Search results for "Mathematical analysis"
showing 10 items of 2409 documents
Fractional mechanical model for the dynamics of non-local continuum
2009
In this chapter, fractional calculus has been used to account for long-range interactions between material particles. Cohesive forces have been assumed decaying with inverse power law of the absolute distance that yields, as limiting case, an ordinary, fractional differential equation. It is shown that the proposed mathematical formulation is related to a discrete, point-spring model that includes non-local interactions by non-adjacent particles with linear springs with distance-decaying stiffness. Boundary conditions associated to the model coalesce with the well-known kinematic and static constraints and they do not run into divergent behavior. Dynamic analysis has been conducted and both…
A numerical method to calculate the muon relaxation function in the presence of diffusion
2014
We present an accurate and efficient method to calculate the effect of random fluctuations of the local field at the muon, for instance in the case muon diffusion, within the framework of the strong collision approximation. The method is based on a reformulation of the Markovian process over a discretized time base, leading to a summation equation for the muon polarization function which is solved by discrete Fourier transform. The latter is formally analogous, though not identical, to the integral equation of the original continuous-time model, solved by Laplace transform. With real-case parameter values, the solution of the discrete-time strong collision model is found to approximate the …
Linear inverse filtering improves spatial separation of nonlinear brain dynamics: a simulation study.
2000
We examined topographic variations in nonlinear measures based on scalp voltages, which were generated by two simulated current dipoles each placed in a different hemisphere of a spherical volume conductor (three-shell model). Dipole dynamics were that of a three-torus and the x-component of the Lorenz-system and scalp voltage were calculated for a configuration of 29 electrode positions. Although estimates for correlation dimension D2 and Lyapunov exponent L1 were close to the theoretical values for the original time series, the simulated scalp voltage data showed almost no topographic resolution of dipole positions. In order to enhance topographic differentiation, we constructed linear in…
Correlation Functions and Finite–Size Effects in Granular Media
2014
A model is considered, where the local order parameter is an n–component vector. This model allows us to calculate correlation functions, describing the correlations between local order parameter at different spatial coordinates. The longitudinal and transverse Fourier–transformed two–point correlation functions \(G_{\parallel }(\mathbf{k})\) and \(G_{\perp }(\mathbf{k})\) in presence of an external field h are considered in some detail. In the thermodynamic limit, these correlation functions exhibit the so-called Goldstone mode singularities below certain critical temperature at an infinitesimal external field \(h = +0\). The actual model can be applied to granular media, in which case it …
Unravelling cosmic velocity flows: a Helmholtz-Hodge decomposition algorithm for cosmological simulations
2021
In the context of intra-cluster medium turbulence, it is essential to be able to split the turbulent velocity field in a compressive and a solenoidal component. We describe and implement a new method for this aim, i.e., performing a Helmholtz-Hodge decomposition, in multi-grid, multi-resolution descriptions, focusing on (but not being restricted to) the outputs of AMR cosmological simulations. The method is based on solving elliptic equations for a scalar and a vector potential, from which the compressive and the solenoidal velocity fields, respectively, are derived through differentiation. These equations are addressed using a combination of Fourier (for the base grid) and iterative (for t…
THEORETISCHE UNTERSUCHUNG UBER DIE MEHRFACHAUFSTELLUNG VON GEOPHONEN*
1958
The receiving of seismic waves by multiple geophones (geophone-group) is described by a system of coupled differential equations considering only effective resistances. For so-called symmetrical connections of the geophone-group which are used in practice nearly in all cases, a method can be given for solving this system of differential equations. The solutions so derived are valid for seismic waves of any shape. The calculation takes into account the coupling of the geophones as well as the building-up transient oscillations. A suitable measure of superposition is defined, based on the energy transferred during the receiving of the seismic waves. By this means effects similar to interferen…
Convergent Strong-Coupling Expansions from Divergent Weak-Coupling Perturbation Theory
1995
Divergent weak-coupling perturbation expansions for physical quantities can be converted into sequences of uniformly and exponentially fast converging approximations. This is possible with the help of an additional variational parameter to be optimized order by order. The uniformity of the convergence for any coupling strength allows us to take all expressions directly to the strong-coupling limit, yielding a simple calculation scheme for the coefficients of convergent strong-coupling expansions. As an example, we determine these coefficients for the ground state energy of the anharmonic oscillator up to 22nd order with a precision of about 20 digits.
Equivalent-Single-Layer discontinuous Galerkin methods for static analysis of multilayered shells
2021
Abstract An original formulation for the elastic analysis of multilayered shells is presented in this work. The key features of the formulation are: the representation of the shell mean surface via a generic system of curvilinear coordinates; the unified treatment of general shell theories via an Equivalent-Single-Layer approach based on the through-the-thickness expansion of the covariant components of the displacement field; and an Interior Penalty discontinuous Galerkin scheme for the solution of the set of governing equations. The combined use of these features enables a high-order solution of the multilayered shell problem. Several numerical tests are presented for isotropic, orthotrop…
Potential and energy of some spheroidal charge distributions with azimuthal symmetry
1989
Abstract The Poisson equation is solved for three types of spheroidal charge distributions with azimuthal symmetry, namely, those depending on one cartesian coordinate, on the radial cylindrical coordinate and on the radial spherical coordinate. The energy of such distributions is found for the case of power functions of these coordinates and it has been normalized, computed and plotted for some low values of the exponent.
Inverse focal shift: A new effect in truncated cylindrical waves
1999
We report on a general analytical procedure to analyse the axial focusing properties of uniform cylindrical waves truncated by a rectangular window. The resulting on-axis diffraction pattern explicitly depends on the square of the window height-to-width ratio. Depending on the value of this parameter, different kinds of axial behaviour are observed. In particular, it is found that for low values of this parameter and low Fresnel number, instead of the expected focal-shift effect, an inverse focal-shift phenomenon can appear, i.e. the maximum of the axial-irradiance distribution is displaced further away from the window.