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We explore the possibility of introducing the special relativity to undergraduate students by restricting the relativity principle to Maxwell’s equations in vacuum. By making some hypothesis of simplicity, we obtain the transformation equations for the electric and magnetic fields among equivalent observers. Later, the transformation equations for the charge and current density are found and, finally, the Lorentz transformations. What is left is to extend the relativity principle to all physical phenomena.

The status of advancement of the VIRGO Project is presented: the first-generation results from the Pisa seismic noise super attenuator give an upper limit to the noise transfer function of 2 × 10 −8 at 10 Hz. The upper limit to the absolute noise of the 400 kg test mass at 10 Hz has been measured to be 1.5 × 10 −13 m/√Hz. The scheme and the related problems of the VIRGO interferometer, which is supposed to work down to 10 Hz, are also presented. At the 3rd Pisa Meeting in 1986 we presented the idea of what could be a very efficient seismic noise reduction system able to give a sensitivity h ∼ 10 −25 at 10 Hz, in a 3 km interferometer for 1 year integration time. Now we have two new facts to present: the first is that the attenuation has been built, is working in Pisa, and shows remarkable characteristics. The second is the Italian-French interferometer VIRGO [1,2], a 3 km long antenna for low and high frequency (10–1000 Hz) gravitational wave (GW) detection. These two items will be presented in this article.

In biochemical dynamical systems during each transition between periodical behaviors, all metabolic intermediaries of the system oscillate with the same frequency but with different phase-shifts. We have studied the behavior of phase-shift records obtained from random transitions between periodic solutions of a biochemical dynamical system. The phase-shift data were analyzed by means of Hurst's rescaled range method (introduced by Mandelbrot and Wallis). The results show the existence of persistent behavior: each value of the phase-shift depends not only on the recent transitions, but also on previous ones. In this paper, the different kind of periodic solutions were determined by different small values of the control parameter. It was assessed the significance of this results through extensive Monte Carlo simulations as well as quantifying the long-range correlations. We have also applied this type of analysis on cardiac rhythms, showing a clear persistent behavior. The relationship of the results with the cellular persistence phenomena conditioned by the past, widely evidenced in experimental observations, is discussed.

We present the analysis of a phase-shift sequence obtained from random transitions between periodic solutions of a biochemical dynamical model, formed by a system of three differential equations and which represent an instability-generating multienzymatic mechanism. The phase-shift series was studied in terms of Hurst’s rescaled range analysis. We found that the data were characterized by a Hurst exponent H = 0.69, which was clearly indicative of long-term trends. This result had a high significance level, as was confirmed through Monte Carlo simulations in which the data were scrambled in the series, destroying its original ordering. For these series we obtained a Hurst exponent which was consistent with the expectation of H = 0.5 for a random independent process. This clearly showed that, although the transitions between the periodic solutions were provoked randomly, the stochastic process obtained exhibited long-term persistence. The fractal dimension was also estimated and found to be consistent with the value of the Hurst exponent.

A method to estimate the persistent behavior from a chaotic time series is proposed. Persistency means that here each value depends to some extent on the previous values and not only on the recent ones. The data were analyzed by means of Hurst's rescaled range method, i.e., R/S analysis (which was introduced by Mandelbrot and Wallis). The relation of the Hurst exponent to the self-affine and self-simialr fractal dimension is discussed.

The numerical study of a glycolytic model formed by a system of three delay differential equations reveals a multiplicity of stable coexisting states: birhythmicity, trirhythmicity, hard excitation and quasiperiodic with chaotic regimes. For different initial functions in the phase space one may observe the coexistence of two different quasiperiodic motions, the existence of a stable steady state with a stable torus, and the existence of a strange attractor with different stable regimes (chaos with torus, chaos with bursting motion, and chaos with different periodic regimes). For a single range of the control parameter values our system may exhibit different bifurcation diagrams: in one case a Feigenbaum route to chaos coexists with a finite number of successive periodic bifurcations, in other conditions it is possible to observe the coexistence of two quasiperiodicity routes to chaos. These studies were obtained both at constant input flux and under forcing conditions.

It is shown that successive approximations can be used to implement a numerical method to integrate forward the Lorentz - Dirac equation, as well as other equations with the same singular structure. The code automatically selects the physical solution and avoids the so-called `runaway solutions'. The method's convergence is analytically discussed in a particular but illustrative case. The convergence is also numerically studied in a capture motion and a chaotic scattering process.

The numerical study of a glycolytic model formed by a system of three delay differential equations reveals a quasiperiodicity route to chaos. When the delay changes in our biochemical system, we can observe the emergence of a strange attractor that replaces a previous torus. This behavior happens both under a constant input flux and when the frequency of the periodic substrate input flux changes. The results obtained under periodic input flux are in agreement with experimental observations.

The problem of embedding a Demianski cavity with small rotation parameter in an appropriate rotational perturbation of a pressureless Friedmann universe with a Λ term is considered. The relation between the coordinate change introduced by Schucking [Z. Phys. 137, 595 (1954)] for this kind of problems and that used for the simple model of Oppenheimer and Snyder [Phys. Rev. 56, 455 (1939)] for gravitational collapse is also discussed.

In an attempt to improve the understanding of complex metabolic dynamic phenomena, we have analysed several ‘metabolic networks’, dynamical systems which, under a single formulation, take into account the activity of several catalytic dissipative structures, interconnected by substrate fluxes and regulatory signals. These metabolic networks exhibit a rich variety of self-organized dynamic patterns, with e.g., phase transitions emerging in the whole activity of each network. We apply Hurst’s R/S analysis to several time series generated by these metabolic networks, and measure Hurst exponents H < 0.5 in most cases. This value of H, indicative of antipersistent processes, is detected at very high significance levels, estimated with detailed Monte Carlo simulations. These results show clearly the considered type of metabolic networks exhibit long-term memory phenomena.

The differential equation governing the time evolution of the self-similar scalar soliton star models, recently proposed by Di Prisco, Herrera, and Esculpi, is studied in detail. All physical plausible modes of evolution are exhibited and compared with the specific solutions presented by Di Prisco, Herrera, and Esculpi

The numerical study of a glycolytic model formed by a system of three delay differential equations reveals a multiplicity of stable coexisting states: birhythmicity, trirhythmicity, hard excitation and quasiperiodic with chaotic regimes. For different initial functions in the phase space one may observe the coexistence of two different quasiperiodic motions, the existence of a stable steady state with a stable torus, and the existence of a strange attractor with different stable regimes (chaos with torus, chaos with bursting motion, and chaos with different periodic regimes). For a single range of the control parameter values our system may exhibit different bifurcation diagrams: in one case a Feigenbaum route to chaos coexists with a finite number of successive periodic bifurcations, in other conditions it is possible to observe the coexistence of two quasiperiodicity routes to chaos. These studies were obtained both at constant input flux and under forcing conditions.

We study the effects of heat flow on the evolution of two different families of self-gravitating, radiating spheres. The sensitivity of the system of differential equations, governing the evolution of the boundary surface, to the emission of radiation is brought out

We consider the linear four-momentum radiated by a system of two point charges during two proper-time infinitesimal intervals. As a simple generalization of Schild's result for a single charge, we show that the radiation rate is independent of the hypersurface which is used to integrate Maxwell's tensor and we give an exact covariant expression for it. Using the preceding result we give, in the framework of predictive relativistic mechanics, a definition of radiated linear four-momentum for a system of two interacting charges. We calculate this quantity at the lowest approximation in perturbation theory and we compare our result to the familiar one obtained in the framework of the slow-motion approximation.

A previous covariant approach in classical field theory to the definition of the energy and linear momentum radiated by two‐point charges is extended to the case of angular momentum. First, the mixed contribution to the radiation rate of angular momentum for two proper time infinitesimal intervals is defined, shown to be independent of the hypersurface used, and computed in an exact covariant way. With this result a definition of the radiated angular momentum for a system of interacting particles is given in the framework of predictive relativistic mechanics. The lowest order of this quantity is calculated and compared with a previous result obtained by means of a different method. The agreement of the results obtained in both approaches can be interpreted as a test for the Lorentz–Dirac equation.

The authors propose a simpler model in order to facilitate calculations of the Feynman paradox concerning the angular momentum of a static electromagnetic field. When an angular momentum is attached to the static electromagnetic field the paradox disappears. The storage of the angular momentum in the field during the assembling process is also analysed.

We show that one expects a cascade of dominant reductions (asymptotic approximation of a retarded equation by an ordinary one) of increasing orders in the process of evolution from the “laminar” regime to the “turbulent” one. We report also on some preliminary numerical evidence confirming the theoretical expectation for the first two steps of the cascade, in particular for optical hybrids with a time delay akin with non linear optical cavities.