Attilio Maccari

Free lance researcher

A model for the Universe is proposed where the general relativity is modified in order to explain the irreversible evolution of the Universe. At the same time, the dichotomy matter-field of the Einstein equation is eliminated and the physical world is described only by means of a unified field. The Universe evolution is characterized by an oscillat...

A new integrable and nonlinear partial differential equation (PDE) in 2+1 dimensions is obtained, by an asymptotically exact reduction method based on Fourier expansion and spatiotemporal rescaling, from the Kadomtsev–Petviashvili equation. The integrability property is explicitly demonstrated, by exhibiting the corresponding Lax pair, that is obta...

Using an asymptotically exact reduction method based on Fourier expansion and spatiotemporal rescaling, a new integrable and nonlinear partial differential equation (PDE) in 2+1 dimensions is obtained starting from the Kadomtsev–Petviashvili equation. We apply the reduction technique to the Lax pair of the Kadomtsev–Petviashvili equation and demons...

We study a very peculiar nonlinear oscillator with an external two period quasiperiodic excitation, being the golden mean the ratio between the two frequencies. The two period quasi periodic forcing configuration gets an infinite frequencies number. As a consequence, we find the motion settles down in a twoperiod quasi periodic atttractor for a wid...

This paper studies a perturbative approach for the double sine–Gordon equation. Following this path, we are able to obtain a system of differential equations that shows the amplitude and phase modulation of the approximate solution. In the case λ = 0, we get the well-known perturbation theory for the sine–Gordon equation. For a special value λ = −1...

This paper presents the perturbation theory for the double–sine–Gordon equation. We obtain a system of differential equations that shows the amplitude and phase modulation of the approximate solution.. In the particular case λ = 0 we get the well-known perturbation theory for the sine–Gordon equation. For a special value λ=-1/8, we derive a phase-l...

Using the Asymptotic Perturbation (AP) method we can find approximate solutions for the Maccari equation with a parametric resonant forcing acting over the frequency of a generic mode. Taking into account its nonlocal behavior and applying symmetry considerations, a system with two coupled equations for the phase and amplitude modulation can be obt...

The nonlocal Hirota–Maccari equation is considered when a parametric excitation is acting over the frequency of a generic mode. Using the well-known asymptotic perturbation (AP) method, two coupled equations for the amplitude and phase can be obtained. We discovered the existence of an infinite-period bifurcation when the parametric force increases...

We consider a weakly nonlinear oscillator with a fractal forcing, given by the Weierstrass function, and use a perturbation method to study its behavior. Being this function nowhere differentiable we can only use adequate approximations. We find that while in the linear case the resulting motion is a simple superposition between the fractal forcing...

We study the Hirota-Maccari equation in 2+1 dimensions when an external excitation is in parametric resonance with the frequency of a generic mode. Using the well known asymptotic perturbation (AP) method, we can obtain two coupled equations for the amplitude and phase. We demonstrate the existence of an infinite-period bifurcation when the paramet...

Self excitations can be dangerous in many nonlinear systems and can produce catastrophic failures, that is a sudden and complete failure that cannot be put right. We extend the nonlocal vibration control to the suppression of the self-excited vibrations of the Liènard system. We introduce a non local control force that yields a third order non line...

The behavior of a mass point moving in a plane under the effect of a central field and an external periodic excitation in resonance with the natural frequency is studied. The as-ymptotic perturbation method is used in order to determine the nonlinear modulation equations for the amplitude and the phase of the oscillation. Firstly, we calculate the...

We consider a very general 3+1 dimensions nonlinear system and using the asymptotic reduction (AP) method based on Fourier expansions and time rescaling we can get a a nonlocal (if we consider only the main field as fundamental) model equation for its behavior. This model equation belongs to the Davey-Stewartson type equations and could be relevant...

Nonlocal equations can be verified through suitable experiments

nonlocal NPDEs methods and physics applications

storia della meccanica quantistica relativistica

nascita dell'eettrodinamica quantistica

la rinormalizzazione dell'elettrodinamica quantistica

The Maccari nonlinear system (MS) has been extensively employed to describe rogue waves but there is no unified framework in order to understand this important nonlinear behavior. In this paper we demonstrate that the MS can be considered as a model system for rogue waves. The MS system can be derived from nonlinear partial differential equations (...

Nei primi anni del Novecento, dopo il lavoro di Planck sul corpo nero e l'introduzione della quantizzazione, si sviluppa la fisica dei quanti, che cerca di applicare la nuova scoperta in altri campi di ricerca. Viene così sviluppata la teoria quantistica del calore specifico dei solidi e Bohr introduce la quantizzazione del momento angolare, per in...

revised version for rogue waves

Una importante rivoluzione concettuale si è verificata negli ultimi venti anni nel campo della fisica e si sta ora espandendo verso altre scienze. Frattali, caos e soli-toni sono i principali aspetti di questa nuova disciplina che è stata denominata fisi-ca (o anche, vista la sua natura interdisciplinare, scienza) non lineare. Un possibile percorso...

1. Introduzione Sul finire dell'Ottocento, il logico tedesco Gottlob Frege inizia una nuova linea di ricerca ten-dente a fornire una base logica alla teoria dei numeri naturali. Il logicismo, come poi sarà chiamata, voleva esprimere tutti i concetti dell'aritmetica mediante i soli concetti logici (§ 2). I numeri naturali non vanno considerati puri...

Il dibattito sulla possibilità di una conoscenza effettiva, sin dalle teorie platoniche e aristoteli-che, è stato sempre molto vivo e ricco di implicazioni epistemologiche ed ontologiche. Pas-sando per la vaga definizione di conoscenza dell'empirismo di Locke e per quella più articola-ta di Russell di conoscenza come credenza vera e giustificata, s...

Una delle maggiori difficoltà concettuali nell'apprendimento della Meccanica Quantistica è costituita dalla doppia natura corpuscolare e ondulatoria della materia e della luce. Un possi-bile percorso storico-didattico può essere costituito dall'analisi del ragionamento, basato mol-to sull'intuizione fisica e assai poco sull'astrazione matematica, c...

A partire dal 1925, viene elaborata, da Heisenberg, Born, Jordan, un gruppo di fisici a Gottinga, in Germania, la mec-canica delle matrici, che culminerà, qual-che anno dopo, nella cosiddetta interpre-tazione ortodossa della meccanica quan-tistica. Le basi fondanti della fisica clas-sica vengono completamente rigettate, il concetto di traiettoria p...

nascita dell'elettromagnetismo classico

La meccanica statistica classica è stata sviluppata da Boltzmann, mentre cercava di dimostrare la validità del secondo principio della termodinamica, sulla base delle leggi della meccanica. Durante i suoi tentativi, introdusse per la prima volta in fisica il calcolo delle probabilità. Il particolare strumento matematico scelto da Boltzmann contribu...

In questo lavoro descrivo un modulo riguardante la scoperta dei raggi cosmici ed i primi studi sulla loro natura che segnano la nascita della fisica delle particelle elementari. Il percorso di-dattico richiede un tempo indicativo di 16 ore ed è consigliabile il suo svolgimento durante l'ultima parte dell'ultimo anno delle superiori. Le modalità di...

teoria della relatività

teoria della relatività

fisica molecolare

1. Introduzione In questo lavoro descrivo un modulo riguardante la fisica delle particelle elementari negli Anni Quaranta, dalla determinazione della vita media del muone alla scoperta delle particelle strane. Il percorso didattico richiede un tempo indicativo di 14 ore ed è consigliabile il suo svolgimento durante l'ultima parte dell'ultimo anno d...

fisica atomica

Planck e la nascita della fisica dei quanti

Sunto. Viene esposta una breve storia sui rapporti fra geometria e fisi-ca ed illustrato il dibattito su quale tipo di geometria, euclidea o non, sia la più adatta a descrivere le nuove caratteristiche dello spazio fisi-co, evidenziate dalla teoria della relatività generale di Einstein. Abstract. It is exposed a brief history about the relations be...

Via Alfredo Casella 3-00013 Mentana (RM) La meccanica quantistica nasce dal-l'unione della meccanica delle matrici, sviluppata soprattutto dai fisici di Got-tinga (Heisenberg, Born e Jordan), con la meccanica ondulatoria, nata con de Broglie e Schrodinger. Un ruolo impor-tante venne giocato anche da Einstein, con il suo lavoro sulla statistica dei...

L'affermazione dell'interpretazione ortodossa

storia fisica nucleare 1

storia fisica nucleare 3

2 Introduzione In questo lavoro descrivo un modulo (proseguimento di un altro descrivente la scoperta dei raggi cosmici [1]) riguardante la scoperta, all'interno dei raggi cosmici, di una nuova particel-la, inizialmente chiamata mesone (per la sua massa intermedia fra quella dell'elettrone e del protone). Il percorso didattico richiede un tempo ind...

storia fisica nucleare 2

scienza e fede

storia dei quark

metodi matematici

The most important properties of strong interactions, confinement and asymptotic freedom, can be explained in a purely geometric way, using a non-local modification of the general relativity. At the same time, the dichotomy matter-field of the Einstein equation is eliminated and the physical world is described only by means of a unified field. Hadr...

A time delay control is applied to the forced Kadomtsev-Petviashvili (KP) equation Using an appropriate perturbation method, we derive nonlinear equations describing amplitude and phase of the response anfd discuss in some detail external force-response and frequency-response curves for the fundamental resonance. For the uncontrolled system we find...

storia dei quark

Usually oscillators with periodic excitations show a periodic motion with frequency equal to the forcing one. A complex-valued nonlinear oscillator under parametric excitation is investigated by an asymptotic perturbation method based on Fourier expansion and time rescaling. Four differential equations for two nonlinearly coupled oscillators are de...

This work represents a possible way to achieve the Einstein-de Broglie soliton-particle concept. The weakly nonlinear Klein-Gordon equation (nonlinear quantum mechanics) is investigated by the asymptotic perturbation (AP) method for a particle confined in a box. It is obtained the quantization of the energy with a slight difference respect to the s...

Isochronous systems are not rare in dynamical systems. Three complex-valued nonlinear systems (quadratic and cubic nonlinearity, van der Pol, gyroscopic oscillator) are investigated by an asymptotic perturbation method based on Fourier expansion and time rescaling. Four coupled equations for the amplitude and the phase of solutions are derived. App...

Parametrically excited van der Pol system dangerous vibrations can be controlled and governed by Jerk dynamics. We choose a non-local force for the vibration control and a third order nonlinear differential equation (jerk dynamics) is necessary for the control method implementation Two slow flow equations on the amplitude and phase of the response...

maccari equations as model system for rogue waves

maccari system and rogue waves

The most important characteristics of the non local oscillator, an oscillator subjected to an additional non local force, are extensively studied by means of a new asymptotic perturbation method that is able to furnish an approximate solution of weakly nonlinear differential equations. The resulting motion is doubly periodic, because a second littl...

A complex nonlinear system under state feedback control with a time delay corresponding to two coupled nonlinear oscillators with a parametric excitation is investigated by an asymptotic perturbation method based on Fourier expansion and time rescaling. Four coupled equations for the amplitude and the phase of solutions are derived. In the system w...

A new integrable and nonlinear system of partial differential equations in 2 + 1 dimensions is obtained by means of an asymptotically exact reduction method based on Fourier expansion and spatio-temporal rescaling. We find interacting coherent excitations such as the soliton, dromion, lump, ring soliton, breather, and instanton solutions. The inter...

7 The asymptotic perturbation (AP) method is applied to the study of the nonlinear Klein-Gordon equation and an 8 external periodic excitation is supposed to be in primary resonance with the frequency of a generic mode. The AP 9 method uses two different procedures for the solutions: introducing an asymptotic temporal rescaling and balancing of 10...

With the help of an asymptotically exact reduction method we derive from the Kadomtsev-Petviashvili equation a new integrable and nonlinear partial differential system of equations in 2+1 dimensions. We find interacting coherent solutions such as solitons, dromions, lumps, ring solitons and breathers. The arbitrariness of the functions included in...

italiano

vibration control

A non-local control force is introduced in such a way to obtain a third order nonlinear differential equation (jerk dynamics) and to control nonlinear vibrations in a externally excited van der Pol oscillator. Two first-order nonlinear ordinary differential equations governing the modulation of the amplitude and the phase of solutions are derived a...

Jerk dynamics is used for a new method for the suppression of self-excited vibrations in nonlinear oscillators. Two cases are considered, the van der Pol equation and nonlinear oscillator with quadratic and cubic nonlinearities. A nonlocal control force is introduced in such a way to obtain a third order nonlinear differential equation (jerk dynami...

A nonlocal feedback is used for the control of nonlinear vibrations in a parametrically excited van der Pol oscillator. A nonlocal control force is introduced in order to obtain a third-order nonlinear differential equation (jerk dynamics). Using the asymptotic perturbation method, two slow flow equations on the amplitude and phase of the response...

A method for time delay vibration control of the principal and fundamental resonances of two nonlinearly coupled van der Pol oscillators is investigated Using the asymptotic perturbation method, four slow-flow equations on the amplitude and phase of the oscillators are obtained. Their fixed points correspond to a two-period quasi-periodic phase-loc...

We consider the bifurcation control for the forced Zakharov–Kusnetsov (ZK) equation by means of delay feedback linear control terms. Using a perturbation method, we obtain two slow flow equations on the amplitude and phase of the response as well as external force–response and frequency–response curves for the fundamental resonance. We observe in t...

A complex nonlinear system under state feedback control with a time delay corresponding to two coupled nonlinear oscillators with a parametric excitation is investigated by an asymptotic perturbation method based on Fourier expansion and time rescaling. Four coupled equations for the amplitude and the phase of solutions are derived. In the system w...

The physical model SOLARMET, elaborated in ENEA (Italian National Agency for New Technologies, Energy and Environment), provides hourly average global solar irradiance on a horizontal surface (GHi) and hourly average direct normal solar irradiance (DNi) for Italy based on primary satellite images in the visible band.In the present study, the hourly...

A new integrable and nonlinear system of partial differential equations in 2+1 dimensions is obtained by means of an asymptotically exact reduction method based on Fourier expansion and spatio-temporal rescaling. We find interacting coherent excitations such as the soliton, dromion, lump, ring soliton, breather, and instanton solutions. The interac...

We consider the bifurcation control for the forced Burgers–KdV equation by means of delay feedback linear terms. We use a perturbation method in order to find amplitude and phase modulation equations as well as external force-response and frequency-response curves. We observe in the resonance response a saddle-node bifurcation that leads to jump an...

Periodic solutions for parametrically excited system under state feedback control with a time delay are investigated. Using the asymptotic perturbation method, two slow-flow equations for the amplitude and phase of the parametric resonance response are derived. Their fixed points correspond to limit cycles (phase-locked periodic solutions) for the...

Periodic solutions for a parametrically excited van der Pol system with nonlinear stiffness and under state feedback control with a time delay are investigated. Two slow flow equations for the amplitude and phase of the parametric resonance response are derived. It is well known that their fixed points correspond to phase-locked periodic solutions...

Solar concentration cells of the type SunPower HECO252 have been tested as photodetectors in fluxmeters for trough solar thermal concentrators. Two types of fluxmeters have been investigated, both realized with a collar-shaped sensor head wrapping round the glass tube protecting the cylindrical thermal receiver. The first fluxmeter has a sensor hea...

A vigorous R&D program on solar concentrating power plants has been recently funded in Italy in order to demonstrate the feasibility of these technologies. Maps of direct normal radiation (DNI) are needed for the selection of construction sites for demonstration plants. This paper describes SOLARMET, a physical model that simulates the atmospheric...

A fluxmeter for measurement of flux density of concentrated solar radiation in parabolic trough solar concentrators is described [1]. The concentrated solar radiation impinging on the receiver at the focal line of the parabolic trough collector is detected by eleven solar concentration cells distributed on the cylindrical outer surface of a sensor...

PURPOSE Method and apparatus (fluxmeter) for measurement of flux density near the focal line of parabolic trough solar concentrators. The sensor head is a collar fixed on the glass tube. The prototype CFV2, manufactured by " CN di Claudio Nappo " (NA, Italy), has eleven SunPower HECO252 concentration cells distributed over the surface of the sensor...

An optical profilometer has been developed based on the idea that the large panels that compose solar-power concentrators and a tolerance threshold for slope-errors to some milliradians, can allow the use of a geometric-optics framework and the investigation of ray-paths by means of a laser beam. The instrument scheme is discussed in detail togethe...

Metodo e relativa apparecchiatura per la misura dell’intensità e distribuzione della radiazione concentrata nei sistemi solari con ricevitore cilindrico, in particolare nei sistemi solari lineari di tipo termico o termodinamico. Il sensore del radiometro, a forma di collare, è realizzato con una molteplicità di fotorivelatori e viene fissato sul ri...

Profound advances have recently interested nonlinear field theories and their exact or approximate solutions. We review the last results and point out some important unresolved questions. It is well known that quantum field theories are based upon Fourier series and the identification of plane waves with free particles. On the contrary, nonlinear f...

We apply a new vibration control method for time delay non-linear oscillators to the principal resonance of a parametrically excited Liénard system under state feedback control with a time delay. Using the asymptotic perturbation method, we obtain two slow flow equations on the amplitude and phase. Their fixed points correspond to limit cycles for...

A spontaneous symmetry breaking (or hidden symmetry) model is reduced to a system nonlinear evolution equations integrable via an appropriate change of variables, by means of the asymptotic perturbation (AP) method, based on spatio-temporal rescaling and Fourier expansion. It is demonstrated the existence of coherent solutions as well as chaotic an...

Two new methods are used in order to obtain arbitrary approximate dromions solutions of the weakly nonlinear Klein-Gordon equation in 3 + 1 dimensions with one or more external fields. Using the asymptotic perturbation (AP) method, based on Fourier expansion and spatio-temporal rescaling, it is found that the amplitude slow modulation of Fourier mo...

We investigate the primary resonance of an externally excited nonlinear system under state feedback control with a time delay. Using an appropriate perturbation method, we obtain two slow flow equations on the amplitude and phase. Their fixed points correspond to limit cycles for the nonlinear system and we determine excitation amplitude-response a...

We investigate the parametric resonance of two nonlinearly coupled van der Pol oscillators under state feedback control with a time delay. Using the asymptotic perturbation method, we obtain four slow flow equations on the amplitude and phase of the oscillators. Their fixed points correspond to a two-period quasi-periodic motion for the starting sy...

By means of the asymptotic perturbation (AP) method, analytical investigation of a nonlinear Dirac equation shows the existence of interacting coherent excitations such as the dromions, lumps, ring soliton solutions and breathers as well as instanton solutions. The interaction between the localized solutions are completely elastic, because they pas...

La nascita della fisica quantica ha vi-sto in Einstein uno degli indiscussi pro-tagonisti, che per primo siè reso conto del vero significato della teoria di Planck sul corpo nero. Nei suoi lavori, dai primi sulla termodinamica statistica e sull'ef-fetto fotoelettrico, a quelli sulle fluttua-zioni energetiche della radiazione elettro-magnetica e sul...

Envelope solitons in the weakly nonlinear Klein–Gordon equation in 1+1 dimensions are investigated by the asymptotic perturbation (AP) method. Two different types of solitons are possible according to the properties of the dispersion relation. In the first case, solitons propagate with the group velocity (less than the light speed) of the carrier w...

Dopo una breve rassegna dei possibili metodi di misura del flusso della radiazione solare concentrata, il metodo del collare fotovoltaico è brevemente descritto e i suoi limiti discussi. Sono poi descritti i due prototipi di collare finora realizzati e le misure con essi eseguite. Il primo prototipo, sviluppato in Casaccia, alloggia una singola fot...

Approximate interacting localized solutions of a vectorial massive nonlinear equation are obtained by using the asymptotic perturbation (AP) method, based on Fourier expansion and spatio-temporal rescaling. The amplitude slow modulation of Fourier modes is described by a system of nonlinear evolution equations solvable via an appropriate change of...