Partial differential equationIn mathematics, a partial differential equation (PDE) is an equation which computes a function between various partial derivatives of a multivariable function. The function is often thought of as an "unknown" to be solved for, similar to how x is thought of as an unknown number to be solved for in an algebraic equation like x2 − 3x + 2 = 0. However, it is usually impossible to write down explicit formulas for solutions of partial differential equations.
Boltzmann distributionIn statistical mechanics and mathematics, a Boltzmann distribution (also called Gibbs distribution) is a probability distribution or probability measure that gives the probability that a system will be in a certain state as a function of that state's energy and the temperature of the system. The distribution is expressed in the form: where pi is the probability of the system being in state i, exp is the exponential function, εi is the energy of that state, and a constant kT of the distribution is the product of the Boltzmann constant k and thermodynamic temperature T.
Maxwell–Boltzmann distributionIn physics (in particular in statistical mechanics), the Maxwell–Boltzmann distribution, or Maxwell(ian) distribution, is a particular probability distribution named after James Clerk Maxwell and Ludwig Boltzmann. It was first defined and used for describing particle speeds in idealized gases, where the particles move freely inside a stationary container without interacting with one another, except for very brief collisions in which they exchange energy and momentum with each other or with their thermal environment.
Differential equationIn mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relations are common; therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology.
Curie temperatureIn physics and materials science, the Curie temperature (TC), or Curie point, is the temperature above which certain materials lose their permanent magnetic properties, which can (in most cases) be replaced by induced magnetism. The Curie temperature is named after Pierre Curie, who showed that magnetism was lost at a critical temperature. The force of magnetism is determined by the magnetic moment, a dipole moment within an atom which originates from the angular momentum and spin of electrons.
Ordinary differential equationIn mathematics, an ordinary differential equation (ODE) is a differential equation (DE) dependent on only a single independent variable. As with other DE, its unknown(s) consists of one (or more) function(s) and involves the derivatives of those functions. The term "ordinary" is used in contrast with partial differential equations which may be with respect to one independent variable. A linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form where a_0(x), .
Curie's lawFor many paramagnetic materials, the magnetization of the material is directly proportional to an applied magnetic field, for sufficiently high temperatures and small fields. However, if the material is heated, this proportionality is reduced. For a fixed value of the field, the magnetic susceptibility is inversely proportional to temperature, that is where is the (volume) magnetic susceptibility, is the magnitude of the resulting magnetization (A/m), is the magnitude of the applied magnetic field (A/m), is absolute temperature (K), is a material-specific Curie constant (K).
Boltzmann constantThe Boltzmann constant (kB or k) is the proportionality factor that relates the average relative thermal energy of particles in a gas with the thermodynamic temperature of the gas. It occurs in the definitions of the kelvin and the gas constant, and in Planck's law of black-body radiation and Boltzmann's entropy formula, and is used in calculating thermal noise in resistors. The Boltzmann constant has dimensions of energy divided by temperature, the same as entropy. It is named after the Austrian scientist Ludwig Boltzmann.
TankA tank is an armoured fighting vehicle intended as a primary offensive weapon in front-line ground combat. Tank designs are a balance of heavy firepower, strong armour, and good battlefield mobility provided by tracks and a powerful engine; usually their main armament is mounted in a turret. They are a mainstay of modern 20th and 21st century ground forces and a key part of combined arms combat.
Boltzmann's entropy formulaIn statistical mechanics, Boltzmann's equation (also known as the Boltzmann–Planck equation) is a probability equation relating the entropy , also written as , of an ideal gas to the multiplicity (commonly denoted as or ), the number of real microstates corresponding to the gas's macrostate: where is the Boltzmann constant (also written as simply ) and equal to 1.380649 × 10−23 J/K, and is the natural logarithm function (also written as , as in the image above).
Project JupyterProject Jupyter (ˈdʒuːpɪtər) is a project to develop open-source software, open standards, and services for interactive computing across multiple programming languages. It was spun off from IPython in 2014 by Fernando Pérez and Brian Granger. Project Jupyter's name is a reference to the three core programming languages supported by Jupyter, which are Julia, Python and R. Its name and logo are an homage to Galileo's discovery of the moons of Jupiter, as documented in notebooks attributed to Galileo.
ParamagnetismParamagnetism is a form of magnetism whereby some materials are weakly attracted by an externally applied magnetic field, and form internal, induced magnetic fields in the direction of the applied magnetic field. In contrast with this behavior, diamagnetic materials are repelled by magnetic fields and form induced magnetic fields in the direction opposite to that of the applied magnetic field. Paramagnetic materials include most chemical elements and some compounds; they have a relative magnetic permeability slightly greater than 1 (i.
Cruiser tankThe cruiser tank (sometimes called cavalry tank or fast tank) was a British tank concept of the interwar period for tanks designed as modernised armoured and mechanised cavalry, as distinguished from infantry tanks. Cruiser tanks were developed after medium tank designs of the 1930s failed to satisfy the Royal Armoured Corps. The cruiser tank concept was conceived by Giffard Le Quesne Martel, who preferred many small light tanks to swarm an opponent, instead of a few expensive and unsatisfactory medium tanks.
Tank destroyerA tank destroyer, tank hunter or tank killer is a type of armoured fighting vehicle, predominantly intended for anti-tank duties. As such, they are typically armed with a direct fire artillery gun, then called self-propelled anti-tank gun, or missile launcher, then called anti-tank missile carrier, and designed specifically to engage and destroy enemy tanks, often with limited operational capacities.
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).
Laplace's equationIn mathematics and physics, Laplace's equation is a second-order partial differential equation named after Pierre-Simon Laplace, who first studied its properties. This is often written as or where is the Laplace operator, is the divergence operator (also symbolized "div"), is the gradient operator (also symbolized "grad"), and is a twice-differentiable real-valued function. The Laplace operator therefore maps a scalar function to another scalar function.
Anti-tank warfareAnti-tank warfare originated from the need to develop technology and tactics to destroy tanks during World War I. Since the Allies deployed the first tanks in 1916, the German Empire developed the first anti-tank weapons. The first developed anti-tank weapon was a scaled-up bolt-action rifle, the Mauser 1918 T-Gewehr, that fired a 13.2 mm cartridge with a solid bullet that could penetrate the thin armor of tanks of the time and destroy the engine or ricochet inside, killing occupants.
Differential geometryDifferential geometry is a mathematical discipline that studies the geometry of smooth shapes and smooth spaces, otherwise known as smooth manifolds. It uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra. The field has its origins in the study of spherical geometry as far back as antiquity. It also relates to astronomy, the geodesy of the Earth, and later the study of hyperbolic geometry by Lobachevsky.
Main battle tankA main battle tank (MBT), also known as a battle tank or universal tank, is a tank that fills the role of armor-protected direct fire and maneuver in many modern armies. Cold War-era development of more powerful engines, better suspension systems and lighter composite armor allowed for the design of a tank that had the firepower of a super-heavy tank, the armor protection of a heavy tank, and the mobility of a light tank, in a package with the weight of a medium tank.
DD tankDD or Duplex Drive tanks, nicknamed "Donald Duck tanks", were a type of amphibious swimming tank developed by the British during the Second World War. The phrase is mostly used for the Duplex Drive variant of the M4 Sherman medium tank, that was used by the Western Allies during and after the Normandy Landings in June 1944. DD tanks worked by erecting a canvas 'flotation screen' around the tank, which enabled it to float in water. DD tanks would use propellers to move forward through water, then lower the flotation screens once they had reached land and fight as an ordinary tank.
