Search results for "Quadrat"
showing 10 items of 344 documents
Cohesive-frictional interface in an equilibrium based finite element formulation
2020
The Hybrid Equilibrium Element (HEE) formulation, with quadratic stress field is defined in the class of statically admissible solutions, which implicitly satisfy the homogeneous equilibrium equations. The inter-element equilibrium condition and the boundary equilibrium condition are exactly imposed by considering a quadratic displacement fields at the element sides, as an interfacial Lagrangian variable, in a classical hybrid formulation. The displacement degrees of freedom are independently defined for each element side, where a cohesive-frictional interface can be embedded. The embedded interface is defined by the same stress fields of the hybrid equilibrium element and it does not requi…
On the geometry of Killing and conformal tensors
2006
The second order Killing and conformal tensors are analyzed in terms of their spectral decomposition, and some properties of the eigenvalues and the eigenspaces are shown. When the tensor is of type I with only two different eigenvalues, the condition to be a Killing or a conformal tensor is characterized in terms of its underlying almost-product structure. A canonical expression for the metrics admitting these kinds of symmetries is also presented. The space-time cases 1+3 and 2+2 are analyzed in more detail. Starting from this approach to Killing and conformal tensors a geometric interpretation of some results on quadratic first integrals of the geodesic equation in vacuum Petrov-Bel type…
Nonsingular charged black holes \`{a} la Palatini
2012
We argue that the quantum nature of matter and gravity should lead to a discretization of the allowed states of the matter confined in the interior of black holes. To support and illustrate this idea, we consider a quadratic extension of General Relativity formulated \`{a} la Palatini and show that nonrotating, electrically charged black holes develop a compact core at the Planck density which is nonsingular if the mass spectrum satisfies a certain discreteness condition. We also find that the area of the core is proportional to the number of charges times the Planck area.
Finite Entanglement Entropy in Asymptotically Safe Quantum Gravity
2018
Entanglement entropies calculated in the framework of quantum field theory on classical, flat or curved, spacetimes are known to show an intriguing area law in four dimensions, but they are also notorious for their quadratic ultraviolet divergences. In this paper we demonstrate that the analogous entanglement entropies when computed within the Asymptotic Safety approach to background independent quantum gravity are perfectly free from such divergences. We argue that the divergences are an artifact due to the over-idealization of a rigid, classical spacetime geometry which is insensitive to the quantum dynamics.
Generalized Conformal Symmetry and Extended Objects from the Free Particle
1998
The algebra of linear and quadratic functions of basic observables on the phase space of either the free particle or the harmonic oscillator possesses a finite-dimensional anomaly. The quantization of these systems outside the critical values of the anomaly leads to a new degree of freedom which shares its internal character with spin, but nevertheless features an infinite number of different states. Both are associated with the transformation properties of wave functions under the Weyl-symplectic group $WSp(6,\Re)$. The physical meaning of this new degree of freedom can be established, with a major scope, only by analysing the quantization of an infinite-dimensional algebra of diffeomorphi…
Loop quantum gravity and Planck-size black hole entropy
2007
The Loop Quantum Gravity (LQG) program is briefly reviewed and one of its main applications, namely the counting of black hole entropy within the framework is considered. In particular, recent results for Planck size black holes are reviewed. These results are consistent with an asymptotic linear relation (that fixes uniquely a free parameter of the theory) and a logarithmic correction with a coefficient equal to -1/2. The account is tailored as an introduction to the subject for non-experts.
Dynamics for a simple graph using the U(N) framework for loop quantum gravity
2012
The implementation of the dynamics in loop quantum gravity (LQG) is still an open problem. Here, we discuss a tentative dynamics for the simplest class of graphs in LQG: Two vertices linked with an arbitrary number of edges. We find an interesting global U(N) symmetry in this model that selects the homogeneous/isotropic sector. Then, we propose a quantum Hamiltonian operator for this reduced sector. Finally, we introduce the spinor representation for LQG in order to propose a classical effective dynamics for this model.
SHIFT AND WIDTH OF HeII LINES
1998
Abstract Based on a quantum statistical many-particle theory, the shift and the width of some He II lines have been evaluated. Ion dynamics have been treated within the model microfield method. Furthermore, fine structure splitting has been taken into account in order to check whether this effect is the cause for the existing large discrepancies between theoretical and experimental line widths. Besides the electronic contributions to the line shift, the shift due to the inhomogeneities of the ionic microfield as well as that due to the quadratic Stark effect has been included.
Location of transition states and stable intermediates by MINIMAX/MINIMI optimization of synchronous transit pathways
1983
The MINIMAX/MINIMI concept for the location of transition states and/or stable intermediates of chemical reactions is introduced, based on the synchronous transit method. According to this strategy, minimization of quadratic synchronous transit path maxima or minima is achieved by constrained exhaustive optimization of internal coordinates. The method and its efficiency are demonstrated for two-dimensional model surfaces as well as for thermally allowed electrocyclic interconversions of cyclopropyl-/allyl-cation and cyclobutene-/butadiene (gauche) within the framework of MNDO-SCF calculations. Thus, in both cases a direct comparison with the exact solution determined by minimization of the …
Nonlinear SDE Excited by External Lévy White Noise Processes
2011
A numerical method for approximating the statistics of the solution of nonlinear stochastic systems excited by Gaussian and non-Gaussian external white noises is proposed. The differential equation governing the evolution in time of the characteristic function is resolved by the convolution quadrature method. This approach is especially suited for those problems in which the nonlinear drift term is not of polynomial form. In such cases the equation governing the evolution in time of the characteristic function is not a partial differential equation. Statistics are found by introducing an integral operator of Wiener-Hopf type, called the transformation operator, and applying the Lubich's con…