Numerical methods for ordinary differential equationsNumerical methods for ordinary differential equations are methods used to find numerical approximations to the solutions of ordinary differential equations (ODEs). Their use is also known as "numerical integration", although this term can also refer to the computation of integrals. Many differential equations cannot be solved exactly. For practical purposes, however – such as in engineering – a numeric approximation to the solution is often sufficient. The algorithms studied here can be used to compute such an approximation.
Asymptotic expansionIn mathematics, an asymptotic expansion, asymptotic series or Poincaré expansion (after Henri Poincaré) is a formal series of functions which has the property that truncating the series after a finite number of terms provides an approximation to a given function as the argument of the function tends towards a particular, often infinite, point. Investigations by revealed that the divergent part of an asymptotic expansion is latently meaningful, i.e. contains information about the exact value of the expanded function.
Respiratory tractThe respiratory tract is the subdivision of the respiratory system involved with the process of respiration in mammals. The respiratory tract is lined with respiratory epithelium as respiratory mucosa. Air is breathed in through the nose to the nasal cavity, where a layer of nasal mucosa acts as a filter and traps pollutants and other harmful substances found in the air. Next, air moves into the pharynx, a passage that contains the intersection between the oesophagus and the larynx.
Emotion and memoryEmotion can have a powerful effect on humans and animals. Numerous studies have shown that the most vivid autobiographical memories tend to be of emotional events, which are likely to be recalled more often and with more clarity and detail than neutral events. The activity of emotionally enhanced memory retention can be linked to human evolution; during early development, responsive behavior to environmental events would have progressed as a process of trial and error.
Asymptotic analysisIn mathematical analysis, asymptotic analysis, also known as asymptotics, is a method of describing limiting behavior. As an illustration, suppose that we are interested in the properties of a function f (n) as n becomes very large. If f(n) = n2 + 3n, then as n becomes very large, the term 3n becomes insignificant compared to n2. The function f(n) is said to be "asymptotically equivalent to n2, as n → ∞". This is often written symbolically as f (n) ~ n2, which is read as "f(n) is asymptotic to n2".
MemoryMemory is the faculty of the mind by which data or information is encoded, stored, and retrieved when needed. It is the retention of information over time for the purpose of influencing future action. If past events could not be remembered, it would be impossible for language, relationships, or personal identity to develop. Memory loss is usually described as forgetfulness or amnesia. Memory is often understood as an informational processing system with explicit and implicit functioning that is made up of a sensory processor, short-term (or working) memory, and long-term memory.
Memory and agingAge-related memory loss, sometimes described as "normal aging" (also spelled "ageing" in British English), is qualitatively different from memory loss associated with types of dementia such as Alzheimer's disease, and is believed to have a different brain mechanism. Mild cognitive impairment Mild cognitive impairment (MCI) is a condition in which people face memory problems more often than that of the average person their age. These symptoms, however, do not prevent them from carrying out normal activities and are not as severe as the symptoms for Alzheimer's disease (AD).
SoundIn physics, sound is a vibration that propagates as an acoustic wave, through a transmission medium such as a gas, liquid or solid. In human physiology and psychology, sound is the reception of such waves and their perception by the brain. Only acoustic waves that have frequencies lying between about 20 Hz and 20 kHz, the audio frequency range, elicit an auditory percept in humans. In air at atmospheric pressure, these represent sound waves with wavelengths of to . Sound waves above 20 kHz are known as ultrasound and are not audible to humans.
Gas exchangeGas exchange is the physical process by which gases move passively by diffusion across a surface. For example, this surface might be the air/water interface of a water body, the surface of a gas bubble in a liquid, a gas-permeable membrane, or a biological membrane that forms the boundary between an organism and its extracellular environment. Gases are constantly consumed and produced by cellular and metabolic reactions in most living things, so an efficient system for gas exchange between, ultimately, the interior of the cell(s) and the external environment is required.
Acoustic metamaterialAn acoustic metamaterial, sonic crystal, or phononic crystal is a material designed to control, direct, and manipulate sound waves or phonons in gases, liquids, and solids (crystal lattices). Sound wave control is accomplished through manipulating parameters such as the bulk modulus β, density ρ, and chirality. They can be engineered to either transmit, or trap and amplify sound waves at certain frequencies. In the latter case, the material is an acoustic resonator.
