Spatially averaged model of complex-plasma discharge with self-consistent electron energy distribution

A global, or averaged, model for complex low-pressure argon discharge plasmas containing dust grains is presented. The model consists of particle and power balance equations taking into account power loss on the dust grains and the discharge wall. The electron energy distribution is determined by a Boltzmann equation. The effects of the dust and the external conditions, such as the input power and neutral gas pressure, on the electron energy distribution, the electron temperature, the electron and ion number densities, and the dust charge are investigated. It is found that the dust subsystem can strongly affect the stationary state of the discharge by dynamically modifying the electron energy distribution, the electron temperature, the creation and loss of the plasma particles, as well as the power deposition. In particular, the power loss to the dust grains can take up a significant portion of the input power, often even exceeding the loss to the wall.

Stationary processes for object detection and non-rigid structure-from-motion

Stationary processes are random variables whose value is a signal and whose distribution is invariant to translation in the domain of the signal. They are intimately connected to convolution, and therefore to the Fourier transform, since the covariance matrix of a stationary process is a Toeplitz matrix, and Toeplitz matrices are the expression of convolution as a linear operator. This thesis utilises this connection in the study of i) efficient training algorithms for object detection and ii) trajectory-based non-rigid structure-from-motion.

Exact path-integral evaluation of the heat distribution function of a trapped Brownian oscillator

Using path integrals, we derive an exact expression-valid at all times t-for the distribution P(Q,t) of the heat fluctuations Q of a Brownian particle trapped in a stationary harmonic well. We find that P(Q, t) can be expressed in terms of a modified Bessel function of zeroth order that in the limit t > infinity exactly recovers the heat distribution function obtained recently by Imparato et al. Phys. Rev. E 76, 050101(R) (2007)] from the approximate solution to a Fokker-Planck equation. This long-time result is in very good agreement with experimental measurements carried out by the same group on the heat effects produced by single micron-sized polystyrene beads in a stationary optical trap. An earlier exact calculation of the heat distribution function of a trapped particle moving at a constant speed v was carried out by van Zon and Cohen Phys. Rev. E 69, 056121 (2004)]; however, this calculation does not provide an expression for P(Q, t) itself, but only its Fourier transform (which cannot be analytically inverted), nor can it be used to obtain P(Q, t) for the case v=0.

Nonequilibrium stationary states of a particle in a gravitational field driven by a vibrating surface

Stationary velocity distribution functions are determined for a particle in a gravitational field driven by a vibrating surface in the limit of small dissipation. It is found that the form of the distribution function is sensitive to the mechanism of energy dissipation, inelastic collisions or viscous drag, and also to the form of the amplitude function of the vibrating surface. The velocity distributions obtained analytically are found to be in excellent agreement with the results of computer simulations in the limit of low dissipation. [S0031-9007(99)08898-5].

On distribution of pollen in lakes. [Translation from: Palynology in geological research in the Baltic Soviet Republics p113-119. Vilnius, 1973.]

Systematic investigations of the distribution of pollen in stationary water bodies until now have hardly been conducted. For clarification of the problem of how the pollen of different plants which falls into a lake is deposited in relation to its physical properties, the character of the lake, wind currents and other factors, pollen analyses were carried out of surface samples of the bottom sediments of 13 Lithuanian lakes. Lakes were selected of different sizes (areas from 2333 ha. to 8 ha.) and different depths, not uniformly overgrown, situated in different physico-geographic regions of Lithuania. As a result of the investigation, it was established that in the surface layer of the sediments of the lakes of Lithuania pollen of woody species predominates.

Stationary absolute distributions for chains of infinite order

Let {Ƶ_n}^∞_{n = -∞} be a stochastic process with state space S₁ = {0, 1, …, D – 1}. Such a process is called a chain of infinite order. The transitions of the chain are described by the functions

Q_i(i⁽⁰⁾) = Ƥ(Ƶ_n = i | Ƶ_{n - 1} = i ⁽⁰⁾₁, Ƶ_{n - 2} = i ⁽⁰⁾₂, …) (i ɛ S₁), where i⁽⁰⁾ = (i⁽⁰⁾₁, i⁽⁰⁾₂, …) ranges over infinite sequences from S₁. If i⁽ⁿ⁾ = (i⁽ⁿ⁾₁, i⁽ⁿ⁾₂, …) for n = 1, 2,…, then i⁽ⁿ⁾ → i⁽⁰⁾ means that for each k, i⁽ⁿ⁾_k = i⁽⁰⁾_k for all n sufficiently large.

Given functions Q_i(i⁽⁰⁾) such that

(i) 0 ≤ Q_i(i⁽⁰) ≤ ξ ˂ 1

(ii)D – 1/Ʃ/i = 0 Q_i(i⁽⁰⁾) Ξ 1

(iii) Q_i(i⁽ⁿ⁾) → Q_i(i⁽⁰⁾) whenever i⁽ⁿ⁾ → i⁽⁰⁾,

we prove the existence of a stationary chain of infinite order {Ƶ_n} whose transitions are given by

Ƥ (Ƶ_n = i | Ƶ_{n - 1}, Ƶ_{n - 2}, …) = Q_i(Ƶ_{n - 1}, Ƶ_{n - 2}, …)

With probability 1. The method also yields stationary chains {Ƶ_n} for which (iii) does not hold but whose transition probabilities are, in a sense, “locally Markovian.” These and similar results extend a paper by T.E. Harris [Pac. J. Math., 5 (1955), 707-724].

Included is a new proof of the existence and uniqueness of a stationary absolute distribution for an Nth order Markov chain in which all transitions are possible. This proof allows us to achieve our main results without the use of limit theorem techniques.

Effects of current speed and turbidity on stationary light-trap catches of larval and juvenile fishes

Light traps are one of a number of different gears used to sample pelagic larval and juvenile fishes. In contrast to conventional towed nets, light traps primarily collect larger size classes, including settlement-size larvae (Choat et al., 1993; Hickford and Schiel, 1999 ; Hernandez and Shaw, 2003), and, therefore, have become important tools for discerning recruitment dynamics (Sponaugle and Cowen, 1996; Wilson, 2001). The relative ease with which multiple synoptic light trap samples can be taken means that larval distribution patterns can be mapped with greater spatial resolution (Doherty, 1987). Light traps are also useful for sampling shallow or structurally complex habitats where towed nets are ineffective or prohibited (Gregory and Powles, 1985; Brogan, 1994; Hernandez and Shaw, 2003).

FIRST PASSAGE APPROXIMATION FOR NORMAL STATIONARY RANDOM PROCESSES.

A new approximate solution for the first passage probability of a stationary Gaussian random process is presented which is based on the estimation of the mean clump size. A simple expression for the mean clump size is derived in terms of the cumulative normal distribution function, which avoids the lengthy numerical integrations which are required by similar existing techniques. The method is applied to a linear oscillator and an ideal bandpass process and good agreement with published results is obtained. By making a slight modification to an existing analysis it is shown that a widely used empirical result for the asymptotic form of the first passage probability can be deduced theoretically.

Short columns with molecularly imprinted monolithic stationary phases for rapid separation of diastereomers and enantiomers

Three molecularly imprinted monolithic columns with different length but almost identical column volume had been prepared. It was observed that the separation factors of diastereomers and enantiomers were almost unaffected by column length. However, the short column with dimension of 38 mm x 8 mm W. showed much lower resistance to flow rate so that it could be operated at much higher flow rates. By combining stepwise gradient elution with elevated flow rate, the diastereomers of cinchonine and cinchonidine and the enantiomers of Cbz-DL-Trp and Fmoc-DL-Trp were successfully separated within 3 min on the short column with dimension of 38 mm. x 8 mm i.d.. Based on the above results, a cinchonine imprinted monolithic disk with dimension of 10 mm x 16 mm W. was further developed. The SEM image and the pore size distribution profile showed that large flow-through pores are present on the prepared monolith, which allowed mobile phase to flow through the disk with very low resistance. Chromatographic performances on the monolithic disk were almost unchanged compared with the long columns. A rapid separation of cinchonine and cinchonidine was achieved in 2.5 min at the flow rate of 9.0 ml/min. Furthermore, it was observed that there was almost no effect of the flow rate on the dynamic binding capacity at high flow rates. In addition, the effect of the loading concentration of analytes on the dynamic binding capacity, namely adsorption isotherm, was also investigated. A non-linear adsorption isotherm of cinchonine was observed on the molecularly imprinted monolith with cinchonine as template, which might be a main reason to result in the peak tailing of template molecule. (C) 2004 Elsevier B.V. All rights reserved.

A simple preparation of stationary phase of alkylamide reversed-phase liquid chromatograph for the separation of basic substances

A simple preparation process of alkylamide phase for reversed-phase HPLC (RP-HPLC) is described. The process includes aminopropyltrimethoxysilane firstly reacted with octanoyl chloride, then the intermediate was coupled onto porous silica. The resultant bonded silica has a reproducible ligand surface concentration and homogenous bonded ligand distribution on the porous silica. Characterization of prepared packing was carried out with elemental analysis, solid-state C-13 NMR and Fourier transform infrared (FT-IR). Chromatographic evaluations were carried out by using a mixture of organic compounds including acidic, basic and neutral analytes under methanol/water as binary mobile phase. The results showed that the stationary phase have excellent chromatographic properties and can be efficiently used for the separation of basic compounds.

Synthesis and characterisation of novel superficially porous silica based stationary phases for use in liquid chromatography

The concept of pellicular particles was suggested by Horváth and Lipsky over fifty years ago. The reasoning behind the idea of these particles was to improve column efficiency by shortening the pathways analyte molecules can travel, therefore reducing the effect of the A and C terms. Several types of shell particles were successfully marketed around this time, however with the introduction of high quality fully porous silica under 10 μm, shell particles faded into the background. In recent years a new generation of core shell particles have become popular within the separation science community. These particles allow fast and efficient separations that can be carried out on conventional HPLC systems. Chapter 1 of this thesis introduces the chemistry of chromatographic stationary phases, with an emphasis on silica bonded phases, particularly focusing on the current state of technology in this area. The main focus is on superficially porous silica particles as a support material for liquid chromatography. A summary of the history and development of these particles over the past few decades is explored, along with current methods of synthesis of shell particles. While commercial shell particles have a rough outer surface, Chapter 2 focuses on the novel approach to growth of smooth surface superficially porous particles in a step-by-step manner. From the Stöber methodology to the seeded growth technique, and finally to the layer-bylayer growth of the porous shell. The superficially porous particles generated in this work have an overall diameter of 2.6 μm with a 350 nm porous shell; these silica particles were characterised using SEM, TEM and BET analysis. The uniform spherical nature of the particles along with their surface area, pore size and particle size distribution are examined in this chapter. I discovered that these smooth surface shell particles can be synthesised to give comparable surface area and pore size in comparison to commercial brands. Chapter 3 deals with the bonding of the particles prepared in Chapter 2 with C18 functionality; one with a narrow and one with a wide particle size distribution. This chapter examines the chromatographic and kinetic performance of these silica stationary phases, and compares them to a commercial superficially porous silica phase with a rough outer surface. I found that the particle size distribution does not seem to be the major contributor to the improvement in efficiency. The surface morphology of the particles appears to play an important role in the packing process of these particles and influences the Van Deemter effects. Chapter 4 focuses on the functionalisation of 2.6 μm smooth surface superficially porous particles with a variety of fluorinated and phenyl silanes. The same processes were carried out on 3.0 μm fully porous silica particles to provide a comparison. All phases were accessed using elemental analysis, thermogravimetric analysis, nitrogen sorption analysis and chromatographically evaluated using the Neue test. I observed comparable results for the 2.6 μm shell pentaflurophenyl propyl silica when compared to 3.0 μm fully porous silica. Chapter 5 moves towards nano-particles, with the synthesis of sub-1 μm superficially porous particles, their characterisation and use in chromatography. The particles prepared are 750 nm in total with a 100 nm shell. All reactions and testing carried out on these 750 nm core shell particles are also carried out on 1.5 μm fully porous particles in order to give a comparative result. The 750 nm core shell particles can be synthesised quickly and are very uniform. The main drawback in their use for HPLC is the system itself due to the backpressure experienced using sub – 1 μm particles. The synthesis of modified Stöber particles is also examined in this chapter with a range of non-porous silica and shell silica from 70 nm – 750 nm being tested for use on a Langmuir – Blodgett system. These smooth surface shell particles have only been in existence since 2009. The results displayed in this thesis demonstrate how much potential smooth surface shell particles have provided more in-depth optimisation is carried out. The results on packing studies reported in this thesis aims to be a starting point for a more sophisticated methodology, which in turn can lead to greater chromatographic improvements.

Reducing quantum control for spin-spin entanglement distribution

We present a protocol that sets maximum stationary entanglement between remote spins through scattering of mobile mediators without initialization, post-selection or feedback of the mediators' state. No time-resolved tuning is needed and, counterintuitively, the protocol generates two-qubit singlet states even when classical mediators are used. The mechanism responsible for this effect is resilient against non-optimal coupling strengths and dephasing affecting the spins. The scheme uses itinerant particles and scattering centres and can be implemented in various settings. When quantum dots and photons are used a striking result is found: injection of classical mediators, rather than quantum ones, improves the scheme efficiency.

Validation of non‑stationary precipitation series for site‑specific impact assessment: comparison of two statistical downscaling techniques

Statistical downscaling (SD) methods have become a popular, low-cost and accessible means of bridging the gap between the coarse spatial resolution at which climate models output climate scenarios and the finer spatial scale at which impact modellers require these scenarios, with various different SD techniques used for a wide range of applications across the world. This paper compares the Generator for Point Climate Change (GPCC) model and the Statistical DownScaling Model (SDSM)—two contrasting SD methods—in terms of their ability to generate precipitation series under non-stationary conditions across ten contrasting global climates. The mean, maximum and a selection of distribution statistics as well as the cumulative frequencies of dry and wet spells for four different temporal resolutions were compared between the models and the observed series for a validation period. Results indicate that both methods can generate daily precipitation series that generally closely mirror observed series for a wide range of non-stationary climates. However, GPCC tends to overestimate higher precipitation amounts, whilst SDSM tends to underestimate these. This infers that GPCC is more likely to overestimate the effects of precipitation on a given impact sector, whilst SDSM is likely to underestimate the effects. GPCC performs better than SDSM in reproducing wet and dry day frequency, which is a key advantage for many impact sectors. Overall, the mixed performance of the two methods illustrates the importance of users performing a thorough validation in order to determine the influence of simulated precipitation on their chosen impact sector.

Markovian Processes, Two-Sided Autoregressions and Finite-Sample Inference for Stationary and Nonstationary Autoregressive Processes.

In this paper, we develop finite-sample inference procedures for stationary and nonstationary autoregressive (AR) models. The method is based on special properties of Markov processes and a split-sample technique. The results on Markovian processes (intercalary independence and truncation) only require the existence of conditional densities. They are proved for possibly nonstationary and/or non-Gaussian multivariate Markov processes. In the context of a linear regression model with AR(1) errors, we show how these results can be used to simplify the distributional properties of the model by conditioning a subset of the data on the remaining observations. This transformation leads to a new model which has the form of a two-sided autoregression to which standard classical linear regression inference techniques can be applied. We show how to derive tests and confidence sets for the mean and/or autoregressive parameters of the model. We also develop a test on the order of an autoregression. We show that a combination of subsample-based inferences can improve the performance of the procedure. An application to U.S. domestic investment data illustrates the method.

Asymptotic Distribution of a Simple Linear Estimator for VARMA Models in Echelon Form

In this paper, we study the asymptotic distribution of a simple two-stage (Hannan-Rissanen-type) linear estimator for stationary invertible vector autoregressive moving average (VARMA) models in the echelon form representation. General conditions for consistency and asymptotic normality are given. A consistent estimator of the asymptotic covariance matrix of the estimator is also provided, so that tests and confidence intervals can easily be constructed.