Fixed points in a Hopfield model with random asymmetric interactions

We calculate analytically the average number of fixed points in the Hopfield model of associative memory when a random antisymmetric part is added to the otherwise symmetric synaptic matrix. Addition of the antisymmetric part causes an exponential decrease in the total number of fixed points. If the relative strength of the antisymmetric component is small, then its presence does not cause any substantial degradation of the quality of retrieval when the memory loading level is low. We also present results of numerical simulations which provide qualitative (as well as quantitative for some aspects) confirmation of the predictions of the analytic study. Our numerical results suggest that the analytic calculation of the average number of fixed points yields the correct value for the typical number of fixed points.

Temperature measurements in the boron carbide manufacturing process - A hot model study

Boron carbide is produced in a heat resistance furnace using boric oxide and petroleum coke as the raw materials. The product yield is very low. Heat transfer plays an important role in the formation of boron carbide. Temperature at the core reaches up to 2600 K. No experimental study is available in the open literature for this high temperature process particularly in terms of temperature measurement and heat transfer. Therefore, a laboratory scale hot model of the process has been setup to measure the temperatures in harsh conditions at different locations in the furnace using various temperature measurement devices such as pyrometer and various types of thermocouple. Particular attention was paid towards the accuracy and reliability of the measured data. The recorded data were analysed to understand the heat transfer process inside the reactor and the effect of it on the formation of boron carbide.

The validity of the Adler-Bardeen theorem in the supersymmetric U(1) gauge model

Using the dimensional reduction regularization scheme, we show that radiative corrections to the anomaly of the axial current, which is coupled to the gauge field, are absent in a supersymmetric U(1) gauge model for both 't Hooft-Veltman and Bardeen prescriptions for γ5. We also discuss the results with reference to conventional dimensional regularization. This result has significant implications with respect to the renormalizability of supersymmetric models.

Standardization and validation of an induced ovulation model system in buffalo cows: Characterization of gene expression changes in the periovulatory follicle

In bovines characterization of biochemical and molecular determinants of the dominant follicle before and during different time intervals after gonadotrophin surge requires precise identification of the dominant follicle from a follicular wave. The objectives of the present study were to standardize an experimental model in buffalo cows for accurately identifying the dominant follicle of the first wave of follicular growth and characterize changes in follicular fluid hormone concentrations as well as expression patterns of various genes associated with the process of ovulation. From the day of estrus (day 0), animals were subjected to blood sampling and ultrasonography for monitoring circulating progesterone levels and follicular growth. On day 7 of the cycle, animals were administered a PGF2α analogue (Tiaprost Trometamol, 750 μg i.m.) followed by an injection of hCG (2000 IU i.m.) 36 h later. Circulating progesterone levels progressively increased from day 1 of the cycle to 2.26 ± 0.17 ng/ml on day 7 of the cycle, but declined significantly after PGF2α injection. A progressive increase in the size of the dominant follicle was observed by ultrasonography. The follicular fluid estradiol and progesterone concentrations in the dominant follicle were 600 ± 16.7 and 38 ± 7.6 ng/ml, respectively, before hCG injection and the concentration of estradiol decreased to 125.8 ± 25.26 ng/ml, but concentration of progesterone increased to 195 ± 24.6 ng/ml, 24 h post-hCG injection. Inh-α and Cyp19A1 expressions in granulosa cells were maximal in the dominant follicle and declined in response to hCG treatment. Progesterone receptor, oxytocin and cycloxygenase-2 expressions in granulosa cells, regarded as markers of ovulation, were maximal at 24 h post-hCG. The expressions of genes belonging to the super family of proteases were also examined; Cathepsin L expression decreased, while ADAMTS 3 and 5 expressions increased 24 h post-hCG treatment. The results of the current study indicate that sequential treatments of PGF2α and hCG during early estrous cycle in the buffalo cow leads to follicular growth that culminates in ovulation. The model system reported in the present study would be valuable for examining temporo-spatial changes in the periovulatory follicle immediately before and after the onset of gonadotrophin surge.

A couple stress model of blood flow in the microcirculation

A simple mathematical model depicting blood flow in the capillary is developed with an emphasis on the permeability property of the blood vessel based on Starling's hypothesis. In this study the effect of inertia has been neglected in comparison with the viscosity on the basis of the smallness of the Reynolds number of the flow in the capillary. The capillary blood vessel is approximated by a circular cylindrical tube with a permeable wall. The blood is represented by a couple stress fluid. With such an ideal model the velocity and pressure fields are determined. It is shown that an increase in the couple stress parameter increases the resistance to the flow and thereby decreases the volume rate flow. A comparison of the results with those of the Newtonian case has also been made.

The neutron-antineutron transition amplitude in the MIT Bag Model

The neutron-antineutron transition amplitude caused by an effective six fermion interaction with strength λeff is calculated within the context of the MIT Bag Model. The transition mass δm is found to have the value λeff×3×10−4(GeV6).

Supersolid and solitonic phases in the one-dimensional extended Bose-Hubbard model

We report our findings on the quantum phase transitions in cold bosonic atoms in a one-dimensional optical lattice using the finite-size density-matrix renormalization-group method in the framework of the extended Bose-Hubbard model. We consider wide ranges of values for the filling factors and the nearest-neighbor interactions. At commensurate fillings, we obtain two different types of charge-density wave phases and a Mott insulator phase. However, departure from commensurate fillings yields the exotic supersolid phase where both the crystalline and the superfluid orders coexist. In addition, we obtain the signatures for the solitary waves and the superfluid phase.

Phases and transitions in the spin-1 Bose-Hubbard model: Systematics of a mean-field theory

We generalize the mean-field theory for the spinless Bose-Hubbard model to account for the different types of superfluid phases that can arise in the spin-1 case. In particular, our mean-field theory can distinguish polar and ferromagnetic superfluids, Mott insulator, that arise at integer fillings at zero temperature, and normal Bose liquids into which the Mott insulators evolve at finite temperatures. We find, in contrast to the spinless case, that several of the superfluid-Mott insulator transitions are of first order at finite temperatures. Our systematic study yields rich phase diagrams that include first-order and second-order transitions and a variety of tricritical points. We discuss the possibility of realizing such phase diagrams in experimental systems.

Gauss law commutator in the chirally gauged Wess-Zumino-Witten model

We evaluate the commutator of the Gauss law constraints starting from the chirally gauged Wess-Zumino-Witten action. The calculations are done at tree level, i.e. by evaluating corresponding Poisson brackets. The results are compared with commutators obtained by others directly from the gauged fermionic theory, and with Faddeev's results based on cohomology.

Spiral states in the square-lattice Hubbard model

We present a variety of physical implications of a mean-field theory for spiral spin-density-wave states in the square-lattice Hubbard model for small deviations from half filling. The phase diagram with the paramagnetic metal, two spiral (semimetallic) states, and ferromagnet is calculated. The momentum distribution function and the (quasiparticle) density of states are discussed. There is a significant broadening of the quasiparticle bands when the antiferromagnetic insulator is doped. The evolution of the Fermi surface and the variation of the plasma frequency and a charge-stiffness constant with U/t and δ are calculated. The connection to results based on the Schwinger-boson-slave-fermion formalism is made.

Aperiodic Variability in the Cane-Zebiak Model: A Diagnostic Study

The finite predictability of the coupled ocean-atmosphere system is determined by its aperiodic variability. To gain insight regarding the predictability of such a system, a series of diagnostic studies has been carried out to investigate the role of convergence feedback in producing the aperiodic behavior of the standard version of the Cane-Zebiak model. In this model, an increase in sea surface temperature (SST) increases atmospheric heating by enhancing local evaporation (SST anomaly feedback) and low-level convergence (convergence feedback). The convergence feedback is a nonlinear function of the background mean convergence field. For the set of standard parameters used in the model, it is shown that the convergence feedback contributes importantly to the aperiodic behaviour of the model. As the strength of the convergence feedback is increased from zero to its standard value, the model variability goes from a periodic regime to an aperiodic regime through a broadening of the frequency spectrum around the basic periodicity of about 4 years. Examination of the forcing associated with the convergence feedback reveals that it is intermittent, with relatively large amplitude only during 2 or 3 months in the early part of the calendar year. This seasonality in the efficiency of the convergence feedback is related to the strong seasonality of the mean convergence over the eastern Pacific. It is shown that if the mean convergence field is fixed at its March value, aperiodic behavior is produced even in the absence of annual cycles in the other mean fields. On the, other hand, if the mean convergence field is fixed at its September value, the coupled model evolution remains close to periodic, even in the presence of the annual cycle in the other fields. The role of convergence feedback on the aperiodic variability of the model for other parameter regimes is also examined. It is shown that a range exists in the strength of the SST anomaly feedback for which the model variability is aperiodic even without the convergence feedback. It appears that in the absence of convergence feedback, enhancement of the strength of the air-sea coupling in the model through other physical processes also results in aperiodicity in the model.

Exotic Physics in the Negative-U, Extended-Hubbard Model for Barium Bismuthates?

We point out possibilities for exotic physics in barium bismuthates, from a detailed study of the negative-U, extended-Hubbard model proposed for these systems. We emphasize the different consequences of electronic and phononic mechanisms for negative U. We show that, for an electronic mechanism, the semiconducting phases must be unique, with their transport properties dominated by charge ± 2e Cooperon bound states. This can explain the observed difference between the optical and transport gaps. We propose other experimental tests for this novel mechanism of charge transport.

Phase diagram of the two-dimensional disordered Hubbard model in the Hartree-Fock approximation

Ground-state properties of the two-dimensional Hubbard model with point-defect disorder are investigated numerically in the Hartree-Fock approximation. The phase diagram in the p(point defect concentration)-delta(deviation from half filling) plane exhibits antiferromagnetic, spin-density-wave, paramagnetic, and spin-glass-like phases. The disorder stabilizes the antiferromagnetic phase relative to the spin-density-wave phase. The presence of U strongly enhances the localization in the antiferromagnetic phase. The spin-density-wave and spin-glass-like phases are weakly localized.