Developing homogeneous isotropic turbulence

We investigate the self-similar evolution of the transient energy spectrum, which precedes the establishment of the Kolmogorov spectrum in homogeneous isotropic turbulence in three dimensions using the EDQNM closure model. The transient evolution exhibits self-similarity of the second kind and has a non-trivial dynamical scaling exponent, which results in the transient spectrum having a scaling that is steeper than the Kolmogorov k^−5/3 spectrum. Attempts to detect a similar phenomenon in DNS data are inconclusive, owing to the limited range of scales available.     

Interaction between parabolic pulses in a dispersion-decreasing fiber

The properties of the self-similar parabolic pulses interaction in a dispersion-decreasing optical fiber with normal group-velocity dispersion are firstly investigated in our paper. We find that two parabolic pulses separated by a time-delay create oscillation with a sinusoidal fit at the beginning of their overlap, and then further evolve into a train of asymptotic dark solitons. Additionally, outside the overlap regime, the evolution is equal to a single pulse’ propagating behavior. The chirp after interaction in the parabolic pulses still allows for efficient and high-quality pulse compression.     

On the extended self similarity and the form function

In this work some investigations on the properties of the so calledform function which characterizes the scaling behavior of the small scales fluctuations in a turbulent flow are presented. The present analysis is based on previous experimental measurements in homogeneous and non-homogeneous grid-generated turbulence at low Re. The universality properties of the form function are investigated in the frame of the Extended Self Similarity (ESS) form of scaling.

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Sommario Nel presente lavoro viene presentato uno studio riguardante le proprietà della cosiddetta funzione di forma che caratterizza le leggi di scala delle fluttuazioni di velocità in un flusso turbolento. L'analisi é basata su precedenti misure sperimentali effettuate in flussi turbolenti generati da griglie a bassi Re ed in condizioni omogenee e non omogenee. Le proprietá di universalitá della funzione di forma sono studiate nell'ambito della cosiddetta Extended Self-Similarity.

     

Selbstähnlichkeit am Beispiel des Aggregationsprozesses von Amphiphilen

The micelle aggregation-process of amphiphiles is described under the viewpoint of self-similarity nearby the critical point. The results allow a deeper insight in the nature of the critical micelle concentration.

     

Large deviations for local time fractional Brownian motion and applications

Let be a fractional Brownian motion of Hurst index H∈(0,1) with values in R, and let be the local time process at zero of a strictly stable Lévy process of index 1<α?2 independent of WH. The α-stable local time fractional Brownian motion is defined by ZH(t)=WH(Lt). The process ZH is self-similar with self-similarity index and is related to the scaling limit of a continuous time random walk with heavy-tailed waiting times between jumps [P. Becker-Kern, M.M. Meerschaert, H.P. Scheffler, Limit theorems for coupled continuous time random walks, Ann. Probab. 32 (2004) 730-756; M.M. Meerschaert, H.P. Scheffler, Limit theorems for continuous time random walks with infinite mean waiting times, J. Appl. Probab. 41 (2004) 623-638]. However, ZH does not have stationary increments and is non-Gaussian. In this paper we establish large deviation results for the process ZH. As applications we derive upper bounds for the uniform modulus of continuity and the laws of the iterated logarithm for ZH.     

Strong convergence towards homogeneous cooling states for dissipative Maxwell models

We show the propagation of regularity, uniformly in time, for the scaled solutions of the inelastic Maxwell model for small inelasticity. This result together with the weak convergence towards the homogeneous cooling state present in the literature implies the strong convergence in Sobolev norms and in the L¹ norm towards it depending on the regularity of the initial data. The strategy of the proof is based on a precise control of the growth of the Fisher information for the inelastic Boltzmann equation. Moreover, as an application we obtain a bound in the L¹ distance between the homogeneous cooling state and the corresponding Maxwellian distribution vanishing as the inelasticity goes to zero.     

Small and Large Scale Asymptotics of some Lévy Stochastic Integrals

We provide general conditions for normalized, time-scaled stochastic integrals of independently scattered, Lévy random measures to converge to a limit. These integrals appear in many applied problems, for example, in connection to models for Internet traffic, where both large scale and small scale asymptotics are considered. Our result is a handy tool for checking such convergence. Numerous examples are provided as illustration. Somewhat surprisingly, there are examples where rescaling towards large times scales yields a Gaussian limit and where rescaling towards small time scales yields an infinite variance stable limit, and there are examples where the opposite occurs: a Gaussian limit appears when one converges towards small time scales and an infinite variance stable limit occurs when one converges towards large time scales.      

Structural fluctuation of dimers on Ge(0 0 1) surface near transition temperature

The structural fluctuation of the orientational arrangement of buckled dimers on a Ge(0 0 1) surface near the transition temperature of the order-disorder phase transition is investigated by time-resolving dynamical Monte Carlo simulations. STM images averaged in a finite period are derived from the simulation. The coexistence of the c(4 × 2) and the apparent (2 × 1) domains in the STM images observed by experiments is reproduced in the simulated STM images. We show that the coexistence on the Ge(0 0 1) surface can be attributed to the critical slowing down near the transition temperature.     

The Spectrum of a Family of Fourth-Order Nonlinear Diffusions Near the Global Attractor

The thin film and quantum drift diffusion equations belong to a fourth-order family of evolution equations proposed in [21 Denzler , J. , McCann , R.J. ( 2008 ). Nonlinear diffusion from a delocalized source: a fine self-similarity, time reversal, and nonradial focusing geometries . Ann. Inst. H. Poincaré Anal. Non Linéaire 25 : 865 – 888 .[Crossref], [Web of Science ®] , [Google Scholar]] to be analogous to the (second-order) porous medium family. They are 2-Wasserstein (=d ₂) gradient flows of the generalized Fisher information I(v) just as the porous medium family was shown to be the d ₂ gradient flow of the generalized entropy E(v) by Otto [41 Otto , F. ( 2001 ). The geometry of dissipative evolution equations: The porous medium equation . Comm. Partial Diff. Eqs. 26 : 101 – 174 .[Taylor &; Francis Online], [Web of Science ®] , [Google Scholar]]. The identity aI(v) = bE(v) + |? _{d 2} E(v)|²/2 implies a Hess _{d 2} I(v _*) = Hess _{d 2} E(v _*)(b + Hess _{d 2} E(v _*)) formally, when the equation is rescaled and linearized around the resulting self-similar critical profile v _*. We couple this relation with the diagonalization of Hess _{d 2} E(v _*) for the porous medium flow computed in [46 Seis , C. ( 2014 ). Long-time asymptotics for the porous medium equation: The spectrum of the linearized operator . J. Diff. Eqs. 256 : 1191 – 1223 .[Crossref], [Web of Science ®] , [Google Scholar]]. This yields information about the leading- and higher-order asymptotics of the equation on R ^N which—outside of special cases—was inaccessible previously.     

Numerical simulations of compressible mixing layers with a discontinuous Galerkin method

Discontinuous Galerkin(DG) method is known to have several advantages for flow simulations,in particular,in fiexible accuracy management and adaptability to mesh refinement. In the present work,the DG method is developed for numerical simulations of both temporally and spatially developing mixing layers. For the temporally developing mixing layer,both the instantaneous fiow field and time evolution of momentum thickness agree very well with the previous results. Shocklets are observed at higher convective Mach numbers and the vortex paring manner is changed for high compressibility. For the spatially developing mixing layer,large-scale coherent structures and self-similar behavior for mean profiles are investigated. The instantaneous fiow field for a three-dimensional compressible mixing layer is also reported,which shows the development of largescale coherent structures in the streamwise direction. All numerical results suggest that the DG method is effective in performing accurate numerical simulations for compressible shear fiows.