The dynamical process of a coronal transient associated with an eruptive prominence .2. Analytical solutions in finite regions

piston

First Biennial Ocean Climate Summit: Finding Solutions for San Francisco Bay Area’s Coast and Ocean. Proceedings of the Summit: April 29, 2008, Golden Gate Club, The Presidio San Francisco, California

Executive Summary: The marine environment plays a critical role in the amount of carbon dioxide (CO2) that remains within Earth’s atmosphere, but has not received as much attention as the terrestrial environment when it comes to climate change discussions, programs, and plans for action. It is now apparent that the oceans have begun to reach a state of CO2 saturation, no longer maintaining the “steady-state” carbon cycle that existed prior to the Industrial Revolution. The increasing amount of CO2 present within the oceans and the atmosphere has an effect on climate and a cascading effect on the marine environment. Potential physical effects of climate change within the marine environment, including ocean acidification, changes in wind and upwelling regimes, increasing global sea surface temperatures, and sea level rise, can lead to dramatic, fundamental changes within marine and coastal ecosystems. Altered ecosystems can result in changing coastal economies through a reduction in marine ecosystem services such as commercial fish stocks and coastal tourism. Local impacts from climate change should be a front line issue for natural resource managers, but they often feel too overwhelmed by the magnitude of this issue to begin to take action. They may not feel they have the time, funding, or staff to take on a challenge as large as climate change and continue to not act as a result. Already, natural resource managers work to balance the needs of humans and the economy with ecosystem biodiversity and resilience. Responsible decisions are made each day that consider a wide variety of stakeholders, including community members, agencies, non-profit organizations, and business/industry. The issue of climate change must be approached as a collaborative effort, one that natural resource managers can facilitate by balancing human demands with healthy ecosystem function through research and monitoring, education and outreach, and policy reform. The Scientific Expert Group on Climate Change in their 2007 report titled, “Confronting Climate Change: Avoiding the Unmanageable and Managing the Unavoidable” charged governments around the world with developing strategies to “adapt to ongoing and future changes in climate change by integrating the implications of climate change into resource management and infrastructure development”. Resource managers must make future management decisions within an uncertain and changing climate based on both physical and biological ecosystem response to climate change and human perception of and response to the issue. Climate change is the biggest threat facing any protected area today and resource managers must lead the charge in addressing this threat. (PDF has 59 pages.)

Black Holes, Cosmological Solutions, Future Singularities, and Their Thermodynamical Properties in Modified Gravity Theorie

54 p.

Small-scale fisheries development in Nigeria: Status, prospects, constraints/recommended solutions

The small-scale fisheries sector has been contributing immensely towards domestic fish production in Nigeria. Despite considerable contributions by the small-scale fisherman of Nigeria, with few exceptions, they continue to live at the margin of subsistence. This paper attempts to review the sector and propose strategies of integrated approach towards small-scale fisheries development in order to ensure that efforts at improving the rural fisheries succeed in over-coming identified constraints which include socio-cultural, political, economic, technological and other barriers

Exact solutions to collisionless external gas flows

This paper presents exact density, velocity and temperature solutions for two problems of collisionless gas flows around a flat plate or a spherical object. At any point off the object, the local velocity distribution function consists of two pieces of Maxwellian distributions: one for the free stream which is characterized by free stream density, temperature and average velocity, n0, T0, U0; and the other is for the wall and it is characterized by density at wall and wall temperature, nw,Tw. Directly integrating the distribution functions leads to complex but exact flowfield solutions. To validate these solutions, we perform numerical simulations with the direct simulation Monte Carlo (DSMC) method. In general, the analytical and numerical results are virtually identical. The evaluation of these analytical solutions only requires less than one minute while the DSMC simulations require several days.

Periodic solutions of integro-differential equations which arise in population dynamics

The problem of the existence and stability of periodic solutions of infinite-lag integra-differential equations is considered. Specifically, the integrals involved are of the convolution type with the dependent variable being integrated over the range (- ∞,t), as occur in models of population growth. It is shown that Hopf bifurcation of periodic solutions from a steady state can occur, when a pair of eigenvalues crosses the imaginary axis. Also considered is the existence of traveling wave solutions of a model population equation allowing spatial diffusion in addition to the usual temporal variation. Lastly, the stability of the periodic solutions resulting from Hopf bifurcation is determined with aid of a Floquet theory.

The first chapter is devoted to linear integro-differential equations with constant coefficients utilizing the method of semi-groups of operators. The second chapter analyzes the Hopf bifurcation providing an existence theorem. Also, the two-timing perturbation procedure is applied to construct the periodic solutions. The third chapter uses two-timing to obtain traveling wave solutions of the diffusive model, as well as providing an existence theorem. The fourth chapter develops a Floquet theory for linear integro-differential equations with periodic coefficients again using the semi-group approach. The fifth chapter gives sufficient conditions for the stability or instability of a periodic solution in terms of the linearization of the equations. These results are then applied to the Hopf bifurcation problem and to a certain population equation modeling periodically fluctuating environments to deduce the stability of the corresponding periodic solutions.

Exact solutions and transformation properties of nonlinear partial differential equations from general relativity

Various families of exact solutions to the Einstein and Einstein-Maxwell field equations of General Relativity are treated for situations of sufficient symmetry that only two independent variables arise. The mathematical problem then reduces to consideration of sets of two coupled nonlinear differential equations.

The physical situations in which such equations arise include: a) the external gravitational field of an axisymmetric, uncharged steadily rotating body, b) cylindrical gravitational waves with two degrees of freedom, c) colliding plane gravitational waves, d) the external gravitational and electromagnetic fields of a static, charged axisymmetric body, and e) colliding plane electromagnetic and gravitational waves. Through the introduction of suitable potentials and coordinate transformations, a formalism is presented which treats all these problems simultaneously. These transformations and potentials may be used to generate new solutions to the Einstein-Maxwell equations from solutions to the vacuum Einstein equations, and vice-versa.

The calculus of differential forms is used as a tool for generation of similarity solutions and generalized similarity solutions. It is further used to find the invariance group of the equations; this in turn leads to various finite transformations that give new, physically distinct solutions from old. Some of the above results are then generalized to the case of three independent variables.