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We derive conjugate momenta variable tensors and the Hamiltonian equation of the source-free f(R) gravity from first principles using the Legendre transformation of these conjugate momenta variable tensors, conjugate coordinates variables--fundamental metric tensor and its first ordinary partial derivatives with respect to space-time coordinates and second ordinary partial derivatives with respect to space-time coordinates--and the Lagrangian of the f(R) gravity. Interpreting the derived Hamiltonian as the energy of the f(R) gravity we have shown that it vanishes for linear Lagrangians in Ricci scalar curvature without source (e.g., Einstein-Hilbert Lagrangian without matter fields), which is the same result obtained using the stress-energy tensor equation derived from variation of the matter field Lagrangian density. The resulting Hamiltonian equation forbids any negative power law model in the dependence of the f(R) gravity on Ricci scalar curvature: f(R) = [alpha][R.sup.-r], where r and a are positive real numbers; it also forbids any polynomial equation that contains terms with negative powers of the Ricci scalar curvature including a constant term, in which cases the Hamiltonian function in the Ricci scalar and therefore the energy of the f(R) gravity would attain a negative value and would not be bounded from below. The restrictions imposed by the non-negative Hamiltonian have [alpha][R.sup.-r] reaching consequences as a result of applying f(R) gravity to the study of black holes and the Friedmann-Lemaitre-Robertson-Walker model in cosmology. Key words: calculus of variations, analytical mechanics, Lagrangian and Hamiltonian formalisms, classical general theory of relativity, modified theory of gravity, f(R) gravity. Nous derivons les tenseurs des variables conjugues d'impulsion, ainsi que les equations de Hamilton pour une gravite f(R) sans source a partir de principes premiers utilisant la transformation de Legendre de ces tenseurs des variables conjugues d'impulsion, variables conjuguees des coordonnees (le tenseur metrique fondamental et ses premieres derivees partielles ordinaires par rapport aux coordonnees d'espace-temps et les secondes derivees partielles ordinaires par rapport aux coordonnees d'espace-temps) et le Lagrangien de la gravite f(R). Interpretant le Hamiltonien obtenu comme etant l'energie de la gravite f(R), nous montrons que qu'il devient nul pour des Lagrangiens lineaires dans le scalaire de courbure de Ricci sans source (e.g. la densite Lagrangienne de Einstein-Hilbert sans champ de matiere), ce qui est le meme resultat obtenu en utilisant l'equation du tenseur d'energie-impulsion derive de la variation de la densite Lagrangienne du champ de matiere. Les equations de Hamilton qui en resultent interdisent tout modele de loi de puissance negative dans la dependance de la gravite f(R) sur le scalaire de Ricci : f(R) = [alpha][R.sup.-r], oU r et a sont des nombres reels positifs et il interdit aussi tout developpement polynomial contenant des termes de puissance negative du salaire de Ricci, auquel cas l'energie de la gravite f(R) aurait une valeur negative sans borne inferieure. Les restrictions imposees aux Hamiltoniens non negatifs ont des consequences importances sur l'application de la gravite f(R) a l'etude des trous noirs et des modeles FLRW en cosmologie. [Traduit par la Redaction] Mots-cles: calcul des variations, mecanique analytique, formalismes de Lagrange et de Hamilton, theorie classique de la relativite generale, theorie modifiee de la gravite, f(R) gravite., 1. Introduction Buchdahl [1] proposed his generalization to the Einstein field equations by considering a generalization of the gravitational Lagrangian to be a general function of the Ricci scalar curvature [...]

We consider time discretizations of the Vlasov-HMF (Hamiltonian mean-field) equation based on splitting methods between the linear and nonlinear parts. We consider solutions starting in a small Sobolev neighborhood of a spatially homogeneous state satisfying a linearized stability criterion (Penrose criterion). We prove that the numerical solutions exhibit a scattering behavior to a modified state, which implies a nonlinear Landau damping effect with polynomial rate of damping. Moreover, we prove that the modified state is close to the continuous one and provide error estimates with respect to the time step size., Author(s): Erwan Faou [sup.1] , Romain Horsin [sup.1] , Frédéric Rousset [sup.2] Author Affiliations: (1) INRIA-Rennes Bretagne Atlantique and IRMAR (UMR 6625), Université de Rennes I, 0000 0001 2191 9284, [...]

We study the particle-antiparticle force in a model scalar quantum field theory (QFT) with a nonlinear Higgs-like mediating field. We use the variational method in a reformulated Hamiltonian formalism of the theory. The trial state consists of a superposition of single-pair and two-pair Fock states. Coupled relativistic integral equations for the one- and two-pair channel functions are derived and their nonrelativistic limit forms are obtained. Variational ansatz are used to derive the correction to the dominant Yukawa interparticle potential for the particle-antiparticle system. The correction is found to be an attractive short-range potential. PACS Nos.: 03.70.+k, 11.10.Ef, 11.10.Lm, 14.80.Bn. Nous etudions l'interaction particule-antiparticule dans un modele scalaire de theorie quantique des champs (TQC), avec un champ mediateur du type Higgs non lineaire. Nous utilisons la methode variationnelle dans un formalisme de Hamiltonien reformule de la TQC. L'etat d'essai est constitue d'une superposition d'etats de Fock a simple et double paire. Nous obtenons des equations integrates relativistes pour les fonctions des canaux a une et deux paires, ainsi que la forme de leurs limites non relativistes. Des ansatz variationnels permettent d'obtenir la correction au potentiel interparticules dominant de Yukawa pour le systeme particule-antiparticule. Nous trouvons que le terme de correction est attractif et de courte portee. [Traduit par la Redaction], Introduction In a previous paper [1], we studied three- and four-particle bound-state systems in a model quantum field theory (QFT) in which scalar particles described by the field φ interact [...]

The fundamental equation of polar piezoelectric media in differential form are established in variational forms and 3-field variational principle with some constraint conditions is studied for a regular region of media from a general principle of physics. The generalized variational principle with the only constraint of initial conditions has produced all the equations of the laminae region, including the interface conditions, as its Euler-Lagrange equations.

This work, besides its fundamental interest, is motivated by the atmospheric and astrophysical importance of formaldehyde ([H.sub.2]CO). The goal of this study is to complete the already existing list of rotational transitions within the ground vibration state by a list of transitions within the four first excited [2.sup.1], [3.sup.1], [4.sup.1], and [6.sup.1] vibrational states, to help the detection of this species by microwave or millimetre wave techniques. For this purpose, the rotational spectra of [H.sub.2]CO in the [2.sup.1], [3.sup.1], [4.sup.1], and [6.sup.1] excited vibrational states have been investigated in Lille and Cologne in the millimetre region at 160-600 GHz and 850-903 GHz, respectively. The results of these millimetre wave measurements were combined with the [2.sup.1], [3.sup.1], [4.sup.1], and [6.sup.1] infrared energy levels, which were obtained from previous analysis of FTS spectra of the [v.sub.4] (out of plane bending mode), [v.sub.6] (C[H.sub.2] rock mode), and [v.sub.3] (C[H.sub.2] bending mode) bands recorded in the 10 µm region (D.C. Reuter, S. Nadler, S.J. Daunt, and J.W.C. Johns. J. Chem. Phys. 91,646 (1989)) and more recently for the [v.sub.2] fundamental band (C=O stretching, located at 1746.009 [cm.sup.-1])(F. Kwabia Tchana, A. Perrin, and N. Lacome. J. Mol. Spectrosc. 245, 141, (2007)). The energy level calculation of the [2.sup.1], [3.sup.1], [4.sup.1], and [6.sup.1] interacting states accounts for the various Coriolis-type resonances that perturb the energy levels of the [2.sup.1], [3.sup.1], [4.sup.1], and [6.sup.1] vibrational states as well as for the anharmonic resonances coupling the [2.sup.1] and [3.sup.1] energy levels, and in this way the microwave and infrared data could be reproduced within their associated experimental uncertainty. However, it is clear that the theoretical model used to account for the very large A-type Coriolis resonance linking the [4.sup.1] and [6.sup.1] energy levels of [H.sub.2]CO is only effective with poor physical meaning. PACS No: 33.20.Sn En dehors de son interet theorique, ce travail, est motive par le role important joue par le formaldehyde ([H.sub.2]CO) dans la chimie de la troposphere terrestre et parce que cette molecule a ete detectee dans de nombreux objets astrophysiques. Le but de ce travail est de completer la liste, deja existante, de transitions rotationnelles du formaldehyde dans l'etat vibrationnel fondamental par une liste complementaire de transitions rotationnelles dans les quatre premiers etats vibrationnels excites [2.sup.1], [3.sup.1], [4.sup.1] et [6.sup.1] de [H.sub.2]CO. Le but est de permettre la detection de cette espece dans des etats vibrationnels excites par technique micro-onde ou submillimetrique. Pour cela le spectre rotationnel de [H.sub.2]CO dans les etats excites [2.sup.1], [3.sup.1], [4.sup.1], et [6.sup.1] a ete mesure a Lille et Cologne dans le domaine millimetrique (a 160-600 GHz et 850-903 GHz, respectivement). Les resultats de ces mesures ont ete combines avec les niveaux d'energie infrarouges pour les etats [2.sup.1], [3.sup.1], [4.sup.1], et [6.sup.1] obtenus precedemment lors d'analyses de spectres enregistres par transformee de Fourier a haute resolution pour les bandes [v.sub.4] (ouverture angulaire hors plan du groupe C[H.sub.2]), [v.sub.6] (torsion dans le plan de C[H.sub.2]) et [v.sub.3] (ouverture angulaire symetrique de C[H.sub.2]) enregistres a 10 µm (D.C. Reuter, S. Nadler, S.J. Daunt, and J.W.C. Johns. J. Chem. Phys. 91, 646 (1989)) et plus receµment pour la bande [v.sub.2] (elongation C = O), situee a 1746 009 [cm.sup.-1]) (F. Kwabia Tchana, A. Perrin, and N. Lacome. J. Mol. Spectrosc. 245, 141, (2007)). Le calcul de niveaux d'energie pour les etats vibrationnels inter agissants [2.sup.1], [3.sup.1], [4.sup.1] et [6.sup.1] tient compte des differentes resonances de type Coriolis qui perturbent les niveaux d'energie des etats [3.sup.1], [4.sup.1] et [6.sup.1] ainsi que des resonances anharmoniques qui couplent les niveaux des etats vibrationnels [2.sup.1] et [3.sup.1]. De cette facon, l'ensemble des measures microondes et niveaux d'energies infrarouges ont pu etre reproduits a leurs precisions experimentales respectives. Cependant, ilest clair que le modele theorique utilise pour tenir compte de la forte resonance de Coriolis de type A qui couple les niveaux d'energie des etats [4.sup.1] et [6.sup.1] de [H.sub.2]CO est purement effectif et donc de peu de signification reellement physique., 1. Introduction Formaldehyde, both its main isotopic species [H.sub.2][sup.12.C][sup.16.O] and its deuterated variants HD[sup.12.C][sup.16.O] and D2CO, was detected by microwave techniques in numerous astrophysical objects. For example, this species was [...]

By utilizing the Hamilton principle and the consistent linearization of the fully nonlinear beam theory, two coupled governing differential equations for a rotating inclined beam are derived. Both the extensional deformation and the Coriolis force effect are considered. It is shown that the vibration system can be considered as the superposition of a static subsystem and a dynamic subsystem. The method of Frobenius is used to establish the exact series solutions of the system. Several frequency relations that provide general qualitative relations between the natural frequencies and the physical parameters are revealed without numerical analysis. Finally, numerical results are given to illustrate the general qualitative relations and the influence of the physical parameters on the natural frequencies of the dynamic system. [DOI: 10.1115/1.2200657]

A general interpretation is provided for the valency interaction formula (VIF), which applies for VIF pictures as one-electron Hamiltonian operators as well as VIF pictures as one-electron density operators. The VIF method has provided the accurate VIF pictures for hydrocarbons and it can also be used to predict thermal barriers to chemical reactions.

An [H.sub.[infinity]] suboptimal state feedback controller for constrained input systems is derived using the Hamilton--Jacobi--Isaacs (HJI) equation of a corresponding zero-sum game that uses a special quasi-norm to encode the constraints on the input. The unique saddle point in feedback strategy form is derived. Using policy iterations on both players, the HJI equation is broken into a sequence of differential equations linear in the cost for which closed-form solutions are easier to obtain. Policy iterations on the disturbance are shown to converge to the available storage function of the associated [L.sub.2]-gain dissipative dynamics. The resulting constrained optimal control feedback strategy has the largest domain of validity within which [L.sub.2]-performance for a given [gamma] is guaranteed. Index Terms--Controller saturation, [H.sub.[[infinity]] control, policy iterations, zero-sum games.

In this paper, we formulate the stacking sequence design of laminated composite flat panels for maximum supersonic flutter speed and maximum thermal buckling capacity. The design is constrained to have stable limit cycle oscillation in the vicinity of the flutter boundary. For the purpose of comparison, we consider both linear and nonlinear panel flutter analyses. Because of manufacturing constraints, the stacking sequence of the laminate is selected from a discrete set of orientation angles. The plate is modeled using von Karman plate equations and assumed to be subjected to uniform temperature differential. The aerodynamic load on the plate is computed using third-order piston theory. The plate equations of motion are derived using Hamilton's principle and discretized using the Rayleigh-Ritz method. The nonlinear panel flutter analysis is performed using an approximate perturbation approach. The Pareto fronts describing the trade-off between thermal buckling and flutter are generated for different panel aspect ratios. It is observed that optimal designs obtained for both linear and nonlinear flutter analyses are similar, with only the predicted flutter speeds different. This suggests that, for the purpose of preliminary stacking sequence design, linear flutter analysis is sufficient. DOI: 10.2514/1.19532

This study proposes a class of variable structure stabilizing laws which make the closed-loop system be capable of tolerating the abnormal operation of actuators within a pre-specified subset of actuators. The ranges of acceptable change in control gain magnitude that preserves system's stability are estimated for the whole set of actuators. These ranges are shown to be able to be made larger than those obtained by linear quadratic regulator (LQR) reliable design (Veillette, 1995, and Liang et al., 2000) by the choice of control parameters. Besides, this approach does not need the solution of Hamilton-Jacobi (HJ) equation or inequality, which is essential for optimal approaches such as LQR and [H.sup.[infinity]] reliable designs. As a matter of fact, this approach can also relax the computational burden for solving the HJ equation or inequality. Index Terms--Hamilton--Jacobi (HJ) equation, nonlinear systems, reliable control, variable structure control (VSC).

Electron dynamics in gyrotron resonators are described in terms of a Hamiltonian map. This map incorporates the dependency of electron dynamics on the parameters of the interacting radio-frequency (RF) field and it can be used for trajectory calculations through successive iteration, resulting in a symplectic integration scheme. The direct relation of the map to the physics of the model, along with its canonical form (phase space volume preserving) and the significant reduction of the number of iteration steps required for acceptable accuracy, are the main advantages of this method in comparison with standard methods such as Runge-Kutta. The general form of the Hamiltonian map allows for wide applications as a part of several numerical algorithms which incorporate CPU-consuming electron trajectories calculations. Index Terms--Gyrotrons, Hamiltonian mappings, microwave sources, symplectic integration.

Byline: M.G. Marmorino (1) Keywords: soluble; solvable; Hamiltonian; cotangent Abstract: The exact ground and first-excited state eigenvalues and eigenfunctions are given for a one-dimensional Hamiltonian with the potential \raise0.7ex$1$ \!/ 1 2.-\!\lower0.7ex$2$ n(n-1)cot.sup.2(x) on the domain xa[0,[pi]]. Furthermore, an exact eigenvalue spectrum is proposed for all n&gt 1 and the exact eigenfunctions are proposed for n=3. These are simply finite linear combinations of sin(mx) for integer m. Author Affiliation: (1) CPO 2027, Department of Chemistry, Berea College, Berea, KY, 40404, USA Article History: Registration Date: 12/10/2004

Byline: I. V. Tupikova (1), A. A. Vakhidov (1) Abstract: A semianalytic theory of motion of minor planets is constructed by means of the Lie-series method involving the Le Verrier expansions of the planetary disturbing function. The averaging procedure is realized symbolically by means of the computer algebra system MAPLE. The averaged Hamiltonian is used for symbolic computation of the right-hand parts of the canonical differential equations of motion. The equations are integrated numerically by means of traditional numerical software. Bibliography: 9 titles. Author Affiliation: (1) Lohrmann Observatory, TU, Dresden, Germany Article History: Registration Date: 12/10/2004

Heisenberg Hamiltonian is widely used for the study of the covalent sates of conjugated molecules and their photochemistry. An extension to the CC triple bonds or to their two pi bonds is presented.

The magnetocaloric effect in ferrimagnetic rare-earth iron garnets [R.sub.3][Fe.sub.5][O.sub.12] where R=Y and Dy is theoretically examined by using a model Hamiltonian, which has considered three coupled magnetic sublattices in the mean field approximation. The studies have shown that in [Dy.sub.3][Fe.sub.5][O.sub.12] the inverse magnetocaloric effect is associated with the compensation temperature.

The effect of anisotropic strain on the valence band structure and related properties, including excitonic transition energies, transition polarization selection rules, band-edge hole effective masses, and exciton reduced effective masses, of polar and nonpolar plane GaN are examined by using the well-known k.p Hamiltonian approach. The band-edge hole effective masses have displayed major in-plane anisotropy and are sensitive to the residual strain, while the effect of the residual strain on the exciton reduced effective masses are relatively weak.

An effective Hamiltonian is used for describing the ferroelectric polarizations in perovskite oxide superlattices. This effective Hamiltonian procedure is also used for developing ferroelectric model of other kinds of oxide superlattices.

The spin-wave excitations in asymmetric ferromagnetic nanorings are calculated by using a Hamiltonian-based formalism. The effects of inter-ring dipolar coupling on the spin-wave (SW) spectrum are examined by using small arrays of nanorings and compared briefly with the disk case.

The Lanczos algorithm and a large basis set are used for computing the vibrational levels of [Ar.sub.4]. The results have shown both even and odd-parity states with wave functions that are invariant with respect to permutations of the Ar atoms.

The influence of surface anisotropy is analyzed on the precessional switching of magnetization in nanoparticles. The approach is used to consider the multispin description of a nanoparticle and investigation of the multispin dynamics by using Landau-Lifshitz equation for each spin with the effective field derived from a Heisenberg-type Hamiltonian.

A concern is shown towards the problems and properties of covering regions of the plane with non-overlapping dominoes. A discussion is presented on whether dominoes can tile the resulting region.

Density functional theory (DFT) calculations was combined with transport Green function approach to explain the molecular gain a thiotolane system. Hamiltonian matrix is used to calculate transport characteristics of dithiotolane molecule.