Simulations of turbulent asymptotic suction boundary layers

A series of large-eddy simulations of a turbulent asymptotic suction boundary layer (TASBL) was performed in a periodic domain, on which uniform suction was applied over a flat plate. Three Reynolds numbers (defined as ratio of free-stream and suction velocity) of Re = 333, 400 and 500 and a variety of domain sizes were considered in temporal simulations in order to investigate the turbulence statistics, the importance of the computational domain size, the arising flow structures as well as temporal development length required to achieve the asymptotic state. The effect of these two important parameters was assessed in terms of their influence on integral quantities, mean velocity, Reynolds stresses, higher order statistics, amplitude modulation and spectral maps. While the near-wall region up to the buffer region appears to scale irrespective of Re and domain size, the parameters of the logarithmic law (i.e. von Kármán and additive coefficient) decrease with increasing Re, while the wake strength decreases with increasing spanwise domain size and vanishes entirely once the spanwise domain size exceeds approximately two boundary-layer thicknesses irrespective of Re. The wake strength also reduces with increasing simulation time. The asymptotic state of the TASBL is characterised by surprisingly large friction Reynolds numbers and inherits features of wall turbulence at numerically high Re. Compared to a turbulent boundary layer (TBL) or a channel flow without suction, the components of the Reynolds-stress tensor are overall reduced, but exhibit a logarithmic increase with decreasing suction rates, i.e. increasing Re. At the same time, the anisotropy is increased compared to canonical wall-bounded flows without suction. The reduced amplitudes in turbulence quantities are discussed in light of the amplitude modulation due to the weakened larger outer structures. The inner peak in the spectral maps is shifted to higher wavelength and the strength of the outer peak is much less than for TBLs. An additional spatial simulation was performed, in order to relate the simulation results to wind tunnel experiments, which – in accordance with the results from the temporal simulation – indicate that a truly TASBL is practically impossible to realise in a wind tunnel. Our unique data set agrees qualitatively with existing literature results for both numerical and experimental studies, and at the same time sheds light on the fact why the asymptotic state could not be established in a wind tunnel experiment, viz. because experimental studies resemble our simulation results from too small simulation boxes or insufficient development times.     

Tails of the density of states of two‐dimensional Dirac fermions

The density of states of Dirac fermions with a random mass on a two‐dimensional lattice is considered. We give the explicit asymptotic form of the single‐electron density of states as a function of both energy and (average) Dirac mass, in the regime where all states are localized. We make use of a weak‐disorder expansion in the parameter g/m², where g is the strength of disorder and m the average Dirac mass for the case in which the evaluation of the (supersymmetric) integrals corresponds to non‐uniform solutions of the saddle point equation. The resulting density of states has tails which deviate from the typical pure Gaussian form by an analytic prefactor.     

Energy fluctuations of thermodynamic systems: Higher moments

Accounts of the energy fluctuations of a thermodynamic system described by a canonical ensemble usually only deal with the second and occasionally with the third moment. This paper examines thenth moment for general values ofn, with particular emphasis on the asymptotic limits in which eithern or the particle numberN or both become large.     

Effects of the quantization ambiguities on the Big Bounce dynamics

In this paper, we investigate dynamics of the modified loop quantum cosmology models using dynamical systems methods. Modifications considered come from the choice of the different field strength operator F̂ and result in different forms of the effective Hamiltonian. Such an ambiguity of the choice of this expression from some class of functions is allowed in the framework of loop quantization. Our main goal is to show how such modifications can influence the bouncing universe scenario in the loop quantum cosmology. In effective models considered we classify all evolutional paths for all admissible initial conditions. The dynamics is reduced to the form of a dynamical system of the Newtonian type on a two-dimensional phase plane. These models are equivalent dynamically to the FRW models with the decaying effective cosmological term parameterized by the canonical variable p (or by the scale factor a). We demonstrate that the evolutional scenario depends on the geometrical constant parameter Λ as well as the model parameter n. We find that for the positive cosmological constant there is a class of oscillating models without the initial and final singularities. The new phenomenon is the appearance of curvature singularities for the finite values of the scale factor, but we find that for the positive cosmological constant these singularities can be avoided. The values of the parameter n and the cosmological constant differentiate asymptotic states of the evolution. For the positive cosmological constant the evolution begins at the asymptotic state in the past represented by the de Sitter contracting (deS₋) spacetime or the static Einstein universe H = 0 or H =  − ∞ state and reaches the de Sitter expanding state (deS₊), the state H = 0 or H =  + ∞ state. In the case of the negative cosmological constant we obtain the past and future asymptotic states as the Einstein static universes.     

On mean flow universality of turbulent wall flows. II. Asymptotic flow analysis

Understanding of the structure of turbulent flows at extreme Reynolds numbers (Re) is relevant because of several reasons: almost all turbulence theories are only valid in the high Re limit, and most turbulent flows of practical relevance are characterized by very high Re. Specific questions about wall-bounded turbulent flows at extreme Re concern the asymptotic laws of the mean velocity and turbulence statistics, their universality, the convergence of statistics towards their asymptotic profiles, and the overall physical flow organization. In extension of recent studies focusing on the mean flow at moderate and relatively high Re, the latter questions are addressed with respect to three canonical wall-bounded flows (channel flow, pipe flow, and the zero-pressure gradient turbulent boundary layer). Main results reported here are the asymptotic logarithmic law for the mean velocity and corresponding scale-separation laws for bulk flow properties, the Reynolds shear stress, the turbulence production and turbulent viscosity. A scaling analysis indicates that the establishment of a self-similar turbulence state is the condition for the development of a strict logarithmic velocity profile. The resulting overall physical flow structure at extreme Re is discussed.     

On the equivalence of scaling,light-cone singularities and asymptotic behaviour of the Jost-Lehmann spectral function

For a local amplitude we prove a one-to-one correspondence between properly defined scaling, the leading light-cone singularity and the asymptotic behaviour of the corresponding Jost-Lehmann spectral function in the sense of distribution theory. The cases of canonical and non-canonical scaling are considered.     

A generalized adiabatic approach to exotic three-body systems

A generalized adiabatic approach providing the asymptotic separation of the fast and slow variables for the three-body muonic scattering problem is considered. A uniform classification scheme of the different adiabatic bases for some typical three-body Coulomb systems is discussed. The estimations of the cross section of the elastic scattering process (t¯p) _n=1+d(t¯p)_n=1+d are presented.     

Dynamic scaling in a simple one-dimensional model of dislocation activity

We examine a simple one-dimensional (1D) model of dislocation activity, including a stress-activated source and mutually interacting dislocations. We demonstrate, through numerical and analytical steps, that the dislocations emitted from a 1D stress-activated source evolve towards a distribution which is self-similar in time, and we derive the power-law forms and distribution function. We show that the asymptotic distribution is a step function, and the dislocation front moves out linearly in time. The spacing between dislocations in the asymptotic distribution is uniform and increases logarithmically in time. The number of dislocations increases as t/ln(t), and the strain increases as t ²/ln(t).     

Optimality of Gaussian attacks in continuous-variable quantum cryptography

We analyze the asymptotic security of the family of Gaussian modulated quantum key distribution protocols for continuous-variables systems. We prove that the Gaussian unitary attack is optimal for all the considered bounds on the key rate when the first and second momenta of the canonical variables involved are known by the honest parties.     

Nonlinear Waves in Nonuniform Complex Astrocloud

The global nonlinear gravito‐electrostatic eigen‐fluctuation behaviors in large‐scale non‐uniform complex astroclouds in quasi‐neutral hydrodynamic equilibrium are methodologically analyzed. Its composition includes warm lighter electrons, ions; and massive bi‐polar multi‐dust grains (inertial) with partial ionization sourced, via plasma‐contact electrification, in the cloud plasma background. The multi‐fluidic viscous drag effects are conjointly encompassed. The naturalistic equilibrium inhomogeneities, gradient forces and nonlinear convective dynamics are considered without any recourse to the Jeans swindle against the traditional perspective. An inho‐mogeneous multiscale analytical method is meticulously applied to derive a new conjugated non‐integrable coupled (via zeroth‐order factors) pair of variable‐coefficient inhomogeneous Korteweg de‐Vries Burger (i ‐KdVB) equations containing unique form of non‐uniform linear self‐consistent gradient‐driven sinks. A numerical illustrative scheme is procedurally constructed to examine the canonical fluctuations. It is seen that the eigenspectrum coevolves as electrostatic rarefactive damped oscillatory shock‐like structures and self‐gravitational compressive damped oscillatory shock‐like patterns . The irregular damping nature is attributable to the i ‐KdVB sinks. The aperiodicity in the hybrid rapid small downstream wavetrains is speculated to be deep‐rooted in the quasi‐linear gravito‐electrostatic interplay. The phase‐evolutionary dynamics grow as atypical non‐chaotic fixed‐point attractors . We, finally, indicate tentative astronomical applications relevant in large‐scale cosmic structure formation aboard facts and faults. (© 2016 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Asymptotic symmetry and the global structure of future null infinity

Space-times for whichI ⁺ (future null infinity) is not necessarily homeomorphic toR×S ² are considered. It is shown that, depending on the global conformal structure ofI ⁺, a given space-time either (1) possesses an asymptotic symmetry group with a normal subgroup of supertranslations, similar in structure to the BMS group, or (2) possesses a simpler kind of asymptotic symmetry group, not involving supertranslations, or (3) has no asymptotic symmetry. The setting is Newman and Unti's approach to asymptotically flat space-times and use is made of the characterization of the asymptotic symmetry transformation as a conformal motion ofI ⁺ that preserves null angles.     

System of interacting harmonic oscillators in rotationally invariant noncommutative phase space

Rotationally invariant space with noncommutativity of coordinates and noncommutativity of momenta of canonical type is considered. A system of N interacting harmonic oscillators in uniform field and a system of N particles with harmonic oscillator interaction are studied. We analyze effect of noncommutativity on the energy levels of these systems. It is found that influence of coordinates noncommutativity on the energy levels of the systems increases with increasing of the number of particles. The spectrum of N free particles in uniform field in rotationally invariant noncommutative phase space is also analyzed. It is shown that the spectrum corresponds to the spectrum of a system of N harmonic oscillators with frequency determined by the parameter of momentum noncommutativity.     

Low-fugacity asymptotic expansion for classical lattice dipole gases

We consider a classical dipole gas in the grand canonical ensemble. We prove that in dimensions greater than or equal to three, and for all temperatures, the free energy and the charges-dipoles correlation functions have an expansion in powers ofz, the fugacity of the system, which is asymptotic to all orders. We also give some information about the decay of correlations.on leave from Institut de Physique Théorique Université de Louvian, Belgium. Supported by N.S.F. grant No. PHY-15920.     

The Dirac Equation in the Bertotti-Robinson Space-Time

The Dirac equation is considered in the uniform electromagnetic field space of Bertotti-Robinson with charge coupling. The methods of separation of variables and decoupling are easily achieved. The separated axial equation is reduced to a rare Riccati type of differential equation. The behaviour of potentials, their asymptotic solutions and the conserved currents of the Dirac equation are found.     

Temperature dependent properties of metallic clusters containing magnetic impurities

The properties of magnetic impurities in small metallic clusters are investigated in the framework of the Anderson model by using exact diagonalization methods. Parameters representative of the Kondo limit are considered. The spin gap ΔE = E(S=1, 3/2) - E(S=0, 1/2) shows a remarkable band-filling dependence that can be interpreted in terms of the cluster-specific conduction-electron spectrum. Finite-temperature properties such as the magnetic susceptibility and specific heat are calculated exactly in the canonical and grand canonical ensembles. The structural dependence is illustrated. Received 30 November 2000     

Relationship between statistical sums of canonical and grand canonical ensembles of interacting particles

A strict asymptotic relation between statistical sums of canonical and grand canonical ensembles is derived. Institute of Applied Physics at Irkutsk State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 43–46, June, 2000.     

Renormalization group and scale invariance in terms of asymptotic fields

The expansion of the massive renormalized field operator in terms of asymptotic fields is studied. We derive the renormalization group equation for the renormalized field operator. We obtain the renormalized scale transformations with Callan-Symanzik corrections as generated by canonical scale transformations of asymptotic fields.     

Construction of uniform asymptotic solutions of wave-type differential equations by methods of catastrophe theory

A mathematical apparatus for solving differential equations of special type by the methods of main, edge, and corner catastrophes is developed. The fundamentals of the wave catastrophe theory are considered, including the classification and methods of constructing uniform asymptotics used to describe the structure of wave fields in these domains, together with an analysis of the structure of the field. Classes of special functions used to construct uniform asymptotic expansions of wave fields are generally described together with the properties of these classes and the methods of computation. Dedicated to the memory of Vladimir Borovikov     

Wild's solution of the nonlinear Boltzmann equation

The relaxation to equilibrium of a spatially uniform pseudo-Maxwellian gas is considered. A modified Wild expansion is defined for solving the nonlinear Boltzmann equation. The positivity and asymptotic conditions, as well as the conservation rules, are maintained at each truncation order. Some particular examples are evaluated. The comparison with exact solutions illustrates the very fast convergence of this method.     

Calculation of the energy density function by the method of steepest descent

We present a unified theory of diatomic molecules which reconciles bound state spectroscopy and atomic scattering theory. The total wave-function is expanded in a complete set of atomic channel states which is entirely equivalent to an expansion in Hund's case (e) electronic-rotational states. An analysis of the coupled radial, that is vibrational, functions places strong constraints on the asymptotic properties of the molecular wave-functions. These are presented in terms of the reactance K and scattering S matrices of atomic scattering theory which offers a uniform treatment for open channels (inelastic scattering and continuum spectroscopy), closed channels (bound state spectroscopy) and mixtures of both (predissociation). The normalization of the total wavefunction is derived and related to the asymptotic boundary conditions both for continuum and bound states.