Temperature effects on capillary instabilities in a thin nematic liquid crystalline fiber embedded in a viscous matrix

Linear stability analysis of capillary instabilities in a thin nematic liquid crystalline cylindrical fiber embedded in an immiscible viscous matrix is performed by formulating and solving the governing nemato-capillary equations, that include the effect of temperature on the nematic ordering as well as the effect of the nematic orientation. A representative axial nematic orientation texture with the planar easy axis at the fiber surface is studied. The surface disturbance is expressed in normal modes, which include the azimuthal wave number m to take into account non-axisymmetric modes. Capillary instabilities in nematic fibers reflect the anisotropic nature of liquid crystals, such as the ordering and orientation contributions to the surface elasticity and surface normal and bending stresses. Surface gradients of normal and bending stresses provide additional anisotropic contributions to the capillary pressure that may renormalize the classical displacement and curvature forces that exist in any fluid fiber. The exact nature (stabilizing and destabilizing) and magnitude of the renormalization of the displacement and curvature forces depend on the nematic ordering and orientation, i.e. the anisotropic contribution to the surface energy, and accordingly capillary instabilities may be axisymmetric or non-axisymmetric. In addition, when the interface curvature effects are accounted for as contributions of the work of interfacial bending and torsion to the total energy of the system, the higher-order bending moment contribution to the surface stress tensor is critical in stabilizing the fiber instabilities. For the planar easy axis, the nematic ordering contribution to the surface energy, which renormalizes the effect of the fiber shape, plays a crucial role to determine the instability mechanisms. Moreover, the unstable modes, which are most likely observed, can be driven by the dependence of surface energy on the surface area. Low-ordering fibers display the classical axisymmetric mode, since the surface energy decreases by decreasing the surface area. Decreasing temperature gives rise to the encounter with a local maximum or to monotonic increase of the characteristic length of the axisymmetric mode. Meanwhile, in the presence of high surface ordering, non-axisymmetric finite wavelength instabilities emerge, with higher modes growing faster since the surface energy decreases by increasing the surface area. As temperature decreases, the pitches of the chiral microstructures become smaller. However, this non-axisymmetric instability mechanism can be regulated by taking account of the surface bending moment, which contains higher order variations in the interface curvatures. More and more non-axisymmetric modes emerge as temperature decreases, but, at constant temperature, only a finite number of non-axisymmetric modes are unstable and a single fastest growing mode emerges with lower and higher unstable modes growing slower. For nematic fibers, the classical fiber-to-droplet transformation is one of several possible instability pathways, while others include chiral microstructures. The capillary instabilities' growth rate of a thin nematic fiber in a viscous matrix is suppressed by increasing either the fiber or matrix viscosity, but the estimated droplet sizes after fiber breakup in axisymmetric instabilities decrease with increasing the matrix viscosity. Received 15 April 2002 and Received in final form 3 October 2002 RID="a" ID="a"e-mail: alejandro.rey@mcgill.ca     

Oscillations of charged particles in an external magnetic field about steady motion

We develop a Hamiltonian formalism that can be used to study the particle dynamics near stable equilibria. The construction of an original canonical transformation allowed us to prove the conservation of the linear momentum P₃, which permitted the expansion of the Hamiltonian about a fixed point. The definition of the rotational variable h whose Poisson algebra properties played the essential role in the diagonalization of the quadratic Hamiltonian yielding two uncoupled oscillators with definite frequencies and amplitudes. It is through applying this variable near a fixed point that come to light Heisenberg's and Harmonic Oscillator equations of motion of the particles, leading thus the association of the fixed point trajectories with arbitrary trajectories in its immediate neighborhood. The present formalism succeeded to treat the problem of free-electron laser dynamics and may be applied to similar cases. Received 20 October 2001     

Stability and instability of a hot and dilute nuclear droplet

The diabatic approach to dissipative collective nuclear motion is reformulated in the local-density approximation in order to treat the normal modes of a spherical nuclear droplet analytically. In a first application the adiabatic isoscalar modes are studied and results for the eigenvalues of compressional (bulk) and pure surface modes are presented as function of density and temperature inside the droplet, as well as for different mass numbers and for soft and stiff equations of state. We find that the region of bulk instabilities (spinodal regime) is substantially smaller for nuclear droplets than for infinite nuclear matter. For small densities below 30% of normal nuclear matter density and for temperatures below 5 MeV all relevant bulk modes become unstable with similar growth rates. The surface modes have a larger spinodal region, reaching out to densities and temperatures way beyond the spinodal line for bulk instabilities. Essential experimental features of multifragmentation, like fragmentation temperatures and fragment-mass distributions (in particular the power-law behavior) are consistent with the instability properties of an expanding nuclear droplet, and hence with a dynamical fragmentation process within the spinodal regime of bulk and surface modes (spinodal decomposition). Received: 4 September 2000 / Accepted: 14 November 2000     

Flow-controlled growth in Langmuir monolayers

We propose a hydrodynamic mechanism, based on the Marangoni flow, to describe growth instabilities of liquid-condensed islands in the supercooled liquid-expanded phase of two-dimensional Langmuir monolayers. This Marangoni instability is intrinsic to Langmuir monolayers and is not controlled by the expulsion of chemical impurities from the liquid-condensed phase. The hydrodynamic transport of the insoluble surfactants is shown to overwhelm passive diffusion and to provide a mechanism for fingering instabilities. The model can explain the observations by Brewster-angle microscopy of ramified liquid-condensed islands in monolayers that do not contain the fluorescent dye impurities, which are normally believed to be responsible for Langmuir-film growth instabilities. Received 21 May 2000 and Received in final form 18 June 2001     

Propagation of waves and chaos in transmission line with strongly anharmonic dangling resonator

Delayed differential equation of motion with multiple lags is derived for an anharmonic stub resonator coupled to a monomode transmission line. Transmission and reflection coefficients are found analytically in the harmonic approximation. Nonlinear response of the system is analysed by an electric circuit obeying the same equations of motion. Enhanced second harmonic generation is found at the frequencies, which in the harmonic approximation correspond to the zeros of transmission. An aperiodic (chaotic) response is found mainly in the frequency range close to the resonance of the dangling resonator. Zeros of transmission and total transmissions are shown to be lifted by the anharmonicity nearly in the same frequency region. Higher harmonics are preferentially transmitted at the zero transmission points in the presence of anharmonicity. Received 14 March 2002 / Received in final form 25 November 2002 Published online 14 March 2003     

Non-linear resonances in the forced responses of plates,part II: Asymmetric responses of circular plates

The dynamic analogue of the von Karman equations is used to study the forced response, including asymmetric vibrations and traveling waves, of a clamped circular plate subjected to harmonic excitations when the frequency of excitation is near one of the natural frequencies. The method of multiple scales, a perturbation technique, is used to solve the non-linear governing equations. The approach presented provides a great deal of insight into the nature of the non-linear forced resonant response. It is shown that in the absence of internal resonance (i.e., a combination of commensurable natural frequencies) or when the frequency of excitation is near one of the lower frequencies involved in the internal resonance, the steady state response can only have the form of a standing wave. However, when the frequency of excitation is near the highest frequency involved in the internal resonance it is possible for a traveling wave component of the highest mode to appear in the steady state response.     

Spatial orders appearing at instabilities of synchronous chaos of spatiotemporal systems

Various spatial orders introduced by the instabilities of synchronous chaotic state of spatiotemporal systems are investigated by considering coupled map lattice and chaotic partial differential equation. In particular, the motions of on-off intermittent states at the onset of the instabilities are studied in detail. The chaotic desynchronized patterns can be described by a simple universal form, including three parts: the synchronous chaos; a spatially ordered pattern, determined by the unstable mode of the reference synchronous chaos; and on-off intermittency of the scale of this given pattern. Received 31 July 2002 / Received in final form 20 November 2002 Published online 31 December 2002     

Instability of spatially periodic patterns due to a zero mode in the phase-field crystal equation

Weakly nonlinear spatially periodic patterns coupled to a Goldstone (zero) mode of the phase-field crystal model are investigated. Rotationally invariant equations for the dynamics of the amplitudes of a hexagonal pattern are derived first, which then allows us to determine stability regions for stripes and hexagons. There are parameter regimes in which all periodic patterns become unstable as a result of long-wavelength instabilities generated by the zero mode.     

On the stability of the inertial circulation in the 11/2-layer, quasi-geostrophic model

The effect of the time-dependent interface, separating an inertial quasi-geostrophic upper fluid layer from the quiescent abyss, on the non-linear stability of a steady circulation that takes place in this layer is explored. The analysis resorts to the method of Arnol'd's invariant resulting in a conditional stability criterion, which proves the stabilizing effect of the interface with respect to the single-layer case. The uniqueness of the stable basic flow field follows. Finally, non-linear and linear analyses are compared in the special case of a channeled flow with a fluctuating interface, the latter leading to an unconditional stability statement, whose meaning is clarified by resorting to the previously obtained nonlinear criterion. Received 8 June 2000 and Received in final form 18 September 2000     

Instabilities of an electron cloud in a Penning trap

We have measured the storage instabilities of electrons in a Penning trap at low magnetic fields. These measurements are carried out as a function of the trapping voltage, for different magnetic fields. It is seen that these instabilities occur at the same positions when the trapping voltage is expressed as a percentage of the maximum voltage, given by the stability limit. The characteristic frequencies at which these instabilities occur, obey a relation that is given by n _zω _z + n ₊ω ₊ + n _-ω _- = 0, where ω _z, ω ₊ and ω _- are the axial, perturbed cyclotron and the magnetron frequencies of the trapped electrons respectively, and the n's are integers. The reason for these instabilities are attributed to higher order static perturbations in the trapping potential. Received 5 August 2002 / Received in final form 14 October 2002 Published online 17 December 2002 RID="a" ID="a"Present address: Dept. of Physics, Rampurhat College, Rampurhat, Birbhum, West Bengal, India. RID="b" ID="b"e-mail: werth@mail.uni-mainz.de     

Electroweak interactions between intense neutrino beams and dense electron-positron magnetoplasmas

The electroweak coupling between intense neutrino beams and strongly degenerate relativistic dense electron-positron magnetoplasmas is considered. The intense neutrino bursts interact with the plasma due to the weak Fermi interaction force, and their dynamics is governed by a kinetic equation. Our objective here is to develop a kinetic equation for a degenerate neutrino gas and to use that equation to derive relativistic magnetohydrodynamic equations. The latter are useful for studying numerous collective processes when intense neutrino beams nonlinearly interact with degenerate, relativistic, dense electron-positron plasmas in strong magnetic fields. If the number densities of the plasma particles are of the order of 10³³ cm^-3, the pair plasma becomes ultra-relativistic, which strongly affects the potential energy of the weak Fermi interaction. The new system of equations allows several neutrino-driven streaming instabilities involving new types of relativistic Alfvén-like waves. The relevance of our investigation to the early universe and supernova explosions is discussed. Received 11 September 2002 Published online 4 February 2003 RID="a" ID="a"Permanent address: Department of Physics, Tbilisi State University, Chavchavadze 3, Tbilisi 38028, Georgia. RID="b" ID="b"Also at the Department of Plasma Physics, Ume? University, 90187 Ume?, Sweden; and the Center for Interdisciplinary Plasma Science, Max-Planck Institut für Plasmaphysik und extraterrestrische Physik, Postfach 1312, 85741 Garching, Germany. e-mail: ps@tp4.ruhr-uni-bochum.de RID="c" ID="c"Permanent address: Department of Plasma Physics, Ume?University, 90187 Ume?, Sweden.     

Valuation and dynamic replication of contingent claims in the framework of the beliefs-preferences gauge symmetry

Although symmetries play a major role in physics, their use in finance is relatively new and, to the best of our knowledge, can be traced to 1995 when Kholodnyi introduced the beliefs-preferences gauge symmetry. One of the main outcomes of the beliefs-preferences gauge symmetry is that it allows for the valuation and dynamic replication of contingent claims in a general market environment, that is, in the case of a general, not necessarily diffusion Markov process for the prices of underlying securities. This valuation and dynamic replication is based on the novel ideas of symmetry in contrast to the standard approach which uses stochastic analysis. The practical applications of the beliefs-preferences gauge symmetry range from the detection of a new type of true arbitrage to the beliefs-preferences-independent valuation and dynamic replication of contingent claims in a general market environment. Received 31 December 2001     

Quantum theory of van der Waals interactions between excited atoms and birefringent dielectric surfaces

A theory of van der Waals (vdW) interaction between an atom (in ground or excited state) and a birefringent dielectric surface with an arbitrary orientation of the principal optic axis (C-axis) is presented. Our theoretical approach is based on quantum-mechanical linear response theory, using generalized susceptibilities for both atom and electromagnetic field. Resonant atom-surface coupling is predicted for excited-state atoms interacting with a dispersive dielectric surface, when an atom de-excitation channel gets into resonance with a surface polariton mode. In the non-retarded regime, this resonant coupling can lead to enhanced attractive or repulsive vdW surface forces, as well as to a dissipative coupling increasing the excited-state relaxation. We show that the strongly non-scalar character of the interaction with the birefringent surface produces a C-axis-dependent symmetry-breaking of the atomic wavefunction. Changes of the C-axis orientation may also lead to a frequency shift of the surface polariton mode, allowing for tuning on or off the resonant coupling, resulting in a special type of engineering of surface forces. This is analysed here in the case of cesium 6D _3/2 level interacting with a sapphire interface, where it is shown that an adequate choice of the sapphire C-axis orientation allows one to transform vdW surface attraction into repulsion, and to interpret recent experimental observations based on selective reflection methods [H. Failache etal., Phys. Rev. Lett. 83, 5467 (1999)]. Received 24 January 2001     

Wilson's renormalization group applied to 2D lattice electrons in the presence of van Hove singularities

The weak coupling instabilities of a two dimensional Fermi system are investigated for the case of a square lattice using a Wilson renormalization group scheme to one loop order. We focus on a situation where the Fermi surface passes through two saddle points of the single particle dispersion. In the case of perfect nesting, the dominant instability is a spin density wave but d-wave superconductivity as well as charge or spin flux phases are also obtained in certain regions in the space of coupling parameters. The low energy regime in the vicinity of these instabilities can be studied analytically. Although saddle points play a major role (through their large contribution to the single particle density of states), the presence of low energy excitations along the Fermi surface rather than at isolated points is crucial and leads to an asymptotic decoupling of the various instabilities. This suggests a more mean-field like picture of these instabilities, than the one recently established by numerical studies using discretized Fermi surfaces. Received 11 April 2001 and Received in final form 6 September 2001     

CHAOTIC BEHAVIOR RESULTING IN TRANSIENT AND STEADY STATE INSTABILITIES OF PRESSURE-LOADED SHALLOW SPHERICAL SHELLS

In this paper, the axisymmetric dynamic behavior and snap-through buckling of thin elastic shallow spherical shells under harmonic excitation is investigated. Based on Marguerre kinematical assumptions, the governing partial differential equations of motion for a pre-loaded cap are presented in the form of a compatibility equation and a transverse motion equation. The continuous model is reduced to a finite degree of freedom system using the Galerkin method and a Fourier-Bessel approach. Results show that pre-loaded shells may exhibit co-existing stable equilibrium states and that with the application of sufficiently large dynamic loads the structure escapes from the well corresponding to pre-buckling configurations to another. This escape load may be much lower than the corresponding quasi-static buckling load. Indeed, complex resonances can occur until the system snaps-through, often signalling the loss of stability. As parameters are slowly varied, steady state instabilities may occur; these can include jumps to resonance, subharmonic period-doubling bifurcations, cascades to chaos, etc. Moreover a sudden pulse of excitation may lead to a transient failure of the system. In this paper, we examine how spherical caps under harmonic loading may be assessed in an engineering context, with a view to design against steady state instabilities as well as the various modes of transient failure. Steady state and transient stability boundaries are presented in which special attention is devoted to the determination of the critical load conditions. From this theoretical analysis, dynamic buckling criteria can be properly established which may constitute a consistent and rational basis for design of these shell structures under harmonic loading.     

Chaotic temperature dependence in a model of spin glasses

We address the problem of chaotic temperature dependence in disordered glassy systems at equilibrium by following states of a random-energy random-entropy model in temperature; of particular interest are the crossings of the free-energies of these states. We find that this model exhibits strong, weak or no temperature chaos depending on the value of an exponent. This allows us to write a general criterion for temperature chaos in disordered systems, predicting the presence of temperature chaos in the Sherrington-Kirkpatrick and Edwards-Anderson spin glass models, albeit when the number of spins is large enough. The absence of chaos for smaller systems may justify why it is difficult to observe chaos with current simulations. We also illustrate our findings by studying temperature chaos in the naıve mean field equations for the Edwards-Anderson spin glass. Received 27 March 2002 Published online 19 July 2002     

Optimizing phase imaging via dynamic force curves

Tapping mode (TM, also called intermittent contact mode) atomic force microscopy (AFM) has been routinely used in many laboratories. However, consistent or deliberate control of measuring conditions and interpretation of results are often difficult. In this article, we demonstrate how measurement parameters (drive frequency, cantilever stiffness and oscillation amplitude) affect the tapping tip's state. This has been done by systematic dynamic force measurements performed on mica and polystyrene surfaces together with computer simulations. Our study shows the following results. (1) Weaker cantilevers, smaller amplitude and higher drive frequency (around the resonance) lead to an extension of the attractive region (greater phase lag) in amplitude–phase–distance curves and thus can help to achieve stable high-setpoint TM imaging with minimal tip–sample pressure. (2) Bistability of tapping tips often exists and may cause height artefacts if the setpoint falls in the bistable region. (3) Tapping tips with high vibrating energy (stiff cantilevers and large amplitude) driven at resonance are only slightly perturbed by tip–sample interactions and usually remain monostable during the sweep of the scanner position. This can help to achieve good phase contrast without significant artefacts when the setpoint falls in a continuous negative–positive phase shift transition region. (4) Low energy cantilevers (compliant cantilevers and small amplitude) usually result in large phase shift and can be used to acquire large phase contrast images. However, height artefacts will occur when the setpoint falls in the bistable region usually existing for such cantilevers. (5) Computer simulations are useful in understanding the bistability in dynamic force curves and determining either material properties or the optimal imaging parameters.     

Dynamic light scattering and <Superscript>31</Superscript>P NMR spectroscopy study of the self-assembly of deoxyguanosine 5'-monophosphate

Self-assembling properties of deoxyguanosine 5'-monophosphate in isotropic solutions of concentrations from 0.5 wt% to 15 wt% were investigated by dynamic light scattering (DLS) and ³¹P NMR spectroscopy. A slow diffusive mode with a diffusion coefficient D _slow∼ 10^-12 m²/s was detected by DLS for the whole concentration range. This mode is assigned to the translational motion of large globular aggregates, similar to those observed in DNA and other polyelectrolyte solutions. The existence of such aggregates was confirmed by freeze fracture electron microscopy. Close to the isotropic-cholesteric phase transition, at 4 wt% c 10 wt%, also a faster diffusive mode is observed in the polarized DLS response and a very fast mode is detected by depolarized DLS. These modes are related to translational and rotational diffusion of the columnar stacks of guanosine molecules, which are favorably formed in the relatively narrow pretransitional region. The stacking was also revealed from the appearance of a secondary resonance line in the ³¹P NMR spectra. Using the hydrodynamic theory of Tirado and Garcia de la Torre, the length of the cylindrical stacks was found to be L = 364±78 ?, which is significantly larger than the values reported for other guanosine derivatives. Received 13 July 2001 and Received in final form 17 October 2001     

Cyclotron resonance of polarons in ternary mixed crystals

Rayleigh-Schr?dinger perturbation theory and an improved Wigner-Brillouin perturbation theory has been used to study the cyclotron resonance of the polarons in ternary mixed crystals in the zero-temperature limit. The interaction between an electron and two branches of longitudinal optical phonon modes is taken into account in the framework of the random-element-isodisplacement model. The numerical results for several ternary mixed crystals show that the polaronic cyclotron energy and mass split successively twice related to the higher and lower branches of longitudinal optical phonon modes of ternary mixed crystals. A non-linear dependence of the polaronic cyclotron energy and mass on the composition x is found. Received 19 March 2002 / Received in final form 21 March 2003 Published online 20 June 2003 RID="a" ID="a"e-mail: xxliang@imu.edu.cn