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.     

High-Thermal-Conductivity Aluminum Nitride Ceramics: The Effect of Thermodynamic, Kinetic, and Microstructural Factors

Improvement in the thermal conductivity of aluminum nitride (AlN) can be realized by additives that have a high thermodynamic affinity toward alumina (Al₂O₃), as is clearly demonstrated in the aluminum nitride-yttria (AlN-Y₂O₃) system. A wide variety of lanthanide dopants are compared at equimolar lanthanide oxide:alumina (Ln₂O₃: Al₂O₃, where Ln is a lanthanide element) ratios, with samaria (Sm₂O₃) and lutetia (Lu₂O₃) being the dopants that give the highest- and lowest-thermal-conductivity AlN composites, respectively. The choice of the sintering aid and the dopant level is much more important than the microstructure that evolves during sintering. A contiguous AlN phase provides rapid heat conduction paths, even at short sintering times. AlN contiguity decreases slightly as the annealing times increase in the range of 1–1000 min at 1850°C. However, a substantial increase in thermal conductivity results, because of purification of AlN grains by dissolution-reprecipitation and bulk diffusion. Removal of grain-boundary phases, with a concurrent increase in AlN contiguity, occurs at high annealing temperatures or at long times and is a natural consequence of high dihedral angles (poor wetting) in liquidphase-sintered AlN ceramics.     

Creep and Stress Rupture Behavior of an Advanced Silicon Nitride: Part I, Experimental Observations

Cylindrical buttuohead specimens of an advanced silicon nitride were tested in uniaxial tension at temperatures between 1422 and 1673 K. In the range 1477 to 1673 K, creep deformation was reliably measured using high-temperature contact probe extensometry. Extensive scanning and transmission electron microscopy has revealed the formation of lenticular cavities at two-grain junctions at all temperatures (1422–1673 K) and extensive triple-junction cavitation occurring at the higher temperatures (1644–1673 K). Cavitation is believed to be part of the net creep process. The stress rupture data show stratification of the Monkman–Grant lines with respect to temperature. Failure strain increased with increase in rupture time or temperature, or decrease in stress. Fractography showed that final failure occurred by subcritical crack growth in all specimens.     

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.     

The evaporation signal from α particles stopped in superfluid helium

Alpha particles stopped in a 3 liter volume of liquid helium at 30 mK are observed by the calorimetric detection of helium atoms evaporated from the free surface of the liquid. Quantum evaporation of the helium is produced by the rotons that are created by the particle. While the energy spectrum of the 5.5 MeV 's from the²⁴¹Am source has a width of less than 0.5%, the energy distribution of the observed evaporation signals extends from the low energy threshold of several keV up to a maximum of several 100 keV, depending on geometrical factors and the collection area of the calorimeter. The origin of the observed distribution may result in part from the presence of the substrate and a dependence on the direction of the track of the particle. A simple model of the generation of rotons by the particle will be discussed.     

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)     

Effect of microwave heating on quality and mycoflora of sorghum grain

Sorghum (cv. Maldandi M35-1) was modified to 12, 14 and 16% moisture content (m.c.) and heat-treated with microwave energy at 3 levels, for 30 sec (=4.5, 9 and 18 kJ), and 60 sec (=9, 18 and 36 kJ). The effect of microwave heating on rise and subsequent fall in grain temperature, reduction in m.c. and quality characteristics including germination, seedling dry matter, free fatty acids (FFA) and contaminant fungi was determined. The temperature attained and the moisture loss in the sorghum grain was affected by grain m.c. and the time of exposure. At the lowest and highest microwave treatment level grain temperatures reached 30–40°C and 90–101°C, respectively. However, a 60-sec treatment at the highest energy level was lethal for the grain, particularly at 14 and 16% m.c. The FFA values were unaffected by microwave treatment. Statistical analyses showed that the microwave power level and time individually, and power level × time interactions were significant for most quality characteristics. The fungi present most abundantly on the sorghum grain were Eurotium spp., Aspergillus candidus, A. niger and Penicillium spp. Increasing m.c. and microwave heating resulted in elimination of most fungi after a 30-sec exposure time. With a 60-sec exposure period, practically all fungi were eliminated from the grain.     

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.