Spin squeezing and quantum correlations

We discuss the notion of spin squeezing considering two mutually exclusive classes of spin-s states, namely, oriented and non-oriented states. Our analysis shows that the oriented states are not squeezed while non-oriented states exhibit squeezing. We also present a new scheme for construction of spin-s states using 2s spinors oriented along different axes. Taking the case of s=1, we show that the ‘non-oriented’ nature and hence squeezing arise from the intrinsic quantum correlations that exist among the spinors in the coupled state.     

Asymptotic solutions to the non-linear cantilever elastica

In this work it is shown that by a series of admissible functional transformations the constructed higher-order strongly non-linear differential equation (ODE), describing the elastica of a cantilever due to a terminal generalized concentrated, as well as to a lateral uniformly distributed loading, is reduced to a first-order non-linear integrodifferential equation consisting of the first intermediate integral of the original equation. The absence of exact analytic solutions in terms of known (tabulated) functions of the above reduced equation leads to the conclusion that there are no exact analytic solutions of this complicated elastica problem. In the limits of small values of the slope parameter of the deflected elastica, we expand asymptotically the above integrodifferential equation to non-linear ODEs of the generalized Emden–Fowler types, exact analytic solutions of which are constructed in parametric form.     

Sleep disturbances in highly stress reactive mice: Modeling endophenotypes of major depression

Background  

Neuronal mechanisms underlying affective disorders such as major depression (MD) are still poorly understood. By selectively breeding mice for high (HR), intermediate (IR), or low (LR) reactivity of the hypothalamic-pituitary-adrenocortical (HPA) axis, we recently established a new genetic animal model of extremes in stress reactivity (SR). Studies characterizing this SR mouse model on the behavioral, endocrine, and neurobiological levels revealed several similarities with key endophenotypes observed in MD patients. HR mice were shown to have changes in rhythmicity and sleep measures such as rapid eye movement sleep (REMS) and non-REM sleep (NREMS) as well as in slow wave activity, indicative of reduced sleep efficacy and increased REMS. In the present study we were interested in how far a detailed spectral analysis of several electroencephalogram (EEG) parameters, including relevant frequency bands, could reveal further alterations of sleep architecture in this animal model. Eight adult males of each of the three breeding lines were equipped with epidural EEG and intramuscular electromyogram (EMG) electrodes. After recovery, EEG and EMG recordings were performed for two days.     

Effects of lipopolysaccharide-induced inflammation on expression of growth-associated genes by corticospinal neurons

Background  

Inflammation around cell bodies of primary sensory neurons and retinal ganglion cells enhances expression of neuronal growth-associated genes and stimulates axonal regeneration. We have asked if inflammation would have similar effects on corticospinal neurons, which normally show little response to spinal cord injury. Lipopolysaccharide (LPS) was applied onto the pial surface of the motor cortex of adult rats with or without concomitant injury of the corticospinal tract at C4. Inflammation around corticospinal tract cell bodies in the motor cortex was assessed by immunohistochemistry for OX42 (a microglia and macrophage marker). Expression of growth-associated genes c-jun, ATF3, SCG10 and GAP-43 was investigated by immunohistochemistry or in situ hybridisation.     

Nonlinear asymptotic analysis in elastica of straight bars—analytical parametric solutions

It is shown that by a series of admissible functional transformations the already derived (third-order) strongly nonlinear ordinary differential equation (ODE), describing the elastica buckling analysis of a straight bar under its own weight [Int.J.Solids Struct.24(12), 1179–1192, 1988, The Theory of Elastic Stability, McGraw-Hill, New York, 1961], is reduced to a first-order nonlinear integrodifferential equation. The absence of exact analytic solutions of the reduced equation leads to the conclusion that there are no exact analytic solutions in terms of known (tabulated) functions of this elastica buckling problem. In the limits of large or small values of the slope of the deflected elastica, we expand asymptotically the above integrodifferential equation to nonlinear ODEs of the Emden–Fowler or Abel nonlinear type. In these cases, using the solution methodology recently developed in Panayotounakos [Appl. Math. Lett. 18:155–162, 2005] and Panayotounakos and Kravvaritis [Nonlin. Anal. Real World Appl., 7(2):634–650, 2006], we construct exact implicit analytic solutions in parametric form of these types of equations and thus approximate implicit analytic solutions of the original elastica buckling nonlinear ODE.     

Propagation of surface (seismic) waves: Ordinary differential equations with strongly nonlinear damping

Second-order ordinary differential equations (ODEs) with strongly nonlinear damping (cubic nonlinearities) govern surface wave motions that entail nonlinear surface seismic motions. They apply to dynamic crack propagation and nonlinear oscillation problems in physics and nonlinear mechanics. It is shown that the nonlinear surface seismic wave equation (Rayleigh equation) admits several functional transformations and it is possible to reduce it to an equivalent first-order Abel ODE of the second kind in normal form. Based on a recently developed methodology concerning the construction of exact analytic solutions for the type of Abel equations under consideration, exact solutions are obtained for the nonlinear seismic wave (NLSW) equation for initial conditions of the physical problem. The method employed is general and can be applied to a large class of relevant ODEs in mathematical physics and nonlinear mechanics.