Fractional Fokker-Planck Equations for Subdiffusion with Space-and-Time-Dependent Forces

We have derived a fractional Fokker-Planck equation for subdiffusion in a general space-and- time-dependent force field from power law waiting time continuous time random walks biased by Boltzmann weights. The governing equation is derived from a generalized master equation and is shown to be equivalent to a subordinated stochastic Langevin equation.Comment: 5 page

Ga^+ beam lithography for nanoscale silicon reactive ion etching

By using a dry etch chemistry which relies on the highly preferential etching of silicon, over that of gallium (Ga), we show resist-free fabrication of precision, high aspect ratio nanostructures and microstructures in silicon using a focused ion beam (FIB) and an inductively coupled plasma reactive ion etcher (ICP-RIE). Silicon etch masks are patterned via Ga^+ ion implantation in a FIB and then anisotropically etched in an ICP-RIE using fluorinated etch chemistries. We determine the critical areal density of the implanted Ga layer in silicon required to achieve a desired etch depth for both a Pseudo Bosch (SF_6/C_4F_8) and cryogenic fluorine (SF_6/O_2) silicon etching. High fidelity nanoscale structures down to 30 nm and high aspect ratio structures of 17:1 are demonstrated. Since etch masks may be patterned on uneven surfaces, we utilize this lithography to create multilayer structures in silicon. The linear selectivity versus implanted Ga density enables grayscale lithography. Limits on the ultimate resolution and selectivity of Ga lithography are also discussed

Surface width scaling in noise reduced Eden clusters

The surface width scaling of Eden A clusters grown from a single aggregate site on the square lattice is investigated as a function of the noise reduction parameter. A two-exponent scaling ansatz is introduced and used to fit the results from simulations covering the range from fully stochastic to the zero-noise limit.Comment: 4 pages, RevTex, 3 figure

The role of M cells and the long QT syndrome in cardiac arrhythmias: simulation studies of reentrant excitations using a detailed electrophysiological model

In this numerical study, we investigate the role of intrinsic heterogeneities of cardiac tissue due to M cells in the generation and maintenance of reentrant excitations using the detailed Luo-Rudy dynamic model. This model has been extended to include a description of the long QT 3 syndrome, and is studied in both one dimension, corresponding to a cable traversing the ventricular wall, and two dimensions, representing a transmural slice. We focus on two possible mechanisms for the generation of reentrant events. We first investigate if early-after-depolarizations occurring in M cells can initiate reentry. We find that, even for large values of the long QT strength, the electrotonic coupling between neighboring cells prevents early-after-depolarizations from creating a reentry. We then study whether M cell domains, with their slow repolarization, can function as wave blocks for premature stimuli. We find that the inclusion of an M cell domain can result in some cases in reentrant excitations and we determine the lifetime of the reentry as a function of the size and geometry of the domain and of the strength of the long QT syndrome

Fractional Chemotaxis Diffusion Equations

We introduce mesoscopic and macroscopic model equations of chemotaxis with anomalous subdiffusion for modelling chemically directed transport of biological organisms in changing chemical environments with diffusion hindered by traps or macro-molecular crowding. The mesoscopic models are formulated using Continuous Time Random Walk master equations and the macroscopic models are formulated with fractional order differential equations. Different models are proposed depending on the timing of the chemotactic forcing. Generalizations of the models to include linear reaction dynamics are also derived. Finally a Monte Carlo method for simulating anomalous subdiffusion with chemotaxis is introduced and simulation results are compared with numerical solutions of the model equations. The model equations developed here could be used to replace Keller-Segel type equations in biological systems with transport hindered by traps, macro-molecular crowding or other obstacles.Comment: 25page

Surface Encapsulation for Low-Loss Silicon Photonics

Encapsulation layers are explored for passivating the surfaces of silicon to reduce optical absorption in the 1500-nm wavelength band. Surface-sensitive test structures consisting of microdisk resonators are fabricated for this purpose. Based on previous work in silicon photovoltaics, coatings of SiNx and SiO2 are applied under varying deposition and annealing conditions. A short dry thermal oxidation followed by a long high-temperature N2 anneal is found to be most effective at long-term encapsulation and reduction of interface absorption. Minimization of the optical loss is attributed to simultaneous reduction in sub-bandgap silicon surface states and hydrogen in the capping material.Comment: 4 pages, 3 figure

Distribution of Mutual Information

The mutual information of two random variables i and j with joint probabilities t_ij is commonly used in learning Bayesian nets as well as in many other fields. The chances t_ij are usually estimated by the empirical sampling frequency n_ij/n leading to a point estimate I(n_ij/n) for the mutual information. To answer questions like "is I(n_ij/n) consistent with zero?" or "what is the probability that the true mutual information is much larger than the point estimate?" one has to go beyond the point estimate. In the Bayesian framework one can answer these questions by utilizing a (second order) prior distribution p(t) comprising prior information about t. From the prior p(t) one can compute the posterior p(t|n), from which the distribution p(I|n) of the mutual information can be calculated. We derive reliable and quickly computable approximations for p(I|n). We concentrate on the mean, variance, skewness, and kurtosis, and non-informative priors. For the mean we also give an exact expression. Numerical issues and the range of validity are discussed.Comment: 8 page

The fishery for California market squid (Loligo opalescens) (Cephalopoda: Myopsida), from 1981 through 2003

The California market squid (Loligo opalescens) has been harvested since the 1860s and it has become the largest fishery in California in terms of tonnage and dollars since 1993. The fishery began in Monterey Bay and then shifted to southern California, where effort has increased steadily since 1983. The California Department of Fish and Game (CDFG) collects information on landings of squid, including tonnage, location, and date of capture. We compared landings data gathered by CDFG with sea surface temperature (SST), upwelling index (UI), the southern oscillation index (SOI), and their respective anomalies. We found that the squid fishery in Monterey Bay expends twice the effort of that in southern California. Squid landings decreased substantially following large El Niño events in 1982−83 and 1997−98, but not following the smaller El Niño events of 1987 and 1992. Spectral analysis revealed autocorrelation at annual and 4.5-year intervals (similar to the time period between El Niño cycles). But this analysis did not reveal any fortnightly or monthly spawning peaks, thus squid spawning did not correlate with tides. A paralarvae density index (PDI) for February correlated well with catch per unit of effort (CPUE) for the following November recruitment of adults to the spawning grounds. This stock– recruitment analysis was significant for 2000−03 (CPUE=8.42+0.41PDI, adjusted coefficient of determination, r2=0.978, P=0.0074). Surveys of squid paralarvae explained 97.8% of the variance for catches of adult squid nine months later. The regression of CPUE on PDI could be used to manage the fishery. Catch limits for the fishery could be set on the basis of paralarvae abundance surveyed nine months earlier

Sharing the Burden of GHG Reductions

Abstract and PDF report are also available on the MIT Joint Program on the Science and Policy of Global Change website (http://globalchange.mit.edu/).The G8 countries propose a goal of a 50% reduction in global emissions by 2050, in an effort that needs to take account of other agreements specifying that developing countries are to be provided with incentives to action and protected from the impact of measures taken by others. To help inform international negotiations of measures to achieve these goals we develop a technique for endogenously estimating the allowance allocations and associated financial transfers necessary to achieve predetermined distributional outcomes and apply it in the MIT Emissions Prediction and Policy Analysis (EPPA) model. Possible burden sharing agreements are represented by different allowance allocations (and resulting financial flows) in a global cap-and-trade system. Cases studied include agreements that allocate the burden based on simple allocation rules found in current national proposals and alternatives that specify national equity goals for both developing and developed countries. The analysis shows the ambitious nature of this reduction goal: universal participation will be necessary and the welfare costs can be both substantial and wildly different across regions depending on the allocation method chosen. The choice of allocation rule is shown to affect the magnitude of the task and required emissions price because of income effects. If developing countries are fully compensated for the costs of mitigation then the welfare costs to developed countries, if shared equally, are around 2% in 2020, rising to some 10% in 2050, and the implied financial transfers are large—over $400 billion per year in 2020 and rising to around$3 trillion in 2050. For success in dealing with the climate threat any negotiation of long-term goals and paths to achievement need to be grounded in a full understanding of the substantial amounts at stake.Development of the EPPA model used has been supported by the U.S. Department of Energy, U.S. Environmental Protection Agency and U.S. National Science Foundation, and by a consortium of industry and foundation sponsors of the MIT Joint Program on the Science and Policy of Global Change