Symmetric Bump Research Articles

Cell adhesion and junctional proteins in the developing skin of snakes indicate they coordinate the differentiation of the epidermis.

The development of scales and the sequence of epidermal layers during snake embryogenesis has been studied by immunofluorescence for the localization of cell adhesion, adherens, and communicating cell junctional proteins. At about 2nd/3rd of embryonic development in snakes the epidermis forms symmetric bumps at the beginning of scale formation, and they rapidly become asymmetric and elongate forming outer and inner surfaces of the very overlapped scales seen at hatching. The dermis separates a superficial loose from a deeper dense part; the latter is joined to segmental muscles and nerves, likely acting on scale orientation during snake movements. N-cam is present in the differentiating epidermis and mesenchyme of forming scales while L-cam is only/mainly detected in the periderm and epidermis. Mesenchymal N-cam is associated with the epidermis of the elongating dorsal scale surface and with the beta-differentiation that occurs in the overlapping outer surface of scales. Beta-catenin and Connexin-43 show a similar distribution, and they are mainly present in the periderm and differentiating suprabasal keratinocytes likely forming an intense connectivity during epidermal differentiation. Beta-catenin also shows nuclear localization in differentiating cells of the shedding and beta-layers at late stages of scale morphogenesis, before hatching. The study suggests that intensification of adhesion and gap junctions allows synchronization of the differentiation of suprabasal cells to produce the ordered sequence of epidermal layers of snake scales, starting from the shedding complex and the beta-layer.

Generalized maximum entropy approach to quasistationary states in long-range systems.

Systems with long-range interactions display a short-time relaxation towards quasistationary states (QSSs) whose lifetime increases with the system size. In the paradigmatic Hamiltonian mean-field model (HMF) out-of-equilibrium phase transitions are predicted and numerically detected which separate homogeneous (zero magnetization) and inhomogeneous (nonzero magnetization) QSSs. In the former regime, the velocity distribution presents (at least) two large, symmetric bumps, which cannot be self-consistently explained by resorting to the conventional Lynden-Bell maximum entropy approach. We propose a generalized maximum entropy scheme which accounts for the pseudoconservation of additional charges, the even momenta of the single-particle distribution. These latter are set to the asymptotic values, as estimated by direct integration of the underlying Vlasov equation, which formally holds in the thermodynamic limit. Methodologically, we operate in the framework of a generalized Gibbs ensemble, as sometimes defined in statistical quantum mechanics, which contains an infinite number of conserved charges. The agreement between theory and simulations is satisfying, both above and below the out-of-equilibrium transition threshold. A previously unaccessible feature of the QSSs, the multiple bumps in the velocity profile, is resolved by our approach.

Two-dimensional Amari neural field model with periodic microstructure: Rotationally symmetric bump solutions

We investigate existence and stability of rotationally symmetric bump solutions to a homogenized two-dimensional Amari neural field model with periodic micro-variations built in the connectivity strength and by approximating the firing rate function with unit step function. The effect of these variations is parameterized by means of one single parameter, called the degree of heterogeneity. The bumps solutions are assumed to be independent of the micro-variable. We develop a framework for study existence of bumps as a function of the degree of heterogeneity as well as a stability method for the bumps. The former problem is based on the pinning function technique while the latter one uses spectral theory for Hilbert–Schmidt integral operators. We demonstrate numerically these procedures for the case when the connectivity kernel is modeled by means of a Mexican hat function. In this case the generic picture consists of one narrow and one broad bump. The radius of the narrow bumps increases with the heterogeneity. For the broad bumps the radius increases for small and moderate values of the activation threshold while it decreases for large values of this threshold. The stability analysis reveals that the narrow bumps remain unstable while the broad bumps are destabilized when the degree of heterogeneity exceeds a certain critical value.

Stability of bumps in a two-population neural-field model with quasi-power temporal kernels

Neural-field models describing the spatio-temporal dynamics of the average neural activity are frequently formulated in terms of partial differential equations, Volterra equations or integro-differential equations. We develop a stability analysis for spatially symmetric bumps in a two-population neural-field model of Volterra form for a large class of temporal kernels. We find that the corresponding Evans matrix can be block-diagonalized, where one block corresponds to the symmetric part of the perturbations while the other block takes care of the antisymmetric part of these perturbations including the translational invariance of the bumps. For the class of quasi-power temporal kernels ∼ t k exp ( − t ) we show that the system of governing equations can be converted to a system of rate equations. We prove that for this class of temporal kernels the stability analysis based on the Evans function approach is equivalent to the phase-space reduction technique termed the generalized Amari approach. We illuminate these results by carrying out numerical simulations based on a fourth-order Runge–Kutta numerical scheme in time for the special mixed case modeled by α -functions in the excitatory equation and exponentially decaying functions in the inhibitory equation. Excellent agreement between analytical predictions from the stability analysis and numerical simulations is obtained. The generic picture consists of an unstable narrow bump pair and a broad bump pair. The broad bump pair is stable for small and moderate values of the relative inhibition time τ , is converted to a stable breather at a critical time constant, τ = τ c r (which is identified as a Hopf-bifurcation point), and becomes unstable as τ exceeds τ c r .

Two-Dimensional Bumps in Piecewise Smooth Neural Fields with Synaptic Depression

We analyze radially symmetric bumps in a two-dimensional piecewise-smooth neural field model with synaptic depression. The continuum dynamics is described in terms of a nonlocal integrodifferential equation, in which the integral kernel represents the spatial distribution of synaptic weights between populations of neurons whose mean firing rate is taken to be a Heaviside function of local activity. Synaptic depression dynamically reduces the strength of synaptic weights in response to increases in activity. We show that in the case of a Mexican hat weight distribution, sufficiently strong synaptic depression can destabilize a stationary bump solution that would be stable in the absence of depression. Numerically it is found that the resulting instability leads to the formation of a traveling spot. The local stability of a bump is determined by solutions to a system of pseudolinear equations that take into account the sign of perturbations around the circular bump boundary.

The topography of drumlins; assessing their long profile shape

AbstractThe literature on drumlins is pervaded by the notion that their longitudinal profile is usually highly asymmetric with a stoss steeper end and a lee gentler end, and that this can be used to infer the palaeo ice flow direction. The idea is built up in many papers covering more than a century of research. However, most of the early published papers were qualitative in nature and more recent quantitative papers appear to challenge the ubiquity of the classical stoss–lee shape. Here the shape of the drumlin longitudinal profile of 29,238 drumlins in the British Isles has been analysed. Drumlins were grouped into flowsets for which a palaeo ice flow direction was inferred independently of the drumlin shape. Given such ice flow directions it was then possible to identify the upflow and downflow ends of each drumlin and to trace and extract its longitudinal profile. Results indicate that the highest point of the drumlin is usually found around half way along the profile. The mean slope angles at the stoss and lee ends were found to be very similar. Finally, the average profile built from all mapped drumlins appears almost symmetric. In conclusion, drumlin longitudinal profile is far from being the classically asymmetric shape widely reported in text‐book descriptions. Drumlins are mostly symmetrical in shape with a very slight tendency towards the classical shape. Highly asymmetric drumlins do exist but are rare and with an almost equal numbers of drumlins that are the reverse of this. These findings are verified both at the entire population level and the flowset level. This demonstrates that the idealized stoss–lee shape of classically‐asymmetric drumlins is not representative of the population and should be replaced with that of mostly symmetric bumps. Drumlin shape is not a good indicator of the palaeo ice flow direction. Copyright © 2010 John Wiley & Sons, Ltd.

Potential-flow models for channelled two-dimensional premixed flames around near-circular obstacles

The dynamics of two-dimensional thin premixed flames is addressed in the framework of mathematical models where the flow field on either side of the front is piecewise incompressible and vorticity free. Flames confined in channels with asymptotically straight impenetrable walls are considered. Besides a few free propagations along straight channels, attention is focused on flames propagating against high-speed flows and positioned near a round central obstacle or near two symmetric bumps protruding inward. Combining conformal maps and Green's functions, a regularized generalization of Frankel's integro-differential equation for the instantaneous front shape in each configuration is derived and solved numerically. This produces a variety of real looking phenomena: steady fronts (symmetric or not), noise-induced subwrinkles, flashback events, and breathing fronts in pulsating flows. Perspectives and open mathematical and physical problems are finally evoked.

A combined time and frequency domain approach for acoustic resonance prediction

A general hybrid time- and frequency-domain methodology has been developed to identify acoustic resonance conditions of internal flow configurations. The acoustic modes are determined by imposing onto the flow a time-dependent excitation at several locations on the boundary. The resulting time-domain pressure responses, which are computed via an unsteady Favre–Reynolds averaged Navier–Stokes solver, are used to determine the frequency response function matrix of the fluid which can be considered to be a multiple-input multiple-output system. The main test case was selected to be a closed-end cylindrical duct for which the effect of different excitation techniques on the predicted acoustic modes is discussed in detail. The last test case deals with the acoustic characterization of a 2-D channel with symmetric bumps and an inlet flow velocity of 17 m s - 1 . It is shown that the methodology was suitable for identifying axial and transverse acoustic modes up to 3 kHz.

Study of Vortical Separation from Three-Dimensional Symmetric Bumps

Surface mean pressures, oilflow visualization, and three-velocity-component laser Doppler velocimeter (LDV) measurements are presented for a turbulent boundary layer of momentum thickness Reynolds number, Re θ 7300, and of thickness 6 over two axisymmetric bumps of height H = 6 and 26 and one symmetric bump of H = 26. LDV data were obtained at one plane, x/H ≥ 3.26, for each case. Complex vortical separations occur on the lee side and merge into large streamwise mean vortices downstream for the two axisymmetric cases. The near-wall flow (y + < 90) is dominated by the wall. For the axisymmetric cases, the vortices in the outer region produce large turbulence levels near the centerline and appear to have low-frequency motions that contribute to turbulent diffusion. For the case with a narrower spanwise shape, there are sharper separation lines and lower turbulence intensities in the vortical downstream flow

Exact theory of secondary supercritical solutions for steady surface waves over a bump

Two-dimensional steady surface waves on an ideal fluid over a small and symmetric bump are studied when the Froude number F of the uniform flow far upstream is greater than unity. Recent numerical results for a symmetric bump indicate that corresponding to F > 1 there may exist two solutions for the problem. One approaches the uniform flow and the other a solitary wave, as the bump size goes to zero. In this paper we use a two-parameter asymptotic expansion to derive an explicit approximate expression for the later solution and show that the expansion is indeed an asymptotic approximation to the solution of the exact nonlinear equations.