Neumann problem for singular degenerate parabolic equations

We prove a comparison theorem for viscosity solutions of singular degenerate parabolic equations with the Neumann boundary condition on a domain not necessarily convex. Our result applies to various level set equations including the Neumann problem for the mean curvature flow equations where every level set of solutions moves by its mean curvature and perpendicularly intersects the boundary of the domain

Microwave Heating of Water, Ice and Saline Solution: Molecular Dynamics Study

In order to study the heating process of water by the microwaves of 2.5-20GHz frequencies, we have performed molecular dynamics simulations by adopting a non-polarized water model that have fixed point charges on rigid-body molecules. All runs are started from the equilibrated states derived from the I$_{c}$ ice with given density and temperature. In the presence of microwaves, the molecules of liquid water exhibit rotational motion whose average phase is delayed from the microwave electric field. Microwave energy is transferred to the kinetic and inter-molecular energies of water, where one third of the absorbed microwave energy is stored as the latter energy. The water in ice phase is scarcely heated by microwaves because of the tight hydrogen-bonded network of water molecules. Addition of small amount of salt to pure water substantially increases the heating rate because of the weakening by defects in the water network due to sloshing large-size negative ions.Comment: 21 pages, 13 figure

Microwave heating and collapse of methane hydrate by molecular dynamics simulations

Microwave heating of methane hydrate is investigated with electrostatic molecular dynamics simulations. The structure I of methane hydrate is constructed. When the methane hydrate with a density of 0.91 $\rm{g/cm}^3$ and temperature of 273 K is exposed to microwave electric fields, it suddenly collapses in liquid after a certain period of irradiation. However, a hydrate with a five percent higher density of 0.95 $\rm{g/cm}^3$ and the same initial temperature shows no collapse as a crystal caused by the microwave. A hydrate with CO$_{2}$ guest molecules has increased kinetic energy but rapidly collapses due to the Lennard-Jones potentials. The methane hydrate with variable density and temperature is presented and exhibits slow heating as a crystal and an unchanging volume.Comment: 16 pages, 2 tables, 8 figure

Magnetocrystalline Anisotropy of Pyrrhotite

Magentization curves in the base plane and along the c-axis of natural pyrrhotite crystals (Fe_7S_8) are measured up to a magnetic field strength of 90 kOe. The results can be expressed in terms of the magnetocrystalline anisotropy energy, E_K=-K_0|cos θ|+K_3 cos^2θ+K_4cos^4θ, the last term being the correction term for the. preceding one. The values of K_0, K_3 and K_4 obtained are K_0=0.51×10^6erg/cc, K_3=3.2×10^6 erg/cc and K_4=0.098×10^6 erg/cc at 293°K and K_0=1.2×10^6 erg/cc, K_3=4.2×10^6 erg/cc and K_4=0.21×10^6 erg/cc at 77°K. These values obtained are discussed on the basis of Adachi\u27s theory of magnetocrystalline anisotropy

Remodeling of Monoplanar Purkinje Cell Dendrites during Cerebellar Circuit Formation

Dendrite arborization patterns are critical determinants of neuronal connectivity and integration. Planar and highly branched dendrites of the cerebellar Purkinje cell receive specific topographical projections from two major afferent pathways; a single climbing fiber axon from the inferior olive that extend along Purkinje dendrites, and parallel fiber axons of granule cells that contact vertically to the plane of dendrites. It has been believed that murine Purkinje cell dendrites extend in a single parasagittal plane in the molecular layer after the cell polarity is determined during the early postnatal development. By three-dimensional confocal analysis of growing Purkinje cells, we observed that mouse Purkinje cells underwent dynamic dendritic remodeling during circuit maturation in the third postnatal week. After dendrites were polarized and flattened in the early second postnatal week, dendritic arbors gradually expanded in multiple sagittal planes in the molecular layer by intensive growth and branching by the third postnatal week. Dendrites then became confined to a single plane in the fourth postnatal week. Multiplanar Purkinje cells in the third week were often associated by ectopic climbing fibers innervating nearby Purkinje cells in distinct sagittal planes. The mature monoplanar arborization was disrupted in mutant mice with abnormal Purkinje cell connectivity and motor discoordination. The dendrite remodeling was also impaired by pharmacological disruption of normal afferent activity during the second or third postnatal week. Our results suggest that the monoplanar arborization of Purkinje cells is coupled with functional development of the cerebellar circuitry

Multidendritic sensory neurons in the adult Drosophila abdomen: origins, dendritic morphology, and segment- and age-dependent programmed cell death

<p>Abstract</p> <p>Background</p> <p>For the establishment of functional neural circuits that support a wide range of animal behaviors, initial circuits formed in early development have to be reorganized. One way to achieve this is local remodeling of the circuitry hardwiring. To genetically investigate the underlying mechanisms of this remodeling, one model system employs a major group of <it>Drosophila </it>multidendritic sensory neurons - the dendritic arborization (da) neurons - which exhibit dramatic dendritic pruning and subsequent growth during metamorphosis. The 15 da neurons are identified in each larval abdominal hemisegment and are classified into four categories - classes I to IV - in order of increasing size of their receptive fields and/or arbor complexity at the mature larval stage. Our knowledge regarding the anatomy and developmental basis of adult da neurons is still fragmentary.</p> <p>Results</p> <p>We identified multidendritic neurons in the adult <it>Drosophila </it>abdomen, visualized the dendritic arbors of the individual neurons, and traced the origins of those cells back to the larval stage. There were six da neurons in abdominal hemisegment 3 or 4 (A3/4) of the pharate adult and the adult just after eclosion, five of which were persistent larval da neurons. We quantitatively analyzed dendritic arbors of three of the six adult neurons and examined expression in the pharate adult of key transcription factors that result in the larval class-selective dendritic morphologies. The 'baseline design' of A3/4 in the adult was further modified in a segment-dependent and age-dependent manner. One of our notable findings is that a larval class I neuron, ddaE, completed dendritic remodeling in A2 to A4 and then underwent caspase-dependent cell death within 1 week after eclosion, while homologous neurons in A5 and in more posterior segments degenerated at pupal stages. Another finding is that the dendritic arbor of a class IV neuron, v'ada, was immediately reshaped during post-eclosion growth. It exhibited prominent radial-to-lattice transformation in 1-day-old adults, and the resultant lattice-shaped arbor persisted throughout adult life.</p> <p>Conclusion</p> <p>Our study provides the basis on which we can investigate the genetic programs controlling dendritic remodeling and programmed cell death of adult neurons, and the life-long maintenance of dendritic arbors.</p

Mechanical tension-stress induces expression of bone morphogenetic protein (BMP)-2 and BMP-4, but not BMP-6, BMP-7, and GDF-5 mRNA, during distraction osteogenesis. J Bone Miner Res

ABSTRACT Bone lengthening with osteotomy and gradual distraction was achieved in 57 rats, and the effect of mechanical tension-stress on gene expression of bone morphogenetic proteins (BMPs) was investigated by in situ hybridization and Northern blot analysis using probes of BMP-2, BMP-4, BMP-6, BMP-7, and growth/differentiation factor (GDF)-5. There was a lag phase for 7 days after femoral osteotomy until gradual distraction was carried out for 21 days at a rate of 0.25 mm/12 h using a small external fixator. The signals of the above BMPs mRNA were not detected in the intact rat bone but they were induced after osteotomy except those for BMP-7. By 4 days after osteotomy, BMP-2 and BMP-4 mRNAs were detected in chondrogenic precursor cells in the subperiosteal immature callus. BMP-6 and GDF-5 mRNA were detected in more differentiated cells in chondroid bone. By 7 days after osteotomy, cartilaginous external callus and bony endosteal callus were formed. Meanwhile, the signals of BMP-2 and BMP-4 mRNAs declined to preoperative levels, whereas the signals of BMP-6 and GDF-5 mRNAs were rather elevated. As distraction was started, the callus elongated and eventually separated into proximal and distal segments forming a fibrous interzone in the middle. Expression of BMP-2 and BMP-4 mRNAs was markedly induced at this stage. Their signals were detected widely among chondrogenic and osteogenic cells and their precursor cells sustaining mechanical tension-stress at the fibrous interzone. BMP-6 and GDF-5 mRNAs were detected exclusively in chondrogenic cells at both ends of the fibrous interzone, where endochondral ossification occurred. But neither mRNA was detected in terminally differentiated hypertrophic chondrocytes. As distraction advanced, the cartilage was progressively resorbed from both ends and new bone was formed directly by intramembranous ossification. There was no new cartilage formation in the advanced stage of distraction. The signals of BMP-6 and GDF-5 mRNA declined by this stage, while those of BMP-2 and BMP-4 were maintained at high level for as long as distraction was continued. After completion of distraction, the fibrous interzone fused and the lengthened segment was consolidated. BMP-2, BMP-4, BMP-6, nor GDF-5 was expressed at this stage. The signals of BMP-7 were not detected throughout the experiment. The present results suggest that excellent and uninterrupted bone formation during distraction osteogenesis owes to enhanced expression of BMP-2 and BMP-4 genes by mechanical tensionstress. Abundant gene products of BMP-2 and BMP-4 could induce in situ bone formation by paracrine and autocrin