A Hessenberg matrix is a special kind of square matrix that has zero entries below the first subdiagonal.
Chirality-induced spin selectivity (CISS) is a physical phenomenon where chiral molecules exhibit a preference for spinning electrons in a certain direction. This effect is observed in systems that include chiral organic molecules, which are structures that cannot be superimposed on their mirror images, much like left and right hands. The key points about CISS are: 1. **Chirality**: Chiral molecules have non-superimposable mirror images.
A Discrete Global Grid (DGG) is a mathematical and conceptual framework used to represent geographic data in a regular, grid-like manner across the Earth's surface. Unlike traditional geographic coordinate systems based on latitude and longitude, which can suffer from issues like varying resolution or distortion, DGGs provide a way to partition the globe into a uniform tiling of cells or grid elements.
Geomagnetic latitude is a coordinate used in geomagnetism to indicate the position of a point on the Earth's surface in relation to the geomagnetic poles. Unlike geographic latitude, which is based on the Earth's rotational axis, geomagnetic latitude is based on the Earth's magnetic field. The geomagnetic latitude is defined as the angle between a point on the Earth's surface and the geomagnetic equator, measured from the center of the Earth.
Grid (often referred to as a spatial index) is a data structure used in Geographic Information Systems (GIS) and spatial databases to efficiently organize and retrieve spatial data based on its location. The grid spatial index divides a geographic space into a series of uniform rectangular cells or grids, each representing a specific area. It allows for faster querying and analysis of spatial data by reducing the number of comparisons that need to be made when searching for nearby points or objects.
The Modified Transverse Mercator (MTM) is a variation of the Transverse Mercator projection, optimized for mapping smaller areas with increased accuracy. This projection is particularly suitable for regions that have a significant east-west extent, offering reduced distortion in both distance and shape compared to standard Transverse Mercator.
PROJ is an open-source software library used for performing cartographic projections and coordinate transformations. It is widely used in geographic information systems (GIS), remote sensing, and mapping applications. PROJ provides a powerful framework for converting geographic coordinates (latitude and longitude) to projected coordinates (e.g., UTM, state plane) and vice versa. Originally developed in the 1970s, PROJ has evolved over the years and is now maintained by a community of developers.
The K-index is a measure used in space weather and geomagnetic studies to assess the intensity of geomagnetic storms. It quantifies disturbances in the Earth's magnetic field, which can be caused by solar activity such as solar flares and coronal mass ejections (CMEs).
The term "L-shell" typically refers to a specific set of electron orbitals in an atom. In the context of atomic physics and quantum mechanics, electrons are arranged in shells around the nucleus of an atom, and these shells are characterized by principal quantum numbers (n). The L-shell corresponds to the second principal quantum number (n = 2). It includes the subshells of 2s and 2p.
The plasmasphere is a region of the Earth's magnetosphere, specifically part of the ionosphere that consists of low-density plasma. It is an extension of the ionosphere and is located above the ionospheric F region, extending from about 1,000 kilometers (620 miles) to several tens of thousands of kilometers in altitude, although it can be shaped and defined by various factors.
Seismo-electromagnetics is a field of study that explores the relationship between seismic activities (such as earthquakes) and electromagnetic phenomena. This interdisciplinary area combines knowledge from geophysics, geochemistry, and electrical engineering to investigate how seismic events can generate or influence electromagnetic fields in the Earth's crust and atmosphere.
The Bishop–Gromov inequality is a fundamental result in Riemannian geometry that provides a comparison between the volume of geodesic balls in a Riemannian manifold and the volume of balls in a model space of constant curvature, specifically spherical or Euclidean spaces. The inequality is particularly useful in the context of manifolds with bounded sectional curvature.
Hessian automatic differentiation (Hessian AD) is a specialized form of automatic differentiation (AD) that focuses on computing second-order derivatives, specifically the Hessian matrix of a scalar-valued function with respect to its input variables. The Hessian matrix is a square matrix of second-order partial derivatives and is essential in optimization, particularly when analyzing the curvature of a function or when applying certain optimization algorithms that leverage second-order information.
Crustal magnetism refers to the magnetic properties and phenomena associated with the Earth's crust, particularly the magnetic characteristics of the rocks and minerals that make up the crust. This field of study is important in geology, geophysics, and paleomagnetism, as it can provide insights into the historical geologic processes, tectonic movements, and the formation of the Earth's crust.
Environmental magnetism is the study of the magnetic properties of natural and anthropogenic (human-made) materials in the environment, particularly sediments, rocks, and soils. It investigates how these magnetic properties can provide insights into various natural processes and environmental changes over time. The key aspects of environmental magnetism include: 1. **Magnetic Minerals**: Environmental magnetism primarily focuses on magnetic minerals, such as magnetite and hematite.
Magnetic dip, also known as magnetic inclination, refers to the angle that the Earth's magnetic field lines make with the horizontal plane at a given location on the Earth's surface. This angle is measured in degrees, and it can indicate whether the magnetic field is pointing downward into the Earth (a positive dip) or upward out of the Earth (a negative dip). - **Positive Magnetic Dip**: When the magnetic field points downwards towards the Earth, the dip is considered positive.
Magnetotellurics (MT) is a geophysical method used to study the electrical properties of the Earth's subsurface. It involves measuring the natural variations of the Earth's electromagnetic fields, specifically the telluric (electric) and magnetic fields, to infer subsurface resistivity structures. The technique is based on the principle that different geological materials conduct electricity differently.
Subauroral ion drift (SAID) refers to a phenomenon in the Earth's ionosphere characterized by the motion of ions at altitudes typically between 1,000 and 3,000 kilometers. This drift occurs predominantly in the subauroral regions—areas located just outside the main auroral oval, which is generally centered around the polar regions.
Formal moduli refers to a branch of algebraic geometry that studies families of algebraic objects (such as varieties or schemes) over a base, typically in a formal or non-archimedean setting. This concept is often used in the context of deformation theory and moduli problems, where one is interested in understanding how objects of a given type can be continuously deformed into one another.
The Riemann–Silberstein vector is a mathematical construct used in the context of electromagnetic theory. It provides a unified way to represent electric and magnetic fields. Named after Bernhard Riemann and Hans Silberstein, the vector is particularly useful in theoretical physics, especially in the study of electromagnetic waves and their propagation.