Conserved Charges and Supersymmetry in Principal Chiral Models

We report on investigations of local (and non-local) charges in bosonic and supersymmetric principal chiral models in 1+1 dimensions. In the bosonic PCM there is a classically conserved local charge for each symmetric invariant tensor of the underlying group. These all commute with the non-local Yangian charges. The algebra of the local charges amongst themselves is rather more subtle. We give a universal formula for infinite sets of mutually commuting local charges with spins equal to the exponents of the underlying classical algebra modulo its Coxeter number. Many of these results extend to the supersymmetric PCM, but with local conserved charges associated with antisymmetric invariants in the Lie algebra. We comment briefly on the quantum conservation of local charges in both the bosonic and super PCMs.Comment: 18 pages, LaTeX. Revised and up-dated version based on conference talks by JME and NJ

Scale-free network topology and multifractality in weighted planar stochastic lattice

We propose a weighted planar stochastic lattice (WPSL) formed by the random sequential partition of a plane into contiguous and non-overlapping blocks and find that it evolves following several non-trivial conservation laws, namely $\sum_i^N x_i^{n-1} y_i^{4/n-1}$ is independent of time $\forall \ n$, where $x_i$ and $y_i$ are the length and width of the $i$th block. Its dual on the other hand, obtained by replacing each block with a node at its center and common border between blocks with an edge joining the two vertices, emerges as a network with a power-law degree distribution $P(k)\sim k^{-\gamma}$ where $\gamma=5.66$ revealing scale-free coordination number disorder since $P(k)$ also describes the fraction of blocks having $k$ neighbours. To quantify the size disorder, we show that if the $i$th block is populated with $p_i\sim x_i^3$ then its distribution in the WPSL exhibits multifractality.Comment: 7 pages, 8 figures, To appear in New Journal of Physics (NJP

USF binding sequences from the HS4 insulator element impose early replication timing on a vertebrate replicator

The nuclear genomes of vertebrates show a highly organized program of DNA replication where GC-rich isochores are replicated early in S-phase, while AT-rich isochores are late replicating. GC-rich regions are gene dense and are enriched for active transcription, suggesting a connection between gene regulation and replication timing. Insulator elements can organize independent domains of gene transcription and are suitable candidates for being key regulators of replication timing. We have tested the impact of inserting a strong replication origin flanked by the β-globin HS4 insulator on the replication timing of naturally late replicating regions in two different avian cell types, DT40 (lymphoid) and 6C2 (erythroid). We find that the HS4 insulator has the capacity to impose a shift to earlier replication. This shift requires the presence of HS4 on both sides of the replication origin and results in an advance of replication timing of the target locus from the second half of S-phase to the first half when a transcribed gene is positioned nearby. Moreover, we find that the USF transcription factor binding site is the key cis-element inside the HS4 insulator that controls replication timing. Taken together, our data identify a combination of cis-elements that might constitute the basic unit of multi-replicon megabase-sized early domains of DNA replication

Human growth hormone alters carbohydrate storage in blood and liver in both genders of an Indian bird, Acridotheres tristis (Linn.)

Background: Growth hormone (GH) is a peptide hormone that plays vital roles in cell growth and metabolism. Aim: The study investigates the effect of GH on carbohydrate metabolism using Indian bird, Acridotheres tristis. Methods: Three different doses (0.4, 0.6, and 0.8mg/100g body weight) of human growth hormone (HGH) given once to both genders of a bird Acridotheres tristis to observe the effect on blood glucose and hepatic glycogen content in the body. Glucose and glycogen were quantitatively assayed. Results: Their effect was recorded for different time intervals (1, 4, 12, 24, 72, 96, and 144 h). Hypoglycaemic condition was recorded within an hour of hormone treatment in male and female birds. The lowest dose (0.4mg/100g body weight) was more effective than other two doses. Simultaneous depletion of hepatic glycogen was also recorded, although initially increase in glycogen level was also noticed in both genders. It was noticed that the highest dose (0.8mg/100g body weight) was most responsive. Conclusion: The effect of human growth hormone was not dose and time dependent in both male and female birds. HGH is thus hypoglycaemic and hepatic glycogenolytic in nature in A. tristis.Key words: Human growth hormone, blood glucose, hepatic glycogen, hypoglycaemia, glycogenolysis, bir

Fractal dimension and degree of order in sequential deposition of mixture

We present a number models describing the sequential deposition of a mixture of particles whose size distribution is determined by the power-law $p(x) \sim \alpha x^{\alpha-1}$, $x\leq l$ . We explicitly obtain the scaling function in the case of random sequential adsorption (RSA) and show that the pattern created in the long time limit becomes scale invariant. This pattern can be described by an unique exponent, the fractal dimension. In addition, we introduce an external tuning parameter beta to describe the correlated sequential deposition of a mixture of particles where the degree of correlation is determined by beta, while beta=0 corresponds to random sequential deposition of mixture. We show that the fractal dimension of the resulting pattern increases as beta increases and reaches a constant non-zero value in the limit $\beta \to \infty$ when the pattern becomes perfectly ordered or non-random fractals.Comment: 16 pages Latex, Submitted to Phys. Rev.

Polyaniline/Polystyrene Blends: In-Depth Analysis of the Effect of Sulfonic Acid Dopant Concentration on AC Conductivity Using Broadband Dielectric Spectroscopy

This work presents an in-depth analysis of the alternating current (AC) conductivity of polyaniline-polystyrene (PANI-PS) blends doped with camphor sulfonic acid (CSA) and prepared using an in situ dispersion polymerization technique. We prepared the blends using fixed ratios of PS to PANI while varying the concentration of the CSA dopant. The AC conductivity of the blends was investigated using broadband dielectric spectroscopy. Increasing CSA resulted in a decrease in the AC conductivity of the blends. This behaviour was explained in terms of the availability of a lone pair of electrons of the NH groups in the polyaniline, which are typically attacked by the electron-withdrawing sulfonic acid groups of CSA. The conductivity is discussed in terms of changes in the dielectric permittivity storage (??), loss (??), and modulus (M?) of the blends over a wide range of temperatures. This is linked to the glass transition temperature of the PANI. Dielectric spectra at low frequencies indicated the presence of pronounced Maxwell-Wagner-Sillars (MWS) interfacial polarization, especially in samples with a low concentration of CSA. Electrical conduction activation energies for the blends were also calculated using the temperature dependence of the direct current (DC) conductivity at a low frequency (?dc), which exhibit an Arrhenius behaviour with respect to temperature. Scanning electron microscopy revealed a fibrous morphology for the pure PANI, while the blends showed agglomeration with increasing CSA concentrations. 2018 Noora Al-Thani et al.The authors would like to acknowledge the financial support of the Qatar University Grant no. QUST-CAM-SPR-2017-6.Scopu