Smoothed-particle hydrodynamicsSmoothed-particle hydrodynamics (SPH) is a computational method used for simulating the mechanics of continuum media, such as solid mechanics and fluid flows. It was developed by Gingold and Monaghan and Lucy in 1977, initially for astrophysical problems. It has been used in many fields of research, including astrophysics, ballistics, volcanology, and oceanography. It is a meshfree Lagrangian method (where the co-ordinates move with the fluid), and the resolution of the method can easily be adjusted with respect to variables such as density.
Meshfree methodsIn the field of numerical analysis, meshfree methods are those that do not require connection between nodes of the simulation domain, i.e. a mesh, but are rather based on interaction of each node with all its neighbors. As a consequence, original extensive properties such as mass or kinetic energy are no longer assigned to mesh elements but rather to the single nodes. Meshfree methods enable the simulation of some otherwise difficult types of problems, at the cost of extra computing time and programming effort.
Continuous uniform distributionIn probability theory and statistics, the continuous uniform distributions or rectangular distributions are a family of symmetric probability distributions. Such a distribution describes an experiment where there is an arbitrary outcome that lies between certain bounds. The bounds are defined by the parameters, and which are the minimum and maximum values. The interval can either be closed (i.e. ) or open (i.e. ). Therefore, the distribution is often abbreviated where stands for uniform distribution.
Femoroacetabular impingementFemoroacetabular impingement (FAI) is a condition involving one or more anatomical abnormalities of the hip joint, which is a ball and socket joint. It is a common cause of hip pain and discomfort in young and middle-aged adults. It occurs when the ball shaped femoral head contacts the acetabulum abnormally or does not permit a normal range of motion in the acetabular socket. Damage can occur to the articular cartilage, or labral cartilage (soft tissue, ring-shaped bumper of the socket), or both.
Plume (fluid dynamics)In hydrodynamics, a plume or a column is a vertical body of one fluid moving through another. Several effects control the motion of the fluid, including momentum (inertia), diffusion and buoyancy (density differences). Pure jets and pure plumes define flows that are driven entirely by momentum and buoyancy effects, respectively. Flows between these two limits are usually described as forced plumes or buoyant jets. "Buoyancy is defined as being positive" when, in the absence of other forces or initial motion, the entering fluid would tend to rise.
HipIn vertebrate anatomy, hip (or coxa in medical terminology; : coxae) refers to either an anatomical region or a joint. The hip region is located lateral and anterior to the gluteal region, inferior to the iliac crest, and overlying the greater trochanter of the femur, or "thigh bone". In adults, three of the bones of the pelvis have fused into the hip bone or acetabulum which forms part of the hip region. The hip joint, scientifically referred to as the acetabulofemoral joint (art.
Probability distributionIn probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different possible outcomes for an experiment. It is a mathematical description of a random phenomenon in terms of its sample space and the probabilities of events (subsets of the sample space). For instance, if X is used to denote the outcome of a coin toss ("the experiment"), then the probability distribution of X would take the value 0.5 (1 in 2 or 1/2) for X = heads, and 0.
Computational fluid dynamicsComputational fluid dynamics (CFD) is a branch of fluid mechanics that uses numerical analysis and data structures to analyze and solve problems that involve fluid flows. Computers are used to perform the calculations required to simulate the free-stream flow of the fluid, and the interaction of the fluid (liquids and gases) with surfaces defined by boundary conditions. With high-speed supercomputers, better solutions can be achieved, and are often required to solve the largest and most complex problems.
Non-uniform random variate generationNon-uniform random variate generation or pseudo-random number sampling is the numerical practice of generating pseudo-random numbers (PRN) that follow a given probability distribution. Methods are typically based on the availability of a uniformly distributed PRN generator. Computational algorithms are then used to manipulate a single random variate, X, or often several such variates, into a new random variate Y such that these values have the required distribution.
Cauchy distributionThe Cauchy distribution, named after Augustin Cauchy, is a continuous probability distribution. It is also known, especially among physicists, as the Lorentz distribution (after Hendrik Lorentz), Cauchy–Lorentz distribution, Lorentz(ian) function, or Breit–Wigner distribution. The Cauchy distribution is the distribution of the x-intercept of a ray issuing from with a uniformly distributed angle. It is also the distribution of the ratio of two independent normally distributed random variables with mean zero.
