The importance of different timings of excitatory and inhibitory pathways in neural field models

In this paper we consider a neural field model comprised of two distinct populations of neurons, excitatory and inhibitory, for which both the velocities of action potential propagation and the time courses of synaptic processing are different. Using recently-developed techniques we construct the Evans function characterising the stability of both stationary and travelling wave solutions, under the assumption that the firing rate function is the Heaviside step. We find that these differences in timing for the two populations can cause instabilities of these solutions, leading to, for example, stationary breathers. We also analyse $quot;anti-pulses,$quot; a novel type of pattern for which all but a small interval of the domain (in moving coordinates) is active. These results extend previous work on neural fields with space dependent delays, and demonstrate the importance of considering the effects of the different time-courses of excitatory and inhibitory neural activity.

A bidomain threshold model of propagating calcium waves

We present a bidomain fire-diffuse-fire model that facilitates mathematical analysis of propagating waves of elevated intracellular calcium (Ca) in living cells. Modelling Ca release as a threshold process allows the explicit construction of travelling wave solutions to probe the dependence of Ca wave speed on physiologically important parameters such as the threshold for Ca release from the endoplasmic reticulum (ER) to the cytosol, the rate of Ca resequestration from the cytosol to the ER, and the total [Ca] (cytosolic plus ER). Interestingly, linear stability analysis of the bidomain fire-diffuse-fire model predicts the onset of dynamic wave instabilities leading to the emergence of Ca waves that propagate in a back-and-forth manner. Numerical simulations are used to confirm the presence of these so-called "tango waves" and the dependence of Ca wave speed on the total [Ca]. The original publication is available at www.springerlink.com (Journal of Mathematical Biology)

Instabilities in threshold-diffusion equations with delay

The introduction of delays into ordinary or partial differential equation models is well known to facilitate the production of rich dynamics ranging from periodic solutions through to spatio-temporal chaos. In this paper we consider a class of scalar partial differential equations with a delayed threshold nonlinearity which admits exact solutions for equilibria, periodic orbits and travelling waves. Importantly we show how the spectra of periodic and travelling wave solutions can be determined in terms of the zeros of a complex analytic function. Using this as a computational tool to determine stability we show that delays can have very different effects on threshold systems with negative as opposed to positive feedback. Direct numerical simulations are used to confirm our bifurcation analysis, and to probe some of the rich behaviour possible for mixed feedback.

Sensitisation waves in a bidomain fire-diffuse-fire model of intracellular Ca²⁺ dynamics

We present a bidomain threshold model of intracellular calcium (Ca²⁺) dynamics in which, as suggested by recent experiments, the cytosolic threshold for Ca²⁺ liberation is modulated by the Ca²⁺ concentration in the releasing compartment. We explicitly construct stationary fronts and determine their stability using an Evans function approach. Our results show that a biologically motivated choice of a dynamic threshold, as opposed to a constant threshold, can pin stationary fronts that would otherwise be unstable. This illustrates a novel mechanism to stabilise pinned interfaces in continuous excitable systems. Our framework also allows us to compute travelling pulse solutions in closed form and systematically probe the wave speed as a function of physiologically important parameters. We find that the existence of travelling wave solutions depends on the time scale of the threshold dynamics, and that facilitating release by lowering the cytosolic threshold increases the wave speed. The construction of the Evans function for a travelling pulse shows that of the co-existing fast and slow solutions the slow one is always unstable.

Neural fields with sigmoidal firing rates: approximate solutions

Many tissue level models of neural networks are written in the language of nonlinear integro-differential equations. Analytical solutions have only been obtained for the special case that the nonlinearity is a Heaviside function. Thus the pursuit of even approximate solutions to such models is of interest to the broad mathematical neuroscience community. Here we develop one such scheme, for stationary and travelling wave solutions, that can deal with a certain class of smoothed Heaviside functions. The distribution that smoothes the Heaviside is viewed as a fundamental object, and all expressions describing the scheme are constructed in terms of integrals over this distribution. The comparison of our scheme and results from direct numerical simulations is used to highlight the very good levels of approximation that can be achieved by iterating the process only a small number of times.

In Situ Characterization of Optical Absorption by Carbonaceous Aerosols: Calibration and Measurement

Light absorption by aerosols has a great impact on climate change. A Photoacoustic spectrometer (PA) coupled with aerosol-based classification techniques represents an in situ method that can quantify the light absorption by aerosols in a real time, yet significant differences have been reported using this method versus filter based methods or the so-called difference method based upon light extinction and light scattering measurements. This dissertation focuses on developing calibration techniques for instruments used in measuring the light absorption cross section, including both particle diameter measurements by the differential mobility analyzer (DMA) and light absorption measurements by PA. Appropriate reference materials were explored for the calibration/validation of both measurements. The light absorption of carbonaceous aerosols was also investigated to provide fundamental understanding to the absorption mechanism. The first topic of interest in this dissertation is the development of calibration nanoparticles. In this study, bionanoparticles were confirmed to be a promising reference material for particle diameter as well as ion-mobility. Experimentally, bionanoparticles demonstrated outstanding homogeneity in mobility compared to currently used calibration particles. A numerical method was developed to calculate the true distribution and to explain the broadening of measured distribution. The high stability of bionanoparticles was also confirmed. For PA measurement, three aerosol with spherical or near spherical shapes were investigated as possible candidates for a reference standard: C60, copper and silver. Comparisons were made between experimental photoacoustic absorption data with Mie theory calculations. This resulted in the identification of C60 particles with a mobility diameter of 150 nm to 400 nm as an absorbing standard at wavelengths of 405 nm and 660 nm. Copper particles with a mobility diameter of 80 nm to 300 nm are also shown to be a promising reference candidate at wavelength of 405 nm. The second topic of this dissertation focuses on the investigation of light absorption by carbonaceous particles using PA. Optical absorption spectra of size and mass selected laboratory generated aerosols consisting of black carbon (BC), BC with non-absorbing coating (ammonium sulfate and sodium chloride) and BC with a weakly absorbing coating (brown carbon derived from humic acid) were measured across the visible to near-IR (500 nm to 840 nm). The manner in which BC mixed with each coating material was investigated. The absorption enhancement of BC was determined to be wavelength dependent. Optical absorption spectra were also taken for size and mass selected smoldering smoke produced from six types of commonly seen wood in a laboratory scale apparatus.

Chemical Reaction Dynamics of the Liquid/Vapor Interface Studied by Mass Spectrometry

This thesis presents investigations of chemical reactions occurring at the liquid/vapor interface studied using novel sampling methodologies coupled with detection by mass spectrometry. Chapters 2 and 3 utilize the recently developed technique of field-induced droplet ionization mass spectrometry (FIDI-MS), in which the application of a strong electric field to a pendant microliter droplet results in the ejection of highly charged progeny droplets from the liquid surface. In Chapter 2, this method is employed to study the base-catalyzed dissociation of a surfactant molecule at the liquid/vapor interface upon uptake of ammonia from the gas phase. This process is observed to occur without significant modulation of the bulk solution pH, suggesting a transient increase in surface pH following the uptake of gaseous ammonia. Chapter 3 presents real-time studies of the oxidation of the model tropospheric organic compound glycolaldehyde by photodissociation of iron (III) oxalate complexes. The oxidation products of glycolaldehyde formed in this process are identified, and experiments in a deoxygenated environment identify the role of oxygen in the oxidation pathway and in the regeneration of iron (III) following photo-initiated reduction. Chapter 4 explores alternative methods for the study of heterogeneous reaction processes by mass spectrometric sampling from liquid surfaces. Bursting bubble ionization (BBI) and interfacial sampling with an acoustic transducer (ISAT) generate nanoliter droplets from a liquid surface that can be sampled via the atmospheric pressure interface of a mass spectrometer. Experiments on the oxidation of oleic acid by ozone using ISAT are also presented. Chapters 5 and 6 detail mechanistic studies and applications of free-radical-initiated peptide sequencing (FRIPS), a technique employing gas-phase free radical chemistry to the sequencing of peptides and proteins by mass spectrometry. Chapter 5 presents experimental and theoretical studies on the anomalous mechanism of dissociation observed in the presence of serine and threonine residues in peptides. Chapter 6 demonstrates the combination of FRIPS with ion mobility-mass spectrometry (IM-MS) for the separation of isomeric peptides.

Improved Dynamic Headspace Sampling and Detection using Capillary Microextraction of Volatiles Coupled to Gas Chromatography Mass Spectrometry

Sampling and preconcentration techniques play a critical role in headspace analysis in analytical chemistry. My dissertation presents a novel sampling design, capillary microextraction of volatiles (CMV), that improves the preconcentration of volatiles and semivolatiles in a headspace with high throughput, near quantitative analysis, high recovery and unambiguous identification of compounds when coupled to mass spectrometry. The CMV devices use sol-gel polydimethylsiloxane (PDMS) coated microglass fibers as the sampling/preconcentration sorbent when these fibers are stacked into open-ended capillary tubes. The design allows for dynamic headspace sampling by connecting the device to a hand-held vacuum pump. The inexpensive device can be fitted into a thermal desorption probe for thermal desorption of the extracted volatile compounds into a gas chromatography-mass spectrometer (GC-MS). The performance of the CMV devices was compared with two other existing preconcentration techniques, solid phase microextraction (SPME) and planar solid phase microextraction (PSPME). Compared to SPME fibers, the CMV devices have an improved surface area and phase volume of 5000 times and 80 times, respectively. One (1) minute dynamic CMV air sampling resulted in similar performance as a 30 min static extraction using a SPME fiber. The PSPME devices have been fashioned to easily interface with ion mobility spectrometers (IMS) for explosives or drugs detection. The CMV devices are shown to offer dynamic sampling and can now be coupled to COTS GC-MS instruments. Several compound classes representing explosives have been analyzed with minimum breakthrough even after a 60 min. sampling time. The extracted volatile compounds were retained in the CMV devices when preserved in aluminum foils after sampling. Finally, the CMV sampling device were used for several different headspace profiling applications which involved sampling a shipping facility, six illicit drugs, seven military explosives and eighteen different bacteria strains. Successful detection of the target analytes at ng levels of the target signature volatile compounds in these applications suggests that the CMV devices can provide high throughput qualitative and quantitative analysis with high recovery and unambiguous identification of analytes.

Preliminary study of a niobium quarter-wave prototype cavity for a heavy-ion superconducting linac

Superconducting quarter-wave resonators, due to their compactness and their convenient shape for tuning and coupling, are very attractive for low-beta beam acceleration. In this paper, two types of cavities with different geometry have been numerically simulated: the first type with larger capacitive load in the beam line and the second type of lollipop-shape for 100 MHz, beta=0.06 beams; then the relative electromagnetic parameters and geometric sizes have been compared. It is found that the second type, whose structural design is optimized with the conical stem and shaping drift-tube, can support the better accelerating performance. At the end of the paper, some structural deformation effects on frequency shifts and appropriate solutions have been discussed.

Nonlinear perpendicular propagation of ordinary mode electromagnetic wave packets in pair plasmas and electron-positron-ion plasmas

The nonlinear amplitude modulation of electromagnetic waves propagating in pair plasmas, e.g., electron-positron or fullerene pair-ion plasmas, as well as three-component pair plasmas, e.g., electron-positron-ion plasmas or doped (dusty) fullerene pair-ion plasmas, assuming wave propagation in a direction perpendicular to the ambient magnetic field, obeying the ordinary (O-) mode dispersion characteristics. Adopting a multiple scales (reductive perturbation) technique, a nonlinear Schrodinger-type equation is shown to govern the modulated amplitude of the magnetic field (perturbation). The conditions for modulation instability are investigated, in terms of relevant parameters. It is shown that localized envelope modes (envelope solitons) occur, of the bright- (dark-) type envelope solitons, i.e., envelope pulses (holes, respectively), for frequencies below (above) an explicit threshold. Long wavelength waves with frequency near the effective pair plasma frequency are therefore unstable, and may evolve into bright solitons, while higher frequency (shorter wavelength) waves are stable, and may propagate as envelope holes.(c) 2007 American Institute of Physics.

Size, electrophoretic mobility, and ion dissociation of vesicles prepared with synthetic amphiphiles

Vesicles prepared with synthetic amphiphiles (dioctadecyldimethylammonium bromide and chloride, dihexadecyl phosphate and its sodium salt) were obtained by sonication, ethanol injections, and chloroform injections. The hydrodynamic diameter of vesicles (Dh), estimated from the diffusivity measured by quasielastic light scattering, ranged from 230 to 3000 Å. The electrophoretic mobility (Um) was measured by free-flow electrophoresis. The zeta potential (ζ) and the degree of counterion dissociation (α) of the vesicles were calculated from Um and conductivity data, α decreased with increasing Dh of the vesicles, probably due to the decreasing headgroup area and the increasing counterion association needed to relax the surface electrostatic potential. The electrophoretic mobility was also calculated (Uc) according to an impenetrable, nonconducting sphere model with a spherically symmetric charge distribution approximation. Within the limits of the experimental error(s) of the (different) methods employed and the assumptions made in the calculations, the fact that the Um/Uc ratio ranged from 1.3 to 7.5 was considered to be a good agreement between the calculated and the experimental values. © 1990 American Chemical Society.