncertain drive periodically modulated DVP oscillator. Adaptation laws on the upper bounds of uncertainties are proposed to guarantee the boundedness of both the synchronization error and the estimated feedback coupling gains. Numerical results are presented to check the effectiveness of the proposed synchronization scheme. The results suggest that the linear and nonlinear terms in the feedback coupling play a complementary role in increasing the synchronization regime in the parameter space of the synchronization manifold. The proposed method can be successfully applied to a large variety of physical systems.     

On the dynamics of a two-mode laser with periodically modulated parameter

The results for a numerical simulation of a two-mode homogeneously-broadened laser due to a periodic pump modulation are presented. The region with the parameters for the complicated periodic and chaotic laser-intensities pulsation to be observed has also been defined. Complex bifurcation diagram versus modulation frequency with the periodic and chaotic regimes alternation is presented.