Renormalization-group analysis for the transition to chaos in Hamiltonian systems

We study the stability of Hamiltonian systems in classical mechanics with two degrees of freedom by renormalization-group methods. One of the key mechanisms of the transition to chaos is the break-up of invariant tori, which plays an essential role in the large scale and long-term behavior. The aim is to determine the threshold of break-up of invariant tori and its mechanism. The idea is to construct a renormalization transformation as a canonical change of coordinates, which deals with the dominant resonances leading to qualitative changes in the dynamics. Numerical results show that this transformation is an efficient tool for the determination of the threshold of the break-up of invariant tori for Hamiltonian systems with two degrees of freedom. The analysis of this transformation indicates that the break-up of invariant tori is a universal mechanism. The properties of invariant tori are described by the renormalization flow. A trivial attractive set of the renormalization transformation characterizes the Hamiltonians that have a smooth invariant torus. The set of Hamiltonians that have a non-smooth invariant torus is a fractal surface. This critical surface is the stable manifold of a single strange set encompassing all irrational frequencies. This hyperbolic strange set characterizes the Hamiltonians that have an invariant torus at the threshold of the break-up. From the critical strange set, one can deduce the critical properties of the tori (self-similarity, universality classes).     

Exactly solvable models of conformal-invariant quantum field theory in D-dimensional space

The method for exact solution of a certain class of models of conformal quantum field theory in D-dimensional Euclidean space is proposed. The method allows one to derive closed differential equations for all the Green functions and also algebraic equations to scale dimensions of all field. A scalar field P of a scale dimension d_p = D − 2 is needed for nontrivial solutions to exist. At D ≠ 2 this field is converted to a constant that coincides with the central charge of two-dimensional theories. A new class of D = 2 models has been obtained, where the infinite-parametric symmetry is not manifest. The two-dimensional Wess-Zumino model is used to illustrate the method of solution.     

Complexity of D-dimensional hydrogenic systems in position and momentum spaces

The internal disorder of a D-dimensional hydrogenic system, which is strongly associated to the non-uniformity of the quantum-mechanical density of its physical states, is investigated by means of the shape complexity in the two reciprocal spaces. This quantity, which is the product of the disequilibrium or averaging density and the Shannon entropic power, is mathematically expressed for both ground and excited stationary states in terms of certain entropic functionals of Laguerre and Gegenbauer (or ultraspherical) polynomials. We emphasize the ground and circular states, where the complexity is explicitly calculated and discussed by means of the quantum numbers and dimensionality. Finally, the position and momentum shape complexities are numerically discussed for various physical states and dimensionalities, and the dimensional and Rydberg energy limits as well as their associated uncertainty products are explicitly given. As a byproduct, it is shown that the shape complexity of the system in a stationary state does not depend on the strength of the Coulomb potential involved.     

Temperature stabilization in dispersed flows of frameless heat removal systems in space

The temperature profile stabilization is studied at radiation cooling of a dispersed veil of droplet coolers-radiators. The stabilization is shown to be nonmonotonic. The influence of the studied process regularities on the characteristics of the radiating systems is analyzed.     

p,q-Duality and Hamiltonian flows in the space of integrable systems or integrable systems as canonical transforms of the free ones

Variation of coupling constants of integrable system can be considered as canonical transformation or, infinitesimally, a Hamiltonian flow in the space of such systems. Any function $\text{T(}\text{p}\text{→}\text{,}\text{q}\text{→}\text{)}$ generates a one-parametric family of integrable systems in vicinity of a single system: this gives an idea of how many integrable systems there are in the space of coupling constants. Inverse flow is generated by a dual “Hamiltonian”, $\text{T}\text{(}\text{p}\text{→}\text{,}\text{q}\text{→}\text{)}$ associated with the dual integrable system. In vicinity of a self-dual point the duality transformation just interchanges momenta and coordinates in such a “Hamiltonian”: $\text{T}\text{(}\text{p}\text{→}\text{,}\text{q}\text{→}\text{)=T(}\text{q}\text{→}\text{,}\text{p}\text{→}\text{)}$. For integrable system with several coupling constants the corresponding “Hamiltonians” $\text{T}{}_{\mathrm{i}}\text{(}\text{p}\text{→}\text{,}\text{q}\text{→}\text{)}$ satisfy Whitham equations and after quantization (of the original system) become operators satisfying the zero-curvature condition in the space of coupling constants: $\text{∂}\text{∂g}{}_{\mathrm{a}}\text{−}\text{T}{}_{\mathrm{a}}\text{(}\text{p}\text{→}\text{̂}\text{,}\text{q}\text{→}\text{̂}\text{),}\text{∂}\text{∂g}{}_{\mathrm{b}}\text{−}\text{T}{}_{\mathrm{b}}\text{(}\text{p}\text{→}\text{̂}\text{,}\text{q}\text{→}\text{̂}\text{)}\text{=0.}$ Some explicit formulas are given for harmonic oscillator and for Calogero–Ruijsenaars–Dell system.     

Multiscale model of gradient evolution in turbulent flows

A multiscale model for the evolution of the velocity gradient tensor in turbulence is proposed. The model couples "restricted Euler" (RE) dynamics describing gradient self-stretching with a cascade model allowing energy exchange between scales. We show that inclusion of the cascade process is sufficient to regularize the finite-time singularity of the RE dynamics. Also, the model retains geometrical features of real turbulence such as preferential alignments of vorticity and joint statistics of gradient tensor invariants. Furthermore, gradient fluctuations are non-Gaussian, skewed in the longitudinal case, and derivative flatness coefficients are in good agreement with experimental data.     

Hamiltonian and gradient structures in the Toda flows

In this paper we consider gradient structures in the dynamics and geometry of the asymmetri nonperiodic tridiagonal and full Toda flow equations. We compare and contrast a number of formulations of the nonperiodic Toda equations. In the case of the full Kostant (asymmetric) Toda flow we explain the role of noncommutative integrability in its qualitative behavior. We describe the relationship between the asymmetric Toda flows and the symmetric and indefinite Toda flows, and prove in particular that one may conjugate from the full Kostant Toda flows to the full symmetric Toda flows via a Poisson map.     

Generalized wall functions for turbulent flows with strong adverse pressure gradient

The generalized wall functions for turbulent flows with strong adverse pressure gradients are derived on the basis of the asymptotic theory of near-wall turbulence. The generalized wall functions have a correct asymptotic behavior in the limit of zero friction velocity and can be applied to computations of flows under a strong adverse pressure gradient and with separation or reattachment. Calculations of a turbulent boundary layer in a strong adverse pressure gradient with the aid of the developed modified k-ɛ model of turbulence and comparison with the experimental data validate the advantages of the generalized wall functions over traditional wall functions based on the logarithmic law of the wall.     

Modified cell theory: Free volume distributions and the equation of state for D-dimensional hard sphere systems

A generalized cell model, using cells of different sizes, is applied to hard rods, disks and spheres. Structures is discussed in terms of free volumes. The derived equation of state is exact for rods. For disks and spheres it provides a good approximation in the dense fluid and solid state.     

Renormalization-group flow for the field strength in scalar self-interacting theories

We consider the renormalization-group coupled equations for the effective potential V(?)$V(?)$ and the field strength Z(?)$Z(?)$ in the spontaneously broken phase as a function of the infrared cutoff momentum k  . In the k→0$k\to 0$ limit, the numerical solution of the coupled equations, while consistent with the expected convexity property of V(?)$V(?)$, indicates a sharp peaking of Z(?)$Z(?)$ close to the end points of the flatness region that define the physical realization of the broken phase. This might represent further evidence in favor of the non-trivial vacuum field renormalization effect already discovered with variational methods.     

Interference action of weakly compliant boundaries in the gradient flows

The conditions for possible reduction of hydrodynamic resistance by the compliant coatings are considered from two points of view: pulling the laminar flow and alteration of turbulence generation in the near-wall zone. A strong effect of the longitudinal pressure gradient and reasonability of the search for the laminarized bypass flows in the presence of compliant coatings are distinguished.     

Fibre optics systems for space applications

Fibre optics offer many advantages over conventional wire systems for satellite communications; they include low weight, large bandwidth capacity, simple architecture for data bussing, electromagnetic interference (EMI) invulnerability, and cost-effectiveness. However, additional development work and reliability data are required for better performance and system implementation. Radiation effects on fibre optics are reviewed, and potential areas of fibre optics space systems application are explored.     

Integral invariants for non-barotropic flows in a four dimensional space time manifold

Properties of non-barotropic flows are described using Lie derivatives of differential forms in a Euclidean four dimensional space-time manifold. Vanishing of the Lie derivative implies that the corresponding physical quantity remains invariant along the integral curves of the flow. Integral invariants of non-barotropic perfect and viscous flows are studied using the concepts of relative and absolute invariance of forms. The four dimensional expressions for the rate of change of the generalized circulation, generalized vorticity flux, generalized helicity and generalized parity in the case of ideal and viscous non-barotropic flows are thereby obtained.     

How to track renormalization group flows in parameter space

A method to track Monte Carlo renormalization group trajectories without searching in a large parameter space is described. The method involves the use of the microcanonical ensemble using Creutz's demons. The two-dimensional Ising model with three couplings is used to demonstrate the efficiency of the method in approximately locating the fixed point.     

MRI gradient fields increase brain mannitol space

Following nephrectomy and intravenous injection of tritiated mannitol, adult male rats were exposed to magnetic resonance imaging (MRI) procedures at 1.5 T, 0.5 T, and 0.3 T. Compared to rats similarly handled but not exposed to MRI procedures, brain mannitol concentration, expressed as a percentage of mean body concentration, was significantly increased at 0.3 T and 0.5 T but not at 1.5 T. At 0.3 T, exposure to gradient-field fluctuations used for imaging increased brain mannitol concentration, but exposures to static main field and pulsed radiofrequency energies did not. Increased brain mannitol associated with gradient-field flux may reflect increased blood-brain barrier permeability or blood volume in brain. MRI effects on brain mannitol space are of uncertain clinical significance, but are consistent with prior evidence of an MRI-induced increase of brain capillary endothelial cell transport observed with horseradish peroxidase. Further studies are needed to confirm these findings and to explore the processes underlying changes in mannitol distribution related to MRI.     

Dynamics of zonal flows in helical systems

A theory for describing collisionless long-time behavior of zonal flows in helical systems is presented and its validity is verified by gyrokinetic-Vlasov simulation. It is shown that, under the influence of particles trapped in helical ripples, the response of zonal flows to a given source becomes weaker for lower radial wave numbers and deeper helical ripples while a high-level zonal-flow response, which is not affected by helical-ripple-trapped particles, can be maintained for a longer time by reducing their bounce-averaged radial drift velocity. This implies a possibility that helical configurations optimized for reducing neoclassical ripple transport can simultaneously enhance zonal flows which lower anomalous transport.     

事件空间中Birkhoff系统的Noether理论

研究事件空间中Birkhoff系统的Noether对称性与Noether守恒量.首先,建立了事件空间中Birkhoff系统的参数方程;其次,基于Pfaff作用量在无限小变换下的不变性,给出了事件空间中Birkhoff系统的Noether定理及其逆定理;最后,举例说明结果的应用. 关键词： 事件空间 Birkhoff系统 Pfaff作用量 Noether对称性