q-Painlevé Systems Arising from q-KP Hierarchy

A system of q-Painlevé type equations with multi-time variables t ₁,...,t _M is obtained as a similarity reduction of the N-reduced q-KP hierarchy. This system has affine Weyl group symmetry of type . Its rational solutions are constructed in terms of q-Schur functions.     

Self-avoiding walk in five or more dimensions I. The critical behaviour

We use the lace expansion to study the standard self-avoiding walk in thed-dimensional hypercubic lattice, ford5. We prove that the numberc _n ofn-step self-avoiding walks satisfiesc _n ~A ⁿ , where is the connective constant (i.e. =1), and that the mean square displacement is asymptotically linear in the number of steps (i.e.v=1/2). A bound is obtained forc _n(x), the number ofn-step self-avoiding walks ending atx. The correlation length is shown to diverge asymptotically like (^––Z)^1/2. The critical two-point function is shown to decay at least as fast as x^–2, and its Fourier transform is shown to be asymptotic to a multiple ofk ^–2 ask0 (i.e. =0). We also prove that the scaling limit is Gaussian, in the sense of convergence in distribution to Brownian motion. The infinite self-avoiding walk is constructed. In this paper we prove these results assuming convergence of the lace expansion. The convergence of the lace expansion is proved in a companion paper.Supported by the Nishina Memorial Foundation and NSF grant PHY-8896163.Supported by NSERC grant A9351     

Observation of magnetic order of Cu-moment aroundx=0.12 in La2−x Ba x CuO4 and La2−x sr x CuO4 by μ+SR

Zero field positive muon spin rotation method ( ⁺SR) is applied on La_2–x Sr _x CuO₄ around forx=0.12 at which the high-T _c superconductivity (SC) is suppressed. The magnetically ordered state of Cu-moments, which is not a spin glass state but an antiferromagnetic like state, appears below 15 K for 0.105x0.120. The magnetic phase boundary is very similar to the one of the La_2–x Ba _x CuO₄ in which the structural transition from the low temperature orthorhombic (LTO) phase to the low temperature tetragonal (LTT) phase is observed aroundx=0.12. The present study suggests that there is no big difference of the electronic state of the CuO₂ plane between the La-Ba system and the La-Sr system and that the magnetic ordering of Cu-moments plays an important role for the suppression of the high-T _c SC aroundx=0.12 in both of the systems, although the LTO-LTT structural transition has not been observed yet in the La-Sr system.     

Triviality of Hierarchical Ising Model¶in Four Dimensions

Existence of critical renormalization group trajectory for a hierarchical Ising model in 4 dimensions is shown. After 70 iterations of renormalization group transformations, the critical Ising model is mapped into a vicinity of the Gaussian fixed point. Convergence of the subsequent trajectory to the Gaussian fixed point is shown by power decay of the effective coupling constant. The analysis in the strong coupling regime is computer-aided and Newman's inequalities on truncated correlations are used to give mathematical rigor to the numerical bounds. In order to obtain a criterion for convergence to the Gaussian fixed point, characteristic functions and Newman's inequalities are systematically used. Received: 27 April 2000 / Accepted: 5 January 2001     

The EPR dipolar broadening of irradiated solids as detected using FID and ESE following selective hole burning

A novel electron spin echo method employing detection of FID and transient echo shape following selective hole burning in the EPR spectrum has been applied to study γ-irradiated malonic acid. The dipolar lineshapes of stabilized free radicals are separated into bulk and pairwise contributions; both of them have proved to be Lorentzian.     

Ni thin films vacuum-evaporated on polyethylene naphthalate substrates with and without the application of magnetic field

We study the structural properties of the surface roughness, the surface mound size and the interfacial structure in Ni thin films vacuum-deposited on polyethylene naphthalate (PEN) organic substrates with and without the application of magnetic field and discuss its feasibility of fabricating quantum cross (QC) devices. For Ni/PEN evaporated without the magnetic field, the surface roughness decreases from 1.3 nm to 0.69 nm and the surface mound size increases from 32 nm to 80 nm with the thickness increased to 41 nm. In contrast, for Ni/PEN evaporated in the magnetic field of 360 Oe, the surface roughness tends to slightly decrease from 1.3 nm to 1.1 nm and the surface mound size shows the almost constant value of 28-30 nm with the thickness increased to 35 nm. It can be also confirmed for each sample that there is no diffusion of Ni into the PEN layer, resulting in clear Ni/PEN interface and smooth Ni surface. Therefore, these experimental results indicate that Ni/PEN films can be expected as metal/insulator hybrid materials in QC devices, leading to novel high-density memory devices.     

Theoretical Demonstration of a Newly Designed Micro-Rotator Driven by Optical Pressure on a Light Incident Surface

A newly designed cylindrical optical micro-rotator which has slopes for trapping and rotation on its upper surface is proposed. The cylindrical shape is effective in decreasing viscous drag force (damping factor) in the medium. A ray-tracing method considering the beam waist is employed to analyze the radiation pressure exerted on the upper surface of the rotator. We have demonstrated optical trapping and high speed rotation for various optical beam parameters such as the lens numerical aperture and the Gaussian mode profile as well as rotator shape parameters including oblique angle, height and diameter.     

Microencapsulation of TiO2 Nanoparticles with Polymer by Rapid Expansion of Supercritical Solution

A novel preparation method is reported for the microencapsulation of TiO₂ nanoparticles by rapid expansion of supercritical solution with a nonsolvent. A suspension of TiO₂ nanoparticles in carbon dioxide containing a cosolvent and dissolved polymer is sprayed through a nozzle to atmospheric pressure. After rapid expansion, polymer microspheres were obtained. The microspheres do not tend to agglomerate, since the pure cosolvent is a nonsolvent for the polymer. The structure and morphology of microspheres were investigated by SEM, TEM and XRD. The obtained polymer microspheres are microcapsules of TiO₂ nanoparticles. The mean particle diameter and particle size distribution of microcapsules, could be controlled by changing the polymer concentration, pre-expansion pressure, temperature and injection distance. The polymer feed compositions are more effective than other factors on the control of particle size.     

Integration of a piezoelectric transformer and an ultrasonic motor

Ultrasonic motors are usually operated at an AC voltage higher than a regular battery. This implies the need of a voltage step-up transformer. In this paper, we report the integration of a piezoelectric transformer (PT) with an ultrasonic motor and a simple drive circuit. The stator of the ultrasonic motor and the PT were operated in the same radial vibration mode. Their dimensions were very close to each other yielding nearly matching resonance frequencies. Consequently, they could be combined together without inductor. The drive circuit was designed by using a 555 timer as an astable multivibrator, and high-speed dual MOSFET drivers as a class D half-bridge switching amplifier. This integrated PT-ultrasonic motor performed reasonably without the use of electromagnetic transformer or inductor.     

Sonochemical preparation of composite nanoparticles of Au/gamma-Fe2O3 and magnetic separation of glutathione

We prepared Au/gamma-Fe2O3 composite nanoparticles by sonochemically reducing Au(III) ions employing no stabilizer in the aqueous solution to form stable Au nanoparticles and allowing them to attach onto the surface of gamma-Fe2O3 particles with an average size of 21 nm. Size of the formed Au nanoparticle depended on the initial concentration of Au(III) ions. The number of the Au nanoparticles, supported on each gamma-Fe2O3 particle was controlled by changing the relative amounts of Au(III) ions and gamma-Fe2O3 particles. The composite nanoparticles exhibited a high affinity with glutathione, a tripeptide with mercapto group so that separation and manipulation of glutathione in aqueous solutions could be performed by application of external magnetic field. Because the surfaces of the Au nanoparticles were not shielded by any stabilizers, or naked, sonochemically prepared Au/gamma-Fe2O3 composite nanoparticles seemed to show stronger affinity to the glutathione than those by the radiochemical method.