Ktisis Cyprus University of Technologyhttps://ktisis.cut.ac.cyThe DSpace digital repository system captures, stores, indexes, preserves, and distributes digital research material.Wed, 22 Sep 2021 17:46:38 GMT2021-09-22T17:46:38Z5061Erratum: Physical meaning of temperature in superstatistics (EPL (2020) 130 (30005) DOI: 10.1209/0295-5075/130/30005)https://ktisis.cut.ac.cy/handle/10488/19332Title: Erratum: Physical meaning of temperature in superstatistics (EPL (2020) 130 (30005) DOI: 10.1209/0295-5075/130/30005)
Authors: Gravanis, Elias; Akylas, Evangelos; Livadiotis, George
Fri, 01 May 2020 00:00:00 GMThttps://ktisis.cut.ac.cy/handle/10488/193322020-05-01T00:00:00ZPhysical meaning of temperature in superstatisticshttps://ktisis.cut.ac.cy/handle/10488/19211Title: Physical meaning of temperature in superstatistics
Authors: Gravanis, Elias; Akylas, Evangelos; Livadiotis, George
Abstract: We show that the fluctuating temperature in the superstatistics construction is proportional to the average (arithmetic mean) energy per degree of freedom of the system in the thermodynamic limit. The latter is a fluctuating quantity due to the strong correlation of statistical nature introduced by superstatistics between degrees of freedom. The necessity for scale dependence of the parameters of superstatistics, which can be explicitly realized through applications of superstatistics in isotropic turbulence, is discussed.
Fri, 01 May 2020 00:00:00 GMThttps://ktisis.cut.ac.cy/handle/10488/192112020-05-01T00:00:00ZKappa distributions and isotropic turbulencehttps://ktisis.cut.ac.cy/handle/10488/18542Title: Kappa distributions and isotropic turbulence
Authors: Gravanis, Elias; Akylas, Evangelos; Panagiotou, Constantinos; Livadiotis, George
Abstract: In this work, the two-point probability density function (PDF) for the velocity field of isotropic turbulence is modeled using the kappa distribution and the concept of superstatistics. The PDF consists of a symmetric and an anti-symmetric part, whose symmetry properties follow from the reflection symmetry of isotropic turbulence, and the associated non-trivial conditions are established. The symmetric part is modeled by the kappa distribution. The anti-symmetric part, constructed in the context of superstatistics, is a novel function whose simplest form (called "the minimal model") is solely dictated by the symmetry conditions. We obtain that the ensemble of eddies of size up to a given length r has a temperature parameter given by the second order structure function and a kappa-index related to the second and the third order structure functions. The latter relationship depends on the inverse temperature parameter (gamma) distribution of the superstatistics and it is not specific to the minimal model. Comparison with data from direct numerical simulations (DNS) of turbulence shows that our model is applicable within the dissipation subrange of scales. Also, the derived PDF of the velocity gradient shows excellent agreement with the DNS in six orders of magnitude. Future developments, in the context of superstatistics, are also discussed.
Thu, 07 Nov 2019 00:00:00 GMThttps://ktisis.cut.ac.cy/handle/10488/185422019-11-07T00:00:00ZVelocity Fluctuations in Isotropic Turbulence and Their Statistical Dependencehttps://ktisis.cut.ac.cy/handle/10488/22450Title: Velocity Fluctuations in Isotropic Turbulence and Their Statistical Dependence
Authors: Akylas, Evangelos; Gravanis, Elias; Panagiotou, Constantinos; Livadiotis, George
Abstract: While velocity differences in turbulence have attracted much interest, velocity fluctuations themselves are also fundamental in describing turbulence. Even though there is a large literature on the non-Gaussian nature of the probability density functions (PDFs) of the turbulent velocity gradients, the PDFs of the velocity fluctuations in homogeneous turbulence is often assumed to be Gaussian. In fact, many experiments yield a sub-Gaussian PDF, which has a less pronounced tail than a Gaussian PDF. Systematic examination of grid turbulence has shown that at small distances from the grid, where the turbulence is still developing, the PDF is sub-Gaussian. At intermediate distances, where the turbulence is fully developed, the PDF is Gaussian. At large distances, where the turbulence decays, the PDF is hyper-Gaussian. Turbulence is induced by supplying kinetic energy at some scale L. This energy could be transferred to both the larger and the smaller scales. However, the energy is on average transferred to smaller scales because it is eventually dissipated into heat at the smallest scales, described by the Kolmogorov length η. The energy transfer from largest scales L to smallest scales η consists of many random steps, each of which occurs preferentially between neighboring scales. Τurbulence exhibits significant velocity fluctuations even at scales much larger than the scales of the energy supply. These large-scale fluctuations have many degrees of freedom and are thereby analogous to thermal fluctuations studied in the statistical mechanics. We perform Direct Numerical Simulations (DNS) in the presence of homogenous isotropic turbulence to show that the deviation from the Gaussian behavior is a natural consequence of the steepness of the energy spectrum, and of the properties of the energy-containing eddies. A clear dependence is observed based on the ratio of the integral length varies as a function of the periodic-box size for different Reynolds numbers.
Sun, 01 Dec 2019 00:00:00 GMThttps://ktisis.cut.ac.cy/handle/10488/224502019-12-01T00:00:00ZStochastic dynamics and superstatistics of the many-particle kappa distributionhttps://ktisis.cut.ac.cy/handle/10488/22685Title: Stochastic dynamics and superstatistics of the many-particle kappa distribution
Authors: Gravanis, Elias; Akylas, Evangelos; Livadiotis, George
Abstract: The diffusion of particles with kappa distributed velocities is strongly influenced by statistical correlations. We argue that the consistent way to deduce the diffusion laws of any one degree of freedom is to analyze the simultaneous diffusion of virtually infinite correlated degrees of freedom. This is done by deriving the diffusion laws (I) by utilizing the superstatistics interpretation of the kappa distribution and averaging the usual Brownian motions correlators over the super-ensemble of fluctuating temperatures, (II) through the one degree of freedom Langevin equation, (III) through the many degrees of freedom Langevin equation, calculating the diffusion of any one degree of freedom. It turns out that only the results (I) and (III) agree. The disagreement between (II) and (III) is a striking outcome of the strong correlations between kappa distributed degrees of freedom. The agreement between (I) and (III) shows that the superstatistics is a fundamental interpretation of the kappa distribution. The discrepancy of (II) shows that focusing on a single degree of freedom or particle is inconsistent with a superstatistics interpretation. Derivation (III) explicitly realizes the recent observation by the authors that the mean energy per degree of freedom is the superstatistical fluctuating temperature in a system with a large number of particles. We conclude that superstatistics is intimately related to a system of correlated degrees of freedom (in our case, kappa distributed); one cannot consistently reason with a single degree of freedom.
Sat, 01 May 2021 00:00:00 GMThttps://ktisis.cut.ac.cy/handle/10488/226852021-05-01T00:00:00ZSuperstatistics and isotropic turbulencehttps://ktisis.cut.ac.cy/handle/10488/22703Title: Superstatistics and isotropic turbulence
Authors: Gravanis, Elias; Akylas, Evangelos; Michailides, Constantine; Livadiotis, George
Abstract: In this work, we analyze the capacity of the superstatistics construction to provide modeling of the velocity field probability density functions (PDFs) of isotropic turbulence. Generalizing along the lines of the kappa distribution, superstatistics is understood here as a PDF for the statistical temperature that depends on a single dimensionful parameter and a dimensionless parameter , which both depend on the size of the fluid eddies and the Reynolds number, and possibly on auxiliary dimensionless constants that depend only on the Reynolds number. We show that such superstatistics –in some sense, the simplest class of models– cannot provide PDFs for scales outside the dissipation subrange for the currently accessible Reynolds numbers in Direct Numerical Simulations (DNS). The obstruction results from realizability constraints and an associated bound, and is related to the flatness factor of the velocity derivative distribution. Greater values of the flatness extend the applicability of superstatistics to larger scales. We argue that phenomenologically effective superstatistics models will require a value of flatness F25 or larger in order to cover the inertial subrange scales. The argument is assisted by constructing and analyzing a family of models which derive from modifying the gamma distribution in the regime of large statistical temperatures and nearly realize the realizability bound.
Thu, 01 Apr 2021 00:00:00 GMThttps://ktisis.cut.ac.cy/handle/10488/227032021-04-01T00:00:00Z