Exponential decayA quantity is subject to exponential decay if it decreases at a rate proportional to its current value. Symbolically, this process can be expressed by the following differential equation, where N is the quantity and λ (lambda) is a positive rate called the exponential decay constant, disintegration constant, rate constant, or transformation constant: The solution to this equation (see derivation below) is: where N(t) is the quantity at time t, N0 = N(0) is the initial quantity, that is, the quantity at time t = 0.
Ballistic missileA ballistic missile is a type of missile that uses projectile motion to deliver warheads on a target. These weapons are powered only during relatively brief periods—most of the flight is unpowered. Short-range ballistic missiles stay within the Earth's atmosphere, while intercontinental ballistic missiles (ICBMs) are launched on a sub-orbital flight. These weapons are in a distinct category from cruise missiles, which are aerodynamically guided in powered flight.
Particle decayIn particle physics, particle decay is the spontaneous process of one unstable subatomic particle transforming into multiple other particles. The particles created in this process (the final state) must each be less massive than the original, although the total invariant mass of the system must be conserved. A particle is unstable if there is at least one allowed final state that it can decay into. Unstable particles will often have multiple ways of decaying, each with its own associated probability.
Sub-orbital spaceflightA sub-orbital spaceflight is a spaceflight in which the spacecraft reaches outer space, but its trajectory intersects the surface of the gravitating body from which it was launched. Hence, it will not complete one orbital revolution, will not become an artificial satellite nor will it reach escape velocity. For example, the path of an object launched from Earth that reaches the Kármán line (about – above sea level), and then falls back to Earth, is considered a sub-orbital spaceflight.
Time constantIn physics and engineering, the time constant, usually denoted by the Greek letter τ (tau), is the parameter characterizing the response to a step input of a first-order, linear time-invariant (LTI) system. The time constant is the main characteristic unit of a first-order LTI system. In the time domain, the usual choice to explore the time response is through the step response to a step input, or the impulse response to a Dirac delta function input.
Exponential growthExponential growth is a process that increases quantity over time. It occurs when the instantaneous rate of change (that is, the derivative) of a quantity with respect to time is proportional to the quantity itself. Described as a function, a quantity undergoing exponential growth is an exponential function of time, that is, the variable representing time is the exponent (in contrast to other types of growth, such as quadratic growth).
Exponential functionThe exponential function is a mathematical function denoted by or (where the argument x is written as an exponent). Unless otherwise specified, the term generally refers to the positive-valued function of a real variable, although it can be extended to the complex numbers or generalized to other mathematical objects like matrices or Lie algebras. The exponential function originated from the notion of exponentiation (repeated multiplication), but modern definitions (there are several equivalent characterizations) allow it to be rigorously extended to all real arguments, including irrational numbers.
Intercontinental ballistic missileAn intercontinental ballistic missile (ICBM) is a ballistic missile with a range greater than , primarily designed for nuclear weapons delivery (delivering one or more thermonuclear warheads). Conventional, chemical, and biological weapons can also be delivered with varying effectiveness, but have never been deployed on ICBMs. Most modern designs support multiple independently targetable reentry vehicle (MIRVs), allowing a single missile to carry several warheads, each of which can strike a different target.
Vibronic couplingVibronic coupling (also called nonadiabatic coupling or derivative coupling) in a molecule involves the interaction between electronic and nuclear vibrational motion. The term "vibronic" originates from the combination of the terms "vibrational" and "electronic", denoting the idea that in a molecule, vibrational and electronic interactions are interrelated and influence each other. The magnitude of vibronic coupling reflects the degree of such interrelation.
Submarine-launched ballistic missileA submarine-launched ballistic missile (SLBM) is a ballistic missile capable of being launched from submarines. Modern variants usually deliver multiple independently targetable reentry vehicles (MIRVs), each of which carries a nuclear warhead and allows a single launched missile to strike several targets. Submarine-launched ballistic missiles operate in a different way from submarine-launched cruise missiles.
