Separation of variables in the generalized 4th Appelrot class

We consider the analogue of the 4th Appelrot class of motions of the Kowalevski top for the case of two constant force fields. The trajectories of this family fill the four-dimensional surface O^4 in the six-dimensional phase space. The constants of three first integrals in involution restricted to this surface fill one of the sheets of the bifurcation diagram in R^3. We point out the pair of partial integrals to obtain the explicit parametric equations of this sheet. The induced system on O^4 is shown to be Hamiltonian with two degrees of freedom having the thin set of points where the induced symplectic structure degenerates. The region of existence of motions in terms of the integral constants is found. We provide the separation of variables on O^4 and the algebraic formulae for the initial phase variables.Comment: LaTex, 16 pages, 1 figur

Aging, rejuvenation and memory phenomena in spin glasses

In this paper, we review several important features of the out-of-equilibrium dynamics of spin glasses. Starting with the simplest experiments, we discuss the scaling laws used to describe the isothermal aging observed in spin glasses after a quench down to the low temperature phase. We report in particular new results on the sub-aging behaviour of spin glasses. We then discuss the rejuvenation and memory effects observed when a spin glass is submitted to temperature variations during aging, from the point of view of both energy landscape pictures and of real space pictures. We highlight the fact that both approaches point out the necessity of hierarchical processes involved in aging. Finally, we report an investigation of the effect of small temperature variations on aging in spin glass samples with various anisotropies which indicates that this hierarchy depends on the spin anisotropy.Comment: submitted for the Proceedings of Stat Phys 22, Bangalore (India

Magnetic Resonance Thermometry at 7T for Real-Time Monitoring and Correction of Ultrasound Induced Mild Hyperthermia

While Magnetic Resonance Thermometry (MRT) has been extensively utilized for non-invasive temperature measurement, there is limited data on the use of high field (≥7T) scanners for this purpose. MR-guided Focused Ultrasound (MRgFUS) is a promising non-invasive method for localized hyperthermia and drug delivery. MRT based on the temperature sensitivity of the proton resonance frequency (PRF) has been implemented in both a tissue phantom and in vivo in a mouse Met-1 tumor model, using partial parallel imaging (PPI) to speed acquisition. An MRgFUS system capable of delivering a controlled 3D acoustic dose during real time MRT with proportional, integral, and derivative (PID) feedback control was developed and validated. Real-time MRT was validated in a tofu phantom with fluoroptic temperature measurements, and acoustic heating simulations were in good agreement with MR temperature maps. In an in vivo Met-1 mouse tumor, the real-time PID feedback control is capable of maintaining the desired temperature with high accuracy. We found that real time MR control of hyperthermia is feasible at high field, and k-space based PPI techniques may be implemented for increasing temporal resolution while maintaining temperature accuracy on the order of 1°C