A Theory of <Emphasis Type="Italic">L</Emphasis><Superscript>1</Superscript>-Dissipative Solvers for Scalar Conservation Laws with Discontinuous Flux

We propose a general framework for the study of L ¹ contractive semigroups of solutions to conservation laws with discontinuous flux:

Birefringence in polycarbonate: Molecular orientation induced by cooling stresses. I. Free quenching

The residual birefringence distributions in polycarbonate disks quenched in a liquid bath under various conditions are determined. Unbalanced distributions of approximately parabolic shape are obtained in the cross-sections in general. A systematic influence of the initial quench temperature on the imblance of the birefringence distributions is observed, with higher initial temperatures leading to a strong shift of birefringence in the positive direction. The systematic variation of the birefringence distribution with quenching conditions is interpreted in terms of a stress and an orientation contribution. The distributions are predicted correctly by a numerical program making use of the linear stress-optical rule with a different stress-optical coefficient above and below the glass-transition temperature. The contribution of molecular orientation is distinguished experimentally from the stress contribution by annealing experiments. © 1993 John Wiley & Sons, Inc.     

Unconditionally Stable Methods for Hamilton–Jacobi Equations

We present new numerical methods for constructing approximate solutions to the Cauchy problem for Hamilton–Jacobi equations of the form u_t+H(D_xu)=0. The methods are based on dimensional splitting and front tracking for solving the associated (non-strictly hyperbolic) system of conservation laws p_t+D_xH(p)=0, where p=D_xu. In particular, our methods depend heavily on a front tracking method for one-dimensional scalar conservation laws with discontinuous coefficients. The proposed methods are unconditionally stable in the sense that the time step is not limited by the space discretization and they can be viewed as “large-time-step” Godunov-type (or front tracking) methods. We present several numerical examples illustrating the main features of the proposed methods. We also compare our methods with several methods from the literature.     

Asymptotic arc-components of unimodal inverse limit spaces

We consider the inverse limit space (I,f) of a unimodal bonding map f as fixed bonding map. If f has a periodic turning point, then (I,f) has a finite non-empty set of asymptotic arc-components. We show how asymptotic arc-components can be determined from the kneading sequence of f. This gives an alternative to the substitution tiling space approach taken by Barge and Diamond [Ergodic Theory Dynamical Systems 21 (2001) 1333].     

Multiple single-peaked solutions of a class of semilinear Neumann problems via the category of the domain boundary

For a smooth domain with compact boundary we investigate the problem with Neumann boundary conditions, where f has superlinear but subcritical growth. Provided that is sufficiently small we show the existence of at least positive solutions with single maximum points that lie on . We replace the standard variational setting used in the case of homogeneous f by considering the restriction of the free functional to a suitable submanifold of the Sobolev Space . Received May 25, 1997 / Accepted October 3, 1997     

Research reactors and radiochemistry: Partners in a changing world

The raison d'etre of research reactors is based on their role in a number of research fields, including radiochemistry. Inversely, it is in the interest of a healthy development of radiochemistry that a sufficient number of reactors will remain in operation and that the downward trend is in this reversed. In this paper, directions for further developments in reactor based radiochemistry are discussed, taking into account also relevant developments in competing fields. The discussion is focused on neutron activation analysis as well as tracer applications and environmental radiochemistry. Moreover, the consequences for reactor operations will be indicated.     

Constant-cutoff approach to radiative decays of hyperons: E2/M1 transition ratios

We suggest a quantum stabilization method for theSU(2) σ-model, based on the constant-cutoff limit of the cutoff quantization method developed by Balakrishnaet al., which avoids the difficulties with the usual soliton boundary conditions pointed out by Iwasaki and Ohyama. We investigate the baryon numberB=1 sector of the model and show that after the collective coordinate quantization it admits a stable soliton solution which depends on a single dimensional arbitrary constant. We then study the radiative decays ofJ ^π=3/2⁺ baryons using the constant-cutoff approach to theSU(3) collective treatment of the Skyrme model for hyperons. Thus we evaluate the widths and E2/M1 ratios, showing that there is a general qualitative agreement with the results obtained using the complete Skyrme model, as well as the nonrelativistic quark model and quenched lattice model, for the total widths.     

Existence of unique SRB-measures is typical for real unicritical polynomial families

We show that for a one-parameter family of unicritical polynomials {fc} with even critical order ??2, for almost all parameters c, fc admits a unique SRB-measure, being either absolutely continuous, or supported on the postcritical set. As a byproduct we prove that if fc has a Cantor attractor, then it is uniquely ergodic on its postcritical set.