Linear Topography

[Jude Petkus]

Thisis an ocean motivated study which investigates the impacts of sinusoidal bottom topography on baroclinic instability of zonal vertically sheared flows in the two-layer quasigeostrophic model. The corresponding linear stability problem is solved by assuming Fourier-mode solutions in both the zonal and meridional directions. In the presence of variable topographic features, the Fourier modes become coupled due to phase shifts in the wavevectors. The spectral discretisation method used in this work retains the primary relationship between different Fourier modes; thus, the linear stability eigenproblem can be solved for any periodic topography. Moreover, this method does not need any additional assumptions, such as considering small-amplitude or large-scale bottom irregularities, as in some previous studies. In this work, the eigenproblem is solved for a range of topographic amplitudes and wavenumbers, and their effects on the growth rates and shapes of the most unstable eigenmodes are discussed. In general, both the zonal and meridional variations in topography tend to suppress the baroclinic instability. However, it is found that only meridionally varying topography affects the magnitudes of the fastest growth rates. In this instance, unstable modes appear to form two clusters well separated in the zonal wavenumber axis and growth rate maxima occur at two distinct zonal wavenumbers. Dependencies of the characteristics of these clusters on the values of topography amplitude and ridge width are reviewed. Finally, doubly periodic numerical simulations are used to verify the results from the linear stability analysis.

To save this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account.Find out more about saving content to Dropbox.

To save this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account.Find out more about saving content to Google Drive.

Do you have any conflicting interests? *Conflicting interests helpClose Conflicting interests help Please list any fees and grants from, employment by, consultancy for, shared ownership in or any close relationship with, at any time over the preceding 36 months, any organisation whose interests may be affected by the publication of the response. Please also list any non-financial associations or interests (personal, professional, political, institutional, religious or other) that a reasonable reader would want to know about in relation to the submitted work. This pertains to all the authors of the piece, their spouses or partners.

The linear instability of circular vortices over isolated topography in a homogeneous and inviscid fluid is examined for the shallow-water and quasi-geostrophic models in the $f$-plane. The eigenvalue problem associated with azimuthal disturbances is derived for arbitrary axisymmetric topographies, either submarine mountains or valleys. Amended Rayleigh and Fjrtoft theorems with topographic effects are given for barotropic instability, obtaining necessary criteria for instability when the potential vorticity gradient is zero somewhere in the domain. The onset of centrifugal instability is also discussed by deriving the Rayleigh circulation theorem with topography. The barotropic instability theorems are applied to a wide family of nonlinear, quasi-geostrophic solutions of circular vortices over axisymmetric topographic features. Flow instability depends mainly on the vortex/topography configuration, as well as on the vortex size in comparison with the width of the topography. It is found that anticyclones/mountains and cyclones/valleys may be unstable. In contrast, cyclone/mountain and anticyclone/valley configurations are stable. These statements are validated with two numerical methods. First, the generalised eigenvalue problem is solved to obtain the wavenumber of the fastest-growing perturbations. Second, the evolution of the vortices is simulated numerically to detect the development of linear perturbations. The numerical results show that for unstable vortices over narrow topographies, the fastest growth rate corresponds to mode $1$, which subsequently forms asymmetric dipolar structures. Over wide topographies, the fastest perturbations are mainly modes $1$ and $2$, depending on the topographic features.

In algebra, a linear topology on a left A \displaystyle A -module M \displaystyle M is a topology on M \displaystyle M that is invariant under translations and admits a fundamental system of neighborhood of 0 \displaystyle 0 that consists of submodules of M . \displaystyle M. [1] If there is such a topology, M \displaystyle M is said to be linearly topologized. If A \displaystyle A is given a discrete topology, then M \displaystyle M becomes a topological A \displaystyle A -module with respect to a linear topology.

The notion is used more commonly in algebra than in analysis. Indeed, "[t]opological vector spaces with linear topology form a natural class of topological vector spaces over discrete fields, analogous to the class of locally convex topological vector spaces over the normed fields of real or complex numbers in functional analysis."[2]

The site is secure.

The ensures that you are connecting to the official website and that any information you provide is encrypted and transmitted securely.

Synapses are often precisely organized on dendritic arbors, yet the role of synaptic topography in dendritic integration remains poorly understood. Utilizing electron microscopy (EM) connectomics we investigate synaptic topography in Drosophila melanogaster looming circuits, focusing on retinotopically tuned visual projection neurons (VPNs) that synapse onto descending neurons (DNs). Synapses of a given VPN type project to non-overlapping regions on DN dendrites. Within these spatially constrained clusters, synapses are not retinotopically organized, but instead adopt near random distributions. To investigate how this organization strategy impacts DN integration, we developed multicompartment models of DNs fitted to experimental data and using precise EM morphologies and synapse locations. We find that DN dendrite morphologies normalize EPSP amplitudes of individual synaptic inputs and that near random distributions of synapses ensure linear encoding of synapse numbers from individual VPNs. These findings illuminate how synaptic topography influences dendritic integration and suggest that linear encoding of synapse numbers may be a default strategy established through connectivity and passive neuron properties, upon which active properties and plasticity can then tune as needed.

Chromatin is of major relevance for gene expression, cell division, and differentiation. Here, we determined the landscape of Arabidopsis thaliana chromatin states using 16 features, including DNA sequence, CG methylation, histone variants, and modifications. The combinatorial complexity of chromatin can be reduced to nine states that describe chromatin with high resolution and robustness. Each chromatin state has a strong propensity to associate with a subset of other states defining a discrete number of chromatin motifs. These topographical relationships revealed that an intergenic state, characterized by H3K27me3 and slightly enriched in activation marks, physically separates the canonical Polycomb chromatin and two heterochromatin states from the rest of the euchromatin domains. Genomic elements are distinguished by specific chromatin states: four states span genes from transcriptional start sites (TSS) to termination sites and two contain regulatory regions upstream of TSS. Polycomb regions and the rest of the euchromatin can be connected by two major chromatin paths. Sequential chromatin immunoprecipitation experiments demonstrated the occurrence of H3K27me3 and H3K4me3 in the same chromatin fiber, within a two to three nucleosome size range. Our data provide insight into the Arabidopsis genome topography and the establishment of gene expression patterns, specification of DNA replication origins, and definition of chromatin domains.

3a8082e126