Novel families of SU(N){\rm SU}(N) AKLT states with arbitrary self-conjugate edge states

Using the Matrix Product State framework, we generalize the Affleck-Kennedy-Lieb-Tasaki (AKLT) construction to one-dimensional spin liquids with global color ${\rm SU}(N)$ symmetry, finite correlation lengths, and edge states that can belong to any self-conjugate irreducible representation (irrep) of ${\rm SU}(N)$. In particular, ${\rm SU}(2)$ spin-$1$ AKLT states with edge states of arbitrary spin $s=1/2,1,3/2,\cdots$ are constructed, and a general formula for their correlation length is given. Furthermore, we show how to construct local parent Hamiltonians for which these AKLT states are unique ground states. This enables us to study the stability of the edge states by interpolating between exact AKLT Hamiltonians. As an example, in the case of spin-$1$ physical degrees of freedom, it is shown that a quantum phase transition of central charge $c = 1$ separates the Symmetry Protected Topological (SPT) phase with spin-$1/2$ edge states from a topologically trivial phase with spin-$1$ edge states. We also address some specificities of the generalization to ${\rm SU}(N)$ with $N>2$, in particular regarding the construction of parent Hamiltonians. For the AKLT state of the ${\rm SU}(3)$ model with the $3$-box symmetric representation, we prove that the edge states are in the $8$-dimensional adjoint irrep, and for the ${\rm SU}(3)$ model with adjoint irrep at each site, we are able to construct two different reflection-symmetric AKLT Hamiltonians, each with a unique ground state which is either even or odd under reflection symmetry and with edge states in the adjoint irrep. Finally, examples of two-column and adjoint physical irreps for ${\rm SU}(N)$ with $N$ even and with edge states living in the antisymmetric irrep with $N/2$ boxes are given, with a conjecture about the general formula for their correlation lengths.Comment: 37 pages, 14 figures, 4 table

Asymptotic Freedom and Large Spin Antiferromagnetic Chains

Building on the mapping of large-$S$ spin chains onto the O($3$) nonlinear $\sigma$ model with coupling constant $2/S$, and on general properties of that model (asymptotic freedom, implying that perturbation theory is valid at high energy, and Elitzur's conjecture that rotationally invariant quantities are infrared finite in perturbation theory), we use the Holstein-Primakoff representation to derive analytic expressions for the equal-time and dynamical spin-spin correlations valid at distances smaller than $S^{-1} \exp(\pi S)$ or at energies larger than $J S^2 \exp(-\pi S)$, where $J$ is the Heisenberg exchange coupling. This is supported by comparing the static correlations with quantum Monte Carlo simulations for $S = 5/2$.Comment: 5 pages, 2 figures, Supplemental Material 10 page

Entomopathogenic Nematodes in Pest Management

The definition “biological control” has been used in different fields of biology, most notably entomology and plant pathology. It has been used to describe the use of live predatory insects, entomopathogenic nematodes (EPNs) or microbial pathogens to repress populations of various pest insects in entomology. EPNs are among one of the best biocontrol agents to control numerous economically important insect pests, successfully. Many surveys have been conducted all over the world to get EPNs that may have potential in management of economically important insect pests. The term “entomopathogenic” comes from the Greek word entomon means insect and pathogenic means causing disease and first occurred in the nematology terminology in reference to the bacterial symbionts of Steinernema and Heterorhabditis. EPNs differ from other parasitic or necromenic nematodes as their hosts are killed within a relatively short period of time due to their mutualistic association with bacteria. They have many advantages over chemical pesticides are in operator and end-user safety, absence of withholding periods, minimising the treated area by monitoring insect populations, minimal damage to natural enemies and lack of environmental pollution. Improvements in mass-production and formulation technology of EPNs, the discovery of numerous efficient isolates and the desirability of increasing pesticide usage have resulted in a surge of scientific and commercial interest in these biological control agents

Determination of association constants between 5 '-guanosine monophosphate gel and aromatic compounds by capillary electrophoresis

Hydro gel formed by 5'-guanosine monophosphate (GMP) in the presence of a potassium ion is expected to exhibit interesting selectivity in capillary electrophoretic separations. Here, we estimated the conditional association constants between the hydro gel (G-gel) and aromatic compounds by capillary electrophoresis in order to investigate the separation selectivity that is induced by the G-gel. Several aromatic compounds were separated in a solution containing GMP and potassium ion at different concentrations. The association constants were calculated by correlating the electrophoretic mobilities of the analytes obtained experimentally using a concentration of G-gel. During semi-quantitative estimation, naphthalene derivatives had larger association constants (K-ass = 10.3-16.8) compared with those of benzene derivatives (K-ass = 3.91-5.31), which means that the binding sites of G-gel match better to a naphthalene ring than to a benzene ring. A hydrophobic interaction was also found when the association constants for alkyl resorcinol were compared with those of different hydrocarbon chains. The association constants of nucleobases and tryptophan ranged from 6.05 to 12.6, which approximated the intermediate values between benzene and naphthalene derivatives. Consequently, the selective interaction between G-gel and aromatic compounds was classified as one of three types: (1) an intercalation into stacked planar GMP tetramers; (2) a hydrophobic interaction with a long alkyl chain; or, (3) a small contribution of steric hindrance and/or hydrogen bonding with functional groups such as amino and hydroxyl groups

Deliverable 3.2 "Production of validated networks"

This document describes the methodology used to validate the LV feeders studied throughout the LV Network Solutions project including feeders with PV systems. The validated feeders presented here are 16 corresponding to three different networks

Between-area communication through the lens of within-area neuronal dynamics

A core problem in systems and circuits neuroscience is deciphering the origin of shared dynamics in neuronal activity: Do they emerge through local network interactions, or are they inherited from external sources? We explore this question with large-scale networks of spatially ordered spiking neuron models where a downstream network receives input from an upstream sender network. We show that linear measures of the communication between the sender and receiver networks can discriminate between emergent or inherited population dynamics. A match in the dimensionality of the sender and receiver population activities promotes faithful communication. In contrast, a nonlinear mapping between the sender to receiver activity, for example, through downstream emergent population-wide fluctuations, can impair linear communication. Our work exposes the benefits and limitations of linear measures when analyzing between-area communication in circuits with rich population-wide neuronal dynamics

A locally modified second-order finite element method for interface problems

The locally modified finite element method, which is introduced in [Frei, Richter: SINUM 52(2014), p. 2315-2334] is a simple fitted finite element method that is able to resolve weak discontinuities in interface problems. The method is based on a fixed structured coarse mesh, which is then refined into sub-elements to resolve an interior interface. In this work, we extend the locally modified finite element method to second order using an isoparametric approach in the interface elements. Thereby we need to take care that the resulting curved edges do not lead to degenerate sub-elements. We prove optimal a priori error estimates in the $L^2$-norm and in a modified energy norm, as well as a reduced convergence order of ${\cal O}(h^{3/2})$ in the standard $H^1$-norm. Finally, we present numerical examples to substantiate the theoretical findings

Numerical Investigation of Multiphase Flow in Pipelines

We present and analyze reliable numerical techniques for simulating complex flow and transport phenomena related to natural gas transportation in pipelines. Such kind of problems are of high interest in the field of petroleum and environmental engineering. Modeling and understanding natural gas flow and transformation processes during transportation is important for the sake of physical realism and the design and operation of pipeline systems. In our approach a two fluid flow model based on a system of coupled hyperbolic conservation laws is considered for describing natural gas flow undergoing hydratization. The accurate numerical approximation of two-phase gas flow remains subject of strong interest in the scientific community. Such hyperbolic problems are characterized by solutions with steep gradients or discontinuities, and their approximation by standard finite element techniques typically gives rise to spurious oscillations and numerical artefacts. Recently, stabilized and discontinuous Galerkin finite element techniques have attracted researchers’ interest. They are highly adapted to the hyperbolic nature of our two-phase flow model. In the presentation a streamline upwind Petrov-Galerkin approach and a discontinuous Galerkin finite element method for the numerical approximation of our flow model of two coupled systems of Euler equations are presented. Then the efficiency and reliability of stabilized continuous and discontinous finite element methods for the approximation is carefully analyzed and the potential of the either classes of numerical schemes is investigated. In particular, standard benchmark problems of two-phase flow like the shock tube problem are used for the comparative numerical study