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.

The stability of traveling wave solutions of parabolic equations

A method for determining by inspection the stability or instability of any solution u(t,x) = ɸ(x-ct) of any smooth equation of the form u_t = f(u_(xx),u_x,u where ∂/∂a f(a,b,c) > 0 for all arguments a,b,c, is developed. The connection between the mean wavespeed of solutions u(t,x) and their initial conditions u(0,x) is also explored. The mean wavespeed results and some of the stability results are then extended to include equations which contain integrals and also to include some special systems of equations. The results are applied to several physical examples.

Existence, uniqueness, and stability of solutions of a class of nonlinear partial differential equations

In this study we investigate the existence, uniqueness and asymptotic stability of solutions of a class of nonlinear integral equations which are representations for some time dependent non- linear partial differential equations. Sufficient conditions are established which allow one to infer the stability of the nonlinear equations from the stability of the linearized equations. Improved estimates of the domain of stability are obtained using a Liapunov Functional approach. These results are applied to some nonlinear partial differential equations governing the behavior of nonlinear continuous dynamical systems.

Some approximate solutions of dynamic problems in the linear theory of thin elastic shells

Some aspects of wave propagation in thin elastic shells are considered. The governing equations are derived by a method which makes their relationship to the exact equations of linear elasticity quite clear. Finite wave propagation speeds are ensured by the inclusion of the appropriate physical effects.

The problem of a constant pressure front moving with constant velocity along a semi-infinite circular cylindrical shell is studied. The behavior of the solution immediately under the leading wave is found, as well as the short time solution behind the characteristic wavefronts. The main long time disturbance is found to travel with the velocity of very long longitudinal waves in a bar and an expression for this part of the solution is given.

When a constant moment is applied to the lip of an open spherical shell, there is an interesting effect due to the focusing of the waves. This phenomenon is studied and an expression is derived for the wavefront behavior for the first passage of the leading wave and its first reflection.

For the two problems mentioned, the method used involves reducing the governing partial differential equations to ordinary differential equations by means of a Laplace transform in time. The information sought is then extracted by doing the appropriate asymptotic expansion with the Laplace variable as parameter.

Promoting innovative stormwater solutions for coastal plain communities

In 2008, the Center for Watershed Protection (CWP) surveyed seventy-three coastal plain communities to determine their current practices and need for watershed planning and low impact development (LID). The survey found that communities had varying watershed planning effectiveness and need better stormwater management, land use planning, and watershed management communication. While technical capacity is improving, stormwater programs are under staffed and innovative site designs may be prohibited under current regulations. In addition, the unique site constraints (e.g., sandy soils, low relief, tidal influence, vulnerability to coastal hazards, etc.) and lack of local examples are common LID obstacles along the coast (Vandiver and Hernandez, 2009). LID stormwater practices are an innovative approach to stormwater management that provide an alternative to structural stormwater practices, reduce runoff, and maintain or restores hydrology. The term LID is typically used to refer to the systematic application of small, distributed practices that replicate pre-development hydrologic functions. Examples of LID practices include: downspout disconnection, rain gardens, bioretention areas, dry wells, and vegetated filter strips. In coastal communities, LID practices have not yet become widely accepted or applied. The geographic focus for the project is the Atlantic and Gulf coastal plain province which includes nearly 250,000 square miles in portions of fifteen states from New Jersey to Texas (Figure 1). This project builds on CWP’s “Coastal Plain Watershed Network: Adapting, Testing, and Transferring Effective Tools to Protect Coastal Plain Watersheds” that developed a coastal land cover model, conducted a coastal plain community needs survey (results are online here: http://www.cwp.org/#survey), created a coastal watershed Network, and adapted the 8 Tools for Watershed Protection Framework for coastal areas. (PDF contains 4 pages)

Local solutions to local problems: A stormwater education collaborative

Currently completing its fifth year, the Coastal Waccamaw Stormwater Education Consortium (CWSEC) helps northeastern South Carolina communities meet National Pollutant Discharge Elimination System (NPDES) Phase II permit requirements for Minimum Control Measure 1 - Public Education and Outreach - and Minimum Control Measure 2 - Public Involvement. Coordinated by Coastal Carolina University, six regional organizations serve as core education providers to eight coastal localities including six towns and cities and two large counties. CWSEC recently finished a needs assessment to begin the process of strategizing for the second NPDES Phase II 5-year permit cycle in order to continue to develop and implement effective, results-oriented stormwater education and outreach programs to meet federal requirements and satisfy local environmental and economic needs. From its conception in May 2004, CWSEC set out to fulfill new federal Clean Water Act requirements associated with the NPDES Phase II Stormwater Program. Six small municipal separate storm sewer systems (MS4s) located within the Myrtle Beach Urbanized Area endorsed a coordinated approach to regional stormwater education, and participated in a needs assessment resulting in a Regional Stormwater Education Strategy and a Phased Education Work Plan. In 2005, CWSEC was formally established and the CWSEC’s Coordinator was hired. The Coordinator, who is also the Environmental Educator at Coastal Carolina University’s Waccamaw Watershed Academy, organizes six regional agencies who serve as core education providers for eight coastal communities. The six regional agencies working as core education providers to the member MS4s include Clemson Public Service and Carolina Clear Program, Coastal Carolina University’s Waccamaw Watershed Academy, Murrells Inlet 2020, North Inlet-Winyah Bay National Estuarine Research Reserve’s Coastal Training and Public Education Programs, South Carolina Sea Grant Consortium, and Winyah Rivers Foundation’s Waccamaw Riverkeeper®. CWSEC’s organizational structure results in a synergy among the education providers, achieving greater productivity than if each provider worked separately. The member small MS4s include City of Conway, City of North Myrtle Beach, City of Myrtle Beach, Georgetown County, Horry County, Town of Atlantic Beach, Town of Briarcliffe Acres, and Town of Surfside Beach. Each MS4 contributes a modest annual fee toward the salary of the Coordinator and operational costs. (PDF contains 3 pages)

Sustainable energy solutions for irrigation and harvesting in developing countries

One of the critical problems currently being faced by agriculture industry in developing nations is the alarming rate of groundwater depletion. Irrigation accounts for over 70% of the total groundwater withdrawn everyday. Compounding this issue is the use of polluting diesel generators to pump groundwater for irrigation. This has made irrigation not only the biggest consumer of groundwater but also one of the major contributors to green house gases. The aim of this thesis is to present a solution to the energy-water nexus. To make agriculture less dependent on fossil fuels, the use of a solar-powered Stirling engine as the power generator for on-farm energy needs is discussed. The Stirling cycle is revisited and practical and ideal Stirling cycles are compared. Based on agricultural needs and financial constraints faced by farmers in developing countries, the use of a Fresnel lens as a solar-concentrator and a Beta-type Stirling engine unit is suggested for sustainable power generation on the farms. To reduce the groundwater consumption and to make irrigation more sustainable, the conceptual idea of using a Stirling engine in drip irrigation is presented. To tackle the shortage of over 37 million tonnes of cold-storage in India, the idea of cost-effective solar-powered on-farm cold storage unit is discussed.