Hydrodynamics of compressible superfluids in confined geometries

We present a study of the hydrodynamics of compressible superfluids in confined geometries. We use a perturbative procedure in terms of the dimensionless expansion parameter $(v/v_s)^2$ where $v$ is the typical speed of the flow and $v_s$ the speed of sound. A zero value of this parameter corresponds to the incompressible limit. We apply the procedure to two specific problems: the case of a trapped superfluid with a gaussian profile of the local density, and that of a superfluid confined in a rotating obstructed cylinder. We find that the corrections due to finite compressibility which are, as expected, negligible for liquid He, are important but amenable to the perturbative treatment for typical ultracold atomic systems.Comment: 17 pages, including 7 figures. To appear in Journ. Phys.

Superfluid Field response to Edge dislocation motion

We study the dynamic response of a superfluid field to a moving edge dislocation line to which the field is minimally coupled. We use a dissipative Gross-Pitaevskii equation, and determine the initial conditions by solving the equilibrium version of the model. We consider the subsequent time evolution of the field for both glide and climb dislocation motion and analyze the results for a range of values of the constant speed $V_D$ of the moving dislocation. We find that the type of motion of the dislocation line is very important in determining the time evolution of the superfluid field distribution associated with it. Climb motion of the dislocation line induces increasing asymmetry, as function of time, in the field profile, with part of the probability being, as it were, left behind. On the other hand, glide motion has no effect on the symmetry properties of the superfluid field distribution. Damping of the superfluid field due to excitations associated with the moving dislocation line occurs in both cases.Comment: 10 pages 7 figures. To appear in Phys. Rev

Dislocation Mobility and Anomalous Shear Modulus Effect in 4^4He Crystals

We calculate the dislocation glide mobility in solid $^4$He within a model that assumes the existence of a superfluid field associated with dislocation lines. Prompted by the results of this mobility calculation, we study within this model the role that such a superfluid field may play in the motion of the dislocation line when a stress is applied to the crystal. To do this, we relate the damping of dislocation motion, calculated in the presence of the assumed superfluid field, to the shear modulus of the crystal. As the temperature increases, we find that a sharp drop in the shear modulus will occur at the temperature where the superfluid field disappears. We compare the drop in shear modulus of the crystal arising from the temperature dependence of the damping contribution due to the superfluid field, to the experimental observation of the same phenomena in solid $^4$He and find quantitative agreement. Our results indicate that such a superfluid field plays an important role in dislocation pinning in a clean solid $^4$He at low temperatures and in this regime may provide an alternative source for the unusual elastic phenomena observed in solid $^4$He.Comment: 17 pages, 2 figures. To appear in JLT

Ising Model on a random network with annealed or quenched disorder

We study the equilibrium properties of an Ising model on a disordered random network where the disorder can be quenched or annealed. The network consists of four-fold coordinated sites connected via variable length one-dimensional chains. Our emphasis is on nonuniversal properties and we consider the transition temperature and other equilibrium thermodynamic properties, including those associated with one dimensional fluctuations arising from the chains. We use analytic methods in the annealed case, and a Monte Carlo simulation for the quenched disorder. Our objective is to study the difference between quenched and annealed results with a broad random distribution of interaction parameters. The former represents a situation where the time scale associated with the randomness is very long and the corresponding degrees of freedom can be viewed as frozen, while the annealed case models the situation where this is not so. We find that the transition temperature and the entropy associated with one dimensional fluctuations are always higher for quenched disorder than in the annealed case. These differences increase with the strength of the disorder up to a saturating value. We discuss our results in connection to physical systems where a broad distribution of interaction strengths is present.Comment: 11 pages including 9 figures. To appear in Phys. Rev.

Multidimensional persistence behaviour in an Ising system

We consider a periodic Ising chain with nearest-neighbour and $r$-th neighbour interaction and quench it from infinite temperature to zero temperature. The persistence probability $P(t)$, measured as the probability that a spin remains unflipped upto time $t$, is studied by computer simulation for suitable values of $r$. We observe that as time progresses, $P(t)$ first decays as $t^{-0.22}$ (-the {\em first} regime), then the $P(t)-t$ curve has a small slope (in log-log scale) for some time (-the {\em second} regime) and at last it decays nearly as $t^{-3/8}$ (-the {\em third} regime). We argue that in the first regime, the persistence behaviour is the usual one for a two-dimensional system, in the second regime it is like that of a non-interacting (`zero-dimensional') system and in the third regime the persistence behaviour is like that of a one dimensional Ising model. We also provide explanations for such behaviour.Comment: 6 pages, 12 figure

Heterogeneity and Vulnerability in the Urban Informal Economy

The focus of this paper is on the low-value urban informal economy in sub-Saharan Africa. The paper presents a case study from Uganda, with the focus on secondary cities where much of the urban population growth is expected in the next decade. There is also good evidence that informality will persist within both dynamic and in slow urban economies in sub-Saharan Africa. Analysis of the results from fieldwork is presented in support of the basic argument that, as the informal economy is likely to persist there is need for a more conducive policy approach to ensure its positive contribution to the urban economic development; seen as a mainstay of Africa’s future economic development. Currently, the informal economy is considered ephemeral, with little institutional engagement, with the focus on restrictive measures. The paper explores the range of theoretical perspectives on the urban informal economy leading to its re-conceptualizing as part of a continuum of activities in which both formal and informal elements are interlinked. Given the need to improve productivity of activities of different constituent groups along the continuum, the aim of this paper is to develop a conceptual framework that would enable the systematic analyses and identification of the internal diversities within the informal economy. It could be used in future policy research to identify diagnostic groups for entry points. The findings from the fieldwork carried out in the cities of Mbale and Mbarara, show that there are several viable options for sustainable livelihoods, particularly in a dynamic urban center. However, while women dominate in numbers, men remain the main actors. This calls for an inclusive, gender-mainstreamed, pro-poor development policy to complement an enterprise-based approach

Magnetic properties of Mn-doped Ge46 and Ba8Ge46 clathrates

We present a detailed study of the magnetic properties of unique cluster assembled solids namely Mn doped Ge46 and Ba8Ge46 clathrates using density functional theory. We find that ferromagnetic (FM) ground states may be realized in both the compounds when doped with Mn. In Mn2Ge44, ferromagnetism is driven by hybridization induced negative exchange splitting, a generic mechanism operating in many diluted magnetic semiconductors. However, for Mn-doped Ba8Ge46 clathrates incorporation of conduction electrons via Ba encapsulation results in RKKY-like magnetic interactions between the Mn ions. We show that our results are consistent with the major experimental observations for this system.Comment: 6 pages, 4 figure

Validity of the linear coupling approximation in heavy-ion fusion reactions at sub barrier energies

The role of higher order coupling of surface vibrations to the relative motion in heavy-ion fusion reactions at near-barrier energies is investigated. The coupled channels equations are solved to all orders, and also in the linear and the quadratic coupling approximations. Taking $^{64}$Ni + $^{92,96}$Zr reactions as examples, it is shown that all order couplings lead to considerably improved agreement with the experimentally measured fusion cross sections and average angular momenta of the compound nucleus for such heavy nearly symmetric systems. The importance of higher order coupling is also examined for asymmetric systems like $^{16}$O + $^{112}$Cd, $^{144}$Sm, for which previous calculations of the fusion cross section seemed to indicate that the linear coupling approximation was adequate. It is shown that the shape of the barrier distributions and the energy dependence of the average angular momentum can change significantly when the higher order couplings are included, even for systems where measured fusion cross sections may seem to be well reproduced by the linear coupling approximation.Comment: Latex file, 15 pages, 6 figure

Persistence in nonequilibrium surface growth

Persistence probabilities of the interface height in (1+1)- and (2+1)-dimensional atomistic, solid-on-solid, stochastic models of surface growth are studied using kinetic Monte Carlo simulations, with emphasis on models that belong to the molecular beam epitaxy (MBE) universality class. Both the initial transient and the long-time steady-state regimes are investigated. We show that for growth models in the MBE universality class, the nonlinearity of the underlying dynamical equation is clearly reflected in the difference between the measured values of the positive and negative persistence exponents in both transient and steady-state regimes. For the MBE universality class, the positive and negative persistence exponents in the steady-state are found to be $\theta^S_{+} = 0.66 \pm 0.02$ and $\theta^S_{-} = 0.78 \pm 0.02$, respectively, in (1+1) dimensions, and $\theta^S_{+} = 0.76 \pm 0.02$ and $\theta^S_{-} =0.85 \pm 0.02$, respectively, in (2+1) dimensions. The noise reduction technique is applied on some of the (1+1)-dimensional models in order to obtain accurate values of the persistence exponents. We show analytically that a relation between the steady-state persistence exponent and the dynamic growth exponent, found earlier to be valid for linear models, should be satisfied by the smaller of the two steady-state persistence exponents in the nonlinear models. Our numerical results for the persistence exponents are consistent with this prediction. We also find that the steady-state persistence exponents can be obtained from simulations over times that are much shorter than that required for the interface to reach the steady state. The dependence of the persistence probability on the system size and the sampling time is shown to be described by a simple scaling form.Comment: 28 pages, 16 figure

Dimension-adaptive bounds on compressive FLD Classification

Efficient dimensionality reduction by random projections (RP) gains popularity, hence the learning guarantees achievable in RP spaces are of great interest. In finite dimensional setting, it has been shown for the compressive Fisher Linear Discriminant (FLD) classifier that forgood generalisation the required target dimension grows only as the log of the number of classes and is not adversely affected by the number of projected data points. However these bounds depend on the dimensionality d of the original data space. In this paper we give further guarantees that remove d from the bounds under certain conditions of regularity on the data density structure. In particular, if the data density does not fill the ambient space then the error of compressive FLD is independent of the ambient dimension and depends only on a notion of ‘intrinsic dimension'