Papers by Alexander A Migdal
arXiv (Cornell University), Sep 25, 2022
We are investigating the inviscid limit of the Navier-Stokes equation, and we find previously unk... more We are investigating the inviscid limit of the Navier-Stokes equation, and we find previously unknown anomalous terms in Hamiltonian, Dissipation, and Helicity, which survive this limit and define the turbulent statistics. We find various topologically nontrivial configurations of the confined Clebsch field responsible for vortex sheets and lines. In particular, a stable vortex sheet family is discovered, but its anomalous dissipation vanishes as √ ν. Topologically stable stationary singular flows, which we call Kelvinons, are introduced. They have a conserved velocity circulation Γ α around the loop C and another one Γ β for an infinitesimal closed loopC encircling C, leading to a finite helicity. The anomalous dissipation has a finite limit, which we computed analytically. The Kelvinon is responsible for asymptotic PDF tails of velocity circulation, perfectly matching numerical simulations. The loop equation for circulation PDF as functional of the loop shape is derived and studied. This equation is exactly equivalent to the Schrödinger equation in loop space, with viscosity ν playing the role of Planck's constant. Kelvinons are fixed points of the loop equation at WKB limit ν → 0. The anomalous Hamiltonian for the Kelvinons contains a large parameter log |Γ β | ν. The leading powers of this parameter can be summed up, leading to familiar asymptotic freedom, like in QCD. In particular, the so-called multifractal scaling laws are, as in QCD, modified by the powers of the logarithm.
Proceedings of the fourth symposium on Virtual reality modeling language, 1999
Elaborate 3-D computer graphics scenes containing highly detailed geometric models are rapidly em... more Elaborate 3-D computer graphics scenes containing highly detailed geometric models are rapidly emerging as the "next frontier" requirement for Internet-based applications. In the past, such models have been represented by single, fixed resolution complex triangular meshes which place rigorous demands upon transmission bandwidth, storage capacity and rendering time. In order to accommodate and foster the transmission of 3-D data across the Internet, streamability, scalability and compression are required. This paper describes MetaStreamTM (MTS), a framework for the storage of multiresomtion 3-D models including associated geometry and texture data. By providing an efficient representation for progressively structured, compressed geometry and texture information while simultaneously preserving appearance attributes, MTS is able to overcome many of the hurdles associated with the practical use of streamable computer graphics and, we believe, represents an enabling technology for graphics over the Internet. Metacreations and Intel have agreed on joint research and development of the MTS file format for 3-D graphics developers, and Microsoft has included MTS in its DirectX 6 and ChromeffectsTM interactive media technology.
Physics Letters B, 1979
Three gauge invariant antisymmetric tensor fields are introduced in the nonabelian gauge theories... more Three gauge invariant antisymmetric tensor fields are introduced in the nonabelian gauge theories. They are certain nonlinear combinations of the conjugate field tensor and they obey 0(3) algebra. An effective chiral lagrangian for these fields is derived. It describes 3 vector and 3 axial mesons with vacuum quantum numbers. The masses are generated by spontaneous restoration of Lorentz invariance.
Fractal and Fractional
We have found an infinite dimensional manifold of exact solutions of the Navier-Stokes loop equat... more We have found an infinite dimensional manifold of exact solutions of the Navier-Stokes loop equation for the Wilson loop in decaying Turbulence in arbitrary dimension d>2. This solution family is equivalent to a fractal curve in complex space Cd with random steps parametrized by N Ising variables σi=±1, in addition to a rational number pq and an integer winding number r, related by ∑σi=qr. This equivalence provides a dual theory describing a strong turbulent phase of the Navier-Stokes flow in Rd space as a random geometry in a different space, like ADS/CFT correspondence in gauge theory. From a mathematical point of view, this theory implements a stochastic solution of the unforced Navier-Stokes equations. For a theoretical physicist, this is a quantum statistical system with integer-valued parameters, satisfying some number theory constraints. Its long-range interaction leads to critical phenomena when its size N→∞ or its chemical potential μ→0. The system with fixed N has diffe...
arXiv (Cornell University), May 4, 2020
We revisit the problem of stationary distribution of vorticity in three dimensional turbulence. U... more We revisit the problem of stationary distribution of vorticity in three dimensional turbulence. Using Clebsch variables we construct an explicit invariant measure on stationary solutions of Euler equations with the extra condition of fixed energy flow/dissipation. The asymptotic solution for large circulation around large loops is studied as a WKB limit (instanton). The Clebsch fields are discontinuous across minimal surface bounded by the loop, with normal vorticity staying continuous. There is also a singular tangential vorticity component proportional to δ(z) where z is the normal direction. Resulting flow has nontrivial topology. This singular tangent vorticity component drops from the flux but dominates the energy dissipation as well as the Biot-Savart integral for velocity field. This leads us to a modified equation for vorticity distribution along the minimal surface compared to that assumed in a loop equations, where the singular terms were not noticed. In addition to describing vorticity distribution over the minimal surface, this approach provides formula for the circulation PDF, which was elusive in the Loop Equations.
Fermion Regge Poles and Branch Points in J Plane
Calculation of anomalous dimensionalities in non-Abelian field gauge theories
A Diagram Technique Near the Curie Point and the Second Order Phase Transition in a Bose Liquid
Journal of Experimental and Theoretical Physics, 1969
Spontaneous Violation of Strong Interaction Symmetry and the Absence of Zero-Mass Particles
Loop equations and 1N expansion
Physics Reports, 1983
Nuclear Physics B - Proceedings Supplements, 1989
Dynamically triangulated random swiaces are studied. In view of the cellular automata description... more Dynamically triangulated random swiaces are studied. In view of the cellular automata description of quantum gravity, the covariant formulation is achieved by varying the adjaciency matrix. Computer simulations are discussed.
Nuclear Physics B, 1984
The four-dimensional twisted Eguchi-Kawai model is investigated numerically using the Langevin eq... more The four-dimensional twisted Eguchi-Kawai model is investigated numerically using the Langevin equation. The results for the plaquette energy agree with those of the known Monte Carlo calculations. The new result is the distribution of the eigenvalues of the plaquette matrix. In the strong coupling phase this distribution is smooth, whereas in the weak coupling phase a gap is clearly seen.
Nuclear Physics B, 1991
A two-dimensional quantum gravity is simulated by means of the dynamical triangulation model. The... more A two-dimensional quantum gravity is simulated by means of the dynamical triangulation model. The size of the lattice was up to hundred thousand triangles. Massively parallel simulations and recursive sampling were implemented independently and produced similar results. Wherever the analytical predictions existed, our results confirmed them. The cascade process of baby universes formulation a la Coleman-Hawking scenario in a two-dimensional case has been observed. We observed that there is a simple universal inclusive probability for a baby universe to appear. This anomalous branching of surfaces led to a rapid growth of the integral curvature inside a circle. The volume of a disk in the internal metric has been proven to grow faster than any power of radius. The scaling prediction for the mean square extent given by the Liouville theory has been confirmed. However, the naive expectation for the average Liouville lagrangian < f (p~6)2 > is about 1 order of magnitude different from the results. This apparently points out to some flaws in the current definition of a Liouville model.
QCD=Fermi string theory
Nuclear Physics B, 1981
The Fermi string theory which was earlier conjectured to be equivalent to QCD is revised and inve... more The Fermi string theory which was earlier conjectured to be equivalent to QCD is revised and investigated in detail. The precise correspondence between the loop average in QCD at N = ∞ and the propagator of the Fermi string with some special boundary conditions for a bispinor field is established. The effective string tension as a function of the bare fermion mass satisfies the scaling law with the critical index 1211.
Physics Letters B, 1982
An explicit representation of the baryon propagator in terms of many-point meson Greens functions... more An explicit representation of the baryon propagator in terms of many-point meson Greens functions is found in multicolor QCD. This representation provides the dual string picture for the multicolor baryon.
Boundary Energy of a Fermi Gas in a Potential Well
The relation between the Fermi energy and number of particles is extended to the case of a gas in... more The relation between the Fermi energy and number of particles is extended to the case of a gas in a potential well with a diffuse edge. The results are employed for calculating the boundary Fermi energy of neutrons in heavy nuclei with an accuracy approximates 1 Mev. The mean distance between the levels and the nuclear surface energy are calculated for the last elements of the Mendeleyev table. The calculations are performed for the optical model potential. (auth)
Theory of interacting pomerons and hadron reactions at high energies
International Journal of Modern Physics A, 2021
We revise the steady vortex surface theory following the recent finding of asymmetric vortex shee... more We revise the steady vortex surface theory following the recent finding of asymmetric vortex sheets (Migdal, 2021). These surfaces avoid the Kelvin–Helmholtz instability by adjusting their discontinuity and shape. The vorticity collapses to the sheet only in an exceptional case considered long ago by Burgers and Townsend, where it decays as a Gaussian on both sides of the sheet. In generic asymmetric vortex sheets (Shariff, 2021), vorticity leaks to one side or another, making such sheets inadequate for vortex sheet statistics and anomalous dissipation. We conjecture that the vorticity in a turbulent flow collapses on a special kind of surface (confined vortex surface or CVS), satisfying some equations involving the tangent components of the local strain tensor. The most important qualitative observation is that the inequality needed for this solution’s stability breaks the Euler dynamics’ time reversibility. We interpret this as dynamic irreversibility. We have also represented the...
Composite models of conformal field theory with a nonintegral number of patrons
Physics Letters B, 1973
Abstract Models are proposed, which have an explicit solution at any space-time dimension with no... more Abstract Models are proposed, which have an explicit solution at any space-time dimension with nontrivial conformal interaction, but in general with ghost states. At two dimensions ghosts can be removed, and one obtains the Thirring model. The problem of ghosts at four dimensions remains open.
Physics Letters B, 1971
Using eonformal invariance with the allon'm].ous dimensions of fields. 3-1)oint amplitude of
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Papers by Alexander A Migdal