Role of rational surfaces on fluctuations and transport in the plasma edge of the TJ-II stellarator

It has been shown that transport barriers in toroidal magnetically confined plasmas tend to be linked to regions of unique magnetic topology such as the location of a minimum in the safety factor, rational surfaces or the boundary between closed and open flux surfaces. In the absence ofE×B sheared flows, fluctuations are expected to show maximum amplitude near rational surfaces, and plasma confinement might tend to deteriorate. On the other hand, if the generation ofE×B sheared flows were linked to low order rational surfaces, these would be beneficial for confinement. Experimental evidence ofE×B sheared flows linked to rational surfaces has been obtained in the plasma edge region of the TJ-II stellarator. Presented at the Workshop on the Role of Electric Fields in Plasma Confinement and Exhaust, Budapest, 18–19 June, 2000.     

3D Visualization of the separated fluid flows

For the detailed investigation of the 3D unsteady incompressible viscous separated fluid flows around a sphere (for 200≤Re≤700) and a circular cylinder (for 200≤Re≤400) the direct numerical simulation and 3D visualization are used. For 3D visualization of the fluid flows around a sphere the definition of vortex core as a connected region containing two negative eigenvalues of theS ²+Ω ² tensor is used (whereS _i,j andΩ _ij are the rate of strain and the rate of rotation tensors). The formation mechanism of vortices in the sphere wake for Re=500 is described in detail. For 3D visualization of the fluid flows around a circular cylinder the 3D isosurfaces of the streamwise component of vorticity ω _x are used.     

On the Superdiffusive Behavior of Passive Tracer with a Gaussian Drift

In the present article we consider a motion of a passive tracer particle, whose trajectory satisfies the Itô stochastic differential equation d x(t) = V(t, x(t)) dt + d w(t), where w(·) is a Brownian motion, V is a stationary Gaussian random field with incompressible realizations independent of w(·) and >0. We prove the superdiffusive character of the motion under certain conditions on the energy spectrum of the velocity field. The result is shown both for steady (time independent) and time dependent and Markovian velocity fields. In addition, we provide explicit upper and lower bounds for the Hurst exponent of the trajectory. All previous rigorous results concerned explicitely solvable shear flows cases.     

Relaxation equations for two-dimensional turbulent flows with a prior vorticity distribution

Using a Maximum Entropy Production Principle (MEPP), we derive a new type of relaxation equations for two-dimensional turbulent flows in the case where a prior vorticity distribution is prescribed instead of the Casimir constraints [R. Ellis, K. Haven, B. Turkington, Nonlinearity 15, 239 (2002)]. The particular case of a Gaussian prior is specifically treated in connection to minimum enstrophy states and Fofonoff flows. These relaxation equations are compared with other relaxation equations proposed by Robert and Sommeria [Phys. Rev. Lett. 69, 2776 (1992)] and Chavanis [Physica D 237, 1998 (2008)]. They can serve as numerical algorithms to compute maximum entropy states and minimum enstrophy states with appropriate constraints. We perform numerical simulations of these relaxation equations in order to illustrate geometry induced phase transitions in geophysical flows.     

Strong thermal self-action of a laser beam in gases and liquids

Solutions which approximately describe the effect of strong thermal self-action of a laser beam in weakly absorbing media (gases and liquids) have been obtained. This paper considers the regimes of thermal conductivity, transverse flows of gases at subsonic and supersonic velocities, transonic nonlinear regime, and gravitational convection in a horizontal beam. Assuming that the shape of transverse intensity distribution is constant, and that the wave front can be approximated by a second-power polynomial, ordinary differential equations and their solutions for average transverse dimensions of beams have been obtained. These approximate solutions are in satisfactory agreement with exact solutions. Zh. éksp. Teor. Fiz. 116, 105–129 (July 1999)     

Numerical simulation of gasdynamic phenomena

The work in computational hydrodynamics related to investigations of the supersonic streamlining of bodies, the interaction of shock waves, multiphase flows, and hyposonic flows in devices for semiconductor technology is reviewed. Zh. Tekh. Fiz. 69, 46–49 (September 1999)     

Effect of the momentum dependence of nuclear symmetry potential on the transverse and elliptic flows

In the framework of the isospin-dependent Boltzmann-Uehling-Uhlenbeck transport model, the effect of the momentum dependence of nuclear symmetry potential on nuclear transverse and elliptic flows in the neutron-rich reaction ¹³²Sn+¹²⁴Sn at a beam energy of 400MeV/nucleon is studied. We find that the momentum dependence of nuclear symmetry potential affects the rapidity distribution of the free neutron to proton ratio, the neutron and the proton transverse flows as a function of rapidity. The momentum dependence of nuclear symmetry potential affects the neutron-proton differential transverse flow more evidently than the difference of neutron and proton transverse flows as well as the difference of proton and neutron elliptic flows. It is thus better to probe the symmetry energy by using the difference of neutron and proton flows since the momentum dependence of nuclear symmetry potential is still an open question. And it is better to probe the momentum dependence of nuclear symmetry potential by using the neutron-proton differential transverse flow the rapidity distribution of the free neutron to proton ratio.     

New Mathematical Models for Particle Flow Dynamics

Abstract

A new class of integro-partial differential equation models is derived for the prediction of granular flow dynamics. These models are obtained using a novel limiting averaging method (inspired by techniques employed in the derivation of infinite-dimensional dynamical systems models) on the Newtonian equations of motion of a many-particle system incorporating widely used inelastic particle-particle force formulas. By using Taylor series expansions, these models can be approximated by a system of partial differential equations of the Navier-Stokes type. The exact or approximate governing equations obtained are far from simple, but they are less complicated than most of the continuum models now being used to predict particle flow behavior. Solutions of the new models for granular flows down inclined planes and in vibrating beds are compared with known experimental and analytical results and good agreement is obtained.     

Uniqueness for Autonomous Planar Differential Equations and the Lagrangian Formulation of Water Flows with Vorticity

Abstract

We prove a uniqueness result for autonomous divergence-free systems of ODE’s in the plane and give an application to the study of water flows with vorticity.     

On the calculation of steady-state magnetohydrodynamic flows of liquid metals in circular ducts of a rectangular cross section

A numerical code has been designed to calculate two-dimensional steady-state magnetohydrodynamic (MHD) flows of incompressible conducting fluids (liquid metals) in linear and circular thin-wall ducts of a rectangular cross section. The flows are caused by the Lorentz force J × B that appears when an electric current passes through a fluid placed in a vertical uniform magnetic field. The code is the generalization of the well-known iteration Gauss-Seidel method to the case of a set of elliptical equations. The method proposed can be used to calculate steady-state flows over wide ranges of Hartmann (Ha = 1–10³) and Reynolds (Re = 1–10⁶) numbers.     

Why is nacre strong? II. Remaining mechanical weakness for cracks propagating along the sheets

In our previous paper (Eur. Phys. J. E 4, 121 (2001)) we proposed a coarse-grained elastic energy for nacre, or stratified structure of hard and soft layers found in certain seashells . We then analyzed a crack running perpendicular to the layers and suggested one possible reason for the enhanced toughness of this substance. In the present paper, we consider a crack running parallel to the layers. We propose a new term added to the previous elastic energy, which is associated with the bending of layers. We show that there are two regimes for the parallel-fracture solution of this elastic energy; near the fracture tip the deformation field is governed by a parabolic differential equation while the field away from the tip follows the usual elliptic equation. Analytical results show that the fracture tip is lenticular, as suggested in a paper on a smectic liquid crystal (P.G. de Gennes, Europhys. Lett. 13, 709 (1990)). On the contrary, away from the tip, the stress and deformation distribution recover the usual singular behaviors ( and 1/, respectively, where x is the distance from the tip). This indicates there is no enhancement in toughness in the case of parallel fracture. Received 16 November 2001     

Study of the equilibrium and motions of the medium in a rotating star with a magnetic field using tools from angular momentum theory

The complicated processes occurring in a rotating magnetized medium are examined by representing all the vector quantities in the form of expansions in a complete system of orthogonal vector spherical harmonics. A separation of variables is ultimately achieved without a loss of accuracy despite the presence of nonlinear forces (the magnetic and Coriolis forces). The distribution of the rates of rotation and circulation motions in an adiabatically stratified, slowly rotating star or an atmospheric convection zone is studied as an example. The postulate of minimum entropy production from nonequilibrium thermodynamics is employed to find the most probable steady-state configuration. One solution satisfactorily describes the differential rotation observed on the Sun. The preliminary data support the notion that the superfast rotation of the type observed in Venus’ atmosphere can also be explained within the theory discussed. Zh. Tekh. Fiz. 69, 15–18 (September 1999)     

A Lattice Boltzmann Kinetic Model for Microflow and Heat Transfer

In this paper, we propose a lattice Boltzmann BGK model for simulation of micro flows with heat transfer based on kinetic theory and the thermal lattice Boltzmann method (He et al., J. Comp. Phys. 146:282, 1998). The relaxation times are redefined in terms of the Knudsen number and a diffuse scattering boundary condition (DSBC) is adopted to consider the velocity slip and temperature jump at wall boundaries. To check validity and potential of the present model in modelling the micro flows, two two-dimensional micro flows including thermal Couette flow and thermal developing channel flow are simulated and numerical results obtained compare well with previous studies of the direct simulation Monte Carlo (DSMC), molecular dynamics (MD) approaches and the Maxwell theoretical analysis     

Continuity of magnetohydrodynamic flows near singular points

The continuity of hydrodynamic and magnetohydrodynamic axisymmetric stationary flows near singular points of acoustic surfaces is investigated when the flows are far from spherical symmetry. It is shown that the flow is still continuous at the time the characteristics undergo a bifurcation, but may become discontinuous when the flow is distorted further. Zh. éksp. Teor. Fiz. 113, 771–785 (March 1998)     

Backscattering in stratified time-dependent random media—CW and narrow-band pulse propagation

Abstract

We consider backscattering in a random stratified medium where the wave-speed fluctuations depend on time and on the range coordinate, which is normal to the planes of stratification. For the limit where the correlation time is shorter than the mean scattering time, we first derive radiation-transport equations that govern the range evolution of the spectra of the ensemble-averaged forward-and back-propagating components of the field and their bichromatic coherence functions. The latter are governed by integro-differential equations that account for the broadening of the signal spectra due to the time dependence of the random fluctuations. When the correlation time is longer than both the period of the radiating signal and the travel time of a wavefront across a range correlation length, the spectrum of the radiation due to a monochromatic CW excitation remains confined to a narrow band over extensive ranges. This permits a quasi-monochromatic approximation, whereby the integro-differential equations produce ordinary differential equations that govern the quantities of interest. We use this approximation to track the power flux associated with the propagation of a narrow-band pulse.     

Handcrafted MRI radiomics and machine learning: Classification of indeterminate solid adrenal lesions

PurposeTo assess a radiomic machine learning (ML) model in classifying solid adrenal lesions (ALs) without fat signal drop on chemical shift (CS) as benign or malignant.Method55 indeterminate ALs (21 lipid poor adenomas, 15 benign pheocromocytomas, 1 oncocytoma, 12 metastases, 6 primary tumors) showing no fat signal drop on CS were retrospectively included. Manual 3D segmentation on T2-weighted and CS images was performed for subsequent radiomic feature extraction. After feature stability testing and an 80–20% train-test split, the train set was balanced via oversampling. Following a multi-step feature selection, an Extra Trees model was tuned with 5-fold stratified cross-validation in the train set and then tested on the hold-out test set.ResultsA total of 3396 features were extracted from each AL, of which 133 resulted unstable while none had low variance (< 0.01). Highly correlated (r > 0.8) features were also excluded, leaving 440 parameters. Among these, Support Vector Machine 5-fold stratified cross-validated recursive feature elimination selected a subset of 6 features. ML obtained a cross-validation accuracy of 0.94 on the train and 0.91 on the test sets. Precision, recall and F1 score were respectively 0.92, 0.91 and 0.91.ConclusionsOur MRI handcrafted radiomics and ML pipeline proved useful to characterize benign and malignant solid indeterminate adrenal lesions.     

On Classes of Lie Solutions of MHD Equations,Expressed via the General Solution of the Heat Equation

Abstract

Large classes of Lie solutions of the MHD equations describing the flows of a viscous homogeneous incompressible fluid of finite electrical conductivity are constructed. These classes contain a number of arbitrary functions of time and the general solutions of the heat equation.     

Differential Constraints Compatible with Linearized Equations

Abstract

Differential constraints compatible with the linearized equations of partial differential equations are examined. Recursion operators are obtained by integrating the differential constraints.     

Nonlinear instability of elementary stratified flows at large Richardson number

Elementary stably stratified flows with linear instability at all large Richardson numbers have been introduced recently by the authors [J. Fluid Mech. 376, 319-350 (1998)]. These elementary stratified flows have spatially constant but time varying gradients for velocity and density. Here the nonlinear stability of such flows in two space dimensions is studied through a combination of numerical simulations and theory. The elementary flows that are linearly unstable at large Richardson numbers are purely vortical flows; here it is established that from random initial data, linearized instability spontaneously generates local shears on buoyancy time scales near a specific angle of inclination that nonlinearly saturates into localized regions of strong mixing with density overturning resembling Kelvin-Helmholtz instability. It is also established here that the phase of these unstable waves does not satisfy the dispersion relation of linear gravity waves. The vortical flows are one family of stably stratified flows with uniform shear layers at the other extreme and elementary stably stratified flows with a mixture of vorticity and strain exhibiting behavior between these two extremes. The concept of effective shear is introduced for these general elementary flows; for each large Richardson number there is a critical effective shear with strong nonlinear instability, density overturning, and mixing for elementary flows with effective shear below this critical value. The analysis is facilitated by rewriting the equations for nonlinear perturbations in vorticity-stream form in a mean Lagrangian reference frame. (c) 2000 American Institute of Physics.     

On Lie Reduction of the Navier-Stokes Equations

Abstract

Lie reduction of the Navier-Stokes equations to systems of partial differential equations in three and two independent variables and to ordinary differential equations is described.