Nonlocal Boundary Value Problems for Two-Dimensional Potential Equation on a Rectangle

Иван Димовски, Юлиан Цанков - Предложено е разширение на принципa на Дюамел. За намиране на явно решение на нелокални гранични задачи от този тип е развито операционно смятане основано върху некласическа двумерна конволюция. Пример от такъв тип е задачата на Бицадзе-Самарски.

Spatiotemporal optical bullets in two-dimensional fiber arrays and their stability

Long-lived light bullets fully localized in both space and time can be generated in novel photonic media such as multicore optical fiber or waveguide arrays. In this paper we present detailed theoretical analysis on the existence and stability of the discrete-continuous light bullets using a very generic model that occurs in a number of applications.

Exact Solutions of Nonlocal Boundary Value Problems for One- and Two-Dimensional Heat Equation

Иван Хр. Димовски, Юлиан Ц. Цанков - Предложен е метод за намиране на явни решения на клас двумерни уравнения на топлопроводността с нелокални условия по пространствените променливи. Методът е основан на директно тримерно операционно смятане. Класическата дюамелова конволюция е комбинирана с две некласически конволюции за операторите ∂xx и ∂yy в една тримерна конволюция. Съответното операционно смятане използва мултипликаторни частни. Мултипликаторните частни позволяват да се продължи принципът на Дюамел за пространствените променливи и да се намерят явни решения на разглежданите гранични задачи. Общите разглеждания са приложени в случая на гранични условия от типа на Йонкин. Намерени са експлицитни решения в затворен вид.

Universal profile of the vortex condensate in two-dimensional turbulence

An inverse turbulent cascade in a restricted two-dimensional periodic domain creates a condensate—a pair of coherent system-size vortices. We perform extensive numerical simulations of this system and carry out theoretical analysis based on momentum and energy exchanges between the turbulence and the vortices. We show that the vortices have a universal internal structure independent of the type of small-scale dissipation, small-scale forcing, and boundary conditions. The theory predicts not only the vortex inner region profile, but also the amplitude, which both perfectly agree with the numerical data.

Langevin dynamics, large deviations and instantons for the quasi-geostrophic model and two-dimensional Euler equations

We investigate a class of simple models for Langevin dynamics of turbulent flows, including the one-layer quasi-geostrophic equation and the two-dimensional Euler equations. Starting from a path integral representation of the transition probability, we compute the most probable fluctuation paths from one attractor to any state within its basin of attraction. We prove that such fluctuation paths are the time reversed trajectories of the relaxation paths for a corresponding dual dynamics, which are also within the framework of quasi-geostrophic Langevin dynamics. Cases with or without detailed balance are studied. We discuss a specific example for which the stationary measure displays either a second order (continuous) or a first order (discontinuous) phase transition and a tricritical point. In situations where a first order phase transition is observed, the dynamics are bistable. Then, the transition paths between two coexisting attractors are instantons (fluctuation paths from an attractor to a saddle), which are related to the relaxation paths of the corresponding dual dynamics. For this example, we show how one can analytically determine the instantons and compute the transition probabilities for rare transitions between two attractors.

Resonance properties of domain boundaries in quasi-two dimensional antiferromagnets

The so-called "internal modes" localized near the domain boundaries in quasi-two dimensional antiferromagnets are investigated. The possible localized states are classified and their frequency dependences on the system discreteness parameter λ=J/β, which describes the ratio of the magnitudes of the exchange interplane interaction and the magnetic anisotropy, are found. A sudden change in the spectrum of the local internal modes is observed at a critical value of this parameter, λ=λb=3/4, where the domain wall shifts from a collinear to a canted shape. When λ<λb there are one symmetric and two antisymmetric local modes, and when λ>λb the modes are two symmetric, one antisymmetric, and one shear. For discreteness parameters close to the critical value, the frequencies of some of the local modes lie deep inside the gap for the linear AFM magnon spectrum and can be observed experimentally. © 2010 American Institute of Physics.

Effect of blood flow patterns on localized platelet adhesion under physiologic flow conditions using two-dimensional and three-dimensional stent models: An experimental and computational approach

This dissertation presents dynamic flow experiments with fluorescently labeled platelets to allow for spatial observation of wall attachment in inter-strut spacings, to investigate their relationship to flow patterns. Human blood with fluorescently labeled platelets was circulated through an in vitro system that produced physiologic pulsatile flow in (1) a parallel plate blow chamber that contained two-dimensional (2D) stents that feature completely recirculating flow, partially recirculating flow, and completely reattached flow, and (2) a three-dimensional (3D) cylindrical tube that contained stents of various geometric designs. ^ Flow detachment and reattachment points exhibited very low platelet deposition. Platelet deposition was very low in the recirculation regions in the 3D stents unlike the 2D stents. Deposition distal to a strut was always high in 2D and 3D stents. Spirally recirculating regions were found in 3D unlike in 2D stents, where the deposition was higher than at well-separated regions of recirculation. ^

Development of advanced capillary electrophoresis techniques with UV and mass spectrometry detection for forensic, pharmaceutical and environmental applications

Capillary electrophoresis (CE) is a modern analytical technique, which is electrokinetic separation generated by high voltage and taken place inside the small capillaries. In this dissertation, several advanced capillary electrophoresis methods are presented using different approaches of CE and UV and mass spectrometry are utilized as the detection methods. ^ Capillary electrochromatography (CEC), as one of the CE modes, is a recent developed technique which is a hybrid of capillary electrophoresis and high performance liquid chromatography (HPLC). Capillary electrochromatography exhibits advantages of both techniques. In Chapter 2, monolithic capillary column are fabricated using in situ photoinitiation polymerization method. The column was then applied for the separation of six antidepressant compounds. ^ Meanwhile, a simple chiral separation method is developed and presented in Chapter 3. Beta cycodextrin was utilized to achieve the goal of chiral separation. Not only twelve cathinone analytes were separated, but also isomers of several analytes were enantiomerically separated. To better understand the molecular information on the analytes, the TOF-MS system was coupled with the CE. A sheath liquid and a partial filling technique (PFT) were employed to reduce the contamination of MS ionization source. Accurate molecular information was obtained. ^ It is necessary to propose, develop, and optimize new techniques that are suitable for trace-level analysis of samples in forensic, pharmaceutical, and environmental applications. Capillary electrophoresis (CE) was selected for this task, as it requires lower amounts of samples, it simplifies sample preparation, and it has the flexibility to perform separations of neutral and charged molecules as well as enantiomers. ^ Overall, the study demonstrates the versatility of capillary electrophoresis methods in forensic, pharmaceutical, and environmental applications.^

Applications of capillary electrophoresis and mass spectrometry for the analysis of thiosalts

Thiosalt species are unstable, partially oxidized sulfur oxyanions formed in sulfur-rich environments but also during the flotation and milling of sulfidic minerals especially those containing pyrite (FeS₂) and pyrrhotite (Fe₍₁₋ₓ₎S, x = 0 to 0.2). Detecting and quantifying the major thiosalt species such as sulfate (SO₄²⁻), thiosulfate (S₂O₃²⁻), trithionate (S₃O₆²⁻), tetrathionate (S₄O₆²⁻) and higher polythionates (SₓO₆²⁻, where 3 ≤ x ≤ 10) in the milling process and in the treated tailings is important to understand how thiosalts are generated and provides insight into potential treatment. As these species are unstable, a fast and reliable analytical technique is required for their analysis. Three capillary zone electrophoresis (CZE) methods using indirect UV-vis detection were developed for the simultaneous separation and determination of five thiosalt anions: SO₄²⁻, S₂O₃²⁻, S₃O₆²⁻, S₄O₆²⁻ and S₅O₆²⁻. Both univariate and multivariate experimental design approaches were used to optimize the most critical factors (background electrolyte (BGE) and instrumental conditions) to achieve fast separation and quantitative analysis of the thiosalt species. The mathematically predicted responses for the multivariate experiments were in good agreement with the experimental results. Limits of detection (LODs) (S/N = 3) for the methods were between 0.09 and 0.34 μg/mL without a sample stacking technique and nearly four-fold increase in LODs with the application of field-amplified sample stacking. As direct analysis of thiosalts by mass spectrometry (MS) is limited by their low m/z values and detection in negative mode electrospray ionization (ESI), which is typically less sensitive than positive ESI, imidazolium-based (IP-L-Imid and IP-T-Imid) and phosphonium-based (IP-T-Phos) tricationic ion-pairing reagents were used to form stable high mass ions non-covalent +1 ion-pairs with these species for ESI-MS analysis and the association constants (Kassoc) determined for these ion-pairs. Kassoc values were between 6.85 × 10² M⁻¹ and 3.56 × 10⁵ M⁻¹ with the linear IP-L-Imid; 1.89 ×10³ M⁻¹ and 1.05 × 10⁵ M⁻¹ with the trigonal IP-T-Imid ion-pairs; and 7.51×10² M⁻¹ and 4.91× 10⁴ M⁻¹ with the trigonal IP-T-Phos ion-pairs. The highest formation constants were obtained for S₃O₆²⁻ and the imidazolium-based linear ion-pairing reagent (IP-L-Imid), whereas the lowest were for IP-L-Imid: SO₄²⁻ ion-pair.

Universal critical behavior of the two-dimensional Ising spin glass

We use finite size scaling to study Ising spin glasses in two spatial dimensions. The issue of universality is addressed by comparing discrete and continuous probability distributions for the quenched random couplings. The sophisticated temperature dependency of the scaling fields is identified as the major obstacle that has impeded a complete analysis. Once temperature is relinquished in favor of the correlation length as the basic variable, we obtain a reliable estimation of the anomalous dimension and of the thermal critical exponent. Universality among binary and Gaussian couplings is confirmed to a high numerical accuracy.

Haptic discrimination of two-dimensional angles : influences of exploratory strategy

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

Levi-flat Minimal Hypersurfaces in Two-dimensional Complex Space Forms

The purpose of this article is to classify the real hypersurfaces in complex space forms of dimension 2 that are both Levi-flat and minimal. The main results are as follows: When the curvature of the complex space form is nonzero, there is a 1-parameter family of such hypersurfaces. Specifically, for each one-parameter subgroup of the isometry group of the complex space form, there is an essentially unique example that is invariant under this one-parameter subgroup. On the other hand, when the curvature of the space form is zero, i.e., when the space form is complex 2-space with its standard flat metric, there is an additional `exceptional' example that has no continuous symmetries but is invariant under a lattice of translations. Up to isometry and homothety, this is the unique example with no continuous symmetries.

Haptic discrimination of two-dimensional angles : influences of exploratory strategy

Mémoire numérisé par la Direction des bibliothèques de l'Université de Montréal.

Quantitative Analysis and Determination of Microcystin in water by Capillary Electrophoresis Mass Spectrometry

The presence of harmful algal blooms (HAB) is a growing concern in aquatic environments. Among HAB organisms, cyanobacteria are of special concern because they have been reported worldwide to cause environmental and human health problem through contamination of drinking water. Although several analytical approaches have been applied to monitoring cyanobacteria toxins, conventional methods are costly and time-consuming so that analyses take weeks for field sampling and subsequent lab analysis. Capillary electrophoresis (CE) becomes a particularly suitable analytical separation method that can couple very small samples and rapid separations to a wide range of selective and sensitive detection techniques. This paper demonstrates a method for rapid separation and identification of four microcystin variants commonly found in aquatic environments. CE coupled to UV and electrospray ionization time-of-flight mass spectrometry (ESI-TOF) procedures were developed. All four analytes were separated within 6 minutes. The ESI-TOF experiment provides accurate molecular information, which further identifies analytes.

Development of Advanced Capillary Electrophoresis Techniques with UV and Mass Spectrometry Detection for Forensic, Pharmaceutical and Environmental Applications

Capillary electrophoresis (CE) is a modern analytical technique, which is electrokinetic separation generated by high voltage and taken place inside the small capillaries. In this dissertation, several advanced capillary electrophoresis methods are presented using different approaches of CE and UV and mass spectrometry are utilized as the detection methods. Capillary electrochromatography (CEC), as one of the CE modes, is a recent developed technique which is a hybrid of capillary electrophoresis and high performance liquid chromatography (HPLC). Capillary electrochromatography exhibits advantages of both techniques. In Chapter 2, monolithic capillary column are fabricated using in situ photoinitiation polymerization method. The column was then applied for the separation of six antidepressant compounds. Meanwhile, a simple chiral separation method is developed and presented in Chapter 3. Beta cycodextrin was utilized to achieve the goal of chiral separation. Not only twelve cathinone analytes were separated, but also isomers of several analytes were enantiomerically separated. To better understand the molecular information on the analytes, the TOF-MS system was coupled with the CE. A sheath liquid and a partial filling technique (PFT) were employed to reduce the contamination of MS ionization source. Accurate molecular information was obtained. It is necessary to propose, develop, and optimize new techniques that are suitable for trace-level analysis of samples in forensic, pharmaceutical, and environmental applications. Capillary electrophoresis (CE) was selected for this task, as it requires lower amounts of samples, it simplifies sample preparation, and it has the flexibility to perform separations of neutral and charged molecules as well as enantiomers. Overall, the study demonstrates the versatility of capillary electrophoresis methods in forensic, pharmaceutical, and environmental applications.