GENERALIZED TODA AND VOLTERRA MODELS

1992 ◽  
Vol 07 (20) ◽  
pp. 4855-4869 ◽  
Author(s):  
J. AVAN
Keyword(s):  
Matrix Models ◽  
Differential System ◽  
Continuum Limit ◽  
Automorphism Groups ◽  
Volterra Models ◽  
The Mean ◽  
The Continuum

The mean procedure of Faddeev-Reshetikhin with non-Abelian automorphism groups is applied to construct generalizations of the open Toda sl(n, C) chain. These models admit a consistent reduction to integrable generalized Volterra models. An example of such models is analyzed: it leads in the continuum limit to the [Formula: see text] Hirota differential system, associated with two-matrix models of discrete gravity. The continuum limit of the general Volterra models and their relation with discretized versions of Wn-algebra are analyzed.

Coupled dynamics of populations supported by discrete sites and their continuum limit

2010 ◽  
Vol 466 (2121) ◽  
pp. 2561-2586 ◽  
Author(s):  
Timothy R. Field ◽  
Robert J. A. Tough
Keyword(s):  
Evolution Equation ◽  
Closed Form ◽  
Generating Function ◽  
Rate Equation ◽  
Continuum Limit ◽  
Infinite Chain ◽  
Migration Process ◽  
The Mean ◽  
The Continuum ◽  
Birth Death

The illumination of single population behaviour subject to the processes of birth, death and immigration has provided a basis for the discussion of the non-Gaussian statistical and temporal correlation properties of scattered radiation. As a first step towards the modelling of its spatial correlations, we consider the populations supported by an infinite chain of discrete sites, each subject to birth, death and immigration and coupled by migration between adjacent sites. To provide some motivation, and illustrate the techniques we will use, the migration process for a single particle on an infinite chain of sites is introduced and its diffusion dynamics derived. A certain continuum limit is identified and its properties studied via asymptotic analysis. This forms the basis of the multi-particle model of a coupled population subject to single site birth, death and immigration processes, in addition to inter-site migration. A discrete rate equation is formulated and its generating function dynamics derived. This facilitates derivation of the equations of motion for the first- and second-order cumulants, thus generalizing the earlier results of Bailey through the incorporation of immigration at each site. We present a novel matrix formalism operating in the time domain that enables solution of these equations yielding the mean occupancy and inter-site variances in the closed form. The results for the first two moments at a single time are used to derive expressions for the asymptotic time-delayed correlation functions, which relates to Glauber’s analysis of an Ising model. The paper concludes with an analysis of the continuum limit of the birth–death–immigration–migration process in terms of a path integral formalism. The continuum rate equation and evolution equation for the generating function are developed, from which the evolution equation of the mean occupancy is derived, in this limit. Its solution is provided in closed form.

scholarly journals ON THE CONTINUUM LIMIT OF THE CONFORMAL MATRIX MODELS

1993 ◽  
Vol 08 (18) ◽  
pp. 3107-3137 ◽  
Author(s):  
A. MIRONOV ◽  
S. PAKULIAK
Keyword(s):  
Matrix Models ◽  
Continuum Limit ◽  
Scaling Limit ◽  
Universality Class ◽  
Partition Functions ◽  
Discrete Level ◽  
New Class ◽  
Double Scaling Limit ◽  
The Continuum

The double scaling limit of a new class of the multi-matrix models proposed in Ref. 1, which possess the W-symmetry at the discrete level, is investigated in detail. These models are demonstrated to fall into the same universality class as the standard multi-matrix models. In particular, the transformation of the W-algebra at the discrete level into the continuum one of the papers2 is proposed and the corresponding partition functions compared. All calculations are demonstrated in full in the first nontrivial case of W(3)-constraints.

N = ½ SUPERSTRING IN ZERO DIMENSION AND THE SPONTANEOUS BREAKDOWN OF THE SUPERSYMMETRY

1992 ◽  
Vol 07 (32) ◽  
pp. 2979-2989 ◽  
Author(s):  
SHIN’ICHI NOJIRI
Keyword(s):  
Matrix Models ◽  
Random Matrix ◽  
Continuum Limit ◽  
Scaling Limit ◽  
Partition Functions ◽  
Spontaneous Breakdown ◽  
Random Matrix Models ◽  
Double Scaling Limit ◽  
The Continuum ◽  
String Theories

We propose random matrix models which have N=1/2 supersymmetry in zero dimension. The supersymmetry breaks down spontaneously. It is shown that the double scaling limit can be defined in these models and the breakdown of the supersymmetry remains in the continuum limit. The exact non-trivial partition functions of the string theories corresponding to these matrix models are also obtained.

THE (ORBIFOLD) EULER CHARACTERISTIC OF THE MODULI SPACE OF CURVES AND THE CONTINUUM LIMIT OF PENNER'S CONNECTED GENERATING FUNCTION

1991 ◽  
Vol 03 (03) ◽  
pp. 285-300 ◽  
Author(s):  
NOUREDDINE CHAIR
Keyword(s):  
Free Energy ◽  
Matrix Models ◽  
Euler Characteristic ◽  
Generating Function ◽  
Moduli Space ◽  
Continuum Limit ◽  
Recursion Relation ◽  
Moduli Space Of Curves ◽  
Genus Zero ◽  
The Continuum

The generating function that gives rise to the orbifold Euler characteristic of the moduli space of punctured compact Rieman surfaces [Formula: see text], g ≥ 0 is derived explicitly. In the derivation, we show that we do not need to use the three-term recursion relation for the orthogonal polynomials. Also the continuum limit of Penner's connected generating function is considered and is shown to be formally equivalent to the free energy obtained recently by Distler and Vafa which exhibits the logarithmic divergences found for genus zero and one in D = 1 matrix models. Finally, it is shown that the free energy and its s-derivatives are nothing but the continuum limit of a certain generating function introduced by Harer and Zagier in obtaining the true Euler characteristic with any number of punctures,[Formula: see text], s ≥ 0.

scholarly journals THE WEINGARTEN MODEL À LA POLYAKOV

1992 ◽  
Vol 07 (18) ◽  
pp. 1651-1660 ◽  
Author(s):  
SIMON DALLEY
Keyword(s):  
Quantum Gravity ◽  
Matrix Models ◽  
Critical Behavior ◽  
Continuum Limit ◽  
Hermitian Matrix ◽  
Gauge Model ◽  
Vertex Models ◽  
Lattice Gauge ◽  
Genus Expansion ◽  
The Continuum

The Weingarten lattice gauge model of Nambu-Goto strings is generalized to allow for fluctuations of an intrinsic worldsheet metric through a dynamical quadrilation. The continuum limit is taken for c≤1 matter, reproducing the results of Hermitian matrix models to all orders in the genus expansion. For the compact c=1 case the vortices are Wilson lines, whose exclusion leads to the theory of non-interacting fermions. As a by-product of the analysis one finds the critical behavior of SOS and vertex models coupled to 2D quantum gravity.

scholarly journals Partition functions and the continuum limit in Penner matrix models

2014 ◽  
Vol 47 (31) ◽  
pp. 315205 ◽  
Author(s):  
Gabriel Álvarez ◽  
Luis Martínez Alonso ◽  
Elena Medina
Keyword(s):  
Matrix Models ◽  
Continuum Limit ◽  
Partition Functions ◽  
The Continuum

scholarly journals On the continuum limit of the conformal matrix models

1993 ◽  
Vol 95 (2) ◽  
pp. 604-625 ◽  
Author(s):  
A. Mironov ◽  
S. Pakuliak
Keyword(s):  
Matrix Models ◽  
Continuum Limit ◽  
The Continuum

EXACTLY SOLUBLE MATRIX MODELS

1992 ◽  
Vol 07 (03) ◽  
pp. 251-257
Author(s):  
R. RAJU VISWANATHAN
Keyword(s):  
Exact Solution ◽  
Energy Spectrum ◽  
Matrix Models ◽  
Morse Potential ◽  
Continuum Limit ◽  
Scaling Behavior ◽  
Quantum Corrections ◽  
One Dimensional ◽  
Dimensional Matrix ◽  
The Continuum

We study examples of one-dimensional matrix models whose potentials possess an energy spectrum that can be explicitly determined. This allows for an exact solution in the continuum limit. Specifically, step-like potentials and the Morse potential are considered. The step-like potentials show no scaling behavior and the Morse potential (which corresponds to a γ=−1 model) has the interesting feature that there are no quantum corrections to the scaling behavior in the continuum limit.

Photo-electric Hβ and uvby photometry

1966 ◽  
Vol 24 ◽  
pp. 170-180
Author(s):  
D. L. Crawford
Keyword(s):  
Narrow Band ◽  
Line Strength ◽  
Interference Filter ◽  
B Stars ◽  
Relative Line ◽  
The Mean ◽  
F Stars ◽  
Two Parameters ◽  
Filter Photometry ◽  
The Continuum

Early in the 1950's Strömgren (1, 2, 3, 4, 5) introduced medium to narrow-band interference filter photometry at the McDonald Observatory. He used six interference filters to obtain two parameters of astrophysical interest. These parameters he calledlandc, for line and continuum hydrogen absorption. The first measured empirically the absorption line strength of Hβby means of a filter of half width 35Å centered on Hβand compared to the mean of two filters situated in the continuum near Hβ. The second index measured empirically the Balmer discontinuity by means of a filter situated below the Balmer discontinuity and two above it. He showed that these two indices could accurately predict the spectral type and luminosity of both B stars and A and F stars. He later derived (6) an indexmfrom the same filters. This index was a measure of the relative line blanketing near 4100Å compared to two filters above 4500Å. These three indices confirmed earlier work by many people, including Lindblad and Becker. References to this earlier work and to the systems discussed today can be found in Strömgren's article inBasic Astronomical Data(7).

Instability and Collapse in Discrete Wave Equations

2005 ◽  
Vol 5 (3) ◽  
pp. 223-241
Author(s):  
A. Carpio ◽  
G. Duro
Keyword(s):  
Continuum Limit ◽  
Wave Equations ◽  
Numerical Solutions ◽  
Blow Up ◽  
Theoretical Predictions ◽  
Initial States ◽  
The Impact ◽  
The Continuum

AbstractUnstable growth phenomena in spatially discrete wave equations are studied. We characterize sets of initial states leading to instability and collapse and obtain analytical predictions for the blow-up time. The theoretical predictions are con- trasted with the numerical solutions computed by a variety of schemes. The behavior of the systems in the continuum limit and the impact of discreteness and friction are discussed.

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