Harmonic and anharmonic oscillations of a cylindrical plasma in the presence of a uniform axial magnetic field and a steady axial current

In the present note we have studied the harmonic and anharmonic oscillations of cylindrical plasma using Lagrangian formalism. In order to study the harmonic oscillations, the equations are linearized and the resulting equation for the displacement has been numerically solved. For situations present in thermonuclear reactors, the presence of axial magnetic field is found necessary to make the periods of oscillation to become comparable with the time required for the thermonuclear reactions to set in. A detailed analysis of the anharmonic oscillations reveals that the significant interaction is between the first and the second mode. The fundamental period of anharmonic oscillation is more than the corresponding period of harmonic oscillations by 9·2%. Graphs have been drawn for the amplitudes of relative variations in density and magnetic field and of the time-varying part of anharmonic oscillation.

Anharmonic Effects in Germanium

A precise X-ray investigation is carried out to probe the lowest-order anharmonic contribution of the atomic potential of the germanium atom. A total number of 1052 reflections (h + k + l = 4n and 4n +/- 1) are precisely measured at room temperature using a spherical single crystal of germanium and using a Nonius CAD-4 X-ray diffractometer with crystal monochromatized MoKalpha radiation. A least-square refinement program is used to refine the harmonic and anharmonic thermal parameters of the crystal. The refinement gives beta(Ge) = (-0.749 +/- 1.79) x 10-(16) J nm-3 with B(Ge) = (0.528 +/- 0.004) x 10(-2) nm2. The reliability index (R) amounts to 1.71% for germanium.

On the anharmonic vibrations in crystalline silicon

Using a total of 1052 Bragg reflections of silicon, an X-ray investigation has been carried out to deduce the anharmonic thermal parameter beta, apart from the estimation of the harmonic contribution of the thermal vibration at room temperature. Reflections of type h + k + l = 4n, and 4n +/- 1 were used to estimate these parameters using MoKalpha radiation and a Nonius CAD-4 X-ray diffractometer. We obtain B(Si) = 0.451 (0.008) angstrom2 and beta(Si) = 0.279(2.630) eV angstrom-3 with R = 3.12%. The present B and beta values are in very good agreement with the earlier studies.

Anharmonic surface interactions for biomolecular screening and characterization.

The acoustic response of conventional mechanical oscillators, such as a piezoelectric crystal, is predominantly harmonic at modest amplitudes. However, here, we observe from the electrical response that significant motional anharmonicity is introduced in the presence of attached analyte. Experiments were conducted with streptavidin-coated polystyrene microbeads of various sizes attached to a quartz crystal resonator via specific and nonspecific molecular tethers in liquid. Quantitative analysis reveals that the deviation of odd Fourier harmonics of the response caused by introduction of microbeads as a function of oscillation amplitude presents a unique signature of the molecular tether. Hence, the described anharmonic detection technique (ADT) based on this function allows screening of biomolecules and provides an additional level of selectivity in receptor-based detection that is often associated with nonspecific interactions. We also propose methods to extract mechanical force-extension characteristics of the molecular tether and activation energy using this technique.

Probing biomolecular interaction forces using an anharmonic acoustic technique for selective detection of bacterial spores.

Receptor-based detection of pathogens often suffers from non-specific interactions, and as most detection techniques cannot distinguish between affinities of interactions, false positive responses remain a plaguing reality. Here, we report an anharmonic acoustic based method of detection that addresses the inherent weakness of current ligand dependant assays. Spores of Bacillus subtilis (Bacillus anthracis simulant) were immobilized on a thickness-shear mode AT-cut quartz crystal functionalized with anti-spore antibody and the sensor was driven by a pure sinusoidal oscillation at increasing amplitude. Biomolecular interaction forces between the coupled spores and the accelerating surface caused a nonlinear modulation of the acoustic response of the crystal. In particular, the deviation in the third harmonic of the transduced electrical response versus oscillation amplitude of the sensor (signal) was found to be significant. Signals from the specifically-bound spores were clearly distinguishable in shape from those of the physisorbed streptavidin-coated polystyrene microbeads. The analytical model presented here enables estimation of the biomolecular interaction forces from the measured response. Thus, probing biomolecular interaction forces using the described technique can quantitatively detect pathogens and distinguish specific from non-specific interactions, with potential applicability to rapid point-of-care detection. This also serves as a potential tool for rapid force-spectroscopy, affinity-based biomolecular screening and mapping of molecular interaction networks.

Probing biomolecular interaction forces using an anharmonic acoustic technique for selective detection of bacterial spores

Receptor-based detection of pathogens often suffers from non-specific interactions, and as most detection techniques cannot distinguish between affinities of interactions, false positive responses remain a plaguing reality. Here, we report an anharmonic acoustic based method of detection that addresses the inherent weakness of current ligand dependant assays. Spores of Bacillus subtilis (Bacillus anthracis simulant) were immobilized on a thickness-shear mode AT-cut quartz crystal functionalized with anti-spore antibody and the sensor was driven by a pure sinusoidal oscillation at increasing amplitude. Biomolecular interaction forces between the coupled spores and the accelerating surface caused a nonlinear modulation of the acoustic response of the crystal. In particular, the deviation in the third harmonic of the transduced electrical response versus oscillation amplitude of the sensor (signal) was found to be significant. Signals from the specifically-bound spores were clearly distinguishable in shape from those of the physisorbed streptavidin-coated polystyrene microbeads. The analytical model presented here enables estimation of the biomolecular interaction forces from the measured response. Thus, probing biomolecular interaction forces using the described technique can quantitatively detect pathogens and distinguish specific from non-specific interactions, with potential applicability to rapid point-of-care detection. This also serves as a potential tool for rapid force-spectroscopy, affinity-based biomolecular screening and mapping of molecular interaction networks. © 2011 Elsevier B.V.

Nonlinearity as a resource for nonclassicality in anharmonic systems

Nonclassicality is a key ingredient for quantum enhanced technologies and experiments involving macro- scopic quantum coherence. Considering various exactly-solvable quantum-oscillator systems, we address the role played by the anharmonicity of their potential in the establishment of nonclassical features. Specifically, we show that a monotonic relation exists between the the entropic nonlinearity of the considered potentials and their ground state nonclassicality, as quantified by the negativity of the Wigner function. In addition, in order to clarify the role of squeezing--which is not captured by the negativity of the Wigner function--we focus on the Glauber-Sudarshan P-function and address the nonclassicality/nonlinearity relation using the entanglement potential. Finally, we consider the case of a generic sixth-order potential confirming the idea that nonlinearity is a resource for the generation of nonclassicality and may serve as a guideline for the engineering of quantum oscillators.

Anharmonic Helmholtz free energy to O(lambdaâ ´) in the non- leading term approximation /|nby Leslie Wilk. -- 260 St. Catharines, Ont. : [s. n.],

Expressions for the anharmonic Helmholtz free energy contributions up to o( f ) ,valid for all temperatures, have been obtained using perturbation theory for a c r ystal in which every atom is on a site of inversion symmetry. Numerical calculations have been carried out in the high temperature limit and in the non-leading term approximation for a monatomic facecentred cubic crystal with nearest neighbour c entralforce interactions. The numbers obtained were seen to vary by a s much as 47% from thos e obtai.ned in the leading term approximati.on,indicating that the latter approximati on is not in general very good. The convergence to oct) of the perturbation series in the high temperature limit appears satisfactory.