Shiro Sawada

Nonlinear analysis of a differential-difference equation with next-nearest-neighbour interaction for traffic flow

We analyse the Newell-Whitham-type car-following model described by a differential-difference equation with a generalized optimal velocity function which depends not only on the headway of each car but also on the headway of the immediately preceding one. Linear stability analysis shows that the model is stabilized for larger delay time by taking into account the headway of the immediately preceding car. From the nonlinear analysis, the propagating kink solution for traffic jams is obtained. The fundamental diagram and the relation between the headway and the delay time are examined by numerical simulation. We find that the result from the nonlinear analysis is in good agreement with that obtained from the numerical simulation.

GENERALIZED OPTIMAL VELOCITY MODEL FOR TRAFFIC FLOW

A generalized optimal velocity model is analyzed, where the optimal velocity function depends not only on the headway of each car but also the headway of the immediately preceding one. The stability condition of the model is derived by considering a small perturbation around the homogeneous flow solution. The effect of the generalized optimal velocity function is also confirmed with numerical simulations, by examining the hysteresis loop in the headway-velocity phase space, and the relation between the flow and density of cars. In the model with a specific parameter choice, it is found that an intermediate state appears for the movement of cars, where the car keeps a certain velocity whether the headway is short or long. This phenomenon is different from the ordinary stop-and-go state.

Spontaneous compactification in generalized Candelas-Weinberg models

Abstract In their recent work on the dimensional reduction, Candelas and Weinberg considered a model which is compactified into a direct product space of the Minkowski space (M4) and an N-dimensional sphere (SN). In the present paper we investigate generalized models of their type which are compactified into M4 × SM × SN and M4 × SM × CP2. The compactification is caused by the quantum loop effect due to a large number of matter fields. The conditions for the vacuum stability are studied. Numerical computation of the loop effect is undertaken, and it is shown that some of the models of the type M4 × SM × SN admit a stable solution which has finite circumferences of both of the extra spaces and positive coupling constants of the Einstein-Yang-Mills theory in four dimensions.

String field theory in curved space

Abstract The purely cubic action in the string field theory is shown to provide a set of equations of motion for background fields which agree to those obtained by the vanishing condition of s-functions in the non-linear sigma model. Using the sigma model as an auxiliary tool, a systematic method for solving the string field theory in curved space is proposed.

String field theory in curved space: A non-linear σ-model analysis

Abstract In a previous paper, the purely cubic action theory was shown to determine the equations of motion for background fields. Here, the details of the calculation are given by the use of the non-linear σ-model. In the dimensional regularization, the effective action and expectation value of the energy-momentum tensor are calculated in the context of the σ-model. Particular attention is paid to the treatment of the antisymmetric tensor e ab ( g ) when the world sheet has a non-vanishing curvature. A consistent extension of e ab ( g ) from two to n dimensions is shown to exist.

Stability of self-consistent dimensional reduction

Abstract The model of Candelas and Weinberg for the dimensional reduction is generalized and analyzed in detail. Considered here is a system of gravity plus a large number of matter fields compactifying due to quantum loop effects into M 4 × S M × S N , M 4 × CP 2 × S N and variations thereof. Stability conditions of the vacuum are inspected. The positivity of the gauge coupling as well as the gravitational constants is examined. Numerical analysis of the loop effect shows that the model M 4 × S 7 × S 4 admits a stable solution with finite circumferences of both extra spaces.

OPTIMAL VELOCITY MODEL WITH RELATIVE VELOCITY

The optimal velocity model which depends not only on the headway but also on the relative velocity is analyzed in detail. We investigate the effect of considering the relative velocity based on the linear and nonlinear analysis of the model. The linear stability analysis shows that the improvement in the stability of the traffic flow is obtained by taking into account the relative velocity. From the nonlinear analysis, the relative velocity dependence of the propagating kink solution for traffic jam is obtained. The relation between the headway and the velocity and the fundamental diagram are examined by numerical simulation. We find that the results by the linear and nonlinear analysis of the model are in good agreement with the numerical results.

Cancellation of the Lorentz anomaly of string field theory in light-cone gauge

Abstract We study the path-integral measure of string fields in the bosonic open-closed interacting string field theory in light-cone gauge. The Lorentz anomaly of the path-integral measure cancels the Lorentz non-invariant terms of the classical string field action. Thus the theory is shown to be Lorentz invariant at the one-loop level. The one-loop divergent amplitude of the planar open string needs some modified counter-term, which is however not discussed here.

NON-PERTURBATIVE EFFECT OF A MODIFIED ACTION IN MATRIX MODELS

A modified matrix model action, which may provide the well-defined two-dimensional pure gravity theory, proposed by Das, Dhar, Sengupta and Wadia is analyzed non-perturbatively. The perturbative solution in genus expansion is also obtained. It is shown that the specific heat satisfies Painleve equation in the double scaling limit. Thus the modified action is found to be in the same universality class as ordinary matrix models.