Active motions of Brownian particles in a generalized energy-depot model

We present a generalized energy-depot model in which the conversion rate of the internal energy into motion can be dependent on the position and the velocity of a particle. When the conversion rate is a general function of the velocity, the active particle exhibits diverse patterns of motion including a braking mechanism and a stepping motion. The phase trajectories of the motion are investigated in a systematic way. With a particular form of the conversion rate dependent on the position and velocity, the particle shows a spontaneous oscillation characterizing a negative stiffness. These types of active behaviors are compared with the similar phenomena observed in biology such as the stepping motion of molecular motors and the amplification in hearing mechanism. Hence, our model can provide a generic understanding of the active motion related to the energy conversion and also a new control mechanism for nano-robots. We also investigate the noise effect, especially on the stepping motion and observe the random walk-like behavior as expected.Comment: to appear in New J. Phy

Nonrelativistic Factorizable Scattering Theory of Multicomponent Calogero-Sutherland Model

We relate two integrable models in (1+1) dimensions, namely, multicomponent Calogero-Sutherland model with particles and antiparticles interacting via the hyperbolic potential and the nonrelativistic factorizable $S$-matrix theory with $SU(N)$-invariance. We find complete solutions of the Yang-Baxter equations without implementing the crossing symmetry, and one of them is identified with the scattering amplitudes derived from the Schr\"{o}dinger equation of the Calogero-Sutherland model. This particular solution is of interest in that it cannot be obtained as a nonrelativistic limit of any known relativistic solutions of the $SU(N)$-invariant Yang-Baxter equations.Comment: 4 pages, latex(uses Revtex), one figur

Critical Behaviour of integrable mixed spins chains

We construct a mixed spin 1/2 and $S$ integrable model and investigate its finite size properties. For a certain conformal invariant mixed spin system the central charge can be decomposed in terms of the conformal anomaly of two single integrable models of spin 1/2 and spin $(S-1/2)$. We also compute the ground state energy and the sound velocity in the thermodynamic limit.Comment: This was the first correct calculation of the central charge in mixed integrable spin chains. For effects of a magnetic field see J.Phys.A:Math.Gen. 26 (1993) 730

The Double-Time Green's Function Approach to the Two-Dimensional Heisenberg Antiferromagnet with Broken Bonds

We improved the decoupling approximation of the double-time Green's function theory, and applied it to study the spin-${1\over 2}$ two-dimensional antiferromagnetic Heisenberg model with broken bonds at finite temperature. Our decoupling approximation is applicable to the spin systems with spatial inhomogeneity, introduced by the local defects, over the whole temperature region. At low temperatures, we observed that the quantum fluctuation is reduced in the neighborhood of broken bond, which is in agreement with previous theoretical expectations. At high temperatures our results showed that the quantum fluctuation close to the broken bond is enhanced. For the two parallel broken bonds cases, we found that there exists a repulsive interaction between the two parallel broken bonds at low temperatures.Comment: Revtex, 6 pages, 5 Postscript figures (include

Resultant pressure distribution pattern along the basilar membrane in the spiral shaped cochlea

Cochlea is an important auditory organ in the inner ear. In most mammals, it is coiled as a spiral. Whether this specific shape influences hearing is still an open problem. By employing a three dimensional fluid model of the cochlea with an idealized geometry, the influence of the spiral geometry of the cochlea is examined. We obtain solutions of the model through a conformal transformation in a long-wave approximation. Our results show that the net pressure acting on the basilar membrane is not uniform along its spanwise direction. Also, it is shown that the location of the maximum of the spanwise pressure difference in the axial direction has a mode dependence. In the simplest pattern, the present result is consistent with the previous theory based on the WKB-like approximation [D. Manoussaki, Phys. Rev. Lett. 96, 088701(2006)]. In this mode, the pressure difference in the spanwise direction is a monotonic function of the distance from the apex and the normal velocity across the channel width is zero. Thus in the lowest order approximation, we can neglect the existance of the Reissner's membrane in the upper channel. However, higher responsive modes show different behavior and, thus, the real maximum is expected to be located not exactly at the apex, but at a position determined by the spiral geometry of the cochlea and the width of the cochlear duct. In these modes, the spanwise normal velocities are not zero. Thus, it indicates that one should take into account of the detailed geometry of the cochlear duct for a more quantitative result. The present result clearly demonstrates that not only the spiral geometry, but also the geometry of the cochlear duct play decisive roles in distributing the wave energy.Comment: 21 pages. (to appear in J. Biol. Phys.

Analysis of events with b-jets and a pair of leptons of the same charge in pp collisions at √s=8 TeV with the ATLAS detector

An analysis is presented of events containing jets including at least one b-tagged jet, sizeable missing transverse momentum, and at least two leptons including a pair of the same electric charge, with the scalar sum of the jet and lepton transverse momenta being large. A data sample with an integrated luminosity of 20.3 fb−1 of pp collisions at √s=8 TeV recorded by the ATLAS detector at the Large Hadron Collider is used. Standard Model processes rarely produce these final states, but there are several models of physics beyond the Standard Model that predict an enhanced rate of production of such events; the ones considered here are production of vector-like quarks, enhanced four-top-quark production, pair production of chiral b′-quarks, and production of two positively charged top quarks. Eleven signal regions are defined; subsets of these regions are combined when searching for each class of models. In the three signal regions primarily sensitive to positively charged top quark pair production, the data yield is consistent with the background expectation. There are more data events than expected from background in the set of eight signal regions defined for searching for vector-like quarks and chiral b′-quarks, but the significance of the discrepancy is less than two standard deviations. The discrepancy reaches 2.5 standard deviations in the set of five signal regions defined for searching for four-top-quark production. The results are used to set 95% CL limits on various models