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Monte Carlo Method For Photon Transport
Modeling photon propagation with Monte Carlo methods is a flexible yet rigorous approach to simulate photon transport. In the method, local rules of photon transport are expressed as probability distributions which describe the step size of photon movement between sites of photon-matter interaction and the angles of deflection in a photon's trajectory when a scattering event occurs. This is equivalent to modeling photon transport analytically by the radiative transfer equation (RTE), which describes the motion of photons using a differential equation. However, closed-form solutions of the RTE are often not possible; for some geometries, the diffusion approximation can be used to simplify the RTE, although this, in turn, introduces many inaccuracies, especially near sources and boundaries. In contrast, Monte Carlo simulations can be made arbitrarily accurate by increasing the number of photons traced. For example, see the movie, where a Monte Carlo simulation of a pencil beam in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monte Carlo Method
Monte Carlo methods, or Monte Carlo experiments, are a broad class of computational algorithms that rely on repeated random sampling to obtain numerical results. The underlying concept is to use randomness to solve problems that might be deterministic in principle. The name comes from the Monte Carlo Casino in Monaco, where the primary developer of the method, mathematician Stanisław Ulam, was inspired by his uncle's gambling habits. Monte Carlo methods are mainly used in three distinct problem classes: optimization, numerical integration, and generating draws from a probability distribution. They can also be used to model phenomena with significant uncertainty in inputs, such as calculating the risk of a nuclear power plant failure. Monte Carlo methods are often implemented using computer simulations, and they can provide approximate solutions to problems that are otherwise intractable or too complex to analyze mathematically. Monte Carlo methods are widely used in va ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Absorption Coefficient
The linear attenuation coefficient, attenuation coefficient, or narrow-beam attenuation coefficient characterizes how easily a volume of material can be penetrated by a beam of light, sound, particles, or other energy or matter. A coefficient value that is large represents a beam becoming 'attenuated' as it passes through a given medium, while a small value represents that the medium had little effect on loss. The (derived) SI unit of attenuation coefficient is the reciprocal metre (m−1). Extinction coefficient is another term for this quantity, often used in meteorology and climatology. Most commonly, the quantity measures the exponential decay of intensity, that is, the value of downward ''e''-folding distance of the original intensity as the energy of the intensity passes through a unit (''e.g.'' one meter) thickness of material, so that an attenuation coefficient of 1 m−1 means that after passing through 1 metre, the radiation will be reduced by a factor of '' e'', and fo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Igor Meglinski
Igor Meglinski is a British, New Zealand and Finnish scientist serving as a principal investigator at thCollege of Engineering & Physical Sciencesat Aston University, where he is a professor in Quantum Biophotonics and Biomedical Engineering. He is a Faculty member in thSchool of Engineering and Technologyat thDepartment of Mechanical, Biomedical & Design Engineering and is also associated witthe Aston Institute of Photonic Technologies (AIPT)anAston Research Centre for Health in Ageing (ARCHA) Background and Education Meglinski obtained his BSc/MSc in Laser Physics from Saratov State University. In 1994, he became the first inaugural recipient of the 'Presidential Boris Yeltsin Award,' the most prestigious award for young scientists in the Russian Federation, supporting overseas study. This accolade facilitated his pursuit of a PhD degree in 1997, which he completed at the interface between Saratov State University and the University of Pennsylvania under the supervision of Pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Monte Carlo Methods For Electron Transport
The Monte Carlo method for electron transport is a semiclassical Monte Carlo (MC) approach of modeling semiconductor transport. Assuming the carrier motion consists of free flights interrupted by scattering mechanisms, a computer is utilized to simulate the trajectories of particles as they move across the device under the influence of an electric field using classical mechanics. The scattering events and the duration of particle flight is determined through the use of random numbers. Background Boltzmann transport equation The Boltzmann transport equation model has been the main tool used in the analysis of transport in semiconductors. The BTE equation is given by: : \frac + \frac \nabla_k E(k) \nabla_r f + \frac \nabla_k f = \left frac\right\mathrm : v = \frac \nabla_k E(k) The distribution function, ''f'', is a dimensionless function which is used to extract all observable of interest and gives a full depiction of electron distribution in both real and k-space. Fur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Convolution For Optical Broad-beam Responses In Scattering Media
Photon transport theories in Physics, Medicine, and Statistics (such as the Monte Carlo method), are commonly used to model light propagation in tissue. The responses to a pencil beam incident on a scattering medium are referred to as Green's functions or impulse responses. Photon transport methods can be directly used to compute broad-beam responses by distributing photons over the cross section of the beam. However, convolution can be used in certain cases to improve computational efficiency. General convolution formulas In order for convolution to be used to calculate a broad-beam response, a system must be time invariant, linear, and translation invariant. Time invariance implies that a photon beam delayed by a given time produces a response shifted by the same delay. Linearity indicates that a given response will increase by the same amount if the input is scaled and obeys the property of superposition. Translational invariance means that if a beam is shifted to a new ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Russian Roulette
Russian roulette () is a potentially lethal game of chance in which a player places a single round in a revolver, spins the cylinder, places the muzzle against the head or body (their opponent's or their own), and pulls the trigger. If the loaded chamber aligns with the barrel after cocking (with a single-action revolver), or is in the position which will be rotated to the barrel upon pulling the trigger (double-action), the weapon fires. Etymology The term ''Russian roulette'' was possibly first used in a 1937 short story of the same name by Georges Surdez, published in the January 30, 1937, edition of ''Collier's'' magazine: References to the term in the context of the ''Collier's'' story appeared in some newspapers during 1937. The first independent appearances of the term in newspapers began in 1938 with the reports of young men being killed while playing it. The earliest instance appears to have been the death of a 21-year-old former journalism student in Austin, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Beer–Lambert Law
The Beer–Bouguer–Lambert (BBL) extinction law is an empirical relationship describing the attenuation in intensity of a radiation beam passing through a macroscopically homogenous medium with which it interacts. Formally, it states that the intensity of radiation decays exponentially in the absorbance of the medium, and that said absorbance is proportional to the length of beam passing through the medium, the concentration of interacting matter along that path, and a constant representing said matter's propensity to interact. The extinction law's primary application is in chemical analysis, where it underlies the Beer–Lambert law, commonly called Beer's law. Beer's law states that a beam of visible light passing through a chemical solution of fixed geometry experiences absorption proportional to the solute concentration. Other applications appear in physical optics, where it quantifies astronomical extinction and the absorption of photons, neutrons, or rarefied gases. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inverse Transform Sampling
Inverse transform sampling (also known as inversion sampling, the inverse probability integral transform, the inverse transformation method, or the Smirnov transform) is a basic method for pseudo-random number sampling, i.e., for generating sample numbers at random from any probability distribution given its cumulative distribution function. Inverse transformation sampling takes uniform samples of a number u between 0 and 1, interpreted as a probability, and then returns the smallest number x\in\mathbb R such that F(x)\ge u for the cumulative distribution function F of a random variable. For example, imagine that F is the standard normal distribution with mean zero and standard deviation one. The table below shows samples taken from the uniform distribution and their representation on the standard normal distribution. We are randomly choosing a proportion of the area under the curve and returning the number in the domain such that exactly this proportion of the area occurs ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Unit Vector
In mathematics, a unit vector in a normed vector space is a Vector (mathematics and physics), vector (often a vector (geometry), spatial vector) of Norm (mathematics), length 1. A unit vector is often denoted by a lowercase letter with a circumflex, or "hat", as in \hat (pronounced "v-hat"). The term ''normalized vector'' is sometimes used as a synonym for ''unit vector''. The normalized vector û of a non-zero vector u is the unit vector in the direction of u, i.e., :\mathbf = \frac=(\frac, \frac, ... , \frac) where ‖u‖ is the Norm (mathematics), norm (or length) of u and \, \mathbf\, = (u_1, u_2, ..., u_n). The proof is the following: \, \mathbf\, =\sqrt=\sqrt=\sqrt=1 A unit vector is often used to represent direction (geometry), directions, such as normal directions. Unit vectors are often chosen to form the basis (linear algebra), basis of a vector space, and every vector in the space may be written as a linear combination form of unit vectors. Orthogonal coordinates ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cartesian Coordinate System
In geometry, a Cartesian coordinate system (, ) in a plane (geometry), plane is a coordinate system that specifies each point (geometry), point uniquely by a pair of real numbers called ''coordinates'', which are the positive and negative numbers, signed distances to the point from two fixed perpendicular oriented lines, called ''coordinate lines'', ''coordinate axes'' or just ''axes'' (plural of ''axis'') of the system. The point where the axes meet is called the ''Origin (mathematics), origin'' and has as coordinates. The axes direction (geometry), directions represent an orthogonal basis. The combination of origin and basis forms a coordinate frame called the Cartesian frame. Similarly, the position of any point in three-dimensional space can be specified by three ''Cartesian coordinates'', which are the signed distances from the point to three mutually perpendicular planes. More generally, Cartesian coordinates specify the point in an -dimensional Euclidean space for any di ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
MonteCarlo
Monte Carlo ( ; ; or colloquially ; , ; ) is an official administrative area of Monaco, specifically the ward of Monte Carlo/Spélugues, where the Monte Carlo Casino is located. Informally, the name also refers to a larger district, the Monte Carlo Quarter (corresponding to the former municipality of Monte Carlo), which besides Monte Carlo/Spélugues also includes the wards of La Rousse/Saint Roman, Larvotto/Bas Moulins and Saint Michel. The permanent population of the ward of Monte Carlo is about 3,500, while that of the quarter is about 15,000. Monaco has four traditional quarters, from west to east they are: Fontvieille (the newest), Monaco-Ville (the oldest), La Condamine, and Monte Carlo. Monte Carlo is situated on a prominent escarpment at the base of the Maritime Alps along the French Riviera. Near the quarter's western end is the "world-famous Place du Casino, the gambling center ... that has made Monte Carlo an international byword for the extravagant display and ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pseudorandom Number Generator
A pseudorandom number generator (PRNG), also known as a deterministic random bit generator (DRBG), is an algorithm for generating a sequence of numbers whose properties approximate the properties of sequences of random number generation, random numbers. The PRNG-generated sequence is not truly random, because it is completely determined by an initial value, called the PRNG's ''random seed, seed'' (which may include truly random values). Although sequences that are closer to truly random can be generated using hardware random number generators, ''pseudorandom number generators'' are important in practice for their speed in number generation and their reproducibility. PRNGs are central in applications such as simulations (e.g. for the Monte Carlo method), electronic games (e.g. for procedural generation), and cryptography. Cryptographic applications require the output not to be predictable from earlier outputs, and more cryptographically-secure pseudorandom number generator, elabora ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
