We prove that for any non-degenerate dendrite D, there exist topologically mixing maps $F : D \to D$ and $f : [0, 1] \to [0, 1]$ such that the natural extensions (as known as shift homeomorphisms) $\sigma _F$ and $\sigma _f$ are conjugate, and consequently the corresponding inverse limits are homeomorphic. Moreover, the map f does not depend on the dendrite D and can be selected so that the inverse limit $\underleftarrow {\lim } (D,F)$ is homeomorphic to the pseudo-arc. The result extends to any finite number of dendrites. Our work is motivated by, but independent of, the recent result of the first and third author on conjugation of Lozi and Hénon maps to natural extensions of dendrite maps.

We are interested in dendrites for which all invariant measures of zero-entropy mappings have discrete spectrum, and we prove that this holds when the closure of the endpoint set of the dendrites is countable. This solves an open question which has been around for awhile, and almost completes the characterization of dendrites with this property.

We characterize dendrites D such that a continuous selfmap of D is generically chaotic (in the sense of Lasota) if and only if it is generically ${\varepsilon }$ -chaotic for some ${\varepsilon }>0$ . In other words, we characterize dendrites on which generic chaos of a continuous map can be described in terms of the behaviour of subdendrites with non-empty interiors under iterates of the map. A dendrite D belongs to this class if and only if it is completely regular, with all points of finite order (that is, if and only if D contains neither a copy of the Riemann dendrite nor a copy of the $\omega $ -star).

We show that any action of a countable amenable group on a uniquely arcwise connected continuum has a periodic point of order $\leq 2$ .

U–Mo metallic alloy is considered as an advanced fast reactor and research reactor fuel material. U–33 at.% Mo has a higher melting point than that of pure uranium metal. This provides a higher safety margin against fuel melting and diminishes fuel and clad interaction. The metallic fuels are fabricated through a melting-casting route, and the cast microstructure of U–33 at.% Mo has been characterized using optical microscope, scanning electron microscopy—energy dispersive spectroscopy, and Electron back scattered diffraction. These microstructures show dendrites of two different morphologies: (i) the γ-(U) dendrite with secondary branches and (ii) the equiaxed (Mo) dendrite without secondary branches and surrounded by a peritectic reaction product. In this article, for the first time, a phase field model has been developed for U–Mo alloys to understand the morphological evolution and the associated microsegregation of γ-(U) dendrites in the U–33 at.% Mo alloy. The evolution of the concentration and temperature field with the time and the effect of undercooling on the growth velocity of γ-(U) and (Mo) dendrites has been studied.

Among the different energy storage technologies under study, lithium–oxygen batteries are one of the most promising due to their great gravimetric energies and capacities 6–10 times greater than other technologies such as conventional lithium-ion cells. The current study provides a comprehensive understanding of how the anodic (e.g., dendrites) and cathodic designs (e.g., porosity of the carbon cathode and mass fraction of oxygen) affect the discharge characteristics of lithium–oxygen cells. When comparing all changes in dendrite surface, porosity and oxygen restriction, it is concluded that although the changes in porosity and oxygen decrease the performance of the cells, the dendrites led to the greatest decrease in performance of the battery when examining the capacity of the cell. This comprehensive understanding will aid in the design of a cyclable and commercially viable lithium–oxygen battery that could be used for a wide range of energy storage applications.

Continua $X$ and $Y$ are monotone equivalent if there exist monotone onto maps $f\,:\,X\,\to \,Y$ and $g:\,Y\to \,X.\,\text{A}$ . A continuum $X$ is isolated with respect to monotone maps if every continuumthat is monotone equivalent to $X$ must also be homeomorphic to $X$ . In this paper we show that a dendrite $X$ is isolated with respect to monotone maps if and only if the set of ramification points of $X$ is finite. In this way we fully characterize the classes of dendrites that are monotone isolated.

In this paper, we propose a space-time rescaling scheme for computing the long time evolution of multiple precipitates in an elastically stressed medium. The algorithm is second order accurate in time, spectrally accurate in space and enables one to simulate the evolution of precipitates in a fraction of the time normally used by fixed-frame algorithms. In particular, we extend the algorithm recently developed for single particle by Li et al. (Li, Lowengrub and Leo, J. Comput. Phys., 335 (2007), 554) to the multiple particle case, which involves key differences in the method. Our results show that without elasticity there are successive tip splitting phenomena accompanied by the formation of narrow channels between the precipitates. In presence of applied elastic field, the precipitates form dendrite-like structures with the primary arms aligned in the principal directions of the elastic field. We demonstrate that when the far-field flux decreases with the effective radius of the system, tip-splitting and dendrite formation can be suppressed, as in the one particle case. Depending on the initial position of the precipitates, we further observe that some precipitates grow while others may shrink, even when a positive far field flux is applied.

We define an infinite class of fractals, called horizontally and vertically blocked labyrinth fractals, which are dendrites and special Sierpiński carpets. Between any two points in the fractal there is a unique arc α; the length of α is infinite and the set of points where no tangent to α exists is dense in α.

The morphology of retinal ganglion cells within the central retina during formation of the fovea was examined in retinal explants with horseradish-peroxidase histochemistry. A foveal depression was first apparent in retinal wholemounts at embryonic day 112 (El 12; gestational term is approximately 165 days). At earlier fetal ages, the site of the future fovea was identified by several criteria that included peak density of ganglion cells, lack of blood vessels in the inner retinal layers, arcuate fiber bundles, and the absence of rod outer segments in the photoreceptor layer. Prior to E112, the terminal dendritic arbor of retinal ganglion cells within the central retina extended into the inner plexiform layer and were located directly beneath their somas of origin or at most were slightly displaced from it. For example, at E90 the mean horizontal displacement of the geometric center of the dendritic arbor from the somas of cells within 600 μm of the estimated center of the future fovea was 4.1 μm (S.D. 2.7, range 1.0-10.0, n = 97). Following formation of the foveal depression the dendritic arbors of cells were significantly displaced from their somas. For example, at E138 the mean displacement was 41.2 μm (S.D. 12.2, range 12.0-56.0, n = 97). The displacement of the dendritic arbor which occurred during this period was not accounted for by areal growth of the dendritic arbor, the somas, or the retina, but was produced by the lengthening of the primary dendritic trunk. Moreover, no significant displacement was observed within the remaining 1.5–6.5 mm of the central retina. These observations provide evidence supporting early speculations that the formation of the foveal pit occurs, in part, by the radial migration of ganglion cells from the center of the fovea during its formation. Our analyses suggest that this migration occurs by the lengthening of the primary dendrite presumably by the addition of membrane. This migration is in a direction opposite to the inward movement of photoreceptors that occurs during late fetal and early postnatal periods (Packer et al., 1990, Journal of Comparative Neurology 298, 472–493).

The passive electrical properties of 17 ON-OFF retinal ganglion cells were derived from electrophysiological recordings. The parameters for each cells' equivalent model were obtained from the transient current responses to small step changes in clamp potential. Thirteen of the cells could be adequately approximated by a spherical soma connected to an equivalent dendritic cable. Estimates for the cell input conductance (GN), membrane time constant (τm), the dendritic-to-soma conductance ratio (ρ), and the normalized electrotonic length (L) were obtained (mean ± standard deviation, n = 13): GN = 580 ± 530 pS, τm = 97 ±72 ms, ρ = 2.8 ± 2.8, and L = 0.34 ± 0.13. Series resistance averaged 32 ± 11 MΩ The mean of the derived soma diameters was 18 ± 6 μm and the mean diameter and length of the equivalent cables were 1.4 ± 0.6 and 470 ± 90 μm, respectively. The average of the specific membrane conductances, 1.67 ± 1.08 S/cm2, corresponded to a membrane resistivity of 60 kΩ-cm2. Computer simulations of synaptic inputs were performed on a representative model, with an electrode at the soma and using the worst-case configuration, in which all synaptic inputs were confined to the tips of the dendrites. We draw three conclusions from the modeling: (1) Under voltage clamp, fast, spontaneous EPSCs would be significantly attenuated and slowed while the time course of the slower, light-evoked non-NMDA and NMDA EPSCs would be minimally distorted by dendritic filtering. (2) Excitatory synaptic reversal potentials can be accurately determined under voltage clamp. (3) In the absence of GABAergic and glycinergic inhibition, the efficacy at the soma of excitatory conductance changes is essentially independent of their dendritic location. The specific membrane resistivity appears to represent a good compromise between having a small membrane time constant and minimal EPSP attenuation.

We have evaluated the spatial distribution of low-voltage-activated calcium currents in ganglion cells of the tiger salamander retina. Whole-cell recordings were obtained from ganglion cells in a retinal slice preparation and from acutely dissociated ganglion cells that were identified through retrograde dye injection. In single dissociated cells, we estimated the magnitude (pA) and current density (pA/pF) of LVA currents in ganglion cells, both with and without dendritic processes. Ganglion cells that retained a portion of their dendritic arbor had larger LVA calcium currents and higher LVA current densities than those which lacked processes. When cell capacitance measurements were used to derive the surface area of the soma and dendritic processes, we concluded that a higher LVA current density was present in the dendrites; we estimate that, on average, the current density in the dendrites is approximately five times that of the soma. The presence of a significant density of LVA calcium channels in the dendrites of ganglion cells suggests that they could be involved in a number of cellular functions, including dendritic integration of synaptic currents, impulse generation, and homeostatic functions related to changes in the intradendritic calcium concentration.

The retinas of adult teleost fish can regenerate following injury, but little is known about the neuronal integration of the visual scene that is performed by the regenerated retina. Using goldfish retinal ganglion cells (RGCs) as the experimental system, an evaluation of dendritic arbor structure and passive electrotonic properties was developed, the aim being to quantitatively test the hypothesis that native and regenerated RGC dendritic arbors have similar structural and modeled electrotonic attributes. Fractal dimension was chosen as the descriptor of RGC dendritic arbor complexity, and the arbors' transfer function magnitudes were estimated using an electrically passive, equivalent-circuit analysis. For both native and regenerated RGCs, arbors qualitatively judged to be simple tended to have lower fractal dimension values than arbors judged to be more complex. All cells had similar cut-off frequencies, and for random stimulation of greater than 25% of an RGC's population of dendritic tips, there was a positive correlation between fractal dimension and transfer function magnitude. Some regenerated RGCs had abnormally long primary dendrites, but neither the distributions of fractal dimension values, nor the estimated transfer function magnitudes, were significantly different between native and regenerated RGCs. The results appear to support the hypothesis that structural and modeled electrotonic attributes of regenerated goldfish RGCs are similar to those of native RGCs, suggesting that regenerated RGCs may restore normal visual function.

Xiong proved that if f: I → I is any map of the unit interval I, then the depth of the centre of f is at most 2, and Ye proved that for any map f: T → T of a finite tree T, the depth of the centre of f is at most 3. It is natural to ask whether the result can be dendrites. In this note, we show that there is dendrite D such that for any countable ordinal number λ there is a map f: D →D such that the depth of centre of f is λ. As a corollary, we show that for any countable ordinal number λ there is a map (respectively a homeomorphism) f of a 2-dimensional ball B2 (respectively a 3-dimensional ball B3) such that the depth of centre of f is λ.