A homomorphism between link and XXZ modules over the periodic Temperley-Lieb algebra

We study finite loop models on a lattice wrapped around a cylinder. A section of the cylinder has N sites. We use a family of link modules over the periodic Temperley-Lieb algebra EPTL_N(\beta, \alpha) introduced by Martin and Saleur, and Graham and Lehrer. These are labeled by the numbers of sites N and of defects d, and extend the standard modules of the original Temperley-Lieb algebra. Beside the defining parameters \beta=u^2+u^{-2} with u=e^{i\lambda/2} (weight of contractible loops) and \alpha (weight of non-contractible loops), this family also depends on a twist parameter v that keeps track of how the defects wind around the cylinder. The transfer matrix T_N(\lambda, \nu) depends on the anisotropy \nu and the spectral parameter \lambda that fixes the model. (The thermodynamic limit of T_N is believed to describe a conformal field theory of central charge c=1-6\lambda^2/(\pi(\lambda-\pi)).) The family of periodic XXZ Hamiltonians is extended to depend on this new parameter v and the relationship between this family and the loop models is established. The Gram determinant for the natural bilinear form on these link modules is shown to factorize in terms of an intertwiner i_N^d between these link representations and the eigenspaces of S^z of the XXZ models. This map is shown to be an isomorphism for generic values of u and v and the critical curves in the plane of these parameters for which i_N^d fails to be an isomorphism are given.Comment: Replacement of "The Gram matrix as a connection between periodic loop models and XXZ Hamiltonians", 31 page

From solar-like to anti-solar differential rotation in cool stars

Stellar differential rotation can be separated into two main regimes: solar-like when the equator rotates faster than the poles and anti-solar when the polar regions rotate faster than the equator. We investigate the transition between these two regimes with 3-D numerical simulations of rotating spherical shells. We conduct a systematic parameter study which also includes models from different research groups. We find that the direction of the differential rotation is governed by the contribution of the Coriolis force in the force balance, independently of the model setup (presence of a magnetic field, thickness of the convective layer, density stratification). Rapidly-rotating cases with a small Rossby number yield solar-like differential rotation, while weakly-rotating models sustain anti-solar differential rotation. Close to the transition, the two kinds of differential rotation are two possible bistable states. This study provides theoretical support for the existence of anti-solar differential rotation in cool stars with large Rossby numbers.Comment: 5 pages, 6 figures, accepted for publication in MNRA

Validity of the Adiabatic Approximation

We analyze the validity of the adiabatic approximation, and in particular the reliability of what has been called the "standard criterion" for validity of this approximation. Recently, this criterion has been found to be insufficient. We will argue that the criterion is sufficient only when it agrees with the intuitive notion of slowness of evolution of the Hamiltonian. However, it can be insufficient in cases where the Hamiltonian varies rapidly but only by a small amount. We also emphasize the distinction between the adiabatic {\em theorem} and the adiabatic {\em approximation}, two quite different although closely related ideas.Comment: 4 pages, 1 figur

What controls the magnetic geometry of M dwarfs?

Context: observations of rapidly rotating M dwarfs show a broad variety of large-scale magnetic fields encompassing dipole-dominated and multipolar geometries. In dynamo models, the relative importance of inertia in the force balance -- quantified by the local Rossby number -- is known to have a strong impact on the magnetic field geometry. Aims: we aim to assess the relevance of the local Rossby number in controlling the large-scale magnetic field geometry of M dwarfs. Methods: we explore the similarities between anelastic dynamo models in spherical shells and observations of active M-dwarfs, focusing on field geometries derived from spectropolarimetric studies. To do so, we construct observation-based quantities aimed to reflect the diagnostic parameters employed in numerical models. Results: the transition between dipole-dominated and multipolar large-scale fields in early to mid M dwarfs is tentatively attributed to a Rossby number threshold. We interpret late M dwarfs magnetism to result from a dynamo bistability occurring at low Rossby number. By analogy with numerical models, we expect different amplitudes of differential rotation on the two dynamo branches.Comment: 4 pages, 4 figures, accepted for publication in A&

Quadrupolar Order in Isotropic Heisenberg Models with Biquadratic Interaction

Through Quantum Monte Carlo simulation, we study the biquadratic-interaction model with the SU(2) symmetry in two and three dimensions. The zero-temperature phase diagrams for the two cases are identical and exhibit an intermediate phase characterized by finite quadrupole moment, in agreement with mean-field type arguments and the semi-classical theory. In three dimensions, we demonstrate that the model in the quadrupolar regime has a phase transition at a finite temperature. In contrast to predictions by mean-field theories, the phase transition to the quadrupolar phase turns out to be of the second order. We also examine the critical behavior in the two marginal cases with the SU(3) symmetry.Comment: 4 pages 5 figure

Thermodynamic metrics and optimal paths

A fundamental problem in modern thermodynamics is how a molecular-scale machine performs useful work, while operating away from thermal equilibrium without excessive dissipation. To this end, we derive a friction tensor that induces a Riemannian manifold on the space of thermodynamic states. Within the linear-response regime, this metric structure controls the dissipation of finite-time transformations, and bestows optimal protocols with many useful properties. We discuss the connection to the existing thermodynamic length formalism, and demonstrate the utility of this metric by solving for optimal control parameter protocols in a simple nonequilibrium model.Comment: 5 page

DeepWalk: Online Learning of Social Representations

We present DeepWalk, a novel approach for learning latent representations of vertices in a network. These latent representations encode social relations in a continuous vector space, which is easily exploited by statistical models. DeepWalk generalizes recent advancements in language modeling and unsupervised feature learning (or deep learning) from sequences of words to graphs. DeepWalk uses local information obtained from truncated random walks to learn latent representations by treating walks as the equivalent of sentences. We demonstrate DeepWalk's latent representations on several multi-label network classification tasks for social networks such as BlogCatalog, Flickr, and YouTube. Our results show that DeepWalk outperforms challenging baselines which are allowed a global view of the network, especially in the presence of missing information. DeepWalk's representations can provide $F_1$ scores up to 10% higher than competing methods when labeled data is sparse. In some experiments, DeepWalk's representations are able to outperform all baseline methods while using 60% less training data. DeepWalk is also scalable. It is an online learning algorithm which builds useful incremental results, and is trivially parallelizable. These qualities make it suitable for a broad class of real world applications such as network classification, and anomaly detection.Comment: 10 pages, 5 figures, 4 table

Developing conceptual hydrogeological model for Potsdam sandstones in southwestern Quebec, Canada

A hydrogeological study was conducted in Potsdam sandstones on the international border between Canada (Quebec) and the USA (New York). Two sandstone formations, arkose and conglomerate (base) and well-cemented quartz arenite (upper), underlie the study area and form the major regional aquifer unit. Glacial till, littoral sand and gravel, and marine silt and clay discontinuously overlie the aquifer. In both sandstone formations, sub-horizontal bedding planes are ubiquitous and display significant hydraulic conductivities that are orders of magnitude more permeable than the intact rock matrix. Aquifer tests demonstrate that the two formations have similar bulk hydrologic properties, with average hydraulic conductivities ranging from 2×10−5 to 4×10−5 m/s. However, due to their different lithologic and structural characteristics, these two sandstones impose rather different controls on groundwater flow patterns in the study area. Flow is sustained through two types of fracture networks: sub-horizontal, laterally extensive fractures in the basal sandstone, where hydraulic connectivity is very good horizontally but very poor vertically and each of the water-bearing bedding planes can be considered as a separate planar two-dimensional aquifer unit; and the more fractured and vertically jointed system found in the upper sandstone that promotes a more dispersed, three-dimensional movement of groundwater. Une étude hydrogéologique a été entreprise dans les grès de Potsdam, sur la frontière entre le Canada (Québec) et les Etats-Unis (New York). Sous le secteur d’étude, deux formations gréseuses, les arkoses et conglomérats (base) et les arénites quartzeuses cimentées (sommet), forment une unité aquifère majeure à l’échelle régionale. Les moraines glaciaires, les sables et graviers littoraux, et les argiles et silts marins recouvrent l’aquifère de manière discontinue. Dans les deux formations gréseuses, les litages sub-horizontaux sont omniprésents, et présentent des conductivités hydrauliques significatives, supérieures de plusieurs ordres de grandeur à celles de la matrice rocheuse intacte. Les pompages d’essai démontrent que les deux formations ont des propriétés hydrologiques apparentes comparables, avec notamment des conductivités hydrauliques comprises entre 2×10−5 et 4× 10−5 m/s. Cependant, du fait de leurs lithologies et de leurs caractéristiques structurales contrastées, ces deux formations gréseuses imposent des contrôles différents sur les écoulements souterrains dans le secteur d’étude. L’écoulement est soutenu par deux types de réseaux de fractures : des fractures latéralement extensives subhorizontales dans les grès de base, où la connectivité hydraulique est très bonne horizontalement mais médiocre verticalement, et où chacun des plans aquifères peut être considéré comme une unité aquifère isolée plane bidimensionnelle, et un système fissuré verticalement et plus fracturé situé dans les grès supérieurs, qui favorise des écoulements souterrains tridimensionnels et plus dispers

A universal optical all-fiber omnipolarizer

Wherever the polarization properties of a light beam are of concern, polarizers and polarizing beamsplitters (PBS) are indispensable devices in linear-, nonlinear-and quantum-optical schemes. By the very nature of their operation principle, transformation of incoming unpolarized or partially polarized beams through these devices introduces large intensity variations in the fully polarized outcoming beam(s). Such intensity fluctuations are often detrimental, particularly when light is post-processed by nonlinear crystals or other polarization-sensitive optic elements. Here we demonstrate the unexpected capability of light to self-organize its own state-of-polarization, upon propagation in optical fibers, into universal and environmentally robust states, namely right and left circular polarizations. We experimentally validate a novel polarizing device-the Omnipolarizer, which is understood as a nonlinear dual-mode polarizing optical element capable of operating in two modes-as a digital PBS and as an ideal polarizer. Switching between the two modes of operation requires changing beam's intensity

Fractured-Aquifer Hydrogeology from Geophysical Logs: Brunswick Group and Lockatong Formation, Pennsylvania

The Brunswick Group and the underlying Lockatong Formation are composed of lithified Mesozoic sediments that constitute part of the Newark Basin in southeastern Pennsylvania. These fractured rocks form an important regional aquifer that consists of gradational sequences of shale, siltstone, and sandstone, with fluid transport occurring primarily in fractures. An extensive suite of geophysical logs was obtained in seven wells located at the borough of Lansdale, Pennsylvania, in order to better characterize the areal hydrogeologic system and provide guidelines for the refinement of numerical ground water models. Six of the seven wells are approximately 120 m deep and the seventh extends to a depth of 335 m. Temperature, fluid conductivity, and flowmeter logs are used to locate zones of fluid exchange and to quantify transmissivities. Electrical resistivity and natural gamma logs together yield detailed stratigraphic information, and digital acoustic televiewer data provide magnetically oriented images of the borehole wall from which almost 900 fractures are identified