### Regular Series

#### Vol. 26 (1995), No. 8, pp. 1321 – 1433

Lyapunov Exponents Analysis of Autonomous and Nonautonomous Sets of Ordinary Differential Equations

Acta Phys. Pol. B 26, 1321 (1995)

page 1321 •

abstract

We compare the Lyapunov exponents for nonautonomous and autono- mous versions of the same dynamical system governed by a set of ordinary differential equations (ODE), for a large class of physical systems admitting of the extraction of explicitly time-dependent terms in ODE. We have found some advantages of the Lyapunov analysis in the nonautonomous version. The main advantage is that we are able to solve the problem of Lyapunov exponents even though the time-dependent external force is nondifferentiable. Optical Kerr effect in a cavity with an external time-dependent field is considered numerically as an example.

Application of the Soft-Gluon Approach

Acta Phys. Pol. B 26, 1333 (1995)

page 1333 •

abstract

The Mebarki–Abbes prescription within the soft-gluon approach is applied and approximate higher order corrections to the cross section of large $P_{\rm T}$ hadronic production of two photons collision are derived.

Color Fields Around the Static Quark–Antiquark Pair

Acta Phys. Pol. B 26, 1347 (1995)

page 1347 •

abstract

We carried out an extensive study of the distribution of the color fields around the static $\bar qq$ pair using the methods of lattice field theory. The measurements have been performed on Monte Carlo configurations with dynamical fermions, at $\beta = 5.35$, on the $16^3 \times 24$ lattice with periodic boundary conditions. We have found some interesting differences with the quenched results published earlier, among them the effect of breaking the flux tube. We also performed perturbative calculations up to one loop level to see which details of the color field distribution obtained using MC methods are purely nonperturbative and which can be understood from the perturbative expansion of the QCD action.

The Supersymmetry Considerations in the First Half of the $sd$ Shell

Acta Phys. Pol. B 26, 1403 (1995)

page 1403 •

abstract

The search for the supersymmetry in light nuclei has been continued. It has been shown that the important ingredient of supersymmetry considerations in the first half of the $sd$ shell has come from the assumption of two fermion+boson model for odd–odd nuclei instead of assuming bosons only. With this improvement the approximate supersymmetry has been visible for the considered supermultiplet $N = 5$.

full authors' list

A. Tutay, A. Budzanowski, H. Fuchs, H. Homeyer, G. Pausch, C. Schwarz, A. Siwek, A. Taymaz

Temporal and Thermal Properties of Intermediate-Mass Fragments from the $^{32}$S$+^{58}$Ni REACTION AT 30 AMeV

Acta Phys. Pol. B 26, 1413 (1995)

page 1413 •

abstract

Information on thermal and temporal aspects of intermediate-mass fragment (IMF) formation was obtained by studying correlations between (a) two IMFs, (b) one IMF and one a particle, and (c) one heavy residue and one $\alpha$ particle produced in collisions of 960 MeV $^{32}$S projectiles with $^{58}$Ni. The fragments and/or light particles were detected in the ARGUS multidetector array at the VICKSI accelerator of the HMI Berlin. The relative-energy distributions are of Maxwellian shape yielding a temperature of 5 MeV for the heavy reaction products, but only of about 3 MeV for the primary IMFs. Thus IMFs seem to be emitted towards the end of the evaporation chain. The relative-velocity correlations between two IMFs (Li, Be, B, C) display longer emission times when one of the IMFs is a lighter one (Li, Be), compatible with the picture that the latter are more likely to result from a multi-step decay.

Interaction Space of Neural Networks with Clipped Couplings

Acta Phys. Pol. B 26, 1423 (1995)

page 1423 •

abstract

Using replica approach we consider a neural network model with synaptic weights that are clipped from below and above by some numbers. Such a model is motivated by certain neurophysiological and technological arguments. For some values of coupling bounds, namely those that select binary synaptic efficacies approximately equal to $\pm 1$, a double-stage first-order phase transition is encountered. This transition occurs at zero temperature and leads to a change of the critical capacity value $\alpha _c(\kappa \to 0)$: $1.27 \to 0.83 \to 0$. An even more interesting situation is observed when synapses take only one value approximately (either $-1$ or $+1$). Here the storage ratio may grow from zero to some finite number if the couplings are allowed to fluctuate. We also study properties of the weights distribution and illustrate the contributions of Dirac’s delta at both boundaries of the allowed range of the synaptic strengths.

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