LOCALIZED STATES AND BAND STRUCTURE
|
|
- Diane Jefferson
- 5 years ago
- Views:
Transcription
1 LOCALIZED STATES AND BAND STRUCTURE F. Bassani To cite this version: F. Bassani. LOCALIZED STATES AND BAND STRUCTURE. Journal de Physique Colloques, 1972, 33 (C3), pp.c3-21-c3-25. < /jphyscol: >. <jpa > HAL Id: jpa Submitted on 1 Jan 1972 HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.
2 JOURNAL DE PHYSIQUE Colloque C3, supplkment au no 5-6, Tome 33, Mai-Juin 1972, page C3-21 LOCALIZED STATES AND BAND STRUCTURE F. BASSANI Istituto di Fisica, Universiti di Roma, Italy Resumb. - On presente la formulation generale du probl6me des Ctats Clectroniques localises sur la base des fonctions de Bloch du cristal parfait. Des calculs recents sur les Btats d'impuretes dans les semi-conducteurs sont discutcs et les limitations dues a l'approximation de la masse effective sont mises en evidence. On propose pour les excitons une approximation valable lorsque la fonction d'onde est 1ocalisBe sur un petit nombre de cellules elementaires. Cette approximation inclut les effets de la structure de bande non perturbce et utilise la localisation des fonctions de Wannier. Les separations singulettriplet et Iongitudinale-transverse sont naturellement incorporees dans l'approximation proposee. Abstract. - The general formulation of the problem of electronic localized states with point symmetry is presented in the basis of the Bloch functions of the perfect lattice. The effective mass approximation is discussed and recent calculations are reviewed as well as recent improvements appropriate to impurity and exciton states in semiconductors. A different approach is proposed for exciton states in insulators, where the localized function extends over a few lattice cells only. The present approach takes into account the unperturbed energy band structure E,(k) and makes use of the localization of the Wannier functions. Singlettriplet and longitudinal-transverse splittings are naturally incorporated in the present treatment. I. Introduction. - The purpose of this talk is to describe a number of problems which arise in the computation of impurity states and exciton states in solids and in the interpretation of the optical excitation spectrum. I will not consider those cases which can be treated satisfactorily with the lattice as a perturbation on the free atom or molecule, but rather the more complex situations where the lattice and the impurity must be treated on equal footing. The problems of impurity states and of exciton states are physically quite different, but their mathematical formulation and the computational methods to be used are so similar that one can deal with both problems at the same time, keeping in mind the specific differences. For impurities we consider oneelectron states which are IocaIized in space over a number of lattice cells ; for excitons we consider twoparticle states (electron and hole) which travel through the lattice as a whole but are also localized over a few lattice cells in their relative position. With the name localized states we indicate both << bound states n, whose wave functions go to zero away from the point defect, and cc resonant states >) which behave like scattering states away from the point defect but have a high density amplitude near it. The available experimental results indicate that in general the states are quite different from those or the free impurity atoms or from those of the atoms which compose the crystal, and are essentially determined by the electron bandstructure of the crystal [I]. The basic problem in studying the localized states is how to make use of all the information contained in the band structure which is supposed to have been computed. The connection between band structure and impurity or exciton states is the basic point to have in mind and is the problem where modern computational techniques can be used to obtain significant results. Until now meaningfull results have been obtained only in those cases where a small portion of the band structure and a small section of the Brillouin zone near critical points are sufficient to determine the localized states, i. e. when the effective mass approximation can be applied. Even within the effective mass approximation some problems still remain to be solved, but deep localized states, whose properties are determined by a large fraction of the Brillouin zone and by a large number of energy bands, are an open problem. In the following I will describe a general formulation of the impurity and exciton problems. I will point out the conditions for the validity of the effective mass approximation following the procedure of Kohn and Luttinger [2] and will describe some recent improvements [3] and some new results. Finally I will indicate a way to overcome the limitations of the effective mass approximation giving a practical procedure for exciton states which can be carried out with modern computational techniques. 11. Formulation of the impurity and of the exciton problem in crystals. - For the impurity case in the one-electron approximation one has to solve the Schrodinger equation : V, being the crystal potential, and U the impurity potential. For the exciton states of the lattice one should find the excited states of the Schrodinger equation of the N electron system Article published online by EDP Sciences and available at
3 C3-22 F. BASSANI where 2, is the charge of the nuclei located of the points R,. In the first case the eigenfunctions can be expanded in the complete set of Bloch functions $,(k, r), such that and we have In the exciton case the wave functions can be expanded in Slater determinants of excited states formed with Bloch functions, where one electron in a valence band v with wave vector k is substituted by an electron in a conduction state c, with wave vector k + q, q being the momentum of the exciton. We can write + q) - - EEx] Aidk) + 2 Ac,vr(k') [- c'v' k' where the Ket indicates the Slater determinant and the subscript S indicates that a combination of the Slater determinants with total spin 0 or 1 must be considered since the total spin is a good quantum number. With the above choice of bases the equations (1) and (2) can be transformed into integral equations on the expansion coefficients. For the impurity problem one obtains straight forwardly the integral equation where the Kernel is the non local matrix element of the impurity potential between Bloch functions. For the exciton problem one obtains after some algebraic manipulations, the equation 6, being 1 or 0 for singlet and triplet states respectively. The two integral equations (6) and (7) for impurities and excitons are very similar except for the fact that one must consider couple of bands in the latter case. The sum over the k vectors can be expressed as an integral over the Brillouin zone while the band indices are discrete. The Kernel of the integral equation (7) consists of a Coulomb two-particle matrix element and of an exchange-like term which appears only for singlet states. To solve the system of integral equations (6) and (7) is a formidable task which has never been attempted for realistic cases. Simplifications have to be made to obtain numerical solutions, but the general approach has always to be kept in mind to establish the connection between band structure and localized states. Some general remarks can be made however from the equations (6) and (7). a) The exciton and impurity states can be considered as bound states when they are not degenerate with band states, i. e. They can be considered as resonant and scattering states when the conditions (8) and (9) are not satisfied. In this case the A(k) of equations (6) and (7) have to be extended into the complex E plane [3]. The eigen- values are complex and when the imaginary part is negative and small we have a resonant state, the imaginary part of the complex solution producing a finite but sufficiently long life time. b) A general way to obtain the solutions of integral equations of type (6) or (7) consists in expressing their kernels as a sum of separable kernels. In this case the expressions in square braket of the above equations become of the general form and the solutions are given in terms of the zeroes of the corresponding Friedholm determinant [3]. Expansion (10) can be obtained in an infinite number of ways, with an infinite sum, but the real problem is to find special expansions for which the Friedholm determinant converges rapidly. c) The convergence properties of secular determinants indicate that one can restrict oneself to one band for the impurity case and to two bands for the exciton case if the other bands are well separated in energy from those which produce the dominant contribution. d) When A(k) of expansions (4) or (5) are peaked near extrema or critical points of the band structure, which is the case for large dielectric constant materials with weak and slowly varying potentials one can use the familiar effective mass approximation [2]. This can be immediately obtained by transforming equation (6)
4 LOCALIZED STATES AND BAND STRUCTURE C3-23 or (7) into a differential equation in real space on the Fourier transform We can expand E(k) and retain only quadratic terms, use plane waves instead of Bloch functions and we must screen the interaction with a dielectric constant E as shown by Kohn [4] and Haken [5]. We obtain for impurity states : where m: indicates the effective mass tensor referred to its principal axes, and the energy is measured from its value at the critical point of the band considered. A similar expression results for the exciton states except that in that case one must consider electron and hole coordinates and effective masses. In the case of isotropic effective masses one obtains from equation (7) where E, is the energy gap between the top of the valence band and the bottom of the conduction band considered. It is immediate to extend equation (13) to the case of anisotropic effective masses and of saddle points, provided one uses an effective mass tensor and allows for negative values of the effective masses Recent developments within the effective mass approximation. - Though the effective mass approximation was very successful in the fifties in explaining the excited levels of donor impurity states in a number of semiconductors and in explaining the hydrogenic series appearing in the excitation spectrum of some semiconductors [I], [2], its potentialities were not fully exploited until very recently with the availability of large size computers. A few results recently obtained may be mentioned. i) The effective mass equation (12) for impurity states has been recently solved by Faulkner [6] for the case of anisotropic effective masses in semiconductors like Si and Ge. A variatioanl procedure has been used since the equation is non separable and cannot be integrated. Kohn and Luttinger [2] could perform the calculation only on the ground state, but the agreement wlth the experiment could be found on the excited states because in that case the effective masse theory applies and the Coulomb potential is appropriate. ii) The exciton effective mass equation for anysotropic crystals was similarly solved by Baldereschi and Diaz 171, who obtained good agreement with the excitonic spectrum of GaSe and with the relative intensities of the exciton lines. After reduction of equation (13) to the center of mass, they use an expansion of the exciton envelop function F(r) in spherical harmonics and use variational parameters in the radial part of the function to improve the convergence. iii) Extensions of equations (12) and (13) have been made to the case of degenerate bands like the valence bands of cubic semiconductors, and reasonable agreement with the acceptor levels has been found [8]. iv) Intervally mixing has been computed for equivalent minima of the Brillouin Zone [9] and for minima of different bands as well [lo]. Altarelli and Iadonisi [lo] have also computed resonant impurity states below secondary minima of the conduction band and their mixing with the states of the lower bands, which is shown to depend on the effective masses and on the separation between secondary minima and the absolute minimum. v) The lowest energy levels have been computed for excitons in the presence of a constant magnetic field. This requires a modification of equation (13) which amounts to substituting the operator p = - ihv, with i p - - A. The resulting equation for the rela- tive coordinate motion is non separable and has to be solved by sofisticated numerical methods. Some recent results on the lowest eigenvalues [Ill indicate that the eigenvalues for high values of the magnetic field, obtained by the adiabatic method as a fine structure on the Landau levels, join with those at low values of the magnetic field, obtained with a variational procedure as a mixing of hydrogenic exciton states, according to the non-crossing rule. Some important problems still remain to be solved even in the effective mass approximation. The deviations from coulumb like behavior of the impurity potential and of the electron-hole interaction near the origine for instance has still to be considered in detail in numerical computations, though Phillips has explained the general trend of the chemical shift of the ground state impurity levels [12]. The question of which is the appropriate dielectric function ~(q, o) for insulators with a strong frequency dependence in the absorption region, is also a problem which needs to be clarified. IV. Suggested approach for intermediate binding. - In most experimental situations, particularly in the case of large gap insulators, the effective mass approximation does not apply and one should solve equations (6) and (7) by taking into account the effect of a large portion of the band structure and not only of
5 C3-24 F. BASSANI a small region in k space about the critical point. The problem can be reduced to that of devising a rapidly converging expansion (10) for the Kernel. Altarelli and Bassani 1131 have suggested that this can be accomplished by expressing the matrix elements as sums of integrals on Wannier functions located at the different lattice points. For the case of impurity states this leads to the results of the method of Slater and Koster [14], who first had the idea to use the localization of Wannier functions for these problems. For the exciton states, in the optical case where q --- 0, by substituting for longitudinal excitons, where no is the number of cells per unit volume. With the definition multiplying equation (15) be eik.ro and suming over k, we obtain the system of liner omogenous equations into equation (7), and keeping only maximum overlap terms ; we obtain : where Di refers to the sum of expression (15) which is different for longitudinal and transverse excitons, and is given by (16a) or (16b) in cubic lattices. The conditions for non zero solutions give the Friedolm determinant equation with Jl(R) = 11 dr, dr2 a3r1) a:(r2 - R) x J2(R) = S dr, dr, a:(r, - R) a:(r2) x The kernel of the integral equation is now a sum of separable terms. The sum on J1@) can be computed as a sum of dipols p, = e draz ray, following the method of Heller and Marcus [15] and gives, in the case of cubic lattices, for transverse excitons, and S and the eigenvalues can be computed provided only a small number of terms are needed to achieve convergence. It is interesting to observe that in equations (18) and (19) both triplet and singlet excitons are included, depending on 6, being 0 or 1, and also the longitudinaltransverse splitting can be obtained depending on the expression used for Di. The convergence should be quite good because A(R) should extend only over a few lattice cells in the case of intermediate binding. For those exciton states for which A(R) is very extended and the determinant converges too slowly, the effective mass approximation should apply. It can also be observed from (15b) and (15d) that the exchange contribution J2@) goes to zero with increasing R more rapidly than the Coulumb contribution Q(R), and this implies that only for the lowest exciton state which has a small radius there is a singiet-triplet splitting. In general the convergence of the determinantal equation (19) gives an estimate of the size of the exciton. We also wish to remark that the above approach can be easily extended to the case of resonant excitons with the procedure described in reference (3). The case of excitons produced by transitions from core states requires the contribution of more bands since the restriction to a couple of bands in no longer justified. The main computational problem is to obtain reliable expressions for the parameters (1 5b), which require a good knowledge of Wannier functions. Calculations are in progress on solid Argon where Wannier functions have been computed for the conduction band [16]. We plan to extend the method to more complicated cases and to core excitons.
6 LOCALIZED STATES AND BAND STRUCTURE C3-25 References [I] See for instance : Kom (W.), c( Shallow Impurity States in Si and Ge >> in Solid State Physics, 5 (Seitz F. and Turubull D. Eds, Academic Press, New York, 1955). PHILLIPS (J. C.), <( The Fundamental Optical Spectra of Solids >> in Solid State Physics, 18 (Seitz F. and Tuubull D. Eds, Academic Press, New York, 1966). NIKITINE (S.), ({ Excitons >> in Optical Properties of Solids, p. 197 (Nudelman S. and Mitra S. S. Eds, Plemun Press, 1969). KNOX (R. S.), (( Theory of Excitons >> in Solid State Physics, Supplement 5 (Academic Press, 1964). [2] LUTTINGER (J. M.) and KOHN (W.), Phys. Rev., 1955, 97, 869. KOHN (W.) and LUTTINGER (J. M.), Phys. Rev., 1955, 95, 915. [3] BASSANI (F.), IADONISI (G.) and PREZIOSI (B.), Phys. Rev., 1969, 186, 735. See also : BASSANI (F.), <<Theory of Impurity States >> in ((Theory of Imperfect Crystalline Solids D, p. 265, International Atomic Energy Agency, Vienna, 1971 and PREZIOSI (B.), cc Scattering and Resonant States in Crystals >>, ibidem. [4] KOHN (W.), Phys. Rev., 1957, 105, 509. [5] HAKEN (H.), ZZ NUOVO Cimento, 1956, 3, [6] FAULKNER (R. A.), Phys. Rev., 1969, 184, 713. [7] BALDERESCHI (A.) and GORFINKIEL DIAZ (M.), I1 Nuovo Cimento B, 1970, 68, 217. DEVERIN (J. A.), I1 Nuovo Cimento B, 1969, 63, 1 and related references. [8] LIPARI (N. 0.) and BALDERESCHI (A.), Phys. Rev. Lett., 1970, 25, See also : KOHN (W.) and SCHECTER (D.), Phys. Rev., 1955, 99, and MENDELSON (K. S.) and JAMES (H. M.), J. Phys. Chem. Solids, 1964, 25, 729. [9] BALDERE~CHI (A.), Phys. Rev. B, 1970, 1, KASTNER (T, G.), Phys. Rev. (to be published). [lo] ALTARELLI (M.) and IADONISI (G.), IZ NUOVO Cimento B, 1971, 5, 21. ALTARELLI (M.) and IADONISI (G.), I1 NUOVO Cimento B, 1971, 5, 36. [ll] BALDERESCHI (A.) and BASSANI (F.), Proceedings of the X International Conference on Phvsics of Semiconductors, p. 191 (Boston, 1970). [12] PHILLIPS (J. C.), Phys. Rev., 1970, 1, See also : HERMANSON (J.) and PHILLIPS (J. C.), Phys. Rev., 1966,150, ALTARELLI (M.) and BASSANI (F.), Journalof Physics C, to appear. [14] KOSTER (G. F.) and SLATER (J. C.), Phys. Rev., 1954, 96, 439. KOSTER (G. F.) and SLATER (J. C.), Phys. Rev., 1954,95, [15] HELLER (W. R.) and MARCUS (A.), Phys. Rev., 1951, 84, 809. [16] MIASEK (M.), J. Math. Phys., 1966, 7, 139.
ELASTIC WAVE PROPAGATION IN THREE-DIMENSIONAL PERIODIC COMPOSITE MATERIALS
ELASTIC WAVE PROPAGATION IN THREE-DIMENSIONAL PERIODIC COMPOSITE MATERIALS B. Auld, Y. Shui, Y. Wang To cite this version: B. Auld, Y. Shui, Y. Wang. ELASTIC WAVE PROPAGATION IN THREE-DIMENSIONAL PERI-
More informationEFFECT OF THE ONE-DIMENSIONAL STRUCTURE ON THE ENERGY TRANSFER IN Li6Gd (BO3)3
EFFECT OF THE ONE-DIMENSIONAL STRUCTURE ON THE ENERGY TRANSFER IN Li6Gd (BO3)3 C. Garapon, B. Jacquier, Y. Salem, R. Moncorge To cite this version: C. Garapon, B. Jacquier, Y. Salem, R. Moncorge. EFFECT
More informationHIGH RESOLUTION ION KINETIC ENERGY ANALYSIS OF FIELD EMITTED IONS
HIGH RESOLUTION ION KINETIC ENERGY ANALYSIS OF FIELD EMITTED IONS J. Liu, T. Tsong To cite this version: J. Liu, T. Tsong. HIGH RESOLUTION ION KINETIC ENERGY ANALYSIS OF FIELD EMITTED IONS. Journal de
More informationAPPROXIMATE NON-EMPIRICAL TIGHT-BINDING BAND STRUCTURE CALCULATIONS WITH APPLICATIONS TO DIAMOND AND SILICON
APPROXIMATE NON-EMPIRICAL TIGHT-BINDING BAND STRUCTURE CALCULATIONS WITH APPLICATIONS TO DIAMOND AND SILICON J. Linderberg, J. Chr. Poulsen To cite this version: J. Linderberg, J. Chr. Poulsen. APPROXIMATE
More informationGENERALIZED OPTICAL BISTABILITY AND CHAOS IN A LASER WITH A SATURABLE ABSORBER
GENERALIZED OPTICAL BISTABILITY AND CHAOS IN A LASER WITH A SATURABLE ABSORBER E. Arimondo, F. De Tomasi, B. Zambon, F. Papoff, D. Hennequin To cite this version: E. Arimondo, F. De Tomasi, B. Zambon,
More informationEFFECT OF TIP-SIZE ON STM IMAGES OF GRAPHITE
EFFECT OF TIP-SIZE ON STM IMAGES OF GRAPHITE C. Horie, H. Miyazaki To cite this version: C. Horie, H. Miyazaki. EFFECT OF TIP-SIZE ON STM IMAGES OF GRAPHITE. Journal de Physique Colloques, 1987, 48 (C6),
More informationQuantum efficiency and metastable lifetime measurements in ruby ( Cr 3+ : Al2O3) via lock-in rate-window photothermal radiometry
Quantum efficiency and metastable lifetime measurements in ruby ( Cr 3+ : Al2O3) via lock-in rate-window photothermal radiometry A. Mandelis, Z. Chen, R. Bleiss To cite this version: A. Mandelis, Z. Chen,
More informationRENORMALISATION ON THE PENROSE LATTICE
RENORMALISATION ON THE PENROSE LATTICE C. Godreche, Henri Orland To cite this version: C. Godreche, Henri Orland. RENORMALISATION ON THE PENROSE LATTICE. Journal de Physique Colloques, 1986, 47 (C3), pp.c3-197-c3-203.
More informationLAWS OF CRYSTAL-FIELD DISORDERNESS OF Ln3+ IONS IN INSULATING LASER CRYSTALS
LAWS OF CRYSTAL-FIELD DISORDERNESS OF Ln3+ IONS IN INSULATING LASER CRYSTALS A. Kaminskii To cite this version: A. Kaminskii. LAWS OF CRYSTAL-FIELD DISORDERNESS OF Ln3+ IONS IN INSULAT- ING LASER CRYSTALS.
More informationOn the nonrelativistic binding energy for positive ions
On the nonrelativistic binding energy for positive ions G.I. Plindov, I.K. Dmitrieva To cite this version: G.I. Plindov, I.K. Dmitrieva. On the nonrelativistic binding energy for positive ions. Journal
More information0.9 ev POTENTIAL BARRIER SCHOTTKY DIODE ON ev GAP GaxIn1-xASSi:H
0.9 ev POTENTIAL BARRIER SCHOTTKY DIODE ON 0.75-0.5 ev GAP GaxIn1-xASSi:H A. Deneuville, F. Valentin, S. Belkouch To cite this version: A. Deneuville, F. Valentin, S. Belkouch. 0.9 ev POTENTIAL BARRIER
More informationA NON - CONVENTIONAL TYPE OF PERMANENT MAGNET BEARING
A NON - CONVENTIONAL TYPE OF PERMANENT MAGNET BEARING J.-P. Yonnet To cite this version: J.-P. Yonnet. A NON - CONVENTIONAL TYPE OF PERMANENT MAG- NET BEARING. Journal de Physique Colloques, 1985, 46 (C6),
More informationDispersion relation results for VCS at JLab
Dispersion relation results for VCS at JLab G. Laveissiere To cite this version: G. Laveissiere. Dispersion relation results for VCS at JLab. Compton Scattering from Low to High Momentum Transfer, Mar
More informationTHE OPTICAL SPECTRA OF Co2+ IN MgAl2O4 SPINEL
THE OPTICAL SPECTRA OF Co IN MgAl2O4 SPINEL P. Deren, W. Strek, B. Jezowska-Trzebiatowska, I. Trabjerg To cite this version: P. Deren, W. Strek, B. Jezowska-Trzebiatowska, I. Trabjerg. THE OPTICAL SPECTRA
More informationAN INTERNAL FRICTION PEAK DUE TO HYDROGEN-DISLOCATION INTERACTION IN NICKEL
AN INTERNAL FRICTION PEAK DUE TO HYDROGEN-DISLOCATION INTERACTION IN NICKEL K. Tanaka, T. Atsumi, M. Yamada To cite this version: K. Tanaka, T. Atsumi, M. Yamada. AN INTERNAL FRICTION PEAK DUE TO HYDROGEN-
More informationYb 3d CORE-LEVEL PHOTOEMISSION OF YbN, YbP AND YbAs
Yb 3d CORE-LEVEL PHOTOEMISSION OF YbN, YbP AND YbAs T. Greber, L. Degiorgi, R. Monnier, L. Schlapbach, F. Hulliger, E. Kaldis To cite this version: T. Greber, L. Degiorgi, R. Monnier, L. Schlapbach, F.
More informationAnisotropy dynamics of CuMn spin glass through torque measurements
Anisotropy dynamics of CuMn spin glass through torque measurements J.B. Pastora, T.W. Adair, D.P. Love To cite this version: J.B. Pastora, T.W. Adair, D.P. Love. Anisotropy dynamics of CuMn spin glass
More informationTransfer matrix in one dimensional problems
Transfer matrix in one dimensional problems M. E. Mora, R. Pérez, Ch. B. Sommers To cite this version: M. E. Mora, R. Pérez, Ch. B. Sommers. Transfer matrix in one dimensional problems. Journal de Physique,
More informationImpulse response measurement of ultrasonic transducers
Impulse response measurement of ultrasonic transducers F. Kadlec To cite this version: F. Kadlec. Impulse response measurement of ultrasonic transducers. Journal de Physique IV Colloque, 1994, 04 (C5),
More informationVALENCE BAND STRUCTURE OF STRAINED-LAYER Si-Si0.5Ge0.5 SUPERLATTICES
VALENCE BAND STRUCTURE OF STRAINED-LAYER Si-Si0.5Ge0.5 SUPERLATTICES U. Ekenberg, W. Batty, E. O Reilly To cite this version: U. Ekenberg, W. Batty, E. O Reilly. VALENCE BAND STRUCTURE OF STRAINED-LAYER
More informationMirage detection for electrochromic materials characterization. Application to iridium oxide films
Mirage detection for electrochromic materials characterization. Application to iridium oxide films V. Plichon, M. Petit To cite this version: V. Plichon, M. Petit. Mirage detection for electrochromic materials
More informationMagnetic field influence on the spin-density wave of the organic conductor (TMTSF)2NO3
Magnetic field influence on the spindensity wave of the organic conductor (TMTSF)2NO3 S. Tomic, N. Biskup, B. KorinHamzic, M. Basletic, A. Hamzic, K. Maki, J.M. Fabre, K. Bechgaard To cite this version:
More informationCr3+, Nd3+ multisites, pairs and energy transfer processes in laser crystal YAlO3
Cr3+, Nd3+ multisites, pairs and energy transfer processes in laser crystal YAlO3 J. Mares, G. Boulon, A. Brenier, L. Lou, S. Rotman, H. Luria To cite this version: J. Mares, G. Boulon, A. Brenier, L.
More informationQUANTITATIVE LIGHT ELEMENT ANALYSIS USING EDS
QUANTITATIVE LIGHT ELEMENT ANALYSIS USING EDS D. Bloomfield, G. Love, V. Scott To cite this version: D. Bloomfield, G. Love, V. Scott. QUANTITATIVE LIGHT ELEMENT ANALYSIS USING EDS. Journal de Physique
More informationSIMULTANEOUS OBSERVATION OF OPTOGALVANIC AND OPTOACOUSTIC EFFECTS IN A NEON DISCHARGE
SIMULTANEOUS OBSERVATION OF OPTOGALVANIC AND OPTOACOUSTIC EFFECTS IN A NEON DISCHARGE E. Arimondo, M. Di Vito, K. Ernst, M. Inguscio To cite this version: E. Arimondo, M. Di Vito, K. Ernst, M. Inguscio.
More informationTHEORY OF SURFACE VIBRATIONS IN SUPERLATTICES
THEORY OF SURFACE VIBRATIONS IN SUPERLATTICES B. Djafari-Rouhani, L. Dobrzynski, O. Hardouin Duparc, R. Camley, A. Maradudin To cite this version: B. Djafari-Rouhani, L. Dobrzynski, O. Hardouin Duparc,
More informationA MAGNETOSTATIC CALCULATION OF FRINGING FIELD FOR THE ROGOWSKI POLE BOUNDARY WITH FLOATING SNAKE
A MAGNETOSTATIC CALCULATION OF FRINGING FIELD FOR THE ROGOWSKI POLE BOUNDARY WITH FLOATING SNAKE Yan Chen, Fan Ming-Wu To cite this version: Yan Chen, Fan Ming-Wu. A MAGNETOSTATIC CALCULATION OF FRINGING
More informationSome consequences of the analytical theory of the ferromagnetic hysteresis
Some consequences of the analytical theory of the ferromagnetic hysteresis G. Biorci, D. Pescetti To cite this version: G. Biorci, D. Pescetti. Some consequences of the analytical theory of the ferromagnetic
More informationCapillary rise between closely spaced plates : effect of Van der Waals forces
Capillary rise between closely spaced plates : effect of Van der Waals forces B. Legait, P.G. De Gennes To cite this version: B. Legait, P.G. De Gennes. Capillary rise between closely spaced plates : effect
More informationPolaritons in semiconductor microcavities : effect of Bragg confinement
Polaritons in semiconductor microcavities : effect of Bragg confinement Y. Chen, A. Tredicucci, F. Bassani To cite this version: Y. Chen, A. Tredicucci, F. Bassani. Polaritons in semiconductor microcavities
More informationApplication of an aerodynamic code to marine propellers
Application of an aerodynamic code to marine propellers M. Schaffar, J. Haertig To cite this version: M. Schaffar, J. Haertig. Application of an aerodynamic code to marine propellers. Journal de Physique
More informationSound intensity as a function of sound insulation partition
Sound intensity as a function of sound insulation partition S. Cvetkovic, R. Prascevic To cite this version: S. Cvetkovic, R. Prascevic. Sound intensity as a function of sound insulation partition. Journal
More informationThe generation of the Biot s slow wave at a fluid-porous solid interface. The influence of impedance mismatch
The generation of the Biot s slow wave at a fluid-porous solid interface. The influence of impedance mismatch T. Gómez-Alvarez Arenas, E. Riera Franco de Sarabia To cite this version: T. Gómez-Alvarez
More informationATOMIC STRUCTURE OF INTERFACES IN GaAs/Ga1-xAlxAs SUPERLATTICES
ATOMIC STRUCTURE OF INTERFACES IN GaAs/Ga1-xAlxAs SUPERLATTICES J. Laval, C. Delamarre, A. Dubon, G. Schiffmacher, G. Teste de Sagey, B. Guenais, A. Regreny To cite this version: J. Laval, C. Delamarre,
More informationRELAXATION OF HIGH LYING EXCITED STATES OF Nd3+ IONS IN YAG : Nd3+ AND IN YAP : Nd3+
RELAXATION OF HIGH LYING EXCITED STATES OF Nd3+ IONS IN YAG : Nd3+ AND IN YAP : Nd3+ M. Joubert, J. Couderc, B. Jacquier To cite this version: M. Joubert, J. Couderc, B. Jacquier. RELAXATION OF HIGH LYING
More informationTEMPERATURE AND FREQUENCY DEPENDENCES OF NMR SPIN-LATTICE RELAXATION TIME T1 IN a-si : H
TEMPERATURE AND FREQUENCY DEPENDENCES OF NMR SPIN-LATTICE RELAXATION TIME T1 IN a-si : H K. Ngai To cite this version: K. Ngai. TEMPERATURE AND FREQUENCY DEPENDENCES OF NMR SPIN-LATTICE RE- LAXATION TIME
More informationCase report on the article Water nanoelectrolysis: A simple model, Journal of Applied Physics (2017) 122,
Case report on the article Water nanoelectrolysis: A simple model, Journal of Applied Physics (2017) 122, 244902 Juan Olives, Zoubida Hammadi, Roger Morin, Laurent Lapena To cite this version: Juan Olives,
More informationELASTIC PROPERTIES OF THE ONE-DIMENSIONAL METAL Mo2 S3
ELASTIC PROPERTIES OF THE ONE-DIMENSIONAL METAL Mo2 S3 Alova, G. Mozurkewich To cite this version: Alova, G. Mozurkewich. ELASTIC PROPERTIES OF THE ONE-DIMENSIONAL METAL Mo2 S3. Journal de Physique Colloques,
More informationA new simple recursive algorithm for finding prime numbers using Rosser s theorem
A new simple recursive algorithm for finding prime numbers using Rosser s theorem Rédoane Daoudi To cite this version: Rédoane Daoudi. A new simple recursive algorithm for finding prime numbers using Rosser
More informationTHEORETICAL ANALYSIS OF THE TWO-TERMINAL MOS CAPACITOR ON SOI SUBSTRATE
THEORETICAL ANALYSIS OF THE TWO-TERMINAL MOS CAPACITOR ON SOI SUBSTRATE P. Paelinck, D. Flandre, A. Terao, F. Van de Wiele To cite this version: P. Paelinck, D. Flandre, A. Terao, F. Van de Wiele. THEORETICAL
More informationDETERMINATION OF THE METAL PARTICLE SIZE OF SUPPORTED Pt, Rh, AND Ir CATALYSTS. A CALIBRATION OF HYDROGEN CHEMISORPTION BY EXAFS
DETERMINATION OF THE METAL PARTICLE SIZE OF SUPPORTED Pt, Rh, AND Ir CATALYSTS. A CALIBRATION OF HYDROGEN CHEMISORPTION BY EXAFS F. Duivenvoorden, B. Kip, D. Koningsberger, R. Prins To cite this version:
More informationSURFACE-WAVE RESONANCE METHOD FOR MEASURING SURFACE TENSION WITH A VERY HIGH PRECISION
SURFAC-WAV RSONANC MTHOD FOR MASURNG SURFAC TNSON WTH A VRY HGH PRCSON M. ino, M. Suzuki, A. kushima To cite this version: M. ino, M. Suzuki, A. kushima. SURFAC-WAV RSONANC MTHOD FOR MA- SURNG SURFAC TNSON
More informationAccurate critical exponents from the ϵ-expansion
Accurate critical exponents from the ϵ-expansion J.C. Le Guillou, J. Zinn-Justin To cite this version: J.C. Le Guillou, J. Zinn-Justin. Accurate critical exponents from the ϵ-expansion. Journal de Physique
More informationOPTICAL CHARACTERIZATION OF Nd3+ DOPED CaF2 LAYERS GROWN BY MOLECULAR BEAM EPITAXY
OPTICAL CHARACTERIZATION OF Nd3+ DOPED CaF2 LAYERS GROWN BY MOLECULAR BEAM EPITAXY L. Bausa, R. Legros, A. Munoz-Yague To cite this version: L. Bausa, R. Legros, A. Munoz-Yague. OPTICAL CHARACTERIZATION
More informationMethylation-associated PHOX2B gene silencing is a rare event in human neuroblastoma.
Methylation-associated PHOX2B gene silencing is a rare event in human neuroblastoma. Loïc De Pontual, Delphine Trochet, Franck Bourdeaut, Sophie Thomas, Heather Etchevers, Agnes Chompret, Véronique Minard,
More informationDetermination of absorption characteristic of materials on basis of sound intensity measurement
Determination of absorption characteristic of materials on basis of sound intensity measurement R. Prascevic, A. Milosevic, S. Cvetkovic To cite this version: R. Prascevic, A. Milosevic, S. Cvetkovic.
More informationUNIVERSAL BINDING ENERGY RELATIONS FOR BIMETALLIC INTERFACES AND RELATED SYSTEMS
UNIVERSAL BINDING ENERGY RELATIONS FOR BIMETALLIC INTERFACES AND RELATED SYSTEMS J. Smith, J. Ferrante, J. Rose To cite this version: J. Smith, J. Ferrante, J. Rose. UNIVERSAL BINDING ENERGY RELATIONS
More informationIrregular wavy flow due to viscous stratification
Irregular wavy flow due to viscous stratification T. Shlang, G.I. Sivashinsky, A.J. Babchin, A.L. Frenkel To cite this version: T. Shlang, G.I. Sivashinsky, A.J. Babchin, A.L. Frenkel. Irregular wavy flow
More informationVisible laser emission of Pr3+ in various hosts
Visible laser emission of Pr3+ in various hosts M. Malinowski, M. Joubert, R. Mahiou, B. Jacquier To cite this version: M. Malinowski, M. Joubert, R. Mahiou, B. Jacquier. Visible laser emission of Pr3+
More informationUltra low frequency pressure transducer calibration
Ultra low frequency pressure transducer calibration A. Semenov To cite this version: A. Semenov. Ultra low frequency pressure transducer calibration. Journal de Physique IV Colloque, 1994, 04 (C5), pp.c7-251-c7-254.
More informationFORMAL TREATMENT OF RADIATION FIELD FLUCTUATIONS IN VACUUM
FORMAL TREATMENT OF RADIATION FIELD FLUCTUATIONS IN VACUUM Frederic Schuller, Renaud Savalle, Michael Neumann-Spallart To cite this version: Frederic Schuller, Renaud Savalle, Michael Neumann-Spallart.
More informationVibro-acoustic simulation of a car window
Vibro-acoustic simulation of a car window Christophe Barras To cite this version: Christophe Barras. Vibro-acoustic simulation of a car window. Société Française d Acoustique. Acoustics 12, Apr 12, Nantes,
More informationPRESSURE FLUCTUATION NUMERICAL SIMULATION IN A CENTRIFUGAL PUMP VOLUTE CASING
PRESSURE FLUCTUATION NUMERICAL SIMULATION IN A CENTRIFUGAL PUMP VOLUTE CASING S. Timushev, B. Ovsyannikov To cite this version: S. Timushev, B. Ovsyannikov. PRESSURE FLUCTUATION NUMERICAL SIMULATION IN
More informationNEGATIVE ION IMAGING IN FIELD ION MICROSCOPY
NEGATIVE ION IMAGING IN FIELD ION MICROSCOPY R. Schmitz, L. Bütfering, F. Röllgen To cite this version: R. Schmitz, L. Bütfering, F. Röllgen. NEGATIVE ION IMAGING IN FIELD ION MICROSCOPY. Journal de Physique
More informationSIZE EFFECTS IN FINE PARTICLES OF Fe3O4
SIZE EFFECTS IN FINE PARTICLES OF Fe3O4 Yu. Krupyanskii, I. Suzdalev To cite this version: Yu. Krupyanskii, I. Suzdalev. SIZE EFFECTS IN FINE PARTICLES OF Fe3O4. Journal de Physique Colloques, 1974, 35
More informationSmart Bolometer: Toward Monolithic Bolometer with Smart Functions
Smart Bolometer: Toward Monolithic Bolometer with Smart Functions Matthieu Denoual, Gilles Allègre, Patrick Attia, Olivier De Sagazan To cite this version: Matthieu Denoual, Gilles Allègre, Patrick Attia,
More informationLight scattering by cooperative diffusion in semi-dilute polymer solutions
Light scattering by cooperative diffusion in semidilute polymer solutions M. Adam, M. Delsanti, G. Jannink To cite this version: M. Adam, M. Delsanti, G. Jannink. Light scattering by cooperative diffusion
More informationExact Comparison of Quadratic Irrationals
Exact Comparison of Quadratic Irrationals Phuc Ngo To cite this version: Phuc Ngo. Exact Comparison of Quadratic Irrationals. [Research Report] LIGM. 20. HAL Id: hal-0069762 https://hal.archives-ouvertes.fr/hal-0069762
More informationSOLUTE STRUCTURE OF COPPER(II)ACETATE SOLUTIONS IN LIQUID AND GLASSY STATES
SOLUTE STRUCTURE OF COPPER(II)ACETATE SOLUTIONS IN LIQUID AND GLASSY STATES M. Nomura, T. Yamaguchi To cite this version: M. Nomura, T. Yamaguchi. SOLUTE STRUCTURE OF COPPER(II)ACETATE SOLUTIONS IN LIQUID
More informationOn the beam deflection method applied to ultrasound absorption measurements
On the beam deflection method applied to ultrasound absorption measurements K. Giese To cite this version: K. Giese. On the beam deflection method applied to ultrasound absorption measurements. Journal
More informationThermally-Stimulated Current Investigation of Dopant-Related D- and A+ Trap Centers in Germanium for Cryogenic Detector Applications
Thermally-Stimulated Current Investigation of Dopant-Related D- and A+ Trap Centers in Germanium for Cryogenic Detector Applications J. Domange, E. Olivieri, N. Fourches, A. Broniatowski To cite this version:
More informationCO3-3 DEFECTS ASSOCIATED WITH LITHIUM IN SYNTHETIC CALCITE
CO3-3 DEFECTS ASSOCIATED WITH LITHIUM IN SYNTHETIC CALCITE G. Bacquet, L. Youdri, J. Dugas To cite this version: G. Bacquet, L. Youdri, J. Dugas. CO3-3 DEFECTS ASSOCIATED WITH LITHIUM IN SYNTHETIC CALCITE.
More informationEaster bracelets for years
Easter bracelets for 5700000 years Denis Roegel To cite this version: Denis Roegel. Easter bracelets for 5700000 years. [Research Report] 2014. HAL Id: hal-01009457 https://hal.inria.fr/hal-01009457
More informationInelastic scattering of 30 Mev polarized protons from 112Cd
Inelastic scattering of 30 Mev polarized protons from 112Cd R. De Swiniarski, G. Bagieu, DinhLien Pham, M. Massaad, J.Y. Grossiord, A. Guichard To cite this version: R. De Swiniarski, G. Bagieu, DinhLien
More informationOn sl3 KZ equations and W3 null-vector equations
On sl3 KZ equations and W3 null-vector equations Sylvain Ribault To cite this version: Sylvain Ribault. On sl3 KZ equations and W3 null-vector equations. Conformal Field Theory, Integrable Models, and
More informationEarly detection of thermal contrast in pulsed stimulated thermography
Early detection of thermal contrast in pulsed stimulated thermography J.-C. Krapez, F. Lepoutre, D. Balageas To cite this version: J.-C. Krapez, F. Lepoutre, D. Balageas. Early detection of thermal contrast
More informationELECTRON CORRELATION IN METALS EVIDENCED BY COMPTON SCATTERING
ELECTRON CORRELATION IN METALS EVIDENCED BY COMPTON SCATTERING A. Issolah, J. Chomilier, Y. Garreau, G. Loupias To cite this version: A. Issolah, J. Chomilier, Y. Garreau, G. Loupias. ELECTRON CORRELATION
More informationCan we reduce health inequalities? An analysis of the English strategy ( )
Can we reduce health inequalities? An analysis of the English strategy (1997-2010) Johan P Mackenbach To cite this version: Johan P Mackenbach. Can we reduce health inequalities? An analysis of the English
More informationInterferences of Peltier thermal waves produced in ohmic contacts upon integrated circuits
Interferences of Peltier thermal waves produced in ohmic contacts upon integrated circuits W. Claeys, S. Dilhaire, V. Quintard, D. Lewis, T. Phan, J. Aucouturier To cite this version: W. Claeys, S. Dilhaire,
More informationOn size, radius and minimum degree
On size, radius and minimum degree Simon Mukwembi To cite this version: Simon Mukwembi. On size, radius and minimum degree. Discrete Mathematics and Theoretical Computer Science, DMTCS, 2014, Vol. 16 no.
More informationMinimal Update of Solid State Physics
Minimal Update of Solid State Physics It is expected that participants are acquainted with basics of solid state physics. Therefore here we will refresh only those aspects, which are absolutely necessary
More informationLow frequency resolvent estimates for long range perturbations of the Euclidean Laplacian
Low frequency resolvent estimates for long range perturbations of the Euclidean Laplacian Jean-Francois Bony, Dietrich Häfner To cite this version: Jean-Francois Bony, Dietrich Häfner. Low frequency resolvent
More informationAn isotropic earth field scalar magnetometer using optically pumped helium 4
An isotropic earth field scalar magnetometer using optically pumped helium 4 C. Guttin, J. Leger, F. Stoeckel To cite this version: C. Guttin, J. Leger, F. Stoeckel. An isotropic earth field scalar magnetometer
More informationINVESTIGATION ON THE PHYSICAL PROPERTIES OF POLYPYRROLE
INVESTIGTION ON THE PHYSICL PROPERTIES OF POLYPYRROLE F. Devreux, F. Genoud, M. Nechtschein, J. Travers, G. Bidan To cite this version: F. Devreux, F. Genoud, M. Nechtschein, J. Travers, G. Bidan. INVESTIGTION
More informationDEVELOPMENT OF THE ULTRASONIC HIGH TEMPERATURE BOLT STRESS MONITOR
DEVELOPMENT OF THE ULTRASONIC HIGH TEMPERATURE BOLT STRESS MONITOR S.-M. Zhu, J. Lu, M.-Z. Xiao, Y.-G. Wang, M.-A. Wei To cite this version: S.-M. Zhu, J. Lu, M.-Z. Xiao, Y.-G. Wang, M.-A. Wei. DEVELOPMENT
More informationThe influence of the global atmospheric properties on the detection of UHECR by EUSO on board of the ISS
The influence of the global atmospheric properties on the detection of UHECR by EUSO on board of the ISS C. Berat, D. Lebrun, A. Stutz, E. Plagnol To cite this version: C. Berat, D. Lebrun, A. Stutz, E.
More informationStickelberger s congruences for absolute norms of relative discriminants
Stickelberger s congruences for absolute norms of relative discriminants Georges Gras To cite this version: Georges Gras. Stickelberger s congruences for absolute norms of relative discriminants. Journal
More informationFIM OBSERVATION OF MONOLAYER Pd ADSORBED ON W AND Mo SURFACES
FIM OBSERVATION OF MONOLAYER Pd ADSORBED ON W AND Mo SURFACES K. Okuno, H. Kim To cite this version: K. Okuno, H. Kim. FIM OBSERVATION OF MONOLAYER Pd ADSORBED ON W AND Mo SURFACES. Journal de Physique
More informationOn Symmetric Norm Inequalities And Hermitian Block-Matrices
On Symmetric Norm Inequalities And Hermitian lock-matrices Antoine Mhanna To cite this version: Antoine Mhanna On Symmetric Norm Inequalities And Hermitian lock-matrices 015 HAL Id: hal-0131860
More informationThomas Lugand. To cite this version: HAL Id: tel
Contribution à la Modélisation et à l Optimisation de la Machine Asynchrone Double Alimentation pour des Applications Hydrauliques de Pompage Turbinage Thomas Lugand To cite this version: Thomas Lugand.
More informationBEYOND THE PAIR DISTRIBUTION FUNCTION IN X-RAY ABSORPTION SPECTRA
BEYOND THE PAIR DISTRIBUTION FUNCTION IN X-RAY ABSORPTION SPECTRA M. Benfatto, C. Natoli To cite this version: M. Benfatto, C. Natoli. BEYOND THE PAIR DISTRIBUTION FUNCTION IN X-RAY AB- SORPTION SPECTRA.
More informationVALENCE BAND STRUCTURE OF PbTe
VALENCE BAND STRUCTURE OF PbTe A. Crocker, L. Rogers To cite this version: A. Crocker, L. Rogers. VALENCE BAND STRUCTURE OF PbTe. Journal de Physique Colloques, 1968, 29 (C4), pp.c4-129-c4-132. .
More informationBest linear unbiased prediction when error vector is correlated with other random vectors in the model
Best linear unbiased prediction when error vector is correlated with other random vectors in the model L.R. Schaeffer, C.R. Henderson To cite this version: L.R. Schaeffer, C.R. Henderson. Best linear unbiased
More informationA Study of the Regular Pentagon with a Classic Geometric Approach
A Study of the Regular Pentagon with a Classic Geometric Approach Amelia Carolina Sparavigna, Mauro Maria Baldi To cite this version: Amelia Carolina Sparavigna, Mauro Maria Baldi. A Study of the Regular
More informationR.F. MAGNETRON SPUTTERING OF a-si : H
R.F. MAGNETRON SPUTTERING OF a-si : H A. Mirza, A. Rhodes, J. Allison, M. Thompson To cite this version: A. Mirza, A. Rhodes, J. Allison, M. Thompson. R.F. MAGNETRON SPUTTERING OF a-si : H. Journal de
More informationSpins and spin-orbit coupling in semiconductors, metals, and nanostructures
B. Halperin Spin lecture 1 Spins and spin-orbit coupling in semiconductors, metals, and nanostructures Behavior of non-equilibrium spin populations. Spin relaxation and spin transport. How does one produce
More informationLocal field effects on the static dielectric constant of crystalline semiconductors or insulators
Local field effects on the static dielectric constant of crystalline semiconductors or insulators M. Lannoo To cite this version: M. Lannoo. Local field effects on the static dielectric constant of crystalline
More informationDetermination of the temperature dependent thermal conductivity of isotopically modified single crystal diamond
Determination of the temperature dependent thermal conductivity of isotopically modified single crystal diamond L. Wei, P. Kuo, R. Thomas To cite this version: L. Wei, P. Kuo, R. Thomas. Determination
More informationWater Vapour Effects in Mass Measurement
Water Vapour Effects in Mass Measurement N.-E. Khélifa To cite this version: N.-E. Khélifa. Water Vapour Effects in Mass Measurement. Measurement. Water Vapour Effects in Mass Measurement, May 2007, Smolenice,
More informationLow-temperature state of Ising spin glass
Low-temperature state of Ising spin glass L.B. Ioffe, M.V. Feigel Man To cite this version: L.B. Ioffe, M.V. Feigel Man. Low-temperature state of Ising spin glass. Journal de Physique Lettres, 1983, 44
More informationInterfacial interaction in PP/EPDM polymer blend studied by positron annihilation
Interfacial interaction in PP/EPDM polymer blend studied by positron annihilation Chen Wang, S. Wang, W. Zheng, Z. Qi To cite this version: Chen Wang, S. Wang, W. Zheng, Z. Qi. Interfacial interaction
More informationPeriod doubling cascade in mercury, a quantitative measurement
Period doubling cascade in mercury, a quantitative measurement A. Libchaber, C. Laroche, S. Fauve To cite this version: A. Libchaber, C. Laroche, S. Fauve. Period doubling cascade in mercury, a quantitative
More informationBand offsets in strained InGaAsP/InGaAsP quantum well optical modulator structures
Band offsets in strained InGaAsP/InGaAsP quantum well optical modulator structures Roland Martin, S. Wong, R. Nicholas, A. Smith, M. Gibbon, E. Thrush, J. Stagg To cite this version: Roland Martin, S.
More informationX-ray absorption near edge spectroscopy (XANES) study of thermostable polyphenylquinoxaline (PPQ) polymer prior to Cu thin films deposition
X-ray absorption near edge spectroscopy (XANES) study of thermostable polyphenylquinoxaline (PPQ) polymer prior to Cu thin films deposition G. Richard, A. Cros, Y. Mathey, G. Tourillon, C. Laffon, Y. Parent
More informationPossible long-range step interaction in 4He due to step oscillation
Possible longrange step interaction in 4He due to step oscillation M. Uwaha To cite this version: M. Uwaha. Possible longrange step interaction in 4He due to step oscillation. Journal de Physique, 1990,
More informationThe exact equation for Brillouin shifts
The exact equation for Brillouin shifts V. Chandrasekharan To cite this version: V. Chandrasekharan. The exact equation for Brillouin shifts. Journal de Physique, 1965, 26 (11), pp.655658. .
More informationEvolution of the cooperation and consequences of a decrease in plant diversity on the root symbiont diversity
Evolution of the cooperation and consequences of a decrease in plant diversity on the root symbiont diversity Marie Duhamel To cite this version: Marie Duhamel. Evolution of the cooperation and consequences
More informationRandom walks on the Sierpinski Gasket
Random walks on the Sierpinski Gasket R. Friedberg, O. Martin To cite this version: R. Friedberg, O. Martin. Random walks on the Sierpinski Gasket. Journal de Physique, 1986, 47 (10), pp.16631669. .
More informationTowards an active anechoic room
Towards an active anechoic room Dominique Habault, Philippe Herzog, Emmanuel Friot, Cédric Pinhède To cite this version: Dominique Habault, Philippe Herzog, Emmanuel Friot, Cédric Pinhède. Towards an active
More informationTHIN-FILM THICKNESS MEASUREMENTS WITH THERMAL WAVES
THIN-FILM THICKNESS MEASUREMENTS WITH THERMAL WAVES A. Rosencwaig, J. Opsal, D. Willenborg To cite this version: A. Rosencwaig, J. Opsal, D. Willenborg. THIN-FILM THICKNESS MEASUREMENTS WITH THERMAL WAVES.
More information