Search results for "Freedom"
showing 10 items of 458 documents
Efficient Iterative Solution of Time-harmonic Scattering by Objects in Layered Fluid
2008
We consider the computation of time-harmonic acoustic scattering by sound-soft or elastic objects in layered media. An example of such problem is the scattering by a mine buried in sediment. The computational domain can be tens or hundreds of meters long while the target requires modeling of details smaller than one centimeter. A discretized problem can have several billion degrees of freedom.
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…
Thermal density fluctuations in amorphous polymers as revealed by small angle X-ray diffraction
1973
In the case of equilibrium the mean square relative fluctuations of the thermodynamic parameters vanish asymptotically as the number of degrees of freedom approach infinity. There are various observable effects, however, which are related to local fluctuations of the thermodynamic quantities within small parts of the macroscopic system. In particular the scattering of electromagnetic waves by a one-component, one-phase system is due to thermal density fluctuations within small volumes V of the sample. Considering a grand canonical ensemble the phenomenological theory of local fluctuations (1) for a one component system shows that the fluctuation of the number of particles N in the volume V …
Derivation of transient relativistic fluid dynamics from the Boltzmann equation
2012
In this work we present a general derivation of relativistic fluid dynamics from the Boltzmann equation using the method of moments. The main difference between our approach and the traditional 14-moment approximation is that we will not close the fluid-dynamical equations of motion by truncating the expansion of the distribution function. Instead, we keep all terms in the moment expansion. The reduction of the degrees of freedom is done by identifying the microscopic time scales of the Boltzmann equation and considering only the slowest ones. In addition, the equations of motion for the dissipative quantities are truncated according to a systematic power-counting scheme in Knudsen and inve…
Field Fluctuations in a One-Dimensional Cavity with a Mobile Wall
2013
We consider a scalar field in a one-dimensional cavity with a mobile wall. The wall is assumed bounded by a harmonic potential and its mechanical degrees of freedom are treated quantum mechanically. The possible motion of the wall makes the cavity length variable, and yields a wall-field interaction and an effective interaction among the modes of the cavity. We consider the ground state of the coupled system and calculate the average number of virtual excitations of the cavity modes induced by the wall-field interaction, as well as the average value of the field energy density. We compare our results with analogous quantities for a cavity with fixed walls, and show a correction to the Casim…
Remarks on the reduced phase space of -dimensional gravity on a torus in the Ashtekar formulation
1998
We examine the reduced phase space of the Barbero-Varadarajan solutions of the Ashtekar formulation of (2 + 1)-dimensional general relativity on a torus. We show that it is a finite-dimensional space due to the existence of an infinite-dimensional residual gauge invariance which reduces the infinite-dimensional space of solutions to a finite-dimensional space of gauge-inequivalent solutions. This is in agreement with general arguments which imply that the number of physical degrees of freedom for (2 + 1)-dimensional Ashtekar gravity on a torus is finite.
Baryon chiral perturbation theory
2009
We provide a short introduction to the one-nucleon sector of chiral perturbation theory and address the issue of power counting and renormalization. We discuss the infrared regularization and the extended on-mass-shell scheme. Both allow for the inclusion of further degrees of freedom beyond pions and nucleons and the application to higher-loop calculations. As applications we consider the chiral expansion of the nucleon mass to order ${\cal O}(q^6)$ and the inclusion of vector and axial-vector mesons in the calculation of nucleon form factors. Finally, we address the complex-mass scheme for describing unstable particles in effective field theory.
Single Particle Levels and ββ-Decay Matrix Elements in The Interacting Boson Model
2018
Recently a new method to calculate the occupancies of single particle levels in atomic nuclei was developed in the context of the microscopic interacting boson model, in which neutron and proton degrees of freedom are treated explicitly (IBM-2). The energies of the single particle levels constitute a very important input for the calculation of the occupancies in this method, and further they play important role in the calculation of double beta decay nuclear matrix elements. Here we discuss how the 0νββ, 0νhββ, and 2νββ-decay nuclear matrix elements (NMEs) are affected when the energies of single particle levels are changed. peerReviewed
Electron and nuclear dynamics of a molecular ion in an intense laser field
2004
The dynamics of a two-dimensional $\mathrm{H}_{2}^{+}$ molecule interacting with a strong laser pulse beyond the usual approximation of fixed nuclei is presented. The motion of the nuclei is studied by using the classical Newton laws while the electron is described with a full quantal treatment. The axis of the molecule, initially not aligned to the laser field, performs a long-period pendular motion around the laser polarization axis. Vibrational degrees of freedom are seen to be excited. The radiation emitted by the oscillating charges presents variations that are synchronous to the pendular motion. The possibility of monitoring the motion of the molecule through the emitted radiation is …
Mode coupling theory for molecular liquids: What can we learn from a system of hard ellipsoids?
1999
Molecular fluids show rich and complicated dynamics close to the glass transition. Some of these observations are related to the fact that translational and orientational degrees of freedom couple in nontrivial ways. A model system which can serve as a paradigm to understand these couplings is a system of hard ellipsoids of revolution. To test this we compare at the ideal glass transition the static molecular correlators of a linear A-B Lennard-Jones molecule obtained from a molecular dynamics simulation with a selected fluid of hard ellipsoids for which the static correlators have been obtained using Percus-Yevick theory. We also demonstrate that the critical non-ergodicity parameters obta…