The renormalization group and the implicit function theorem for amplitude equations

This article lays down the foundations of the renormalization group (RG) approach for differential equations characterized by multiple scales. The renormalization of constants through an elimination process and the subsequent derivation of the amplitude equation [Chen, Phys. Rev. E 54, 376 (1996)] are given a rigorous but not abstract mathematical form whose justification is based on the implicit function theorem. Developing the theoretical framework that underlies the RG approach leads to a systematization of the renormalization process and to the derivation of explicit closed-form expressions for the amplitude equations that can be carried out with symbolic computation for both linear and nonlinear scalar differential equations and first order systems but independently of their particular forms. Certain nonlinear singular perturbation problems are considered that illustrate the formalism and recover well-known results from the literature as special cases. © 2008 American Institute of Physics.

Extending FORK-256 attack to the full hash function

In a paper published in FSE 2007, a way of obtaining near-collisions and in theory also collisions for the FORK-256 hash function was presented [8]. The paper contained examples of near-collisions for the compression function, but in practice the attack could not be extended to the full function due to large memory requirements and computation time. In this paper we improve the attack and show that it is possible to find near-collisions in practice for any given value of IV. In particular, this means that the full hash function with the prespecified IV is vulnerable in practice, not just in theory. We exhibit an example near-collision for the complete hash function.

Executive function and postural instability in people with Parkinson’s disease

The specific aspects of cognition contributing to balance and gait have not been clarified in people with Parkinson’s disease (PD). Twenty PD participants and twenty age- and gender-matched healthy controls were assessed on cognition and clinical mobility tests. General cognition was assessed with the Mini Mental State Exam and the Addenbrooke’s Cognitive Exam. Executive function was evaluated using the Trail Making Tests (TMT-A and TMT-B) and a computerized cognitive battery which included a series of choice reaction time (CRT) tests. Clinical gait and balance measures included the Tinetti, Timed Up & Go, Berg Balance and Functional Reach tests. PD participants performed significantly worse than the controls on the tests of cognitive and executive function, balance and gait. PD participants took longer on Trail Making Tests, CRT-Location and CRT-Colour (inhibition response). Furthermore, executive function, particularly longer times on CRT-Distracter and greater errors on the TMT-B were associated with worse balance and gait performance in the PD group. Measures of general cognition were not associated with balance and gait measures in either group. For PD participants, attention and executive function were impaired. Components of executive function, particularly those involving inhibition response and distracters, were associated with poorer balance and gait performance in PD.

Pulsed dc- and sine-wave-excited cold atmospheric plasma plumes: A comparative analysis

Cold atmospheric-pressure plasma plumes are generated in the ambient air by a single-electrode plasma jet device powered by pulsed dc and ac sine-wave excitation sources. Comprehensive comparisons of the plasma characteristics, including electrical properties, optical emission spectra, gas temperatures, plasma dynamics, and bacterial inactivation ability of the two plasmas are carried out. It is shown that the dc pulse excited plasma features a much larger discharge current and stronger optical emission than the sine-wave excited plasma. The gas temperature in the former discharge remains very close to the room temperature across the entire plume length; the sine-wave driven discharge also shows a uniform temperature profile, which is 20-30 degrees higher than the room temperature. The dc pulse excited plasma also shows a better performance in the inactivation of gram-positive staphylococcus aureus bacteria. These results suggest that the pulsed dc electric field is more effective for the generation of nonequilibrium atmospheric pressure plasma plumes for advanced plasma health care applications.

A model of a large-area planar plasma producer based on surface wave propagation in a plasma-metal structure with a dielectric sheath

A theoretical model of a large-area planar plasma producer based on surface wave (SW) propagation in a plasma-metal structure with a dielectric sheath is presented. The SW which produces and sustains the microwave gas discharge in the planar structure propagates along an external magnetic field and possesses an eigenfrequency within the range between electron cyclotron and electron plasma frequencies. The spatial distributions of the produced plasma density, electromagnetic fields, energy flow density, phase velocity and reverse skin depth of the SW are obtained analytically and numerically.

The effect of near-sheath dusts on a surface-wave-sustained gas discharge

The effect of near-sheath dusts on the rf power loss in a surface-wave-sustained gas discharge is studied. The planar plasma is bounded by a dielectric and consists of an inhomogeneous near-wall transition layer (sheath), a dusty plasma layer and an outer dust-free plasma. The discharge is maintained by high-frequency axially symmetrical surface waves. The surface-wave power loss from the most relevant dissipative mechanisms in typical discharge plasmas is analysed.

Nonresonant power transfer in plasma-surface interactions via two-surface wave decay

The excitation of pairs of electron surface waves via nonresonant decay of plasma waves incident onto a solid surface is studied in the context of controlling the interaction of pulsed electromagnetic radiation with plasma-exposed solid surfaces. The role of the plasma-exposed surfaces in nonlinear heating of the plasma edge and related power transfer is discussed. It is shown that the maximum efficiency of the power transfer at solid surfaces with dielectric permittivity εd <3 corresponds to the resonant two-surface wave decay. On the other hand, for solids with εd >3 the maximum power transfer efficiency is achieved through nonresonant excitation of the quasistatic surface waves. In this case the plasma waves generated by external radiation dissipate their energy into the plasma periphery most effectively.

Parameters and equilibrium profiles for large-area surface-wave sustained plasmas

The equilibrium profiles of the plasma parameters of large-area if discharges in a finite-length metal-shielded dielectric cylinder are computed using a two-dimensional fluid code. The rf power is coupled to the plasma through edge-localized surface waves traveling in the azimuthal direction along the plasma edge. It is shown that self-consistent accounting for axial plasma diffusion and radial nonuniformity of the electron temperature can explain the frequently reported deviations of experimentally measured radial density profiles from that of the conventional linear diffusion models. The simulation results are in a good agreement with existing experimental data obtained from surface-wave sustained large-diameter plasmas. © 2002 The American Physical Society.

Two-surface wave decay : controlling power transfer in plasma-surface interactions

Controlled interaction of high-power pulsed electromagnetic radiation with plasma-exposed solid surfaces is a major challenge in applications spanning from electron beam accelerators in microwave electronics to pulsed laser ablation-assisted synthesis of nanomaterials. It is shown that the efficiency of such interaction can be potentially improved via an additional channel of wave power dissipation due to nonlinear excitation of two counterpropagating surface waves, resonant excitations of the plasma-solid system.Physics.

Electron energy distribution function in low-pressure complex plasmas

The effect of density and size of dust grains on the electron energy distribution function (EEDF) in low-temperature complex plasmas is studied. It is found that the EEDF depends strongly on the dust density and size. The behavior of the electron temperature can differ significantly from that of a pristine plasma. For low-pressure argon glow discharge, the Druyvesteyn-like EEDF often found in pristine plasmas can become nearly Maxwellian if the dust density and/or sizes are large. One can thus control the plasma parameters by the dust grains.

Charging and trapping of macroparticles in near-electrode regions of fluorocarbon plasmas with negative ions

Charging and trapping of macroparticles in the near-electrode region of fluorocarbon etching plasmas with negative ions is considered. The equilibrium charge and forces on particles are computed as a function of the local position in the plasma presheath and sheath. The ionic composition of the plasma corresponds to the etching experiments in 2.45 GHz surface-wave sustained and 13.56 MHz inductively coupled C4F8+Ar plasmas. It is shown that despite negligible negative ion currents collected by the particles, the negative fluorine ions affect the charging and trapping of particulates through modification of the sheath/presheath structure.

Resonant generation of the second harmonic of a surface wave on a plasma-metal boundary

The process of resonant generation of the second harmonic of the surface wave, propagating along the external magnetic field at the plasma-metal boundary is considered. The periodic process of the energy exchange between the first and the second harmonics of the wave is investigated as well. It is shown that the process under study is periodic one. The analytical expressions are obtained and numerical estimations are presented for characteristic time of nonlinear energy exchange. The self-action effect of main frequency wave is account for harmonics interaction. It is shown that the effect leads to nonlinear phenomena attenuation, which expresses in narrowing possible value interval of harmonics amplitudes during energy exchange process and in increasing the nonlinear interaction time.

Third harmonic generation of the surface wave in the semiconductor-metal slowing-down structure

A nonlinear process is considered of the surface wave third harmonics generation in a slowing-down semiconductor-metal structure. The process is conditioned by non-parabolicity of the charge carrier dispersion law. It is shown that in narrow-gap semiconducting materials it is necessary to account for the process together with the surface wave second harmonics generation conditioned by nonlinearity of quasi-hydrodynamics and the Maxwell equations. The conclusion is made that the third harmonies amplitude in narrow-gap semiconductors may exceed substantially the signal amplitude at the 3w frequency in a gas plasma and be of the same order with the surface waves second harmonies amplitude.

Effects of wall transition regions on surface-wave propagation in a plasma layer bounded by a metal

Effect of near-wall transition regions on the surface wave propagation in a magnetoactive plasma layer bounded by a metal. It is shown that the account for inhomogeneities of plasma density or magnetic field causes an appearance of coupling between surface waves, propagating across magnetic field and localized near difference boundaries of the structure. The resonance damping of surface waves is analyzed too.