Travelling waves for a velocity–jump model of cell migration and proliferation

Cell invasion, characterised by moving fronts of cells, is an essential aspect of development, repair and disease. Typically, mathematical models of cell invasion are based on the Fisher–Kolmogorov equation. These traditional parabolic models can not be used to represent experimental measurements of individual cell velocities within the invading population since they imply that information propagates with infinite speed. To overcome this limitation we study combined cell motility and proliferation based on a velocity–jump process where information propagates with finite speed. The model treats the total population of cells as two interacting subpopulations: a subpopulation of left–moving cells, $L(x,t)$, and a subpopulation of right–moving cells, $R(x,t)$. This leads to a system of hyperbolic partial differential equations that includes a turning rate, $\Lambda \ge 0$, describing the rate at which individuals in the population change direction of movement. We present exact travelling wave solutions of the system of partial differential equations for the special case where $\Lambda = 0$ and in the limit that $\Lambda \to \infty$. For intermediate turning rates, $0 < \Lambda < \infty$, we analyse the travelling waves using the phase plane and we demonstrate a transition from smooth monotone travelling waves to smooth nonmonotone travelling waves as $\Lambda$ decreases through a critical value $\Lambda_{crit}$. We conclude by providing a qualitative comparison between the travelling wave solutions of our model and experimental observations of cell invasion. This comparison indicates that the small $\Lambda$ limit produces results that are consistent with experimental observations.

Waves for change : the role of the South Tarawa-based women's interests program in the decolonisation process of the Gilbert Islands

This thesis has created a space for women in the history of the decolonisation of the Gilbert Islands. It traces the historical development of the national women's interests program in the Republic of Kiribati (formerly of the Gilbert and Ellice Islands Colony (GEIC)) as it was implemented through a network of women's clubs during the 1960s and 1970s. This thesis has provided the first history and interpretation of the Indigenous women's interests movement as it impacted the Gilbert Islands. It offers a narrative of the movement in terms of three overlapping waves of women leaders, based on an analysis of fieldwork, archival research and interviews conducted on South Tarawa, Kiribati.

The impact of heat waves on children's health : a systematic review

Young children are thought to be particularly sensitive to heatwaves, but relatively less research attention has been paid to this field to date. A systematic review was conducted to elucidate the relationship between heat waves and children’s health. Literature published up to August 2012 were identified using the following MeSH terms and keywords: “heatwave”, “heat wave”, “child health”, “morbidity”, “hospital admission”, “emergency department visit”, “family practice”, “primary health care”, “death” and “mortality”. Of the 628 publications identified, 12 met the selection criteria. The existing literature does not consistently suggest that mortality among children increases significantly during heat waves, even though infants were associated with more heat-related deaths. Exposure to heat waves in the perinatal period may pose a threat to children’s health. Pediatric diseases or conditions associated with heat waves include renal disease, respiratory disease, electrolyte imbalance and fever. Future research should focus on how to develop a consistent definition of a heat wave from a children’s health perspective, identifying the best measure of children’s exposure to heat waves, exploring sensitive outcome measures to quantify the impact of heat waves on children, evaluating the possible impacts of heat waves on children’s birth outcomes, and understanding the differences in vulnerability to heat waves among children of different ages and from different income countries. Projection of the children’s disease burden caused by heat waves under climate change scenarios, and development of effective heat wave mitigation and adaptation strategies that incorporate other child protective health measures, are also strongly recommended.

Nonlinear effects of ionization on surface waves on a plasma-metal interface

Nonlinear effects associated with density modulation caused by wave-induced ionization in magnetized plasmas were studied. The ionizing surface waves propagate at the interface between the plasma and a metallic surface. It is shown that the ionization nonlinearity can be important for typical experimental conditions.

Interaction of transverse electromagnetic waves with counterpropagating surface waves at a plasma-dielectric interface

The nonlinear interaction of high-frequency transverse electromagnetic waves normally incident from a plasma region on to a dielectric with two surface waves (SWs) propagating in the opposite directions along the interface is studied. This interaction is found to be stable causing a slight modulation to the SWs in contrast to the decay instability for longitudinal plasma waves. The corresponding nonlinear frequency shift of the SWs is obtained and analyzed.

Excitation of surface plasmon-polariton waves at a semiconductor-metal interface

The excitation of surface plasmon-polariton waves propagating across an external magnetic field (Voigt geometry) in a semiconductor-metal structure by means of the attenuated total reflection method is investigated. The phase matching conditions for the surface waves excitation in the Kretchmann configuration are derived and analyzed. The effect of different nonlinearities on the excitation of the surface waves is studied as well.

Surface waves at the interface of a dusty plasma and a metallic wall

Electrostatic surface waves at the interface between a low-temperature nonisothermal dusty plasma and a metallic wall are investigated. The plasma contains massive negatively charged impurity or dust particles. It is shown that the impurities can significantly alter the characteristics and damping of the surface waves by reducing their phase velocity and causing charging-related damping.

Evolution of Langmuir waves in a plasma contaminated by variable-charge impurities

The propagation of Langmuir waves in nonisothermal plasmas contaminated by fine dust particles with variable charge is investigated for a self-consistent closed system. Dust charge relaxation, ionization, recombination, and collisional dissipation are taken into account. It is shown that the otherwise unstable coupling of the Langmuir and dust-charge relaxation modes becomes stable and the Langmuir waves are frequency down-shifted.

Dispersion properties of surface waves in a two-layer plasma structure bounded by a metal

The effect of the nonuniformity of the electron density on the dispersion properties of surface waves propagating in a direction transverse to an external magnetic field is studied for the model of a two-layer plasma structure bounded by a metal. It is shown that the spectra of the waves can be effectively controlled by varying the degree of nonuniformity of the density and the dimensions of the layers.

Self-interaction of magnetoplasma surface waves at a plasma-metal boundary

We investigate nonlinear self-interacting magnetoplasma surface waves (SW) propagating perpendicular to an external magnetic field at a plasma-metal boundary. We obtain the nonlinear dispersion equation and nonlinear Schroedinger equation for the envelope field of the SW. The solution to this equation is studied with regard to stability relative to longitudinal and transverse perturbations.

Self-action of high-frequency surface waves in a magnetoactive planar plasma waveguide

The self-modulation process of a high-frequency surface wave (SW) in a wave-guiding structure - a semibounded magnetoactive plasma and perfectly conducting metal wall - is considered for the weak nonlinearity approximation. Estimates are given for the contributions to the nonlinear frequency shift of the SW from the two principal self-action channels: via the generation of a signal of the doubled frequency and of static surface perturbations, arising as the result of the action of a ponderomotive force. Solutions for the field envelope of the nonlinear wave are examined with regard to their stability with respect to longitudinal and transverse perturbations.

Bistable regime of surface magnetoplasma waves excitation at a semiconductor-metal interface

The theoretical analysis of the bistability associated with the excitation of surface magnetoplasma waves (SWs) propagating across an external magnetic field at the semiconductor-metal interface by the attenuated total reflection (ATR) method is presented. The Kretschmann-Raether configuration of the ATR method is considered, i.e. a plane electromagnetic wave is incident onto a metal surface through a coupling prism. The third-order nonlinearity of the semiconductor medium is considered in the general form using the formalism of the third-order nonlinear susceptibilities and of the perturbation theory. The examples of the nonlinear mechanisms which influence the SW propagation are given. The analytical and numerical analyses show that the realization of bistable regimes of the SW excitation is possible. The SW amplitude values providing bistability in the structure are evaluated and are reasonably low to provide the experimental observation.

Self-modulation of surface waves at a plasma-metal interface

The ponderomotive force effects on surface waves at a plasma-metal interface are studied. The waves propagate across an external magnetic field parallel to the interface. It is shown that the account of the ponderomotive force can lead to the appearance of solitons, which are not possible when the second-harmonic and magnetic nonlinearities are concerned. © 1998 American Institute of Physics.

Self-interaction of high-frequency surface waves in magnetoactive plasma planar waveguide

The nonlinear effect of hf surface waves self-interaction in a magnetoactive planar plasma waveguide is studies. The waveguide structure under consideration can be formed by gaseous or semiconducting homogeneous plasma, which is limited by a perfectly conducting metal surface. The surface (localized near the surface) wave perturbations propagating on the plasma-metal boundary perpendicular to the constant external magnetic field, are investigated. The nonlinear frequency shift connected with interaction of the second harmonic and static surface perturbations with the main frequency wave, is determined using the approximation of weak nonlinearity. It is shown that the process of double-frequency signal generation is the dissipative one as a result of bulk wave excitation on the surface wave second harmonic.

Effect of heating nonlinearity on propagation of high-frequency surface waves at the semiconductor-metal interface

In approximation of weak heating influence of electron heating in the high-frequency surface wave field on propagation of surface wave (heating nonlinearity) is considered. It is shown that high-frequency surface wave propagates in direction perpendicular to the external magnetic field at the semiconductor-metal interface. A nonlinear dispersion equation is obtained and studied that allows to make conclusions about the contribution of heating nonlinearity to nonlinear process of considered interaction.