Weakly nonlinear effects associated with transverse oscillations in dusty plasma crystals

We study the amplitude modulation of transverse dust lattice waves (TDLW) propagating in a single- and double-layer dusty plasma (DP) crystal. It is shown that a modulational instability mechanism, which is related to an intrinsic nonlinearity of the sheath electric field, may occur under certain conditions. Possibility of the formation of localized excitations (envelope solitons) in the dusty plasma crystal is discussed.

Discrete breather modes associated with vertical dust grain oscillations in dusty plasma crystals

Accounting for the lattice discreteness and the sheath electric field nonlinearity in dusty plasma crystals, it is demonstrated that highly localized structures (discrete breathers) involving vertical (transverse, off-plane) oscillations of charged dust grains may exist in a dust lattice. These structures correspond to either extremely localized bright breather excitations (pulses) or dark excitations composed of dips/voids. Explicit criteria for selecting different breather modes are presented. (C) 2005 American Institute of Physics.

Dust lattice wave dispersion relations in two-dimensional hexagonal crystals including the effect of dust charge polarization

A dusty plasma crystalline configuration with equal charge dust grains and mass is considered. Both charge and mass of each dust species are taken to be constant. Two differential equations for a two-dimensional hexagonal crystal on the basis of a Yukawa-type potential energy and a

Nonlinearly modulated dust lattice wave packets in two-dimensional hexagonal dust crystals

The amplitude modulation of dust lattice waves (DLWs) propagating in a two-dimensional hexagonal dust crystal is investigated in a continuum approximation, accounting for the effect of dust charge polarization (dressed interactions). A dusty plasma crystalline configuration with constant dust grain charge and mass is considered. The dispersion relation and the group velocity for DLWs are determined for wave propagation in both longitudinal and transverse directions. The reductive perturbation method is used to derive a (2+1)-dimensional nonlinear Schrodinger equation (NLSE). New expressions for the coefficients of the NLSE are derived and compared, for a Yukawa-type potential energy and for a

Modulated transverse off-plane dust-lattice wave packets in hexagonal two-dimensional dusty plasma crystals

The propagation of nonlinear dust-lattice waves in a two-dimensional hexagonal crystal is investigated. Transverse (off-plane) dust grain oscillatory motion is considered in the form of a backward propagating wave packet whose linear and nonlinear characteristics are investigated. An evolution equation is obtained for the slowly varying amplitude of the first (fundamental) harmonic by making use of a two-dimensional lattice multiple scales technique. An analysis based on the continuum approximation (spatially extended excitations compared to the lattice spacing) shows that wave packets will be modulationally stable and that dark-type envelope solitons (density holes) may occur in the long wavelength region. Evidence is provided of modulational instability and of the occurrence of bright-type envelopes (pulses) at shorter wavelengths. The role of second neighbor interactions is also investigated and is shown to be rather weak in determining the modulational stability region. The effect of dissipation, assumed negligible in the algebra throughout the article, is briefly discussed.

Phonons, Instabilities and Origin of Polarization in KDP Crystals

The -phonons of KH2PO4 (KDP) and its deuterated analog DKDP are studied via first-principles linear response calculations. The paraelectric phase shows two instabilities. One for a z-polarized mode, which leads to the spontaneous polarization Ps of the ferroelectric phase. The other corresponds to a two-fold degenerate xy-polarized mode. Other phonons are analyzed, which couple to the ferroelectric one at large amplitudes and are relevant for the ferroelectric transition. We show that Ps is mainly of electronic nature, since it arises mostly from an off-diagonal component of the Born effective charge tensor of H, with minor contribution from P atoms displacements.

Quantum ground state of self-organized atomic crystals in optical resonators

Cold atoms, driven by a laser and simultaneously coupled to the quantum field of an optical resonator, may self-organize in periodic structures. These structures are supported by the optical lattice, which emerges from the laser light they scatter into the cavity mode and form when the laser intensity exceeds a threshold value. We study theoretically the quantum ground state of these structures above the pump threshold of self-organization by mapping the atomic dynamics of the self-organized crystal to a Bose-Hubbard model. We find that the quantum ground state of the self-organized structure can be the one of a Mott insulator, depending on the pump strength of the driving laser. For very large pump strengths, where the intracavity-field intensity is maximum and one would expect a Mott-insulator state, we find intervals of parameters where the phase is compressible. These states could be realized in existing experimental setups.

Structural phase transitions in low-dimensional ion crystals

A chain of singly charged particles, confined by a harmonic potential, exhibits a sudden transition to a zigzag configuration when the radial potential reaches a critical value, depending on the particle number. This structural change is a phase transition of second order, whose order parameter is the crystal displacement from the chain axis. We study analytically the transition using Landau theory and find full agreement with numerical predictions by Schiffer [Phys. Rev. Lett. 70, 818 (1993)] and Piacente [Phys. Rev. B 69, 045324 (2004)]. Our theory allows us to determine analytically the system's behavior at the transition point.

Verification of McCabe's Delta L Law for Growth of Lysozyme Crystals by Hanging Drop Method

Lysozyme is a naturally occurring enzyme in egg white and has high commercial importance due to its antimicrobial properties. The main objective of this work was to study the growth rate of lysozyme crystals isolated from egg for the first 72 hours and verify the results with McCabe’s constant crystal growth theory. Hanging drop crystallization method was used to form high purity lysozyme crystals from the embryonic stage. To this end, this work differs from an earlier work of Forsythe et al., who used seed crystals in the size range of 10 µm - 40 µm for face growth measurements at different pH values. The maximum crystal size recorded in the present work was 392.86 µm, which is within the typical size range of 50 µm - 500 µm for which constant crystal growth is expected to hold according to McCabe’s ?L law. Electron micrographs (SEM) revealed the structure and dimensions of the crystals while SDS-Page was used to measure the purity of the crystals. The SEM results showed that that lysozyme growth rate was linear and agreed with McCabe’s constant growth theory, producing a growth rate of 1.77 x 10-3 µm .s-1

Method for the in situ preparation of a single layer of zeolite Beta crystals on a molybdenum substrate for microreactor applications

A method for the hydrothermal synthesis of a single layer of zeolite Beta crystals on a molybdenum substrate for microreactor applications has been developed. Before the hydrothermal synthesis, the surface of the substrate was modified by an etching procedure that increases the roughness at the nanoscale level without completely eliminating the surface lay structure. Then, thin films of Al2O3 (170 nm) and TiO2 (50 nm) were successively deposited by atomic layer deposition (ALD) on the substrate. The internal Al2O3 film protects the Mo substrate from oxidation up to 550 degrees C in an oxidative environment. The high wettability of the external TiO2 film after UV irradiation increases zeolite nucleation on its surface. The role of the metal precursor (TiCl4 vs TiI4), deposition temperature (300 vs 500 degrees C), and film thickness (50 vs 100 nm) was investigated to obtain titania films with the slowest decay in the superhydrophilic behavior after UV irradiation. Zeolite Beta coatings with a Si/Al ratio of 23 were grown at 140 degrees C for 48 It. After ion exchange with a 10(-4) M cobalt acetate solution, the activity of the coatings was determined in the ammoxidation of ethylene to acetonitrile in a microstructured reactor. A maximum reaction rate of 220 mu mol C2H3N g(-1) s(-1) was obtained at 500 degrees C, with 42% carbon selectivity to acetonitrile. (C) 2007 Elsevier Inc. All rights reserved.