Superstatistics and temperature fluctuations

Superstatistics [Beck and Cohen (2003) [1]] is a formalism aimed at describing statistical properties of a generic extensive quantity E in complex out-of-equilibrium systems in terms of a linear superposition of equilibrium canonical distributions. The weight function $P(\beta )$ is argued to be provided by the statistics of the intensive thermodynamic quantity β conjugate to E [Beck (2011) [14]], and therefore is expected to be determined by the spatiotemporal dynamics alone of the system under consideration. In this paper, recalling a previous work [Beck (2006) [21]], I show by examples that, in some cases fulfilling all the conditions for the superstatistics formalism to be applicable, $P(\beta )$ cannot be defined uniquely, but rather depends upon the way the measurement of E is performed.     

Vortex structures in nano-scaled superconducting networks

Using the de Gennes–Alexander equation, we have investigated the stable vortex structures in finite superconducting networks (10 × 10 holes) with disordered wires under an external magnetic field. Vortex structures change gradually with increasing magnetic field. For the network with a disordered wire at the edge, vortices are not pinned disordered hole, but enter into the network at the holes with the disorder. But for the network with two disordered wires, the vortex enters at the hole between two disordered wires. This behavior can be considered as the result of the nonlocality of superconductivity.     

Vortex field structures in a laser with multiply connected aperture

The scheme and operating principle of a new polarizing optical microscope for observing physical fields on object surfaces are described for the first time. New functions of the microscope are achieved because its optical scheme includes a liquid-crystal space-time light modulator, which achieves the contact of the surface under study with a layer of nematic liquid crystal. Examples and prospects of application of this microscope in photonics are considered.     

Spontaneous fluctuations of a temperature filament in a magnetized plasma

This experiment illustrates the spatiotemporal pattern of the fluctuations that spontaneously develop in a magnetized temperature filament whose transverse scale is comparable to the electron skin depth. A high-frequency mode exhibits a striking spiral structure and is identified as a drift-Alfven eigenmode. A low-frequency mode is found to be localized near the center of the filament. It is documented that the fluctuations significantly increase the transport of heat beyond the prediction of classical theory based on Coulomb collisions.     

Vortex fluctuations in the critical Casimir effect of superfluid and superconducting films

Vortex-loop renormalization techniques are used to calculate the magnitude of the critical Casimir forces in superfluid films. The force is found to become appreciable when the size of the thermal vortex loops is comparable to the film thickness, and the results for TT(c). When applied to a high-T(c) superconducting film connected to a bulk sample, the Casimir force causes a voltage difference to appear between the film and the bulk, and estimates show that this may be readily measurable.     

Sound amplitude fluctuations due to a temperature microstructure

The experiments reported in this paper were carried out in a water tank in which a random medium was generated by convective mixing from an array of heaters. An approximate thermodynamic model of the medium was derived. Temperature measurements were made which showed that the temperature microstructure created in this way could be considered as a passive additive of turbulence. Furthermore, it was possible to characterize the random refractive index in terms of a spectral distribution by using an adapted version of a spectrum proposed by Medwin for the upper ocean. By using the adapted Medwin model and the single-scatter theoretical results of Tatarski, theoretical estimates were obtained of the fluctuations of an acoustic signal propagating in this particular medium. Experiments were carried out to measure acoustic signal amplitude fluctuations at frequencies of 9 MHz and 1 MHz. The empirical results were in agreement with the theoretical estimates. Measurements are also reported for the spatial correlation functions of the acoustic signal amplitude fluctuations. The results are discussed in the light of currently available theoretical results.     

Dynamical fluctuations in the hadronic temperature

A density two-point correlation function calculation and a power-spectrum analysis of non-statistical event-by-event fluctuations in the mean transverse momentum at large multiplicityn is performed. Good agreement with the data ofK. Braune et al. is obtained if thep _t-density function of the exponential form in the transverse mass with an event-by-event fluctuating slope is used. The pattern of the fluctuating slope is Gaussian with the mean determined by the data on \(\left\langle {\bar p_t (n)} \right\rangle \) for eachn, and the normalized standard deviation as the only free parameter taken to be 0.68. In thermodynamical models, the slope fluctuations may be interpreted as fluctuations in the temperature of the hadronic system.     

Density correlations induced by temperature fluctuations in a photon gas

The impact of angular temperature variations on the thermodynamic variables and real-space correlation functions of black-body radiation are analyzed. In particular, the effect of temperature fluctuations on the number density and energy density correlations of the cosmic microwave background (CMB) is studied. The angular temperature fluctuations are modeled by an isotropic and homogeneous Gaussian random field, whose autocorrelation function is defined on the unit sphere in momentum space. This temperature correlation function admits an angular Fourier transform which determines the density correlations in real space induced by temperature fluctuations. In the case of the CMB radiation, the multipole coefficients of the angular power spectrum defining the temperature correlation function have been measured by the Planck satellite. The fluctuation-induced perturbation of the equilibrium variables (internal energy, entropy, heat capacity and compressibility) can be quantified in terms of the measured multipole coefficients by expanding the partition function around the equilibrium state in powers of the temperature random field. The real-space density correlations can also be extracted from the measured temperature power spectrum. Both the number density and energy density correlations of the electromagnetic field are long-range, admitting power-law decay; in the case of the energy density correlation, the fluctuation-induced correlation overpowers the isotropic equilibrium correlation in the long-distance limit.     

Thermodynamic fluctuations in two-dimensional degenerate antiferromagnetic structures

A model of a two-dimensional antiferromagnet with an arbitrary anisotropic interaction that allows for degeneracy of the ground state is proposed. The lifting of degeneracy by thermodynamic fluctuations and the accompanying effects are studied by a method of self-consistent calculations of Gaussian angular fluctuations that is asymptotically exact at low temperatures. Fluctuations are shown to lead to collinear ordering of the orientations of magnetic sublattices, an effect that initiates long-range orientational order in systems with anisotropic interaction but retains only short-range order in systems with isotropic short-range interaction. The temperature patterns of the orientational correlators are given for the particular cases of dipole and isotropic short-range interaction models. The nature of the Ising-like behavior of the system is discussed for the case of a strong anisotropy of the correlators, which corresponds to quasi-one-dimensional behavior. Zh. éksp. Teor. Fiz. 111, 669–680 (February 1997)     

Spin fluctuations and high temperature superconductivity

Theory of spin fluctuations for itinerant magnetism and its application to high temperature superconductivity are reviewed. After a brief introduction to the whole subject the developments of the self-consistent renormalization theory of spin fluctuations are summarized with particular emphasis on critical properties at the quantum phase transitions. Most of the anomalous properties in the normal state of high-T_c cuprates are understood as due to the critical behaviours for the two dimensional antiferromagnetic metals. By analysing the nuclear magnetic relaxation rate and the T-linear term of resistivity, the set of parameters to specify the spin fluctuations are determined. It is shown that by using the parameters thus obtained one can describe other quantities as well, e.g. optical conductivity. Then we proceed to the theory of superconductivity by the spin fluctuation mechanism. After some discussion on the weak coupling treatments, the strong coupling theory is reviewed. It is shown that the set of parameters determined by the normal state properties of the high-T _c cuprates just give a transition temperature of the right order of magnitude. Among the parameters, the most sensitive one for T _c is the frequency spread of the spin fluctuations. This fact enables us to present a possible unified picture of the antiferromagnetic spin fluctuation-induced superconductors, including heavy fermion superconductors and organic superconductors. This point of view may be confirmed to a certain extent by microscopic calculations based on the fluctuation exchange approximation for the two-dimensional Hubbard models representing not only the cuprates but also organic and trellis lattice compounds. The review is concluded with some discussions on future problems, e.g. the pseudo spin-gap in the under-doped region.     

LES-CMC simulations of a turbulent bluff-body flame

The large Eddy simulations (LES)-conditional moment closure (CMC) method with detailed chemistry is applied to a bluff-body stabilized flame. Computations of the velocity and mixture fraction fields show good agreement with the experiments. Temperature and major species are well-predicted throughout the flame with the exception of the flow regions in the outer shear layer close to the nozzle where the pure mixing between hot recirculating products and fresh oxidizer cannot be captured. LES-CMC generally improves on results obtained with RANS-CMC and on LES that uses one representative flamelet to model the dependence of reactive species on mixture fraction. Simulated CO mass fractions are generally in good agreement with the experimental data although a 10% overprediction can be found at downstream positions. NO predictions show a distinct improvement over the flamelet approach, however, simulations overpredict NO mass fractions at all downstream locations due to an overprediction of temperature close to the nozzle. The potential of LES-CMC to predict unsteady finite rate effects is demonstrated by the prediction of endothermic—or “flame cooling”—regions close to the neck of the recirculation zone that favours ethylene production via the methane fuel decomposition channel.     

Analysis of daily temperature fluctuations

We study daily temperature fluctuations over more than 50 yr in two places on the globe that are separated by more than 3000 km. We analyze the temperature fluctuations ΔT_i with respect to the mean noon temperature 〈T_i〉 averaged, for each day of the year, over the whole year, ΔT_i = T_i − 〈T_i〉. We find that the ΔT_i are correlated and can be characterized for up to at least 10³ days by a power law correlation with an exponent α ≅ 0.65.     

The distribution function for a subsystem experiencing temperature fluctuations

A nonlinear generalization of the Landau-Lifshitz theory of hydrodynamic fluctuations for the simplest case in which only energy flux and temperature fluctuations are observed is used to derive the distribution function for a subsystem with a fluctuating temperature, which coincides with the Levy distribution taken to be one of the main results of the so-called Tsallis’s nonextensive statistics. It is demonstrated that the same distribution function is obtained from the principle of maximum of information entropy if the latter is provided by Renyi’s entropy, which is an extensive quantity. The obtained distribution function is to be used instead of the Gibbs distribution in constructing the thermodynamics of systems with significant temperature fluctuations.