Strain energy density functionA strain energy density function or stored energy density function is a scalar-valued function that relates the strain energy density of a material to the deformation gradient. Equivalently, where is the (two-point) deformation gradient tensor, is the right Cauchy–Green deformation tensor, is the left Cauchy–Green deformation tensor, and is the rotation tensor from the polar decomposition of . For an anisotropic material, the strain energy density function depends implicitly on reference vectors or tensors (such as the initial orientation of fibers in a composite) that characterize internal material texture.
StrokeA stroke is a medical condition in which poor blood flow to the brain causes cell death. There are two main types of stroke: ischemic, due to lack of blood flow, and hemorrhagic, due to bleeding. Both cause parts of the brain to stop functioning properly. Signs and symptoms of a stroke may include an inability to move or feel on one side of the body, problems understanding or speaking, dizziness, or loss of vision to one side. Signs and symptoms often appear soon after the stroke has occurred.
Probabilistic numericsProbabilistic numerics is an active field of study at the intersection of applied mathematics, statistics, and machine learning centering on the concept of uncertainty in computation. In probabilistic numerics, tasks in numerical analysis such as finding numerical solutions for integration, linear algebra, optimization and simulation and differential equations are seen as problems of statistical, probabilistic, or Bayesian inference.
Linear elasticityLinear elasticity is a mathematical model of how solid objects deform and become internally stressed due to prescribed loading conditions. It is a simplification of the more general nonlinear theory of elasticity and a branch of continuum mechanics. The fundamental "linearizing" assumptions of linear elasticity are: infinitesimal strains or "small" deformations (or strains) and linear relationships between the components of stress and strain. In addition linear elasticity is valid only for stress states that do not produce yielding.
Elasticity (physics)In physics and materials science, elasticity is the ability of a body to resist a distorting influence and to return to its original size and shape when that influence or force is removed. Solid objects will deform when adequate loads are applied to them; if the material is elastic, the object will return to its initial shape and size after removal. This is in contrast to plasticity, in which the object fails to do so and instead remains in its deformed state. The physical reasons for elastic behavior can be quite different for different materials.
AtherosclerosisAtherosclerosis is a pattern of the disease arteriosclerosis in which the wall of the artery develops abnormalities, called lesions. These lesions may lead to narrowing due to the buildup of atheromatous plaque. At onset there are usually no symptoms, but if they develop, symptoms generally begin around middle age. When severe, it can result in coronary artery disease, stroke, peripheral artery disease, or kidney problems, depending on which arteries are affected. The exact cause is not known and is proposed to be multifactorial.
Intracranial aneurysmAn intracranial aneurysm, also known as a cerebral aneurysm, is a cerebrovascular disorder in which weakness in the wall of a cerebral artery or vein causes a localized dilation or ballooning of the blood vessel. Aneurysms in the posterior circulation (basilar artery, vertebral arteries and posterior communicating artery) have a higher risk of rupture. Basilar artery aneurysms represent only 3–5% of all intracranial aneurysms but are the most common aneurysms in the posterior circulation.
Physical cosmologyPhysical cosmology is a branch of cosmology concerned with the study of cosmological models. A cosmological model, or simply cosmology, provides a description of the largest-scale structures and dynamics of the universe and allows study of fundamental questions about its origin, structure, evolution, and ultimate fate. Cosmology as a science originated with the Copernican principle, which implies that celestial bodies obey identical physical laws to those on Earth, and Newtonian mechanics, which first allowed those physical laws to be understood.
Mathematical logicMathematical logic is the study of formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory). Research in mathematical logic commonly addresses the mathematical properties of formal systems of logic such as their expressive or deductive power. However, it can also include uses of logic to characterize correct mathematical reasoning or to establish foundations of mathematics.
Coronary artery bypass surgeryCoronary artery bypass surgery, also known as coronary artery bypass graft (CABG, pronounced "cabbage") is a surgical procedure to treat coronary artery disease (CAD), the buildup of plaques in the arteries of the heart. It can relieve chest pain caused by CAD, slow the progression of CAD, and increase life expectancy. It aims to bypass narrowings in heart arteries by using arteries or veins harvested from other parts of the body, thus restoring adequate blood supply to the previously ischemic (deprived of blood) heart.
