Search results for "integral"
showing 10 items of 902 documents
Gamma-X-ray coincidence Mössbauer emission spectroscopy on57Co/CoO
1994
The time integral Mossbauer emission spectrum of a57Co/Co1−xO source (x ≈ 10−5) at RT consists of two single Lorentzian lines of an Fe2+ (76%) charge state and an Fe3+ (24%) aliovalent charge state. The spectrum measured by γ-X-ray coincidence spectrpscopy shows the same fraction of the aliovalent charge state, contrary to the expectation derived from the competing acceptor model as successfully applied by Tejada and Parak [1], who could explain the dependence of the formation of aliovalent charge states after the nuclear transformation on the stoichiometric parameterx. The consequences of this unexpected behaviour for the competing acceptor model are discussed.
Blowing up Feynman integrals
2008
In this talk we discuss sector decomposition. This is a method to disentangle overlapping singularities through a sequence of blow-ups. We report on an open-source implementation of this algorithm to compute numerically the Laurent expansion of divergent multi-loop integrals. We also show how this method can be used to prove a theorem which relates the coefficients of the Laurent series of dimensionally regulated multi-loop integrals to periods.
Heuristic Algorithm for the Analysis of Fast Field Cycling (FFC) NMR Dispersion Curves
2021
Evaluation of nuclear magnetic relaxation dispersion (NMRD) curves obtained by the fast field cycling nuclear magnetic resonance (FFC-NMR) relaxometry technique is a valuable tool for analyzing the microscopic dynamics of condensed matter systems. However, quantitative data analysis involves several conceptual and practical issues. Moving forward from previous literature approaches, we propose a new analysis method, relying on the elaboration of the inverse integral transform of the NMRD curve. Our approach results in a true heuristic method, able to unambiguously individuate the dynamic domains in the system, thereby avoiding the possible introduction of any element of discretion. The anal…
Numerical evaluation of NLO multiparton processes
2013
We discuss an algorithm for the numerical evaluation of NLO multiparton processes. We focus hereby on the virtual part of the NLO calculation, i.e. on evaluating the one-loop integration numerically. We employ and extend the ideas of the subtraction method to the virtual part and we use subtraction terms for the soft, collinear and ultraviolet regions, which allows us to evaluate the loop integral numerically in four dimensions. A second ingredient is a method to deform the integration contour of the loop integration into the complex plane. The algorithm is derived on the level of the primitive amplitudes, where we utilise recursive relations to generate the corresponding one-loop off-shell…
Coulomb effects in deuteron breakup by proton impact
1994
We present the first results of a calculation of kinematically complete differential cross sections for the proton-induced deuteron breakup reaction, obtained by using a three-body formalism based on momentum space integral equations which correctly takes into account the Coulomb repulsion between the two protons. Comparison with experimental data is made.
Computational aspects in 2D SBEM analysis with domain inelastic actions
2009
The Symmetric Boundary Element Method, applied to structures subjected to temperature and inelastic actions, shows singular domain integrals. In the present paper the strong singularity involved in the domain integrals of the stresses and tractions is removed, and by means of a limiting operation, this traction is evaluated on the boundary. First the weakly singular domain integral in the Somigliana Identity (S.I.) of the displacements is regularized and the singular integral is transformed into a boundary one using the Radial Integration Method; subsequently, using the differential operator applied to the displacement field, the S.I. of the tractions inside the body is obtained and through…
A note on the uniqueness and attractive behavior of solutions for nonlinear Volterra equations
2001
In this paper we prove that positive solutions of some nonlinear Volterra integral equations must be locally bounded and global attractors of positive functions. These results complete previous results about the existence and uniqueness of solutions and their attractive behavior.
Euler integral as a source of chaos in the three–body problem
2022
In this paper we address, from a purely numerical point of view, the question, raised in [20, 21], and partly considered in [22, 9, 3], whether a certain function, referred to as "Euler Integral", is a quasi-integral along the trajectories of the three-body problem. Differently from our previous investigations, here we focus on the region of the "unperturbed separatrix", which turns to be complicated by a collision singularity. Concretely, we reduce the Hamiltonian to two degrees of freedom and, after fixing some energy level, we discuss in detail the resulting three-dimensional phase space around an elliptic and an hyperbolic periodic orbit. After measuring the strength of variation of the…
Inversion Formulas for the Discretized Hilbert Transform on the Unit Circle
1998
A discrete version of the Hilbert transform on the unit circle is considered. Its Moore--Penrose inverse with respect to suitable scalar products is derived for different side conditions. Furthermore, stability of the pseudo-inverse is studied. These results allow the efficient computation of approximate solutions of singular integral equations with Hilbert kernel. Furthermore, the stability analysis of such methods becomes much easier even for graded meshes which are useful for weakly singular solutions.
Fractional differential equations solved by using Mellin transform
2014
In this paper, the solution of the multi-order differential equations, by using Mellin Transform, is proposed. It is shown that the problem related to the shift of the real part of the argument of the transformed function, arising when the Mellin integral operates on the fractional derivatives, may be overcame. Then, the solution may be found for any fractional differential equation involving multi-order fractional derivatives (or integrals). The solution is found in the Mellin domain, by solving a linear set of algebraic equations, whose inverse transform gives the solution of the fractional differential equation at hands.