Search results for "Mathematical analysis"
showing 10 items of 2409 documents
Enclosure method for the p-Laplace equation
2014
We study the enclosure method for the p-Calder\'on problem, which is a nonlinear generalization of the inverse conductivity problem due to Calder\'on that involves the p-Laplace equation. The method allows one to reconstruct the convex hull of an inclusion in the nonlinear model by using exponentially growing solutions introduced by Wolff. We justify this method for the penetrable obstacle case, where the inclusion is modelled as a jump in the conductivity. The result is based on a monotonicity inequality and the properties of the Wolff solutions.
Granulometric moments and corneal endothelium status
2001
Abstract Specular microscopy is a common practice in Ophthalmology. The corneal endothelium status is usually evaluated by means of the density, the hexagonality, the mean, the standard deviation and the coefficient of variation of cell areas. We propose to replace the cell area moments by the corresponding moments of a different probability distribution, the granulometric size distribution associated to a disc. All cells touching the frame are ignored by the area moments but used by the granulometric moments. Twenty images have been analyzed. When the size of the focused region is reduced, the area moments show a greater variation than the corresponding granulometric moments.
A wideband car-to-car channel model based on a geometrical semicircular tunnel scattering model
2013
In this paper, we present a wideband single-input single-output (SISO) car-to-car (C2C) channel model based on a geometrical semicircular tunnel (SCT) scattering model. Starting from the geometrical scattering model, a reference channel model is derived under the assumption of single-bounce scattering in line-of-sight (LOS) and non-LOS (NLOS) propagation environments. In the proposed channel model, it is assumed that an infinite number of scatterers are uniformly distributed on the tunnel wall. Starting from the geometrical scattering model, the time-variant transfer function (TVTF) is derived and its correlation properties are studied. Expressions are presented for the two-dimensional (2D)…
Fluctuation-dissipation relations for Markov processes.
2005
The fluctuation-dissipation relation is calculated for stochastic models obeying a master equation with continuous time. In the general case of a nonstationary process, there appears to be no simple relation between the response and the correlation. Also, if one considers stationary processes, the linear response cannot be expressed via time-derivatives of the correlation function alone. In this case, an additional function, which has rarely been discussed previously, is required. This so-called asymmetry depends on the two times also relevant for the response and the correlation and it vanishes under equilibrium conditions. The asymmetry can be expressed in terms of the propagators and the…
Time-Dependent Correlation and Response Functions
2014
The dynamics of liquids is discussed with the help of time-dependent correlation functions. They are related to response functions by the fluctuation-dissipation theorem. This theorem enables to relate experimentally measured inelastic scattering data to the Fourier-transformed correlation and response functions. The Laplace transform of the correlation functions can be represented as a continuous fraction with suitable residual terms (memory functions). The projection formalism of Mori and Zwanzig is introduced.
Analytic second derivatives for general coupled-cluster and configuration-interaction models.
2004
Analytic second derivatives of energy for general coupled-cluster (CC) and configuration-interaction (CI) methods have been implemented using string-based many-body algorithms. Wave functions truncated at an arbitrary excitation level are considered. The presented method is applied to the calculation of CC and CI harmonic frequencies and nuclear magnetic resonance chemical shifts up to the full CI level for some selected systems. The present benchmarks underline the importance of higher excitations in high-accuracy calculations.
Scaling behaviour of non-hyperbolic coupled map lattices
2006
Coupled map lattices of non-hyperbolic local maps arise naturally in many physical situations described by discretised reaction diffusion equations or discretised scalar field theories. As a prototype for these types of lattice dynamical systems we study diffusively coupled Tchebyscheff maps of N-th order which exhibit strongest possible chaotic behaviour for small coupling constants a. We prove that the expectations of arbitrary observables scale with \sqrt{a} in the low-coupling limit, contrasting the hyperbolic case which is known to scale with a. Moreover we prove that there are log-periodic oscillations of period \log N^2 modulating the \sqrt{a}-dependence of a given expectation value.…
Numerical Simulation of Thermal Effects in Electric Circuits via Energy Transport equations
2006
In this work we present the coupling of stationary energy-transport (ET) equations with Modified Nodal Analysis (MNA)-equations to model electric circuits containing semiconductor devices. The one-dimensional ET-equations are discretised in space by an exponential fitting mixed hybrid finite element approach to ensure current continuity and positivity of charge carriers. The discretised ET-equations are coupled to MNA-equations and the resulting system is solved with backwarddifference formulas. Numerical examples are shown for a test circuit containing a pn-diode, and the results are compared to those achieved using the drift-diffusion model to describe the semiconductor devices in the cir…
Boundary controlled irreversible port-Hamiltonian systems
2021
Abstract Boundary controlled irreversible port-Hamiltonian systems (BC-IPHS) defined on a 1-dimensional spatial domain are defined by extending the formulation of reversible BC-PHS to irreversible thermodynamic systems controlled at the boundaries of their spatial domain. The structure of BC-IPHS has clear physical interpretation, characterizing the coupling between energy storing and energy dissipating elements. By extending the definition of boundary port variables of BC-PHS to deal with the irreversible energy dissipation, a set of boundary port variables are defined such that BC-IPHS are passive with respect to a given set of conjugated inputs and outputs. As for finite dimensional IPHS…
The polar method as a tool for solving inverse problems of the classical laminated plate theory
2000
Publisher Summary Fiber reinforced laminates are widely used in modem applications. For these kinds of structures, the Classical Laminated Plate Theory and its various extensions provide efficient methods for theoretical analysis, that is, when the stacking sequence, the orientations, and the properties of the individual laminas are known. For design of laminates, a very limited number of rules are available. For stiffriess design, two are currently known and used in practical applications: the Werren and Norris rule to get membrane isotropy, and the symmetrical sequence rule to suppress stretching/bending coupling. This chapter deals with the resolution of inverse problems of the Classical…