Renormalization of Drift and Diffusivity in Random Gradient Flows

We investigate the relationship between the effective diffusivity and effective drift of a particle moving in a random medium. The velocity of the particle combines a white noise diffusion process with a local drift term that depends linearly on the gradient of a gaussian random field with homogeneous statistics. The theoretical analysis is confirmed by numerical simulation. For the purely isotropic case the simulation, which measures the effective drift directly in a constant gradient background field, confirms the result previously obtained theoretically, that the effective diffusivity and effective drift are renormalized by the same factor from their local values. For this isotropic case we provide an intuitive explanation, based on a {\it spatial} average of local drift, for the renormalization of the effective drift parameter relative to its local value. We also investigate situations in which the isotropy is broken by the tensorial relationship of the local drift to the gradient of the random field. We find that the numerical simulation confirms a relatively simple renormalization group calculation for the effective diffusivity and drift tensors.Comment: Latex 16 pages, 5 figures ep

Metropolized Randomized Maximum Likelihood for sampling from multimodal distributions

This article describes a method for using optimization to derive efficient independent transition functions for Markov chain Monte Carlo simulations. Our interest is in sampling from a posterior density $\pi(x)$ for problems in which the dimension of the model space is large, $\pi(x)$ is multimodal with regions of low probability separating the modes, and evaluation of the likelihood is expensive. We restrict our attention to the special case for which the target density is the product of a multivariate Gaussian prior and a likelihood function for which the errors in observations are additive and Gaussian

Thermal Casimir effect with soft boundary conditions

We consider the thermal Casimir effect in systems of parallel plates coupled to a mass-less free field theory via quadratic interaction terms which suppress (i) the field on the plates (ii) the gradient of the field in the plane of the plates. These boundary interactions correspond to (i) the presence of an electrolyte in the plates and (ii) a uniform field of dipoles, in the plates, which are polarizable in the plane of the plates. These boundary interactions lead to Robin type boundary conditions in the case where there is no field outside the two plates. In the appropriate limit, in both cases Dirichlet boundary conditions are obtained but we show that in case (i) the Dirichlet limit breaks down at short inter-plate distances and in (ii) it breaks down at large distances. The behavior of the two plate system is also seen to be highly dependent on whether the system is open or closed. In addition we analyze the Casimir force on a third plate placed between two outer plates. The force acting on the central plate is shown to be highly sensitive to whether or not the fluctuating scalar field is present in the region exterior to the two confining plates.Comment: 8 pages RevTex, 2 .eps figure

Metastable states of spin glasses on random thin graphs

In this paper we calculate the mean number of metastable states for spin glasses on so called random thin graphs with couplings taken from a symmetric binary distribution $\pm J$. Thin graphs are graphs where the local connectivity of each site is fixed to some value $c$. As in totally connected mean field models we find that the number of metastable states increases exponentially with the system size. Furthermore we find that the average number of metastable states decreases as $c$ in agreement with previous studies showing that finite connectivity corrections of order $1/c$ increase the number of metastable states with respect to the totally connected mean field limit. We also prove that the average number of metastable states in the limit $c\to\infty$ is finite and converges to the average number of metastable states in the Sherrington-Kirkpatrick model. An annealed calculation for the number of metastable states $N_{MS}(E)$ of energy $E$ is also carried out giving a lower bound on the ground state energy of these spin glasses. For small $c$ one may obtain analytic expressions for $$.Comment: 13 pages LateX, 3 figures .ep

Dynamical transition for a particle in a squared Gaussian potential

We study the problem of a Brownian particle diffusing in finite dimensions in a potential given by $\psi= \phi^2/2$ where $\phi$ is Gaussian random field. Exact results for the diffusion constant in the high temperature phase are given in one and two dimensions and it is shown to vanish in a power-law fashion at the dynamical transition temperature. Our results are confronted with numerical simulations where the Gaussian field is constructed, in a standard way, as a sum over random Fourier modes. We show that when the number of Fourier modes is finite the low temperature diffusion constant becomes non-zero and has an Arrhenius form. Thus we have a simple model with a fully understood finite size scaling theory for the dynamical transition. In addition we analyse the nature of the anomalous diffusion in the low temperature regime and show that the anomalous exponent agrees with that predicted by a trap model.Comment: 18 pages, 4 figures .eps, JPA styl

Abundance of Rice Root Aphid Among Selected Plant Species and on Plants Grown With Different Soil-Surface Media

The rice root aphid, Rhopalosiphum rufiabdominalis (Sasaki), is distributed worldwide and colonizes a wide range of plants. However, relatively little is known about the suitability of different host plants, optimal rearing techniques, and the aphid’s impact on plant fitness. To improve understanding of these factors, laboratory experiments were conducted to compare the abundance of rice root aphid on plants grown using three different soil-surface media and among selected monocotyledonous and dicotyledonous plants. Rice root aphid was more abundant on plants grown with a sandy soil surface than a surface with fine wood chips or only bare non-sandy soil. Rice root aphid was more abundant on ‘Elbon’ rye than on ‘Bart 38,’ ‘Dart,’ ‘Fletcher’ and ‘Ramona 50’ wheat. More winged rice root aphids were produced on Elbon rye than on Dart wheat, but the number of winged aphids on Elbon rye did not differ from that on other wheat lines. Rice root aphid was more abundant on Elbon rye and ‘TAM 110’ wheat than on ‘Marmin,’ ‘Marshall’ and ‘Sharp’ wheat. Additional observations with monocotyledonous plants showed that abundance of rice root aphid on ‘Kivu 85’ triticale was comparable to that on Elbon rye. Rice root aphid did not reproduce on potato or soybean, although winged adults persisted up to 24 days on caged potato plants. The implications of differential abundance of rice root aphid on plants are discussed in regard to colony rearing, future experiments and possible pest management considerations

Effective diffusion constant in a two dimensional medium of charged point scatterers

We obtain exact results for the effective diffusion constant of a two dimensional Langevin tracer particle in the force field generated by charged point scatterers with quenched positions. We show that if the point scatterers have a screened Coulomb (Yukawa) potential and are uniformly and independently distributed then the effective diffusion constant obeys the Volgel-Fulcher-Tammann law where it vanishes. Exact results are also obtained for pure Coulomb scatterers frozen in an equilibrium configuration of the same temperature as that of the tracer.Comment: 9 pages IOP LaTex, no figure

Using Experimental Economics to Measure Social Capital And Predict Financial Decisions

Questions remain as to whether results from experimental economics games are generalizable to real decisions in non-laboratory settings. Furthermore, important questions persist about whether social capital can help solve seemingly missing credit markets. I conduct two experiments, a Trust game and a Public Goods game, and a survey to measure social capital. I then examine whether behavior in the games predicts repayment of loans to a Peruvian group lending microfinance program. Since the structure of these loans relies heavily on social capital to enforce repayment, this is a relevant and important test of the games, as well as of other measures of social capital. I find that individuals identified as "trustworthy" by the Trust game are in fact less likely to default on their loans. I do not find similar support for the Trust game as a measure of trust.trust game, experimental economics, microfinance

Social Connections and Group Banking

Lending to the poor is expensive due to high screening, monitoring, and enforcement costs. Group lending advocates believe lenders overcome this by harnessing social connections. Using data from FINCA-Peru, I exploit a quasi-random group formation process to find evidence of peers successfully monitoring and enforcing joint-liability loans. Individuals with stronger social connections to their fellow group members (i.e., either living closer or being of a similar culture) have higher repayment and higher savings. Furthermore, I observe direct evidence that relationships deteriorate after default, and that through successful monitoring, individuals know who to punish and who not to punish after default.Microfinance, Group lending, informal savings, social capital