Matrix product state approach for a two-lead, multi-level Anderson impurity model

We exploit the common mathematical structure of the numerical renormalization group and the density matrix renormalization group, namely, matrix product states, to implement an efficient numerical treatment of a two-lead, multi-level Anderson impurity model. By adopting a star-like geometry, where each species (spin and lead) of conduction electrons is described by its own Wilson chain, instead of using a single Wilson chain for all species together, we achieve a very significant reduction in the numerical resources required to obtain reliable results. We illustrate the power of this approach by calculating ground state properties of a four-level quantum dot coupled to two leads. The success of this proof-of-principle calculation suggests that the star geometry constitutes a promising strategy for future calculations the ground state properties of multi-band, multi-level quantum impurity models. Moreover, we show that it is possible to find an "optimal" chain basis, obtained via a unitary transformation (acting only on the index distinguishing different Wilson chains), in which degrees of freedom on different Wilson chains become effectively decoupled from each other further out on the Wilson chains. This basis turns out to also diagonalize the model's chain-to-chain scattering matrix. We demonstrate this for a spinless two-lead model, presenting DMRG-results for the mutual information between two sites located far apart on different Wilson chains, and NRG results with respect to the scattering matrix.Comment: extended version, 11 pages, 12 figure

On turbulent entrainment and dissipation in dilute polymer solutions

We present a comparative experimental study of a turbulent flow developing in clear water and dilute polymer solutions (25 and 50 wppm polyethylene oxide). The flow is forced by a planar grid that oscillates vertically with stroke S and frequency f in a square container of initially still fluid. Two-component velocity fields are measured in a vertical plane passing through the center of the tank by using time resolved particle image velocimetry. After the forcing is initiated, a turbulent layer develops that is separated from the initially irrotational fluid by a sharp interface, the so-called turbulent/nonturbulent interface (TNTI). The turbulent region grows in time through entrainment of surrounding fluid until the fluid in the whole container is in turbulent motion. From the comparison of the experiments in clear water and polymer solutions we conclude: (i) Polymer additives modify the large scale shape of the TNTI. (ii) Both, in water and in the polymer solution the mean depth of the turbulent layer, H(t), follows the theoretical prediction for Newtonian fluids H(t)∞√Kt, where K∞S^2f is the “grid action.” (iii) We find a larger grid action for dilute polymer solutions than for water. As a consequence, the turbulent kinetic energy of the flow increases and the rate of energy input becomes higher. (iv) The entrainment rate β=v_e/v_(rms) (where v_e=dH/dt is the interface propagation velocity and v_(rms) is the root mean square of the vertical velocity) is lower for polymers (β_p≈0.7) than for water (β_w≈0.8). The measured values for β are in good agreement with similarity arguments, from which we estimate that in our experiment about 28% of the input energy is dissipated by polymers

Viscous tilting and production of vorticity in homogeneous turbulence

Viscous depletion of vorticity is an essential and well known property of turbulent flows, balancing, in the mean, the net vorticity production associated with the vortex stretching mechanism. In this letter, we, however, demonstrate that viscous effects are not restricted to a mere destruction process, but play a more complex role in vorticity dynamics that is as important as vortex stretching. Based on the results from three dimensional particle tracking velocimetry experiments and direct numerical simulation of homogeneous and quasi-isotropic turbulence, we show that the viscous term in the vorticity equation can also locally induce production of vorticity and changes of the orientation of the vorticity vector (viscous tilting)

Acceleration, pressure and related quantities in the proximity of the turbulent/non-turbulent interface

This paper presents an analysis of flow properties in the proximity of the turbulent/non-turbulent interface (TNTI), with particular focus on the acceleration of fluid particles, pressure and related small scale quantities such as enstrophy, ω2 = ωiωi, and strain, s2 = sijsij. The emphasis is on the qualitative differences between turbulent, intermediate and non-turbulent flow regions, emanating from the solenoidal nature of the turbulent region, the irrotational character of the non-turbulent region and the mixed nature of the intermediate region in between. The results are obtained from a particle tracking experiment and direct numerical simulations (DNS) of a temporally developing flow without mean shear. The analysis reveals that turbulence influences its neighbouring ambient flow in three different ways depending on the distance to the TNTI: (i) pressure has the longest range of influence into the ambient region and in the far region non-local effects dominate. This is felt on the level of velocity as irrotational fluctuations, on the level of acceleration as local change of velocity due to pressure gradients, Du/Dt ∂u/∂t − p/ρ, and, finally, on the level of strain due to pressure-Hessian/strain interaction, (D/Dt)(s2/2) (∂/∂t)(s2/2) −sijp,ij > 0; (ii) at intermediate distances convective terms (both for acceleration and strain) as well as strain production −sijsjkski > 0 start to set in. Comparison of the results at Taylor-based Reynolds numbers Reλ = 50 and Reλ = 110 suggests that the distances to the far or intermediate regions scale with the Taylor microscale λ or the Kolmogorov length scale η of the flow, rather than with an integral length scale; (iii) in the close proximity of the TNTI the velocity field loses its purely irrotational character as viscous effects lead to a sharp increase of enstrophy and enstrophy-related terms. Convective terms show a positive peak reflecting previous findings that in the laboratory frame of reference the interface moves locally with a velocity comparable to the fluid velocity fluctuation

A Lagrangian investigation of the small-scale features of turbulent entrainment through particle tracking and direct numerical simulation

We report an analysis of small-scale enstrophy ω2 and rate of strain s2 dynamics in the proximity of the turbulent/non-turbulent interface in a flow without strong mean shear. The techniques used are three-dimensional particle tracking (3D-PTV), allowing the field of velocity derivatives to be measured and followed in a Lagrangian manner, and direct numerical simulations (DNS). In both experiment and simulation the Taylor-microscale Reynolds number is Reλ = 50. The results are based on the Lagrangian viewpoint with the main focus on flow particle tracers crossing the turbulent/non-turbulent interface. This approach allowed a direct investigation of the key physical processes underlying the entrainment phenomenon and revealed the role of small-scale non-local, inviscid and viscous processes. We found that the entrainment mechanism is initiated by self-amplification of s2 through the combined effect of strain production and pressure--strain interaction. This process is followed by a sharp change of ω2 induced mostly by production due to viscous effects. The influence of inviscid production is initially small but gradually increasing, whereas viscous production changes abruptly towards the destruction of ω2. Finally, shortly after the crossing of the turbulent/non-turbulent interface, production and dissipation of both enstrophy and strain reach a balance. The characteristic time scale of the described processes is the Kolmogorov time scale, τη. Locally, the characteristic velocity of the fluid relative to the turbulent/non-turbulent interface is the Kolmogorov velocity, u

Voz y voto: participación política y calidad de la democracia en México

[ES] La igualdad intrínseca de cada ciudadano es una suposición fundamental de cualquier sistema democrático. Por esto, cualquier evaluación de la calidad de la democracia tiene que considerar la «igualdad de voz», o sea, el grado en que los ciudadanos tienen oportunidades más o menos iguales de participar en la toma de decisiones colectivas. Este ensayo hace una evaluación de la calidad de la democracia en México con especial atención a las desigualdades que existen en la participación política de ciudadanos con niveles de ingresos altos y bajos. Los pobres en México votan menos y participan menos que los ciudadanos de mayores recursos económicos en actividades políticas dirigidas directamente a los gobernantes. Cuando participan tienden a hacerlo en actividades con poca capacidad de comunicar información sobre sus preferencias o de presionar a las autoridades, produciendo las condiciones para que los gobiernos no respondan por igual a las demandas de todos los grupos sociales.[EN] Because intrinsic equality of each citizen is a fundamental assumption of democracies, any assessments of the quality of democracy must consider the equality of political voice, that is whether a political system provides citizens with more or less equal opportunities to participate in collective decisions. This essay examines patterns of political participation in Mexico to assess whether there are systematic inequalities in the abilities of Mexicans from different income groups to exercise their voice in the political process. The evidence shows that the poor in Mexico vote less often and participate less frequently in government-directed political acts than the wealthy. When they do participate, the poor do so in activities which have little capacity to inform about their needs and preferences, and with little capacity to put pressure on government officials. This creates conditions for governments to not be responsive to or representative of the demands of different social groups

Effects of mean shear on the local turbulent entrainment process

We report on effects of mean shear on the turbulent entrainment process, focusing in particular on their relation to small-scale processes in the proximity of the turbulent/non-turbulent interface (TNTI). Three-dimensional particle tracking velocimetry (3D-PTV) measurements of an axisymmetric jet are compared to data from a direct numerical simulation (DNS) of a zero-mean-shear (ZMS) flow. First, conditional statistics relative to the interface position are investigated in a pseudo-Eulerian view (i.e. in a fixed frame relative to the interface position) and in a Lagrangian view. We find that in a pseudo-Eulerian frame of reference, both vorticity fluctuations and mean shear contribute to the vorticity jump at the boundary between irrotational and turbulent regions. In contrast, the Lagrangian evolution of enstrophy along trajectories crossing the entrainment interface is almost exclusively dominated by vorticity fluctuations, at least during the first Kolmogorov time scales after passing the interface. A mapping between distance to the instantaneous interface versus conditional time along the trajectory shows that entraining particles remain initially close to the TNTI and therefore attain lower average enstrophy values. The ratio between the rate of change of enstrophy in the two frames of references defines the local entrainment velocity ${v}_{n} = - (\mathrm{D} {\omega }^{2} / \mathrm{D} t)/ (\partial {\omega }^{2} / \partial {\hat {x} }_{n} )$ , where ${\omega }^{2}$ is enstrophy and ${\hat {x} }_{n}$ is the coordinate normal to the TNTI. The quantity ${v}_{n}$ is decomposed into mean and fluctuating components and it is found that mean shear enhances the local entrainment velocity via inviscid and viscous effects. Further, the analysis substantiates that for all investigated flow configurations the local entrainment velocity depends considerably on the geometrical shape of the interface. Depending on the surface shape, different small-scale mechanisms are dominant for the local entrainment process, i.e. viscous effects for convex shapes and vortex stretching for concave shapes, looking from the turbulent region towards the convoluted boundary. Moreover, turbulent fluctuations display a stronger dependence on the shape of the interface than mean shear effect

Occupancy of wild southern pig-tailed macaques in intact and degraded forests in Peninsular Malaysia

Deforestation is a major threat to terrestrial tropical ecosystems, particularly in Southeast Asia where human activities have dramatic consequences for the survival of many species. However, responses of species to anthropogenic impact are highly variable. In order to establish effective conservation strategies, it is critical to determine a species’ ability to persist in degraded habitats. Here, we used camera trapping data to provide the first insights into the temporal and spatial distribution of southern pig-tailed macaques (Macaca nemestrina, listed as ‘Vulnerable’ by the IUCN) across intact and degraded forest habitats in Peninsular Malaysia, with a particular focus on the effects of clear-cutting and selective logging on macaque occupancy. Specifically, we found a 10% decline in macaque site occupancy in the highly degraded Pasoh Forest Reserve from 2013 to 2017. This may be strongly linked to the macaques’ sensitivity to intensive disturbance through clear-cutting, which significantly increased the probability that M. nemestrina became locally extinct at a previously occupied site. However, no clear relationship between moderate disturbance, i.e. selective logging, and the macaques’ local extinction probability as well as site occupancy was found in the Pasoh Forest Reserve and Belum-Temengor Forest Complex. Further, an identical age and sex structure of macaques in selectively logged and completely undisturbed habitat types within the Belum-Temengor Forest Complex indicated that the macaques did not show increased mortality or declining birth rates when exposed to selective logging. Overall, this suggests that low to moderately disturbed forests may still constitute valuable habitats that support viable populations of M. nemestrina, and thus need to be protected against further degradation. Our results emphasize the significance of population monitoring through camera trapping for understanding the ability of threatened species to cope with anthropogenic disturbance. This can inform species management plans and facilitate the development of effective conservation measures to protect biodiversity