Linear and nonlinear hydromagnetic stability in laminar and turbulent flows.

We consider the evolution of arbitrarily large perturbations of a prescribed pure hydrodynamical flow of an electrically conducting fluid. We study whether the flow perturbations as well as the generated magnetic fields decay or grow with time and constitute a dynamo process. For that purpose we derive a generalized Reynolds-Orr equation for the sum of the kinetic energy of the hydrodynamic perturbation and the magnetic energy. The flow is confined in a finite volume so the normal component of the velocity at the boundary is zero. The tangential component is left arbitrary in contrast with previous works. For the magnetic field we mostly employ the classical boundary conditions where the field extends in the whole space. We establish critical values of hydrodynamic and magnetic Reynolds numbers below which arbitrarily large initial perturbations of the hydrodynamic flow decay. This involves generalization of the Rayleigh-Faber-Krahn inequality for the smallest eigenvalue of an elliptic operator. For high Reynolds number turbulence we provide an estimate of critical magnetic Reynolds number below which arbitrarily large fluctuations of the magnetic field decay.

Reynolds number dependence of Lyapunov exponents of turbulence and fluid particles.

The Navier-Stokes equations generate an infinite set of generalized Lyapunov exponents defined by different ways of measuring the distance between exponentially diverging perturbed and unperturbed solutions. This set is demonstrated to be similar, yet different, from the generalized Lyapunov exponent that provides moments of distance between two fluid particles below the Kolmogorov scale. We derive rigorous upper bounds on dimensionless Lyapunov exponent of the fluid particles that demonstrate the exponent's decay with Reynolds number Re in accord with previous studies. In contrast, terms of cumulant series for exponents of the moments have power-law growth with Re. We demonstrate as an application that the growth of small fluctuations of magnetic field in ideal conducting turbulence is hyperintermittent, being exponential in both time and Reynolds number. We resolve the existing contradiction between the theory, that predicts slow decrease of dimensionless Lyapunov exponent of turbulence with Re, and observations exhibiting quite fast growth. We demonstrate that it is highly plausible that a pointwise limit for the growth of small perturbations of the Navier-Stokes equations exists.

Density and tracer statistics in compressible turbulence: Phase transition to multifractality.

We study the statistics of fluid (gas) density and concentration of passive tracer particles (dust) in compressible turbulence. As Ma increases from small or moderate values, the density and the concentration in the inertial range go through a phase transition from a finite continuous smooth distribution to a singular multifractal spatial distribution. Multifractality is associated with scaling, which would not hold if the solenoidal and the potential components of the flow scaled differently, producing transport which is not self-similar. Thus, we propose that the transition occurs when the difference of the scaling exponents of the components, decreasing with Ma, becomes small. Under the smallness assumption, the particles' volumes obey a power-law evolution. That, by the use of conservation of the total volume of the flow, entails the volumes' shrinking to zero with probability 1 and formation of a singular distribution. We discuss various concepts of multifractality and propose a way to calculate fractal dimensions from numerical or experimental data. We derive a simple expression for the spectrum of fractal dimensions of isothermal turbulence and describe limitations of lognormality. The expression depends on a single parameter: the scaling exponent of the density spectrum. We demonstrate that the pair-correlation function of the tracer concentration has the Markov property. This implies applicability of the compressible version of the Kraichnan turbulence model. We use the model to derive an explicit expression for the tracer pair correlation that demonstrates their smooth transition to multifractality and confirms the transition's mechanism. The obtained fractal dimension explains previous numerical observations. Our results have potentially important implications for astrophysical problems such as star formation as well as technological applications such as supersonic combustion. As an example, we demonstrate the strong increase of planetesimal formation rate at the transition. We prove that finiteness of internal energy implies vanishing of the sum of Lyapunov exponents in the dissipation range. Our study leads to the question of whether the fluid density which is an active field that reacts back on the transporting flow and the passive concentration of tracers must coincide in the steady state. This is demonstrated to be crucial both theoretically and experimentally. The fields' coincidence is provable at small Mach numbers; however, at finite Mach numbers, the assumption of mixing is needed, which we demonstrate to be not self-evident because of the possibility of self-organization.

Somatic Mutations of FOXE1 in Papillary Thyroid Cancer.

BACKGROUND: Population-based studies have demonstrated an association of single nucleotide polymorphisms close to the thyroid transcription factor forkhead box E1 (FOXE1) gene with thyroid cancer. The dysregulation of forkhead proteins is increasingly recognized to play a role in the development and progression of cancer. The objective of the study was to seek to identify novel mutations in FOXE1 in papillary thyroid cancer (PTC) and to assess the effect of these mutations on protein expression and transcriptional function on FOXE1 responsive promoters. METHODS: The study was conducted at two tertiary referral hospitals. The coding region of FOXE1 was sequenced in tissue-derived DNA or RNA from 120 patients with PTC and 110 patients with multinodular goiter (MNG). In vitro studies were performed to examine the protein expression and transcriptional function of FOXE1 mutants. A molecular model of the forkhead domain (FHD) of FOXE1 was generated using the SWISS-MODEL online server with the three-dimensional structure of FOXD3 as a template. RESULTS: Three somatic missense mutations were detected in PTC resulting in the amino acid substitutions P54Q, K95Q, and L112F. One additional mutation was detected in a MNG (G140R). In vitro studies demonstrated marked impairment in transcriptional activation by all four FOXE1 mutants, which was not explained by differences in protein expression. Molecular modeling localized three of the mutations to highly conserved regions of the FHD. CONCLUSIONS: We have identified novel somatic mutations of FOXE1 in PTC. Mutational inactivation of FOXE1 is an uncommon event in thyroid tumors but may contribute to thyroid carcinogenesis and dedifferentiation in concert with other oncogenic drivers.

Nuclear receptor expression in human differentiated thyroid tumors.

BACKGROUND: Nuclear receptors (NRs) play a key role in endocrine signaling and metabolism and are important therapeutic targets in a number of hormone-dependent malignancies. Studies on the role of NRs in thyroid cancer are limited. OBJECTIVE: The objective of the study was to examine systematically the expression of the 48 human NRs in a series of benign and malignant thyroid tissues. Within the papillary carcinoma cohort, we sought to determine if NR expression differed significantly by BRAF mutation status. PATIENTS AND METHODS: RNA was isolated from multinodular goiter (MNG; n=6), papillary carcinoma (PTC, n=14), follicular carcinoma (FC; n=5), and Hürthle cell carcinoma (HCC; n=7). The 48 human NRs were profiled in this panel by quantitative real time polymerase chain reaction. Protein expression for selected NRs (Rev-erbα and LXR-ß) was examined by immunohistochemistry (IHC) on tissue microarrays comprising benign and malignant thyroid tissues. RESULTS: Across all groups of benign and malignant thyroid tissue, there was prominent expression of LXR-ß and ROR-γ. Key findings in PTC were marked overexpression of RXR-γ and Rev-erbα compared to MNG. Within the PTC cohort, when BRAF(V600E) tumors were compared with wild type BRAF, there was relative upregulation of RXR-γ and Rev-erbα and downregulation of AR, ERR-γ, and ROR-γ. In FC, EAR-2 was overexpressed, while PPAR-α and PPAR-δ were underexpressed compared to MNG. The NR expression profile of HCC was distinct, characterized by significant downregulation of a wide range of NRs. IHC for Rev-erbα and LXR-ß localized protein expression to the tumor cells. Moderate to strong Rev-erbα immunostaining was seen in 22 out of 23 PTC, and, overall, staining was stronger than in the benign group. CONCLUSIONS: These results represent the first systematic examination of NR expression in thyroid cancer. Our finding of tumor-specific patterns of NR expression, as well as significant differences in NR expression between BRAF(V600E) and wild type BRAF PTC, provides a basis for further mechanistic studies and highlights potential novel therapeutic targets for this malignancy.

Magnetorotational decay instability in Keplerian disks.

The saturation of the magnetorotational instability (MRI) in thin Keplerian disks through three-wave resonant interactions is introduced and discussed. That mechanism is a natural generalization of the fundamental decay instability discovered five decades ago for infinite, homogeneous, and immovable plasmas. The decay instability relies on the energy transfer from the MRI to stable slow Alfvén-Coriolis as well as magnetosonic waves. A second-order forced Duffing amplitude equation for the initially unstable MRI as well as two first-order equations for the other two waves are derived. The solutions of those equations exhibit bounded bursty nonlinear oscillations for the MRI as well as unbounded growth for the linearly stable slow Alfvén-Coriolis and magnetosonic perturbations, thus giving rise to the magnetorotational decay instability.

Nondissipative saturation of the magnetorotational instability in thin disks.

A new nondissipative mechanism is proposed for the saturation of the axisymmetric magnetorotational (MRI) instability in thin Keplerian disks that are subject to an axial magnetic field. That mechanism relies on the energy transfer from the MRI to stable magnetosonic waves. Such mode interaction is enabled due to the vertical stratification of the disk that results in the discretization of its MRI spectrum, as well as by applying the appropriate boundary conditions. A second order Duffing-like amplitude equation for the initially unstable MRI modes is derived. The solutions of that equation exhibit bursty nonlinear oscillations with a constant amplitude that signifies the saturation level of the MRI. Those results are verified by a direct numerical solution of the full nonlinear reduced set of thin disk magnetohydrodynamics equations.

Ultrasound attenuation in ferrofluids.

The absorption of acoustic energy by internal degrees of freedom of short chains is proposed as a new viable mechanism of ultrasound attenuation in ferrofluids. It is demonstrated that even though the volume fraction of the chains may be quite small, such an effect may reach the order of magnitude of viscous damping. In addition, by investigating the statistical properties of dimers in ferrofluids, it is shown that an applied magnetic field modifies the sound attenuation in a highly anisotropic manner. The proposed mechanism provides new insight into the fundamental issue of colloidal response, and, in particular, may lead to its utilization in novel experimental concepts.