Onsite sewage facilityOnsite sewage facilities (OSSF), also called septic systems, are wastewater systems designed to treat and dispose of effluent on the same property that produces the wastewater, in areas not served by public sewage infrastructure. A septic tank and drainfield combination is a fairly common type of on-site sewage facility in the Western world. OSSFs account for approximately 25% of all domestic wastewater treatment in the US. Onsite sewage facilities may also be based on small-scale aerobic and biofilter units, membrane bioreactors or sequencing batch reactors.
Renewable energyRenewable energy is energy from renewable resources that are naturally replenished on a human timescale. Renewable resources include sunlight, wind, the movement of water, and geothermal heat. Although most renewable energy sources are sustainable, some are not. For example, some biomass sources are considered unsustainable at current rates of exploitation. Renewable energy is often used for electricity generation, heating and cooling.
Differential equationIn mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relations are common; therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology.
Sustainable energyEnergy is sustainable if it "meets the needs of the present without compromising the ability of future generations to meet their own needs." Most definitions of sustainable energy include considerations of environmental aspects such as greenhouse gas emissions and social and economic aspects such as energy poverty. Renewable energy sources such as wind, hydroelectric power, solar, and geothermal energy are generally far more sustainable than fossil fuel sources.
Linear differential equationIn mathematics, a linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form where a0(x), ..., an(x) and b(x) are arbitrary differentiable functions that do not need to be linear, and y′, ..., y(n) are the successive derivatives of an unknown function y of the variable x. Such an equation is an ordinary differential equation (ODE).
Anaerobic respirationAnaerobic respiration is respiration using electron acceptors other than molecular oxygen (O2). Although oxygen is not the final electron acceptor, the process still uses a respiratory electron transport chain. In aerobic organisms undergoing respiration, electrons are shuttled to an electron transport chain, and the final electron acceptor is oxygen. Molecular oxygen is an excellent electron acceptor. Anaerobes instead use less-oxidizing substances such as nitrate (NO3-), fumarate (C4H2O42-), sulfate (SO42-), or elemental sulfur (S).
Energy return on investmentIn energy economics and ecological energetics, energy return on investment (EROI), also sometimes called energy returned on energy invested (ERoEI), is the ratio of the amount of usable energy (the exergy) delivered from a particular energy resource to the amount of exergy used to obtain that energy resource. Arithmetically the EROI can be defined as: When the EROI of a source of energy is less than or equal to one, that energy source becomes a net "energy sink", and can no longer be used as a source of energy.
Homogeneous differential equationA differential equation can be homogeneous in either of two respects. A first order differential equation is said to be homogeneous if it may be written where f and g are homogeneous functions of the same degree of x and y. In this case, the change of variable y = ux leads to an equation of the form which is easy to solve by integration of the two members. Otherwise, a differential equation is homogeneous if it is a homogeneous function of the unknown function and its derivatives.
Stability theoryIn mathematics, stability theory addresses the stability of solutions of differential equations and of trajectories of dynamical systems under small perturbations of initial conditions. The heat equation, for example, is a stable partial differential equation because small perturbations of initial data lead to small variations in temperature at a later time as a result of the maximum principle. In partial differential equations one may measure the distances between functions using Lp norms or the sup norm, while in differential geometry one may measure the distance between spaces using the Gromov–Hausdorff distance.
Lyapunov stabilityVarious types of stability may be discussed for the solutions of differential equations or difference equations describing dynamical systems. The most important type is that concerning the stability of solutions near to a point of equilibrium. This may be discussed by the theory of Aleksandr Lyapunov. In simple terms, if the solutions that start out near an equilibrium point stay near forever, then is Lyapunov stable. More strongly, if is Lyapunov stable and all solutions that start out near converge to , then is said to be asymptotically stable (see asymptotic analysis).
