Navier–Stokes equationsThe Navier–Stokes equations (nævˈjeː_stəʊks ) are partial differential equations which describe the motion of viscous fluid substances, named after French engineer and physicist Claude-Louis Navier and Irish physicist and mathematician George Gabriel Stokes. They were developed over several decades of progressively building the theories, from 1822 (Navier) to 1842-1850 (Stokes). The Navier–Stokes equations mathematically express momentum balance and conservation of mass for Newtonian fluids.
Numerical methods for partial differential equationsNumerical methods for partial differential equations is the branch of numerical analysis that studies the numerical solution of partial differential equations (PDEs). In principle, specialized methods for hyperbolic, parabolic or elliptic partial differential equations exist. Finite difference method In this method, functions are represented by their values at certain grid points and derivatives are approximated through differences in these values.
Cauchy stress tensorIn continuum mechanics, the Cauchy stress tensor , true stress tensor, or simply called the stress tensor is a second order tensor named after Augustin-Louis Cauchy. The tensor consists of nine components that completely define the state of stress at a point inside a material in the deformed state, placement, or configuration. The tensor relates a unit-length direction vector e to the traction vector T(e) across an imaginary surface perpendicular to e: or, The SI units of both stress tensor and traction vector are N/m2, corresponding to the stress scalar.
Marfan syndromeMarfan syndrome (MFS) is a multi-systemic genetic disorder that affects the connective tissue. Those with the condition tend to be tall and thin, with long arms, legs, fingers, and toes. They also typically have exceptionally flexible joints and abnormally curved spines. The most serious complications involve the heart and aorta, with an increased risk of mitral valve prolapse and aortic aneurysm. The lungs, eyes, bones, and the covering of the spinal cord are also commonly affected. The severity of the symptoms is variable.
Stress (biology)Stress, either physiological, biological or psychological, is an organism's response to a stressor such as an environmental condition. Stress is the body's method of reacting to a condition such as a threat, challenge or physical and psychological barrier. There are two hormones that an individual produces during a stressful situation, well known as adrenaline and cortisol. There are two kinds of stress hormone levels. Resting (basal) cortisol levels are normal everyday quantities that are essential for standard functioning.
Intra-aortic balloon pumpThe intra-aortic balloon pump (IABP) is a mechanical device that increases myocardial oxygen perfusion and indirectly increases cardiac output through afterload reduction. It consists of a cylindrical polyurethane balloon that sits in the aorta, approximately from the left subclavian artery. The balloon inflates and deflates via counter pulsation, meaning it actively deflates in systole and inflates in diastole. Systolic deflation decreases afterload through a vacuum effect and indirectly increases forward flow from the heart.
Coronary stentA coronary stent is a tube-shaped device placed in the coronary arteries that supply blood to the heart, to keep the arteries open in the treatment of coronary heart disease. It is used in a procedure called percutaneous coronary intervention (PCI). Coronary stents are now used in more than 90% of PCI procedures. Stents reduce angina (chest pain) and have been shown to improve survival and decrease adverse events in an acute myocardial infarction. Similar stents and procedures are used in non-coronary vessels (e.
Shear stressShear stress (often denoted by τ (Greek: tau)) is the component of stress coplanar with a material cross section. It arises from the shear force, the component of force vector parallel to the material cross section. Normal stress, on the other hand, arises from the force vector component perpendicular to the material cross section on which it acts. The formula to calculate average shear stress is force per unit area.: where: τ = the shear stress; F = the force applied; A = the cross-sectional area of material with area parallel to the applied force vector.
ProsthodonticsProsthodontics, also known as dental prosthetics or prosthetic dentistry, is the area of dentistry that focuses on dental prostheses. It is one of 12 dental specialties recognized by the American Dental Association (ADA), Royal College of Surgeons of England, Royal College of Surgeons of Edinburgh, Royal College of Surgeons of Ireland, Royal College of Surgeons of Glasgow, Royal College of Dentists of Canada, and Royal Australasian College of Dental Surgeons.
Finite element methodThe finite element method (FEM) is a popular method for numerically solving differential equations arising in engineering and mathematical modeling. Typical problem areas of interest include the traditional fields of structural analysis, heat transfer, fluid flow, mass transport, and electromagnetic potential. The FEM is a general numerical method for solving partial differential equations in two or three space variables (i.e., some boundary value problems).
