Kolkata Restaurant Problem as a generalised El Farol Bar Problem

Generalisation of the El Farol bar problem to that of many bars here leads to the Kolkata restaurant problem, where the decision to go to any restaurant or not is much simpler (depending on the previous experience of course, as in the El Farol bar problem). This generalised problem can be exactly analysed in some limiting cases discussed here. The fluctuation in the restaurant service can be shown to have precisely an inverse cubic behavior, as widely seen in the stock market fluctuations.Comment: 2 column RevTeX4, 4 pages, 3 eps figs; to be published in 'Econophysics of Markets and Business Networks', [Proc. Econophys-Kolkata III], Eds. A. Chatterjee, B. K. Chakrabarti, New Economic Windows Series, Springer, Milan, 2007, pp. 220-22

Effects of stoichiometry, purity, etching and distilling on resistance of MgB2 pellets and wire segments

We present a study of the effects of non-stoichiometry, boron purity, wire diameter and post-synthesis treatment (etching and Mg distilling) on the temperature dependent resistance and resistivity of sintered MgB2 pellets and wire segments. Whereas the residual resistivity ratio (RRR) varies between RRR \~ 4 to RRR > 20 for different boron purity, it is only moderately affected by non-stoichiometry (from 20% Mg deficiency to 20% Mg excess) and is apparently independent of wire diameter and presence of Mg metal traces on the wire surface. The obtained set of data indicates that RRR values in excess of 20 and residual resistivities as low as rho{0} ~ 0.4 mu Ohm cm are intrinsic material properties of high purity MgB2

Dynamic critical behavior of failure and plastic deformation in the random fiber bundle model

The random fiber bundle (RFB) model, with the strength of the fibers distributed uniformly within a finite interval, is studied under the assumption of global load sharing among all unbroken fibers of the bundle. At any fixed value of the applied stress (load per fiber initially present in the bundle), the fraction of fibers that remain unbroken at successive time steps is shown to follow simple recurrence relations. The model is found to have stable fixed point for applied stress in the range 0 and 1; beyond which total failure of the bundle takes place discontinuously. The dynamic critical behavior near this failure point has been studied for this model analysing the recurrence relations. We also investigated the finite size scaling behavior. At the critical point one finds strict power law decay (with time t) of the fraction of unbroken fibers. The avalanche size distribution for this mean-field dynamics of failure has been studied. The elastic response of the RFB model has also been studied analytically for a specific probability distribution of fiber strengths, where the bundle shows plastic behavior before complete failure, following an initial linear response.Comment: 13 pages, 5 figures, extensively revised and accepted for publication in Phys. Rev.

Failure due to fatigue in fiber bundles and solids

We consider first a homogeneous fiber bundle model where all the fibers have got the same stress threshold beyond which all fail simultaneously in absence of noise. At finite noise, the bundle acquires a fatigue behavior due to the noise-induced failure probability at any stress. We solve this dynamics of failure analytically and show that the average failure time of the bundle decreases exponentially as the stress increases. We also determine the avalanche size distribution during such failure and find a power law decay. We compare this fatigue behavior with that obtained phenomenologically for the nucleation of Griffith cracks. Next we study numerically the fatigue behavior of random fiber bundles having simple distributions of individual fiber strengths, at stress less than the bundle's strength (beyond which it fails instantly). The average failure time is again seen to decrease exponentially as the stress increases and the avalanche size distribution shows similar power law decay. These results are also in broad agreement with experimental observations on fatigue in solids. We believe, these observations regarding the failure time are useful for quantum breakdown phenomena in disordered systems.Comment: 13 pages, 4 figures, figures added and the text is revise

Effects of Boron Purity, Mg Stoichiometry and Carbon Substitution on Properties of Polycrystalline MgB2_{2}

By synthesizing MgB$_{2}$ using boron of different nominal purity we found values of the residual resistivity ratio ($RRR = R(300 K) / R(42 K)$) from 4 to 20, which covers almost all values found in literature. To obtain high values of $RRR$, high purity reagents are necessary. With the isotopically pure boron we obtained the highest $RRR \sim$ 20 for the stoichiometric compound. We also investigated Mg$_{x}$$^{11}$B$_{2}$ samples with 0.8 $< x <$ 1.2. For the range Mg$_{0.8}$$^{11}$B$_{2}$ up to Mg$_{1.2}$$^{11}$B$_{2}$ we found average values of $RRR$ between 14 and 24. For smaller variations in stoichiometry ($x=1\pm 0.1$) $RRR = 18 \pm 3$. All of our data point to the conclusion that high $RRR$ ($\sim 20$) and low $\rho_{0}$ ($\leq 0.4 \mu \Omega cm$) are intrinsic material properties associated with high purity MgB$_{2}$. In addition we have performed initial work on optimizing the formation of carbon doped MgB$_{2}$ via the use of B$_{4}$C. Nearly single phase material can be formed by reaction of nominal Mg(B$_{0.8}$C$_{0.2}$)$_{2}$ for 24 hours at $1200^{\circ}C$. The $T_{c}$ for this composition is between $21.9 K$ and $22.7 K$ (depending on criterion).Comment: accepted to Physica C, special MgB2 issu

Determining Chemically and Spatially Resolved Atomic Profile of Low Contrast Interface Structure with High Resolution

We present precise measurements of atomic distributions of low electron density contrast at a buried interface using soft x ray resonant scattering. This approach allows one to construct chemically and spatially highly resolved atomic distribution profile upto several tens of nanometer in a non destructive and quantitative manner. We demonstrate that the method is sensitive enough to resolve compositional differences of few atomic percent in nano scaled layered structures of elements with poor electron density differences 0.05 . The present study near the edge of potential impurities in soft x ray range for low Z system will stimulate the activity in that fiel

Precursors of catastrophe in the BTW, Manna and random fiber bundle models of failure

We have studied precursors of the global failure in some self-organised critical models of sand-pile (in BTW and Manna models) and in the random fiber bundle model (RFB). In both BTW and Manna model, as one adds a small but fixed number of sand grains (heights) to any central site of the stable pile, the local dynamics starts and continues for an average relaxation time (\tau) and an average number of topplings (\Delta) spread over a radial distance (\xi). We find that these quantities all depend on the average height (h_{av}) of the pile and they all diverge as (h_{av}) approaches the critical height (h_{c}) from below: (\Delta) (\sim (h_{c}-h_{av}))(^{-\delta}), (\tau \sim (h_{c}-h_{av})^{-\gamma}) and (\xi) (\sim) ((h_{c}-h_{av})^{-\nu}). Numerically we find (\delta \simeq 2.0), (\gamma \simeq 1.2) and (\nu \simeq 1.0) for both BTW and Manna model in two dimensions. In the strained RFB model we find that the breakdown susceptibility (\chi) (giving the differential increment of the number of broken fibers due to increase in external load) and the relaxation time (\tau), both diverge as the applied load or stress (\sigma) approaches the network failure threshold (\sigma_{c}) from below: (\chi) (\sim) ((\sigma_{c}) (-)(\sigma)^{-1/2}) and (\tau) (\sim) ((\sigma_{c}) (-)(\sigma)^{-1/2}). These self-organised dynamical models of failure therefore show some definite precursors with robust power laws long before the failure point. Such well-characterised precursors should help predicting the global failure point of the systems in advance.Comment: 13 pages, 9 figures (eps

Pseudogap and Conduction Dimensionalities in High-T_c Superconductors

The nature of normal state charge-carriers' dynamics and the transition in conduction and gap dimensionalities between 2D and 3D for YBa_2 Cu_3 O_{7-delta} and Bi_2 Sr_2 Ca_{1-x} Y_x Cu_2 O_8 high-T_c superconductors were described by computing and fitting the resistivity curves, rho(T,delta,x). These were carried out by utilizing the 2D and 3D Fermi liquid (FL) and ionization energy (E_I) based resistivity models coupled with charge-spin (CS) separation based t-J model [Phys. Rev. B 64, 104516 (2001)]. rho(T,delta,x) curves of Y123 and Bi2212 samples indicate the beginning of the transition of conduction and gap from 2D to 3D with reduction in oxygen content (7-delta) and Ca^{2+} (1-x) as such, c-axis pseudogap could be a different phenomenon from superconductor and spin gaps. These models also indicate that the recent MgB_2 superconductor is at least not Y123 or Bi2212 type.Comment: To be published in Physica

Time evolution of damage under variable ranges of load transfer

We study the time evolution of damage in a fiber bundle model in which the range of interaction of fibers varies through an adjustable stress transfer function recently introduced. We find that the lifetime of the material exhibits a crossover from mean field to short range behavior as in the static case. Numerical calculations showed that the value at which the transition takes place depends on the system's disorder. Finally, we have performed a microscopic analysis of the failure process. Our results confirm that the growth dynamics of the largest crack is radically different in the two limiting regimes of load transfer during the first stages of breaking.Comment: 8 pages, 7 figures, revtex4 styl

Modelling and Prediction of Soil Organic Carbon using Digital Soil Mapping in the Thar Desert Region of India

Not AvailableIn the present study, the distribution of soil organic carbon (SOC) was investigated using digital soil mapping for an area of ~29 lakhs ha in Bikaner district, Rajasthan, India. To achieve this goal, 187 soil profiles were used for SOC estimation by Quantile regression forest (QRF) model technique. Landsat data, terrain attributes and bioclimatic variables were used as environmental variables. 10-fold cross-validation was used to evaluate model. Equal-area quadratic splines were fitted to soil profile datasets to estimate SOC at six standard soil depths (0-5, 5-15, 15-30, 30-60, 60-100 and 100-200 cm). Results showed that the mean SOC concentration was very low with values varied from 1.18 to 1.53 g kg-1 in different depths. While predicting SOC at different depths, the model was able to capture low variability (R2 = 1–7%). Overall, the Lin’s concordance correlation coefficient (CCC) values ranged from 0.01 to 0.18, indicating poor agreement between the predicted and observed values. Root mean square error (RMSE) and mean error (ME) were 0.97 and 0.16, respectively. The values of prediction interval coverage probability (PICP) recorded 87.2–89.7% for SOC contents at different depths. The most important variables for predicting SOC concentration variations were the annual range of temperature, latitude, Landsat 8 bands 2, 5 and 6. Temperature-related variables and remote sensed data products are important for predicting SOC concentrations in arid regions. We anticipate that this digital information of SOC will be useful for frequent monitoring and assessment of carbon cycle in arid regions.Not Availabl