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; typically one runs simulations many times over in order to obtain the distribution of an unknown probabilistic entity.
The name comes from the resemblance of the technique to the act of playing and recording your results in a real gambling casino. They are often used in physical and mathematical problems and are most useful when it is difficult or impossible to obtain a closed-form expression, or infeasible to apply a deterministic algorithm. Monte Carlo methods are mainly used in three distinct problems classes: optimization, numerical integration and generation of draws from a probability distribution. Astronomers discover complex organic matter exists throughout the universe -- ScienceDaily. Astronomers report in the journal Nature that organic compounds of unexpected complexity exist throughout the Universe.
The results suggest that complex organic compounds are not the sole domain of life but can be made naturally by stars. Prof. Random walk. Example of eight random walks in one dimension starting at 0.
The plot shows the current position on the line (vertical axis) versus the time steps (horizontal axis). A random walk is a mathematical formalization of a path that consists of a succession of random steps. For example, the path traced by a molecule as it travels in a liquid or a gas, the search path of a foraging animal, the price of a fluctuating stock and the financial status of a gambler can all be modeled as random walks, although they may not be truly random in reality. The term random walk was first introduced by Karl Pearson in 1905. Random walks have been used in many fields: ecology, economics, psychology, computer science, physics, chemistry, and biology. Random walks explain the observed behaviors of processes in these fields, and thus serve as a fundamental model for the recorded stochastic activity.
Markov process. Markov process example Introduction A Markov process is a stochastic model that has the Markov property.
This undated image provided by the journal Science a picokeystone, extracted from an aerogel tile from the Stardust interstellar dust collector. Scientists said seven microscopic particles collected by NASA's comet-chasing spacecraft, Stardust, appear to. Espace Toutes les photos de l'espace, frontière de l'infini.
Vista galleria:Espace 1 - 16 di 30. Special relativity. Special relativity implies a wide range of consequences, which have been experimentally verified, including length contraction, time dilation, relativistic mass, mass–energy equivalence, a universal speed limit, and relativity of simultaneity.
It has replaced the conventional notion of an absolute universal time with the notion of a time that is dependent on reference frame and spatial position. Rather than an invariant time interval between two events, there is an invariant spacetime interval. Relativistic Doppler effect. Diagram 1.
A source of light waves moving to the right, relative to observers, with velocity 0.7c. The frequency is higher for observers on the right, and lower for observers on the left. The relativistic Doppler effect is the change in frequency (and wavelength) of light, caused by the relative motion of the source and the observer (as in the classical Doppler effect), when taking into account effects described by the special theory of relativity. Maxwell's equations. Maxwell's equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electrodynamics, classical optics, and electric circuits.
These fields in turn underlie modern electrical and communications technologies. Maxwell's equations describe how electric and magnetic fields are generated and altered by each other and by charges and currents. Kennedy–Thorndike experiment. Figure 1.
The Kennedy–Thorndike experiment Improved variants of the Kennedy–Thorndike experiment have been conducted using optical cavities or Lunar Laser Ranging. Ives–Stilwell experiment. Ives–Stilwell experiment (1938).
"Canal rays" (a mixture of mostly H2+ and H3+ ions) were accelerated through perforated plates charged from 6,788 to 18,350 volts. The beam and its reflected image were simultaneously observed with the aid of a concave mirror offset 7° from the beam. (The offset in this illustration is exaggerated.) The Ives–Stilwell experiment tested the contribution of relativistic time dilation to the Doppler shift of light. The result was in agreement with the formula for the transverse Doppler effect, and was the first direct, quantitative confirmation of the time dilation factor.
Since then, many Ives–Stilwell type experiments have been performed with increased precision. Together with the Michelson–Morley and Kennedy–Thorndike experiments, it forms one of the fundamental tests of special relativity theory. Other tests confirming the relativistic Doppler effect, are the Mössbauer rotor experiment and modern Ives–Stilwell experiments. Michelson–Morley experiment. Figure 1. Michelson and Morley's interferometric setup, mounted on a stone slab and floating in a pool of mercury. The Michelson–Morley experiment was performed in 1887 by Albert Michelson and Edward Morley at what is now Case Western Reserve University in Cleveland, Ohio. It attempted to detect the relative motion of matter through the stationary luminiferous aether ("aether wind").
The negative results are generally considered to be the first strong evidence against the then prevalent aether theory, and initiated a line of research that eventually led to special relativity, in which the stationary aether concept has no role. [A 1] The experiment has been referred to as "the moving-off point for the theoretical aspects of the Second Scientific Revolution". [A 2] Cahier physique - physics workbook. PART I click here (from Copernicus to Newton) movie to watch: greatest discoveries in Astronomy from discovery channel (42 minutes)Willam Herschel He gave up music for astronomy.
Time dilation of moving particles. Relation between the Lorentz factor γ and the time dilation of moving clocks. Time dilation of moving particles as predicted by special relativity can be measured in particle lifetime experiments. According to special relativity, the rate of clock C traveling between two synchronized laboratory clocks A and B is slowed with respect to the laboratory clock rates. This effect is called time dilation. Since any periodic process can be considered a clock, also the lifetimes of unstable particles such as muons must be affected, so that moving muons should have a longer lifetime than resting ones. Variations of experiments that actually confirmed this effect took place in the atmosphere or in particle accelerators.
Biologist warn of early stages of Earth's sixth mass extinction event -- ScienceDaily. The planet's current biodiversity, the product of 3.5 billion years of evolutionary trial and error, is the highest in the history of life. But it may be reaching a tipping point. In a new review of scientific literature and analysis of data published in Science, an international team of scientists cautions that the loss and decline of animals is contributing to what appears to be the early days of the planet's sixth mass biological extinction event.
Lists of unsolved problems. Why Probability in Quantum Mechanics is Given by the Wave Function Squared. One of the most profound and mysterious principles in all of physics is the Born Rule, named after Max Born. In quantum mechanics, particles don’t have classical properties like “position” or “momentum”; rather, there is a wave function that assigns a (complex) number, called the “amplitude,” to each possible measurement outcome. The Born Rule is then very simple: it says that the probability of obtaining any possible measurement outcome is equal to the square of the corresponding amplitude. (The wave function is just the set of all the amplitudes.) Library - Google Search. History of writing. Why study things? - An introduction to material culture. Oulipo.
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