Scaling for Interfacial Tensions near Critical Endpoints

Parametric scaling representations are obtained and studied for the asymptotic behavior of interfacial tensions in the \textit{full} neighborhood of a fluid (or Ising-type) critical endpoint, i.e., as a function \textit{both} of temperature \textit{and} of density/order parameter \textit{or} chemical potential/ordering field. Accurate \textit{nonclassical critical exponents} and reliable estimates for the \textit{universal amplitude ratios} are included naturally on the basis of the ``extended de Gennes-Fisher'' local-functional theory. Serious defects in previous scaling treatments are rectified and complete wetting behavior is represented; however, quantitatively small, but unphysical residual nonanalyticities on the wetting side of the critical isotherm are smoothed out ``manually.'' Comparisons with the limited available observations are presented elsewhere but the theory invites new, searching experiments and simulations, e.g., for the vapor-liquid interfacial tension on the two sides of the critical endpoint isotherm for which an amplitude ratio $-3.25 \pm 0.05$ is predicted.Comment: 42 pages, 6 figures, to appear in Physical Review

Fractal Droplets in Two Dimensional Spin Glasses

The two-dimensional Edwards-Anderson model with Gaussian bond distribution is investigated at T=0 with a numerical method. Droplet excitations are directly observed. It turns out that the averaged volume of droplets is proportional to l^D with D = 1.80(2) where l is the spanning length of droplets, revealing their fractal nature. The exponent characterizing the l dependence of the droplet excitation energy is estimated to be -0.42(4), clearly different from the stiffness exponent for domain wall excitations.Comment: 4 pages 4 figure

Critical adsorption and critical Casimir forces for geometrically structured confinements

We study the behavior of fluids, confined by geometrically structured substrates, upon approaching a critical point at T = Tc in their bulk phase diagram. As generic substrate structures periodic arrays of wedges and ridges are considered. Based on general renormalization group arguments we calculate, within mean field approximation, the universal scaling functions for order parameter profiles of a fluid close to a single structured substrate and discuss the decay of its spatial variation into the bulk. We compare the excess adsorption at corrugated substrates with the one at planar walls. The confinement of a critical fluid by two walls generates effective critical Casimir forces between them. We calculate corresponding universal scaling functions for the normal critical Casimir force between a flat and a geometrically structured substrate as well as the lateral critical Casimir force between two identically patterned substrates.Comment: 25 pages, 21 figure

Numerical Study on Aging Dynamics in the 3D Ising Spin-Glass Model. II. Quasi-Equilibrium Regime of Spin Auto-Correlation Function

Using Monte Carlo simulations, we have studied isothermal aging of three-dimensional Ising spin-glass model focusing on quasi-equilibrium behavior of the spin auto-correlation function. Weak violation of the time translational invariance in the quasi-equilibrium regime is analyzed in terms of {\it effective stiffness} for droplet excitations in the presence of domain walls. Within the range of computational time window, we have confirmed that the effective stiffness follows the expected scaling behavior with respect to the characteristic length scales associated with droplet excitations and domain walls, whose growth law has been extracted from our simulated data. Implication of the results are discussed in relation to experimental works on ac susceptibilities.Comment: 18 pages, 6 figure

On the finite-size behavior of systems with asymptotically large critical shift

Exact results of the finite-size behavior of the susceptibility in three-dimensional mean spherical model films under Dirichlet-Dirichlet, Dirichlet-Neumann and Neumann-Neumann boundary conditions are presented. The corresponding scaling functions are explicitly derived and their asymptotics close to, above and below the bulk critical temperature $T_c$ are obtained. The results can be incorporated in the framework of the finite-size scaling theory where the exponent $\lambda$ characterizing the shift of the finite-size critical temperature with respect to $T_c$ is smaller than $1/\nu$, with $\nu$ being the critical exponent of the bulk correlation length.Comment: 24 pages, late

Aging and multiscaling in out of equilibrium dynamical processes in granular media

In the framework of recently introduced frustrated lattice gas models, we study the out of equilibrium dynamical processes during the compaction process in granular media. We find irreversible-reversible cycles in agreement with recent experimental observations. Moreover in analogy with the phenomenology of the glass transition we find aging effects during the compaction process In particular we find that the two time density correlation function $C(t,t')$ asymptotically scales as a function of the single variable $\ln(t')/\ln(t)$. This result is interpreted in terms of multiscaling properties of the system.Comment: 4 page

Adaptability of Irrigation to a Changing Monsoon in India: How far can we go?

Agriculture and the monsoon are inextricably linked in India. A large part of the steady rise in agricultural production since the onset of the Green Revolution in the 1960’s has been attributed to irrigation. Irrigation is used to supplement and buffer crops against precipitation shocks, but water availability for such use is itself sensitive to the erratic, seasonal and spatially heterogeneous nature of the monsoon. Most attention in the literature is given to crop yields (Guiteras, 2009; Fishman, 2012; Auffhammer et al, 2011) and their ability to withstand precipitation shocks, in the presence of irrigation (Fishman, 2012). However, there remains limited evidence about how natural weather variability and realized irrigation outcomes are related. We provide new evidence on the relationship between monsoon changes, irrigation variability and water availability by linking a process based hydrology model with an econometric model for one of the world’s most water stressed countries. India uses more groundwater for irrigation than any other country, and there is substantial evidence that this has led to depletion of groundwater aquifers. First, we build an econometric model of historical irrigation decisions using detailed crop-wise agriculture and weather data spanning 35 years from 1970-2004 for 311 districts across 19 major agricultural states in India. The source of agricultural data comes from the Village Dynamics in South Asia database at the International Crop Research Institute for the Semi-Arid Tropics (ICRISAT). Weather data is sourced from the only long term continental scale daily observationally gridded precipitation and temperature dataset called APHRODITE (Asian Precipitation- Highly Resolved Observational Data Integration Towards Evaluation of the Water Resources), that captures the spatial extent of the monsoon across the Himalayas, South and South-East Asia, and the Middle East in great detail. We use panel data approaches to control for unobserved and omitted variables that can confound the true impacts of weather variability on irrigation. Exploiting the exogenous inter-annual variability in the monsoon, our multivariate regression models reveal that for crops grown in the wet season, irrigation is sensitive to distribution and total monsoon rainfall but not to ground or surface water availability. For crops grown in the dry season, total monsoon rainfall matters most, and its effect is sensitive to groundwater availability but differentially so for shallow dug wells and deep tube wells. The historical estimates from the econometric model are used to calculate future irrigated areas using three different bias-corrected climate model projections of monsoon climate for the years 2010 – 2050 under the strongest warming scenario ( business as usual scenario) RCP-8.5 from the CMIP5 (Coupled Model Intercomparison Project) models. These projections are then used as input to a physical hydrology model, such as the Water Balance Model, that tracks water use and exchange between the ground, atmosphere, runoff and stream networks. This enables us to quantify supply of water required to meet irrigation needs from sustainable sources such as rechargeable shallow groundwater, rivers and reservoirs, as well as unsustainable sources such as non- rechargeable groundwater. Preliminary results show that the significant variation in monsoon projections lead to very different results. Crops grown in the dry season show particularly divergent trends between model projections, leading to very different groundwater resource requirements. By combining the strengths of the economic and hydrology components, this work highlights potential sustainable or unsustainable water use trajectories that different regions within India will face

Aging in Spin Glasses in three, four and infinite dimensions

The SUE machine is used to extend by a factor of 1000 the time-scale of previous studies of the aging, out-of-equilibrium dynamics of the Edwards-Anderson model with binary couplings, on large lattices (L=60). The correlation function, $C(t+t_w,t_w)$, $t_w$ being the time elapsed under a quench from high-temperature, follows nicely a slightly-modified power law for $t>t_w$. Very tiny (logarithmic), yet clearly detectable deviations from the full-aging $t/t_w$ scaling can be observed. Furthermore, the $t<t_w$ data shows clear indications of the presence of more than one time-sector in the aging dynamics. Similar results are found in four-dimensions, but a rather different behaviour is obtained in the infinite-dimensional $z=6$ Viana-Bray model. Most surprisingly, our results in infinite dimensions seem incompatible with dynamical ultrametricity. A detailed study of the link correlation function is presented, suggesting that its aging-properties are the same as for the spin correlation-function.Comment: J.P.A special issue on glasses and spin-glasses. Some improvements in citations over printed versio

Ordering of Random Walks: The Leader and the Laggard

We investigate two complementary problems related to maintaining the relative positions of N random walks on the line: (i) the leader problem, that is, the probability {\cal L}_N(t) that the leftmost particle remains the leftmost as a function of time and (ii) the laggard problem, the probability {\cal R}_N(t) that the rightmost particle never becomes the leftmost. We map these ordering problems onto an equivalent (N-1)-dimensional electrostatic problem. From this construction we obtain a very accurate estimate for {\cal L}_N(t) for N=4, the first case that is not exactly soluble: {\cal L}_4(t) ~ t^{-\beta_4}, with \beta_4=0.91342(8). The probability of being the laggard also decays algebraically, {\cal R}_N(t) ~ t^{-\gamma_N}; we derive \gamma_2=1/2, \gamma_3=3/8, and argue that \gamma_N--> ln N/N$ as N-->oo.Comment: 7 pages, 4 figures, 2-column revtex 4 forma