Terahertz wave characteristics of a single-walled carbon nanotube containing a fluid flow using the nonlocal Timoshenko beam model

This paper presents the effect of nonlocal scaling parameter on the terahertz wave propagation in fluid filled single walled carbon nanotubes (SWCNTs). The SWCNT is modeled as a Timoshenko beam,including rotary inertia and transverse shear deformation by considering the nonlocal scale effects. A uniform fluid velocity of 1000 m/s is assumed. The analysis shows that, for a fluid filled SWCNT, the wavenumbers of flexural and shear waves will increase and the corresponding wave speeds will decrease as compared to an empty SWCNT. The nonlocal scale parameter introduces certain band gap region in both flexural and shear wave mode where no wave propagation occurs. This is manifested in the wavenumber plots as the region where the wavenumber tends to infinite (or wave speed tends to zero). The frequency at which this phenomenon occurs is called the ``escape frequency''. The effect of fluid density on the terahertz wave propagation in SWCNT is also studied and the analysis shows that as the fluid becomes denser, the wave speeds will decrease. The escape frequency decreases with increase in nonlocal scaling parameter, for both wave modes. We also show that the effect of fluid density and velocity are negligible on the escape frequencies of flexural and shear wave modes. (C) 2010 Elsevier B.V. All rights reserved.

Slow m=1 instabilities of softened gravity Keplerian discs

We present the simplest model that permits a largely analytical exploration of the m =1 counter-rotating instability in a `hot' nearly Keplerian disc of collisionless self-gravitating matter. The model consists of a two-component softened gravity disc, whose linear modes are analysed using the Wentzel-Kramers-Brillouin approximation. The modes are slow in the sense that their (complex) frequency is smaller than the Keplerian orbital frequency by a factor which is of order the ratio of the disc mass to the mass of the central object. Very simple analytical expressions are derived for the precession frequencies and growth rates of local modes; it is shown that a nearly Keplerian discm must be unrealistically hot to avoid an overstability. Global modes are constructed for the case of zero net rotation.

Localised modes due to impurities in III–V semiconductors

Local mode frequencies due to substitutional impurities in some III–V semiconductors are calculated using Green functions on the mass defect approximation and compared with experimental results.

Instability of Coupled Longitudinal and Transverse Electromagnetic Modes of Wave‐Propagation in Bounded Streaming Plasmas

The instability of coupled longitudinal and transverse electromagnetic modes associated with long wavelengths is studied in bounded streaming plasmas. The main conclusions are as follows: (i) For long waves for which O (k 2)=0, in the absence of relative streaming motion of electrons and ions and aωp/c<0.66, the whole spectrum of harmonic waves is excited due to finite temperature and boundary effects consisting of two subseries. One of these subseries can be identified with Tonks-Dattner resonance oscillations for the electrons, and arises primarily due to the electrons with frequencies greater than the electrostatic plasma frequency corresponding to the electron density in the midplane in the undisturbed state. The other series arises primarily due to ion motion. When aωp/c>0.66, in addition to the above spectrum of harmonic waves, the system admits an infinite number of growing and decaying waves. The instability associated with these modes is found to arise due to the interaction of the waves inside the plasma with the external electromagnetic field. (ii) For modes with comparatively shorter wavelengths for which O (k3)=0, the coupling due to finite temperature sets in, and it is found that the two series of harmonic waves obtained in (i) deriving energy from the transverse modes also become unstable. Thus, for these wavelengths the system admits three sets of growing and decaying modes, first two for all values of aωp/c and the third for (aωp/c) > 0.66. (iii) The presence of streaming velocities introduces various other coupling mechanisms, and we find that even for the wavelengths for which O (k2)=0, we get three sets of growing and decaying waves. The numerical values for the growth rates show that the streaming velocities enhance the growth rates of instability significantly.

The vibration spectrum of rutile

The long-wave lattice dynamics of rutile has been studied using a rigid ion model. The vibration frequencies for the zero wavevector have been calculated using the expressions for the frequencies of the normal modes derived group theoretically. The observed Raman and infrared frequencies have been explained.

Localized modes due to impurities in caesium iodide

The nature of the localized modes due to single substitutional impurities in a caesium iodide lattice is investigated using the models of Elliott, Dawber and Maradudin. The infra-red absorption due to U centres and their relation to the lattice spacing is also discussed.

Molecular model for localised modes in zincblende structures

A molecular model for substitutional defects in a zincblende lattice has been worked out. The infrared absorption due to A1 in InSb and Li in GaAs are interpreted on the basis of this model.

Natural frequencies and modes of tapered skew plates

The vibration of simply supported skew plates having a linear variation in thickness in one direction is considered. Approximate analysis is made by using Lagrange's equations employing the double Fourier sine series in oblique co-ordinates to represent the deflected surface. Natural frequencies are obtained for rhombic plates for several ranges of thickness variation and skew angle. The nodal patterns plotted for a few typical configurations show interesting metamorphoses with variation in thickness and skew angle.

Rough Justice or Zero Tolerance? - Reassessing the Nature of Copyright in Light of Collective Licensing (Part I)

Starting point in the European individualistic copyright ideology is that an individual author creates a work and controls the use of it. However, this paper argues that it is (and has always been) impossible to control the use of works after their publication. This has also been acknowledged by the legislator, who has introduced collective licensing agreements because of this impossibility. Since it is impossible to rigorously control the use of works this writing "Rough Justice or Zero Tolerance - Reassessing the Nature of Copyright in Light of Collective Licensing" examines what reality of copyright is actually about. Finding alternative (and hopefully more "true") ways to understand copyright helps us to create alternative solutions in order to solve possible problems we have as it comes e.g. to use of content in online environment. The paper makes a claim that copyright is actually about defining negotiation points for different stakeholders and that nothing in the copyright reality prevents us from defining e.g. a new negotiation point where representatives of consumers would meet representatives of right holders in order to agree on the terms of use for certain content types in online environment.

Two-Phase Thermodynamic Model for Efficient and Accurate Absolute Entropy of Water from Molecular Dynamics Simulations

Presented here is the two-phase thermodynamic (2PT) model for the calculation of energy and entropy of molecular fluids from the trajectory of molecular dynamics (MD) simulations. In this method, the density of state (DoS) functions (including the normal modes of translation, rotation, and intramolecular vibration motions) are determined from the Fourier transform of the corresponding velocity autocorrelation functions. A fluidicity parameter (f), extracted from the thermodynamic state of the system derived from the same MD, is used to partition the translation and rotation modes into a diffusive, gas-like component (with 3Nf degrees of freedom) and a nondiffusive, solid-like component. The thermodynamic properties, including the absolute value of entropy, are then obtained by applying quantum statistics to the solid component and applying hard sphere/rigid rotor thermodynamics to the gas component. The 2PT method produces exact thermodynamic properties of the system in two limiting states: the nondiffusive solid state (where the fluidicity is zero) and the ideal gas state (where the fluidicity becomes unity). We examine the 2PT entropy for various water models (F3C, SPC, SPC/E, TIP3P, and TIP4P-Ew) at ambient conditions and find good agreement with literature results obtained based on other simulation techniques. We also validate the entropy of water in the liquid and vapor phases along the vapor-liquid equilibrium curve from the triple point to the critical point. We show that this method produces converged liquid phase entropy in tens of picoseconds, making it an efficient means for extracting thermodynamic properties from MD simulations.

Natural modes of a coupled non-linear system

The natural modes of a non-linear system with two degrees of freedom are investigated. The system, which may contain either hard or soft springs, is shown to possess three modes of vibration one of which does not have any counterpart in the linear theory. The stability analysis indicates the existence of seven different modal stability patterns depending on the values of two parameters of non-linearity.

Exact energy eigenvalues for an attractive Coulomb potential with zero-radius hard core

Following a peratization procedure, the exact energy eigenvalues for an attractive Coulomb potential, with a zero-radius hard core, are obtained as roots of a certain combination of di-gamma functions. The physical significance of this entirely new energy spectrum is discussed.

Anomalous behavior of hydrodynamic modes in the two dimensional shear flow of a granular material

The growth rates of the hydrodynamic modes in the homogeneous sheared state of a granular material are determined by solving the Boltzmann equation. The steady velocity distribution is considered to be the product of the Maxwell Boltzmann distribution and a Hermite polynomial expansion in the velocity components; this form is inserted into them Boltzmann equation and solved to obtain the coeificients of the terms in the expansion. The solution is obtained using an expansion in the parameter epsilon =(1 - e)(1/2), and terms correct to epsilon(4) are retained to obtain an approximate solution; the error due to the neglect of higher terms is estimated at about 5% for e = 0.7. A small perturbation is placed on the distribution function in the form of a Hermite polynomial expansion for the velocity variations and a Fourier expansion in the spatial coordinates: this is inserted into the Boltzmann equation and the growth rate of the Fourier modes is determined. It is found that in the hydrodynamic limit, the growth rates of the hydrodynamic modes in the flow direction have unusual characteristics. The growth rate of the momentum diffusion mode is positive, indicating that density variations are unstable in the limit k--> 0, and the growth rate increases proportional to kslash} k kslash}(2/3) in the limit k --> 0 (in contrast to the k(2) increase in elastic systems), where k is the wave vector in the flow direction. The real and imaginary parts of the growth rate corresponding to the propagating also increase proportional to kslash k kslash(2/3) (in contrast to the k(2) and k increase in elastic systems). The energy mode is damped due to inelastic collisions between particles. The scaling of the growth rates of the hydrodynamic modes with the wave vector I in the gradient direction is similar to that in elastic systems. (C) 2000 Elsevier Science B.V. All rights reserved.