Universal Asymptotic Form Research Articles

Non-symmetric branching of fluid flows in 3D vessels

Nonsymmetric branching flow through a three-dimensional (3D) vessel is considered at medium-to-high flow rates. The branching is from one mother vessel to two or more daughter vessels downstream, with laminar steady or unsteady conditions assumed. The inherent 3D nonsymmetry is due to the branching shapes themselves, or the differences in the end pressures in the daughter vessels, or the incident velocity profiles in the mother. Computations based on lattice-Boltzmann methodology are described first. A subsequent analysis focuses on small 3D disturbances and increased Reynolds numbers. This reduces the 3D problem to a two-dimensional one at the outer wall in all pressure-driven cases. As well as having broader implications for feeding into a network of vessels, the findings enable predictions of how much swirling motion in the cross-plane is generated in a daughter vessel downstream of a 3D branch junction, and the significant alterations provoked locally in the shear stresses and pressures at the walls. Nonuniform incident wall-shear and unsteady effects are examined. A universal asymptotic form is found for the flux change into each daughter vessel in a 3D branching of arbitrary cross-section with a thin divider.

NONSYMMETRIC BRANCHING OF FLUID FLOWS IN 3D VESSELS

Nonsymmetric branching flow through a three-dimensional (3D) vessel is considered at medium-to-high flow rates. The branching is from one mother vessel to two or more daughter vessels downstream, with laminar steady or unsteady conditions assumed. The inherent 3D nonsymmetry is due to the branching shapes themselves, or the differences in the end pressures in the daughter vessels, or the incident velocity profiles in the mother. Computations based on lattice-Boltzmann methodology are described first. A subsequent analysis focuses on small 3D disturbances and increased Reynolds numbers. This reduces the 3D problem to a two-dimensional one at the outer wall in all pressure-driven cases. As well as having broader implications for feeding into a network of vessels, the findings enable predictions of how much swirling motion in the cross-plane is generated in a daughter vessel downstream of a 3D branch junction, and the significant alterations provoked locally in the shear stresses and pressures at the walls. Nonuniform incident wall-shear and unsteady effects are examined. A universal asymptotic form is found for the flux change into each daughter vessel in a 3D branching of arbitrary cross-section with a thin divider.

Coarse-graining and renormalization of atomistic binding relations and universal macroscopic cohesive behavior

We present two approaches for coarse-graining interplanar potentials and determining the corresponding macroscopic cohesive laws based on energy relaxation and the renormalization group. We analyze the cohesive behavior of a large—but finite—number of interatomic planes and find that the macroscopic cohesive law adopts a universal asymptotic form. The universal form of the macroscopic cohesive law is an attractive fixed point of a suitably-defined renormalization-group transformation.

Noise-driven evolution in stellar systems - I. Theory

We present a theory for describing the evolution of a galaxy caused by stochastic events such as weak mergers, transient spiral structure, orbiting blobs, etc. This noise excites large-scale patterns that drive the evolution of the galactic density profile. In a dark matter halo, the repeated stochastic perturbations preferentially ring the lowest-order modes with only a very weak dependence on the details of their source. The subsequent redistribution of halo mass is determined only by the mechanics of these modes. The halo profile then evolves toward a universal asymptotic form for a wide variety of noise sources. Such a convergence may help explain the similarity of normal galaxy morphology in diverse environments. A variety of other applications are discussed.

Universal asymptotic eigenvalue distribution of density matrices and corner transfer matrices in the thermodynamic limit

We study the asymptotic behavior of the eigenvalue distribution of the corner transfer matrix (M(CTM)) and the density matrix (M(DM)) in the density-matrix renormalization group. We utilize the relationship M(DM)=M(4)(CTM), which holds for noncritical systems in the thermodynamic limit. We derive the exact and universal asymptotic form of the M(DM) eigenvalue distribution for a class of integrable models in the massive regime. For nonintegrable models, the universal asymptotic form is also verified by numerical renormalization group calculations.

A Justification for the Scaling of the Thom-System

In the present paper we discuss the critical behavior of Thom-system using Catastrophe Theory. The universal critical asymptotic form of the family of free energy functions for Thom-system with one order parameter and two field parameters is obtained. The expressions of critical exponents, the scaling laws, and the scaling hypotheses are all derived from this universal asymptotic form.

A JUSTIFICATION FOR THE SCALING OF THE THOM-SYSTEM

In the present paper, we discuss the critical behavior of Thom-system using Catastrophe Theory. The universal critical asymptotic form of the family of free energy functions for Thom-system with one order parameter and two field parameters is obtained. The expressions of critical exponents, the scaling laws, the scaling hypotheses, all are derived from this universal asymptotic form.

Energy-momentum sum rules and inclusive reactions

Some properties of inclusive reactions are studied and the energy-momentum sum rules are rederived in a simpler and more powerful way, both in the case of identical as well as of nonidentical particles. A universal asymptotic form for the inclusive cross-sections which is suggested by the consideration of the sum rules is briefly discussed.