Search results for "Exponent"
showing 10 items of 896 documents
Luminescence of different modifications of crystalline silicon dioxide: Stishovite and coesite
2003
Abstract Luminescence of very small samples of single crystals of coesite and stishovite has been studied. The spectra were detected under ionizing radiation (X-ray and electron beam) and the decay kinetics of cathodoluminescence in the range of time from 10 ns to 3 ms was measured. The coesite luminescence possesses a broad band at 3 eV with exponential decay about 680 μs at 80 K. The nature of this luminescence was explained as a self-trapped exciton creation in tetrahedron framework. The stishovite luminescence possesses two bands—blue (2.8 eV) and UV (4.7 eV). The UV band intensity grows more than 20 times with irradiation dose from initial level. This shows that the corresponding lumin…
Fatigue crack propagation from a cold-worked hole
2007
Abstract The cold expansion process is widely used to enhance the fatigue life of structures with fastener holes. Various studies assert that the cold expansion improves the fatigue strength of fastener holes; however, the improvement of fatigue life is difficult to quantify. Therefore, the influence on fatigue life of cold-worked process was studied by numerical and experimental tests. Then, a parametric study on material hardening behavior and Bauschinger’s parameter was performed for several loading conditions in order to determine their effect on crack growth propagation. The results of the numerical tests have exhibited a good prediction of the fatigue life of the component.
Detecting the chaotic nature of advection in complex river flows
2012
In order to detect signatures of chaotic advection in river surface motion, surface buoys equipped with GPS were deployed in a field experiment in River Danube, Hungary. The buoys were released in the vicinity of groynes where complex mixing processes occur. A detailed analysis of the trajectories was carried out, focusing on the time evolution of the distance between buoy pairs. The analysis included the determination and comparison of local Lyapunov exponents and prediction times of finite-time hyperbolic behaviour, which is related to strong mixing. Despite of the small number of applied buoys we found evidence on Lagrangian chaos in the wake of a groyne field. In order to supplement the…
Correlation at low temperature I. Exponential decay
2003
Abstract The present paper generalizes the analysis in (Ann. H. Poincare 1 (2000) 59, Math. J. (AMS) 8 (1997) 123) of the correlations for a lattice system of real-valued spins at low temperature. The Gibbs measure is assumed to be generated by a fairly general Hamiltonian function with pair interaction. The novelty, as compared to [2,20], is that the single-site (self-) energies of the spins are not required to have only a single local minimum and no other extrema. Our derivation of exponential decay of correlations goes through the spectral analysis of a deformed Laplacian closely related to the Witten Laplacian studied in [2,20]. We prove that this Laplacian has a spectral gap above zero…
Correlation at Low Temperature: II. Asymptotics
2004
The present paper is a continuation of ref. 4, where the truncated two-point correlation function for a class of lattice spin systems was proved to have exponential decay at low temperature, under a weak coupling assumption. In this paper we compute the asymptotics of the correlation function as the temperature goes to zero. This paper thus extends ref. 3 in two directions: The Hamiltonian function is allowed to have several local minima other than a unique global minimum, and we do not require translation invariance of the Hamiltonian function. We are in particular able to handle spin systems on a general lattice.
Periodic Discrete Splines
2014
Periodic discrete splines with different periods and spans were introduced in Sect. 3.4. In this chapter, we discuss families of periodic discrete splines, whose periods and spans are powers of 2. As in the polynomial splines case, the Zak transform is extensively employed. It results in the Discrete Spline Harmonic Analysis (DSHA). Utilization of the Fast Fourier transform (FFT) enables us to implement all the computations in a fast explicit way.
Hessian PDF reweighting meets the Bayesian methods
2014
We discuss the Hessian PDF reweighting - a technique intended to estimate the effects that new measurements have on a set of PDFs. The method stems straightforwardly from considering new data in a usual $\chi^2$-fit and it naturally incorporates also non-zero values for the tolerance, $\Delta\chi^2>1$. In comparison to the contemporary Bayesian reweighting techniques, there is no need to generate large ensembles of PDF Monte-Carlo replicas, and the observables need to be evaluated only with the central and the error sets of the original PDFs. In spite of the apparently rather different methodologies, we find that the Hessian and the Bayesian techniques are actually equivalent if the $\Delta…
PDF reweighting in the Hessian matrix approach
2014
We introduce the Hessian reweighting of parton distribution functions (PDFs). Similarly to the better-known Bayesian methods, its purpose is to address the compatibility of new data and the quantitative modifications they induce within an existing set of PDFs. By construction, the method discussed here applies to the PDF fits that carried out a Hessian error analysis using a non-zero tolerance $\Delta\chi^2$. The principle is validated by considering a simple, transparent example. We are also able to establish an agreement with the Bayesian technique provided that the tolerance criterion is appropriately accounted for and that a purely exponential Bayesian likelihood is assumed. As a practi…
Biophysical parameter retrieval with warped Gaussian processes
2015
This paper focuses on biophysical parameter retrieval based on Gaussian Processes (GPs). Very often an arbitrary transformation is applied to the observed variable (e.g. chlorophyll content) to better pose the problem. This standard practice essentially tries to linearize/uniformize the distribution by applying non-linear link functions like the logarithmic, the exponential or the logistic functions. In this paper, we propose to use a GP model that automatically learns the optimal transformation directly from the data. The so-called warped GP regression (WGPR) presented in [1] models output observations as a parametric nonlinear transformation of a GP. The parameters of such prior model are…
Subleading Regge limit from a soft anomalous dimension
2018
Wilson lines capture important features of scattering amplitudes, for example soft effects relevant for infrared divergences, and the Regge limit. Beyond the leading power approximation, corrections to the eikonal picture have to be taken into account. In this paper, we study such corrections in a model of massive scattering amplitudes in N = 4 super Yang-Mills, in the planar limit, where the mass is generated through a Higgs mechanism. Using known three-loop analytic expressions for the scattering amplitude, we find that the first power suppressed term has a very simple form, equal to a single power law. We propose that its exponent is governed by the anomalous dimension of a Wilson loop w…