The absence of physical aging effects on the relaxation of rubbing-induced birefringence in polystyrene

We found, through extensive experimental studies, that the physical aging effects are absent in the relaxation of rubbing-induced birefringence (RIB) in polystyrene (PS), and the relaxation involves very small length scale. A phenomenological model based on individual birefringence elements is proposed for the RIB relaxation. The relaxation times (RTs) of the elements are found to be independent of the thermal or stress history of the samples, either before or after the formation of the birefringence. The RTs are also independent of the molecular weight, rubbing conditions, and film thickness, while the RTs distribution function does depend on the molecular weight and rubbing conditions. The model provides quantitative interpretations that agree very well with all the reported experimental results, and sheds important light on the novel behaviors of the RIB relaxation. The absence of physical aging effects is probably due to the combined effects of small length scale of the RIB relaxation, and the accelerated aging speed in the near surface region in which the RIB concentrates.     

From Schwarzschild to Kerr due to Black Hole Quantum Tunnelling

Hawking radiation can be viewed as a process of quantum tunnelling near black hole horizon. When a particle with angular momentum tunnels across the event horizon of Schwarzschild black hole, the black hole will change into a Kerr black hole. The emission rate of the massless particles with angular momentum is calculated, and the result is consistent with an underlying unitary theory.     

A numerical study of the target system of an ADSS with different flow guides

The mechanical design of the target module of an accelerator driven subcritical nuclear reactor system (ADSS) calls for an analysis of the related thermal-hydraulic issues because of large amount of heat deposition in the spallation region during the course of nuclear interactions with the molten lead bismuth eutectic (LBE) target. The LBE also should carry the entire heat generated as a consequence of the spallation reaction. The problem of heat removal by the LBE is a challenging thermal-hydraulic issue. For this, one has to examine the flows of low Prandtl number fluids (LBE) in a complex ADSS geometry. In this study, the equations governing the laminar flow and thermal energy are solved numerically using the streamline upwind Petrov-Galerkin (SUPG) finite element (FE) method. The target systems with a straight and a nozzle guide have been considered. The principal purpose of the analysis is to trace the flow and temperature distribution and thereby to check the suitability of the flow guide in avoiding the recirculation or stagnation zones in the flow space that may lead to hot spots.      

The Fixed Point of a Generalization of the Renormalization Group Maps for Self-Avoiding Paths on Gaskets

Let W(x,y) = ax ³+ bx ⁴+ f ₅ x ⁵+ f ₆ x ⁶+ (3 ax ²)² y+ g ₅ x ⁵ y + h ₃ x ³ y ² + h ₄ x ⁴ y ² + n ₃ x ³ y ³+a ₂₄ x ² y ⁴+a ₀₅ y ⁵+a ₁₅ xy ⁵+a ₀₆ y ⁶, and X = , , where the coefficients are non-negative constants, with a > 0, such that X ²(x,x ²)−Y(x,x ²) is a polynomial of x with non-negative coefficients. Examples of the 2 dimensional map Φ: (x,y)↦ (X(x,y),Y(x,y)) satisfying the conditions are the renormalization group (RG) maps (modulo change of variables) for the restricted self-avoiding paths on the 3 and 4 dimensional pre-gaskets. We prove that there exists a unique fixed point (x _f ,y _f ) of Φ in the invariant set . 2000 Mathematics Subject Classification Numbers: 82B28; 60G99; 81T17; 82C41.     

Nonlinear interaction of strong laser fields in vacuum

Quantum electrodynamics (QED) predicts that electromagnetic fields interact with each other in vacuum. We study the possibility of revealing this interaction experimentally with intensities on the order of 10²⁴–10²⁶ W/cm², which may be available in the next generation of laser systems. In particular, we investigate high-order harmonic generation in vacuum via the collision of two ultrastrong counterpropagating laser pulses. The experimental feasibility of the related process of stimulated light-by-light scattering is also examined. Finally, the importance of including diffractive effects to describe the nonlinear interaction between an x-ray probe and a strong, focused optical standing wave is pointed out.     

Quantum secret sharing between multiparty and multiparty with four states

A protocol of quantum secret sharing between multiparty and multiparty with four states was presented. It was shown that this protocol can nullify the Trojan horse attack with a multi-photon signal, the fake-signal attack with Einstein-Podolsky-Rosen pairs, the attack with single photons, and the attack with invisible photons. In addition, the upper bounds of the average success probabilities were given for dishonest agent eavesdropping encryption using the fake-signal attack with any two-particle entangled states. Supported by the National Natural Science Foundation of China (Grant No. 10671054), the Key Project of Science and Technology Research of Education Ministry of China (Grant No. 207011) and the Natural Science Foundation of Hebei Province, China (Grant Nos. A2005000140 and 07M006)     

A Fe<Superscript>3+</Superscript>/Hg<Superscript>2+</Superscript>-Selective Anthracene-Based Fluorescent PET Sensor with Tridentate Ionophore of Amide/β-Amino Alcohol

A new anthracene-based fluorescent PET sensor 1 with a tridentate ionophore of amide/β-amino alcohol displays very good selectivity and sensitivity for Fe³⁺ (K _a = 1.6 × 10³ M⁻¹) and Hg²⁺ (K _a = 2.1 × 10³ M⁻¹) in CH₃CN–H₂O (3:7, v/v) with detection limit of 1 μM. More fluorescence enhancement was observed when 1 selectively detected Fe³⁺ or Hg²⁺ in CH₃CN and its detection limit was up to 0.03 μM.     

Unitarity in “Quantization Commutes with Reduction”

Let M be a compact Kähler manifold equipped with a Hamiltonian action of a compact Lie group G. In this paper, we study the geometric quantization of the symplectic quotient M // G. Guillemin and Sternberg [Invent. Math. 67, 515–538 (1982)] have shown, under suitable regularity assumptions, that there is a natural invertible map between the quantum Hilbert space over M //G and the G-invariant subspace of the quantum Hilbert space over M.Reproducing other recent results in the literature, we prove that in general the natural map of Guillemin and Sternberg is not unitary, even to leading order in Planck’s constant. We then modify the quantization procedure by the “metaplectic correction” and show that in this setting there is still a natural invertible map between the Hilbert space over M // G and the G-invariant subspace of the Hilbert space over M. We then prove that this modified Guillemin–Sternberg map is asymptotically unitary to leading order in Planck’s constant. The analysis also shows a good asymptotic relationship between Toeplitz operators on M and on M // G.     

Optical and Thermal Simulator for Laser-assisted Magnetic Recording

“Laser-assisted magnetic recording”, in which a recording media is heated by a laser beam while writing data, is attracting attention as a technology that enables a recording density of 1 Tb/in.². There exists another technology for media in which the recording layer is constructed with many small projections that enable high magnetic coercivity. This is called “patterned media”. For developing hard disk drives using these methods, we developed a simulator that analyzes the optical intensity distribution from the optical head for laser-assisted recording and the temperature profile on the patterned media. The simulator calculates the optical model using the finite-difference time-domain (FDTD) method. The thermal analysis of the three-dimensional model allows fast calculations using the alternating direction implicit (ADI) method. The heat source distribution data for thermal analysis is calculated in order to use the results of optical analysis. The optical and thermal analyses of the laser-assisted recording model were investigated with the simulator.     

Constant and Equivariant Cyclic Cohomology

In this note, we prove that the constant and equivariant cyclic cohomology of algebras coincide. This shows that constant cyclic cohomology is rich and computable.