Existence of Chandrasekhar's limit in generalized uncertainty white dwarfs.

The existence of Chandrasekhar's limit has played various decisive roles in astronomical observations for many decades. However, various recent theoretical investigations suggest that gravitational collapse of white dwarfs is withheld for arbitrarily high masses beyond Chandrasekhar's limit if the equation of state incorporates the effect of quantum gravity via the generalized uncertainty principle. There have been a few attempts to restore the Chandrasekhar limit but they are found to be inadequate. In this paper, we rigorously resolve this problem by analysing the dynamical instability in general relativity. We confirm the existence of Chandrasekhar's limit as well as stable mass-radius curves that behave consistently with astronomical observations. Moreover, this stability analysis suggests gravitational collapse beyond the Chandrasekhar limit signifying the possibility of compact objects denser than white dwarfs.

Conserved nonlocal dynamics and critical behavior of uranium ferromagnetic superconductors.

A recent theoretical study [Phys. Rev. Lett. 112, 037202 (2014)10.1103/PhysRevLett.112.037202] has revealed that systems such as uranium ferromagnetic superconductors obey conserved dynamics. To capture the critical behavior near the paramagnetic to ferromagnetic phase transition of these compounds, we study the conserved critical dynamics of a nonlocal Ginzburg-Landau model. A dynamic renormalization-group calculation at one-loop order yields the critical indices in the leading order of ε=d_{c}-d, where d_{c}=4-2ρ is the upper critical dimension, with ρ an exponent in the nonlocal interaction. The predicted static critical exponents are found to be comparable with the available experimentally observed critical exponents for strongly uniaxial uranium ferromagnetic superconductors. The corresponding dynamic exponent z and linewidth exponent w are found to be z=4-ρε/4+O(ε^{2}) and w=1+ρ+3ε/4+O(ε^{2}).

Critical dynamics of a nonlocal model and critical behavior of perovskite manganites.

We investigate the nonconserved critical dynamics of a nonlocal model Hamiltonian incorporating screened long-range interactions in the quartic term. Employing dynamic renormalization group analysis at one-loop order, we calculate the dynamic critical exponent z=2+εf_{1}(σ,κ,n)+O(ε^{2}) and the linewidth exponent w=-σ+εf_{2}(σ,κ,n)+O(ε^{2}) in the leading order of ε, where ε=4-d+2σ, with d the space dimension, n the number of components in the order parameter, and σ and κ the parameters coming from the nonlocal interaction term. The resulting values of linewidth exponent w for a wide range of σ is found to be in good agreement with the existing experimental estimates from spin relaxation measurements in perovskite manganite samples.

Nonlocal quartic interactions and universality classes in perovskite manganites.

A modified Ginzburg-Landau model with a screened nonlocal interaction in the quartic term is treated via Wilson's renormalization-group scheme at one-loop order to explore the critical behavior of the paramagnetic-to-ferromagnetic phase transition in perovskite manganites. We find the Fisher exponent η to be O(ε) and the correlation exponent to be ν=1/2+O(ε) through epsilon expansion in the parameter ε=d(c)-d, where d is the space dimension, d(c)=4+2σ is the upper critical dimension, and σ is a parameter coming from the nonlocal interaction in the model Hamiltonian. The ensuing critical exponents in three dimensions for different values of σ compare well with various existing experimental estimates for perovskite manganites with various doping levels. This suggests that the nonlocal model Hamiltonian contains a wide variety of such universality classes.

Skewness in (1+1)-dimensional Kardar-Parisi-Zhang-type growth.

We use the (1+1)-dimensional Kardar-Parisi-Zhang equation driven by a Gaussian white noise and employ the dynamic renormalization-group of Yakhot and Orszag without rescaling [J. Sci. Comput. 1, 3 (1986)]. Hence we calculate the second- and third-order moments of height distribution using the diagrammatic method in the large-scale and long-time limits. The moments so calculated lead to the value S=0.3237 for the skewness. This value is comparable with numerical and experimental estimates.

Spectral calculations in stably stratified turbulence.

We perform a Leslie-type perturbative treatment on stably stratified turbulence with Boussinesq approximation, where the buoyancy terms in the corresponding dynamical equations are treated as perturbations against the isotropic background fields. Thus we calculate the anisotropic corrections to various correlation functions, namely, velocity-velocity, temperature-temperature, and velocity-temperature correlations, up to second order in this scheme. We find that the prefactors associated with the anisotropic corrections depend on the energy flux, scalar flux, Kolmogorov constant, Batchelor constant, and the eddy-damping amplitudes. The correlation functions further yield the anisotropic parts of the energy and mean-square temperature spectra as k(-3) and the anisotropic buoyancy spectrum as k(-7/3). The resulting angle-dependent energy density is found to be concentrated predominantly around the vertical wave vector signifying layered structures in the physical space.

Perturbative evaluation of universal numbers in homogeneous shear turbulence.

We employ Leslie's perturbation scheme coupled with renormalization group calculations to obtain the anisotropic velocity correlation tensor in the inertial range of homogeneous shear turbulence. Hence we evaluate two universal numbers associated with the anisotropic part of the equal-time correlation tensor in the leading order of the perturbative scheme. Our theoretical results for these universal numbers are found to be in fairly good agreement with experimental values as well as estimates coming from direct numerical simulations.

Heisenberg approximation in passive scalar turbulence.

We use Heisenberg's approximation to derive analytic expressions for eddy viscosity and eddy diffusivity from the transfer integrals of energy and mean-square scalar arising from the Navier-Stokes and passive scalar dynamics. In the same scheme, we evaluate the flux integrals for the transports of energy and mean-square scalar. These procedures allow for the evaluation of relevant amplitude ratios, from which we calculate the universal numbers, namely, Batchelor constant B, Kolmogorov constant C, and turbulent Prandtl number σ, under two different schemes (with and without ε expansion). Our results are comparable with existing theoretical, numerical, and experimental values. As a byproduct, we obtain a relation between C, B, and σ, namely, B=σ C. To compare our results with the experimental values, we calculate Batchelor constant in one dimension (B'). Within the same framework, we also see that with increasing values of space dimension d, the Prandtl number σ increases and approaches unity, while the Kolmogorov constant C and Batchelor constant B approach very close to each other. For large space dimensions, we find the asymptotic B=B(0)d(1/3), and evaluate B(0).

Infrared decimation renormalization-group calculations for two-dimensional test-field turbulence.

We perform a decimation of modes starting from the infrared end of wave numbers on the randomly stirred test-field dynamics augmented by linear (Rayleigh) drag terms to model turbulence in two dimensions. A renormalization-group scheme shows relevant corrections to the drag coefficients and the existence of ultraviolet attractive fixed points, facilitating calculations of the universal numbers in both the energy and the enstrophy regimes. Marginal behavior in the enstrophy range yields logarithmic renormalization. We make a detailed comparison of the renormalization-group results with the numerical and analytical results following from Kraichnan's test-field closure.

Perturbative evaluation of Kolmogorov constant in a self-consistent model of fluid turbulence.

The response integrals of the almost Markovian-Galelian invariant test-field model (TFM) of Kraichnan, generalized to d dimensions, are analyzed. They are found to be both ultraviolet and infrared finite in the range 0