Unitary relation between a harmonic oscillator of time-dependent frequency and a simple harmonic oscillator with and without an inverse-square potential

The unitary operator which transforms a harmonic oscillator system of time-dependent frequency into that of a simple harmonic oscillator of different time-scale is found, with and without an inverse-square potential. It is shown that for both cases, this operator can be used in finding complete sets of wave functions of a generalized harmonic oscillator system from the well-known sets of the simple harmonic oscillator. Exact invariants of the time-dependent systems can also be obtained from the constant Hamiltonians of unit mass and frequency by making use of this unitary transformation. The geometric phases for the wave functions of a generalized harmonic oscillator with an inverse-square potential are given.Comment: Phys. Rev. A (Brief Report), in pres

Exact quantum states of a general time-dependent quadratic system from classical action

A generalization of driven harmonic oscillator with time-dependent mass and frequency, by adding total time-derivative terms to the Lagrangian, is considered. The generalization which gives a general quadratic Hamiltonian system does not change the classical equation of motion. Based on the observation by Feynman and Hibbs, the propagators (kernels) of the systems are calculated from the classical action, in terms of solutions of the classical equation of motion: two homogeneous and one particular solutions. The kernels are then used to find wave functions which satisfy the Schr\"{o}dinger equation. One of the wave functions is shown to be that of a Gaussian pure state. In every case considered, we prove that the kernel does not depend on the way of choosing the classical solutions, while the wave functions depend on the choice. The generalization which gives a rather complicated quadratic Hamiltonian is simply interpreted as acting an unitary transformation to the driven harmonic oscillator system in the Hamiltonian formulation.Comment: Submitted to Phys. Rev.

Streamer Wave Events Observed in Solar Cycle 23

In this paper we conduct a data survey searching for well-defined streamer wave events observed by the Large Angle and Spectrometric Coronagraph (LASCO) on-board the Solar and Heliospheric Observatory (SOHO) throughout Solar Cycle 23. As a result, 8 candidate events are found and presented here. We compare different events and find that in most of them the driving CMEs ejecta are characterized by a high speed and a wide angular span, and the CME-streamer interactions occur generally along the flank of the streamer structure at an altitude no higher than the bottom of the field of view of LASCO C2. In addition, all front-side CMEs have accompanying flares. These common observational features shed light on the excitation conditions of streamer wave events. We also conduct a further analysis on one specific streamer wave event on 5 June 2003. The heliocentric distances of 4 wave troughs/crests at various exposure times are determined; they are then used to deduce the wave properties like period, wavelength, and phase speeds. It is found that both the period and wavelength increase gradually with the wave propagation along the streamer plasma sheet, and the phase speed of the preceding wave is generally faster than that of the trailing ones. The associated coronal seismological study yields the radial profiles of the Alfv\'en speed and magnetic field strength in the region surrounding the streamer plasma sheet. Both quantities show a general declining trend with time. This is interpreted as an observational manifestation of the recovering process of the CME-disturbed corona. It is also found that the Alfv\'enic critical point is at about 10 R$_\odot$ where the flow speed, which equals the Alfv\'en speed, is $\sim$ 200 km s$^{-1}$

Distribution and inter-regional relationship of amyloid-beta plaque deposition in a 5xFAD mouse model of Alzheimer’s disease

Alzheimer’s disease (AD) is the most common form of dementia. Although previous studies have selectively investigated the localization of amyloid-beta (Aβ) deposition in certain brain regions, a comprehensive characterization of the rostro-caudal distribution of Aβ plaques in the brain and their inter-regional correlation remain unexplored. Our results demonstrated remarkable working and spatial memory deficits in 9-month-old 5xFAD mice compared to wildtype mice. High Aβ plaque load was detected in the somatosensory cortex, piriform cortex, thalamus, and dorsal/ventral hippocampus; moderate levels of Aβ plaques were observed in the motor cortex, orbital cortex, visual cortex, and retrosplenial dysgranular cortex; and low levels of Aβ plaques were located in the amygdala, and the cerebellum; but no Aβ plaques were found in the hypothalamus, raphe nuclei, vestibular nucleus, and cuneate nucleus. Interestingly, the deposition of Aβ plaques was positively associated with brain inter-regions including the prefrontal cortex, somatosensory cortex, medial amygdala, thalamus, and the hippocampus. In conclusion, this study provides a comprehensive morphological profile of Aβ deposition in the brain and its inter-regional correlation. This suggests an association between Aβ plaque deposition and specific brain regions in AD pathogenesis

The novel transcriptional regulator SczA mediates protection against Zn2+ stress by activation of the Zn2+-resistance gene czcD in Streptococcus pneumoniae

Maintenance of the intracellular homeostasis of metal ions is important for the virulence of many bacterial pathogens. Here, we demonstrate that the czcD gene of the human pathogen Streptococcus pneumoniae is involved in resistance against Zn2+, and that its transcription is induced by the transition-metal ions Zn2+, Co2+ and Ni2+. Upstream of czcD a gene was identified, encoding a novel TetR family regulator, SczA, that is responsible for the metal ion-dependent activation of czcD expression. Transcriptome analyses revealed that in a sczA mutant expression of czcD, a gene encoding a MerR-family transcriptional regulator and a gene encoding a zinc-containing alcohol dehydrogenase (adhB) were downregulated. Activation of the czcD promoter by SczA is shown to proceed by Zn2+-dependent binding of SczA to a conserved DNA motif. In the absence of Zn2+, SczA binds to a second site in the czcD promoter, thereby fully blocking czcD expression. This is the first example of a metalloregulatory protein belonging to the TetR family that has been described. The presence in S. pneumoniae of the Zn2+-resistance system characterized in this study might reflect the need for adjustment to a fluctuating Zn2+ pool encountered by this pathogen during infection of the human body

A geometric approach to time evolution operators of Lie quantum systems

Lie systems in Quantum Mechanics are studied from a geometric point of view. In particular, we develop methods to obtain time evolution operators of time-dependent Schrodinger equations of Lie type and we show how these methods explain certain ad hoc methods used in previous papers in order to obtain exact solutions. Finally, several instances of time-dependent quadratic Hamiltonian are solved.Comment: Accepted for publication in the International Journal of Theoretical Physic

Hydrodynamics and Flow

In this lecture note, we present several topics on relativistic hydrodynamics and its application to relativistic heavy ion collisions. In the first part we give a brief introduction to relativistic hydrodynamics in the context of heavy ion collisions. In the second part we present the formalism and some fundamental aspects of relativistic ideal and viscous hydrodynamics. In the third part, we start with some basic checks of the fundamental observables followed by discussion of collective flow, in particular elliptic flow, which is one of the most exciting phenomenon in heavy ion collisions at relativistic energies. Next we discuss how to formulate the hydrodynamic model to describe dynamics of heavy ion collisions. Finally, we conclude the third part of the lecture note by showing some results from ideal hydrodynamic calculations and by comparing them with the experimental data.Comment: 40 pages, 35 figures; lecture given at the QGP Winter School, Jaipur, India, Feb.1-3, 2008; to appear in Springer Lecture Notes in Physic

Comparison of TCP and TCP/HA Hybrid Scaffolds for Osteoconductive Activity

Two types of porous ceramic scaffolds were prepared, consisting of β-tricalcium phosphate (TCP) or the mixed powder of TCP and hydroxyapatite (HA) at a 2:1 mass ratio. A variety of methods have been used to fabricate bone scaffolds, while the sintering approach was adopted in this work. An extremely high temperature was used on sintering that proposed to consolidate the ceramic particles. As revealed by SEM, a well opened pore structure was developed within the scaffolds. The θ-values were measured to be of 73.3° and 6.5° for the composite scaffold and TCP sample, respectively. According to XRD patterns, the existence of grains coalescence and partial bonding between HA and TCP powders was demonstrated. Scaffold mechanical property in the term of flexural strength was also determined. The result showed decreasing of the strength by HA supplement, suggesting the more brittle characteristic of HA in comparison with TCP. By soaking the composite scaffold in PBS for a period of 2 weeks, transformation from particles to flank-like crystalline was clearly observed. Such change was found to be favorable for cell attachment, migration, and growth. By implanting cell-seeded scaffolds into nude mice, an abundant osseous extracellular matrix was identified for the composite implants. In contrast, the matrix was minimally detected in TCP implanted samples. Thus, the composite scaffold was found superior for hard tissue regeneration

Multi-spectral intravascular photoacoustic/ultrasound/optical coherence tomography tri-modality system with a fully-integrated 0.9-mm full field-of-view catheter for plaque vulnerability imaging

Myocardial infarctions are most often caused by the so-called vulnerable plaques, usually featured as non-obstructive lesions with a lipid-rich necrotic core, thin-cap fibroatheroma, and large plaque size. The identification and quantification of these characteristics are the keys to evaluate plaque vulnerability. However, single modality intravascular methods, such as intravascular ultrasound, optical coherence tomography and photoacoustic, can hardly achieve all the comprehensive information to satisfy clinical needs. In this paper, for the first time, we developed a novel multi-spectral intravascular tri-modality (MS-IVTM) imaging system, which can perform 360° continuous rotation and pull-backing with a 0.9-mm miniature catheter and achieve simultaneous acquisition of both morphological characteristics and pathological compositions. Intravascular tri-modality imaging demonstrates the ability of our MS-IVTM system to provide macroscopic and microscopic structural information of the vessel wall, with identity and quantification of lipids with multi-wavelength excitation. This study offers clinicians and researchers a novel imaging tool to facilitate the accurate diagnosis of vulnerable atherosclerotic plaques. It also has the potential of clinical translations to help better identify and evaluate high-risk plaques during coronary interventions