Chiral field theory of 0−+0^{-+} glueball

A chiral field theory of $0^{-+}$ glueball is presented. By adding a $0^{-+}$ glueball field to a successful Lagrangian of chiral field theory of pseudoscalar, vector, and axial-vector mesons, the Lagrangian of this theory is constructed. The couplings between the pseodoscalar glueball field and mesons are via U(1) anomaly revealed. Qualitative study of the physical processes of the $0^{-+}$ glueball of $m=1.405\textrm{GeV}$ is presented. The theoretical predictions can be used to identify the $0^{-+}$ glueball.Comment: 29 page

Unique continuation property and control for the Benjamin-Bona-Mahony equation on the torus

We consider the Benjamin-Bona-Mahony (BBM) equation on the one dimensional torus T = R/(2{\pi}Z). We prove a Unique Continuation Property (UCP) for small data in H^1(T) with nonnegative zero means. Next we extend the UCP to certain BBM-like equations, including the equal width wave equation and the KdV-BBM equation. Applications to the stabilization of the above equations are given. In particular, we show that when an internal control acting on a moving interval is applied in BBM equation, then a semiglobal exponential stabilization can be derived in H^s(T) for any s \geq 1. Furthermore, we prove that the BBM equation with a moving control is also locally exactly controllable in H^s(T) for any s \geq 0 and globally exactly controllable in H s (T) for any s \geq 1

Control and Stabilization of the Nonlinear Schroedinger Equation on Rectangles

This paper studies the local exact controllability and the local stabilization of the semilinear Schr\"odinger equation posed on a product of $n$ intervals ($n\ge 1$). Both internal and boundary controls are considered, and the results are given with periodic (resp. Dirichlet or Neumann) boundary conditions. In the case of internal control, we obtain local controllability results which are sharp as far as the localization of the control region and the smoothness of the state space are concerned. It is also proved that for the linear Schr\"odinger equation with Dirichlet control, the exact controllability holds in $H^{-1}(\Omega)$ whenever the control region contains a neighborhood of a vertex

Advancements in resonant column testing of soils using random vibration techniques

This study focuses on advancements in resonant column testing of soil and rock using random vibration techniques. A large free-free resonant column device was built and modified to enable the direct measurement of rotational transfer functions of soil specimens in the frequency domain. Theoretical rotational transfer functions and strain measures were derived and programmed for the new approach. Random (white noise) and swept-sine excitation types were used to vibrate soil specimens over a range of strain levels, confining pressures, and frequencies, while rotational accelerations of the end platens were measured. Shear modulus and damping were then determined by fitting the measured peak frequencies and amplitudes by theoretical rotational transfer functions. Nonlinear strain-dependent modulus and damping curves were generated by measurement of the multi-modal vibration response over a range of excitation intensities. To provide a preliminary validation, results for the new technique are evaluated against those from the current ASTM Standard D4015 for the same soil specimens. Results were found to compare well in terms of maximum shear modulus as a function of confining pressure. The nonlinear strain-dependent modulus reduction and damping curves were found to be similar in shape, but have different values of shear strain, possibly due to the need to account for strain energy at all frequencies in the broadband transfer function tests

BIOMECHANICAL STUDIES ON TRIPLE JUMP TECHNIQUES: THEORETICAL CONSIDERATIONS AND APPLICATIONS

The purpose of this paper is to summarise some most recent studies on the biomechanics of the triple jump. A linear relationship between the loss in the horizontal velocity and the gain in the vertical velocity during three support phases was found for individual athletes. Optimisation models were developed for determining optimum phase ratio and the actual distance with a given phase ratio for any given athlete. A biomechanical model of free limb motions was developed to determine the effects of free limb motions on the performance of the triple jump. The relationship between the loss in the horizontal velocity and the gain in the vertical velocity during support phases has a significant effect on the optimum phase ratio and the actual distance with optimised phase ratio. The free limb motions are associated with the gain in the vertical velocity and loss in the horizontal velocity. Optimum arm swing techniques for the triple jump were determined based on the functions of free limb motions

Monte Carlo Studies of the Critical Phenomena in Carbon Monoxide Oxidation.

It is well established that anisotropy does not affect the critical behavior of a system in thermodynamic equilibrium undergoing a second order phase transition. We study here an anisotropic kinetic model for heterogeneous catalysis which mimics the oxidation of CO on the (110) surface of a transition metal like Pd. In this model, the oxidation process occurs at an infinite reaction rate. We mapped out the phase diagram of possible steady states for various anisotropic reaction and absorption processes as a function of the O\sb2/CO adsorption rate and the CO diffusion rate. The phase diagram depends upon the amount of anisotropy and exhibits both a first order and a second order phase transition. We also examined the critical behavior at the second order phase transition with finite size scaling and found that this model belongs to the directed percolation universality class irrespective of the anisotropy. Furthermore, we extended this model to include finite reaction rates. We found evidence of a new feature here, namely a tricritical point. We have developed a theory to account for this new feature. The critical behavior of this modified model belongs to the same universality class as the original model except at the tricritical point. To better understand the physics of nonequilibrium transitions, we studied the behavior of various dynamic modes utilizing the master equation and finite size scaling. This master equation approach indicated that dynamic phase transition is a consequence of the emergence of new steady states. This approach affords a connection with the traditional method of transfer matrix

RAFT Synthesis of Water-Soluble, Stimuli-Responsive (Co)polymers and Post-Polymerization End Group Modification Via the Thiol-ene Reaction

A series of water-soluble, stimuli-responsive (co)polymers was synthesized via the reversible addition-fragmentation chain transfer (RAFT) polymerization. The end group of a RAFT polymer, poly(jV-isopropylacrylamide), was modified to ene or yne function via thiol-ene click chemistry. The ene or yne end group subsequently underwent thiol-ene or thiol-yne addition affording mono- or di-functional end group. First, three methacrylic monomers containing 2 or 3 pendent tertiary amine functional groups, l,3-bis(dimethylamino)propan-2-yl methacrylate (Ml), l-(bis(3-(dimethylamino)propyl)amino)propan-2-yl methacrylate (M2), and 2-((2-(2-(dimethylamino)ethoxy)ethyl)methylamino)ethyl acrylate (M3), were synthesized via an acylation reaction between methacryloyl chloride and the corresponding aminoalcohol. All of these three monomers were successfully homopolymerized under RAFT conditions with 1 -methyl-1 -cyanoethyl dithiobenzoate (CPDB) as chain transfer agent (CTA). For each monomer, homopolymerization using two different CTA:Initiator ratio was conducted. The effect of the CTATnitiator ratio on the kinetics is in agreement with the prediction by RAFT mechanism. The stimuli-responsive properties of polyMl, polyM2, and polyM3 in aqueous solution were tested and all the homopolymers shows reversible thermo-responsive and pH-responsive properties. Second, a monomer with excellent biocompatibility, 2-(methacryloyloxy)ethyl phosphorylcholine (MPC), was homopolymerized in water via RAFT polymerization mediated by 4-cyanopentanoic acid dithiobenzoate (CTP). The prepared MPC homopolymer was used as a macro-CTA in the RAFT polymerization of four stimuli-responsive monomers, JV,iV-diethylacrylamide (DEAm), 4-vinylbenzoic acid (VBZ) 7V-(3-sulfopropyl)-A^-methacrylooxyethyl-A^,A^-dimethylammonium betaine (DMAPS), and the newly synthesized 7V,yV-di-H-propylbenzylvinylamine (DnPBVA), yielding a series of water-soluble, stimuli-responsive AB diblock copolymers. The stimuli-responsive properties of there copolymers were examined by a combination of H NMR spectroscopy and dynamic light scattering. The results show that aggregates with - varied sizes formed upon application of the corresponding stimulus (change of pH, temperature, or electrolyte concentration). And the removal of the stimulus caused the dissociation of the aggregates, proving the reversibility of the stimuli-responsive property. Finally, a well-defined precursor homopolymer of iV-Isopropylacrylamide (NIPAm) was prepared using RAFT polymerization in DMF at 70°C employing the CPDB as CTA. The dithiobenzoate end-groups were subsequently modified to give ene or yne functional end groups via a thiol-ene click reaction catalyzed using a combination of octylamine and dimethylphenylphosphine to induce a thio-Michael reaction with either allyl methacrylate or propargyl aery late. The conversion of the end-group was near quantitative according to \u27H NMR spectroscopy. The ene and yne groups were then reacted quantitatively via radical thiol-ene and radical thiol-yne reactions under UV-irradiation with three representative thiols yielding the mono and bis-end functional NIPAm homopolymers. The lower critical solution temperatures (LCST) were then determined for all NIPAm homopolymers using a combination of optical measurements and dynamic light scattering. Results show that the LCST varies depending on the chemical nature of the end-groups with measured values lying in the range 26-3 5°C