Modified Zakharov equations for plasmas with a quantum correction

Quantum Zakharov equations are obtained to describe the nonlinear interaction between quantum Langmuir waves and quantum ion-acoustic waves. These quantum Zakharov equations are applied to two model cases, namely the four-wave interaction and the decay instability. In the case of the four-wave instability, sufficiently large quantum effects tend to suppress the instability. For the decay instability, the quantum Zakharov equations lead to results similar to those of the classical decay instability except for quantum correction terms in the dispersion relations. Some considerations regarding the nonlinear aspects of the quantum Zakharov equations are also offered.Comment: 4 figures. Accepted for publication in Physics of Plasmas (2004

On the linearization of the generalized Ermakov systems

A linearization procedure is proposed for Ermakov systems with frequency depending on dynamic variables. The procedure applies to a wide class of generalized Ermakov systems which are linearizable in a manner similar to that applicable to usual Ermakov systems. The Kepler--Ermakov systems belong into this category but others, more generic, systems are also included

Novel tau filament fold in chronic traumatic encephalopathy encloses hydrophobic molecules

Chronic traumatic encephalopathy (CTE) is a neurodegenerative tauopathy that is associated with repetitive head impacts or exposure to blast waves. First described as punch-drunk syndrome and dementia pugilistica in retired boxers1-3, CTE has since been identified in former participants of other contact sports, ex-military personnel and after physical abuse4-7. No disease-modifying therapies currently exist, and diagnosis requires an autopsy. CTE is defined by an abundance of hyperphosphorylated tau protein in neurons, astrocytes and cell processes around blood vessels8,9. This, together with the accumulation of tau inclusions in cortical layers II and III, distinguishes CTE from Alzheimer's disease and other tauopathies10,11. However, the morphologies of tau filaments in CTE and the mechanisms by which brain trauma can lead to their formation are unknown. Here we determine the structures of tau filaments from the brains of three individuals with CTE at resolutions down to 2.3 Å, using cryo-electron microscopy. We show that filament structures are identical in the three cases but are distinct from those of Alzheimer's and Pick's diseases, and from those formed in vitro12-15. Similar to Alzheimer's disease12,14,16-18, all six brain tau isoforms assemble into filaments in CTE, and residues K274-R379 of three-repeat tau and S305-R379 of four-repeat tau form the ordered core of two identical C-shaped protofilaments. However, a different conformation of the β-helix region creates a hydrophobic cavity that is absent in tau filaments from the brains of patients with Alzheimer's disease. This cavity encloses an additional density that is not connected to tau, which suggests that the incorporation of cofactors may have a role in tau aggregation in CTE. Moreover, filaments in CTE have distinct protofilament interfaces to those of Alzheimer's disease. Our structures provide a unifying neuropathological criterion for CTE, and support the hypothesis that the formation and propagation of distinct conformers of assembled tau underlie different neurodegenerative diseases

The novel MAPT mutation K298E:mechanisms of mutant tau toxicity, brain pathology and tau expression in induced fibroblast-derived neurons

Frontotemporal lobar degeneration (FTLD) consists of a group of neurodegenerative diseases characterized by behavioural and executive impairment, language disorders and motor dysfunction. About 20-30 % of cases are inherited in a dominant manner. Mutations in the microtubule-associated protein tau gene (MAPT) cause frontotemporal dementia and parkinsonism linked to chromosome 17 (FTDP-17T). Here we report a novel MAPT mutation (K298E) in exon 10 in a patient with FTDP-17T. Neuropathological studies of post-mortem brain showed widespread neuronal loss and gliosis and abundant deposition of hyperphosphorylated tau in neurons and glia. Molecular studies demonstrated that the K298E mutation affects both protein function and alternative mRNA splicing. Fibroblasts from a skin biopsy of the proband taken at post-mortem were directly induced into neurons (iNs) and expressed both 3-repeat and 4-repeat tau isoforms. As well as contributing new knowledge on MAPT mutations in FTDP-17T, this is the first example of the successful generation of iNs from skin cells retrieved post-mortem

Anisotropic Bose-Einstein condensates and completely integrable dynamical systems

A Gaussian ansatz for the wave function of two-dimensional harmonically trapped anisotropic Bose-Einstein condensates is shown to lead, via a variational procedure, to a coupled system of two second-order, nonlinear ordinary differential equations. This dynamical system is shown to be in the general class of Ermakov systems. Complete integrability of the resulting Ermakov system is proven. Using the exact solution, collapse of the condensate is analyzed in detail. Time-dependence of the trapping potential is allowed

Lie symmetries for two-dimensional charged particle motion

We find the Lie point symmetries for non-relativistic two-dimensional charged particle motion. These symmetries comprise a quasi-invariance transformation, a time-dependent rotation, a time-dependent spatial translation and a dilation. The associated electromagnetic fields satisfy a system of first-order linear partial differential equations. This system is solved exactly, yielding four classes of electromagnetic fields compatible with Lie point symmetries

Nyquist method for Wigner-Poisson quantum plasmas

By means of the Nyquist method, we investigate the linear stability of electrostatic waves in homogeneous equilibria of quantum plasmas described by the Wigner-Poisson system. We show that, unlike the classical Vlasov-Poisson system, the Wigner-Poisson case does not necessarily possess a Penrose functional determining its linear stability properties. The Nyquist method is then applied to a two-stream distribution, for which we obtain an exact, necessary and sufficient condition for linear stability, as well as to a bump-in-tail equilibrium.Comment: 6 figure