The Experts below are selected from a list of 17043 Experts worldwide ranked by ideXlab platform
B P Leonard - One of the best experts on this subject based on the ideXlab platform.
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the atomic scale unit entity key to a direct and easily understood definition of the si base unit for amount of substance
Metrologia, 2007Co-Authors: B P LeonardAbstract:The atomic-scale unit, entity (ent), is defined as the number-specific amount of substance, n/N, the amount of substance of a single entity. This unit is an invariant physical quantity (the reciprocal of the Avogadro constant) that serves as the basis for reDefining the SI base unit for amount of substance in a direct and easily understood manner. It is argued here that the kilomole should be the base unit in order to avoid factors of 10−3 or 103 appearing in relationships involving both mass and amount of substance expressed in base units. Since, in a compatible formulation, the amount-specific number of entities, N/n (= NA), is equal to Mu/Da, exactly, where Mu = kg kmol−1 = g mol−1 = Da ent−1, exactly, then NA = (kg/Da) kmol−1 = (g/Da) mol−1 = 1 ent−1, exactly. The kilomole can thus be defined very simply as: , exactly, where , the exact kilomole-to-entity amount ratio, is identical to the kilogram-to-dalton mass ratio: . The Avogadro constant, , does not appear explicitly in the Defining Equation, its reciprocal having been replaced by one entity. Like the dalton, the entity would be categorized as a unit in use with SI.
Daniel T Gillespie - One of the best experts on this subject based on the ideXlab platform.
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exact numerical simulation of the ornstein uhlenbeck process and its integral
Physical Review E, 1996Co-Authors: Daniel T GillespieAbstract:A numerical simulation algorithm that is exact for any time step \ensuremath{\Delta}tg0 is derived for the Ornstein-Uhlenbeck process X(t) and its time integral Y(t). The algorithm allows one to make efficient, unapproximated simulations of, for instance, the velocity and position components of a particle undergoing Brownian motion, and the electric current and transported charge in a simple R-L circuit, provided appropriate values are assigned to the Ornstein-Uhlenbeck relaxation time \ensuremath{\tau} and diffusion constant c. A simple Taylor expansion in \ensuremath{\Delta}t of the exact simulation formulas shows how the first-order simulation formulas, which are implicit in the Langevin Equation for X(t) and the Defining Equation for Y(t), are modified in second order. The exact simulation algorithm is used here to illustrate the zero-\ensuremath{\tau} limit theorem. \textcopyright{} 1996 The American Physical Society.
Enric Nart - One of the best experts on this subject based on the ideXlab platform.
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a new computational approach to ideal theory in number fields
arXiv: Number Theory, 2010Co-Authors: Jordi Guardia, Jesus Montes, Enric NartAbstract:Let $K$ be the number field determined by a monic irreducible polynomial $f(x)$ with integer coefficients. In previous papers we parameterized the prime ideals of $K$ in terms of certain invariants attached to Newton polygons of higher order of the Defining Equation $f(x)$. In this paper we show how to carry out the basic operations on fractional ideals of $K$ in terms of these constructive representations of the prime ideals. From a computational perspective, these results facilitate the manipulation of fractional ideals of $K$ avoiding two heavy tasks: the construction of the maximal order of $K$ and the factorization of the discriminant of $f(x)$. The main computational ingredient is Montes algorithm, which is an extremely fast procedure to construct the prime ideals.
Gerhard Grossing - One of the best experts on this subject based on the ideXlab platform.
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on the thermodynamic origin of the quantum potential
Physica A-statistical Mechanics and Its Applications, 2009Co-Authors: Gerhard GrossingAbstract:Abstract In a new thermodynamic interpretation, the quantum potential is shown to result from the presence of a subtle thermal vacuum energy distributed across the whole domain of an experimental setup. Explicitly, its form is demonstrated to be exactly identical to the heat distribution derived from the Defining Equation for classical diffusion wave fields. For a single free particle path, this thermal energy does not significantly affect particle motion. However, in between different paths, or at interfaces, the accumulation–depletion law for diffusion waves provides an immediate new understanding of the quantum potential’s main features.
Jordi Guardia - One of the best experts on this subject based on the ideXlab platform.
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a new computational approach to ideal theory in number fields
arXiv: Number Theory, 2010Co-Authors: Jordi Guardia, Jesus Montes, Enric NartAbstract:Let $K$ be the number field determined by a monic irreducible polynomial $f(x)$ with integer coefficients. In previous papers we parameterized the prime ideals of $K$ in terms of certain invariants attached to Newton polygons of higher order of the Defining Equation $f(x)$. In this paper we show how to carry out the basic operations on fractional ideals of $K$ in terms of these constructive representations of the prime ideals. From a computational perspective, these results facilitate the manipulation of fractional ideals of $K$ avoiding two heavy tasks: the construction of the maximal order of $K$ and the factorization of the discriminant of $f(x)$. The main computational ingredient is Montes algorithm, which is an extremely fast procedure to construct the prime ideals.