Statistical-mechanical description of classical test-particle dynamics in the presence of an external force field: modelling noise and damping from first principles

Aiming to establish a rigorous link between macroscopic random motion (described e.g. by Langevin-type theories) and microscopic dynamics, we have undertaken a kinetic-theoretical study of the dynamics of a classical test-particle weakly coupled to a large heat-bath in thermal equilibrium. Both subsystems are subject to an external force field. From the (time-non-local) generalized master equation a Fokker-Planck-type equation follows as a "quasi-Markovian" approximation. The kinetic operator thus defined is shown to be ill-defined; in specific, it does not preserve the positivity of the test-particle distribution function f(x, v; t). Adopting an alternative approach, previously introduced for quantum open systems, is proposed to lead to a correct kinetic operator, which yields all the expected properties. A set of explicit expressions for the diffusion and drift coefficients are obtained, allowing for modelling macroscopic diffusion and dynamical friction phenomena, in terms of an external field and intrinsic physical parameters.

Integrated Optimal Power Flow for Distribution Networks in Local and Urban Scales

This paper develops an integrated optimal power flow (OPF) tool for distribution networks in two spatial scales. In the local scale, the distribution network, the natural gas network, and the heat system are coordinated as a microgrid. In the urban scale, the impact of natural gas network is considered as constraints for the distribution network operation. The proposed approach incorporates unbalance three-phase electrical systems, natural gas systems, and combined cooling, heating, and power systems. The interactions among the above three energy systems are described by energy hub model combined with components capacity constraints. In order to efficiently accommodate the nonlinear constraint optimization problem, particle swarm optimization algorithm is employed to set the control variables in the OPF problem. Numerical studies indicate that by using the OPF method, the distribution network can be economically operated. Also, the tie-line power can be effectively managed.

Particle Image Velocimetry Investigation of a finite amplitude pressure wave

Particle image velocimetry is used to study the motion of gas within a duct subject to the passage of a finite amplitude pressure wave. The wave is representative of the pressure waves found in the exhaust systems of internal combustion engines. Gas particles are accelerated from stationary to 150 m/s and then back to stationary in 8 ms. It is demonstrated that gas particles at the head of the wave travel at the same velocity across the duct cross section at a given point in time. Towards the tail of the wave viscous effects are plainly evident causing the flow profile to tend towards parabolic. However, the instantaneous mean particle velocity across the section is shown to match well with the velocity calculated from a corresponding measured pressure history using 1D gas dynamic theory. The measured pressure history at a point in the duct was acquired using a high speed pressure transducer of the type typically used for engine research in intake and exhaust systems. It is demonstrated that these are unable to follow the rapid changes in pressure accurately and that they are prone to resonate under certain circumstances.

Solving the advection-dispersion equation using the discrete puff particle method

A flexible, mass-conservative numerical technique for solving the advection-dispersion equation for miscible contaminant transport is presented. The method combines features of puff transport models from air pollution studies with features from the random walk particle method used in water resources studies, providing a deterministic time-marching algorithm which is independent of the grid Peclet number and scales from one to higher dimensions simply. The concentration field is discretised into a number of particles, each of which is treated as a point release which advects and disperses over the time interval. The dispersed puff is itself discretised into a spatial distribution of particles whose masses can be pre-calculated. Concentration within the simulation domain is then calculated from the mass distribution as an average over some small volume. Comparison with analytical solutions for a one-dimensional fixed-duration concentration pulse and for two-dimensional transport in an axisymmetric flow field indicate that the algorithm performs well. For a given level of accuracy the new method has lower computation times than the random walk particle method.

Space and time resolved rotational state populations and gas temperatures in an inductively coupled hydrogen RF discharge

Gas temperature is of major importance in plasma based surface treatment, since the surface processes are strongly temperature sensitive. The spatial distribution of reactive species responsible for surface modification is also influenced by the gas temperature. Industrial applications of RF plasma reactors require a high degree of homogeneity of the plasma in contact with the substrate. Reliable measurements of spatially resolved gas temperatures are, therefore, of great importance. The gas temperature can be obtained, e.g. by optical emission spectroscopy (OES). Common methods of OES to obtain gas temperatures from analysis of rotational distributions in excited states do not include the population dynamics influenced by cascading processes from higher electronic states. A model was developed to evaluate this effect on the apparent rotational temperature that is observed. Phase resolved OES confirmed the validity of this model. It was found that cascading leads to higher apparent temperatures, but the deviation (similar or equal to 25 K) is relatively small and can be ignored in most cases. This analysis is applied to investigate axially and radially resolved temperature profiles in an inductively coupled hydrogen RF discharge.

Comparison between fluid simulations and experiments in inductively coupled argon/chlorine plasmas

Comparisons of 2D fluid simulations with experimental measurements of Ar/Cl-2 plasmas in a low-pressure inductively coupled reactor are reported. Simulations show that the wall recombination coefficient of Cl atom (gamma) is a crucial parameter of the model and that neutral densities are very sensitive to its variations. The best agreement between model and experiment is obtained for gamma = 0.02, which is much lower than the value predicted for stainless steel walls (gamma = 0.6). This is consistent with reactor wall contaminations classically observed in such discharges. The electron density, negative ion fraction and Cl atom density have been investigated under various conditions of chlorine and argon concentrations, gas pressure and applied rf input power. The plasma electronegativity decreases with rf power and increases with chlorine concentration. At high pressure, the power absorption and distribution of charged particles become more localized below the quartz window. Although the experimental trends are well reproduced by the simulations, the calculated charged particle densities are systematically overestimated by a factor of 3-5. The reasons for this discrepancy are discussed in the paper.

Analysis procedure for calculation of electron energy distribution functions from incoherent Thomson scattering spectra

Incoherent Thomson scattering (ITS) provides a nonintrusive diagnostic for the determination of one-dimensional (1D) electron velocity distribution in plasmas. When the ITS spectrum is Gaussian its interpretation as a three-dimensional (3D) Maxwellian velocity distribution is straightforward. For more complex ITS line shapes derivation of the corresponding 3D velocity distribution and electron energy probability distribution function is more difficult. This article reviews current techniques and proposes an approach to making the transformation between a 1D velocity distribution and the corresponding 3D energy distribution. Previous approaches have either transformed the ITS spectra directly from a 1D distribution to a 3D or fitted two Gaussians assuming a Maxwellian or bi-Maxwellian distribution. Here, the measured ITS spectrum transformed into a 1D velocity distribution and the probability of finding a particle with speed within 0 and given value v is calculated. The differentiation of this probability function is shown to be the normalized electron velocity distribution function. (C) 2003 American Institute of Physics.

Nonlinear theory of solitary waves associated with longitudinal particle motion in lattices - Application to longitudinal grain oscillations in a dust crystal

The nonlinear aspects of longitudinal motion of interacting point masses in a lattice are revisited, with emphasis on the paradigm of charged dust grains in a dusty plasma (DP) crystal. Different types of localized excitations, predicted by nonlinear wave theories, are reviewed and conditions for their occurrence (and characteristics) in DP crystals are discussed. Making use of a general formulation, allowing for an arbitrary (e.g. the Debye electrostatic or else) analytic potential form phi(r) and arbitrarily long site-to-site range of interactions, it is shown that dust-crystals support nonlinear kink-shaped localized excitations propagating at velocities above the characteristic DP lattice sound speed v(0). Both compressive and rarefactive kink-type excitations are predicted, depending on the physical parameter values, which represent pulse- (shock-)like coherent structures for the dust grain relative displacement. Furthermore, the existence of breather-type localized oscillations, envelope-modulated wavepackets and shocks is established. The relation to previous results on atomic chains as well as to experimental results on strongly-coupled dust layers in gas discharge plasmas is discussed.

Fokker-Planck equation for a test-particle weakly coupled to a magnetized plasma

We consider the derivation of a kinetic equation for a charged test particle weakly interacting with an electrostatic plasma in thermal equilibrium, subject to a uniform external magnetic field. The Liouville equation leads to a generalized master equation to second order in the `weak' interaction; a Fokker-Planck-type equation then follows as a `Markovian' approximation. It is shown that such an equation does not preserve the positivity of the distribution function f(x,v;t). By applying techniques developed in the theory of open systems, a correct Fokker-Planck equation is derived. Explicit expressions for the diffusion and drift coefficients, depending on the magnetic field, are obtained.

Effects of particle plasticity characteristics on local interface stress in particle reinforced composite during uniaxial tension

For elastoplastic particle reinforced metal matrix composites, failure may originate from interface debonding between the particles and the matrix, both elastoplastic and matrix fracture near the interface. To calculate the stress and strain distribution in these regions, a single reinforcing particle axisymmetric unit cell model is used in this article. The nodes at the interface of the particle and the matrix are tied. The development of interfacial decohesion is not modelled. Finite element modelling is used, to reveal the effects of particle strain hardening rate, yield stress and elastic modulus on the interfacial traction vector (or stress vector), interface deformation and the stress distribution within the unit cell, when the composite is under uniaxial tension. The results show that the stress distribution and the interface deformation are sensitive to the strain hardening rate and the yield stress of the particle. With increasing particle strain hardening rate and yield stress, the interfacial traction vector and internal stress distribution vary in larger ranges, the maximum interfacial traction vector and the maximum internal stress both increase, while the interface deformation decreases. In contrast, the particle elastic modulus has little effect on the interfacial traction vector, internal stress and interface deformation.

Comparison of Experimental PIV Data and CFD Simulations for Flow in a Diesel Particulate Filter Inlet Diffuser

Flow maldistribution of the exhaust gas entering a Diesel Particulate Filter (DPF) can cause uneven soot distribution during loading and excessive temperature gradients during the regeneration phase. Minimising the magnitude of this maldistribution is therefore an important consideration in the design of the inlet pipe and diffuser, particularly in situations where packaging constraints dictate bends in the inlet pipe close to the filter, or a sharp diffuser angle. This paper describes the use of Particle Image Velocimetry (PIV) to validate a Computational Fluid Dynamic (CFD) model of the flow within the inlet diffuser of a DPF so that CFD can be used with confidence as a tool to minimise this flow maldistribution. PIV is used to study the flow of gas into a DPF over a range of steady state flow conditions. The distribution of flow approaching the front face of the substrate was of particular interest to this study. Optically clear diffusing cones were designed and placed between pipe and substrate to allow PIV analysis to take place. Stereoscopic PIV was used to eliminate any error produced by the optical aberrations caused by looking through the curved wall of the inlet cone. In parallel to the experiments, numerical analysis was carried out using a CFD program with an incorporated DPF model. Boundary conditions for the CFD simulations were taken from the experimental data, allowing an experimental validation of the numerical results. The CFD model incorporated a DPF model, the cement layers seen in segmented filters and the intumescent matting that is commonly used to pack the filter into a metal casing. The mesh contained approximately 580,000 cells and used the realizable ?-e turbulence model. The CFD simulation predicted both pressure drop across the DPF and the velocity field within the cone and at the DPF face with reasonable accuracy, providing confidence in the use the CFD in future work to design new, more efficient cones.

The Hekla 1947 tephra in the North of Ireland: regional distribution, concentration and geochemistry.

A cryptotephra layer from the eruption of Hekla in 1947 has recently been discovered in Irish peatlands. This tephra layer represents the most recent deposition of volcanic ash in the UK prior to the eruption of Eyjafjallajökull in 2010. Here we examine the concentration and geochemistry of the Hekla 1947 tephra in 14 peat profiles from across Northern Ireland. Electron probe microanalysis of individual tephra shards (n?=?91) reveals that the tephra is of dacitic–andesitic geochemistry and is highly similar to the Hekla 1510 tephra, although spheroidal carbonaceous particle profiles can be used for successful discrimination of the two layers. The highest concentrations of Hekla 1947 are found in western sites, probably reflecting the pathway of the ash fall event due to the prevailing wind direction. Comparable tephra concentrations from two cores (1?km apart) from a single bog and from nearby sites may suggest that tephra shard concentrations in peat profiles reflect ash fallout densities across a specific region, rather than site-specific factors associated with peatlands. This paper firmly establishes Hekla 1947 as a useful chronostratigraphic marker for the twentieth century, although within a restricted zone.

IR laser desorption of oligonucleotides A novel gas phase target for radiation damage studies

The desorption of oligonucleotides by 3 mu m laser irradiation has been studied by laser induced fluorescence imaging of the resulting gas phase plumes. Fitting of the plume data has been achieved by using a modified Maxwell Boltzmann distribution which incorporates a range of stream velocities. Spatial density profiles, velocities and temperature variation have been determined from these fits indicating that the oligonucleotide plume only achieves a partial thermal relaxation. This laser desorption technique may provide a means of overcoming the limited mass range of gas phase biomolecules available from thermal evaporation techniques.