Instability of coherent states of a real scalar field

We investigate stability of both localized time-periodic coherent states (pulsons) and uniformly distributed coherent states (oscillating condensate) of a real scalar field satisfying the Klein-Gordon equation with a logarithmic nonlinearity. The linear analysis of time-dependent parts of perturbations leads to the Hill equation with a singular coefficient. To evaluate the characteristic exponent we extend the Lindemann-Stieltjes method, usually applied to the Mathieu and Lame equations, to the case that the periodic coefficient in the general Hill equation is an unbounded function of time. As a result, we derive the formula for the characteristic exponent and calculate the stability-instability chart. Then we analyze the spatial structure of the perturbations. Using these results we show that the pulsons of any amplitudes, remaining well-localized objects, lose their coherence with time. This means that, strictly speaking, all pulsons of the model considered are unstable. Nevertheless, for the nodeless pulsons the rate of the coherence breaking in narrow ranges of amplitudes is found to be very small, so that such pulsons can be long-lived. Further, we use the obtaned stability-instability chart to examine the Affleck-Dine type condensate. We conclude the oscillating condensate can decay into an ensemble of the nodeless pulsons.Comment: 11 pages, 8 figures, submitted to Physical Review

Signal invariance and trajectory steering problem for an autonomous wheeled robot

We give a new convenient parametrization of linear controllers that solve the problem of signal invariance (or disturbance cancellation) for MIMO plants. As an example of application of the obtained results we consider the trajectory tracking problem for non-holonomic wheeled transport robots

Dissipativity of T-periodic linear systems

It is proved that the existence of a positive definite storage function is necessary and sufficient for strict dissipativity of linear systems with periodic coefficients. The connection between strict dissipativity of the system and a nonoscillatory property of an associated Hamiltonian system is establishe

Encephalopathy-causing mutations in G beta(1) (GNB1) alter regulation of neuronal GIRK channels

Mutations in the GNB1 gene, encoding the Gβ(1) subunit of heterotrimeric G proteins, cause GNB1 Encephalopathy. Patients experience seizures, pointing to abnormal activity of ion channels or neurotransmitter receptors. We studied three Gβ(1) mutations (K78R, I80N and I80T) using computational and functional approaches. In heterologous expression models, these mutations did not alter the coupling between G protein-coupled receptors to G(i/o), or the Gβγ regulation of the neuronal voltage-gated Ca(2+) channel Ca(V)2.2. However, the mutations profoundly affected the Gβγ regulation of the G protein-gated inwardly rectifying potassium channels (GIRK, or Kir3). Changes were observed in Gβ(1) protein expression levels, Gβγ binding to cytosolic segments of GIRK subunits, and in Gβγ function, and included gain-of-function for K78R or loss-of-function for I80T/N, which were GIRK subunit-specific. Our findings offer new insights into subunit-dependent gating of GIRKs by Gβγ, and indicate diverse etiology of GNB1 Encephalopathy cases, bearing a potential for personalized treatment