Lattice Lotka-Volterra model with long range mixing

A spatio-temporal process in the Lattice Lotka Volterra (LLV) model, when realized on low dimensional support, is studied. It is shown that the introduction of a long-range mixing causes a drastic change in the system’s behavior, which transits from small random-like fluctuations to global oscillations when the mixing rate transcends above a critical point. The amplitude of the induced oscillations is well defined by the mixing rate and is insensitive to the initial conditions and the lattice size variations. The observed behavior essentially differs from that predicted by the Mean-Field model which is conservative. The oscillations are of limit-cycle type and appear as a stochastic analog of a Hopf bifurcation.     

Active Brownian motion models and applications to ratchets

We give an overview over recent studies on the model of Active Brownian Motion (ABM) coupled to reservoirs providing free energy which may be converted into kinetic energy of motion. First, we present an introduction to a general concept of active Brownian particles which are capable to take up energy from the source and transform part of it in order to perform various activities. In the second part of our presentation we consider applications of ABM to ratchet systems with different forms of differentiable potentials. Both analytical and numerical evaluations are discussed for three cases of sinusoidal, staircaselike and Mateos ratchet potentials, also with the additional loads modelled by tilted potential structure. In addition, stochastic character of the kinetics is investigated by considering perturbation by Gaussian white noise which is shown to be responsible for driving the directionality of the asymptotic flux in the ratchet. This stochastically driven directionality effect is visualized as a strong nonmonotonic dependence of the statistics of the right versus left trajectories of motion leading to a net current of particles. Possible applications of the ratchet systems to molecular motors are also briefly discussed.     

Accounting for the energies and entropies of kinesin’s catalytic cycle

When the processive motor protein kinesin walks along the biopolymer microtubule it can occasionally make a backward step. Recent single molecule experiments on moving kinesin have revealed that the forward-to-backward step ratio decreases exponentially with the load force. Carter and Cross (Nature 435, 308-312, 2005) found that this ratio tightly followed 802 × exp[−0.95F], where F is the load force in piconewtons. A straightforward analysis of a Brownian step leads to L/(2k _B T) as the factor in front of the load force, where L is the 8 nm stepsize, k _B is the Boltzmann constant, and T is the temperature. The factor L/(2k _B T) does indeed equal 0.95 pN⁻¹. The same analysis shows how the 802 prefactor derives from the power stroke energy G as exp[G/(2k _B T)]. There are indications that the power stroke derives from the entropically driven coiling of the 30 amino acid neck linker that connects the two kinesin heads. This idea is examined and consequences are deduced.     

Coherent quantum transport in two-dimensional electron gas/superconductor double junctions with Rashba spin-orbit coupling

Based on the extended Blonder-Tinkham-Klapwijk (BTK) approach, we have investigated the coherent quantum transport in two-dimensional electron gas/superconductor (2DEG/SC) double tunneling junctions in the presence of the Rashba spin-orbit coupling (RSOC). It is found that all the reflection coefficients in BTK theory as well as conductance spectra oscillate with the external voltage and energy. The oscillation feature of conductance can be tuned largely by the RSOC for low insulating barriers, while for high insulating barriers it is almost independent of the RSOC. These phenomena are essentially different from those found in ferromagnet/superconductor double tunneling junctions.     

The effect of controlled ion bombardment on the electronic structure of the Si(0 0 1) surface

We have studied the effects of controlled ion bombardment on the electronic structure of the Si(0 0 1) surface. The surface was exposed to various doses of Ar⁺ ions accelerated towards the surface at 500 eV. X-ray photoelectron spectroscopy (XPS) spectra of the irradiated H-terminated Si(0 0 1) surface reveal the appearance of peaks that are associated with the presence of cleaved Si bonds. Ultraviolet photoelectron spectroscopy (UPS) spectra of the irradiated Si(0 0 1)2 × 1 surface show that the dimer dangling-bond surface state decays monotonically with increasing dose. These results, coupled with previous scanning tunneling microscopy (STM) studies, indicate that the breaking of dimers, and possibly the creation of adatom-like defects, during ion irradiation are responsible for the changes in the electronic structure of the valence band for this surface.     

Flow dynamics in the short asymmetric Taylor-Couette cavities at low Reynolds numbers

This paper reports on the numerical investigations of Taylor-Couette flow of radius ratio η = 0.25–0.6 performed at low Reynolds numbers Re = 100–200. The inner cylinder and the bottom end-wall rotate, while the outer cylinder and the top end-wall are held fixed. A fully 3D DNS code based on the spectral Chebyshev – Fourier approximation is used. This study is complementary to those of Mullin and Blohm (Phys. of Fluids 2001, vol 13, 136–140) and Lopez et al. (J. Fluid Mech. 2004, vol 501, 327–354) where investigations have been performed for radius ratio 0.5. The 1-cell and 3-cell structures found by these authors are shown to exist for a wide range of radius ratios, and the transition processes between them are qualitatively similar. These structures show hysteresis, disappearing at saddle-node bifurcations which connect at a cusp point in the (Re, Γ) plane. This cusp exists for the entire range of 0.1 < η < 0.75, and it traces out a parabolic curve in the (Re, Γ) plane, reaching a minimum Re at η = 0.375. The detailed 3D DNS computations provide a lot of new information about such phenomena as the modulated rotating wave, the period doubling cascade and homoclinic collision. The results show that the period doubling bifurcation is important in the flow when the radius ratio is close to η = 0.375.     

Two-dimensional problem of two Coulomb centers at small intercenter distances

We use analytic methods to analyze the discrete spectrum for the problem (Z₁eZ₂)₂ in the united-atom limit (R ≪ 1) and obtain asymptotic expansions for the quantum defect and energy terms of the system (Z₁eZ₂)₂ at small intercenter distances R up to terms of the order O(R⁶). We investigate the effect of the dimensionality factor on the energy spectrum of the hydrogen molecular ion H ₂ ⁺ . __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 148, No. 2, pp. 269–287, August, 2006.     

Enhanced field ionization of water adsorbed on a carbon monoxide-covered, platinum field emitter tip

The influence of carbon monoxide, adsorbed on a platinum field emitter tip, on field ionization of adsorbed water was examined. Ramped field desorption (RFD) measurements of water ionization were performed at 108 K for water layer thicknesses up to 80 ML on a clean or CO-saturated tip surface. In RFD the applied field is ramped linearly in time until water ionization is detected, giving the onset field of ionization. Water ionization yields hydrated hydroxide ions and protons; the hydroxide ions remain within the water layer on the tip, while the hydrated protons are emitted into vacuum. At a low water coverage of 1.5 ML, the CO adlayer substantially reduced the onset field of ionization (that is, facilitated ionization) of water by 40%, from a value of 0.43 V/Å for water on clean Pt to 0.26 V/Å for water on CO-covered Pt. The extent of the reduction gradually diminished with thicker coverages of water and was absent at coverages of 20 ML or greater. The characteristic decay length of the field enhancement was 4.7 ± 1 ML. The results were analyzed with the charge exchange model of ionization kinetics and changes in dipole moments of water adsorbed without and with CO. The analysis reveals that a change in water structure (dipole moment) caused by CO is an important contributor in field enhancement and that the dipole moment for hydrated hydroxide ion in an ice-like layer must be greater than that for bulk ice-like water. The significance of these results with respect to electrochemical oxidation of CO is discussed.     

Stochastic resonance in a model of opinion formation on small-world networks

We analyze the phenomenon of stochastic resonance in an Ising-like system on a small-world network. The system, which is subject to the combined action of noise and an external modulation, can be interpreted as a stylized model of opinion formation by imitation under the effects of a “fashion wave”. Both the amplitude threshold for the detection of the external modulation and the width of the stochastic-resonance peak show considerable variation as the randomness of the underlying small-world network is changed. Received 19 December 2001     

Tunneling and EPR linewidths due to dislocations in Mn acetate

We compute the width and shape of the EPR and tunneling resonances due to dislocations in Mn₁₂ acetate crystals. Uncorrelated dislocations produce the Gaussian shape of resonances while dislocations bound in pairs produce the Lorentzian shape. We stress that the uniaxial spin Hamiltonian together with crystal defects can explain the totality of experimental data on Mn₁₂. Received 2 August 2001 / Received in final form 15 March 2002 Published online 17 September 2002