Statistical state dynamics of weak jets in barotropic beta-plane turbulence

Zonal jets in a barotropic setup emerge out of homogeneous turbulence through a flow-forming instability of the homogeneous turbulent state (`zonostrophic instability') which occurs as the turbulence intensity increases. This has been demonstrated using the statistical state dynamics (SSD) framework with a closure at second order. Furthermore, it was shown that for small supercriticality the flow-forming instability follows Ginzburg-Landau (G-L) dynamics. Here, the SSD framework is used to study the equilibration of this flow-forming instability for small supercriticality. First, we compare the predictions of the weakly nonlinear G-L dynamics to the fully nonlinear SSD dynamics closed at second order for a wide ranges of parameters. A new branch of jet equilibria is revealed that is not contiguously connected with the G-L branch. This new branch at weak supercriticalities involves jets with larger amplitude compared to the ones of the G-L branch. Furthermore, this new branch continues even for subcritical values with respect to the linear flow-forming instability. Thus, a new nonlinear flow-forming instability out of homogeneous turbulence is revealed. Second, we investigate how both the linear flow-forming instability and the novel nonlinear flow-forming instability are equilibrated. We identify the physical processes underlying the jet equilibration as well as the types of eddies that contribute in each process. Third, we propose a modification of the diffusion coefficient of the G-L dynamics that is able to capture the asymmetric evolution for weak jets at scales other than the marginal scale (side-band instabilities) for the linear flow-forming instability.Comment: 27 pages, 17 figure

Fluctuation-induced traffic congestion in heterogeneous networks

In studies of complex heterogeneous networks, particularly of the Internet, significant attention was paid to analyzing network failures caused by hardware faults or overload, where the network reaction was modeled as rerouting of traffic away from failed or congested elements. Here we model another type of the network reaction to congestion -- a sharp reduction of the input traffic rate through congested routes which occurs on much shorter time scales. We consider the onset of congestion in the Internet where local mismatch between demand and capacity results in traffic losses and show that it can be described as a phase transition characterized by strong non-Gaussian loss fluctuations at a mesoscopic time scale. The fluctuations, caused by noise in input traffic, are exacerbated by the heterogeneous nature of the network manifested in a scale-free load distribution. They result in the network strongly overreacting to the first signs of congestion by significantly reducing input traffic along the communication paths where congestion is utterly negligible.Comment: 4 pages, 3 figure

A mutation in the semaphorin signalling pathway and its consequences in prostate cancer

Prostate cancer kills over 10,000 men every year in the UK, mainly as a consequence of the spread of the disease to other sites in the body. It is important to understand what controls the spread of prostate cancer cells, as this may lead to treatments that either slow down or prevent metastasis, and perhaps result in the cure of some of the advanced prostate cancers. Semaphorins act as chemotactic cues for axon guidance and cell movement, via their transmembrane receptors, plexins. It has been found that semaphorins and their receptors are overexpressed in some human prostate cancer cell lines. These cell lines have been screened for mutations in genes in the semaphorin signalling pathway. 13 somatic missense mutations in the cytoplasmic domain of the Plexin B1 gene have been identified in clinical samples of primary and metastatic prostate cancers. One of the mutations C5662T was predicted to result in a substitution of a Proline to a Serine. The aim of this research is to determine if the mutation C5662T in the Plexin B1 gene alters cell behaviour and contributes to prostate cancer progression. This thesis describes the method of constructing an expression vector containing the mutation and transfecting the mutation into COS7 cells to produce stable and transient clones. The effect of the mutation on cell collapse was examined. It was possible to show that Plexin B1 is involved in cell collapse and that Rnd1 is required for this process and this effect is independent of its ligand Semaphorin 4D (Sema4D). Although no functional difference between the wild type Plexin B1 and the mutant (C5662T) was observed, the rate of cell collapse may be important and more work will be needed to define whether this is a mutation that alters prostate cancer cell behaviour