Amplitude equations for coupled electrostatic waves in the limit of weak instability

We consider the simplest instabilities involving multiple unstable electrostatic plasma waves corresponding to four-dimensional systems of mode amplitude equations. In each case the coupled amplitude equations are derived up to third order terms. The nonlinear coefficients are singular in the limit in which the linear growth rates vanish together. These singularities are analyzed using techniques developed in previous studies of a single unstable wave. In addition to the singularities familiar from the one mode problem, there are new singularities in coefficients coupling the modes. The new singularities are most severe when the two waves have the same linear phase velocity and satisfy the spatial resonance condition $k_2=2k_1$. As a result the short wave mode saturates at a dramatically smaller amplitude than that predicted for the weak growth rate regime on the basis of single mode theory. In contrast the long wave mode retains the single mode scaling. If these resonance conditions are not satisfied both modes retain their single mode scaling and saturate at comparable amplitudes.Comment: 34 pages (Latex), no figure

FUNNet:a novel biologically-inspired routing algorithm based on fungi

Future data communication networks show three emerging trends: increasing size of networks, increasing traffic volumes and dynamic network topologies. Efficient network management solutions are required that are scalable, can cope with large, and increasing, traffic volumes and provide decentralised and adaptive routing strategies that cope with the dynamics of the network topology. Routing strategies are an important aspect of network management as they have a significant influence on the overall network performance. This paper introduces the preliminary studies for FUNNet, a new routing algorithm inspired by the kingdom of Fungi. Fungi form robust, resilient and responsive networks and these networks change topology as a consequence of changes in local conditions. Fungi are capable of expanding in size as they self-regulate and optimise the balance between exploration and exploitation which is dependent on the transport of the internal resource, i.e. ‘traffic’, within the network. FUNNet exploits the biological processes that are responsible for simulating fungal networks in a bio-inspired routing protocol. The initial results are positive and suggest that fungal metaphors can improve network management, although further evaluation of more complex scenarios is required

Universal trapping scaling on the unstable manifold for a collisionless electrostatic mode

An amplitude equation for an unstable mode in a collisionless plasma is derived from the dynamics on the two-dimensional unstable manifold of the equilibrium. The mode amplitude $\rho(t)$ decouples from the phase due to the spatial homogeneity of the equilibrium, and the resulting one-dimensional dynamics is analyzed using an expansion in $\rho$. As the linear growth rate $\gamma$ vanishes, the expansion coefficients diverge; a rescaling $\rho(t)\equiv\gamma^2\,r(\gamma t)$ of the mode amplitude absorbs these singularities and reveals that the mode electric field exhibits trapping scaling $|E_1|\sim\gamma^2$ as $\gamma\rightarrow0$. The dynamics for $r(\tau)$ depends only on the phase $e^{i\xi}$ where $d\epsilon_{{k}} /dz=|{\epsilon_{{k}}}|e^{-i\xi/2}$ is the derivative of the dielectric as $\gamma\rightarrow0$.Comment: 11 pages (Latex/RevTex), 2 figures available in hard copy from the Author ([email protected]); paper accepted by Physical Review Letter

Social behavior following traumatic brain injury and its association with emotion recognition, understanding of intentions, and cognitive flexibility

Although the adverse consequences of changes in social behavior following traumatic brain injury (TBI) are well documented, relatively little is known about possible underlying neuropsychological deficits. Following a model originally developed for social behavior deficits in schizophrenia, we investigated whether impairments in emotion recognition, understanding of other people's intentions ("theory of mind"), and cognitive flexibility soon after first TBI or 1 year later were associated with self and proxy ratings of behavior following TBI. Each of the three functions was assessed with two separate tests, and ratings of behavior were collected on three questionnaires. Patients with TBI (n = 33) were impaired in emotion recognition, "theory of mind," and cognitive flexibility compared with matched orthopedic controls (n = 34). Proxy ratings showed increases in behavioral problems 1 year following injury in the TBI group but not in the control group. However, test performance was not associated with questionnaire data. Severity of the impairments in emotion recognition, understanding intention, and flexibility were unrelated to the severity of behavioral problems following TBI. These findings failed to confirm the used model for social behavior deficits and may cast doubt on the alleged link between deficits in emotion recognition or theory of mind and social functioning

Scaling and singularities in the entrainment of globally-coupled oscillators

The onset of collective behavior in a population of globally coupled oscillators with randomly distributed frequencies is studied for phase dynamical models with arbitrary coupling. The population is described by a Fokker-Planck equation for the distribution of phases which includes the diffusive effect of noise in the oscillator frequencies. The bifurcation from the phase-incoherent state is analyzed using amplitude equations for the unstable modes with particular attention to the dependence of the nonlinearly saturated mode $|\alpha_\infty|$ on the linear growth rate $\gamma$. In general we find $|\alpha_\infty|\sim \sqrt{\gamma(\gamma+l^2D)}$ where $D$ is the diffusion coefficient and $l$ is the mode number of the unstable mode. The unusual $(\gamma+l^2D)$ factor arises from a singularity in the cubic term of the amplitude equation.Comment: 11 pages (Revtex); paper submitted to Phys. Rev. Let

Nonlinear saturation of electrostatic waves: mobile ions modify trapping scaling

The amplitude equation for an unstable electrostatic wave in a multi-species Vlasov plasma has been derived. The dynamics of the mode amplitude $\rho(t)$ is studied using an expansion in $\rho$; in particular, in the limit $\gamma\rightarrow0^+$, the singularities in the expansion coefficients are analyzed to predict the asymptotic dependence of the electric field on the linear growth rate $\gamma$. Generically $|E_k|\sim \gamma^{5/2}$, as $\gamma\rightarrow0^+$, but in the limit of infinite ion mass or for instabilities in reflection-symmetric systems due to real eigenvalues the more familiar trapping scaling $|E_k|\sim \gamma^{2}$ is predicted.Comment: 13 pages (Latex/RevTex), 4 postscript encapsulated figures which are included using the utility "uufiles". They should be automatically included with the text when it is downloaded. Figures also available in hard copy from the authors ([email protected]

Limits to Interstellar C_4 and C_5 Towards zeta Ophiuchi

We have made a sensitive search for the origin bands in the known electronic transitions of the linear carbon chains C_4 and C_5 at 3789 and 5109 A towards zeta Oph (A_V <= 1). The incentive was a recent detection of C_3 in this interstellar cloud with a column density of 1.6 x 10^12 cm^-2 plus the availability of laboratory gas phase spectra of C_4 and C_5. Further, some models of diffuse interstellar clouds predict that the abundance of these latter species should be within an order of magnitude of C_3. Despite achieving S/N of 2300 to 2600 per pixel at a resolution of ~110,000, the searches were negative, leading to 3 sigma upper limits to the column density of N(C_5) = 2 x 10^11 cm^-2 and N(C_4) = 4 x 10^12-13 cm^-2 where these values rely on theoretically calculated oscillator strengths. The implication of these limits are discussed on the choice of molecules for study in future attempts to identify the carriers of the stronger diffuse interstellar bands.Comment: 12 pages, 3 figure

Establishment and operation of a Good Manufacturing Practice-compliant allogeneic Epstein-Barr virus (EBV)-specific cytotoxic cell bank for the treatment of EBV-associated lymphoproliferative disease

Funded by Wellcome Trust Translational Award SNBTSPeer reviewedPublisher PD