Properties Of Configuration Space Research Articles

Effects of general relativistic post-Newtonian approximations on the configuration space properties of elliptical orbital trajectories

Post-Newtonian approximations have been successful in describing various astronomical phenomena that classical Newtonian gravity could not. One such phenomenon is the precession of the periapsis of elliptical orbits. Einstein originally solved the problem in 1916 and since then others have been applying the technique to numerous complex systems. However, not much attention has been given to studying the changes in the configuration space when switching from Newtonian to post-Newtonian mechanics. Here, we compare the sizes and topologies of the configuration spaces of both these approaches and further explore the likelihood of planetary collisions in other star systems when configuration space expansion due to general relativity is taken into account.

Configuration Space of Geometric Objects

The concept of configuration space of geometric objects is introduced. Its generalized variables are metric parameters of the spatial form and parameters of the location of objects. The properties of configuration spaces of complex geometric objects are considered. The structures of configuration spaces for various classes of geometric object placement problems, including packing and covering problems, are analyzed. The concept of Φ-function of geometric objects with variable metrical parameters is generalized.

Origin of end-of-aging and subaging scaling behavior in glassy dynamics

Linear response functions of aging systems are routinely interpreted using the scaling variable t(obs)/t(w)(mu), where t(w) is the time at which the field conjugated to the response is turned on or off, and where t(obs) is the "observation" time elapsed from the field change. The response curve obtained for different values of t(w) are usually collapsed using values of mu slightly below one, a scaling behavior generally known as subaging. Recent spin glass thermoremanent magnetization experiments have shown that the value of mu is strongly affected by the form of the initial cooling protocol [G. F. Rodriguez, Phys. Rev. Lett. 91, 037203 (2003)], and even more importantly [G. G. Kenning, Phys. Rev. Lett. 97, 057201 (2006)], that the t(w) dependence of the response curves vanishes altogether in the limit t(obs)>>t(w). The latter result shows that t(obs)/t(w)(mu) scaling of linear response data cannot be generally valid, thereby casting some doubt on the theoretical significance of the exponent mu . In this work, a common mechanism is proposed for the origin of both subaging and end of aging behavior in glassy dynamics. The mechanism combines real and configuration space properties of the state produced by the initial thermal quench which initiates the aging process.

Higher Tamm-Dankoff approximation for rotational nuclear states

Within the Higher Tamm Dancoff Approximation (HTDA), single particle states associated with a mean field of the Hartree-Fock type are used into shell model like calculations. Recently, this approach has been used for ground state calculations in magic nuclei and in the N = Z mass region, as well as to study properties of some important isomeric states. The Cranking version of this formalism (Cr. HTDA) represents an attempt to reproduce rotational bands up to high spins in heavy nuclei. In this context, through the use of the mean field part of HTDA, many deformation and rotation effects (as intruder orbitals and effects of the time reversal symmetry breaking) are included in the configuration space. This work discusses the Cr. HTDA results obtained for two Pb isotopes (in order to test the approach), when using up to 2 particles – 2 holes excitations and provides tests for enlargement of the configuration space by 4 particle – 4 holes excitations. It is focused on the configuration space properties, improvement of truncation schemes, computational problems and saturation behavior of some physical quantities.

On the metrical properties of the configuration space

AbstractWe study some topological and metrical properties of configuration spaces. In particular, we introduce a family of metrics on the configuration space Γ, which makes it a Polish space. Compact functions on Γ are also considered. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Configuration spaces of labeled particles and finite Eilenberg-MacLane complexes

For any Coxeter system (W, S), the group W acts naturally on the complement of the associated complex hyperplane arrangement. By the well-known conjecture, the orbit space of this action is the classifying space of the corresponding Artin group. We describe some properties of configuration spaces of particles labeled by elements of a partial monoid and use them to prove that the orbit space mentioned in the conjecture is the classifying space of the positive Artin monoid. In particular, the conjecture reduces to a problem concerning the group completion of this monoid.

Collective hyperspherical coordinates for polyatomic molecules and clusters

For n-body dynamics an analysis is made of the properties of configuration space within a symmetric hyperspherical framework. Coordinates are conveniently broken up into spatial (or external) rotations, kinematic invariants (related to the inertia moments) and kinematic (or internal) rotations. Their usefulness is demonstrated for the study of constrained intramolecular motions and of concerted reactions and for collective modes of polyatomic molecules and clusters. For a fixed hyperradius, which is a measure of total inertia, the space of kinematic invariants is the surface of a right spherical triangle that leads to the tetrahedral (for n = 4) or octahedral (for n ≥ 5) tessellation of the sphere. Alternative parametrizations are discussed, including the proper one to deal with the umbrella inversion motion of ammonia.

Instantaneous normal mode analysis of supercooled water

We use the instantaneous normal mode approach to provide a description of the local curvature of the potential energy surface of a model for water. We focus on the region of the phase diagram in which the dynamics may be described by mode-coupling theory. We find that the diffusion constant depends on the fraction of directions in configuration space connecting different local minima, supporting the hypothesis that the dynamics are controlled by the geometric properties of configuration space. Furthermore, we find a relation between the number of basins accessed in equilibrium and the connectivity between them.

On configuration spaces, their homology, and Lie algebras

Homological and geometric properties of configuration spaces of points in Euclidean space are described. Connections to non-abelian analogues of exterior algebras and mapping class groups are also given.

Exact two-dimensional plasma pair-correlation function in the Singwi-Tosi-Land-Sjolander approximation. II. Configuration-space analysis

The configuration-space properties of the pair-correlation function in the Singwi-Tosi-Land-Sjolander approximation scheme for a two-dimensional one-component plasma are derived here, using the exact solution in k space in Paper I (Phys. Rev. A 20, 329 (1979)). We also study in detail the effective static potential around a test particle for three cases representing weak, intermediate, and strong coupling.