Search results for "Mathematical physics"
showing 10 items of 2687 documents
Existence, nonexistence and uniqueness of positive solutions for nonlinear eigenvalue problems
2017
We study the existence of positive solutions for perturbations of the classical eigenvalue problem for the Dirichlet $p-$Laplacian. We consider three cases. In the first the perturbation is $(p-1)-$sublinear near $+\infty$, while in the second the perturbation is $(p-1)-$superlinear near $+\infty$ and in the third we do not require asymptotic condition at $+\infty$. Using variational methods together with truncation and comparison techniques, we show that for $\lambda\in (0, \widehat{\lambda}_1)$ -$\lambda>0$ is the parameter and $\widehat{\lambda}_1$ being the principal eigenvalue of $\left(-\Delta_p, W^{1, p}_0(\Omega)\right)$ -we have positive solutions, while for $\lambda\geq \widehat{\…
Many-body applications of the stochastic limit: a review
2005
We review some applications of the perturbative technique known as the {\em stochastic limit approach} to the analysis of the following many-body problems: the fractional quantum Hall effect, the relations between the Hepp-Lieb and the Alli-Sewell models (as possible models of interaction between matter and radiation), and the open BCS model of low temperature superconductivity.
Quantum Monte Carlo Simulations of Models Related to High-Tc Superconductivity on a Transputer Network
1991
Much of the insight into the low temperature behaviour of two-dimensional quantum antiferromagnets has been recently obtained by extensive Monte Carlo. These models are relevant in the study of the magnetic behaviour of high Tc compounds containing copper-oxide layers. While of little technical importance, the physical properties of these models are certainly important for the understanding of the new type of behaviour that leads to superconductivity under certain conditions.
Calibration of the Norwegian motion laboratory using conformal geometric algebra
2017
This paper applies Conformal Geometric Algebra (CGA) as a tool for calibrating the robotic equipment found in the Norwegian Motion Laboratory. By using the inner product of CGA to measure the distance between a point and the surface of a plane/sphere, the least-squares method can be used to solve for the unknown parameters describing the plane/sphere in an efficient and intuitive way given n measured points. Positional data samples were acquired from using a high precision Laser tracker (FARO Xi), and the overall calibration error was found to be no more than 4.90mm, and the maximum standard deviation 3.25mm. In addition, the applied least-squares algorithm using CGA was twice as fast, when…
Arithmetic and geometry of a K3 surface emerging from virtual corrections to Drell–Yan scattering
2020
We study a K3 surface, which appears in the two-loop mixed electroweak-quantum chromodynamic virtual corrections to Drell--Yan scattering. A detailed analysis of the geometric Picard lattice is presented, computing its rank and discriminant in two independent ways: first using explicit divisors on the surface and then using an explicit elliptic fibration. We also study in detail the elliptic fibrations of the surface and use them to provide an explicit Shioda--Inose structure. Moreover, we point out the physical relevance of our results.
Digit replacement: A generic map for nonlinear dynamical systems
2016
A simple discontinuous map is proposed as a generic model for nonlinear dynamical systems. The orbit of the map admits exact solutions for wide regions in parameter space and the method employed (digit manipulation) allows the mathematical design of useful signals, such as regular or aperiodic oscillations with specific waveforms, the construction of complex attractors with nontrivial properties as well as the coexistence of different basins of attraction in phase space with different qualitative properties. A detailed analysis of the dynamical behavior of the map suggests how the latter can be used in the modeling of complex nonlinear dynamics including, e.g., aperiodic nonchaotic attracto…
On the gonality and the slope of a fibered surface
2018
Abstract Let f : X → B be a locally non-trivial relatively minimal fibration of curves of genus g ≥ 2 . We obtain a lower bound of the slope λ ( f ) increasing with the gonality of the general fiber of f. In particular, we show that λ ( f ) ≥ 4 provided that f is non-hyperelliptic and g ≥ 16 .
New construction of algebro-geometric solutions to the Camassa-Holm equation and their numerical evaluation
2011
An independent derivation of solutions to the Camassa-Holm equation in terms of multi-dimensional theta functions is presented using an approach based on Fay's identities. Reality and smoothness conditions are studied for these solutions from the point of view of the topology of the underlying real hyperelliptic surface. The solutions are studied numerically for concrete examples, also in the limit where the surface degenerates to the Riemann sphere, and where solitons and cuspons appear.
Atomistic Calculations of Positron Surface States
1983
We report on the results of an atomistic, discrete-lattice calculation of positron surface states on the three principal surfaces of Al and Cu. We are able to (i) accurately reproduce the observed values and anisotropy of the binding energies, and (ii) predict the surface state life times. Furthermore, we calculate (iii) the positron lateral diffusion constant, and find it considerably enhanced over the bulk value. We also investigate (iv) the positron trapping at surface vacancies, and (v) the effect of ordered chemisorbed monolayers of oxygen. We find that the oxidation lowers the binding energy and makes the surface state unstable with respect to positronium emission on Al (100) and Al (…
Sodium Adsorption on the TiO2110 Surface an XAFS Structural Study
2005
The adsorption site of sodium atoms deposited onto a clean TiO2(110) surface has been determined by EXAFS. The best result is obtained for an 'in-between' site where the sodium is bound to two bridging oxygen atoms at 2.25 A and one in-plane one at 2.40 A in full agreement with DFT calculations. At higher coverage the site becomes a hollow site where Na is equidistant to the three oxygen atoms at 2.30 A.