Multiplicative Operator Splittings in Nonlinear Diffusion: From Spatial Splitting to Multiple Timesteps

Operator splitting is a powerful concept used in many diversed fields of applied mathematics for the design of effective numerical schemes. Following the success of the additive operator splitting (AOS) in performing an efficient nonlinear diffusion filtering on digital images, we analyze the possibility of using multiplicative operator splittings to process images from different perspectives.We start by examining the potential of using fractional step methods to design a multiplicative operator splitting as an alternative to AOS schemes. By means of a Strang splitting, we attempt to use numerical schemes that are known to be more accurate in linear diffusion processes and apply them on images. Initially we implement the Crank-Nicolson and DuFort-Frankel schemes to diffuse noisy signals in one dimension and devise a simple extrapolation that enables the Crank-Nicolson to be used with high accuracy on these signals. We then combine the Crank-Nicolson in 1D with various multiplicative operator splittings to process images. Based on these ideas we obtain some interesting results. However, from the practical standpoint, due to the computational expenses associated with these schemes and the questionable benefits in applying them to perform nonlinear diffusion filtering when using long timesteps, we conclude that AOS schemes are simple and efficient compared to these alternatives.We then examine the potential utility of using multiple timestep methods combined with AOS schemes, as means to expedite the diffusion process. These methods were developed for molecular dynamics applications and are used efficiently in biomolecular simulations. The idea is to split the forces exerted on atoms into different classes according to their behavior in time, and assign longer timesteps to nonlocal, slowly-varying forces such as the Coulomb and van der Waals interactions, whereas the local forces like bond and angle are treated with smaller timesteps. Multiple timestep integrators can be derived from the Trotter factorization, a decomposition that bears a strong resemblance to a Strang splitting. Both formulations decompose the time propagator into trilateral products to construct multiplicative operator splittings which are second order in time, with the possibility of extending the factorization to higher order expansions. While a Strang splitting is a decomposition across spatial dimensions, where each dimension is subsequently treated with a fractional step, the multiple timestep method is a decomposition across scales. Thus, multiple timestep methods are a realization of the multiplicative operator splitting idea. For certain nonlinear diffusion coefficients with favorable properties, we show that a simple multiple timestep method can improve the diffusion process.     

Directionality from anisotropic phonon production in solid state dark matter detection

We present results from computer simulations of the events immediately following the scattering of a dark matter particle off a nucleus in a crystal detector. Our simulations show that with NaF as the target, the recoil produces solitary waves that decay slowly, resulting in a narrow wake of phonons. The phonon wake allows a determination of direction of the nuclear recoil.     

Reducing the Health and Digital Divides: A Model for Using Community‐Based Participatory Research Approach to E‐Health Interventions in Low‐Income Hispanic Communities

Low‐income Hispanics are the most digitally underserved population in the U.S. This article examines the potential of community‐based participatory research approach to e‐health to decrease the disparities in access to technology and health information in low‐income Hispanic communities. To demonstrate this framework, we describe the process of designing a community‐based e‐health intervention to increase knowledge and parental self‐efficacy in coping with young children's mental health problems including mental health service utilization. Our model incorporates utilizing promotoras de salud (lay community health educators) and community media principles to create the content of e‐health interventions and train community members in using the technology. This case study illustrates the processes involved in using this approach, barriers for participatory e‐health interventions in bridging the Digital Divide, and lessons learned.     

Orthographic Structure Versus Morphological Structure: Principles of Lexical Organization in a Given Language.

Most models of visual word recognition in alphabetic orthographies assume that words are lexically organized according to orthographic similarity. Support for this is provided by form-priming experiments that demonstrate robust facilitation when primes and targets share similar sequences of letters. The authors examined form-orthographic priming effects in Hebrew, Arabic, and English. Hebrew and Arabic have an alphabetic writing system but a Semitic morphological structure. Hebrew morphemic units are composed of noncontiguous phonemic (and letter) sequences in a given word. Results demonstrate that form-priming effects in Hebrew or Arabic are unreliable, whereas morphological priming effects with minimal letter overlap are robust. Hebrew bilingual subjects, by contrast, showed robust form-priming effects with English material, suggesting that Semitic words are lexically organized by morphological rather than orthographic principles. The authors conclude that morphology can constrain lexical organization even in alphabetic orthographies and that visual processing of words is first determined by morphological characteristics. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Myo-Inositol Limits Kainic Acid-Induced Epileptogenesis in Rats

Epilepsy is a severe neurological disease characterized by spontaneous recurrent seizures (SRS). A complex pathophysiological process referred to as epileptogenesis transforms a normal brain into an epileptic one. Prevention of epileptogenesis is a subject of intensive research. Currently, there are no clinically approved drugs that can act as preventive medication. Our previous studies have revealed highly promising antiepileptogenic properties of a compound–myo-inositol (MI) and the present research broadens previous results and demonstrates the long-term disease-modifying effect of this drug, as well as the amelioration of cognitive comorbidities. For the first time, we show that long-term treatment with MI: (i) decreases the frequency and duration of electrographic SRS in the hippocampus; (ii) has an ameliorating effect on spatial learning and memory deficit associated with epileptogenesis, and (iii) attenuates cell loss in the hippocampus. MI treatment also alters the expression of the glial fibrillary acidic protein, LRRC8A subunit of volume-regulated anion channels, and protein tyrosine phosphatase receptor type R, all expected to counteract the epileptogenesis. All these effects are still present even 4 weeks after MI treatment ceased. This suggests that MI may exert multiple actions on various epileptogenesis-associated changes in the brain and, therefore, could be considered as a candidate target for prevention of epileptogenesis.     

Investigation of the inhibitory effect of silica on the degradation of 1,1,1-trichloroethane by granular iron

Although iron-based permeable reactive barriers are gaining importance for treating groundwater contaminants, little is currently known about the effect of cosolutes on barrier longevity. Because of their corrosion inhibiting properties, dissolved silica species are of particular concern. This research investigates the effect of silica on the reduction of 1,1,1-trichloroethane by granular iron as a function of added silica concentration, pH, and duration of iron exposure to dissolved silica. Batch studies reveal that, at pH 8.5 and above, added silica concentrations as low as 0.17 mM cause a 30% reduction in the reactivity of iron. At higher silica concentrations, reactivity decreases by 65-75%. The inhibitory effect is greater at higher pH: 0.83 mM silica has no apparent adverse effect at pH 7.5, but leads to a 46% decrease in reaction rate at pH 8 and 90% at pH 9. This corresponds to observed trends in silica adsorption onto iron, which is low at pH 7.3 but increases at higher pH. Extending the duration of iron exposure to silica solutions also leads to a more pronounced inhibitory effect. This is in good agreement with the increase in silica coverage on the iron surface as revealed by X-ray photoelectron spectroscopy.     

On Boundary Condition Capturing for Multiphase Interfaces

This review paper begins with an overview of the boundary condition capturing approach to solving problems with interfaces. Although the authors’ original motivation was to extend the ghost fluid method from compressible to incompressible flow, the elliptic nature of incompressible flow quickly quenched the idea that ghost cells could be defined and used in the usual manner. Instead the boundary conditions had to be implicitly captured by the matrix formulation itself, leading to the novel approach. We first review the work on the variable coefficient Poisson equation, noting that the simplicity of the method allowed for an elegant convergence proof. Simplicity and robustness also allowed for a quick extension to three-dimensional two-phase incompressible flows including the effects of viscosity and surface tension, which is discussed subsequently. The method has enjoyed popularity in both computational physics and computer graphics, and we show some comparisons with the traditional delta function approach for the visual simulation of bubbles. Finally, we discuss extensions to problems where the velocity is discontinuous as well, as is the case for premixed flames, and show an example of multiple interacting liquids that includes all of the aforementioned phenomena.     

Social learning of an artificial fruit task in capuchin monkeys (Cebus apella).

Social learning in 11 human-raised capuchin monkeys (Cebus apella) was investigated using an artificial fruit that was designed as an analogue of natural foraging problems faced by primates. Each subject observed a human model open each of 3 principal components on the fruit in 1 of 2 alternative ways ("morphs"). The capuchin monkeys reproduced, to differing extents, the alternative techniques used for opening 1 component of the task (poking vs. pulling while twisting out a pair of smooth plastic bolts) but not the other 2. From the subjects' actions on the bolt latch, independent coders could recognize which morph they had witnessed, and they observed a degree of matching to the demonstrator's act consistent with simple imitation or object movement reenactment (A learns from watching B how an object, or parts of an object, move). Thus, these capuchins were capable of more complex social learning than has been recently ascribed to monkeys. (PsycINFO Database Record (c) 2010 APA, all rights reserved)     

Nonadiabatic vibronic dynamics as a tool. From surface nanochemistry to coherently driven molecular machines

Resonances are ubiquitous in molecular heterojunctions and in scanning tunneling microscopy (STM) experiments. In the former environment, resonance tunneling is essential for favorable wire-length-dependence of the conductance and is often the mechanism underlying conductance enhancement through application of a gate voltage. In the latter environment, resonance tunneling has served to develop a powerful vibrational spectroscopy. Resonance conductance is often strongly nonadiabatic; in the course of the tunneling event, electron energy is channelled into vibrational modes and triggers molecular dynamics. The qualitative physics underlying current-driven, resonance-mediated dynamics in molecular electronics is very simple, and is familiar from related phenomena such as gas phase electron-molecule scattering and photochemistry on conducting surfaces. Equilibrium displacement between the initial and resonant states translates into vibronic coupling in the language of the Marcus theory of electron transfer; it produces a nonstationary superposition in the nuclear subspace that evolves during the resonance lifetime. Upon relaxation the system is internally excited and interesting dynamics is likely to ensue. While the underlying physics is very general, the single-molecule STM and molecular heterojunction environments open unique and exciting opportunities. The former introduces the possibility of determining resonance lifetimes through fit of experimental voltage dependencies to a quantum mechanical theory. The latter introduces the possibility of developing coherently driven molecular machines, a new form of nanolithography, and a new means of manipulating the conductivity of molecular-scale devices. We briefly review the theory of current-driven dynamics in molecular-scale devices, discuss the results of ongoing research on surface nanochemistry and molecular machines, and sketch a variety of potential applications.