Stability, free energy and dynamics of multi-spikes in the minimal Keller-Segel model

<p style='text-indent:20px;'>One of the most impressive findings in chemotaxis is the aggregation that randomly distributed bacteria, when starved, release a diffusive chemical to attract and group with others to form one or several stable aggregates in a long time. This paper considers pattern formation within the minimal Keller–Segel chemotaxis model with a focus on the stability and dynamics of its multi-spike steady states. We first show that any steady-state must be a periodic replication of the spatially monotone one and they present multi-spikes when the chemotaxis rate is large; moreover, we prove that all the multi-spikes are unstable through their refined asymptotic profiles, and then find a fully-fledged hierarchy of free entropy energy of these aggregates. Our results also complement the literature by finding that when the chemotaxis is strong, the single boundary spike has the least energy hence is the most stable, the steady-state with more spikes has larger free energy, while the constant has the largest free energy and is always unstable. These results provide new insights into the model's intricate global dynamics, and they are illustrated and complemented by numerical studies which also demonstrate the metastability and phase transition behavior in chemotactic movement.</p>

Porosity and Play: Sustaining Public Life in New Zealand's Suburban Shopping Centres

<p>Throughout history, public plazas and town squares have provided the public realm for people to meet and "people watch". However the privatisation of public space has resulted in the demise of these traditional exterior public domains. These have been replaced by strictly controlled interior shopping malls, which place limitations on public behaviour. The concepts of 'play' and 'porosity' are possible remedies to the limitations. The purpose of this research is therefore to discover how the concepts of ‘play’ and ‘porosity’ can guide the redevelopment of New Zealand’s suburban shopping malls so as to enhance the quality of public space without detracting from the malls' commercial performance. In essence, 'play' is the spontaneous interaction which enriches public life and space, and is an encapsulation of the ideas of Jan Gehl, Elizabeth Farrelly and Quentin Stevens. 'Porosity', a concept coined by Nan Ellin, involves mixing views, programmes, ecology and paths within the same space. This revealed itself to be a method by which a space might be manipulated to support play. The 'boundary' is considered by both Stevens and Gehl to be an ideal space for play to occur, as it provides people with something to work against. Consequently, the boundary is investigated as the space where play and porosity interact. The investigation of play, porosity and the boundary includes an examination of international mall precedents and New Zealand case studies. The findings from these studies and a review of relevant literature are eventually tested in a design case study. This involves a redevelopment of Pakuranga Mall in Auckland, and includes a detailed investigation of a single boundary at an architectural scale. The design successfully proves that that a specific type of play can interact with porosity at a boundary in order to locally enhance the quality of public space. However the design also raises further questions about the concepts of porosity and play. Porosity was achieved in both the master plan and the design of the single boundary and was therefore developed at both the macro and micro scales. However the concept of play was successfully introduced only at the micro level of architectural development at the boundary. Therefore, the conclusion to this thesis discusses whether the interaction of play and porosity is limited to the boundary, or if the two concepts can be developed further to interact at a macro scale beyond the confines of a single boundary.</p>

Porosity and Play: Sustaining Public Life in New Zealand's Suburban Shopping Centres

<p>Throughout history, public plazas and town squares have provided the public realm for people to meet and "people watch". However the privatisation of public space has resulted in the demise of these traditional exterior public domains. These have been replaced by strictly controlled interior shopping malls, which place limitations on public behaviour. The concepts of 'play' and 'porosity' are possible remedies to the limitations. The purpose of this research is therefore to discover how the concepts of ‘play’ and ‘porosity’ can guide the redevelopment of New Zealand’s suburban shopping malls so as to enhance the quality of public space without detracting from the malls' commercial performance. In essence, 'play' is the spontaneous interaction which enriches public life and space, and is an encapsulation of the ideas of Jan Gehl, Elizabeth Farrelly and Quentin Stevens. 'Porosity', a concept coined by Nan Ellin, involves mixing views, programmes, ecology and paths within the same space. This revealed itself to be a method by which a space might be manipulated to support play. The 'boundary' is considered by both Stevens and Gehl to be an ideal space for play to occur, as it provides people with something to work against. Consequently, the boundary is investigated as the space where play and porosity interact. The investigation of play, porosity and the boundary includes an examination of international mall precedents and New Zealand case studies. The findings from these studies and a review of relevant literature are eventually tested in a design case study. This involves a redevelopment of Pakuranga Mall in Auckland, and includes a detailed investigation of a single boundary at an architectural scale. The design successfully proves that that a specific type of play can interact with porosity at a boundary in order to locally enhance the quality of public space. However the design also raises further questions about the concepts of porosity and play. Porosity was achieved in both the master plan and the design of the single boundary and was therefore developed at both the macro and micro scales. However the concept of play was successfully introduced only at the micro level of architectural development at the boundary. Therefore, the conclusion to this thesis discusses whether the interaction of play and porosity is limited to the boundary, or if the two concepts can be developed further to interact at a macro scale beyond the confines of a single boundary.</p>

Interpolating between multi-boundary wormholes and single-boundary geometries in holography

The recent paper [1] described how states of a holographic CFT can be approximated by states of a large collection of non-interacting BCFTs, such that the dual of the new system accurately approximates an arbitrarily large causal patch of the original geometry. In this paper, we first describe in more detail the geometries dual to such discrete BCFT systems, emphasizing that they are multi-boundary wormholes in which it is not possible to move causally between different asymptotic regions. By reintroducing couplings between the BCFTs in various ways, we show that the wormholes can be made traversable, giving an intermediate class of geometries that interpolate between the multi-boundary wormhole and the original geometry that it approximates.

Distributed Extended Kalman Filtering Based Techniques for 3-D UAV Jamming Localization

Wireless networks are vulnerable to jamming attacks. Jamming in wireless communication becomes a major research problem due to ease in Unmanned Aerial Vehicle (UAV) launching and blocking of communication channels. Jamming is a subset of Denial of Service Attack (DoS) and an intentional interference where the malicious node disrupts the wireless communication by increasing the noise at the receiver node through transmission interference signal towards the target channel. In this work, the considered jammer is a UAV hovering around the target area to block the communication channel between two transceivers. We proposed a three-dimensional (3-D) UAV jamming localization scheme to track and detect the jammer position at each time step by employing a single boundary node observer. For this purpose, we developed two distributed Extended Kalman Filter (EKF) based schemes: (1) the Distributed EKF (DEKF) scheme using the information of the received power from the jammer at a single nearby boundary node only and (2) Distance Ratio aided Distributed EKF (DEKF-DR) based scheme utilizing an edge node in addition to a single boundary node. Extensive simulations are conducted in order to evaluate the performance of the proposed distributed algorithms for a 3-D trajectory and compared with that of the conventional Centralized EKF (EKF-Centr) based method (which is also modified for the 3-D scenario). The results show the clear supremacy of the proposed distributed algorithms with much lesser complexity in contrast to the conventional EKF-Centr technique.

Knitting wormholes by entanglement in supergravity

We construct a single-boundary wormhole geometry in type IIB supergravity by perturbing two stacks of N extremal D3-branes in the decoupling limit. The solution interpolates from a two-sided planar AdS-Schwarzschild geometry in the interior, through a harmonic two-center solution in the intermediate region, to an asymptotic AdS space. The construction involves a CPT twist in the gluing of the wormhole to the exterior throats that gives a global monodromy to some coordinates, while preserving orientability. The geometry has a dual interpretation in $$ \mathcal{N} $$ N = 4 SU(2N) Super Yang-Mills theory in terms of a Higgsed SU(2N) → S(U(N) × U(N)) theory in which $$ \mathcal{O} $$ O (N2) degrees of freedom in each SU(N) sector are entangled in an approximate thermofield double state at a temperature much colder than the Higgs scale. We argue that the solution can be made long-lived by appropriate choice of parameters, and comment on mechanisms for generating traversability. We also describe a construction of a double wormhole between two universes.