Charge stripes due to electron correlations in the two-dimensional spinless Falicov-Kimball model

We calculate the restricted phase diagram for the Falicov-Kimball model on a two-dimensional square lattice. We consider the limit where the conduction electron density is equal to the localized electron density, which is the limit related to the S_z=0 states of the Hubbard model. After considering over 20,000 different candidate phases (with a unit cell of 16 sites or less) and their thermodynamic mixtures, we find only about 100 stable phases in the ground-state phase diagram. We analyze these phases to describe where stripe phases occur and relate these discoveries to the physics behind stripe formation in the Hubbard model.Comment: (34 pages, 9 figures, submitted to Journal of Statistical Physics to celebrate Elliott Lieb's 70th birthday

Infinite partition monoids

Let $\mathcal P_X$ and $\mathcal S_X$ be the partition monoid and symmetric group on an infinite set $X$. We show that $\mathcal P_X$ may be generated by $\mathcal S_X$ together with two (but no fewer) additional partitions, and we classify the pairs $\alpha,\beta\in\mathcal P_X$ for which $\mathcal P_X$ is generated by $\mathcal S_X\cup\{\alpha,\beta\}$. We also show that $\mathcal P_X$ may be generated by the set $\mathcal E_X$ of all idempotent partitions together with two (but no fewer) additional partitions. In fact, $\mathcal P_X$ is generated by $\mathcal E_X\cup\{\alpha,\beta\}$ if and only if it is generated by $\mathcal E_X\cup\mathcal S_X\cup\{\alpha,\beta\}$. We also classify the pairs $\alpha,\beta\in\mathcal P_X$ for which $\mathcal P_X$ is generated by $\mathcal E_X\cup\{\alpha,\beta\}$. Among other results, we show that any countable subset of $\mathcal P_X$ is contained in a $4$-generated subsemigroup of $\mathcal P_X$, and that the length function on $\mathcal P_X$ is bounded with respect to any generating set

Formalising the Continuous/Discrete Modeling Step

Formally capturing the transition from a continuous model to a discrete model is investigated using model based refinement techniques. A very simple model for stopping (eg. of a train) is developed in both the continuous and discrete domains. The difference between the two is quantified using generic results from ODE theory, and these estimates can be compared with the exact solutions. Such results do not fit well into a conventional model based refinement framework; however they can be accommodated into a model based retrenchment. The retrenchment is described, and the way it can interface to refinement development on both the continuous and discrete sides is outlined. The approach is compared to what can be achieved using hybrid systems techniques.Comment: In Proceedings Refine 2011, arXiv:1106.348

Quantum Complex Scalar Field in the Two-Dimensional Spacetime with Closed Timelike Curves and a Time-Machine Problem

It is considered the quantum complex scalar field which obeys the authomorphic condition in the two-dimensional spacetime with closed timelike curves and the chronology horizon. The renormalized stress-energy tensor is obtained. It is shown that the value of the stress-energy tensor is regular at the chronology horizon for specific authomorphic parameters. Thus the particular example of field configuration is given for which the Hawking's chronology protection conjecture is violated.Comment: 21(Latex)Postscript file of the figure may be received from author, CQG-94-100

Casimir Effect in E3E^3 closed spaces

As it is well known the topology of space is not totally determined by Einstein's equations. It is considered a massless scalar quantum field in a static Euclidean space of dimension 3. The expectation value for the energy density in all compact orientable Euclidean 3-spaces are obtained in this work as a finite summation of Epstein type zeta functions. The Casimir energy density for these particular manifolds is independent of the type of coupling with curvature. A numerical plot of the result inside each Dirichlet region is obtained.Comment: Version accepted for publication. The most general coupling with curvature is chose

Ecophysiology and dynamics of nitrogen removal bacteria in a sequencing batch reactor during wastewater treatment start‑up

Nitrogen removal communities performing wastewater treatment consist of ammonia oxidisers, nitrite oxidisers, denitrifiers, and anammox bacteria, and the proportion and activity of particular microbial groups depend not only on the physiochemical parameters of the bioreactor, but also on the composition of the inoculum. Nitrifiers and denitrifiers usually dominate in conventional wastewater treatment systems due to the fact that nitrification and denitrification are the most commonly used nitrogen removal processes. However, from the economical point of view in case of wastewater with high ammonia concentrations, anammox-based technologies are desirable for their treatment. The disadvantage of such systems is slow anammox bacteria growth, which extends an effective technological start-up. Thus, in this study, a fast start-up of the anammox process supported with an anammox-rich inoculum was performed in a sequencing batch reactor (SBR). Using anammox inoculation of SBR laboratory system, the start-up can be fastened to 85 days with 84.5% of nitrogen removal efficacy. The spatial distribution of nitrogen removal bacteria analysed with fluorescent in situ hybridisation revealed that anammox and nitrifiers are located side by side in the flocs and the relative number of ammonia and nitrite oxidisers decreased after 85 days of the experiment

Towards a method for rigorous development of generic requirements patterns

We present work in progress on a method for the engineering, validation and verification of generic requirements using domain engineering and formal methods. The need to develop a generic requirement set for subsequent system instantiation is complicated by the addition of the high levels of verification demanded by safety-critical domains such as avionics. Our chosen application domain is the failure detection and management function for engine control systems: here generic requirements drive a software product line of target systems. A pilot formal specification and design exercise is undertaken on a small (twosensor) system element. This exercise has a number of aims: to support the domain analysis, to gain a view of appropriate design abstractions, for a B novice to gain experience in the B method and tools, and to evaluate the usability and utility of that method.We also present a prototype method for the production and verification of a generic requirement set in our UML-based formal notation, UML-B, and tooling developed in support. The formal verification both of the structural generic requirement set, and of a particular application, is achieved via translation to the formal specification language, B, using our U2B and ProB tools

Altilix\uae Supplement Containing Chlorogenic Acid and Luteolin Improved Hepatic and Cardiometabolic Parameters in Subjects with Metabolic Syndrome: A 6 Month Randomized, Double-Blind, Placebo-Controlled Study

The objective was to evaluate the eects of 6 months of supplementation with Altilix\uae, containing chlorogenic acid and its derivatives, and luteolin and its derivatives, on cardiovascular risk and hepatic markers in subjects with metabolic syndrome (MetS). A randomized, double-blind, placebo-controlled study was performed in 100 subjects with MetS with a follow-up period of 6 months; 50 subjects were randomized to Altilix\uae (26 men and 24 women, mean age 63 8 years) and the other 50 to placebo (28 men and 22 women, mean age 63 11 years). Anthropometric, cardiometabolic, and hepatic parameters were assessed at baseline and at the end of follow-up. Carotid intima-media thickness and endothelial function were assessed by doppler ultrasound and by flow-mediated dilation of the brachial artery, respectively. The presence and degree of non-alcoholic fatty liver disease (NAFLD) was assessed by the fatty liver index (FLI), and subjects were divided into three subgroups: (1) without NAFLD; (2) with borderline NAFLD; and (3) with NAFLD. After 6 months of Altilix\uae supplementation, we found a significant improvement vs. placebo in most of the evaluated parameters, including body weight (2.40% (95% CI 3.79, 1.01); p < 0.001), waist circumference (2.76% (95% CI 4.55, 0.96); p = 0.003), HbA1c (0.95% (95% CI 1.22, 0.67); p < 0.001), plasma lipids, FLI (21.83% (95% CI 27.39, 16.27); p < 0.001), hepatic transaminases, flow-mediated dilation (10.56% (95% CI 5.00, 16.12); p < 0.001), and carotid intima-media thickness (39.48% (95% CI 47.98, 30.97); p < 0.001). Further, the improvement in cardiometabolic variables was independent of the degree of hepatic steatosis. Altilix\uae supplementation improved hepatic and cardio-metabolic parameters in MetS subjects. Altilix\uae supplementation was a beneficial approach in the management of hepatic and cardiometabolic alterations in MetS subjects