From simple to complex networks: inherent structures, barriers and valleys in the context of spin glasses

Given discrete degrees of freedom (spins) on a graph interacting via an energy function, what can be said about the energy local minima and associated inherent structures? Using the lid algorithm in the context of a spin glass energy function, we investigate the properties of the energy landscape for a variety of graph topologies. First, we find that the multiplicity Ns of the inherent structures generically has a lognormal distribution. In addition, the large volume limit of ln/ differs from unity, except for the Sherrington-Kirkpatrick model. Second, we find simple scaling laws for the growth of the height of the energy barrier between the two degenerate ground states and the size of the associated valleys. For finite connectivity models, changing the topology of the underlying graph does not modify qualitatively the energy landscape, but at the quantitative level the models can differ substantially.Comment: 10 pages, 9 figs, slightly improved presentation, more references, accepted for publication in Phys Rev

Lie systems and integrability conditions for t-dependent frequency harmonic oscillators

Time-dependent frequency harmonic oscillators (TDFHO's) are studied through the theory of Lie systems. We show that they are related to a certain kind of equations in the Lie group SL(2,R). Some integrability conditions appear as conditions to be able to transform such equations into simpler ones in a very specific way. As a particular application of our results we find t-dependent constants of the motion for certain one-dimensional TDFHO's. Our approach provides an unifying framework which allows us to apply our developments to all Lie systems associated with equations in SL(2,R) and to generalise our methods to study any Lie system

Quantum chaos of a mixed, open system of kicked cold atoms

The quantum and classical dynamics of particles kicked by a gaussian attractive potential are studied. Classically, it is an open mixed system (the motion in some parts of the phase space is chaotic, and in some parts it is regular). The fidelity (Lochshmidt echo) is found to exhibit oscillations that can be determined from classical considerations but are sensitive to phase space structures that are smaller than Planck's constant. Families of quasi-energies are determined from classical phase space structures. Substantial differences between the classical and quantum dynamics are found for time dependent scattering. It is argued that the system can be experimentally realized by cold atoms kicked by a gaussian light beam.Comment: 19 pages, 21 figures, (accepted for publication in Phys. Rev. E

Inlet conditions for large eddy simulation of gas-turbine swirl injectors

Copyright © 2008 American Institute of Aeronautics and AstronauticsIn this paper, we present a novel technique for generating swirl inlets for large eddy simulation. The velocity a short distance downstream of the inlet to the main domain is sampled and the flow velocity data are reintroduced back into the domain inlet, creating an inlet section integrated into the main domain in which turbulence can develop. Additionally, variable artificial body forces and velocity corrections are imposed in this inlet section, with feedback control to force the flow toward desired swirl, mean, and turbulent profiles. The method was applied to flow in an axisymmetric sudden expansion, with and without swirl at the inlet, and compared against experimental and literature large eddy simulation data and against similar results in the literature. The method generates excellent results for this case and is elegant and straightforward to implement

Scarring and the statistics of tunnelling

We show that the statistics of tunnelling can be dramatically affected by scarring and derive distributions quantifying this effect. Strong deviations from the prediction of random matrix theory can be explained quantitatively by modifying the Gaussian distribution which describes wavefunction statistics. The modified distribution depends on classical parameters which are determined completely by linearised dynamics around a periodic orbit. This distribution generalises the scarring theory of Kaplan [Phys. Rev. Lett. {\bf 80}, 2582 (1998)] to describe the statistics of the components of the wavefunction in a complete basis, rather than overlaps with single Gaussian wavepackets. In particular it is shown that correlations in the components of the wavefunction are present, which can strongly influence tunnelling-rate statistics. The resulting distribution for tunnelling rates is tested successfully on a two-dimensional double-well potential.Comment: 20 pages, 4 figures, submitted to Ann. Phy

Is classical reality completely deterministic?

The concept of determinism for a classical system is interpreted as the requirement that the solution to the Cauchy problem for the equations of motion governing this system be unique. This requirement is generally assumed to hold for all autonomous classical systems. We give counterexamples of this view. Our analysis of classical electrodynamics in a world with one temporal and one spatial dimension shows that the solution to the Cauchy problem with the initial conditions of a particular type is not unique. Therefore, random behavior of closed classical systems is indeed possible. This finding provides a qualitative explanation of how classical strings can split. We propose a modified path integral formulation of classical mechanics to include indeterministic systems.Comment: Replace the paper with a revised versio

Exploring shear alignment of concentrated wormlike micelles using rheology coupled with small-angle neutron scattering

Wormlike micelles (WLMs) are vital components of many consumer products and industrial fluids, adding a shear-dependent viscous texture through their entanglement in solutions. It is now well accepted from experiments such as coupling rheology and scattering that, similar to many polymer solutions and dispersions of highly anisotropic particles, WLM behavior during shear arises from the alignment of the "worms"with the shear field, resulting in ordering that is rapidly lost in the cessation of shear. Most studies of such systems have been limited to dilute systems that are far below concentrations used industrially and commercially, due to the complexity of analyzing shear-induced many-body effects in high volume fraction dispersions. Here, we explore the shear alignment of concentrated WLM solutions comprising sodium laureth sulfate and cocamidopropyl betaine in 0.38 M aqueous sodium chloride. By analyzing only scattering data at high values of the scattering vector (i.e., correlations at short length scales that are dominant in such concentrated systems), we explore whether useful information can be obtained by naïvely approximating the WLMs as an ensemble of unconnected short rods representing sections of the worms. By taking this reductionist approach to analyzing the obtained two-dimensional scattering patterns from these systems under shear, we find that in this regime, such concentrated worms can be approximated as cylinders that become more aligned with the direction of shear as volume fraction and shear rate increase

Cosmological Effects of Powerful AGN Outbursts in Galaxy Clusters: Insights from an XMM-Newton Observation of MS0735+7421

We report on the results of an analysis of XMM-Newton observations of MS0735+7421, the galaxy cluster which hosts the most energetic AGN outburst currently known. The previous Chandra image shows twin giant X-ray cavities (~200 kpc diameter) filled with radio emission and surrounded by a weak shock front. XMM data are consistent with these findings. The total energy in cavities and shock (~6 \times 10^{61} erg) is enough to quench the cooling flow and, since most of the energy is deposited outside the cooling region (~100 kpc), to heat the gas within 1 Mpc by ~1/4 keV per particle. The cluster exhibits an upward departure (factor ~2) from the mean L-T relation. The boost in emissivity produced by the ICM compression in the bright shells due to the cavity expansion may contribute to explain the high luminosity and high central gas mass fraction that we measure. The scaled temperature and metallicity profiles are in general agreement with those observed in relaxed clusters. Also, the quantities we measure are consistent with the observed M-T relation. We conclude that violent outbursts such as the one in MS0735+7421 do not cause dramatic instantaneous departures from cluster scaling relations (other than the L-T relation). However, if they are relatively common they may play a role in creating the global cluster properties.Comment: 69 pages, 30 figures, accepted for publication in ApJ Main Journa

Supersymmetry versus Integrability in two-dimensional Classical Mechanics

Supersymmetric extensions of Hamilton-Jacobi separable Liouville mechanical systems with two degrees of freedom are defined. It is shown that supersymmetry can be implemented in this type of systems in two independent ways. The structure of the constants of motion is unveiled and the entanglement between integrability and supersymmetry is explored.Comment: 28 pages, Added reference