Dissipative Lévy random searches: universal behavior at low target density

Although gaseous molecules travel at tremendous speeds (hundreds of meters per second), they collide with other gaseous molecules and travel in many different directions before reaching the desired target. At room temperature, a gaseous molecule will experience billions of collisions per second. The mean free path is the average distance a molecule travels between collisions. The mean free path increases with decreasing pressure; in general, the mean free path for a gaseous molecule will be...

Newton's first law of motion states that a body at rest remains at rest, or if in motion, remains in motion at constant velocity, unless acted on by a net external force. It also states that there must be a cause for any change in velocity (a change in either magnitude or direction) to occur. This cause is a net external force. For example, consider what happens to an object sliding along a rough horizontal surface. The object quickly grinds to a halt, due to the net force of friction. If we...

Recall that a particle in equilibrium is one for which the external forces are balanced. Static equilibrium involves objects at rest, and dynamic equilibrium involves objects in motion without acceleration; but it is important to remember that these conditions are relative. For instance, an object may be at rest when viewed from one frame of reference, but that same object would appear to be in motion when viewed by someone moving at a constant velocity.
Newton's first law tells us about the...

A random variable is a single numerical value that indicates the outcome of a procedure. The concept of random variables is fundamental to the probability theory and was introduced by a Russian mathematician, Pafnuty Chebyshev, in the mid-nineteenth century.
Uppercase letters such as X or Y denote a random variable. Lowercase letters like x or y denote the value of a random variable. If X is a random variable, then X is written in words, and x is given as a number.
For example, let X = the...

To understand intra-specific interactions in populations, scientists measure the spatial arrangement of species individuals. This geographic arrangement is known as the species distribution or dispersion. Highly territorial species exhibit a uniform distribution pattern, in which individuals are spaced at relatively equal distances from one another. Species that are highly tied to particular resources, such as food or shelter, tend to concentrate around those resources, and thus exhibit a...

The uniform distribution is a continuous probability distribution of events with an equal probability of occurrence. This distribution is rectangular.Two essential properties of this distribution are The area under the rectangular shape equals 1. There is a correspondence between the probability of an event and the area under the curve.Further, the mean and standard deviation of the uniform distribution can be calculated when the lower and upper cut-offs, denoted as a and b,...