Robust exponential attractors for the strongly damped wave equation with memory. I

We consider the singular limit of the semilinear strongly damped wave equation with memory

On the Strongly Damped Wave Equation

We prove the existence of the universal attractor for the strongly damped semilinear wave equation, in the presence of a quite general nonlinearity of critical growth. When the nonlinearity is subcritical, we prove the existence of an exponential attractor of optimal regularity, having a basin of attraction coinciding with the whole phase-space. As a byproduct, the universal attractor is regular and of finite fractal dimension. Moreover, we carry out a detailed analysis of the asymptotic behavior of the solutions in dependence of the damping coefficient.Research partially supported the Italian MIUR Research Projects Problemi di Frontiera Libera nelle Scienze Applicate, Aspetti Teorici e Applicativi di Equazioni a Derivate Parziali and Metodi Variazionali e Topologici nello Studio dei Fenomeni Nonlineari. The second author was also supported by the Istituto Nazionale di Alta Matematica F. Severi (INdAM).     

Analysis on configuration spaces and Gibbs cluster ensembles

The distribution μ of a Gibbs cluster point process in χ = ℝ^d (with n-point clusters) is studied via the projection of an auxiliary Gibbs measure defined on the space of configurations in χ × χ ⁿ. We show that μ is quasi-invariant with respect to the group Diff₀(χ) of compactly supported diffeomorphisms of χ and prove an integration-by-parts formula for μ. The corresponding equilibrium stochastic dynamics is then constructed by using the method of Dirichlet forms. Dedicated to the memory of Vladimir Geyler Research supported in part by DFG Grant 436 RUS 113/722.     

Formal structure of kinetic theory

We study the Liouville equation in the domain of small deviations from absolute equilibrium. The solution is expressed in terms of amplitudes ofn-body additive functions which are orthogonal with respect to the Gibbs weight factor. In the memory operator approach the memory operators are formally exact continued fractions. We show that with the isolation in the Liouville operator of a one-body additive operatorL _o, any memory operator can be written alternatively as an exact infinite series, each term of which can be calculated exactly. This yields improvements of the dressed particle approximation. We discuss the choice ofL _o, which is in general time dependent. The theory is developed both for smooth potentials and for hard spheres, where we use pseudo-Liouville operators. The theory can be formulated in an equivalent manner by introducing modified cumulant distributions, which are closely related to the amplitudes. The modified cumulants have the same spatial asymptotic properties as ordinary cumulants, but have superior short-time and small-distance behavior.Work supported by the National Science Foundation.     

Positroniumlike system in quartz

Summary The ortho-state of the Ps-like system, which in crystalline quartz lives in Bloch states, has been detected in the time annihilation spectrum. Its lifetime and abundance are τ₃=0.49ns,I ₃=0.13. The magnetic quenching of this system has been measured and compared with that of Ps-like system living in other molecular media. This work was supported by CISM (Centro Interuniversitario di Struttura della Materia) of Ministero della Pubblica Istruzione and by GNSM (Gruppo Nazionale di Struttura della Materia) of CNR.     

On the energy spectrum and parameter spaces of classicalCP n models

It is known that a large class of smooth solutions ofCP ⁿ models can be constructed starting from holomorphic maps of an algebraic curve into complex projective spaces. Here we apply results from algebraic geometry to describe the energy spectrum and the parameter spaces for such models.Work partially supported by Gruppo Nazionale di Fisica Matematica, CNR and Gruppo Nazionale per le Strutture Algebriche e Geometriche e Applicazioni, CNR     

Solution of the Hartree-Fock equations

We suggest to use the Newton iteration method for constructing a (locally unique) solution of the atomic and nuclear Hartree-Fock equations for an arbitrary number of particles. Our proposal is based on a theorem by Kantorovi and rests on the following points: 1) the two-body potential must satisfy a boundedness condition; 2) the zero-order approximation, used to start the iteration sequence, must satisfy certain conditions, to be proved numerically. Condition 1) holds, for instance, for all local potentials, defined by a bounded function and for a class of nonlocal potentials; it does not hold for local potentials, behaving as 1/r near the origin.This work has been supported in part by Istituto Nazionale di Fisica Nucleare (Sezione di Catania) and by Centro Siciliano di Fisica Nucleare e di Struttura della Materia (Catania).     

Abstract Hodge Decomposition and Minimal Models for Cyclic Algebras

We show that an algebra over a cyclic operad supplied with an additional linear algebra datum called Hodge decomposition admits a minimal model whose structure maps are given in terms of summation over trees. This minimal model is unique up to homotopy. J. Chuang is supported by an EPSRC advanced research fellowship. A. Lazarev is partially supported by an EPSRC research grant.     

Influence of electrical and optical losses on fundamental solar-cell parameters

Summary We present here an analysis of the dependence of the light-generated current on the current at maximum power in lossy solar cells. that is, cells with both series and shunt resistances present simultaneously — that is, a real cell. It is essentially seen that this dependence is highly sensitive to series resistance. However, for cells with series resistance of the order of 3 Ω, ϖI _g/ϖI _mp=1. We also look at the influence of TiO_x antireflection coatings on the open-circuit voltage and short-circuit current in silicon solar cells.

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Riassunto Si presenta un'analisi della dipendenza della fotocorrente dalla corrente di massima potenza nelle celle solari quando sono contemporaneamente presenti le resistenze serie e di shunt. Su tale dipendenza influisce molto la resistenza serie. Tuttavia, se questa è dell'ordine di 3 Ω, è ϖI _g/ϖI _mp=1. Si studia anche l'influenza di rivestimenti antiriflettenti di TiO_x sulla tensione di circuito aperto, sulla corrente di circuito aperto e sulla corrente di corto circuito nelle celle di silicio.

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Quantum theory of polaritons with spatial dispersion: Exact solutions

Summary We give the exact solution of the quantum polariton problem with spatial dispersion. The exact polariton eigenstates are obtained in terms of photon and polariton states. For all values ofk a nonlinear contribution of the photon and polarization states is present in the polariton wave function. Two- and three-photon components are explicitly singled out.

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Riassunto Si presentano le soluzioni esatte del problema quantistico del polaritone con dispersione spaziale. Gli autostati polaritonici esatti sono ottenuti come combinazioni di stati fotonici e di stati di polarizzazione. Contributi non lineari di fotoni e di quanti di polarizzazione sono presenti a tutti i valori dik. Componenti a due fotoni e a tre fotoni sono date in forma esplicita.

     

Computation of theoreticalSH seismograms with a finite source

Summary We have generated complete theoretical seismograms, which include both body and surface waves, for realistic sources buried in a radially heterogeneous, anelastic, spherical Earth. The effect of the source finiteness on the time series, for a particular case, has been investigated by simulating rupture propagation along a fault plane with a series of point sources distributed along a straight line. On the time series, this source model seems to produce, by increasing the time duration of the rupture, a broadening of the body wave bursts, a shortening of the time lag between the phasesS andsS, and a decrease in the amplitude of body waves relative to surface waves.

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Riassunto Si generano sismogrammi teorici completi, comprendenti sia onde di volume chesuperficiali, relativi a sorgenti sismiche realistiche in una struttura terrestre sferica, radialmente eterogenea e anelastica. L'effetto delle dimensioni non infinitesime della sorgente è analizzato simulando la propagazione di una frattura lungo un piano di faglia per mezzo di una serie di ?punti sorgente? distribuiti lungo una linea retta. Questo tipo di sorgente produce, con l'aumentare del tempo di propagazione della frattura, uno spargimento del pacchetto delle onde di volume, un accorciamento dell'intervallo di tempo tra le fasiS edsS e una diminuzione dell'ampiezza delle onde di volume rispetto a quelle superficiali.

     

Coherence effects in the exciton transfer in LH2 unit

The LH2 subunit ofRps. acidophila consists of a ring of 9αβ heterodimers to which BChl’s are associated. We apply the strong exciton coupling model in which allαβ BChl₂ pairs are organized in a cyclic unit cell and strongly excitonically coupled. We investigate the exciton energy structure with heterogeneity both in the local BChl850 energies and in transfer integrals. We calculate the pure coherent memory functions of the LH2 subunit which enter the time nonlocal Generalized Master Equations in various regimes of the exciton transfer. We discuss the influence of the exciton interaction with a bath (phonons) on the time dependence of the memory functions and we show limits of the use of the time local Pauli Master Equations. We study also the influence of the heterogeneity in the local BChl850 energies and in transfer integrals on the delivery time of the exciton inside of the LH2. Presented at the Czech-Israeli-German Symposium “Dynamical Processes in Condensed Molecular Systems”, Prague, Czech Republic, 26–30 May 1997. This work was supported by the Grants 105/95 of the Charles University and 1235/96 of the Development Fund.     

Stochastic modelling of solar-radiation data

Summary Daily global solar-radiation sequences are studied for Italy. We show that the experimental data can be described as a first-order autoregressive stochastic process independent of locality or season: the only climatic information needed is the monthly average of the clearness index. We also show that the clearness index sequences can be transformed in sequences with normal distribution but with the same autocorrelation properties; it is then easy to construct synthetic sequences of radiation data with the same statistical properties as the real data, useful for performance prediction of solar systems.

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Riassunto Si analizzano le serie temporali dei valori giornalieriK _T (rapporto tra la radiazione solare globale su superficie orizzontale e la radiazione extra-atmosferica) per il territorio italiano. Si dimostra che i dati possono essere descritti con processi stocastici autoregressivi del primo ordine indipendentemente dalla località o stagione: la sola informazione necessaria è il valore medio mensile dei rapportiK _T . Si dimostra inoltre che le successioni dei valoriK _T possono essere trasformate in successioni con funzione di distribuzione normale e con le stesse caratteristiche statistiche di autocorrelazione dei dati originari; in tal modo è poi possibile costruire successioni di dati di radiazione, di lunghezza pari al numero di giorni in un mese e con le stesse proprietà statistiche dei dati sperimentali, utili per il calcolo delle prestazioni di sistemi solari.

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d-core transitions in ZnTe,CdTe and HgTe

Summary We have measured the reflectivity spectra of monocrystalline ZnTe, CdTe and HgTe between 5 and 35 eV. We have interpreted the sharp structures above approximately 10 eV as transitions originating in the metal uppermostd levels. The structures give a picture of the projected densities of states of the conduction bands and supply a better understanding of their states.

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Riassunto Abbiamo misurato gli spettri di riflettività di monocristalli di ZnTe, CdTe ed HgTe tra 5 e 35 eV. Oltre i 10 eV gli spettri presentano delle strutture fini, interpretate come transizioni che hanno origine nei livellid piú alti del catione. Questa interpretazione permette di ricavare una rappresentazione schematica della densità proiettata degli stati di conduzione e di ottenere una migliore comprensione sulla natura degli stati finali stessi.

     

Many-body effects in the electron spectroscopies of incompletely filled bands

Summary Photoemission and Auger line shapes from almost completely filled bands have been widely discussed in recent years within a simplified model based on an Anderson Hamiltonian in which the virtual level shift due to the interactions is suitably compensated for. Up to now, the theory has been much more successful with XPS than with AES, and the reason for this was obscured by the lack of an exact solution and by the difficulty to assess the degree of validity of various approximate treatments that have been proposed. Here we present a Green’s function formalism that allows us to extend the closed band solution to the partially occupied case and lends itself to the exact numerical treatment of finite systems. By applying the theory to 27 and 125 atom clusters, we analyse the dependence of the spectra on hole-hole repulsionU with a degree of unfillingn _h≤0.25. We also consider the case when one of the spin subbands is full as a rough model for ferromagnetic metals. Correlation effects on the one-hole density of states produce a narrowing of the band region, while a split-off structure develops below the band forU comparable to the band width. The low-density approximation is good agreement with the exact results forn _h=0.1 and also forn _h=0.25 for small and moderateU. Our results on the Auger line shapes justify somewhat the suggestion by Haak and Bennetet al. that split-off states observed in photoemission must be discarded before computing the two-hole spectrum. Indeed self-energy corrections must be excluded also in bandlike cases, when the simple procedure of cutting off the unwanted structure is not applicable. This arises because, in a wide range of physical situations, the Auger line shape reflects the mutual scattering of undressed final-state holes.

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Riassunto Il modello teorico piú usato negli ultimi anni per le forme di riga di fotoemissione ed Auger di bande quasi completamente occupate si basa su un hamiltoniano di Anderson in cui lo spostamento del livello virtuale dovuto alle interazioni è opportunamente compensato. Finora la teoria ha dato risultati molto migliori per la fotoemissione che per lo spettro Auger. Le ragioni di ciò non sono chiare poiché non si dispone di una soluzione esatta ed è difficile valutare l’attendibilità delle varie approssimazioni note. Pertanto noi proponiamo un formalismo basato sulle funzioni di Green che permette, nel caso di aggregati finiti di atomi, di estendere la soluzione esatta, nota nel caso di bande chiuse, al caso di bande parzialmente occupate. Applicando il metodo a sistemi di 27 e 125 atomi, analizziamo la dipendenza degli spettri dalla repulsioneU tra lacune, per una concentrazione di lacunen _h≤0.25. Abbiamo considerato anche il caso in cui una delle sottobande di spin è completamente occupata come una prima approssimazione al problema di metalli ferromagnetici. Gli effetti di correlazione restringono il continuo nella densità di stati ad una particella e producono una struttura discreta sotto la banda seU è confrontabile con la larghezza della stessa. L’approssimazione di bassa densità è in buon accordo coi risultati esatti pern _h=0.1 ed anche pern _h=0.25 seU è piccolo o moderato. I nostri risultati sulla forma di riga Auger legittimano in qualche modo quanto suggerito da Haak e Bennetet al., e cioè che il picco satellite di fotoemissione deve essere soppresso nel calcolo della forma di riga Auger. Anzi, tutte le correzioni al propagatore ad un corpo, dovute agli effetti di correlazione, debbono essere escluse anche nel caso di spettri di tipo banda, dove, per l’assenza della struttura satellite in fotoemissione, il procedimento di Bennettet al. non è piú applicabile: infatti nella maggior parte dei casi d’interesse fisico, la forma di riga Auger riflette la dinamica di lacune non rinormalizzate.

     

The method of virtual quanta as a probe of the equivalence principle

We consider bremsstrahlung encounters between a test body of massm, chargee, and a large fixed massM with chargeQ. We use the method of virtual quanta, and calculate the total electromagnetic and gravitational energy radiated in such encounters. We consider both the case in which the deflection is principally electromagnetic in nature, and the case in which the deflection is principally gravitational. The results are interpreted by considering the predictions of the equivalence principle, for the behavior of the test particle,and for the behavior of the virtual quanta. As expected from the equivalence principle, the total radiation produced is larger for electromagnetic deflection than for a gravitational deflection through the same angle.Dedicated to the memory of Alfred Schild, born7 September 1921; died 24 May 1977. A good man, a great scholar, the best of friends.Research supported in part by NSF grant no. PHV76-07919 and by NATO Research grant no. 1002.     

Bernoulli property for a one-dimensional system with localized interaction

We consider a one-dimensional system of particles on the half line =[0, ] interacting through elastic collisions among themselves and with a wall at the origin. On the first particle a constant forceE is acting, no external forces act on the other particles. All particles are identical except the first one which has a larger mass. We prove that ifE is such that the Gibbs equilibrium state exists, the corresponding equilibrium dynamical system is a Bernoulli flow.On leave from Dipartimento di Matematica e Fisica, Università di Camerino, Camerino, Italy. Partially supported by NSF Grant DMR-81-14726     

Asymptotic solutions to the Knizhnik-Zamolodchikov equation and crystal base

The Knizhnik-Zamolodchikov equation associated withsl ₂ is considered. The transition functions between asymptotic solutions to the Knizhnik-Zamolodchikov equation are described. A connection between asymptotic solutions and the crystal base in the tensor product of modules over the quantum groupU _q sl ₂ is established, in particular, a correspondence between the Bethe vectors of the Gaudin model of an inhomogeneous magnetic chain and the Q-basis of the crystal base.Dedicated to the memory of Ansgar SchnizerThe author was supported by NSF Grant DMS-9203929     

Fusion Rules for the Vertex Operator Algebras <Emphasis Type="Italic">M</Emphasis>(1)<Superscript>+</Superscript> and <Emphasis Type="Italic">V</Emphasis><Superscript>+</Superscript><Subscript><Emphasis Type="Italic">L</Emphasis></Subscript>

The fusion rules for the vertex operator algebras M(1)⁺ (of any rank) and V⁺_L (for any positive definite even lattice L) are determined completely.Supported by JSPS Research Fellowships for Young ScientistsPartially supported by NSF grants and a research grant from the Committee on Research, UC Santa CruzPartially supported by a NSA grant and a grant from Rutgers University Research Council     

Two-photon transitions between discretenS states in atomic He

Summary The two-photon transition probabilities from the ground state 1¹ S and from the metastable states 2¹ S and 2³ S to the lowest excited states are computed in He. A configuration interaction approach is used, and a detailed comparison between the ?length? and the ?velocity? gauges leads to an estimate of 1% accuracy. Correlation effects are found to account for about 20% of the transition probabilities. The life-time of the 2¹ S state is ≅19.6 ms. The two-photon transition probabilities display a dramatic dependence on frequency, characterized by resonances and transparencies. Based on work supported in part by the Gruppo Nazionale di Struttura della Materia of the C.N.R. and by the Frascati Synchrotron Radiation Contract (P.U.L.S.).