Enhancing vibration mitigation in a Jeffcott rotor with active magnetic bearings through parametric excitation

Nonlinear Dynamics - In previous studies of linear rotary systems with active magnetic bearings, parametric excitation was introduced as an open-loop control strategy. The parametric excitation was...     

Some norm inequalities involving convex functions of operators

Positivity - We describe lower semi-Fredholm and Fredholm spectra of weighted composition operators on C(K) in the case when the corresponding map is an open map of the compact space K onto itself....     

Use of cyclodextrins in isotachophoresis. VII. Resolution of structurally related and chiral phenothiazines

Commercially available phenothiazine derivatives were used for the study of cyclodextrin complex formation by cationic isotachophoresis with alpha-, beta- and gamma-cyclodextrin and methylated analogues of beta-cyclodextrin as leading electrolyte additives. The relationships between the type of solute substituent in the 10- and/or 2-position and the stability of the created cyclodextrin complex were studied and the results were utilized for the optimization of isotachophoretic conditions suitable for the resolution of the studied phenothiazine derivatives. Successful resolution of three racemic solutes was achieved.     

Vibration suppression of self-excited oscillations by parametric inertia excitation

The main objective of this contribution is to show the phenomenon of full vibration suppression of a simple two degrees of freedom rotary oscillator by interaction between self-excitation and parametric excitation. One disk is under the influence of self-excitation, modelled by a negative damping coefficient, while the moment of inertia of the second disk is periodically varied in time within an open-loop control with a fixed frequency. Both disks are coupled by a linear spring-element. Parametric excitation develops equations of motion with time-periodic coefficients. Using the averaging method for a firstorder approximation general conditions for full vibration suppression are analytically derived for the two degrees of freedom system with harmonic inertia variation. The approximated analytical stability predictions are verified and compared to results obtained from numerical time integration of the original equations of motion. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Optical Soliton Bullets in (2+1)D Nonlinear Bragg Resonant Periodic Geometries

We consider light propagation in a Kerr-nonlinear 2D waveguide with a Bragg grating in the propagation direction and homogeneous in the transverse direction. Using Newton's iteration method we construct both stationary and travelling solitary wave solutions of the corresponding mathematical model, the 2D nonlinear coupled mode equations (2D CME). We call these solutions 2D gap solitons due to their similarity with the gap solitons of 1D CME (fiber grating). Long-time stable evolution preserving the solitary fashion is demonstrated numerically despite the fact that, as we show, for the 2D CME no local constrained minima of the Hamiltonian functional exist. Building on the 1D study of [ 1 ], we demonstrate trapping of slow enough 2D gap solitons at localized defects. We explain the mechanism of trapping as resonant transfer of energy from the soliton to one or more nonlinear defect modes. For a special class of defects, we construct a family of nonlinear defect modes by numerically following a bifurcation curve starting at analytically or numerically known linear defect modes. Compared to 1D the dynamics of trapping are harder to fully analyze and the existence of many defect modes for a given defect potential causes that slow solitons store a part of their energy for virtually all of the studied attractive defects.     

High-performance liquid chromatography/inductively coupled plasma mass spectrometry and tandem mass spectrometry for the detection of carbon-containing compounds

High-performance liquid chromatography (HPLC) combined with inductively coupled plasma mass spectrometry (ICPMS) has been studied as a means for the detection of carbon to provide a 'universal' method for detecting organic compounds in chromatographic eluents. Carbon is particularly difficult to ionise and the amount of carbon present in normal chromatographic systems leads to high backgrounds, making detection a challenge. Novel separation approaches were therefore employed, using either entirely aqueous eluents (at temperatures of 60 and 160 degrees C, dependent on the column used) to eliminate the organic modifier completely, or isotopically enriched solvents. For the aqueous eluents, detection limits for sulphanilamide were found to be 2.26 microg, corresponding to 1.13 micromol (0.47 micromol of carbon), injected on a conventional 4.6 mm i.d. column. The use of a narrow bore column with highly isotopically enriched 12C-methanol (99.95 atom%) as organic modifier for the mobile phase enabled the detection of 86 micromol for 13C-triple-labelled caffeine and 79 micromol for 13C-double-labelled phenacetin. The sensitive detection of 12C-compounds with 13C-enriched methanol as organic modifier proved impractical due to a lower level of isotopic enrichment (99 atom%) of this solvent, with the residual 12C-methanol resulting in significant interference.     

Gas–liquid partitioning of halogenated volatile organic compounds in aqueous cyclodextrin solutions

Gas–liquid partitioning coefficients (K_GL) were measured for halogenated volatile organic compounds (VOCs), namely 1-chlorobutane, methoxyflurane, pentafluoropropan-1-ol, heptafluorobutan-1-ol, α,α,α-trifluorotoluene, and toluene in aqueous solutions of natural α-, β-, and γ-cyclodextrins (CDs) at temperatures from (273.35 to 326.35) K employing the techniques of headspace gas chromatography and inert gas stripping. The binding constants of the 1:1 inclusion complex formation between the VOCs and CDs were evaluated from the depression of the VOCs volatility as a function of CD concentration. The host–guest size matching and the hydrophobic interaction concept were used to rationalize the observed widely different affinity of the VOC–CD pairs to form the inclusion complex. The enthalpic and entropic component of the standard Gibbs free energy of complex formation as derived from the temperature dependence of the binding constant indicate the thermodynamic origin of the binding to vary greatly among the systems studied, but follow the global enthalpy–entropy compensation relationships reported previously in the literature.     

Vibration quenching in a large scale rotor-bearing system using journal bearings with variable geometry

In large scale rotating machinery the resonance amplitude during the passage through resonance is a matter of consideration because of its influence in the surrounding environment of the rotational system and foundation. In this paper, a variable geometry journal bearing (VGJB), recently patented, is applied for the mounting of a large scale rotor bearing system operating at the range of medium speed. The simulation of the rotor-bearing system incorporates a recent method for simulation of a multi-segment continuous rotor in combination with nonlinear bearing forces. The use of the current bearing gives results that encourage the use of such a bearing in rotating machinery since the vibration amplitude during the passage through the critical speed can be reduced up to 60–70%. In the presented study, the developed amplitude and the rotor stresses are severely reduced compared to those of the system with normal cylindrical journal bearings during a virtual start up of the system.     

Surface Gap Soliton Ground States for the Nonlinear Schr?dinger Equation

We consider the nonlinear Schr?dinger equation