Tsallis' q index and Mori's q phase transitions at edge of chaos

We uncover the basis for the validity of the Tsallis statistics at the onset of chaos in logistic maps. The dynamics within the critical attractor is found to consist of an infinite family of Mori's $q$-phase transitions of rapidly decreasing strength, each associated to a discontinuity in Feigenbaum's trajectory scaling function $\sigma$. The value of $q$ at each transition corresponds to the same special value for the entropic index $q$, such that the resultant sets of $q$-Lyapunov coefficients are equal to the Tsallis rates of entropy evolution.Comment: Significantly enlarged version, additional figures and references. To be published in Physical Review

Validity of the N\'{e}el-Arrhenius model for highly anisotropic Co_xFe_{3-x}O_4 nanoparticles

We report a systematic study on the structural and magnetic properties of Co_{x}Fe_{3-x}O_{4} magnetic nanoparticles with sizes between $5$ to $25$ nm, prepared by thermal decomposition of Fe(acac)_{3} and Co(acac)_{2}. The large magneto-crystalline anisotropy of the synthesized particles resulted in high blocking temperatures ($42$ K \leqq $T_B$ $\leqq 345$ K for $5 \leqq$ d $\leqq 13$ nm ) and large coercive fields ($H_C \approxeq 1600$ kA/m for $T = 5$ K). The smallest particles ($=5$ nm) revealed the existence of a magnetically hard, spin-disordered surface. The thermal dependence of static and dynamic magnetic properties of the whole series of samples could be explained within the N\'{e}el-Arrhenius relaxation framework without the need of ad-hoc corrections, by including the thermal dependence of the magnetocrystalline anisotropy constant $K_1(T)$ through the empirical Br\"{u}khatov-Kirensky relation. This approach provided $K_1(0)$ values very similar to the bulk material from either static or dynamic magnetic measurements, as well as realistic values for the response times ($\tau_0 \simeq 10^{-10}$ s). Deviations from the bulk anisotropy values found for the smallest particles could be qualitatively explained based on Zener\'{}s relation between $K_1(T)$ and M(T)

Farnesyl Phosphatase, a Corpora allata Enzyme Involved in Juvenile Hormone Biosynthesis in Aedes aegypti

Background: The juvenile hormones (JHs) are sesquiterpenoid compounds that play a central role in insect reproduction, development and behavior. The late steps of JH III biosynthesis in the mosquito Aedes aegypti involve the hydrolysis of farnesyl pyrophosphate (FPP) to farnesol (FOL), which is then successively oxidized to farnesal and farnesoic acid, methylated to form methyl farnesoate and finally transformed to JH III by a P450 epoxidase. The only recognized FPP phosphatase (FPPase) expressed in the corpora allata (CA) of an insect was recently described in Drosophila melanogaster (DmFPPase). In the present study we sought to molecularly and biochemically characterize the FPP phosphatase responsible for the transformation of FPP into FOL in the CA of A. aegypti. Methods: A search for orthologs of the DmFPPase in Aedes aegypti led to the identification of 3 putative FPPase paralogs expressed in the CA of the mosquito (AaFPPases-1, -2, and -3). The activities of recombinant AaFPPases were tested against general phosphatase substrates and isoprenoid pyrophosphates. Using a newly developed assay utilizing fluorescent tags, we analyzed AaFPPase activities in CA of sugar and blood-fed females. Double-stranded RNA (dsRNA) was used to evaluate the effect of reduction of AaFPPase mRNAs on JH biosynthesis. Conclusions: AaFPPase-1 and AaFPPase-2 are members of the NagD family of the Class IIA C2 cap-containing haloalkanoic acid dehalogenase (HAD) super family and efficiently hydrolyzed FPP into FOL. AaFPPase activities were different in CA of sugar and blood-fed females. Injection of dsRNAs resulted in a significant reduction of AaFPPase-1 and AaFPPase-2 mRNAs, but only reduction of AaFPPase-1 caused a significant decrease of JH biosynthesis. These results suggest that AaFPPase-1 is predominantly involved in the catalysis of FPP into FOL in the CA of A. aegypti

Diagnosis of Transient/Latent HPV Infections - A Point of View!

© 2018 IMSS Diagnosis of transient/latent HPV infections requires a rethinking of ideas concerning the host virus relationship. With this in mind, we address several concepts, such as mutualism and commensalism, to understand better the different stages of development, in addition to briefly covering current methods of detection. We suggest analyzing molecules related to the innate immune response for earlier diagnosis

A phase-field model of Hele-Shaw flows in the high viscosity contrast regime

A one-sided phase-field model is proposed to study the dynamics of unstable interfaces of Hele-Shaw flows in the high viscosity contrast regime. The corresponding macroscopic equations are obtained by means of an asymptotic expansion from the phase-field model. Numerical integrations of the phase-field model in a rectangular Hele-Shaw cell reproduce finger competition with the final evolution to a steady state finger the width of which goes to one half of the channel width as the velocity increases

Intermittency at critical transitions and aging dynamics at edge of chaos

We recall that, at both the intermittency transitions and at the Feigenbaum attractor in unimodal maps of non-linearity of order $\zeta >1$, the dynamics rigorously obeys the Tsallis statistics. We account for the $q$-indices and the generalized Lyapunov coefficients $\lambda_{q}$ that characterize the universality classes of the pitchfork and tangent bifurcations. We identify the Mori singularities in the Lyapunov spectrum at the edge of chaos with the appearance of a special value for the entropic index $q$. The physical area of the Tsallis statistics is further probed by considering the dynamics near criticality and glass formation in thermal systems. In both cases a close connection is made with states in unimodal maps with vanishing Lyapunov coefficients.Comment: Proceedings of: STATPHYS 2004 - 22nd IUPAP International Conference on Statistical Physics, National Science Seminar Complex, Indian Institute of Science, Bangalore, 4-9 July 2004. Pramana, in pres

Minority and mode conversion heating in (3He)-H JET plasma

Radio frequency (RF) heating experiments have recently been conducted in JET (He-3)-H plasmas. This type of plasmas will be used in ITER's non-activated operation phase. Whereas a companion paper in this same PPCF issue will discuss the RF heating scenario's at half the nominal magnetic field, this paper documents the heating performance in (He-3)-H plasmas at full field, with fundamental cyclotron heating of He-3 as the only possible ion heating scheme in view of the foreseen ITER antenna frequency bandwidth. Dominant electron heating with global heating efficiencies between 30% and 70% depending on the He-3 concentration were observed and mode conversion (MC) heating proved to be as efficient as He-3 minority heating. The unwanted presence of both He-4 and D in the discharges gave rise to 2 MC layers rather than a single one. This together with the fact that the location of the high-field side fast wave (FW) cutoff is a sensitive function of the parallel wave number and that one of the locations of the wave confluences critically depends on the He-3 concentration made the interpretation of the results, although more complex, very interesting: three regimes could be distinguished as a function of X[He-3]: (i) a regime at low concentration (X[He-3] < 1.8%) at which ion cyclotron resonance frequency (ICRF) heating is efficient, (ii) a regime at intermediate concentrations (1.8 < X[He-3] < 5%) in which the RF performance is degrading and ultimately becoming very poor, and finally (iii) a good heating regime at He-3 concentrations beyond 6%. In this latter regime, the heating efficiency did not critically depend on the actual concentration while at lower concentrations (X[He-3] < 4%) a bigger excursion in heating efficiency is observed and the estimates differ somewhat from shot to shot, also depending on whether local or global signals are chosen for the analysis. The different dynamics at the various concentrations can be traced back to the presence of 2 MC layers and their associated FW cutoffs residing inside the plasma at low He-3 concentration. One of these layers is approaching and crossing the low-field side plasma edge when 1.8 < X[He-3] < 5%. Adopting a minimization procedure to correlate the MC positions with the plasma composition reveals that the different behaviors observed are due to contamination of the plasma. Wave modeling not only supports this interpretation but also shows that moderate concentrations of D-like species significantly alter the overall wave behavior in He-3-H plasmas. Whereas numerical modeling yields quantitative information on the heating efficiency, analytical work gives a good description of the dominant underlying wave interaction physics

Infinite ergodic theory and Non-extensive entropies

We bring into account a series of result in the infinite ergodic theory that we believe that they are relevant to the theory of non-extensive entropie

Black hole thermodynamical entropy

As early as 1902, Gibbs pointed out that systems whose partition function diverges, e.g. gravitation, lie outside the validity of the Boltzmann-Gibbs (BG) theory. Consistently, since the pioneering Bekenstein-Hawking results, physically meaningful evidence (e.g., the holographic principle) has accumulated that the BG entropy $S_{BG}$ of a $(3+1)$ black hole is proportional to its area $L^2$ ($L$ being a characteristic linear length), and not to its volume $L^3$. Similarly it exists the \emph{area law}, so named because, for a wide class of strongly quantum-entangled $d$-dimensional systems, $S_{BG}$ is proportional to $\ln L$ if $d=1$, and to $L^{d-1}$ if $d>1$, instead of being proportional to $L^d$ ($d \ge 1$). These results violate the extensivity of the thermodynamical entropy of a $d$-dimensional system. This thermodynamical inconsistency disappears if we realize that the thermodynamical entropy of such nonstandard systems is \emph{not} to be identified with the BG {\it additive} entropy but with appropriately generalized {\it nonadditive} entropies. Indeed, the celebrated usefulness of the BG entropy is founded on hypothesis such as relatively weak probabilistic correlations (and their connections to ergodicity, which by no means can be assumed as a general rule of nature). Here we introduce a generalized entropy which, for the Schwarzschild black hole and the area law, can solve the thermodynamic puzzle.Comment: 7 pages, 2 figures. Accepted for publication in EPJ