Search results for " integration"
showing 10 items of 1034 documents
Set valued Kurzweil-Henstock-Pettis integral
2005
It is shown that the obvious generalization of the Pettis integral of a multifunction obtained by replacing the Lebesgue integrability of the support functions by the Kurzweil--Henstock integrability, produces an integral which can be described -- in case of multifunctions with (weakly) compact convex values -- in terms of the Pettis set-valued integral.
Kurzweil--Henstock and Kurzweil--Henstock--Pettis integrability of strongly measurable functions
2006
We study the integrability of Banach valued strongly measurable functions defined on $[0,1]$. In case of functions $f$ given by $\sum _{n=1}^{\infty } x_n\chi _{E_n}$, where $x_n $ belong to a Banach space and the sets $E_n$ are Lebesgue measurable and pairwise disjoint subsets of $[0,1]$, there are well known characterizations for the Bochner and for the Pettis integrability of $f$ (cf Musial (1991)). In this paper we give some conditions for the Kurzweil-Henstock and the Kurzweil-Henstock-Pettis integrability of such functions.
Compression of Silver Sulfide: X-ray Diffraction Measurements and Total-Energy Calculations
2012
[EN] Angle-dispersive X-ray diffraction measurements have been performed in acanthite, Ag2S, up to 18 GPa in order to investigate its high-pressure structural behavior. They have been complemented by ab initio electronic structure calculations. From our experimental data, we have determined that two different high-pressure phase transitions take place at 5 and 10.5 GPa. The first pressure-induced transition is from the initial anti-PbCl2-like monoclinic structure (space group P2(1)/n) to an orthorhombic Ag2Se-type structure (space group P2(1)2(1)2(1)). The compressibility of the lattice parameters and the equation of state of both phases have been determined. A second phase transition to a …
MONTE CARLO METHODS FOR FIRST ORDER PHASE TRANSITIONS: SOME RECENT PROGRESS
1992
This brief review discusses methods to locate and characterize first order phase transitions, paying particular attention to finite size effects. In the first part, the order parameter probability distribution and its fourth-order cumulant is discussed for thermally driven first-order transitions (the 3-state Potts model in d=3 dimensions is treated as an example). First-order transitions are characterized by a minimum of the cumulant, which gets very deep for large enough systems. In the second part, we discuss how to locate first order phase boundaries ending in a critical point in a large parameter space. As an example, the study of the unmixing transition of asymmetric polymer mixtures…
Highly granular calorimeters: technologies and results
2017
The CALICE collaboration is developing highly granular calorimeters for experiments at a future lepton collider primarily to establish technologies for particle flow event reconstruction. These technologies also find applications elsewhere, such as detector upgrades for the LHC. Meanwhile, the large data sets collected in an extensive series of beam tests have enabled detailed studies of the properties of hadronic showers in calorimeter systems, resulting in improved simulation models and development of sophisticated reconstruction techniques. In this proceeding, highlights are included from studies of the structure of hadronic showers and results on reconstruction techniques for imaging ca…
An operator-like description of love affairs
2010
We adopt the so--called \emph{occupation number representation}, originally used in quantum mechanics and recently considered in the description of stock markets, in the analysis of the dynamics of love relations. We start with a simple model, involving two actors (Alice and Bob): in the linear case we obtain periodic dynamics, whereas in the nonlinear regime either periodic or quasiperiodic solutions are found. Then we extend the model to a love triangle involving Alice, Bob and a third actress, Carla. Interesting features appear, and in particular we find analytical conditions for the linear model of love triangle to have periodic or quasiperiodic solutions. Numerical solutions are exhibi…
Efficient numerical integration of neutrino oscillations in matter
2016
A special purpose solver, based on the Magnus expansion, well suited for the integration of the linear three neutrino oscillations equations in matter is proposed. The computations are speeded up to two orders of magnitude with respect to a general numerical integrator, a fact that could smooth the way for massive numerical integration concomitant with experimental data analyses. Detailed illustrations about numerical procedure and computer time costs are provided.
Numerical integration of subtraction terms
2016
Numerical approaches to higher-order calculations often employ subtraction terms, both for the real emission and the virtual corrections. These subtraction terms have to be added back. In this paper we show that at NLO the real subtraction terms, the virtual subtraction terms, the integral representations of the field renormalisation constants and -- in the case of initial-state partons -- the integral representation for the collinear counterterm can be grouped together to give finite integrals, which can be evaluated numerically. This is useful for an extension towards NNLO.
Ultrasonic cavity solitons
2007
We report on a new type of localized structure, an ultrasonic cavity soliton, supported by large aspect-ratio acoustic resonators containing viscous media. These states of the acoustic and thermal fields are robust structures, existing whenever a spatially uniform solution and a periodic pattern coexist. Direct proof of their existence is given both through the numerical integration of the model and through the analysis and numerical integration of a generalized Swift-Hohenberg equation, derived from the microscopic equations under conditions close to nascent bistability. An analytical solution for the ultrasonic cavity soliton is given.