Shaping of molecular weight distribution by iterative learning probability density function control strategies

A mathematical model is developed for the molecular weight distribution (MWD) of free-radical styrene polymerization in a simulated semi-batch reactor system. The generation function technique and moment method are employed to establish the MWD model in the form of Schultz-Zimmdistribution. Both static and dynamic models are described in detail. In order to achieve the closed-loop MWD shaping by output probability density function (PDF) control, the dynamic MWD model is further developed by a linear B-spline approximation. Based on the general form of the B-spline MWD model, iterative learning PDF control strategies have been investigated in order to improve the MWD control performance. Discussions on the simulation studies show the advantages and limitations of the methodology

Probing New Physics From CP Violation in Radiative B Decays

When new CP-violating interactions are dominated by flavor changing neutral particle exchanges, that may occur in many extensions of the standard model. We examine a type 3 two Higgs doublet model and find that direct CP asymmetries can be as large as about 25% . Time-dependent and time-integrated mixing-induced CP asymmetries up to 85 and 40 %, respectively, are possible without conflict with other constraints. It mainly requirs an enhanced chromo-magnetic dipole $b\to sg$ decay to be close to the present experimental bound.Comment: 7 pages, latex, no figure

Slave particle approach to the finite temperature properties of ultracold Bose gases in optical lattices

By using slave particle (slave boson and slave fermion) technique on the Bose-Hubbard model, we study the finite temperature properties of ultracold Bose gases in optical lattices. The phase diagrams at finite temperature are depicted by including different types of slave particles and the effect of the finite types of slave particles is estimated. The superfluid density is evaluated using the Landau second order phase transition theory. The atom density, excitation spectrum and dispersion curve are also computed at various temperatures, and how the Mott-insulator evolves as the temperature increases is demonstrated. For most quantities to be calculated, we find that there are no qualitatively differences in using the slave boson or the slave fermion approaches. However, when studying the stability of the mean field state, we find that in contrast to the slave fermion approach, the slave boson mean field state is not stable. Although the slave boson mean field theory gives a qualitatively correct phase boundary, it corresponds to a local maximum of Landau free energy and can not describe the second order phase transition because the coefficient $a_4$ of the fourth order term is always negative in the free energy expansion.Comment: 27 pages, 8 figures, final version for publicatio

Symmetry-preserving Loop Regularization and Renormalization of QFTs

A new symmetry-preserving loop regularization method proposed in \cite{ylw} is further investigated. It is found that its prescription can be understood by introducing a regulating distribution function to the proper-time formalism of irreducible loop integrals. The method simulates in many interesting features to the momentum cutoff, Pauli-Villars and dimensional regularization. The loop regularization method is also simple and general for the practical calculations to higher loop graphs and can be applied to both underlying and effective quantum field theories including gauge, chiral, supersymmetric and gravitational ones as the new method does not modify either the lagrangian formalism or the space-time dimension of original theory. The appearance of characteristic energy scale $M_c$ and sliding energy scale $\mu_s$ offers a systematic way for studying the renormalization-group evolution of gauge theories in the spirit of Wilson-Kadanoff and for exploring important effects of higher dimensional interaction terms in the infrared regime.Comment: 13 pages, Revtex, extended modified version, more references adde

Multi-Stability of Electromagnetically Induced Transparency in Atom-Assisted Optomechanical Cavities

We study how an oscillating mirror affects the electromagnetically induced transparency (EIT) of an atomic ensemble, which is confined in a gas cell placed inside a micro-cavity with an oscillating mirror in one end. The oscillating mirror is modeled as a quantum mechanical harmonic oscillator. The cavity field acts as a probe light of the EIT system and also produces a light pressure on the oscillating mirror. The back-action from the mirror to the cavity field results in several (from one to five) steady-states for this atom-assisted optomechanical cavity, producing a complex structure in its EIT. We calculate the susceptibility with respect to the few (from one to three) stable solutions found here for the equilibrium positions of the oscillating mirror. We find that the EIT of the atomic ensemble can be significantly changed by the oscillating mirror, and also that the various steady states of the mirror have different effects on the EIT.Comment: 10 pages, 9 figure

Robust signal processing for material noise suppression in ultrasonic nondestructive testing

Ultrasonic nondestructive inspection of materials is often limited by the presence of backscattered echoes from the material structure, known as material or grain noise. The material noise can be difficult to distinguish from flaw echoes because their spectra overlap to a large extent. Due to the overlapping, application of conventional linear filters is generally not adequate for attenuating this type of noise. However, a suitable choice of the inspection frequency will cause the grain response to be considerable more noncoherent than the flaw response. This property arise from the fact that the material noise can be considered as an interference pattern made up of unresolved scatterers, while the flaw echoes will bear more resemblance to specular reflections. The implication of this difference is that the material noise can be suppressed by means of frequency diversity techniques which take advantage of its noncoherent nature

Multi-Atomic Mirror for Perfect Reflection of Single Photons in A Wide Band of Frequency

A resonant two level atom doped in one dimensional waveguide behaves as a mirror, but this single-atom "mirror" can only reflect single photon perfectly at a specific frequency. For a one dimensional coupled-resonator waveguide, we propose to extend the perfect reflection region from a specific frequency to a wide band by placing many atoms individually in the resonators in a finite coordinate region of the waveguide. Such a doped resonator array promises us to control the propagation of a practical photon wave packet with certain momentum distribution instead of a single photon, which is ideally represented by a plane wave with specific momentum. The studies based on the discrete-coordinate scattering theory display that such hybrid structure indeed provides a near-perfect reflection for single photon in a wide band. We also calculated photon group velocity distribution, which shows that the perfect reflection with wide band exactly corresponds to the stopping light region.Comment: 8 pages, 10 figure