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The space and time dependence of physical constants is currently a debated issue for experimental findings, and theoretical reasons seem to indicate that this is not a mere speculative possibility. The paper provides a relativistic description of a free fermion evolving under the assumption of temporal variation of the physical constants. The assumed generalisation of the Dirac equation is particularly simple and permits a grouping of the constants in one single parameter and a consequent agile treatment of the problem. The form of the equations suggests a rescaling of the temporal coordinate $$x^0=ct$$ which allows a plane wave solution. Two are the main results of the treatment. First, the effects of the variation of the constants are better seen in the weak relativistic regime which indicates that experiments can be carried out without having to resort to super accelerators and, second, that a slow particle–antiparticle oscillation occurs in the evolution of a plane wave. This prediction of charge non-conserving oscillation is the analytical outcome of the generalised Dirac equation and appears to be a necessary consequence of the variation of the physical constants.

Nonlinearity in Quantum Mechanics may have extrinsic or intrinsic origins and is a liable route to a chaotic behaviour that can be of difficult observations. In this paper, we propose two forms of nonlinear Hamiltonian, which explicitly depend upon the phase of the wave function and produce chaotic behaviour. To speed up the slow manifestation of chaotic effects, a resonant laser field assisting the time evolution of the systems causes cumulative effects that might be revealed, at least in principle. The nonlinear Schr&ouml, dinger equation is solved within the two-state approximation, the solution displays features with characteristics similar to those found in chaotic Classical Mechanics: sensitivity on the initial state, dense power spectrum, irregular filling of the Poincar&eacute, map and exponential separation of the trajectories of the Bloch vector &sigma, in the Bloch sphere.

The high-harmonic generation from a structured quantum ring (SQR) driven by an intense laser field is presented within the single active electron approximation. The spectrum is studied by varying the symmetry of the physical system. The standard SQR (six identical and equidistant dots in a ring) presents a 60° rotational symmetry, that in this work is broken, moving or changing only one potential hole. We find that careful designed breaking of the geometrical symmetry of the SQR opens the possibility of controlling the characteristics of the harmonic lines such as intensity and polarization. HHG analysis of the emission spectrum performed through a Morlet wavelet, shows that the high-frequency emission occurs during short time intervals.

The effect of a static magnetic field on the high harmonic generation (HHG) from a quantum ring driven by one laser polarized along the x-axis is studied. The spin polarization (Formula presented.) and the temporal emission of the harmonics are studied by varying the intensity of the magnetic field and it is shown how these results have a significant technological impact in computer technology; in fact a boolean algebra can be implemented by assigning 0 and 1 values to low and high pulse intensities of the emitted harmonics and logic gates like the NOT can becreated.

Reduced dimensionality systems (RDS) are materials extending along one or two dimensions much more than the other(s). The degrees of freedom of the small dimension are not explored by the electrons since their energy is very large. The time dependent wave function of a particle in a short nanotube, taken as a paradigm of the RDS family, is calculated by solving the Klein–Gordon equation; the confining condition produces a small change in the mass of the particles and of the energy levels. These changes are of relativistic origin and therefore small, but can be measured by use of a weak resonant laser field which produces cumulative effects in the time development of the wave function. The shift of the energy of the levels are within today's spectroscopy capacity.

Linearity is a fundamental postulate of quantum mechanics which is occasionally the subject of debate. This paper investigates the possibility of checking this assumption by using a laser field. We study the corrections caused by the presence of a small nonlinearity in the Hamiltonian of a quantum system. As a model we use a simplified two-level quantum system whose states are coupled by a small off-diagonal term proportional to the population of the upper level. The nonlinearity causes spontaneous decay of the upper level, shift and broadening of the line and the sensitive dependence of the final state on the initial condition. The presence of a strong laser field, resonant with the atomic transition, enhances the population transfer among the levels and introduces quantitative and qualitative modifications of the spectra of high order harmonic generation (HHG); these are cumulative effects which can be subject to experimental checks. Experiments are needed in order to set an upper limit to the nonlinear term.

We study the application of one nanoring driven by a laser field in different states of polarization in logic circuits. In particular we show that assigning Boolean values to different states of the incident laser field and to the emitted signals, we can create logic gates such as OR, XOR and AND. We also show the possibility of making logic circuits such as half-adder and full-adder using one and two nanorings respectively. Using two nanorings we made the Toffoli gate. Finally we use the final angular momentum acquired by the electron to store information and hence show the possibility of using an array of nanorings as a mass memory device.

We discuss an experiment on wind energy performed with home-made apparatus. The experiment reproduces a laboratory windmill, which can pump water from a lower level to a higher one. By measuring the gain of the gravitational potential energy of the pumped water, one can determine the power extracted from the wind. The activity was carried out with high-school students, in the framework of the Italian National Plan for Scientific Degrees-Physics. The proposed experiment allows teachers to discuss renewable energy sources with students whose knowledge of physics is limited to mechanics. It gives students the possibility to gain experience with energy and to increase their awareness of this renewable energy source.

The dynamics of a one-dimensional atom driven by three-laser fields is investigated. The total electric field is made up of a fundamental laser field of intensity W cm−2 and wavelength λ = 820 nm and two weak lasers with larger wavelengths. The intensity of the two weak fields is with k = 0.25. The frequencies of the weak fields are and , with and . The three lasers have a Gaussian envelope of 72 fs FWHM. It is shown, by numerical computation and using the semiclassical theory of high-harmonic generation, that the atom interacting with this combined field is able to emit an isolated attosecond burst of radiation.

The electron of a H 2 + driven by a strong electromagnetic field induces molecular vibrations. Numerical and analytical results show that the molecule behaves as a parametric oscillator and can be treated as a kicked oscillator. The results are discussed from the point of view of the electron's periodic dressing and undressing processes.

We study the application of one nanoring driven by a laser field in different states of polarization in logic circuits. In particular we show that assigning boolean values to different state of the incident laser field and to the emitted signals, we can create logic gates such as OR, XOR and AND. we also show the possibility to make logic circuits such as half-adder and full-adder using one and two nanoring respectively. Using two nanorings we made tho Toffoli gate. Finally we use the final angular momentum acquired by the eelctron to store information and hence show the possibility to use and array of nanorings as a mass device.

Atoms, molecules , clusters and other systems driven by a strong laser field of frequency \omega_L can emit a spectrum of laser harmonics. The high harmonics generation (HHG) phenomen is strongly affected by the symmetries of the system. It is well known that systems with rotational symmetries emit only odd harmonics. Numerous researcher make mainly attention to the possibilities to set different initial conditions in order to control the spectrum. Recently, the study of nanotechnology is hot-topics and in particular the study of very symmetric systems such as fullerene, nanoring and structured nanoring (nanoring with identical and symmetric scattering centers). Therefore, it is natural and interestring to study the HHG emission from these systems and the effects of the symmetry break. In this poster we present the HHG spectrum emitted by a nanoring consisting of six symmetric scattering centers; as a second step we study the effects on the spectrum by small symmetry breakings. We show that tiny modifications of th symmetry allow a good control of the spectrum.

We use a 5-level system to investigate the HHG spectrum emitted by an atom driven by a linearly or elliptically polarized laser field. For this model the Schrodinger equation is numerically solved and we study the dipendence of the spectra, harmonic intensity and polarization of emitted radiation on the laser field ellipticity. Studying the intensity of the emitted radiation we find that un alsoder high laser ellipticity the harmonic emission is greatly reduced; the analysis of results shows that the harmonic intensity and the emitted radiation depend on the laser ellipticity.

Atomic and molecular systems, subjected to intense laser pulse, emit typical High-Order Armonic Generation (HHG) spectra. This work aims to investigate the possibility to obtain a laser device by HHG. At this end, we analyzed the emission spectra by a molecular ion driven by a linearly polarized laser field. The temporal behaviour is obtained using the Morlet wavelets transform of emission. The results show that, after filtration of the electromagnetic radiation emitted, it is possible to select a frequency which seems to have almost constant intensity and phase. This characteristic makes possible that HHG from a molecule can be used as high frequency laser fields.

The interaction of graphene nanoparticles and strong 64 fs pulses is examined. We demonstrate high-order harmonic generation in the plasma contained in crumpled sheets of graphene. The morphological studies of the debris of ablated graphene, application of single-color and two-color pumps of graphene-containing plasma, and theoretical consideration of the high-order harmonic generation in this medium are presented.

Many instruments of the Historical Collection of the Physics Instruments of the University of Palermo date back to the early nineteenth century, when experimental Physics begun to be taught in university studies by using instruments and apparatuses in the classroom to illustrate the laws of Physics. Among the various instruments belonging to the Collection, there are also the so-called 'paradoxes', instruments with surprising properties that do not seem to follow the laws of Physics. In this article we analyze two 'mechanical paradoxes' of the Collection and discuss their possible educational use., Comment: 11 Pages, in Italian, 9 Figures. Accepted for publication in Quaderni di Ricerca in Didattica (Science), special Issue in Italian language

We report on numerical results of energy spectra of photoelectrons emitted by irradiating an hydrogen atom with a relatively weak single attosecond XUV pulse in the presence of a two-color IR laser pulse. The densities of probabilities have been obtained by treating the interaction of the atom with the XUV radiation at the first order of the time-dependent perturbation theory and describing the emitted electron through the Coulomb-Volkov wavefunction. The results of the calculations agree with the ones found by numerically solving the time-dependent Schrödinger equation. Specifically, we use an algorithm that implements an high recision variant of the Cranck Nicolson integration method and allows to take into account the singularity in the Coulomb potential. Analysis of the spectra obtained for very long pulses show that certain features may be explained in terms of quantum interferences in the time domain.

We present the electromagnetic emission from one electron confined in a quantum ring driven by an intense laser field. We consider both a plain ring and one structured by six potential wells that produce a static tangential force. Through a suitable one-dimensional model we numerically solve the associated Schroedinger equation obtaining the correspondent time evolution of the wave-function. We show that the emission is formed by a wide plateau that can be both quasi-continuum or resolved in discrete lines. We study the dependence of the emitted spectra from the polarization status of the external laser field and in particular we concentrate on the intensity of the emitted lines and of their polarization characteristic. The results illustrate how the fabrication of such systems provide important practical sources of creation and control of the radiation. Moreover, the dynamic of the ring, studied from the classical point of view, presents interesting chaotic behavior and can represent an important example of transition from classical chaos to quantum behavior.

The radiation diffused by a one-dimensional homonuclear molecular ion driven by a laser field is studied as a function of the time. When the photon energy is resonant with the energy gap between the ground and the first excited state, the electronic probability density is seen to undergo slow and deep oscillations between the two nuclei. Synchronous to such oscillations, deep modulations of the emitted power are observed. The period of oscillation is of the order of 10 optical cycles. Detection of the variation in the intensity of the emitted electromagnetic spectrum therefore brings information on the position of the electron in the molecule.

We propose an experiment for investigating how objects cool down toward the thermal equilibrium with its surrounding through convection. We describe the time dependence of the temperature difference of the cooling object and the environment with an exponential decay function. By measuring the thermal constant tau, we determine the convective heat-transfer coefficient, which is a characteristic constant of the convection system., Comment: 8 pages, 2 embedded figures. Accepted for publication in The Physics Teacher

We study the high harmonic generation and the polarization of the harmonics emitted by a nanoring driven by two laser fields of angular frequency ?1 and ?2, with ?2?=?2?1, and ?1 resonant between the ground and the first excited state. We show that by varying parameters, such as laser intensity, photon energy and the delay between the two laser pulses, we can control the number of harmonics and the polarization of the radiation. In particular we show that with this choice of two-laser photon frequency rate we obtain more harmonics with respect to other configurations. We also calculated the average absorbed energy and the average angular momentum acquired by the electron as a function of the intensity of the two lasers obtaining spikes of angular momentum.

We study the polarization of the harmonics generated by a homonuclear diatomic molecule in the presence of an intense, linearly polarized laser field. The polarization parameters of the emitted radiation are investigated as function of the angle $\theta$ between the laser electric field and the molecular axis. The calculations are carried out by assuming a single active electron model with fixed nuclei; a two-dimensional model of the system is used. We find a different dependence of the parameters of the harmonics vs $\theta$ in the first or second half of the emitted spectrum. In particular, the differences are accentuated for $0^\circ < \theta < 50^\circ$, while for higher angles, until the perpendicular orientation, almost all the harmonics present similar characteristics

We present the dynamics of an electron constrained over an 1D ring with radius of 0.142 nm driven by a laser field. The temporal evolution of the system is evaluated by a semi-analytical solution of the full quantum time dependent Schr¨odinger equation. In our calculation the gap energy between the ground and the first excited state of the nanoring is three times the photon energy laser (0.63 eV) and the laser intensity is 4·1014 W/cm2 . Our analysis is performed by considering different polarization states of the incident laser. Our attention is mainly focused on the study of the High Harmonic Generation (HHG), the energy and the angular momentum absorbed by the driven system. We observe 1) that the harmonic yield is strongly dependent upon the pump polarization field and almost vanishes for circular polarization and 2) that the ring can be left in a state with average angular momentum different than zero. In figure we show the time average of the absorbed angular momentum (in atomic units) versus polarization angle (θ = 0◦ and θ = 90◦ correspond to linear polarization along x and y axes respectively; θ = 45◦ corresponds to circular polarization).

We study the full quantum dynamics of a simple molecular ion driven by an intense laser field. In particular we show that the quantum nature of the nuclear dynamics affects the emitted high harmonic generation (HHG) spectra, strongly reshaping the plateau region. In fact, it is evident that the characteristic flat trend is transformed into a descending trend, with the lower harmonics being two orders of magnitude more intense than the higher harmonics. We show that this effect is more pronounced in the lighter isotopic species of H$_2^+$ molecular ions and we also demonstrate that in this case the contribution to HHG from the antibonding electronic energetic surface is of the same order of magnitude as that from the bonding state.

The time-dependent wave function of a nanoring driven by a laser field is obtained by exploiting the symmetries inherent to the system and used for studying the properties of the electromagnetic radiation emitted by the nanoring as a function of the polarization state of the laser. The diffused radiation has the characteristics of high-order-harmonic generation. For a noncircularly polarized laser field an extension of the expected cutoff position is evident, indicating that nanorings are efficient sources of radiation. The polarization state of the emitted harmonics can be opportunely controlled by varying the parameters of the pump field. The profile of the absorbed angular moment shows that a magnetic moment can be induced depending on the polarization of the driven field.

High frequency lasing device by HHG

A quantum ring driven by an intense laser field emits light in the form of high-harmonic radiation resulting from the strong acceleration experienced by the active electrons forced to move on a curved trajectory. The spectrum of the emitted light is rich and strongly dependent on the parameters of the problem. In order to investigate the physical origin of such variability, we focus on the seemingly simple problem of a laser-driven charge constrained to a ring from a classical standpoint. As it turns out, the dynamics of such a classical electron is governed by a nonlinear equation which results into a chaotic motion - by nature depending on the initial conditions in an unpredictable way. Our results indicate that the quantum harmonic spectra are reminiscent of the classical counterpart and suggest the existence of a line connecting the quantum and classical realms.

We discuss the physical properties of a noninteracting electron gas constrained to a spherical surface. In particular we consider its chemical potentials, its ionization potential, and its electric static polarizability. All these properties are discussed analytically as functions of the number $N$ of electrons. The trends obtained with increasing $N$ are compared with those of the corresponding properties experimentally measured or theoretically evaluated for quasispherical hollow atomic and molecular clusters. Most of the properties investigated display similar trends, characterized by a prominence of shell effects. This leads to the definition of a scale-invariant distribution of magic numbers which follows a power law with critical exponent $\ensuremath{-}0.5$. We conclude that our completely mechanistic and analytically tractable model can be useful for the analysis of self-assembling complex systems.

In this paper we discuss isotopic effects in simple molecular ions subjected to strong laser fields. We show that the intensity of the emitted spectra strongly depends upon both the nuclear mass of the molecular ions and the laser pulse duration. In particular, for short pulse duration [up to 8 optical cycles (o.c.)], we confirm the trend described in the most studied case in which the high-order harmonic generation is more efficient for heavier isotopes; in contrast, an interesting physical phenomenon is predicted for pulses longer than 16 o.c. characterized by an inverse effect in which lighter molecular species are responsible for higher-order harmonic emission.

In the framework of the Italian National Plan ‘Lauree Scientifiche’ (PLS) in collaboration with secondary schools, we have investigated the mechanical paradox of the double cone. We have calculated the geometric condition for obtaining an upward movement. Based on this result, we have built a mechanical model with a double cone made of aluminum and a couple of wooden rails.

Il terremoto avvenuto in Giappone l'11 Marzo del 2011 ha riaperto il dibattito sull'energia quale elemento centrale di sviluppo della societa' moderna. L'esperienza didattica su tematiche energetiche, maturata a Palermo nell'ambito del Piano Nazionale Lauree Scientifiche - Fisica (PLS-Fisica), si inserisce in questo contesto. Noi proponiamo un percorso formativo di laboratorio riguardante tematiche energetiche, al fine di stimolare i docenti di fisica a portare in aula e in laboratorio questi argomenti e contribuire cosi' ad aumentare la consapevolezza che gli studenti hanno riguardo alle fonti energetiche rinnovabili, ma anche riguardo alle fonti basate sui combustibili fossili e nucleari. Le esperienze proposte sono state scelte sia per la loro valenza concettuale sia per la loro realizzazione semplice, volti a studiare quantitativamente i processi di trasformazione dell'energia. *** The catastrophic earthquake and subsequent tsunami occurred in Japan in March 11, 2011 gave rise again to a world-wide debate on the energy sources as a central issue for the development of the human society. The experience on the energy topics, gained at the University of Palermo in the framework of the Piano Nazionale Luree Scientifiche - Fisica (PLS-Fisica) (National Plan for Scientific Degrees - Physics), can be naturally integrated in this larger context. We propose a laboratory pedagogical path to stimulate physics teachers to introduce the energy concept by discussing the issue of renewable, fossil and nuclear energy sources. The activity can raise the awareness of students on this very important issue. We propose easy, but conceptually well-based, laboratory experiences with the purpose to study the energy transformation processes from a quantitative point of view.

We report on an experiment performed with a home-made flat-plate solar collector, carried out together with high-school students. To explain the experimental results, we propose a model that describes the heating process of the solar collector. The model accounts quantitatively for the experimental data. We suggest that solar-energy topics should be included in school programmes to give students the opportunity to gain experience with solar energy and increase their awareness of the benefits that can be obtained from this remarkable and renewable energy source.

The time dependent Schrodinger equation of a homonuclear diatomic molecule in the presence of a linearly polarized laser field is numerically solved by means of a split-operator parallel code. The calculations are carried out by assuming a single active electron model with fixed nuclei; a simplified two-dimensional model of the system is used. The highly nonlinear response of the electron wave function to the laser electric field stimulates the molecule to emit electromagnetic radiation consisting of a wide plateau of odd harmonics of the laser field. It is shown that the emitted spectrum can be finely controlled by changing the angle between the laser electric field and the molecular axis; this can be used to achieve a tunable source of high frequency radiation.

Quarta di copertina - Frutto di alcuni anni di lavoro degli autori nell'ambito del progetto "Lauree Scientifiche", il presente volume è rivolto agli studenti delle scuole secondarie e ai loro docenti con l'obiettivo di rafforzare quanto affrontato nelle lezioni in classe e stimolare la curiosità e la creatività dello studente. La prima parte introduce i concetti di base per una corretta impostazione metodologica nelle attivita' di laboratorio. Nella seconda parte sono trattati argomenti di meccanica e termodinamica volti allo studio dell'energia nelle sue diverse forme: cinetica, potenziale, termica. Infine, la terza parte raccoglie esperienze di meccanica e di termodinamica emerse durante le attivita' laboratoriali.

The soil CO2 degassing is a ected by processes of isotope exchange and fractionation during transport across the soil, which can deeply modify the pristine isotope composition. This has been observed in 10 the Solfatara volcano, upon a eld survey of 110 points, where the CO2 ux was measured, together with temperature, CO2 concentra- tion and oxygen and carbon isotopes within the soil. Furthermore, in some selected sites, the measurements were made at di erent depths, in order to analyze vertical gradients. Oxygen isotope composition 15 appears controlled by exchange with soil water (either meteoric or fumarolic condensate), due to the fast kinetic of the isotopic equilib- rium between CO2 and water. Carbon isotope composition is reliably controlled by transport-driven fractionation, due to the di erences in di usion coe cients between 13C16O2 and 12C16O2. We model the 20 processes a ecting CO2 transport across the soil in La Solfatara vol- cano by means of the Dusty Gas Model applied to a multicomponent system, to evaluate the reciprocal e ect on di usion of involved gases, i.e. 12C16O2, 13C16O2, N2 and O2 in our case. Both numerical and simpli ed analytical solutions of the equations based on the Dusty 25 Gas Model are given. The modeling results t well with the experimental data and put in evidence an isotope fractionation of carbon up to about +4:4h with respect to the source value in the soil gas. This fractionation is independent from the entity of the CO2 ux, and occurs as long as a concentration gradient exists within the soil. On 30 these grounds, the Dusty Gas Model can be applied to whichever dif- fusing gas mixture to evaluate the extent of chemical and/or isotopic fractionation that can a ect ascending gases upon di usion in any geothermal, volcanic or tectonic area.

We show that it is possible to use a piecewise constant Hamiltonian to describe the main features of the dynamics of an atom interacting with a laser field. In particular we show that using this approximation we are able to give a good description of the ionization signal, of the HHG spectra and of the attosecond pulses generated by the radiating electron. Finally, we give an explicit formula to evaluate the ionization rate in the time dependent laser field. This formula, which is a generalization of the Landau formula for the ionization rate of an atom in a static electric field, fairly well reproduces the numerical ionization rates for a broad range of laser frequency and intensity. The main advantage of this formula is that it can be used well beyond the limits of the quasi-static formula for the ionization rate of an atom.

A new scheme to generate isolated attosecond pulses is presented that involves the use of a laser field and of a unipolar field. The laser field has a pulse of intensity I = 1.5×1014 W cm−2 and wavelength λ = 820 nm. The unipolar pulse is an asymmetric pulse consisting of a sharp peak, lasting approximately half a laser period, i.e. nearly 1.4 fs, followed by a long and shallow tail. We show that on combining these two fields, it is possible to generate isolated attosecond pulses as short as 1/10 of a laser period, i.e. approximately 270 as. Moreover, it is argued that this scheme is robust either against small variations of the laser envelope, or against small changes in the delay between the laser pump and the unipolar pulse.

In this paper we investigate the single and double ionization signals of ${\text{H}}_{2}$ molecules, with fixed and moving nuclei, as a function of laser intensity, for two different values of laser wavelength ($\ensuremath{\lambda}=390\text{ }\text{nm}$ and $\ensuremath{\lambda}=780\text{ }\text{nm}$), using an approach for evaluating the ionization signals which allows the investigation of relatively long-lasting pulses. The He system is first investigated to benchmark our calculation against already known results. We confirm the evidence of nonsequentiality in the ionization processes of all the systems investigated. Furthermore, we show that the nuclei motion enhances the double ionization signals by means of a mechanism which is very similar to a charge-resonant enhanced ionization (CREI) effect [Zuo and Bandrauk, Phys. Rev. A 52, R2511 (1995)].

We study the dynamics of an electron constrained over the surface of a rigid sphere, with geometrical parameters similar to those of the C60 fullerene, embedded in a low intensity linearly polarized laser field. The model is shown to emit odd harmonics of the laser even at very low field intensity. For more intense laser fields, the spectrum presents odd harmonics and hyper-Raman lines shaped in a broad plateau. The spectrum of the model is compared to that theoretically obtained by other authors for more realistic models of C60. It is concluded that the model can be used as a paradigm for mesoscopic molecules in the fullerene family, particularly in practical applications where it is convenient to have a simple model of fullerene molecules. It is also concluded that the model is an example lending support to the concept of universality introduced by other authors some time ago.

In this paper we show how it is possible to investigate the nuclear dynamics of simple molecular ions and molecules by looking at the high-order harmonic generation spectra they emit in the presence of a laser field. In particular we investigate two different effects: the presence of sidebands in the emitted spectra around the usual odd harmonics and an isotopic effect which affects the height of the plateau lines. We further study the advantages and the limitations of the semiclassical approach.

We propose a new scheme to produce isolated attosecond pulses, involving the use of three laser pulses: a fundamental laser field of intensity I = 3.5 × 1014 W cm−2 and of wavelength λ = 820 nm, and two properly chosen weak lasers with wavelengths 1.5λ and 0.5λ. The three lasers have a Gaussian envelope of 36 fs full width at half maximum. The resulting total field is an asymmetric electric field with an isolated peak. We show that a model atom, interacting with the above-defined total field, generates an isolated attosecond pulse as short as 1/10 of a laser period, i.e. approximately 270 as.