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Any of several leguminous plants, or their seeds, long utilized as food by humans or livestock. There are more than 40,000 varieties of beans, with only a small number of these being mass-produced for human or animal consumption. In particular,…

The branch of biological science that embraces the study of plants and plant life. Botany is the scientific study of plants (see illustration), encompassing investigations of plant anatomy, physiology, genetics, phylogeny, ecology, pathology, and…

Any interaction between objects that causes motion. Fundamentally, objects interact through the four known physical forces: gravity, electromagnetism, and the strong and weak nuclear interactions. In practice, however, many of the forces worked with…

The highest-energy form of electromagnetic radiation, or light. The energies of gamma rays range from a few kiloelectronvolts [(keV), where the prefix kilo (k) means 103] to several hundreds of megaelectronvolts [(MeV), where the prefix mega (M)…

Electromagnetic radiation whose wavelengths are in the range from about 0.75 micrometer (μm) to 1 millimeter (mm). Infrared radiation (Fig. 1) is outside the range of visible light and cannot be seen with the unaided eye. Infrared radiation was…

The change in the position of an object in a physical space over time. A familiarly encountered phenomenon, motion (see illustration) occurs on all levels of reality, from the constant movements of subatomic particles (conveyed by probabilities of…

An annual leafy leguminous vine, Pisum sativum (order Fabales), cultivated for its smooth or wrinkled, round edible seeds, which are borne in dehiscent pods. The garden pea (Fig. 1) is one of the world's oldest cultivated crops. It is a native of…

In physics, the transference of energy that occurs when a force is applied to a body that is moving in such a way that the force has a component in the direction of the body's motion. Work is accordingly done on a weight that is being lifted (Fig.…

A departure of an optical image-forming system from ideal behavior. Ideally, such a system will produce a unique image point corresponding to each object point. In addition, every straight line in the object space will have as its corresponding…

The time rate of change of velocity. Acceleration is a physics term that measures the rate of change of velocity per unit of time. Because velocity is a directed or vector quantity involving both magnitude and direction, a velocity may change by a…

The technique of measuring the magnitude and direction of acceleration. Measurement of acceleration (see illustration) includes translational acceleration with tangential and radial components and angular acceleration. Acceleration The May 16, 2011…

The use of a combination of mass spectrometers and an accelerator to measure the natural abundances of very rare radioactive isotopes. These abundances are frequently lower than parts per trillion. The most important applications of accelerator mass…

An instrument that utilizes focused acoustic waves to produce images of surface and subsurface features in materials, and to measure elastic properties on a microscopic scale. It has been used to image and measure local elastic properties in metals,…

Unwanted sound. Noise control is the process of obtaining an acceptable noise environment for people in different situations. These definitions and the words “unwanted” and “acceptable” suggest that criteria need to be established to determine when…

The discipline of acoustic phonetics can be narrowly defined as the study of the acoustic output of the vocal tract for speech, but ultimately it encompasses much more. Acoustic phonetics makes direct contact with, and in many cases is the…

A device to measure the acoustic power or intensity of a sound beam by means of the force or torque that the beam exerts on an inserted object or interface. The underlying theory involves the concept of radiation pressure, which is the…

A discipline that deals generally with the extraction of information from acoustic signals in the presence of noise and uncertainty. Acoustic signal processing has expanded from the improvement of music and speech sounds and a tool to search for oil…

The ratio of the current to the voltage in an alternating-current circuit.In terms of complex current I and voltageV, the admittance of a circuit is given by Eq. (1), and is related to the impedance of the circuit Z by Eq. (2). Y is a complex number…

The force retarding an airplane, especially in supersonic flight, as a consequence of the formation of shock waves. Although the physical laws governing flight at speeds in excess of the speed of sound are the same as those for subsonic flight, the…

An informal assemblage of predominantly aquatic organisms that carry out oxygen-evolving photosynthesis, but lack specialized water-conducting and food-conducting tissues. Algae (Fig. 1) may be either prokaryotic organisms (lacking an organized…

The branch of mathematics dealing with the solution of equations. These equations involve unknowns, or variables, along with fixed numbers from a specified system (Fig. 1). The origins of algebra were based on the need to develop equations that…

The study of zero sets of polynomial equations. Examples of zero sets of polynomial equations studied in algebraic geometry are the parabola y − x2 = 0, thought of as sitting in the (x, y)-plane, and the locus of all points (t, t2, t3, t4), which is…

A natural process in which harmful or beneficial effects are caused by secondary metabolites that spread from a donor organism to a recipient and are produced by plants, algae, bacteria, and fungi. Allelopathy is a key ecological process and has…

Helium nuclei, which are abundant throughout the universe both as radioactive-decay products and as key participants in stellar fusion reactions. Alpha particles can also be generated in the laboratory, either by ionizing helium or from nuclear…

The analog of linear momentum for rotational motion. A particle with mass m moving with velocity v has linear momentum p = m v (Note: This article follows the convention of using bold, non-italicized variables for vectors and using non-bold,…

A deciduous tree (genus Malus) in the order Rosales, which produces an edible, simple, fleshy, pome-type fruit. Apples (Fig. 1) belong to the family Rosaceae, which includes many other deciduous fruits, including pears, peaches, and cherries. There…

An analytical technique for determining the composition of a sample in terms of the chemical elements present and their quantities or concentrations. Unlike other methods of elemental analysis, however, the sample is decomposed into its constituent…

A large tropical plant of the genus Musa and its edible fruit. The banana belongs to the family Musaceae (order Zingiberales). The banana of commerce (Musa acuminata), which is believed to have originated in the Asian tropics, was one of the…

A sound-reproducing system in which sound is recorded or transmitted by using two microphones mounted at the ears of a dummy human head. To preserve the binaural effect, the sound must be monitored by a listener wearing a set of earphones…

A process in which a liquid phase is converted into a vapor phase. The energy for phase change is generally supplied by the surface on which boiling occurs. Boiling differs from evaporation at predetermined vapor/gas–liquid interfaces because it…

A device for detecting and measuring small amounts of thermal radiation. The bolometer is a simple electric circuit, the essential element of which is a slab of material with an electrical property, most often resistance, that changes with…

A constant occurring in practically all statistical formulas and having a numerical value of 1.3807 × 10−23 joule/K. It is represented by the letter k. If the temperature T is measured from absolute zero, the quantity kT has the dimensions of an…

To describe a system consisting of a large number of particles in a physically useful manner, recourse must be had to so-called statistical procedures. If the mechanical laws operating in the system are those of classical mechanics, and if the…

An equation which is used to study the nonequilibrium behavior of a collection of particles. In a state of equilibrium a gas of particles has uniform composition and constant temperature and density. If the gas is subjected to a temperature…

A circuit composed of a source and four impedances that is used in the measurement of a wide range of physical quantities. The bridge circuit is useful in measuring impedances (resistors, capacitors, and inductors) and in converting signals from…

The resultant vertical force exerted on a body by a static fluid in which the body is submerged or floating. Buoyancy is the upward force exerted by a fluid (liquid or gas) on a body that is placed within it (see illustration). The buoyant force FB…

The branch of mathematics dealing with two fundamental operations, differentiation and integration, which are carried out on functions. The subject of calculus (Fig. 1), as traditionally developed in college textbooks, is partly an elementary…

A genus comprising yeasts that cause a variety of human diseases referred to as candidiasis. All Candida species are single-celled yeasts (fungal organisms) that are ovoid in shape and 3–5 μm in size, and they multiply by a process called budding.…

A set of generalized coordinates of a classical dynamical system together with their conjugate momenta, and transformations among these coordinates and momenta that leave the form of Hamilton's equations of motion unchanged. Explanation of some of…

A heart-shaped curve generated by a point of a circle that rolls (without slipping) on a fixed circle of the same diameter. In point-wise construction of the curve, let O be a fixed point of a circle C of diameter a, and Q a variable point of C. Lay…

A biennial umbellifer (Daucus carota) of Asiatic and Mediterranean origin belonging to the plant order Apiales. The carrot (Daucus carota; Fig. 1) is grown for its edible roots, which are eaten raw or cooked. Cultivated forms of the root vegetable…

A theory of mathematical structure in which smooth continuous inputs lead to discontinuous responses. Water suddenly boils, ice melts, a building crashes to the ground, or the earth unexpectedly buckles and quakes. The French mathematician René Thom…

The name given to the electrons originating at the cathodes of gaseous discharge devices. The term has now been extended to include low-pressure devices such as cathode-ray tubes. Furthermore, cathode rays are now used to designate electron beams…

A luminescence resulting from the bombardment of a substance with an electron (cathode-ray) beam. The principal applications of cathodoluminescence are in television, computer, radar, and oscilloscope displays. In these a thin layer of luminescent…

In physics, the requirement that interactions in any spacetime region can influence the evolution of the system only at subsequent times; that is, past events are causes of future events, and future events can never be the causes of events in the…

The formation of vapor- or gas-filled cavities in liquids. If understood in this broad sense, cavitation includes the familiar phenomenon of bubble formation when water is brought to a boil under constant pressure and the effervescence of champagne…

An enclosure capable of resounding or resonating and thereby intensifying sound tones or electromagnetic waves. Resonance is the phenomenon which results when the frequency of the impressed driving force is the same as the natural vibration of the…

A set of four numbers used to specify the orientation of a body, or equivalently, the rotation R which produces that orientation, starting from some reference orientation. They can be expressed in terms of the Euler angles ψ, θ, and ϕ, as in Eqs.…

Cameras in mobile phones or smartphones that can capture images and videos.The cellphone, the world’s favorite must-have gadget, has been with us for nearly a half-century, while experiencing continuous and often phenomenal improvements. Much of the…

A fixed point in a body of matter through which the resultant force of gravitational attraction acts. The center of gravity is an imaginary point in any given body that is convenient when performing calculations and conducting mechanical studies…