Beats and periodicity for the forced harmonic oscillator

This note presents some simple examples illustrating the differences between the concepts of continuity, existence of partial derivatives and differentiability.     

Coulomb damping

Viscous damping is commonly discussed in beginning differential equations and physics texts but dry friction or Coulomb friction is not despite dry friction being encountered in many physical applications. One reason for avoiding this topic is that the equations involve a jump discontinuity in the damping term. In this article, we adopt an energy approach which permits a general discussion on how to investigate trajectories for second-order differential equations representing mechanical vibration models having dry friction. This approach is suitable for classroom discussion and computer laboratory investigation in beginning courses, hence introduction of dry friction need not be delayed for more advanced courses in mechanics or modelling. Our method is applied to a harmonic oscillator example and a pendulum model. One advantage of this method is that the values of the maximum deflections of a solution can be calculated without solving the differential equation either analytically or numerically, a technique that depends on only the initial conditions.     

Progranulin is expressed within motor neurons and promotes neuronal cell survival

Background

Progranulin is a secreted high molecular weight growth factor bearing seven and one half copies of the cysteine-rich granulin-epithelin motif. While inappropriate over-expression of the progranulin gene has been associated with many cancers, haploinsufficiency leads to atrophy of the frontotemporal lobes and development of a form of dementia (frontotemporal lobar degeneration with ubiquitin positive inclusions, FTLD-U) associated with the formation of ubiquitinated inclusions. Recent reports indicate that progranulin has neurotrophic effects, which, if confirmed would make progranulin the only neuroprotective growth factor that has been associated genetically with a neurological disease in humans. Preliminary studies indicated high progranulin gene expression in spinal cord motor neurons. However, it is uncertain what the role of Progranulin is in normal or diseased motor neuron function. We have investigated progranulin gene expression and subcellular localization in cultured mouse embryonic motor neurons and examined the effect of progranulin over-expression and knockdown in the NSC-34 immortalized motor neuron cell line upon proliferation and survival.

Results

In situ hybridisation and immunohistochemical techniques revealed that the progranulin gene is highly expressed by motor neurons within the mouse spinal cord and in primary cultures of dissociated mouse embryonic spinal cord-dorsal root ganglia. Confocal microscopy coupled to immunocytochemistry together with the use of a progranulin-green fluorescent protein fusion construct revealed progranulin to be located within compartments of the secretory pathway including the Golgi apparatus. Stable transfection of the human progranulin gene into the NSC-34 motor neuron cell line stimulates the appearance of dendritic structures and provides sufficient trophic stimulus to survive serum deprivation for long periods (up to two months). This is mediated at least in part through an anti-apoptotic mechanism. Control cells, while expressing basal levels of progranulin do not survive in serum free conditions. Knockdown of progranulin expression using shRNA technology further reduced cell survival.

Conclusion

Neurons are among the most long-lived cells in the body and are subject to low levels of toxic challenges throughout life. We have demonstrated that progranulin is abundantly expressed in motor neurons and is cytoprotective over prolonged periods when over-expressed in a neuronal cell line. This work highlights the importance of progranulin as neuroprotective growth factor and may represent a therapeutic target for neurodegenerative diseases including motor neuron disease.     

Strong tunable coupling between a superconducting charge and phase qubit

We have realized a tunable coupling over a large frequency range between an asymmetric Cooper pair transistor (charge qubit) and a dc SQUID (phase qubit). Our circuit enables the independent manipulation of the quantum states of each qubit as well as their entanglement. The measurement of the charge qubit's quantum states is performed by an adiabatic quantum transfer from the charge to the phase qubit. The measured coupling strength is in agreement with an analytic theory including a capacitive and a tunable Josephson coupling between the two qubits.     

Sound source localization by the plainfin midshipman fish, Porichthys notatus

The aim of this study was to use plainfin midshipman fish (Porichthys notatus) as a general model to explore how fishes localize an underwater sound source in the relatively simple geometry of a monopole sound field. The robust phonotaxic responses displayed by gravid females toward a monopole sound projector (J-9) broadcasting a low-frequency (90 Hz) tone similar to the fundamental frequency of the male's advertisement call were examined. The projector's sound field was mapped at 5 cm resolution azimuth using an eight-hydrophone array. Acoustic pressure was measured with the array and acoustic particle motion was calculated from pressure gradients between hydrophones. The response pathways of the fish were analyzed from video recordings and compared to the sound field. Gravid females at initial release were directed toward the sound source, and the majority (73%) swam to the playback projector with straight to slightly curved tracks in the direction of the source and in line with local particle motion vectors. In contrast, the initial direction of the control (sound-off) group did not differ from random. This paper reports on a comparison of fish localization behavior with directional cues available in the form of local particle motion vectors.     

Frequency discrimination in the goldfish (Carassius auratus): effects of roving intensity, sensation level, and the direction of frequency change

The ability of goldfish to detect a change in the frequency of 400-Hz pure-tone bursts was studied using classical respiratory conditioning. The frequency discrimination threshold was measured at 15-, 35-, and 55-dB sensation level (SL), under conditions of (1) constant intensity, (2) roving intensity (plus and minus 6-dB burst-to-burst variation in intensity), (3) upward frequency change, and (4) downward frequency change. There was no overall effect of SL on frequency discrimination, but roving the intensity elevated thresholds by about 6 Hz (33%) and increased variability. Upward shifts in frequency elevated thresholds slightly (by 2 Hz or 10%) relative to downward shifts. These relatively small and statistically insignificant effects suggest that earlier measures of frequency discrimination in the goldfish are not due to the detection of simple changes in spike rate within individual peripheral channels.