Eccentricity Evolution of Extrasolar Multiple Planetary Systems due to the Depletion of Nascent Protostellar Disks

Most extrasolar planets are observed to have eccentricities much larger than those in the solar system. Some of these planets have sibling planets, with comparable masses, orbiting around the same host stars. In these multiple planetary systems, eccentricity is modulated by the planets' mutual secular interaction as a consequence of angular momentum exchange between them. For mature planets, the eigenfrequencies of this modulation are determined by their mass and semi-major axis ratios. But, prior to the disk depletion, self gravity of the planets' nascent disks dominates the precession eigenfrequencies. We examine here the initial evolution of young planets' eccentricity due to the apsidal libration or circulation induced by both the secular interaction between them and the self gravity of their nascent disks. We show that as the latter effect declines adiabatically with disk depletion, the modulation amplitude of the planets' relative phase of periapse is approximately invariant despite the time-asymmetrical exchange of angular momentum between planets. However, as the young planets' orbits pass through a state of secular resonance, their mean eccentricities undergo systematic quantitative changes. For applications, we analyze the eccentricity evolution of planets around Upsilon Andromedae and HD168443 during the epoch of protostellar disk depletion. We find that the disk depletion can change the planets' eccentricity ratio. However, the relatively large amplitude of the planets' eccentricity cannot be excited if all the planets had small initial eccentricities.Comment: 50 pages including 11 figures, submitted to Ap

Three-Dimensional Cytoskeletal Structures of the Chinchilla Organ of Corti: Scanning Electron Microscopy Application of the Polyethylene Glycol Method

We describe the application of a polyethylene glycol (PEG) embedding technique to examine the sensory and supporting structures of the inner ear. The chinchilla organ of Corti was exposed by cracking PEG embedded cochleas. A range of PEG molecular weights (2000-8000) were utilized; PEG 2000, with a melting point of 57°C was preferred. After removal of the PEG, the three-dimensional aspects of intracellular structures were observed using scanning electron microscopy. Filamentous elements in the hair cell cuticular plate and in the supporting cells were clearly observed, as was the mesh work of cross-linked actin filaments in the cuticular portion of sensory hair cells. Microtubule and microfilament alignment patterns in pillar and Deiters cells were also clearly demonstrated. Characteristic structures in the outer hair cell synaptic region, such as the post-synaptic cistern and synaptic body, were well preserved using the PEG method

Three Dimensional Intracellular Structure of the Cochlea Using the A-O-D-O Method

We have observed the three-dimensional intracellular structure of the organ of Corti and the spiral ganglion of the chinchilla using the aldehyde osmium-DMSO-osmium (A-O-D-O) method, and compared our findings with previous studies in the guinea pig. In cells of the spiral ganglion and the organ of Corti, microtubules and other cytoplasmic filaments were digested by OsO4 during processing to provide a clear view of membranous structures such as mitochondria, endoplasmic reticulum and Golgi apparatus. The appropriate digestion time with 0.1% OsO4 solution was found to be 60-80 hrs for the organ of Corti and 70-90 hrs for the spiral ganglion. The A-O-D-O method has been especially useful to show the organization of the endoplasmic reticulum of the outer hair cells. We have made a further characterization of the apical cistern, a reticular network which appears to link the basal body of the (vestigial) kinocilium to both Hensen\u27s body and the subsurface cisternae

Correlation of Cochlear Pathology with Auditory Brainstem and Cortical Responses in Cats with High Frequency Hearing Loss

Newborn kittens were treated with the aminoglycoside amikacin to produce a bilateral high frequency cochlear hearing loss. The degree and stability of hearing loss were confirmed by recording auditory brainstem evoked potentials (ABR audiograms). After maturation, cochleotopic frequency representation within primary auditory cortex (Al) was mapped using standard microelectrode recording techniques. The cochlear sensory epithelium was assessed with SEM and the pattern of damage compared with the ABR audiograms and cortical frequency maps. Amikacin treatment resulted in various patterns of haircell damage towards the base of the cochlea. A relatively abrupt transition between damaged and undamaged haircell regions resulted in an ABR audiogram with normal threshold to low frequencies and a high frequency elevation with a steep cut-off slope. In the cortical map, low frequency representation was normal, but anterior areas contained only neurons tuned to a common frequency which corresponded to the frequency-place position of the boundary of the haircell lesion and to the cut-off frequency of the audiogram. A large transitional zone of the cochlear lesion correlated with a gradual cut-off slope to the audiogram and again a remapping of the anterior and normally high frequency area to a common lower frequency. Haircell loss or damage (i.e. disarray of stereocilia) in lower frequency regions of the cochlea correlated with a significant reorganization of the lower frequency bands in the cortical map. We conclude from this study that the pattern of cochleotopic organization of the cortex is dependent on the pattern of activity in the ascending sensory pathway during early stages of development

Entropy, time irreversibility and Schroedinger equation in a primarily discrete space-time

In this paper we show that the existence of a primarily discrete space-time may be a fruitful assumption from which we may develop a new approach of statistical thermodynamics in pre-relativistic conditions. The discreetness of space-time structure is determined by a condition that mimics the Heisenberg uncertainty relations and the motion in this space-time model is chosen as simple as possible. From these two assumptions we define a path-entropy that measures the number of closed paths associated with a given energy of the system preparation. This entropy has a dynamical character and depends on the time interval on which we count the paths. We show that it exists an like-equilibrium condition for which the path-entropy corresponds exactly to the usual thermodynamic entropy and, more generally, the usual statistical thermodynamics is reobtained. This result derived without using the Gibbs ensemble method shows that the standard thermodynamics is consistent with a motion that is time-irreversible at a microscopic level. From this change of paradigm it becomes easy to derive a $H-theorem$. A comparison with the traditional Boltzmann approach is presented. We also show how our approach can be implemented in order to describe reversible processes. By considering a process defined simultaneously by initial and final conditions a well defined stochastic process is introduced and we are able to derive a Schroedinger equation, an example of time reversible equation.Comment: latex versio

Entropy: From Black Holes to Ordinary Systems

Several results of black holes thermodynamics can be considered as firmly founded and formulated in a very general manner. From this starting point we analyse in which way these results may give us the opportunity to gain a better understanding in the thermodynamics of ordinary systems for which a pre-relativistic description is sufficient. First, we investigated the possibility to introduce an alternative definition of the entropy basically related to a local definition of the order in a spacetime model rather than a counting of microstates. We show that such an alternative approach exists and leads to the traditional results provided an equilibrium condition is assumed. This condition introduces a relation between a time interval and the reverse of the temperature. We show that such a relation extensively used in the black hole theory, mainly as a mathematical trick, has a very general and physical meaning here; in particular its derivation is not related to the existence of a canonical density matrix. Our dynamical approach of thermodynamic equilibrium allows us to establish a relation between action and entropy and we show that an identical relation exists in the case of black holes. The derivation of such a relation seems impossible in the Gibbs ensemble approach of statistical thermodynamics. From these results we suggest that the definition of entropy in terms of order in spacetime should be more general that the Boltzmann one based on a counting of microstates. Finally we point out that these results are obtained by reversing the traditional route going from the Schr\"{o}dinger equation to statistical thermodynamics

Analiza oborine (1923-2004) u Ataru-Mauretaniji

The shortage of water resources in Adrar region, especially in Atar (Capital city of Adrar prefecture) and the surrounding villages along Seguelli watershed has been taken the concern of the policy maker and populations of this region since long time. This area had been suffering from recurrent droughts and faced water crises many times. Several attempts have been made to overcome these problems. Meanwhile the risk is still endangering the life and agricultural activities in one of the most important oasis areas. This study analyzed Atar rainfall time series periodicity, trends, and its relationship with Sea Surface Temperature (SST). The nonparametric Spearman test was used for trend analysis and the serial autocorrelation for persistency. Also, power spectrum and Fourier fit were deployed for analysis of frequency and periodicity. The tendency of Atar rainfall time series shows rainy periods in 1920’s and 1950’s and decreased rainfall since the late of 1950s. On the other hand, the prolonged drought periods appeared during 1970’s in contemporaneous with the Sahelian drought. The persistency analysis indicated the presence of biennial components in the annual and bimonthly rainfall in last three decades. SSTs of Atlantic, Indian and Pacific Ocean were modulating Atar rainfall during 1923–1992 period.U području Adrara, posebno u Ataru (glavnom gradu pokrajine Adrar) i okolnim selima duž Seguelli sliva proučavao se manjak vodenih resursa u odnosu na političke odnose i stanovništvo tog područja kroz duže vrijeme. To je područje karakterizirano čestim periodičnim sušama i nedostacima vode. Usprkos pokušajima da se taj problem prebrodi, život i poljoprivreda su i dalje ugroženi u jednoj od najvažnijih oaza u tom području. Ova studija analizira periodičnost vremenskog niza oborine u Ataru, trendove niza i njegov međuodnos s površinskom temperaturom mora. Pri analizi trenda koristio se neparametarski Spearman-ov test, dok je perzistencija analizirana putem autokorelacije. Također se koristio i spektar snage i harmonijska analiza za određivanje frekvencija i periodičnosti. Tendencija vremenskog niza oborina u Ataru pokazuje kišne periode u dvadesetim i pedesetim godinama 20. stoljeća i smanjenje oborine od kasnih pedesetih godina 20. stoljeća. Dugotrajni periodi suše pojavljuju se tijekom 70-tih istovremeno sa sušom u Sahelu. Analiza perzistencije ukazala je na postojanje dvogodišnjih komponenti u godišnjoj i dvomjesečnoj oborini u zadnje tri dekade. Površinske temperature mora Atlantika, Indijskog i Pacifičkog oceana utjecale su na količinu oborine u Ataru u razdoblju od 1923. do 1992. godine

Evolution of Topological Defects During Inflation

Topological defects can be formed during inflation by phase transitions as well as by quantum nucleation. We study the effect of the expansion of the Universe on the internal structure of the defects. We look for stationary solutions to the field equations, i.e. solutions that depend only on the proper distance from the defect core. In the case of very thin defects, whose core dimensions are much smaller than the de Sitter horizon, we find that the solutions are well approximated by the flat space solutions. However, as the flat space thickness parameter $\delta_0$ increases we notice a deviation from this, an effect that becomes dramatic as $\delta_0$ approaches $(H)^{-1}/{\sqrt 2}$. Beyond this critical value we find no stationary solutions to the field equations. We conclude that only defects that have flat space thicknesses less than the critical value survive, while thicker defects are smeared out by the expansion.Comment: 14 page

On the stochastic mechanics of the free relativistic particle

Given a positive energy solution of the Klein-Gordon equation, the motion of the free, spinless, relativistic particle is described in a fixed Lorentz frame by a Markov diffusion process with non-constant diffusion coefficient. Proper time is an increasing stochastic process and we derive a probabilistic generalization of the equation $(d\tau)^2=-\frac{1}{c^2}dX_{\nu}dX_{\nu}$. A random time-change transformation provides the bridge between the $t$ and the $\tau$ domain. In the $\tau$ domain, we obtain an \M^4-valued Markov process with singular and constant diffusion coefficient. The square modulus of the Klein-Gordon solution is an invariant, non integrable density for this Markov process. It satisfies a relativistically covariant continuity equation