Extended phase diagram of the Lorenz model

The parameter dependence of the various attractive solutions of the three variable nonlinear Lorenz model equations for thermal convection in Rayleigh-B\'enard flow is studied. Its bifurcation structure has commonly been investigated as a function of r, the normalized Rayleigh number, at fixed Prandtl number \sigma. The present work extends the analysis to the entire (r,\sigma) parameter plane. An onion like periodic pattern is found which is due to the alternating stability of symmetric and non-symmetric periodic orbits. This periodic pattern is explained by considering non-trivial limits of large r and \sigma. In addition to the limit which was previously analyzed by Sparrow, we identify two more distinct asymptotic regimes in which either \sigma/r or \sigma^2/r is constant. In both limits the dynamics is approximately described by Airy functions whence the periodicity in parameter space can be calculated analytically. Furthermore, some observations about sequences of bifurcations and coexistence of attractors, periodic as well as chaotic, are reported.Comment: 36 pages, 20 figure

Epigenetic modification of the oxytocin receptor gene is associated with emotion processing in the infant brain

The neural capacity to discriminate between emotions emerges early in development, though little is known about specific factors that contribute to variability in this vital skill during infancy. In adults, DNA methylation of the oxytocin receptor gene (OXTRm) is an epigenetic modification that is variable, predictive of gene expression, and has been linked to autism spectrum disorder and the neural response to social cues. It is unknown whether OXTRm is variable in infants, and whether it is predictive of early social function. Implementing a developmental neuroimaging epigenetics approach in a large sample of infants (N = 98), we examined whether OXTRm is associated with neural responses to emotional expressions. OXTRm was assessed at 5 months of age. At 7 months of age, infants viewed happy, angry, and fearful faces while functional near-infrared spectroscopy was recorded. We observed that OXTRm shows considerable variability among infants. Critically, infants with higher OXTRm show enhanced responses to anger and fear and attenuated responses to happiness in right inferior frontal cortex, a region implicated in emotion processing through action-perception coupling. Findings support models emphasizing oxytocin's role in modulating neural response to emotion and identify OXTRm as an epigenetic mark contributing to early brain function

Non-Oberbeck-Boussinesq effects in two-dimensional Rayleigh-Benard convection in glycerol

We numerically analyze Non-Oberbeck-Boussinesq (NOB) effects in two-dimensional Rayleigh-Benard flow in glycerol, which shows a dramatic change in the viscosity with temperature. The results are presented both as functions of the Rayleigh number (Ra) up to $10^8$ (for fixed temperature difference between the top and bottom plates) and as functions of "non-Oberbeck-Boussinesqness'' or "NOBness'' ($\Delta$) up to 50 K (for fixed Ra). For this large NOBness the center temperature $T_c$ is more than 5 K larger than the arithmetic mean temperature $T_m$ between top and bottom plate and only weakly depends on Ra. To physically account for the NOB deviations of the Nusselt numbers from its Oberbeck-Boussinesq values, we apply the decomposition of $Nu_{NOB}/Nu_{OB}$ into the product of two effects, namely first the change in the sum of the top and bottom thermal BL thicknesses, and second the shift of the center temperature $T_c$ as compared to $T_m$. While for water the origin of the $Nu$ deviation is totally dominated by the second effect (cf. Ahlers et al., J. Fluid Mech. 569, pp. 409 (2006)) for glycerol the first effect is dominating, in spite of the large increase of $T_c$ as compared to $T_m$.Comment: 6 pages, 7 figure

Interaction of Human Chorionic Gonadotropin (hCG) and Asialo-hCG with Recombinant Human Thyrotropin Receptor.

hCG is a putative thyroid stimulator. The present studies were undertaken to examine its interaction and that of its desialylated variant asialo-hCG with recombinant human TSH (hTSH) receptor (hTSHr). To this end, we transfected a human thyroid carcinoma cell line (HTC) lacking endogenous TSHr with the full-length cDNA of the hTSHr. Unlike the wild type, the transfected cells, termed HTC-TSHr cells, were able to bind bovine TSH (bTSH) with high affinity and increase cAMP production in response to bTSH stimulation. Of the hCG forms, intact hCG displayed a weak activity to inhibit [125I] bTSH binding to HTC-TSHr cells, with 100 mg/L (2.6 x 10(-6) mol/L) producing maximally a 20% inhibition, whereas asialo-hCG achieved half-maximum binding inhibition at a concentration of 8 mg/L (2.3 x 10(-7) mol/L). The inhibitory constant (Ki) of asialo-hCG for recombinant hTSHr was calculated from saturation experiments in the presence of variable doses of bTSH and a fixed concentration of asialo-hCG to be approximately 8 x 10(-8) mol/L. The interaction of asialo-hCG with TSHr was further assessed by studies of the direct binding of the radioactively labeled hormone to both HTC and HTC-TSHr cells. [125I]Asialo-hCG binding to HTC-TSHr cells was 4.7%, compared to 1.5% in the wild-type cells lacking TSHr and was displaceable by bTSH (0.1-100 IU/L), indicating specific binding of the tracer to TSHr. Functionally, hCG (up to 100 mg/L; 2.6 x 10(-6) mol/L) proved unable to evoke any significant cAMP response over basal values in HTC-TSHr cells, as did asialo-hCG. Asialo-hCG, but not hCG, inhibited bTSH-stimulated adenylate cyclase activity in the cells in a dose-dependent manner. In conclusion, the present data show that intact hCG binds only weakly to HTC-TSHr cells and produces no significant cAMP stimulation, which is at variance with data obtained in FRTL-5 and Chinese hamster ovary-TSHr cells, but in good accord with previous findings in human thyroid membranes. Asialo-hCG, on the other hand, strongly binds to recombinant TSHr and inhibits the cAMP response to bTSH in HTC-TSHr cells, indicating that the desialylated hCG variant directly interacts with the receptor and truly is an antagonist of the hTSHr

Yang-Lee zeroes for an urn model for the separation of sand

We apply the Yang-Lee theory of phase transitions to an urn model of separation of sand. The effective partition function of this nonequilibrium system can be expressed as a polynomial of the size-dependent effective fugacity $z$. Numerical calculations show that in the thermodynamic limit, the zeros of the effective partition function are located on the unit circle in the complex $z$-plane. In the complex plane of the actual control parameter certain roots converge to the transition point of the model. Thus the Yang-Lee theory can be applied to a wider class of nonequilibrium systems than those considered previously.Comment: 4 pages, 3 eps figures include

Electron-Ion Interaction Effects in Attosecond Time-Resolved Photoelectron Spectra

Photoionization by attosecond (as) extreme ultraviolet (xuv) pulses into the laser-dressed continuum of the ionized atom is commonly described in strong-field approximation (SFA), neglecting the Coulomb interaction between the emitted photoelectron (PE) and residual ion. By solving the time-dependent Sch\"{o}dinger equation (TDSE), we identify a temporal shift $\delta \tau$ in streaked PE spectra, which becomes significant at small PE energies. Within an eikonal approximation, we trace this shift to the combined action of Coulomb and laser forces on the released PE, suggesting the experimental and theoretical scrutiny of their coupling in streaked PE spectra. The initial state polarization effect by the laser pulse on the xuv streaked spectrum is also examined.Comment: 9 pages, Accepted by Phys. Rev.

Classification of phase transitions of finite Bose-Einstein condensates in power law traps by Fisher zeros

We present a detailed description of a classification scheme for phase transitions in finite systems based on the distribution of Fisher zeros of the canonical partition function in the complex temperature plane. We apply this scheme to finite Bose-systems in power law traps within a semi-analytic approach with a continuous one-particle density of states $\Omega(E)\sim E^{d-1}$ for different values of $d$ and to a three dimensional harmonically confined ideal Bose-gas with discrete energy levels. Our results indicate that the order of the Bose-Einstein condensation phase transition sensitively depends on the confining potential.Comment: 7 pages, 9 eps-figures, For recent information on physics of small systems see "http://www.smallsystems.de

Stokes diagnostics of simulated solar magneto-convection

We present results of synthetic spectro-polarimetric diagnostics of radiative MHD simulations of solar surface convection with magnetic fields. Stokes profiles of Zeeman-sensitive lines of neutral iron in the visible and infrared spectral ranges emerging from the simulated atmosphere have been calculated in order to study their relation to the relevant physical quantities and compare with observational results. We have analyzed the dependence of the Stokes-I line strength and width as well as of the Stokes-V signal and asymmetries on the magnetic field strength. Furthermore, we have evaluated the correspondence between the actual velocities in the simulation with values determined from the Stokes-I (Doppler shift of the centre of gravity) and Stokes-V profiles (zero-crossing shift). We confirm that the line weakening in strong magnetic fields results from a higher temperature (at equal optical depth) in the magnetic flux concentrations. We also confirm that considerable Stokes-V asymmetries originate in the peripheral parts of strong magnetic flux concentrations, where the line of sight cuts through the magnetopause of the expanding flux concentration into the surrounding convective donwflow.Comment: Astronomy & Astrophysics, in pres

Universality in fully developed turbulence

We extend the numerical simulations of She et al. [Phys.\ Rev.\ Lett.\ 70, 3251 (1993)] of highly turbulent flow with $15 \le$ Taylor-Reynolds number $Re_\lambda\le 200$ up to $Re_\lambda \approx 45000$, employing a reduced wave vector set method (introduced earlier) to approximately solve the Navier-Stokes equation. First, also for these extremely high Reynolds numbers $Re_\lambda$, the energy spectra as well as the higher moments -- when scaled by the spectral intensity at the wave number $k_p$ of peak dissipation -- can be described by {\it one universal} function of $k/k_p$ for all $Re_\lambda$. Second, the ISR scaling exponents $\zeta_m$ of this universal function are in agreement with the 1941 Kolmogorov theory (the better, the large $Re_\lambda$ is), as is the $Re_\lambda$ dependence of $k_p$. Only around $k_p$ viscous damping leads to slight energy pileup in the spectra, as in the experimental data (bottleneck phenomenon).Comment: 14 pages, Latex, 5 figures (on request), 3 tables, submitted to Phys. Rev.