Uniform Mixing Condition Research Articles

Limit theorems of additive functionals for regime-switching diffusions with infinite delay

This paper focuses on a class of regime-switching functional diffusion processes with infinite delay and develops a central limit theorem (CLT) for additive functionals under uniform mixing conditions. In addition, a law of iterated logarithm (LIL) for the additive functionals is also established by using the square integrable martingale difference sequences. Finally, two examples are given to illustrate our results.

On the asymptotic normality conditions for the number of repetitions in a stationary random sequence

Abstract We study conditions of the asymptotic normality of the number of repetitions (pairs of equal values) in a segment of strict sense stationary random sequence of values from {1, 2, …, N} satisfying the strong uniform mixing condition. It is shown that under natural conditions for the number of repetitions to be asymptotically normal as the length of the segment tends to infinity it is necessary for the stationary distribution to be different from the equiprobable one. Under additional conditions the accuracy of the normal approximation in the uniform metrics is estimated.

The Mixing Character within Oxidation Reactor in Titanium Dioxide Production by Chloride Process

Chloride process is cost effective and environmental benefit, and the TiCl4 oxidation is the most important stage in this process. The structure of the jet ring has an obviously effect on the mixing of TiCl4 and O2 in the oxidation reactor, which is the key equipment in the production of titanium pigment. In this paper, the gas mixing condition with five jet rings of different structure was simulated and analyzed by computational fluid dynamics (CFD) simulation. The radial concentration distribution of TiCl4 and the non-uniformity of the mixture with different jet rings were obtained. The results showed the structure of the jet ring has great effect on the gas mixing. The mixing condition of the jet ring with combined opening orifice is better than that of the jet ring with uniform opening orifice， which is more effective in realizing fast and uniform mixing condition of TiCl4 and O2.

The Mixing Character within Oxidation Reactor in Titanium Dioxide Production by Chloride Process

Chloride process is cost effective and environmental benefit, and the TiCl4 oxidation is the most important stage in this process. The structure of the jet ring has an obviously effect on the mixing of TiCl4 and O2 in the oxidation reactor, which is the key equipment in the production of titanium pigment. In this paper, the gas mixing condition with five jet rings of different structure was simulated and analyzed by computational fluid dynamics (CFD) simulation. The radial concentration distribution of TiCl4 and the non-uniformity of the mixture with different jet rings were obtained. The results showed the structure of the jet ring has great effect on the gas mixing. The mixing condition of the jet ring with combined opening orifice is better than that of the jet ring with uniform opening orifice， which is more effective in realizing fast and uniform mixing condition of TiCl4 and O2.

Extreme Value Laws for sequences of intermittent maps

We study non-stationary stochastic processes arising from sequential dynamical systems built on maps with a neutral fixed point and prove the existence of Extreme Value Laws for such processes. We use an approach developed in an earlier work of the authors, where we generalised the theory of extreme values for non-stationary stochastic processes, mostly by weakening the uniform mixing condition that was previously used in this setting. The present work is an extension of our previous results for concatenations of uniformly expanding maps.

Extreme Value Laws for non stationary processes generated by sequential and random dynamical systems

Nous developpons et generalisons la theorie des valeurs extremes pour des processus stochastiques non-stationnaires, en affaiblissant la condition de melange uniforme qui avait ete utilisee auparavant. Nous appliquons nos resultats a des systemes dynamiques non autonomes, en particulier aux systemes dynamiques sequentiels engendres par des applications dilatantes et a une large classe de systemes dynamiques aleatoires. Quelques exemples sont presentes et calcules en detail.

On the rate of convergence in the strong law of large numbers for martingales

The aim of this note is to establish the Baum–Katz type rate of convergence in the Marcinkiewicz–Zygmund strong law of large numbers for martingales, which improves the recent works of Stoica [Series of moderate deviation probabilities for martingales, J. Math. Anal. Appl. 336 (2005), pp. 759–763; Baum–Katz–Nagaev type results for martingales, J. Math. Anal. Appl. 336 (2007), pp. 1489–1492; A note on the rate of convergence in the strong law of large numbers for martingales, J. Math. Anal. Appl. 381 (2011), pp. 910–913]. Furthermore, we also study some relevant limit behaviours for the uniform mixing process. Under some uniform mixing conditions, the sufficient and necessary condition of the convergence of the martingale series is established.

One-dimensional projective subdynamics of uniformly mixing shifts of finite type

We investigate under which circumstances the projective subdynamics of multidimensional shifts of finite type can be non-sofic. In particular, we give a sufficient condition ensuring the one-dimensional projective subdynamics of such $\mathbb{Z}^{d}$ systems to be sofic and we show that this condition is already met (along certain, respectively all, sublattices) by most of the commonly used uniform mixing conditions. (Examples of the different situations are given.) Complementary to this we are able to prove a characterization of one-dimensional projective subdynamics for strongly irreducible $\mathbb{Z}^{d}$ shifts of finite type for every $d\geq 2$: in this setting the class of possible subdynamics coincides exactly with the class of mixing $\mathbb{Z}$ sofics. This stands in stark contrast to the much more diverse situation in merely topologically mixing multidimensional shifts of finite type.

Averaging over fast variables in the fluid limit for Markov chains: Application to the supermarket model with memory

We set out a general procedure which allows the approximation of certain Markov chains by the solutions of differential equations. The chains considered have some components which oscillate rapidly and randomly, while others are close to deterministic. The limiting dynamics are obtained by averaging the drift of the latter with respect to a local equilibrium distribution of the former. Some general estimates are proved under a uniform mixing condition on the fast variable which give explicit error probabilities for the fluid approximation. Mitzenmacher, Prabhakar and Shah [In Proc. 43rd Ann. Symp. Found. Comp. Sci. (2002) 799-808, IEEE] introduced a variant with memory of the "join the shortest queue" or "supermarket" model, and obtained a limit picture for the case of a stable system in which the number of queues and the total arrival rate are large. In this limit, the empirical distribution of queue sizes satisfies a differential equation, while the memory of the system oscillates rapidly and randomly. We illustrate our general fluid limit estimate by giving a proof of this limit picture.

Effects of flows in auto-organization, self-assembly, and emergence of chirality

The motion of molecular species in solution, in stagnant, and under simple stirring conditions is dominated by Brownian dynamics. However, when the hydrodynamic forces of laminar flows (imperfect mixing conditions) are such that can align chemical species, these may show a different chemical behaviour to that under conditions of Brownian dynamics (stagnant and uniform mixing conditions). Supra- and macro-molecular species show sizes and shapes that may cause alignment in common laminar flows and thus, within these flows, a different behaviour to that under uniform mixing conditions can be expected. Experimental evidence on this has been reported on the growth of J-aggregates of amphiphilic porphyrins, where diastereoselective and enantioselective effects by consequence of laminar flows have been detected. Furthermore, the hydrodynamic torque originated by a vortex stirring may select the chiral sign in the spontaneous mirror symmetry breaking that occurs during the auto-organization processes of these systems. In consequence, mechanical torques must be considered to form part of the specific group of chiral fields capable of determining the chiral sign outcome in bifurcation scenarios of spontaneous mirror symmetry breaking, as those that we can imagine that may have taken place in the route from chemical evolution to biological evolution.

1D AND 2D MODELING AND SIMULATION OF RADIAL COMBUSTION PROPAGATION ON Fe2O3/Al THERMITE SYSTEMS

and composition dependency for all system properties during propagation. Therefore, an adaptive numerical algorithm that conjugates a method of lines (MOL) strategy based on finite differences space discretizations, with a collocation scheme based on increasing level dyadic grids is applied for the solution of the problem. The particular integration method proves to cope satisfactorily with the steep traveling thermal wave in 1D and 2D spatial domains, either for trivial uniform mixing conditions, as in complex examples developed to feature more sophisticated circumstances, such as nonhomogeneous reactant mixing, which realistically replicate the observed experimental conditions.

Determination of conventional velocity gradient (G) using CFD technique for a pilot-scale flocculation system

Research Article| December 01 2010 Determination of conventional velocity gradient (G) using CFD technique for a pilot-scale flocculation system Yamuna S. Vadasarukkai; Yamuna S. Vadasarukkai 1Department of Civil & Resource Engineering, Dalhousie University, Halifax NS B3J 1Z1, Canada Search for other works by this author on: This Site PubMed Google Scholar Graham A. Gagnon Graham A. Gagnon 1Department of Civil & Resource Engineering, Dalhousie University, Halifax NS B3J 1Z1, Canada Tel.: 902.494.3268 Fax: 902.494.3108; E-mail: graham.gagnon@dal.ca Search for other works by this author on: This Site PubMed Google Scholar Journal of Water Supply: Research and Technology-Aqua (2010) 59 (8): 459–470. https://doi.org/10.2166/aqua.2010.081 Article history Received: August 26 2009 Accepted: March 22 2010 Views Icon Views Article contents Figures & tables Video Audio Supplementary Data Share Icon Share Facebook Twitter LinkedIn MailTo Tools Icon Tools Cite Icon Cite Permissions Search Site Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentAll JournalsThis Journal Search Advanced Search Citation Yamuna S. Vadasarukkai, Graham A. Gagnon; Determination of conventional velocity gradient (G) using CFD technique for a pilot-scale flocculation system. Journal of Water Supply: Research and Technology-Aqua 1 December 2010; 59 (8): 459–470. doi: https://doi.org/10.2166/aqua.2010.081 Download citation file: Ris (Zotero) Reference Manager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex Achieving uniform mixing conditions are essential for the flocculation process to optimize floc size and avoid floc-breakup. Limited literature is available on establishing consistent operational conditions and procedures for pilot-scale flocculation systems, which have tank sizes smaller than full-scale and larger than jar-test equipment. In this study, the influence of mixing speeds on the determination of the conventional design parameter, the average velocity gradient (G), was investigated for pilot-scale paddle flocculators. The pilot-scale plant for this paper was hosted at the J.D. Kline Water Supply Plant (JDKWSP) in Halifax, Canada. Computational fluid dynamics (CFD) was evaluated as an alternative design technique and compared against traditionally used empirical-based calculations. Comparison of both approaches showed that the G-values of empirical method were substantially higher than the predicted values for rotational speeds greater than 5 rpm. In contrast, CFD predictions found that G-values used for tapered paddle flocculation process (up to 60 s−1) could be achieved at lower rotational speed (around 15 rpm), which minimizes the power input required for mixing. The practical implications of operating at higher than required G-values relates to potential negative consequences such as floc break up, and the reliance of chemical additives to avoid floc break-up. These very practical outcomes could impact the interpretation of findings from pilot-scale treatment systems. average velocity gradient (G), computational fluid dynamics, flocculation, hydrodynamics, pilot-scale water treatment This content is only available as a PDF. © IWA Publishing 2010 You do not currently have access to this content.

Controlled liquid antisolvent precipitation using a rapid mixing device

Particle formation by the liquid antisolvent (LAS) process involves two steps: mixing of solution–antisolvent streams to generate supersaturation and precipitation (which includes nucleation and growth by coagulation and condensation) of particles. Uniform mixing conditions ensure rapid and uniform supersaturation, making it a precipitation controlled process where the particle size is not further affected by mixing conditions and results in precipitation of ultra-fine particles with narrow particle size distribution (PSD). In this work, we demonstrate that the use of an ultrasonically driven T-shaped mixing device significantly improves mixing of solution and antisolvent streams for precipitation of ultra-fine particles in a continuous operation mode. LAS precipitation of ultra-fine particles of multiple active pharmaceutical ingredients (APIs) such as itraconazole (ITZ), ascorbyl palmitate (ASC), fenofibrate (FNB), griseofulvin (GF), and sulfamethoxazole (SFMZ) in the size range 0.1–30 μm has been carried out from their organic solutions in acetone, dimethyl sulfoxide (DMSO), tetrahydrofuran (THF), and ethanol (EtOH). Classical theory of homogeneous nucleation has been used to analyze the result, which suggests that higher nucleation rate results in finer particle size. Interestingly, experimental determination of degree of supersaturation indicates that higher supersaturation does not necessarily result in higher nucleation rate and nucleation rates can be correlated to solvent polarity.

The Split Property and the Symmetry Breaking¶of the Quantum Spin Chain

We consider the relationship between the symmetry breaking and the split property of pure states of quantum spin chains. We obtain a representation theoretic condition implying that the half-sided uniform mixing condition leads to symmetry breaking of translationally invariant pure states. This is a mathematical generalization of Dichotomy previously found by I. Affleck and E. Lieb and M. Aizenman and B. Nachtergaele for ground states of a special class of Hamiltonians.

Analysis of Barrel-Stratified Lean-Burn Flame Structure by Two-Dimensional Chemiluminescence Measurement.

The postflame reaction zone structure of a lean-burn flame was studied by two-dimensional consecutive imaging of flame chemiluminescence using an image intensifier with short-decay phosphor. Quantitative and statistical analyses were performed to elucidate the effect of tumble and charge stratification on the flame behavior. It was found that in the early stage of combustion, significant air entrainment enhancement was realized by tumble but its effect on eddy burning was small. After the completion of flame propagation, however, tumble activated the eddy burning process. Charge stratification activated both air entrainment and eddy burning. These phenomena could be related to the flow field structure after the collapse of tumble. A procedure to derive the tomographic image of the reaction zone was proposed. It was found that under a uniform mixing condition, no reaction-zone structure was observed. When charge was stratified, however, an annular postflame reaction zone was observed behind the flame front.