Nanoscale Biosensors Based on Self-Propelled Objects

Understanding how an object moves along a path requires distinguishing between motion over a time span and motion at a precise moment. A useful example is a vehicle traveling along a straight and level path, where its position at any given time is known. The initial step in analyzing this motion is to measure how far the vehicle travels over a fixed time period. This measurement, called average velocity, is computed by dividing the total change in position by the duration over which the change...

A neutral atom consists of a positively charged nucleus surrounded by a negatively charged electron cloud. When placed in an external electric field, the external electric force pulls the electrons and nucleus apart, opposite to the intrinsic attraction between the nucleus and the electrons. The opposing forces balance each other with a slight shift between the center of masses of the nucleus and the electron cloud, resulting in a polarized atom. On the other hand, a few molecules, like water,...

Magnetic dipoles in magnetic materials are aligned when placed under an external magnetic field. For paramagnets and ferromagnets, dipole alignment occurs in the direction of the magnetic field. However, the dipoles align opposite to the field in the case of diamagnets. This state of magnetic polarization due to the external field is called magnetization. Magnetization is defined as the dipole moment per unit volume. It plays a similar role to polarization in electrostatics.
The vector...

The moment of inertia is a quantitative measure of the rotational inertia of an object. It is defined as the sum of the products obtained by multiplying the mass of each particle of matter in a given body by the square of its distance from the axis. The total moment of inertia for compound objects can be found by determining and adding the moment of inertia of individual components together.
Consider a child of mass (mc) 25 kg standing at a distance (rc) of 1 m from the axis of a rotating...

Consider a system comprising several point masses. The coordinates of the center of mass for this system can be expressed as the summation of the product of each mass and its position vector divided by the total mass:

In 1923, G. N. Lewis proposed a generalized definition of acid-base behavior in which acids and bases are identified by their ability to accept or to donate a pair of electrons and form a coordinate covalent bond.
A coordinate covalent bond (or dative bond) occurs when one of the atoms in the bond provides both bonding electrons. For example, a coordinate covalent bond occurs when a water molecule combines with a hydrogen ion to form a hydronium ion. A coordinate covalent bond also results when...