Quantum phase transition as an interplay of Kitaev and Ising interactions

We study the interplay between the Kitaev and Ising interactions on both ladder and two dimensional lattices. We show that the ground state of the Kitaev ladder is a symmetry-protected topological (SPT) phase, which is protected by a $\mathbb{Z}_2 \times \mathbb{Z}_2$ symmetry. It is confirmed by the degeneracy of the entanglement spectrum and non-trivial phase factors (inequivalent projective representations of the symmetries), which are obtained within infinite matrix-product representation of numerical density matrix renormalization group. We derive the effective theory to describe the topological phase transition on both ladder and two-dimensional lattices, which is given by the transverse field Ising model with/without next-nearest neighbor coupling. The ladder has three phases, namely, the Kitaev SPT, symmetry broken ferro/antiferromagnetic order and classical spin-liquid. The non-zero quantum critical point and its corresponding central charge are provided by the effective theory, which are in full agreement with the numerical results, i.e., the divergence of entanglement entropy at the critical point, change of the entanglement spectrum degeneracy and a drop in the ground-state fidelity. The central charge of the critical points are either c=1 or c=2, with the magnetization and correlation exponents being 1/4 and 1/2, respectively. In the absence of frustration, the 2D lattice shows a topological phase transition from the $\mathbb{Z}_2$ spin-liquid state to the long-range ordered Ising phase at finite ratio of couplings, while in the presence of frustration, an order-by-disorder transition is induced by the Kitaev term. The 2D classical spin-liquid phase is unstable against the addition of Kitaev term toward an ordered phase before the transition to the $\mathbb{Z}_2$ spin-liquid state.Comment: 16 pages, 18 figure

Symmetry fractionalization: Symmetry-protected topological phases of the bond-alternating spin-1/21/2 Heisenberg chain

We study different phases of the one-dimensional bond-alternating spin-$1/2$ Heisenberg model by using the symmetry fractionalization mechanism. We employ the infinite matrix-product state representation of the ground state (through the infinite-size density matrix renormalization group algorithm) to obtain inequivalent projective representations of the (unbroken) symmetry groups of the model, which are used to identify the different phases. We find that the model exhibits trivial as well as symmetry-protected topological phases. The symmetry-protected topological phases are Haldane phases on even/odd bonds, which are protected by the time-reversal (acting on the spin as $\sigma\rightarrow-\sigma$), parity (permutation of the chain about a specific bond), and dihedral ($\pi$-rotations about a pair of orthogonal axes) symmetries. Additionally, we investigate the phases of the most general two-body bond-alternating spin-$1/2$ model, which respects the time-reversal, parity, and dihedral symmetries, and obtain its corresponding twelve different types of the symmetry-protected topological phases.Comment: 9 pages, 5 figure

On entrainment in sheared convective boundary layers

The purpose of this dissertation is to advance our knowledge of wind-shear effects on entrainment in a convective boundary layer (CBL) and to synthesize this new knowledge in the form of closure equations for bulk models. It is well-known that wind shear generally enhances entrainment, which thickens the entrainment zone and increases the growth rate of the CBL. Although previous work has identified major sensitivities of entrainment, and accordingly of sheared CBL properties, to changes in environmental conditions, the characterization of the shear enhancement of entrainment and of its dependence on environmental conditions remains elusive. In particular, scaling laws for different properties of sheared CBLs as functions of the surface and free-atmosphere conditions are lacking. Given that local scales within the entrainment zone become more relevant in sheared CBLs than in shear-free CBLs, one potential reason for the lack of a characterization of wind-shear effects on CBLs is the limitation of previous single-case studies in resolving the required small scales, which are of the order of tens of meters. We use direct numerical simulation and dimensional analysis, for the first time in the context of sheared CBLs, to reduce the uncertainty associated with small scales and to perform a systematic study. We scrutinize the vertical structure of the sheared CBL and show that wind-shear effects on the CBL structure remain constrained within the entrainment zone. We further show that the entrainment zone in sheared CBLs, consistent with shear-free CBLs, is better described as a composition of two sublayers. However, contrary to shear-free CBLs in which only the upper entrainment-zone sublayer is characterized by a local length scale, we demonstrate that both lower and upper entrainment-zone sublayers in sheared CBLs are characterized by local length scales. We perform an integral analysis of the turbulence kinetic energy budget and find an independent variable that fully embeds the dependence of sheared CBL properties on environmen- tal conditions. The reduction in the number of independent variables to one enables us to provide the scaling laws for different CBL properties, such as different defini- tions of the CBL height and the entrainment-flux ratio, as functions of environmental conditions. These scaling laws allow us to tackle a major long-standing limitation of previous bulk models, which is the singularity at a finite wind strength, and to propose non-singular bulk models of sheared CBLs. We argue that zero-order bulk models, despite their simplicity compared to higher-order models, can accurately predict bulk properties of sheared CBLs when the relevant features of the actual entrainment zone are considered in the entrainment closures.Das Ziel dieser Dissertation ist es, besser zu verstehen, wie Windscherung Entrain- ment in einer atmosphärischen konvektiven Grenzschicht beeinflusst und dieses neue Wissen im Form der Schließungsgleichungen für Massenmodelle zu synthetisieren. Es ist bekannt, dass Windscherung Entrainment im Allgemeinen verstärkt und dadurch die Dicke der Entrainmenzone und die Wachstumsrate der konvektiven Grenzschicht erhöht. Obwohl frühere Forschungsarbeiten herausgefunden haben, wie Entrainment — und somit die Eigenschaften einer gescherten konvektiven Grenzschicht im Allge- meinen — von den Umgebungsbedingungen abhängen, bleibt es schwierig diese Ef- fekte zu charakterisieren. Insbesondere fehlen Skalierungsgesetze, welche beschreiben, wie verschiedene Eigenschaften der gescherten konvektiven Grenzschicht von den Oberflächen und Atmosphäreneigenschafen abhängen. Die Tatsache, dass Wind die Bedeutung der lokalen Skalen innerhalb der Entrainmentzone erhöht, legt nahe, dass der Grund für die fehlende Charakterisierung von Windscherungseffekten, in der Unfähigkeit früherer Studien liegt, diese kleinskaligen Prozesse darzustellen. Daher verwendet diese Dissertation das erste Mal direkte numerische Simulationen um die Unsicherheiten, welche als Folge kleinskaliger Prozesse entstehen, zu reduzieren. Des weiteren führen wir eine Dimensionsanalyse durch, um Windscherungseffekte systematisch zu analysieren. Wir untersuchen die vertikale Struktur der gescherten konvektiven Grenzschicht und zeigen, dass Windscherungseffekte in der Entrainmentzone lokalisiert bleiben. Des weiteren zeigen wir, dass sich die Entrainmentzone, auch in der Gegenwart von Wind, gut als Zusammensetzung von zwei Teilschichten beschreiben lässt. Allerdings ändert Wind die Skalierung der unteren Teilschicht. Während sich in der scherfreien konvektiven Grenzschicht nur die obere Teilschicht mit einer lokalen Längenskala charakterisieren lässt, lassen sich in einer gescherten konvektiven Grenzschicht beide Teilschichten mit Hilfe lokaler Längenskalen charakterisieren. Darüber hinaus zeigt eine Integralanalyse des Turbulenz-Energiebudgets, dass sich verschiedene Eigen- schaften einer gescherten konvektiven Grenzschicht als Funktion einer einzigen unab- hängigen Variable charakterisieren lassen. Diese neuen Skalierungsgesetze erlauben es uns, eine bekannte Schwachstelle bestehender Massenmodelle zu beheben. Diese Schwachstelle besteht darin, dass bisherige Massenmodelle aufgrund einer Singular- ität bei einer endlichen Windstärke divergieren. Wir führen ein Massenmodell nullter Ordnung ein, welches frei von einer solchen Singularität ist. Des weiteren zeigen wir, dass dieses Massenmodell, trotz seiner Einfachheit im Vergleich zu Massenmodellen höherer Ordnung, die Eigenschaften einer gescherten konvektiven Grenzschicht akku- rat darstellt. Dies folgt daraus, dass die verwendete Schließungsgleichung relevante Eigenschaften der Entrainmentzone implizit berücksichtigt

Effect of enriched rotifer (Brachionus plicatilis) with probiotic lactobacilli on growth, survival and resistance indicators of western white shrimp (Litopenaeus vannamei) larvae

This study examined the effects of a commercial Lactobacillus probiotic on growth, survival and resistance of western white shrimp (Litopenaeus vannamei) larvae against salinity and formalin stresses in the Persian Gulf and Oman Sea Ecology Research Center. In this experiment, larvae were fed 6 times a day from mysis I (M1) step to post larvae 5 over 3 treatments including a control treatment C (without probiotic) and 2 experimental treatments namely A (having probiotic enriched rotifer) and B (having probiotic enriched rotifer and adding probiotic powder directly to the water). Larvae were stocked in 9 plastic tanks (20-liter) containing 10 L of seawater at a density of 50 larvae per liter. Three replicates were used for each treatment. At the end of the experimental period biometric larvae were studied under salinity and formalin stresses. Results showed that using probiotic bacteria had significant and positive effects on shrimp resistance, survival and growth (p0.05). According to the results we may conclude that the use of probiotic powder is effective in increasing growth, survival and resistance rate of western white shrimp in the larval and post larval stages

On the non-monotonic variation of the entrainment buoyancy flux with wind shear

The magnitude of the entrainment buoyancy flux, and hence the growth rate of the convective boundary layer, does not increase monotonically with wind shear. Explanations for this have previously been based on wind-shear effects on the turbulence kinetic energy. By distinguishing between turbulent and non-turbulent regions, we provide an alternative explanation based on two competing wind-shear effects: the initial decrease in the correlation between buoyancy and vertical velocity fluctuations, and the increase in the turbulent area fraction. The former is determined by the change in the dominant forcing; without wind shear, buoyancy fluctuations drive vertical velocity fluctuations and the two are thus highly correlated; with wind shear, vertical velocity fluctuations are partly determined by horizontal velocity fluctuations via the transfer of kinetic energy through the pressure-strain correlation, thus reducing their correlation with the buoyancy field. The increasing turbulent area fraction, on the other hand, is determined by the increasing shear production of turbulence kinetic energy inside the entrainment zone. We also show that the dependence of these conditional statistics on the boundary-layer depth and on the magnitude of the wind shear can be captured by a single non-dimensional variable, which can be interpreted as an entrainment-zone Froude number

A new conventional criterion for the performance evaluation of gang saw machines

Available online 20 June 2019The process of cutting dimension stones by gang saw machines plays a vital role in the productivity and efficiency of quarries and stone cutting factories. The maximum electrical current (MEC) is a key variable for assessing this process. This paper proposes two new models based on multiple linear regression (MLP) and a robust non-linear algorithm of gene expression programming (GEP) to predict MEC. To do so, the parameters of Mohs hardness (Mh), uniaxial compressive strength (UCS), Schimazek’s F-abrasiveness factor (SF-a), Young’s modulus (YM) and production rate (Pr) were measured as input parameters using laboratory tests. A statistical comparison was made between the developed models and a previous study. The GEP-based model was found to be a reliable and robust modelling approach for predicting MEC. Finally, according to the conducted parametric analysis, Mh was identified as the most influential parameter on MEC prediction.Sina Shaffiee Haghshenas, Roohollah Shirani Faradonbeh, Reza Mikaeil, Sami Shaffiee Haghshenas, Abbas Taheri, Amir Saghatforoush, Alireza Dormish