Emergence of a Non-Van der Waals Magnetic Phase in a Van der Waals Ferromagnet.

Manipulation of long-range order in 2D van der Waals (vdW) magnetic materials (e.g., CrI3 , CrSiTe3 ,etc.), exfoliated in few-atomic layer, can be achieved via application of electric field, mechanical-constraint, interface engineering, or even by chemical substitution/doping. Usually, active surface oxidation due to the exposure in the ambient condition and hydrolysis in the presence of water/moisture causes degradation in magnetic nanosheets that, in turn, affects the nanoelectronic /spintronic device performance. Counterintuitively, the current study reveals that exposure to the air at ambient atmosphere results in advent of a stable nonlayered secondary ferromagnetic phase in the form of Cr2 Te3 (TC2 ≈160 K) in the parent vdW magnetic semiconductor Cr2 Ge2 Te6 (TC1 ≈69 K). The coexistence of the two ferromagnetic phases in the time elapsed bulk crystal is confirmed through systematic investigation of crystal structure along with detailed dc/ac magnetic susceptibility, specific heat, and magneto-transport measurement. To capture the concurrence of the two ferromagnetic phases in a single material, Ginzburg-Landau theory with two independent order parameters (as magnetization) with a coupling term can be introduced. In contrast to the rather common poor environmental stability of the vdW magnets, the results open possibilities of finding air-stable novel materials having multiple magnetic phases.

A randomly stirred model for Bolgiano-Obukhov scaling in turbulence in a stably stratified fluid.

A randomly stirred model, akin to the one used by DeDominicis and Martin for homogeneous isotropic turbulence, is introduced to study Bolgiano-Obukhov scaling in fully developed turbulence in a stably stratified fluid. The energy spectrum E(k), where k is a wavevector in the inertial range, is expected to show the Bolgiano-Obukhov scaling at a large Richardson number Ri (a measure of the stratification). We find that the energy spectrum is anisotropic. Averaging over the directions of the wavevector, we find [Formula: see text], where εθ is the constant energy transfer rate across wavenumbers with very little contribution coming from the kinetic energy flux. The constant K0 is estimated to be of O(0.1) as opposed to the Kolmogorov constant, which is O(1). Further for a pure Bolgiano-Obukhov scaling, the model requires that the large distance 'stirring' effects dominate in the heat diffusion and be small in the velocity dynamics. These could be reasons why the Bolgiano-Obukhov scaling is difficult to observe both numerically and experimentally. This article is part of the theme issue 'Scaling the turbulence edifice (part 2)'.

Nonlinear parametric oscillator: A tool for probing quantum fluctuations.

Nanomechanical oscillators have, over the last few years, started probing regimes where quantum fluctuations are important. Here we consider a nonlinear parametric oscillator in the quantum domain. We show that in the classical subharmonic resonance zone, the quantum fluctuations are finite but greatly magnified depending on the strength of the nonlinear coupling. This should make such oscillators useful in probing quantum fluctuations.

Kolmogorov or Bolgiano-Obukhov scaling: Universal energy spectra in stably stratified turbulent fluids.

We set up the scaling theory for stably stratified turbulent fluids. For a system having infinite extent in the horizontal directions, but with a finite width in the vertical direction, this theory predicts that the inertial range can display three possible scaling behavior, which are essentially parametrized by the buoyancy frequency N, or dimensionless horizontal Froude number F_{h}, and the vertical length scale l_{v} that sets the scale of variation of the velocity field in the vertical direction for a fixed Reynolds number. For very low N or very high Re_{b} or F_{h}, and with l_{v}≫l_{h}, the typical horizontal length scale, buoyancy forces are irrelevant and hence, unsurprisingly, the kinetic energy spectra show the well-known K41 scaling in the inertial range. In this regime, the local temperature behaves as a passively advected scalar, without any effect on the flow fields. For intermediate ranges of values of N,F_{h}∼O(1), corresponding to moderate stratification, buoyancy forces are important enough to affect the scaling. This leads to the Bolgiano-Obukhov scaling which is isotropic, when l_{v}∼l_{h}. Finally, for very large N, corresponding to strong stratification, together with a very small l_{v}, the inertial-range flow fields effectively two-dimensionalize. The kinetic energy spectra are predicted to be anisotropic with only the horizontal part of the kinetic energy spectra following the K41 scaling. This suggests an intriguing re-entrant K41 scaling, as a function of stratification, for the horizontal components of the velocity field in this regime. The scaling theory further predicts the scaling of the thermal energy in each of these three scaling regimes. Our theory can be tested in large-scale simulations and appropriate laboratory-based experiments.

Frequency spectra of turbulent thermal convection with uniform rotation.

The frequency spectra of the entropy and kinetic energy along with the power spectrum of the thermal flux are computed from direct numerical simulations for turbulent Rayleigh-Bénard convection with uniform rotation about a vertical axis in low-Prandtl-number fluids (Pr<0.6). Simulations are done for convective Rossby numbers Ro≥0.2. The temporal fluctuations of these global quantities show two scaling regimes: (i) ω(-2) at higher frequencies for all values of Ro and (ii) ω(-γ1) at intermediate frequencies with γ1≈4 for Ro>1, while 4<γ1<6.6 for 0.2≤Ro<1.

Entropy and energy spectra in low-Prandtl-number convection with rotation.

We present results for entropy and kinetic energy spectra computed from direct numerical simulations for low-Prandtl-number (Pr < 1) turbulent flow in Rayleigh-Bénard convection with uniform rotation about a vertical axis. The simulations are performed in a three-dimensional periodic box for a range of the Taylor number (0 ≤ Ta ≤ 10(8)) and reduced Rayleigh number r = Ra/Ra(∘)(Ta,Pr) (1.0 × 10(2) ≤ r ≤ 5.0 × 10(3)). The Rossby number Ro varies in the range 1.34 ≤ Ro ≤ 73. The entropy spectrum E(θ)(k) shows bisplitting into two branches for lower values of wave number k. The entropy in the lower branch scales with k as k(-1.4 ± 0.1) for r>10(3) for the rotation rates considered here. The entropy in the upper branch also shows scaling behavior with k, but the scaling exponent decreases with increasing Ta for all r. The energy spectrum E(v)(k) is also found to scale with the wave number k as k(-1.4 ± 0.1) for r>10(3). The scaling exponent for the energy spectrum and the lower branch of the entropy spectrum vary between -1.7 and -2.4 for lower values of r (<10(3)). We also provide some simple arguments based on the variation of the Kolmogorov picture to support the results of simulations.

On noise induced Poincaré-Andronov-Hopf bifurcation.

It has been numerically seen that noise introduces stable well-defined oscillatory state in a system with unstable limit cycles resulting from subcritical Poincaré-Andronov-Hopf (or simply Hopf) bifurcation. This phenomenon is analogous to the well known stochastic resonance in the sense that it effectively converts noise into useful energy. Herein, we clearly explain how noise induced imperfection in the bifurcation is a generic reason for such a phenomenon to occur and provide explicit analytical calculations in order to explain the typical square-root dependence of the oscillations' amplitude on the noise level below a certain threshold value. Also, we argue that the noise can bring forth oscillations in average sense even in the absence of a limit cycle. Thus, we bring forward the inherent general mechanism of the noise induced Hopf bifurcation naturally realisable across disciplines.

Fluctuations near the critical micelle concentration. II. Ultrasonic attenuation spectra and scaling.

Based on a thermodynamic model of amphiphile solutions derived in the first part of the paper, the ultrasonic attenuation of such systems has been considered theoretically, including fluctuations of local concentrations and micelle sizes. At amphiphile concentrations smaller than the critical micelle concentration (cmc), scaling behavior in terms of the concentration distance to the cmc is predicted by theory, in fair agreement with experimental evidence. The scaling function in the sound attenuation below the cmc reveals the unsymmetric broadening in the spectra that clearly emerges from measurements when approaching the cmc. The shape of the scaling function corresponds to the experimental spectra of solutions with comparatively large cmc as well as with the relaxation spectral function of the unifying model of non-critical concentration fluctuations. Above the cmc, an additional relaxation term is predicted in correspondence with the Landau-Khalatnikov term in the sound attenuation of superfluid helium. This term is difficult to verify by measurements because, in the relevant frequency range, other processes may also contribute the ultrasonic attenuation spectra.

Fluctuations near the critical micelle concentration. I. Premicellar aggregation, relaxation rate, and isentropic compressibility.

A thermodynamic model including fluctuations of micelle sizes has been derived to describe solution properties of amphiphile systems close to the critical micelle concentration. Owing to the consideration of an affinity field in the free energy of the system, the model is capable of featuring experimental findings that are incorrectly reflected by established theories of the micelle formation and disintegration kinetics. In conformity with experiments, the thermodynamic theory predicts the onset of micellar structure formation already at amphiphile concentrations below the critical micelle concentration. It also applies well for the distinctive concentration dependency of the relaxation rate of monomer exchange and likewise for the sound velocity and thus the isentropic compressibility variations with concentration. Comparison of the theoretical predictions is made with special emphasis to short-chain surfactant systems, which allowed for reliable measurements in the range below the critical micelle concentration.

Fluctuating hydrodynamics and turbulence in a rotating fluid: universal properties.

We analyze the statistical properties of three-dimensional (3D) turbulence in a rotating fluid. To this end we introduce a generating functional to study the statistical properties of the velocity field v. We obtain the master equation from the Navier-Stokes equation in a rotating frame and thence a set of exact hierarchical equations for the velocity structure functions for arbitrary angular velocity Ω. In particular we obtain the differential forms for the analogs of the well-known von Karman-Howarth relation for 3D fluid turbulence. We examine their behavior in the limit of large rotation. Our results clearly suggest dissimilar statistical behavior and scaling along directions parallel and perpendicular to Ω. The hierarchical relations yield strong evidence that the nature of the flows for large rotation is not identical to pure two-dimensional flows. To complement these results, by using an effective model in the small-Ω limit, within a one-loop approximation, we show that the equal-time correlation of the velocity components parallel to Ω displays Kolmogorov scaling q(-5/3) wherein as for all other components, the equal-time correlators scale as q(-3) in the inertial range where q is a wave vector in 3D. Our results are generally testable in experiments and/or direct numerical simulations of the Navier-Stokes equation in a rotating frame.

Turbulence in rotating Rayleigh-Bénard convection in low-Prandtl-number fluids.

The heat flux in rotating Rayleigh-Bénard convection in a fluid of Prandtl number Pr=0.1 enclosed between free-slip top and bottom boundaries is investigated using direct numerical simulation in a wide range of Rayleigh numbers (10(4)≤Ra≤10(8)) and Taylor numbers (0≤Ta≤10(8)). The Nusselt number Nu scales with the Rayleigh number Ra as Ra(ß) with ß=2/7 for values of Nu greater than a critical value Nu(c), which occurs for Ta/Ra∼1. The exponent ß is not universal for Nu1) but a function of Ta showing a minimum for some intermediate value of Ta. The critical Nusselt number Nu(c) and the corresponding critical Rossby number Ro(c) scale with Ta as Ta(0.277±0.001) and Ta(-0.015±0.003), respectively.

Anomalous dynamics of solutions of nonionic micelles in water.

In addition to a previous theory on the coupling between noncritical concentration fluctuations and elementary chemical processes, an alternative treatment is presented which allows for a closed-form solution of ultrasonic attenuation spectra. This analytical form is first compared to a previous model and also to experimental spectra of binary liquid mixtures. The broadening of the spectra is briefly discussed in terms of molecular interactions and of the ratio of the relaxation times of the chemical equilibrium and of the diffusion of fluctuations. Extension of the theoretical model to apply to nonionic micelle solutions reveals that a flat contribution in the experimental spectra of such quasi-ternary systems may be simply due to different structure factors of the monomers and the micelles. Some exceptional findings for polyethylene glycol monoalkyl ether/water mixtures are discussed in light of the theory.

Work probability distribution and tossing a biased coin.

We show that the rare events present in dissipated work that enters Jarzynski equality, when mapped appropriately to the phenomenon of large deviations found in a biased coin toss, are enough to yield a quantitative work probability distribution for the Jarzynski equality. This allows us to propose a recipe for constructing work probability distribution independent of the details of any relevant system. The underlying framework, developed herein, is expected to be of use in modeling other physical phenomena where rare events play an important role.

Bulk viscosity universality and scaling function near the binary liquid consolute point.

The hydrodynamical equations and the notion of a frequency dependent complex specific heat near the critical point of binary liquids are used to obtain an expression for the low-frequency bulk viscosity. In this way the interrelations between different theoretical models, treating the critical sound attenuation from either a specific heat or a bulk viscosity approach, are made evident. The general structure of the bulk viscosity relation agrees with that of Onuki [Phys. Rev. E 55, 403 (1997)] but a universal number emerges only if a normalization to the critical point value is done.

Large deviation theory for coin tossing and turbulence.

Large deviations play a significant role in many branches of nonequilibrium statistical physics. They are difficult to handle because their effects, though small, are not amenable to perturbation theory. Even the Gaussian model, which is the usual initial step for most perturbation theories, fails to be a starting point while discussing intermittency in fluid turbulence, where large deviations dominate. Our contention is: in the large deviation theory, the central role is played by the distribution associated with the tossing of a coin and the simple coin toss is the "Gaussian model" of problems where rare events play significant role. We illustrate this by applying it to calculate the multifractal exponents of the order structure factors in fully developed turbulence.

The phase-modulated logistic map.

We study the logistic mapping with the nonlinearity parameter varied through a delayed feedback mechanism. This history dependent modulation through a phaselike variable offers an enhanced possibility for stabilization of periodic dynamics. Study of the system as a function of nonlinearity and modulation parameters reveals new phenomena: In addition to period-doubling and tangent bifurcations, there can be bifurcations where the period increases by unity. These are extensions of crises that arise in nonlinear dynamical systems. Periodic orbits in this system can be systematized via the kneading theory, which in the present case extends the analysis of Metropolis, Stein, and Stein for unimodal maps.

Shear thinning of a critical viscoelastic fluid.

The frequency and shear dependent critical viscosity at a correlation length xi= kappa(-1) has the form eta= eta(0) kappa(- x(eta) ) G ( z(1) , z(2) ) , where z(1) and z(2) are the independent dimensionless numbers in the problem defined as z(1) =-iomega/2 Gamma(0) kappa(3) and z(2) =-iomega/2 Gamma(0) kappa(3)(c) . The decay rate of critical fluctuations of correlation length kappa(-1) is Gamma(0) kappa(3) and k(c) is the effective wave number for which Gamma(0) k(3)(c) =S , the shear rate. The function G ( z(1) , z(2) ) is calculated in a one-loop self-consistent theory.

Critical viscosity exponent for classical fluids.

A self-consistent mode-coupling calculation of the critical viscosity exponent z(eta) for classical fluids is performed by including the memory effect and the vertex corrections. The incorporation of the memory effect is through a self-consistency procedure that evaluates the order parameter and shear momentum relaxation rates at nonzero frequencies, thereby taking their frequency dependence into account. This approach offers considerable simplification and efficiency in the calculation. The vertex corrections are also demonstrated to have significant effects on the numerical value for the critical viscosity exponent, in contrast to some previous theoretical work which indicated that the vertex corrections tend to cancel out from the final result. By carrying out all of the integrations analytically, we have succeeded in tracing the origin of this discrepancy to an error in earlier work. We provide a thorough treatment of the two-term epsilon expansion, as well as a complete three-dimensional analysis of the fluctuating order-parameter and transverse hydrodynamic modes. The study of the interactions of these modes is carried out to high order so as to arrive at z(eta) = 0.0679+/-0.0007 for comparison with the experimentally observed value, 0.0690+/-0.0006 .

Scaling function for the critical diffusion coefficient of a critical fluid in a finite geometry.

The long-wavelength diffusion coefficient of a critical fluid confined between two parallel plates, separated by a distance L, is strongly affected by the finite size. Finite size scaling leads us to expect that the vanishing of the diffusion coefficient as xi(-1) for xi<>L. We show that this is not strictly true. There is a logarithmic scaling violation. We construct a Kawasaki-like scaling function that connects the thermodynamic regime to the extreme critical (xi>>L) regime.

Critical viscosity exponent for fluids: effect of the higher loops.

We arrange the loopwise perturbation theory for the critical viscosity exponent x(eta), which happens to be very small, as a power series in x(eta) itself, and argue that the effect of loops beyond two is negligible. We claim that the critical viscosity exponent should be very closely approximated by x(eta)=(8/15pi(2))(1+8/3pi(2)) approximately 0.0685.