A dynamical mechanism for quark mixing and neutrino oscillations

We show that, if one assumes fermion generations to be given by a gauge symmetry, together with a certain Higgs mechanism for breaking it, then the known empirical features of quark and lepton mixing can be largely explained, including, in particular, the fact that the mixing (CKM) matrix element , responsible for the muon anomaly in atmospheric neutrinos, is near maximal, and much larger than its quark counterparts and , while the corner elements for both quarks () and leptons () are all very small. The mechanism also automatically gives a hierarchical fermion-mass spectrum which is intimately related to the mixing pattern. Received: 8 February 1999 / Published online: 15 July 1999     

Periodic oscillations of the relativistic pendulum with friction

It is proved that the forced pendulum equation with friction and a singular ?-Laplacian operator of relativistic type has periodic solutions, in contrast to what happen in the Newtonian case.     

Plasma oscillations of edge Dirac fermions

The dispersion law of one-dimensional plasmons in a quasi-one-dimensional system of massless Dirac fermions has been calculated. Two model two-dimensional systems where bands of edge states filled with such Dirac fermions appear at the edge have been considered. Edge states in the first system, topological insulator, are due to topological reasons. Edge states in the second system, system of massive Dirac fermions, have Tamm origin. It has been shown that the dispersion laws of plasmons in both systems in the long-wavelength limit differ only in the definition of the parameters (velocity and localization depth of Dirac fermions). The frequency of plasmons is formally quantum (ω ∝ ? ^?1/2) and, in the case of the Coulomb interaction between electrons, depends slightly on the Fermi level E _F. The dependence on E _F is stronger in the case of short-range interaction. The quantum features of oscillations of massless one-dimensional Dirac fermions are removed by introducing the mass of Dirac fermions at the Fermi level and their density. Correspondence to the dispersion law of classical one-dimensional plasma oscillations in a narrow stripe of “Schrödinger” electrons has been revealed.     

Plasma oscillations in a two-dimensional semimetal

Collective oscillations of an electron-hole plasma in a two-dimensional semimetal have been investigated. It has been shown that two undamped branches of plasma oscillations exist under certain conditions on the parameters of the structure. Acoustic plasmons are not damped in a finite wavenumber range. When the Fermi velocities of the electrons and holes are equal to each other, this range expands to the range of the applicability of the theory (the momentum of the plasmon is much lower than the Fermi momenta of the particles).     

Dry friction in the Frenkel-Kontorova-Tomlinson model: dynamical properties

Wearless friction is investigated in a simple mechanical model called Frenkel-Kontorova-Tomlinson model. We have introduced this model in [Phys. Rev. B, 53, 7539 (1996)] where the static friction has already been considered. Here the model is treated for constant sliding speed. The motion of the internal degrees of freedom is regular for small sliding velocities or weak interaction between the sliding surfaces. The regular motion for large velocities is strongly determined by normal and superharmonic resonance of phonons excited by the so-called “washboard wave”. The kinetic friction has maxima near these resonances. For increasing interaction strength the regular motion becomes unstable due to parametric resonance leading to quasistatic and chaotic motion. For sliding velocities beyond first-order parametric resonance bistability occurs between the strongly chaotic motion (fluid sliding state), where friction is large and a regular motion (solid sliding state), where friction is weak. The fluid sliding state is mainly determined by the density of decay channels of m washboard waves into n phonons. This density describes qualitatively the effectiveness of the energy transfer from the uniform sliding motion into the microscopic, irregular motion of the degrees of freedom at the sliding interface. For a narrow interval of the sliding velocities we also found enhanced friction due to coherent motion. In the regime of coherent motion nondestructive interactions of dark envelope solitons occur.     

The internal friction of torsional oscillations in ferromagnetic materials

The paper is a continuation of the first part [1] and deals with the internal friction of torsional oscillations of ferromagnetic materials in a static and an alternating magnetic field. The calculation differs considerably from the case of longitudinal oscillations, particularly in the following points. In the first place, the internal friction of torsional oscillations depends quite differently on the dimensions of the sample, and the continuous distribution of magnetic domains and Bloch walls cannot be so easily defined. Secondly, a magnetic field created as a result of eddy currents during torsional oscillations does not penetrate the surroundings, so that the internal friction in an electrically conducting medium is the same as in vacuum. Thirdly, the deformation here is an antisymmetrical function of the field, so that the coefficient is an even function while with longitudinal oscillations it was expressed by an odd function. Despite these different conditions the results are very similar to those with longitudinal oscillations and agree well with experiment. In an alternating magnetic field the internal friction of torsional oscillations has a sharp maximum atH=0.64H _S whereH _S is the saturated value of the field for which magnetoelastic effects disappear.

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The internal friction of longitudinal oscillations in ferromagnetic materials

The paper deals with the theory of the new magnetomechanical phenomenon in an alternating field [6, 7]. The first part concerns the internal friction of longitudinal oscillations of a ferromagnetic material in the shape of a wire in a constant magnetic field. It is assumed that the medium in which the sample oscillates is conducting and has a certain permeability. Equations defining the magnetic field in the oscillating material are derived from the basic thermodynamic relations. The term describing the non-conservative force component in a complex formulation is used to determine the internal friction. A general relation between the internal friction and the magnetic field is derived, as well as other expressions, which are a simplification of it. The second part of the paper deals with internal friction in an alternating field. It is shown that the solution can be transformed to the sum of the internal frictions of the different harmonic oscillations, which are obtained as a partial solution of the problem on the assumption that the elastic oscillations in interaction with the field oscillations are separated into their harmonic components. The calculation then becomes that of the internal friction considered in the first part of the paper. In this case the internal friction significantly depends on the field amplitude. The functional dependence of the internal friction peak on the frequency of the mechanical oscillations is also calculated. The agreement of the theory with experiment is satisfactory.

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Plasma oscillations in oxide free Al clusters

Plasma oscillations in oxide free Al clusters with radii of the order 10 Å are excited by 50 keV electrons. Only surface plasma oscillations are observed. Results are in excellent agreement with the hydrodynamic theory put forward by Fujimoto and Komaki. This theory is for the first time quantitatively confirmed.     

Plasma oscillations in a one-dimensional many-fermion system

Following the Shevchik technique, a model Hamiltonian of collective oscillations (plasmons) in a one-dimensional system of complete degenerate fermions is obtained in terms of the Tomonaga boson operators. This Hamiltonian is diagonalized by means of the Mattis and Lieb canonical transformation and the plasma frequency is derived. The equation-of-motion method is applied in the RPA in order to include the coupling between the collective and individual degrees of freedom. The generalization to finite temperatures is performed and connection with the Tomonaga model is discussed.     

Plasma oscillations and expansion of an ultracold neutral plasma

Parallel molecular dynamics simulations are performed to determine atomic-level stresses in Si(111)/Si(3)N4(0001) and Si(111)/a-Si3N4 nanopixels. Compared to the crystalline case, the stresses in amorphous Si3N4 are highly inhomogeneous in the plane of the interface. In silicon below the interface, for a 25 nm square mesa stress domains with triangular symmetry are observed, whereas for a rectangular, 54 nmx33 nm, mesa tensile stress domains ( approximately 300 A) are separated by Y-shaped compressive domain wall. Maximum stresses in the domains and domain walls are -2 GPa and +2 GPa, respectively.     

Plasma oscillations in spheres and the magnetoresistance of potassium

We have observed in potassium the spectrum of the longitudinal helicon oscillations. We have used these oscillations to measure the magnetoresistance and Hall coefficient. In addition, a low frequency method for the measurement of magnetoresistance in metals is demonstrated with experiments on single crystal potassium spheres. The magnetoresistance saturates, but its magnitude depends upon sample history.     

Swirling spray flames dynamical blow out induced by transverse acoustic oscillations

Recent experiments on a laboratory scale annular system comprising multiple injectors (namely, MICCA-Spray), indicate that combustion instabilities coupled with azimuthal modes may induce large amplitude oscillations, which under certain conditions, lead to blow out of some of the flames established in the system, a phenomenon designated as dynamical blow out (DBO). An attempt is made in the present investigation to reproduce this phenomenon in a linear array of injectors (namely, TACC-Spray), where the acoustic field is externally applied to flames established by injector units that are identical to those used in the annular combustor. The acoustic field is generated by driver units placed on the lateral sides of a rectangular cavity. The pressure level induced in TACC-Spray can reach a peak value of 1700 Pa in a frequency range extending from 680 to 780 Hz, which corresponds to the typical frequency of azimuthal instabilities observed in the annular system. A theoretical model based on dimensional analysis serves to guide the choice of operating conditions that may lead to the DBO phenomenon. Experiments carried out in TACC-Spray and MICCA-Spray are then used to determine the DBO boundary, define the conditions that need to be fulfilled to observe this phenomenon, and gather high-speed visualizations providing some insights on the mechanisms that induce blow out.     

Plasma oscillations in fullerene molecules during electron capture

The anomalously wide energy range for the formation of long-lived negative molecular ions during electron capture by fullerene molecules is explained by the excitation of collective electron (plasma) oscillations in these molecules. A model for such excitations for fullerenes C₆₀ and C₇₀ is proposed on the basis of the Thomas-Fermi model. This model provides good correlation between the experimental curves of resonant electron capture and the theoretical energy dependences of the density of plasma oscillation modes.     

Plasma oscillations in nanotubes and the Aharonov-Bohm effect for plasmons

We theoretically analyze the collective oscillations of 2D electrons in nanotubes. In the presence of a magnetic field parallel to the tube axis, the plasmon frequencies undergo Aharonov-Bohm oscillations. The effect can manifest itself in infrared absorption and in Raman scattering. We calculate the cross sections for inelastic light scattering by plasmons.     

Surface friction constant and range of dynamical interaction between adatoms on metal surfaces

The electronic contribution to the surface friction constant of an adatom on a metal surface is calculated using: (i) the Dirac density matrix for an infinite barrier model of an inhomogeneous electron gas, and (ii) two simple models of screened potentials at the surface based on reliable asymptotes in and outside the surface respectively. Though the results are clearly approximate, attention is drawn especially to the predictions of the models concerning long-range dynamic interactions between adatoms on metal surfaces.     

Nonlinear dynamical modelling of chaotic electrostatic ion cyclotron oscillations by jerk equations

Plasma being a nonlinear and complex system, is capable of sustaining a wide spectrum of waves, oscillations and instabilities. These fluctuations interact nonlinearly amongst themselves and also with particles: electrons/ions and thus lead to nonlinear wave-wave or wave-particle interaction. In the presence of coherent waves the particles are accelerated whereas irregular oscillations can give rise to particle heating which is also called stochastic heating. Particle orbits are known to be randomized by the wave fields such that their motion can also become stochastic. For fusion to be sustained one needs a very high temperature plasma for an extended duration. It quite common to deploy external waves like electron cyclotron waves or ion cyclotron waves for plasma heating and current drive. These external waves also work only in certain regimes. Conventional plasma techniques have been able to answer several of the observations of the above processes related to heating transport etc, but nonlinear dynamics as a tool has helped in comprehending the plasma oscillations better. We have for the first time obtained a Third Order nonlinear ordinary differential equation (TONLODE) also known as jerk equation to describe the electrostatic ion cyclotron plasma oscillations in a magnetic field. The interesting feature of this equation is that it does not require an external forcing term to obtain chaotic behaviour.     

Book review: Nonlinear oscillations,dynamical systems,and bifurcations of vector fields

Journal of Statistical Physics -