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We obtain x-ray absorption near-edge structures (XANES) by solving the equation of motion for the two-particle Green's function for the electron-hole pair, the Bethe-Salpeter equation (BSE), within the all-electron full-potential linearized augmented plane wave method (FPLAPW). The excited states are calculated for the Li K-edge in the insulating solids LiF, Li_2O and Li_2S, and absorption spectra are compared with independent particle results using the random phase approximation (RPA), as well as supercell calculations using the core-hole approximation within density functional theory (DFT). The binding energies of strongly bound excitations are determined in the materials, and core-exciton wavefunctions are demonstrated for LiF.

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The Kadomtsev-Petviashvili equation describes nonlinear dispersive waves which travel mainly in one direction, generalizing the Korteweg-de Vries equation for purely uni-directional waves. In this Letter we derive an improved KP-equation that has exact dispersion in the main propagation direction and that is accurate in second order of the wave height. Moreover, different from the KP-equation, this new equation is also valid for waves on deep water. These properties are inherited from the AB-equation (E. van Groesen, Andonowati, 2007 ) which is the unidirectional improvement of the KdV equation. The derivation of the equation uses the variational formulation of surface water waves, and inherits the basic Hamiltonian structure.

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The perturbations of the L.R.S. class A spatially homogeneous spacetimes are treated using Hamiltonian methods in conjunction with techniques from the theory of Lie group harmonic analysis. These latter techniques lead to a simple way of handling any set of tensor equations on these background spacetimes which has the same symmetry group as the space-time metric. Once this approach is developed, the Hamiltonian formulation is used to recover in a clean way the Bonanos equations for the perturbations of the perfect fluid models of the class of spacetimes under consideration. The conserved quantities associated with the four-dimensional symmetry group are evaluated and their role in the linearized Hamiltonian dynamics is discussed. The time-dependent linear canonical transformation of the linearized vacuum gravitational phase space adapted to Moncrief's gauge invariant decomposition ...

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One of the hallmarks of linear coupling is the resonant exchange of oscillation amplitude between the horizontal and vertical planes when the difference between the unperturbed tunes is close to an integer. The standard derivation of this phenomenon (known as the difference resonance) can be found, for example, in the classic papers of Guignard [1, 2]. One starts with an uncoupled lattice and adds a linear perturbation that couples the two planes. The equations of motion are expressed in hamiltonian form. As the difference between the unperturbed tunes approaches an integer, one finds that the perturbing terms in the hamiltonian can be divided into terms that oscillate slowly and ones that oscillate rapidly. The rapidly oscillating terms are discarded or transformed to higher order with an appropriate canonical transformation. The resulting approximate hamiltonian gives equations of ...

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HAMILTON is a computer code performing all algebraic operations necessary for an analytic determination of the power series of the Hamiltonian equations of motion in the electromagnetic fields with at least one plane of symmetry. It is written entirely in FORTRAN in order to achieve fast machine performance, a requirement which is essential due to the complexity of the equations of motion in higher orders. HAMILTON is considerably faster than common more versatile formula manipulators and uses noticeably less storage. Besides the mere solution of the equations of motion, HAMILTON also produces FORTRAN code compatible with the program COSY 5.0 allowing the computation of matrix elements of individual optical elements and their concatenation. The produced FORTRAN code is highly optimized and on average requires only 30% of the execution time of a handwritten comparable code. (orig.).

CERN Document Server

We review various field theory approaches to the description of neutrino oscillations in vacuum and external fields. First we discuss a relativistic quantum mechanics based approach which involves the temporal evolution of massive neutrinos. To describe the dynamics of the neutrinos system we use exact solutions of wave equations in presence of an external field. It allows one to exactly take into account both the characteristics of neutrinos and the properties of an external field. In particular, we examine flavor oscillations an vacuum and in background matter as well as spin flavor oscillations in matter under the influence of an external electromagnetic field. Moreover we consider the situation of hypothetical nonstandard neutrino interactions with background fermions. In the case of ultrarelativistic particles we reproduce an effective Hamiltonian which is used in the standard quantum mechanical approach for the description of neutrino ...

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New partial differential equations (PDEs) for the full order weak schemes of the Langevin simulations are formulated. They are solved recursively in full order series solutions with respect to {radical}(t) (the full order weak Taylor schemes). Arbitrariness involved in the solutions is analyzed and clarified in detail. Specific solutions within some orders are presented as examples of the weak Taylor schemes. These PDEs and their solutions will serve for further developments of efficient higher order Runge-Kutta-like schemes. The similar formulation is possible for the imaginary time Hamiltonian evolution kernels as well. (orig.). 9 refs.

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The Lorentz and coordinate covariant calculus of spinors in Riemannian spacetime, which is the mathematical model for the description of the quantum mechanics of elementary particles with spin interacting with the classical gravitation field, is explored. The Dirac equation describing the interaction of neutrinos with the gravitational fields of the Robertson-Walker cosmological world models is separated, and the spectrum of eigenfunctions and eigenvalues for particular choices of the set of quantum numbers is given explicitly for the k = 0 and k = +1 models, although only the radial equations determining the final quantum number are given for the k = -1 model. The mathematical theory of the motion of a perfect fluid whose elements interact via long-range neutrino-exchange forces, as well as gravitationally, is developed. The formalism for calculating, by calculating the Bogoliubov transformation of the Fock space operators that instantaneously ...

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We outline basic principles of a canonical formalism for the Nambu mechanics - a generalization of Hamiltonian mechanics proposed by Yoichiro Nambu in 1973. It is based on the notion of a Nambu bracket, which generalizes the Poisson bracket - a 'binary'' operation on classical observables on the phase space - to the 'multiple' operation of higher order n#>=#3. Nambu dynamics is described by the phase flow given by Nambu-Hamilton equations of motion - a system of ODE's which involves n-1 'Hamiltonians'. We introduce the fundamental identity for the Nambu bracket - a generalization of the Jacobi identity - as a consistency condition for the dynamics. We show that Nambu bracket structure defines a hierarchy of infinite families of 'subordinated' structures of lower order, including Poisson bracket structure, which satisfy certain matching conditions. The notion of Nambu bracket enables us to define Nambu-Poisson manifolds - ...

CERN Document Server

We consider a Josephson junction system installed with a finite length inhomogeneity, either of microresistor or of microresonator type. The system can be modelled by a sine-Gordon equation with a piecewise-constant function to represent the varying Josephson tunneling critical current. The existence of pinned fluxons depends on the length of the inhomogeneity, the variation in the Josephson tunneling critical current and the applied bias current. We establish that a system may either not be able to sustain a pinned fluxon, or - for instance by varying the length of the inhomogeneity - may exhibit various different types of pinned fluxons. Our stability analysis shows that changes of stability can only occur at critical points of the length of the inhomogeneity as a function of the (Hamiltonian) energy density inside the inhomogeneity - a relation we determine explicitly. In combination with continuation arguments and Sturm-Liouville theory, we ...

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The systems for which the algebra of gauge transformations in the lagrangian formalism is closed, are considered. The hamiltonian BRST charge and the BRST-invariant hamiltonian are found explicitly. Their expansions in powers of the ghost variables contain, in general, an infinite number of terms. (orig.).

International Nuclear Information System (INIS)

We calculated the energies of asymmetric nuclear matter at zero and finite temperatures with the cluster variational method. At zero temperature, the expectation value of the two-body Hamiltonian composed of the kinetic energies and the AV18 two-body forces is calculated with the Jastrow wave function in the two-body cluster approximation. The obtained two-body energy is in good agreement with the result with the Fermi Hypernetted Chain (FHNC) calculation by Akmal et al. The energy caused by the UIX three-body forces is treated somewhat phenomenologically so that the total energy reproduces the empirical saturation point. Furthermore, the parameters included in the three-body energy are readjusted so that the Thomas-Fermi (TF) calculations with use of the obtained energy of nuclear matter reproduce the gross feature of the experimental data on atomic nuclei. The nuclear species in the neutron star crust obtained by the TF calculation are reasonable. The free ...

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The linearized-augmented-plane-wave (LAPW) method for thin films is generalized by removing the remaining shape approximation to the potential inside the atomic spheres. A new technique for solving Poisson's equation for a general charge density and potential is described and implemented in the film LAPW method. In the resulting full-potential LAPW method (FLAPW), all contributions to the potential are completely taken into account in the Hamiltonian matrix elements. The accuracy of the method: already well known for clean metal surfaces: is demonstrated for the case of a nearly free (noninteracting) O_2 molecule which is a severe test case of the method because of its large anisotropic charge distribution. Detailed comparisons show that the accuracy of the FLAPW results for O_2 exceeds that of existing state-of-the-art local-density linear-combination-of-atomic-orbitals (LCAO)-type calculations, and that taking the full potential LAPW results ...

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The authors derive in full details the Hamiltonian formulation of the N = 1D = 10 supergravity coupled to super Yang-Mills theory. In particular, they present the explicit form of the first class constraints and compute the constraints gauge algebra.

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... deformed nuclei eigenvalues even-odd nuclei gold 195 hamiltonians iridium

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... collective model hamiltonians iridium 187 matrix elements nuclear cores

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A review is made of some recent developments in the application of the Bohr Hamiltonian to transitional nulcei. The primary concern is to understand the advantages and limitations inherent to the basic model and its many variants. (author).

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Constraining the SL(3) WZW-model we construct a reduced theory which is invariant with respect to the new chiral algebra W_3"2. This symmetry is generated by the stress-energy tensor, two bosonic currents with spins 3/2 and the U(1) current. We conjecture a Kac formula that describes the highly reducible representation for this algebra. We also discuss the quantum Hamiltonian reduction for the general type of constraints that leads to the new extended conformal algebras. (orig.).

CERN Document Server

In this paper we prove the existence of isomorphisms between certain non-commutative algebras that are interesting from representation theoretic perspective and arise as quantizations of certain Poisson algebras. We show that quantizations of Kleinian resolutions obtained by three different constructions are isomorphic to each other. The constructions are via symplectic reflection algebras, quantum Hamiltonian reduction, and W-algebras. Next, we prove that parabolic W-algebras in type A are isomorphic to quantum Hamiltonian reductions associated to quivers of type A. Finally, we show that the symplectic reflection algebras for wreath-products of the symmetric group and a Kleinian group are isomorphic to certain quantum Hamiltonian reductions. Our results involving W-algebras are new, while for those dealing with symplectic reflection algebras we just give new proofs. A key ingredient in our proofs is the study of ...

CERN Document Server

Using some modification of the standard fermion technique we derive factorized formula for spin operator matrix elements (form-factors) between general eigenstates of the Hamiltonian of quantum Ising chain in a transverse field of finite length. The derivation is based on the approach recently used to derive factorized formula for Z_N-spin operator matrix elements between ground eigenstates of the Hamiltonian of the Z_N-symmetric superintegrable chiral Potts quantum chain. The obtained factorized formulas for the matrix elements of Ising chain coincide with the corresponding expressions obtained by the Separation of Variables Method.

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Properties of unique parity states in odd-proton (/sub 77/Ir, /sub 79/Au) and odd-neutron nuclei (/sub 78/Pt) are investigated in the framework of the interacting boson-fermion approximation model. The core (boson)-particle (fermion) interaction is represented by a quadrupole-quadrupole interaction and an exchange term, which takes into account the effects of the Pauli exclusion principle. The even-even core nucleus is described in terms of the IBA-1 hamiltonian. The change in the properties of the corresponding odd-A nuclei can be interpreted in terms of a transition of the core hamiltonian between the O(6) and SU(3) limiting cases.

CERN Document Server

The Belinskii, Khalatnikov and Lifshitz conjecture \\cite{bkl1} posits that on approach to a space-like singularity in general relativity the dynamics are well approximated by `ignoring spatial derivatives in favor of time derivatives.' In \\cite{ahs1} we examined this idea from within a Hamiltonian framework and provided a new formulation of the conjecture in terms of variables well suited to loop quantum gravity. We now present the details of the analytical part of that investigation. While our motivation came from quantum considerations, thanks to some of its new features, our formulation should be useful also for future analytical and numerical investigations within general relativity.

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In this paper, the authors first describe a fourth order accurate finite difference discretization for both the Laplace equation and the heat equation with Dirichlet boundary conditions on irregular domains. In the case of the heat equation, they use an i...

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Our investigation concerns the class of Josephson-like systems, sharing the same nonlinear Hamiltonian. Among the latter a Josephson junction with an external biasing circuit is considered. We diagonalize the fully nonlinear Hamiltonian (in the superconductive regime of the junction) in the Fock space of the TBHA (two-boson Heisenberg algebra) and prove that such algebra leads quite naturally to the theoretical realization of codewords and logical operators: the codewords are defined as the even and odd coherent states of the TBHA, while the logical operators are expressed in terms of operators in the same algebra. Our theoretical construction corresponds to a continuous variable quantum computation scheme; the continuous variables are identified in terms of the physical operators of the junction. The link between this scheme and the technique of fermionization of bosonic systems is also discussed.

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The dynamical effects of spatially homogeneous electromagnetic fields on anisotropic Bianchi type-IX models are studied. The Lagrangians and Hamiltonians affecting the evolution of anisotropy (including the gravitational and electromagnetic potentials) are obtained for very general spatially homogeneous metrics by means of the Arnowitt-Deser-Misner Hamiltonian formalism. For models having diagonal metrics an exact solution for the electromagnetic fields is obtained. This solution allows a qualitative solution for the gravitational variables. The total solution is similar to that of Brill. For Bianchi type-IX models having symmetric and general metrics, a discussion of the qualitative behavior of the universe point under the influence of the above potentials is given. In particular, it is shown that in some cases the presence of the electromagnetic potential inhibits some types of singularities.

International Nuclear Information System (INIS)

A one-dimensional tachyon Klein-Gordon equation is reduced to a nonrelativistic-tachyon equation of motion. The interpretation of this reduced equation leads to the following conclusions: 1) tachyons can be localized in time instead of in space as compared with bradyons, 2) space representation and momentum representation of bradyonic quantum equation of motion are replaced by time representation and energy representation in tachyon quantum equation of motion and 3) with the aid of these results, it has been found that the solutions of the tachyon Klein-Gordon equation of motion form a complete set. (author).

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Given the spectrum of a Hamiltonian, a methodology is developed which employs the Landau-Ginsburg theory for characterizing phase transitions in infinite systems to identify phase transition remnants in finite fermion systems. As a first application of our approach we discuss pairing in finite nuclei. (orig.)

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Calculations of total and angle-differential excitation cross sections for the electron impact excitation of lithium-like iron were performed with the R-matrix formulation. The alignments of the excited states 1s{sup 2}np {sup 2}P{sub 3/2} are also presented for n=3 and 4 along with the angular photon distribution from these states to the ground state. Relativistic effects were included in the present calculations by the Breit-Pauli Hamiltonian.

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We show that the chaotic dynamical behaviour displayed by diagonal Bianchi type IX metrics in general relativity does not occur on approach to the singularity in higher-order lagrangian theories of gravity. However, chaotic behaviour does occur in the more general non-diagonal type IX models in these theories. An interpretation of these results in terms of the hamiltonian potential picture of the type IX evolution is given. (orig.).

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Implementation of quantum logical gates for multilevel systems is demonstrated through decoherence control under the quantum adiabatic method using simple phase modulated laser pulses. We make use of selective population inversion and Hamiltonian evolution with time to achieve such goals robustly instead of the standard unitary transformation language. (letter to the editor)

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In the procedure of the hydraulic control system analysis, a linearized approximate equation described by the first order term of Taylor's series has been widely used. Such a linearized equation is effective just near the operating point. In this study, the authors estimate computational errors in the process of applying the existing linearized equation stated above. For evaluating the computational accuracy in practical applications of the linearized equations, dynamic behaviors of hydraulic control systems are investigated through simulations with several kinds of representative hydraulic systems and the linearized equations suggested in this study.

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A method for calculating flow through an airfoil cascade drawn on a surface of revolution is discussed. The three-dimensional flow was assumed to be represented by part-channels of varying width. The basic equations are the equation of continuity and the ...

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... 4 II. INERTIAL NAVIGATION ERROR EQUATIONS ..... 5 ... 4- Page 20. Chapter II INERTIAL NAVIGATION ERROR EQUATIONS ...

CERN Document Server

In this paper, we study the existence and uniqueness of periodic solutions of the differential equation of the form . Here, we obtain some sufficient conditions which guarantee the existence of periodic solutions. This equation is a quite general third- order nonlinear vector differential equation, and one example is given for illustration of the subject.

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The hierarchy of integrable nonlinear equations associated with the quadratic bundle is considered. The expressions for the solution of linearization of these equations and their conservation law in the terms of solutions of corresponding Lax pairs are found. It is shown for the first member of the hierarchy that the conservation law is connected with the solution of linearized equation due to the Noether's theorem. The local hierarchy and three nonlocal ones of the infinitesimal symmetries and conservation laws explicitly expressed through the variables of the nonlinear equations are derived. (author)

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No abstract prepared.

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This two-volume reference uses many equations to provide detailed information on atomic and nuclear decay phenomena.

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The problem in perturbation theory in general relativity is finding a natural gauge which simplifies the equations considerably. We solved the first and second order perturbation equations in the ''Lorentz gauge'' using the two-timing method. The equations were deduced from the equations of Einstein in the presence of a matter energy-momentum tensor of a perfect fluid with equation of state p = (#gamma#-1) rho. It is found that the 0--0 component of the first order equations together with the gauge conditions are consistent with the Bianchi type V model, without axial symmetry. It represents a ''ground state'' situation of the Bianchi type IX model (Mixmaster model.) The second order equations, describing the reaction back of the gravitational waves on the slowly varying background, give rise to rotation and will disturb the isotropization ...

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We carry out a Lie group analysis of the Sachs equations for a time-dependent axisymmetric non-rotating space-time in which the Ricci tensor vanishes. These equations, which are the first two members of the set of Newman-Penrose equations, define the characteristic initial-value problem for the space-time. We find a particular form for the initial data such that these equations admit a Lie symmetry, and so defines a geometrically special class of such spacetimes. These should additionally be of particular physical interest because of this special geometric feature.

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We revisited the quantum Zeno paradox, which claims that a generic quantum system prepared in a state which is not an eigenstate of the Hamiltonian operator and is continuously observed never decays. Since any perfectly isolated quantum system always interact with a vacuum field, we analyze the possibility of using this fact to solve the above mentioned conceptual problem. Therefore we discuss a two-level system or qubit-Bose field interaction Hamiltonians. We consider the quantum dynamics of this two-level system, prepared in the excited state interacting with a Bose field prepared in the Poincare invariant vacuum state. Using a first-order approximation in time-dependent perturbation theory, we evaluate the probability of spontaneous decay of the two-level system driven by the vacuum field. This probability is evaluated for a finite time interval. Using the standard argument to obtain the quantum Zeno paradox, we consider N measurements where ...

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Predictions for E2, M1, and M4 transition rates and moments, together with examples of transition-charge densities, are presented for states of N = 50 nuclei. These predictions are based on one-body spectroscopic amplitudes obtained from the wave functions of a new N = 50 shell-model calculation which incorporates the 0f/sub 5/2/, 1p/sub 3/2/, 1p/sub 1/2/, and 0g/sub 9/2/ single-particle orbits and an empirically determined effective Hamiltonian for this space. The predictions are compared with experimental data, first in order to evaluate how well the model space, as applied by this Hamiltonian, accounts for observations, and then to assess the importance of configurations excluded from the model space and to determine the values of the operator renormalizations (effective charges and effective g factors) which optimally map the theoretical results onto the corresponding experimental values.

CERN Document Server

Given an invariant gauge potential and a periodic scalar potential \\tilde{V} on a Riemannian manifold \\tilde{M} with a discrete symmetry group \\Gamma, consider a \\Gamma-periodic quantum Hamiltonian \\tilde{H}=-\\tilde{\\Delta}_{B}+\\tilde{V} where \\tilde{\\Delta}_{B} is the Bochner Laplacian. Both the gauge group and the symmetry group \\Gamma can be noncommutative, and the gauge field need not vanish. On the other hand, \\Gamma is supposed to be of type I. To any unitary representation \\Lambda of \\Gamma one relates a Hamiltonian H^{\\Lambda}=-\\Delta_{B}^{\\Lambda}+V on M=\\tilde{M}/\\Gamma where V is the projection of \\tilde{V} to M. We describe a construction of the Bloch decomposition of \\tilde{H} into a direct integral whose components are H^{\\Lambda}, with \\Lambda running over the dual space \\hat{\\Gamma}. The evolution operator and the resolvent decompose correspondingly. Conversely, given \\Lambda\\in\\hat{\\Gamma}, one can ...

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A phenomenological simulation was carried out for 41 experimental crystal-field (CF) levels within the {sup 4}I{sub 9/2-15/2}, {sup 4}F{sub 3/2-9/2}, {sup 4}S{sub 3/2} and {sup 2}H{sub 9/2} J manifolds, including the available infrared (IR) data up to {approx}15 000 cm{sup -1} for the Nd{sup 3+} ions in the Nd{sub 2}CuO{sub 4} single crystals. The CF Hamiltonian for the tetragonal C{sub 4v} symmetry was diagonalized together with the free-ion Hamiltonian in a basis that spans the entire 4f{sup 3} configuration. A rms error of 9 cm{sup -1} between the calculated and experimental energy level schemes was obtained. A comparison of the spectra in the visible region between the insulating Nd{sub 2}CuO{sub 4} and the metallic Nd{sub 2-x}Ce{sub x}CuO{sub 4}, allowed identifying the absorption bands associated with the development of the charge-doping induced local structural distortions in the superconducting regime.

CERN Document Server

The Hamiltonian structure of the Classical Heisenberg Spin Chain (CHSC) has been extensively studied by a number of authors. First of all, we mention Faddeev and Thaktadjan that, in their fundamental monograph "Hamiltonian Methods in the Theory of Soliton", elucidate the main properties of both continuous and (semi-)discrete models. An analysis of the su(2) continuous model in the context of the reduction theory for Poisson Nijenhuis manifolds was performed by Magri et al in1985, while through a similar approach a few years later Ragnisco and Santini analyzed the discrete case. In the meantime, among the condensed matter community there was some renewed interest on Potts models, sort of generalized spin chains where the relevant field variable is allowed to take values at the $N^{th}$ roots of unity. The proper theoretical setting for such models, at least at the classical level, would have been the extension to NxN matrices of the approach ...

International Nuclear Information System (INIS)

The absorption, emission and magnetic circular dichroism spectra of the anionic complex (Cp_3Pr. NCS)"- were measured at room and low temperatures. On the basis of these spectra the electronic structure in the f-f range could be derived. The parameters of an empirical Hamiltonian were fitted to the experimentally determined crystal field splitting pattern. Compared with the previously examined neutral Cp_3 Pr.X complexes the quadratic crystal field parameter B_0"2 is considerably reduced.

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This paper presents a new algorithm for the optimal long-range generation planning for a thermal system with pumped-storage plants. The algorithm is based upon the analytical production costing model developed under the assumption of Gaussian probabilistic distribution of random load fluctuations and plant outages. The optimization problem consists of the master problem to determine the annual investment, and the pumped-storage subproblem to determine the optimal pumped-storage operation. The master problem is formulated as a Hamiltonian minimization problem, and the pumped-storage subproblem is solved using the concept of peak-shaving operation on the original load curve.

International Nuclear Information System (INIS)

Single-crystalline CeRh_2Si_2 and CePd_2Si_2 were grown by the Czochralsky pulling method and the temperature dependence of magnetic susceptibility was investigated. The crystalline electric field (CEF) states in each compound were determined by considering the tetragonal CEF Hamiltonian with mean-field approximation. Interactions between Ce"3"+ ion and the surrounding ligands in CeRh_2Si_2 turned out to be strong and highly anisotropic in comparison to CePd_2Si_2. (orig.)

International Nuclear Information System (INIS)

This paper is concerned with the determination of a unique scaling parameter in complex scaling analysis and with accurate calculation of dynamics resonances. In the preceding paper we have presented a theoretical analysis and provided a formalism for dynamical resonance calculations. In this paper we present accurate numerical results for two non-trivial dynamical processes, namely, models of diatomic molecular predissociation and of barrier potential scattering for resonances. The results presented in this paper confirm our theoretical analysis, remove a theoretical ambiguity on determination of the complex scaling parameter, and provide an improved understanding for dynamical resonance calculations in rigged Hilbert space.

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The diagonal and symmetric Bianchi type IX models are coupled to a homogeneous spinor field. An action for the combined fields is constructed, where the orthonormal basis used is given explicitly in terms of the metric. This allows one to vary the action with respect to the metric and the spinor fields only. Next, a Hamiltonian formulation is given, and a qualitative solution for the problem is presented. We also show that the k = +1 FRW (Friedmann--Robertson--Walker) model is not compatible with a homogeneous spinor field, while the more complicated models are.

CERN Document Server

n an early approach, we proposed a kinetic model with multiple translational temperature [K. Xu, H. Liu and J. Jiang, Phys. Fluids {\\bf 19}, 016101 (2007)], to simulate non-equilibrium flows. In this paper, instead of using three temperatures in $x-$, $y-$, and $z$-directions, we are going to further define the translational temperature as a second-order symmetric tensor. Based on a multiple stage BGK-type collision model and the Chapman-Enskog expansion, the corresponding macroscopic gas dynamics equations in three-dimensional space will be derived. The zeroth-order expansion gives the 10 moment closure equations of Levermore [C.D. Levermore, J. Stat. Phys {\\bf 83}, pp.1021 (1996)]. To the 1st-order expansion, the derived gas dynamic equations can be considered as a regularization of Levermore's 10 moments equations. The new gas dynamic equations have the same structure as the ...

International Nuclear Information System (INIS)

To develop the advanced subchannel analysis code, the dominant factors that influence the boiling transitional process must be taken into account in the mechanistic constitutive equations based on the flow geometries and the fluid properties. The dominant factors that influence the boiling transitional processes are (1) the gas-liquid re-distribution by cross flow, (2) the liquid film dryout, (3) the two-phase flow regime transition, (4) the droplet deposition, and (5) the spacer-droplet interaction. At first, we indicated the strategy for the development of the constitutive equations for the five dominant factors based on the experimental database by the latest measurement technique and the latest computational fluid dynamics method. Then, the problems of the present constitutive equations and the improvement plan of the constitutive equations were indicated. Finally, the layered structure for the ...

International Nuclear Information System (INIS)

The static thermophysical properties of the molten salt system like LiF-NaF-BeF_2 influence the design and construction of the fuel salt and coolant in the Molten Salt Reactor for the new generation. In this paper, the equation of state of the ternary system 0.15LiF-0.58NaF-0.27BeF_2, over the temperature range from 873.15K to 1073.15K at one atmosphere pressure, is described by using modified Peng-Robinson equation. The density of the ternary system is evaluated by this equation directly, and compared with the experimental data. Base on the equation of state, the other static thermophysical properties such as the enthalpy, entropy and heat capacity at constant pressure are evaluated by the fugacity coefficient and residual function methods respectively. The density calculated by Peng-Robinson equation is in highly agreement with the experimental data, and the enthalpy, entropy and ...

Science.gov (United States)

The static thermophysical properties of the molten salt system like LiF-NaF-BeF2 influence the design and construction of the fuel salt and coolant in the Molten Salt Reactor for the new generation. In this paper, the equation of state of the ternary system 0.15LiF-0.58NaF-0.27BeF2, over the temperature range from 873.15K to 1073.15K at one atmosphere pressure, is described by using modified Peng-Robinson equation. The density of the ternary system is evaluated by this equation directly, and compared with the experimental data. Base on the equation of state, the other static thermophysical properties such as the enthalpy, entropy and heat capacity at constant pressure are evaluated by the fugacity coefficient and residual function methods respectively. The density calculated by Peng-Robinson equation is in highly agreement with the experimental data, and the enthalpy, entropy and ...

British Library Electronic Table of Contents (United Kingdom)

An elliptic equation in a rectangle with coefficients depending on a fast variable and with its period being a small parameter is considered. An asymptotic expansion of the solution up to an arbitrary degree of the small parameter is constructed and substantiated by applying the two-scale expansion method.

UK PubMed Central (United Kingdom)

A generalized Fisher equation (GFE) relates the time derivative of the average of the intrinsic rate of growth to its variance. The GFE is an exact mathematical result that has been widely used in population...Full Text Available

British Library Electronic Table of Contents (United Kingdom)

We apply the group theory to Kadomtsev-Petviashvili-Burgers (KPBII) equation which is a natural model for the propagation of the two-dimensional damped waves. In correspondence with the generators of the symmetry group allowed by the equation, new types of symmetry reductions are performed. Some new exact solutions are obtained, which can be in the form of solitary waves and periodic waves. Specially, our solutions indicate that the equation may have time-dependent nonlinear shears. Such exact explicit solutions and symmetry reductions are important in both applications and the theory of nonlinear science.

International Nuclear Information System (INIS)

The wave equation for spin;1/2 tachyons is derived from the Dirac equation and the principle of relativity extended to superluminal Lorentz frames. From this wave equation and the Dirac equation infinite velocity spinor transformations are obtained. They yield bispinors of the plane-wave states of the tachyon, their interpretation and covariant orthogonality relations satisfied by them. The transformation properties of the bispinors under Lorentz transformation are discussed. The boundary conditions for the free propagator of wave functions of tachyons are obtained and the propagator is constructed. Then the covariant S-matrix for scattering from an electromagnetic field is derived. It is applied to the scattering of electron-tachyons from the Coulomb field.

CERN Document Server

P. Galenko et al. proposed a modified Cahn-Hilliard equation to model rapid spinodal decomposition in non-equilibrium phase separation processes. This equation contains an inertial term which causes the loss of any regularizing effect on the solutions. Here we consider an initial and boundary value problem for this equation in a two-dimensional bounded domain. We prove a number of results related to well-posedness and large time behavior of solutions. In particular, we analyze the existence of bounded absorbing sets in two different phase spaces and, correspondingly, we establish the existence of the global attractor. We also demonstrate the existence of an exponential attractor.

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... Union (INTAS), Brussels (Belgium) Science and Technology Center in Unkraine,

Science.gov (United States)

... AT 1170 DEG C. A UNIQUE CREEP CONSTITUTIVE EQUATION CONSISTING OF LINEAR AND POWER LAW TERMS WAS PROPOSED, AND ...

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down inertial navigation systemshavebeenreported. Shibata (1986)describesthe strapdown inertial navigation error equations basedon a quaternion relationship ...

International Nuclear Information System (INIS)

One normally identifies the prediction of tachyons with a higher spin problem. We show that the same phenomenon also happens with certain spin-1/2 equations, in exactly the same circumstances. Furthermore, we prove that these equations also have the defect of possessing solutions with complex energies, even with the smallest external fields. The consequences of these results are analyzed.

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A boundary value problem for Laplace?s equation in a bounded two-dimensional domain filled with a piecewise homogeneous medium is considered. The boundary of the inhomogeneity is assumed to be unknown. The inverse problem of determining the inhomogeneity boundary and the solution of the equation given the solution and its normal derivative on the boundary of the domain is discussed. Numerical methods are proposed for solving the inverse problem, and the results of numerical experiments are presented.

British Library Electronic Table of Contents (United Kingdom)

In this paper we present a new efficient sixth-order scheme for nonlinear equations. The method is compared to several members of the family of methods developed by Neta (1979) [B. Neta, A sixth-order family of methods for nonlinear equations, Int. J. Comput. Math. 7 (1979) 157-161]. It is shown that the new method is an improvement over this well known scheme.

Energy Technology Data Exchange (ETDEWEB)

The linearized collective Schroedinger equation for nuclear quadrupole surface vibrations incorporates a new spin degree of freeedom with a spin value of 3/2. We use this equation to describe the low energy spectrum of certain even-odd Ir nuclei which have a spin 3/2 in their ground state. For that purpose we explicitly introduce collective spin-dependent potentials which simulate the interaction of the valence nucleon with the core. The linearized Schroedinger equation is transformed into an effective Schroedinger equation with collective spin-dependent potentials. Already collective spin-orbit couplings of SO(3) and SO(5) type are sufficient to reproduce the lowest excited states of even-odd Ir nuclei. (orig.).

British Library Electronic Table of Contents (United Kingdom)

Abstract The importance of evaluating greenhouse gas (GHG) emissions from dairy cows within the whole farm setting is being realized as more important than evaluating these emissions in isolation. Current whole farm models aimed at evaluating GHG emissions make use of simple regression equations to predict enteric methane (CH4) production. The objective of the current paper is to evaluate the performance of nine CH4 prediction equations that are currently being used in whole farm GHG models. Data used to evaluate the prediction equations came from a collection of individual (IND) and treatment averaged (TRT) data. Equations were compared based on mean square prediction error (MSPE) and concordance correlation coefficient (CCC) analysis. In general, predictions were poor, with root MSPE (as...

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In this paper, a complete solution of the steady-state Newton-Euler equations describing the motion of the balls in high speed thrust bill bearings is presented. Kinematic equations are derived and used as ancillary equations to obtain the numerical solution of the Newton-Euler equations. This differs from previously reported work where extraneous assumptions (instead of kinematic analysis) are used to allow solutions of these equations. It is shown that the no-slip condition for the ball motion reported in the literature is based on an unnecessary assumption. The correct form of the condition is developed and used in the analysis of the ball motion. The analysis shows the importance of contact angle on both ball motion and contact force. An approximate theory is then developed for determining the optimum contact angle that would result in minimum contact force in high speed ball ...

International Nuclear Information System (INIS)

The interfacial area transport equation dynamically models the two-phase flow regime transitions and predicts continuous change of the interfacial area concentration along the flow field. Hence, when employed in the numerical thermal-hydraulic system analysis codes, it eliminates artificial bifurcations stemming from the use of the static flow regime transition criteria. Accounting for the substantial differences in the transport phenomena of various sizes of bubbles, the two-group interfacial area transport equations have been developed. The group 1 equation describes the transport of small-dispersed bubbles that are either distorted or spherical in shapes, and the group 2 equation describes the transport of large cap, slug or churn-turbulent bubbles. The source and sink terms in the right-hand-side of the transport equations have been established by mechanistically modeling the ...

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The theory of ..cap alpha.. decay in first-order perturbation theory is presented. The theory is designed for a strongly deformed nucleus in an isomeric state which changes its deformation dynamically through decay from a very deformed to an almost spherical shape. It is shown that other channels are not coupled to the ..cap alpha.. channel in first-order perturbation theory. The collective degrees of freedom of the daughter nucleus are described by shape vibrational states, eigenstates of a Hamiltonian whose potential has two minima. The parent nucleus is described by dynamically coupling the vibrational degrees of freedom to the ..cap alpha..-particle motion and also taking rotations into account. The ..cap alpha.. particle is taken to be a point-like particle. The theory is applied to the ..cap alpha.. decay of the isomeric state of /sub 95//sup 242/Am.

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The Kernel Polynomial Method (KPM) has been successfully applied to tight-binding electronic structure calculations as an O(N) method. Here the authors extend this method to nonorthogonal basis sets with a sparse overlap matrix S and a sparse Hamiltonian H. Since the KPM method utilizes matrix vector multiplications it is necessary to apply S{sup {minus}1}H onto a vector. The multiplication of S{sup {minus}1} is performed using a preconditioned conjugate gradient method and does not involve the explicit inversion of S. Hence the method scales the same way as the original KPM method, i.e. O(N), although there is an overhead due to the additional conjugate gradient part. The authors show an application of this method to defects in a titanate/platinum interface and to a large scale electronic structure calculation of amorphous diamond.

CERN Document Server

Tensor network states are used to approximate ground states of local Hamiltonians on a lattice in D spatial dimensions. Different types of tensor network states can be seen to generate different geometries. Matrix product states (MPS) in D=1 dimensions, as well as projected entangled pair states (PEPS) in D>1 dimensions, reproduce the D-dimensional physical geometry of the lattice model; in contrast, the multi-scale entanglement renormalization ansatz (MERA) generates a (D+1)-dimensional holographic geometry. Here we focus on homogeneous tensor networks, where all the tensors in the network are copies of the same tensor, and argue that certain structural properties of the resulting many-body states are preconditioned by the geometry of the tensor network and are therefore largely independent of the choice of variational parameters. Indeed, the asymptotic decay of correlations in homogeneous MPS and MERA for D=1 systems is seen to be determined by the structure ...

International Nuclear Information System (INIS)

The dynamical decoupling (DD) aims at suppressing the decoherence by means of coherent control pulses. Even if devices exist where instantaneous pulses are an adequate approximation, experimentally a finite duration #tau#_p and a bounded amplitude are inevitable. They are the cause of additional errors which can be corrected by designing the pulse shape appropriately. The new pulse has the overall effect of an ideal, instantaneous pulse with the advantage of decoupling the spin (or qubit) from the bath up to the order O(#tau#_p"3). The limitation of the no-go theorem for #pi# pulses is avoided. Hence, the Uhrig sequence (UDD), originally thought for ideal #pi# pulses, works also for bounded control Hamiltonians. Numerical simulations show that concatenated sequences of real pulses are effective against general decoherence.

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The purpose of this work is the elucidation of the f"n electronic structure of neutral mono base adducts derived from tris(#eta#"5-cyclopentadienyl)-lanthanide(III) (Cp_2Ln). The available data on related compounds like bis adducts and anionic mono adducts of the same moiety was also analyzed. The first aim was to derive the experimental crystal field splitting pattern from optical, magnetooptical and magnetochemical measurements and to reproduce it using an empirical Hamiltonian operator. The eigenvalues and eigenvectors obtained in this manner were used for a quantitative interpretation of the magnetochemical, EPR- and NMR-spectroscopic properties. For the latter subject it was necessary to develop an own procedure for the NMR analysis of paramagnetic compounds. This method is based on factor analysis and as demonstrated in the second part of this work, is clearly superior to all previous procedures. (orig.).

International Nuclear Information System (INIS)

The band crossing in "1"3"2Ba has been investigated by using the interacting boson model. A broken neutron pair has been coupled to a collective boson core. The boson-fermion interaction hamiltonian contains terms which can transform a boson into a pair of quasiparticles and vice versa. The parameters were partly determined by fitting the collective states of "1"3"2","1"3"4Ba and the yrast states of "1"3"1Ba. The energy backbending has been satisfactorily reproduced. Good agreement of the electromagnetic moments has been reached. The structure of the wave functions has been discussed. (author)

CERN Document Server

Amplitudes for fermion-fermion, boson-boson and fermion-boson interactions are calculated in the second order of perturbation theory in the Lobachevsky space. An essential ingredient of the model is the Weinberg's 2(2j+1)-component formalism for describing a particle of spin j. The boson-boson amplitude is then compared with the two-fermion amplitude obtained long ago by Skachkov on the basis of the Hamiltonian formulation of quantum field theory on the mass hyperboloid, p_0^2 - p^2=M^2, proposed by Kadyshevsky. The parametrization of the amplitudes by means of the momentum transfer in the Lobachevsky space leads to same spin structures in the expressions of T-matrices for the fermion case and the boson case. However, certain differences are found. Possible physical applications are discussed.

International Nuclear Information System (INIS)

The absorption spectra of an unoriented single crystal of the title compound (1) have been measured at room and at low temperatures. Assuming a similar sequence of crystal field (CF) levels as for the previously analyzed Nd[N(SiMe_3)_2]_3 (2) a truncated CF splitting pattern is derived from the spectra obtained. The parameters of an empirical Hamiltonian are fitted to the energies of 71 levels to give an r.m.s. deviation of 24.2 cm"-"1. The parameters obtained are compared with those of 2 and Nd[N(SiMe_3)_2]_3(CNC_6H_1_1)_2 (3). The observed trends of CF parameters are consistent with the results of simple model calculations in the framework of the angular overlap model. (orig.)

International Nuclear Information System (INIS)

The energy levels, wavelengths, oscillator strengths, Auger rates and level-to-level dielectronic recombination rate coefficients describing dielectronic recombination into excited levels of Ne-like titanium from F-like low-lying states are calculated. Our calculations are based on Dr. R.D. Cowan's semi-relativistic mass-velocity and Darwin corrections are included in the Hamiltonian, and the distorted-wave model is used for the calculation of free electron wavefunctions. In order to set the recombination rate coefficients on a level by level basis, in a manner compatible with detailed level population kinetics modelling of highly-stripped ions in plasma, the dielectronic recombination rate coefficients as a function of free electron temperatures are given in an analytical form, which is not only very convenient in practice, but also hopefully accurate compared with the exactly calculated numerical results. (orig.).

CERN Document Server

A prescription is given for computing anomalous dimensions of single trace operators in SYM at strong coupling and large $N$ using a reduced model of matrix quantum mechanics. The method involves treating some parts of the operators as "BPS condensates" which, in certain limit, have a dual description as null geodesics on the $S^5$. In the gauge theory, the condensate is similar to a representative of the chiral ring and it is described by a background of commuting matrices. Excitations around these condensates correspond to excitations around this background and take the form of ``string bits" which are dual to the "giant magnons" of Hofman and Maldacena. In fact, the matrix model approach gives a {\\it quantum} description of these string configurations and explains why the infinite momentum limit suppresses the quantum effects. This method allows, not only to derive part of the classical sigma model Hamiltonian of the dual string (in the infinite momentum ...

Science.gov (United States)

Hamiltonians of Landau-Ginzburg-Wilson type are constructed for order parameters which are bases for certain high-dimensional irreducible or physically irreducible representations in A-15 structure. These are all the representations with wave vectors ?, X, and R and encompass cases of dimension 1, 2, 3, 4, and 6. A renormalization-group analysis was performed on each new distinct Hamiltonian using the Wilson-Fisher "? expansion" method to order ?, in order to determine fixed points and stability, and critical exponents. For representations of R wave-vector symmetry, only the two-dimensional R(1) has a stable fixed point and may produce a second-order phase transition; for all other R wave vector representations, fluctuations prevent second-order transition. No X point representation gives a second-order transition. Representations at ? which are permitted to be second order by "Landau theory" remain so in this analysis. Generally, if the ...

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We present an efficient parallel algorithm and its implementation for computing the diagonal of $H^-1$ where $H$ is a 2D Kohn-Sham Hamiltonian discretized on a rectangular domain using a standard second order finite difference scheme. This type of calculation can be used to obtain an accurate approximation to the diagonal of a Fermi-Dirac function of $H$ through a recently developed pole-expansion technique \\cite{LinLuYingE2009}. The diagonal elements are needed in electronic structure calculations for quantum mechanical systems \\citeHohenbergKohn1964, KohnSham 1965,DreizlerGross1990. We show how elimination tree is used to organize the parallel computation and how synchronization overhead is reduced by passing data level by level along this tree using the technique of local buffers and relative indices. We analyze the performance of our implementation by examining its load balance and communication overhead. We show that our implementation exhibits an excellent ...

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In this dissertation, a two-phase, air-droplets, dilute, turbulent, and steady state flow in a horizontal rectangular channel, is modeled and numerically simulated using a modified KIVA-3V code. The deposition of different sizes of droplets on the walls of the channel is also studied. In this model, the interaction effects between the phases (two-way coupling) are considered by source terms in the momentum and energy equations for the continuous phase and by the instantaneous local velocity of the air in the droplet equation of motion, which includes the aerodynamic and gravitational forces. The turbulence is modeled by a k-? model. The interaction effects between the turbulence and the dispersed droplets are also taken into account. The effects of the turbulence on the droplets are modeled by a fluctuating component added to the local air velocity in the droplet equation of motion. The effects of the droplets on the ...

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Formulation is introduced for discretizing a boundary integral equation into an indirect boundary element method for the solution of 3-dimensional topographic problems. Yokoi and Takenaka propose an analytical solution-capable reference solution (solution for the half space elastic body with flat free surface) to problems of topographic response to seismic motion in a 2-dimensional in-plane field. That is to say, they propose a boundary integral equation capable of effectively suppressing the non-physical waves that emerge in the result of computation in the wake of the truncation of the discretized ground surface making use of the wave field in a semi-infinite elastic body with flat free surface. They apply the proposed boundary integral equation discretized into the indirect boundary element method to solve some examples, and succeed in proving its validity. In this report, the equation is expanded to ...

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Solving a coupled set of differential equations formed by a Fokker-Planck equation and a set of master equations, we can calculate the number of 'prefission' particles (n,p,a), which are emitted from a hot, rotating compound nucleus. Furthermore we get their energy spectrum and their angular momentum distribution. Our results depend sensitively on the friction parameter {gamma}, the inertia M and the fission potential. Comparing the results with experimental data, we may learn something about these quantities. The investigations have been made for {sup 187}Ir and {sup 185}Os. (orig.).

CERN Document Server

Constrained quantum dynamics is used to propose a nonlinear dynamical equation for pure states of a generalized coarse-grained system. The relevant constraint is given either by the generalized purity or by the generalized invariant fluctuation, and the coarse-grained pure states correspond to the generalized coherent i.e. generalized nonentangled states. Open system model of the coarse-graining is discussed. It is shown that in this model and in the weak coupling limit the constrained dynamical equations coincide with an equation for pointer states, based on Hilbert-Schmidt distance, that was previously suggested in the context of the decoherence theory.

CERN Document Server

Big Bang nucleosynthesis requires a fine balance between equations of state for photons and relativistic fermions. Several corrections to equation of state parameters arise from classical and quantum physics, which are derived here from a canonical perspective. In particular, loop quantum gravity allows one to compute quantum gravity corrections for Maxwell and Dirac fields. Although the classical actions are very different, quantum corrections to the equation of state are remarkably similar. To lowest order, these corrections take the form of an overall expansion-dependent multiplicative factor in the total density. We use these results, along with the predictions of Big Bang nucleosynthesis, to place bounds on these corrections.

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Pippenger (2011) recently proposed a solution to the longstanding forward-bias puzzle. He argues that the puzzling estimates obtained using the standard equation for the efficient markets hypothesis are due to omitted variable bias. He identifies the missing variables as the future change in the forward exchange rate and the future interest differential. When these are added to the standard equation, he finds a one-to-one relationship between the future change in the spot rate and the forward premium. However, we argue that his equation can only test covered interest parity and offers no insight into the forward-bias puzzle.

CERN Document Server

Within the framework of a modified Balitsky-Kovchegov equation, we calculated and provide estimates of non-linear saturation effects expected in the LHC range of energies.

International Nuclear Information System (INIS)

In this paper, research on pass schedule of tandem cold mill (TCM) is carried out. According to load (reduction, rolling force, motor power) balance, non-linear equations set with variables of inter-stand thickness is constructed. The pass schedule optimization is carried out by solving the non-linear equations set. As the traditional method, the Newton-Raphson method is used for solving the non-linear equations set. In this paper a new simple method is brought up. On basis of the monotone relations between thickness and load, the inter-stands thickness is adjusted dynamically. The solution of non-linear equations set can be converged by iterative calculation. This method can avoid the derivative calculation used by traditional method. So, this method is simple and calculation speed is high. It is suitable for on-line control. (author)

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The validity is given to the newly proposed two weighting {delta}f scheme (Wang et al., Research Report of National Institute for Fusion Science NIFS-588, 1999) for collisional or neoclassical transport calculations, which can solve the drift kinetic equation taking account of effects of steep plasma gradients, large radial electric field, finite banana width, and the non-standard orbit topology near the axis. The marker density functions in weight equations are successively solved by using the idea of {delta}f method and a hierarchy of equations for weight and marker density functions is obtained. These hierarchy equations are solved by choosing an appropriate source function for each marker density. Thus the validity of the two weighting {delta}f scheme is mathematically proved. (author)

Science.gov (United States)

... A. Fasano, SD Howison. JR Ockendon & M. Primicerio. Some remarks on the regularisation of the supercooled one-phase Stefan problem. Quart. ...

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Most gas dynamic computations in industrial ducts are done in one dimension with cross-section-averaged Euler equations. This poses a fundamental difficulty as soon as geometrical discontinuities are present. The momentum equation contains a non-conservative term involving a surface pressure integral, responsible for momentum loss. Definition of this integral is very difficult from a mathematical standpoint as the flow may contain other discontinuities (shocks, contact discontinuities). From a physical standpoint, geometrical discontinuities induce multidimensional vortices that modify the surface pressure integral. In the present paper, an improved 1D flow model is proposed. An extra energy (or entropy) equation is added to the Euler equations expressing the energy and turbulent pressure ...

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In this report we present a suite of subroutines for the solution of sparse unsymmetric sets of linear equations using a variant of Gaussian elimination. The subroutines are divided into three distinct phases. The first phase optionally preorders the matrix to block triangular form and then performs a sparsity oriented factorization, the second factorizes a matrix of a similar sparsity pattern, while the third uses these decompositions to solve the equations. In this revised edition, the actual Fortran listings have been replaced by a reference to their availability in machine readable form. Other changes to the first edition are minor. This revision is essentially a reprint of the 1979 revision, the only changes being that the MA28A specification sheet has been typeset and has a few minor changes and the existence of a version of the package for complex equations is announced. 11 refs., 11 tabs.

CERN Document Server

No Kerr-like exact solution has yet been found in Chern-Simons modified gravity. Intrigued by this absence, we study stationary and axisymmetric metrics that could represent the exterior field of spinning black holes. For the standard choice of the background scalar, the modified field equations decouple into the Einstein equations and additional constraints. These constraints eliminate essentially all solutions except for Schwarzschild. For non-canonical choices of the background scalar, we find several exact solutions of the modified field equations, including mathematical black holes and pp-waves. We show that the ultrarelativistically boosted Kerr metric can satisfy the modified field equations, and we argue that physical spinning black holes may exist in Chern-Simons modified gravity only if the metric breaks stationarity, axisymmetry or energy-momentum conservation.

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major radius of the toroidal containment volume. The containment time was calculated using equation (4) as derived in references 16 and 17. The solid ...

Science.gov (United States)

... 2.5.6 Development of Observation Equations . . . . . 25 2.6 Inertial Navigation Error Model . . . . . ... 2 , as expected. 2.6 Inertial Navigation Error Model ...

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... Abstract : The purpose of this paper is to introduce strapdown inertial navigation error equations based on a quaternion relation between body-fixed ...

UK PubMed Central (United Kingdom)

Diffusion in the extracellular space (ECS) of the brain is constrained by the volume fraction and the tortuosity and a modified diffusion equation represents the transport behavior of many molecules...Full Text Available

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The interaction of thermal radiation with conduction and convection in thermally developing absorbing, emitting, nongray gas-particulate turbulent suspension flow through a circular tube is investigated. The contribution of thermal radiation is obtained through evaluation of the total hemispherical emittance of the particulate cloud and through evaluation of single band absorptances for molecular gases, modified to account for the interaction with the particles. The governing differential equation is derived as a (nonlinear) energy equation, coupled with integral equations to find the thermal radiation contributions. The energy equation is solved numerically by an implicit finite difference method with an iterative procedure. Qualitative results for Nusselt numbers are shown for a variety and range of parameters, such as optical thickness of particulates and single molecular gas bands, relative gas band ...

International Nuclear Information System (INIS)

The presence of an extraneous light gas must be taken into account in consideration of centrifugal separation of uranium isotopes, when there is inevitable leakage of such a gas through the gas sealant and/or leaking in from the atmosphere. Consideration is first given to the influence of the presence of the light gas on the maximum separative power. Then the basic equation for isotope separation containing a light gas is derived from Hirschfelder's diffusion equations. This equation is solved and the separative performance is expressed in terms of the shape factor and reflux parameter. The formulas for expressing the flow configurations of the gases are obtained for a simple model in which inflow and outflow prevail throughout the centrifuge. The corresponding equation for a model in which the gases flow in two concentric thin streams is also derived. It is concluded that the influence provided by the ...

International Nuclear Information System (INIS)

The set of nonlinear equations describing the standard model kinematics of the top quark antiquark production system in the dilepton decay channel has at most a fourfold ambiguity due to two not fully reconstructed neutrinos. Its most precise solution is of major importance for measurements of top quark properties like the top quark mass and tt spin correlations. Simple algebraic operations allow one to transform the nonlinear equations into a system of two polynomial equations with two unknowns. These two polynomials of multidegree eight can in turn be analytically reduced to one polynomial with one unknown by means of resultants. The obtained univariate polynomial is of degree 16. The number of its real solutions is determined analytically by means of Sturm's theorem, which is as well used to isolate each real solution into a unique pairwise disjoint interval. The solutions are polished by seeking the sign change of the ...

International Nuclear Information System (INIS)

We consider particle evaporation and fission of an ensemble of hot, rotating compound nuclei as a stochastic process. We derive a set of coupled differential equations formed by a Fokker-Planck equation describing fission, and master equations for calculating particle evaporation. From these equations, we are able to determine multiplicities of prefission neutrons, protons and #alpha#-particles, their energy spectra and their angular momentum distributions. A comparison of our results with experimental data provides us with information regarding the reduced friction coefficient #beta#, the fission barrier height and the level density parameter. For different iridium isotopes, ("1"8"1","1"8"5","1"8"7Ir), "1"8"5Os and "1"5"8Er, we obtain as an upper limit #beta##<=#8.0x10"2"1 s"-"1. (orig.).

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... 3. Critical constants, and triple point 4. Compressibility isothermE S. Density, molar volume (of a condensed phase) 6. Equations of state, general ...

British Library Electronic Table of Contents (United Kingdom)

An operator of FE-closure is introduced on the set of functions of a multivalued logic based on the systems of functional equations. It is proved that, for every k ? 2, the FE-closure operator generates a finite classification on the set P k of functions of k-valued logic. The least class in this classification is shown to be the class H k of all homogeneous functions. Also a series of corollaries are obtained concerning the finite FE-generating sets in the FE-closed classes.

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The spin-up problem of He II in a cylindrical container of infinite and finite height is considered on the basis of the Hall-Vinen-Bekarevich-Khalatnikov equations. The boundary conditions include the assumption of the generation of superfluid vorticity at the walls of the container. In the lowest order approximation with respect to viscosity, the problem is reduced to a Stefan problem for a single diffusion-type equation. Examples of solutions are given which show that the method used gives a good insight into the physical development of the spin-up flow.

International Nuclear Information System (INIS)

For a system of noninteracting electrons scattered by resonant levels of neutral impurities, we show that virial and quasiparticle corrections have nearly equal magnitudes. We propose a modification of the Boltzmann equation that includes quasiparticle and virial corrections and discuss their interplay on a dielectric function. copyright 1997 The American Physical Society.

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To simulate the effects of the breakup channel on rearrangement amplitudes, the conventional coupled-reaction-channel (CRC) expansion is augmented by pseudoreaction channels. The construction of the projector for the extended CRC space is discussed, and transition-operator equations on this space are given. By solving the full and post-approximation forms of the CRC equations for a model three-particle problem, the crucial role played by the nonorthogonality terms is demonstrated.

CERN Document Server

We study the dynamics of the scalar tensor cosmological model in the presence of tachyon field. In an alternative approach, in two exponential and power law form of the scalar field functions in the model, field equations are solved by simultaneously best fitting the model parameters with the most recent observational data. This approach gives us an observationally verified interpretation of the dynamics of the universe. We then discuss the best fitted of equation of state parameter, the statefinder parameters and the reconstructed scalar field in the model.

International Nuclear Information System (INIS)

A method of auxiliary spectrum is modified so that matrix elements of the reaction matrix in final nuclei are determined by means of algebraic operations alone (inversion of matrices). No differential equations need to be solved; Pauli's exclusion principle is accurately taken into account. A single-particle potential may be of any kind, but a two-particle interaction must have no solid core.

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By a variant version of Fountain Theorem due to Zou [W. Zou, Variant fountain theorems and their applications, Manuscripta Math. 104 (2001) 343-358], the existence of infinitely many solutions is obtained for a class of biharmonic equations where the nonlinearity involves a combination of superlinear and asymptotically linear terms.

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Zanker has recently presented nomographs for determining particle settling velocities in solid-liquid systems. These nomographs were based on the general correlations developed by Barnea and Mizrahi and Barnea and Mednick. This work presents an equation directly computing particle settling velocities, eliminating the uncertainty associated with nomographs.

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The interfacial area transport equation dynamically models the two-phase flow regime transitions and predicts continuous change of the interfacial area concentration along the flow field. Hence, when employed in the numerical thermal-hydraulic system analysis codes, it eliminates artificial bifurcations stemming from the use of the static flow regime transition criteria. Accounting for the substantial differences in the transport phenomena of various sizes of bubbles, the two-group interfacial area transport equations have been developed. The group 1 equation describes the transport of small-dispersed bubbles that are either distorted or spherical in shapes, and the group 2 equation describes the transport of large cap, slug or churn-turbulent bubbles. The source and sink terms in the right-hand-side of the transport equations have been established by mechanistically modeling the ...

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This demonstration project uses modern simulation techniques to illustrate the important technologies and design variables that an auto-designer would consider in production a high efficiency, low emissions vehicle. Simulation and modeling techniques use the idea of capturing the relationships between real components of the systems with mathematical equations. These equations are then solved on a computer to simulate the behavior or performance of the system under various conditions. In the current demonstration project, we focus on many variations of a hydrogen-powered vehicle.

British Library Electronic Table of Contents (United Kingdom)

Four solutions of the Cauchy problem for Mathieu?s equation away from parametric resonance domains are analytically constructed using an asymptotic averaging method in the fourth approximation. Three solutions occur near fractional parameter values at which slow combination phases exist. The fourth solution occurs in the absence of slow phases away from parametric resonance domains and the fractional parameter values.

International Nuclear Information System (INIS)

To calculate the energy band structures in semiconductors using the relativistic augmented plane wave method, atomic potential and charge density are needed, which are calculated by self-consistent method. Wave function for one electron is determined by solving the Dirac equation with the Hartree-Fock equation based on the slater's exchange potential. The results of calculation for Cu"+"1 are given. (Author).

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The effect of finite gyroradius on the current diffusive ballooning mode is examined. Starting from the reduced MHD equations including turbulent transports, coupling with drift motion and finite gyroradius effect of ions, we derive a ballooning mode equation with complex transport coefficients. The eigenfrequency, saturation level and thermal diffusivity are evaluated numerically from the marginal stability condition. Preliminary results of their parameter dependence is presented. (author)

International Nuclear Information System (INIS)

A formula for calculating the Dirac S-matrix for central Lorentz scalar and vector potentials is derived by use of a new amplitude-phase method. The derivation also makes use of certain invariants of the reduced 2-spinor radial Dirac equations.

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We consider the problem of rotation in a homogeneous Bianchi type IX cosmological model. Studying the Wheeler-De Witt equation corresponding to this minisuperspace, and adopting a particular choice of the factor ordering, we are able to find a particular solution which is strongly peaked about isotropy. This result confirms all the previous investigations in this field, and suggests the conclusion that the machian nature of our universe is the natural, i.e. most likely, outcome of the Planck epoch. (orig.).

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Numerical simulations of compressible flows are commonly based on the Euler equations when effects of viscosity are thought to be negligible. These equations admit singular solutions, even in cases where the initial and boundary conditions are smooth. So-called ''Euler solvers'' rely on numerical dissipation, explicitly or implicitly present in the scheme, to regularize the problem, such that physical solutions are selected.

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The Schroedinger equation for nuclear quadruple surface vibrations is linearized with the consequence that a new spin degree of freedom appears in the wave function of the linearized equation. This spin is called collective spin and has a value of 3/2. The linearized Schroedinger equation for quadrupole vibrations is used for the description of certain collective aspects of even-odd {sup 187,189,191}Ir nuclei which have a spin 3/2 in their ground state. As a potential we use the {gamma}-soft collective potential of the neighboring even-even nuclei, which is inserted into the linearized Schroedinger equation via a scalar coupling. This leads to a collective spin-dependent fine structure splitting of the energy levels governed by a collective SO(5) spin-orbit coupling and a correction to the kinetic energy. Further, we consider explicitly spin-dependent potentials which effectively describe the ...

International Nuclear Information System (INIS)

We analyze the stability of the structure equations of the vacuum in the brane world models, by using both the linear (Lyapunov) stability analysis, and the Jacobi stability analysis, the Kosambi-Cartan-Chern theory. In the brane world models the four-dimensional effective Einstein equations acquire extra terms, called dark radiation and dark pressure, respectively, which arise from the embedding of the three-brane in the bulk. Generally, the spherically symmetric vacuum solutions of the brane gravitational field equations have properties quite distinct as compared to the standard black hole solutions of general relativity. We close the structure equations by assuming a simple linear equation of state for the dark pressure. In this case the vacuum is Jacobi stable only for a small range of values of the proportionality constant relating the dark pressure and the dark radiation. The ...

CERN Document Server

A linear structural equation model relates random variables of interest and corresponding Gaussian noise terms via a linear equation system. Each such model can be represented by a mixed graph in which directed edges encode the linear equations, and bidirected edges indicate possible correlations among noise terms. We study parameter identifiability in these models, that is, we ask for conditions that ensure that the edge coefficients and correlations appearing in a linear structural equation model can be uniquely recovered from the covariance matrix of the associated normal distribution. We treat the case of generic identifiability, where unique recovery is possible for almost every choice of parameters. We give a new graphical criterion that is sufficient for generic identifiability. It improves criteria from prior work and does not require the directed part of the graph to be acyclic. We also develop ...

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Full text of publication follows:In the current thermal-hydraulic system analysis codes using the two-fluid model, the empirical correlations that are based on the two-phase flow regimes and regime transition criteria are being employed as closure relations for the interfacial transfer terms. Due to its inherent shortcomings, however, such static correlations are inaccurate and present serious problems in the numerical analysis. In view of this, a new dynamic approach employing the interfacial area transport equation has been studied. The interfacial area transport equation dynamically models the two-phase flow regime transitions and predicts continuous change of the interfacial area concentration along the flow field. Hence, when employed in the thermal-hydraulic system analysis codes, it eliminates artificial bifurcations stemming from the use of the static flow regime transition criteria. Therefore, the interfacial area transport ...

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We consider spatially homogeneous (but generally non-isotropic) cosmologies in the recently proposed Horava-Lifshitz gravity and compare them to those of general relativity using Hamiltonian methods. In all cases, the problem is described by an effective point particle moving in a potential well with exponentially steep walls. Focusing on the closed-space cosmological model (Bianchi type IX), the mixmaster dynamics is now completely dominated by the quadratic Cotton tensor potential term for a very small volume of the universe. Unlike general relativity, where the evolution toward the initial singularity always exhibits chaotic behavior with alternating Kasner epochs, the anisotropic universe in Horava-Lifshitz gravity (with parameter lambda > 1/3) is described by a particle moving in a frozen potential well with fixed (but arbitrary) energy E. Alternating Kasner epochs still provide a good description of the early universe for very large E, but the ...

International Nuclear Information System (INIS)

In this work, a full ligand-field energy matrix (10x10) diagonalization treatment for 3d"1 ions in tetragonal symmetry is developed on the basis of the two-s.o.-coupling-parameter model. Spin Hamiltonian parameters (g factors g_|_|, g_p_e_r_p_e_n_d_i_c_u_l_a_r and hyperfine structure constants A_|_|, A_p_e_r_p_e_n_d_i_c_u_l_a_r) of the tetragonal V"4"+ center in Zn(antipyrine)_2(NO_3)_2 are calculated from the complete energy matrix diagonalization method and the perturbation theory method. The calculated results from both methods are not only close to each other but also in good agreement with the experimental values. Furthermore, the compressed defect structure of V"4"+ center is discussed.

CERN Document Server

The mean-field pictures based on the standard time-dependent variational approach have widely been used in the study of nonlinear many-boson systems such as the Bose-Hubbard model. The mean-field schemes relevant to Gutzwiller-like trial states $|F>$, number-preserving states $|\\xi >$ and Glauber-like trial states $|Z>$ are compared to evidence the specific properties of such schemes. After deriving the Hamiltonian picture relevant to $|Z>$ from that based on $|F>$, the latter is shown to exhibit a Poisson algebra equipped with a Weyl-Heisenberg subalgebra which preludes to the $|Z>$-based picture. Then states $|Z>$ are shown to be a superposition of $\\cal N$-boson states $|\\xi>$ and the similarities/differences of the $|Z>$-based and $|\\xi>$-based pictures are discussed. Finally, after proving that the simple, symmetric state $|\\xi>$ indeed corresponds to a SU(M) coherent state, a dual version of states $|Z>$ and ...

CERN Document Server

We summarize results of recent studies of heavy quarkonia correlators and spectral functions at finite temperatures from lattice QCD and systematic T-matrix studies using QCD motivated finite-temperature potentials. We argue that heavy quarkonia dissociation shall occur in the temperature range $1.2 \\le T_d/T_c \\le 1.5$ by the interplay of both screening and absorption in the strongly correlated plasma medium. We discuss these effects on the quantum mechanical evolution of quarkonia states within a time-dependent harmonic oscillator model with complex oscillator strength and compare the results with data for $R_{\\rm AA}/R_{\\rm AA}^{\\rm CNM}$ from RHIC and SPS experiments. We speculate whether the suppression pattern of the rather precise NA60 data from In-In collisions may be related to the recently discovered X(3872) state. Theoretical support for this hypothesis comes from the cluster expansion of the plasma Hamiltonian for heavy quarkonia in a strongly ...

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We present a description of the ground state and low-lying excited states of two holes in the 4x4 cluster t-J model in terms of a simple model for the motion of a single bipolaron. The existence of short-range antiferromagnetic correlations has been assumed. According to the suggested scenario, the formation of the bipolaron is mediated by the reduction of the magnetic energy in the case of two holes occupying nearest neighbor sites. The relevant part of the Hilbert space consists of wave functions corresponding to holes oscillating around pairs of nearest neighbor sites and trapped in a potential well due to strings of spin defects. Virtual processes which connect these states involve both the kinetic term and the transverse part of the Heisenberg Hamiltonian. Many properties of energy level schemes obtained by numerical diagonalizations such as the sequence of the lowest states for each irreducible representation of the k vector point groups can be reproduced ...

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The decays of charmed mesons into two body nonleptonic final states are investigated. Weak interaction amplitudes of interest in these decays are extracted from lattice four-point correlation functions using a effective weak Hamiltonian including effects to order G{sub f} in the weak interactions yet containing effects to all orders in the strong interactions. The lattice calculation allows a quantitative examination of non-spectator processes in charm decays helping to elucidate the role of effects such as color coherence, final state interactions and the importance of the so called weak annihilation process. For D {yields} K{pi}, we find that the non-spectator weak annihilation diagram is not small, and we interpret this as evidence for large final state interactions. Moreover, there is indications of a resonance in the isospin {1/2} channel to which the weak annihilation process contributes exclusively. Findings from the lattice calculation are compared to ...

International Nuclear Information System (INIS)

The quantum behavior of the vacuum Bianchi type-IX universe with the cosmological constant is investigated in terms of the Ashtekar variables. An exact solution to the quantum Hamiltonian constraint in the holomorphic representation is given. This solution reduces to the Hartle-Hawking wave function in the spatially isotropic sector and extends in the triad representation to the classically forbidden region where the determinant of the spatial metric becomes negative. The analysis of the quantum Robertson-Walker universe indicates that if the superspace is extended to such a classically forbidden region, the holomorphic representation picks up some restricted class of solutions in general. This observation leads to a new ansatz on the boundary condition of the Universe. In particular, the behavior of the Lorentzian and Euclidean WKB orbits corresponding to the solution suggests a new picture on the semiclassical behavior of the quantum Universe: that the Universe ...

International Nuclear Information System (INIS)

A Tm"3"+- Ho"3"+ -codoped single crystal of monoclinic BaY_2F_8 has been characterized by means of high resolution FTIR spectroscopy in the wave number range 2000-24000 cm"-"1 and in the temperature range 9-300 K. The energy level schemes of the two lanthanide ions as determined by the optical absorption spectra is presented, analyzed, and fitted within a single ion Hamiltonian model. The very small energy separation (about 0.6-1.6 cm"-"1) measured between the first and second sublevels of the ground state manifolds for both the ions is in line with the theoretical predictions. The impurity-phonon coupling is put into evidence by the thermally induced line shift and broadening, and by the detection of vibronic replicas of a few lines. (copyright 2005 WILEY-VCH Verlag GmbH and Co. KGaA, Weinheim) (orig.)

CERN Document Server

The detailed formulation for loop quantum cosmology (LQC) in the Bianchi I model with a scalar massless field has been constructed. In this paper, its effective dynamics is studied in two improved strategies for implementing the LQC discreteness corrections. Both schemes show that the big bang is replaced by the big bounces, which take place up to three times, once in each diagonal direction, when the area or volume scale factor approaches the critical values in the Planck regime measured by the reference of the scalar field momentum. These two strategies give different evolutions: In one scheme, the effective dynamics is independent of the choice of the finite sized cell prescribed to make Hamiltonian finite; in the other, the effective dynamics reacts to the macroscopic scales introduced by the boundary conditions. Both schemes reveal interesting symmetries of scaling, which are reminiscent of the relational interpretation of quantum mechanics and also suggest ...

CERN Document Server

In this review, we show how advances in the theory of magnetic pseudodifferential operators (magnetic $\\Psi$DO) can be put to good use in space-adiabatic perturbation theory (SAPT). As a particular example, we extend results of [PST03] to a more general class of magnetic fields: we consider a single particle moving in a periodic potential which is subjectd to a weak and slowly-varying electromagnetic field. In addition to the semiclassical parameter $\\eps \\ll 1$ which quantifies the separation of spatial scales, we explore the influence of additional parameters that allow us to selectively switch off the magnetic field. We find that even in the case of magnetic fields with components in $C_b^{\\infty}(\\R^d)$, e. g. for constant magnetic fields, the results of Panati, Spohn and Teufel hold, i.e. to each isolated family of Bloch bands, there exists an associated almost invariant subspace of $L^2(\\R^d)$ and an effective hamiltonian which generates the dynamics ...

International Nuclear Information System (INIS)

The isostructural uranium monopnictides and monochalcogenides have become prototype systems in actinide research with respect to their unusual magnetic properties. We have investigated the origins in the electronic structure of the variation in magnetic behavior as the degree of 5f-electron localization changes from localized to itinerant on going up the pnictogen or chalcogen column, thus decreasing the U-U separation. We have applied a synthesis of: (1) A phenomenological theory of orbitally driven magnetic ordering which includes both the hybridization-induced and the RKKY exchange interactions on an equal footing, and (2) Ab initio electronic structure calculations, based on the linear-muffin-tin-orbital method, allowing a first-principles evaluation of the parameters entering the model Hamiltonian. We have investigated systematically characteristic trends and changes of the 5f-state resonance width, the hybridization potential, and the hybridization-induced ...

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Singlet oxygen generators are multiphase flow chemical reactors used to generate energetic oxygen to be used as a fuel for chemical oxygen iodine lasers. In this paper, a theoretical model of the generator is presented along with its solutions over ranges of parameter space and oxygen maximizing optimizations. The singlet oxygen generator (SOG) is a low-pressure, multiphase flow chemical reactor that is used to produce molecular oxygen in an electronically excited state, i.e. singlet delta oxygen. The primary product of the reactor, the energetic oxygen, is used in a stage immediately succeeding the SOG to dissociate and energize iodine. The gas mixture including the iodine is accelerated to a supersonic speed and lased. Thus the SOG is the fuel generator for the chemical oxygen iodine laser (COIL). The COIL has important application for both military purposes--it was developed by the US Air Force in the 1970s--and, as the infrared beam is readily absorbed by metals, industrial cutting ...

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A wavelet transformation is performed over each of the spatial coordinates of the scalar wave equation. This transformed equation is solved directly with a finite-difference scheme for both homogeneous and smooth inhomogeneous media. Wavefield extrapolation is performed completely in the spatial wavelet domain without transforming back into the space domain at each time step. The wavelet coefficients are extrapolated, rather than the wavefield itself. The numerical solution of the scalar wave equation in the spatial wavelet domain is closely related to the finite-difference method because of the compact support of the wavelet bases. Poststack reverse-time migration is implemented as an application. The resolution spaces of the wavelet transform provide a natural framework for multigrid analysis. Migrated images are constructed from various resolution spaces.

International Nuclear Information System (INIS)

Heat capacities and densities of aqueous MgCl/sub 2/, CaCl/sub 2/, and SrCl/sub 2/ from the accompanying paper are combined with literature data up to 473 K to yield temperature-dependent equations by using the ion-interaction model of Pitzer. These heat capacity equations have been integrated to yield the enthalpy and the Gibbs energy. The enthalpy parameters for 298 K are evaluated in separate calculations using published high-temperature osmotic data as well as heats of dilution, while the Gibbs energy parameters for 298 K are taken from the literature. The range of validity of the final equations is described.

International Nuclear Information System (INIS)

A new formulation of the theory of tachyons using the same two postulates as in special relativity is applied to the electrodynamics of material media. A discussion of Lagrange's equations and Hamilton's equations for 'classical' charged tachyons shows that such a formalism is a viable approach. An essay is included on why tachyons can be considered to be localised particles for the purpose of calculations. Tachyonic transformations of the electromagnetic fields D, P, H and M are shown to be the same as for bradyonic transformations. Examples discussed include the electric dipole moment of a tachyonic current loop, constitutive equations, polarisation in tachyonic dielectric materials and the velocity of light in tachyonic dielectric media. This is followed by discussions of the collision energy loss for charged tachyons interacting with a material medium and a mathematical proof that tachyons cannot emit Cherenkov ...

British Library Electronic Table of Contents (United Kingdom)

Abstract The available surface equation of state for pure pulmonary surfactant monolayers is generalised to binary mixture monolayers by introducing a group of parameters, i(i-=-1-4) in the form of $x_{r}^{\\beta _{i} } $ to express the influence of the components in new mixing rules and a new factor, I $\\left[ { = \\left( {\\prod\\limits_{i = 1}^{4} {\\beta _{i} } } \\right)^{{\\raise0.5ex\\hbox{$\\scriptstyle 1$}\\kern-0.1em/\\kern-0.15em\\lower0.25ex\\hbox{$\\scriptstyle {4}$}}} } \\right]$, is defined to represent the interaction intensity between two different components. The ---A isotherms getting by the surface equations of state agree with the experimental data for protein-lipid binary monolayers, and the average deviation is about 11.41%. The result shows the order of the interaction intensity b...

CERN Document Server

We study perturbations of a Schwarzschild black hole in Chern-Simons modified gravity. We begin by showing that Birkhoff's theorem holds for a wide family of Chern-Simons coupling functions, a scalar field present in the theory that controls the strength of the Chern-Simons correction to the Einstein-Hilbert action. After decomposing the perturbations in spherical harmonics, we study the linearized modified field equations and find that axial and polar modes are coupled, in contrast to general relativity. The divergence of the modified equations leads to the Pontryagin constraint, which forces the vanishing of the Cunningham-Price-Moncrief master function associated with axial modes. We analyze the structure of these equations and find that the appearance of the Pontryagin constraint yields an overconstrained system that does not allow for generic black hole oscillations. We illustrate this situation by studying the case ...

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Equilibrium and energy equations have been developed in describing the solid-fluid transition zone during the melting and solidification of the binary alloys. Due to the existence of the transition region exhibited both solid and fluid phases at the same material point from continuum point of view, mixture theory was utilized to analyze the region. Unlike the Stefan problem, the latent heat due to the phase change appears as a source term in the heat equation. The molten fluid is treated as a thermoviscous and incompressible fluid, whereas the solid is thermoviscoplastic described by the Bodner-Partom/Walker type of constitutive equations. Thermal mechanical behaviors of the solid and the fluid phases are determined separately because of insignificant mechanical interactions between them. Volume fractions of the phases are obtained according to the equilibrium phase diagram. The simulation process of the transition zone and ...

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This paper presents research work concerning the mathematical modelling of air pollution in the Athens basin. A mathematical model based on aerodynamics and conservation equations together with turbulence modelling in body-fitted coordinates is used to provide the necessary input information to a similar but more detailed (i.e. small scale) model around Athens. Both models consist of solving the full Navier-Stokes equations and take into account the precise topography of the region. Different roughness heights are used for sea, coastal regions and land. The smaller scale model makes use of a two-equation turbulence model ({kappa}-{epsilon}) and the large scale model assumes a constant turbulence viscosity. The pollutant sources used in these models are based on actual emissions in the Athens area and are distributed in space. The results of this work appear promising and demonstrate the capability of the model as a tool for ...

International Nuclear Information System (INIS)

Within the framework of the Bianchi type-IX homogeneous space, we set up a system of coupled equations for the cosmic scale factors, scalar field, and radiative energy density. At the tree level, the equations are written in a self-consistent, Hartree-Fock form. For phi"4 theory, the system of nine first-order differential equations is solved numerically for a varying ratio of the energy of anisotropy to the vacuum energy. As the vacuum energy increases, there appears to be less reheating, since the energy of anisotropy is more efficiently converted into isotropic expansion. If the energy of anisotropy is large enough, the inflationary phase is prevented. In this case, a series of cosmological phase transitions will take place each time the square of the effective mass changes its sign.

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The code is being developed starting from the steady-state finite element code FENDER for the solution of the diffusion equation by extending it to become time-dependent. The numerical solution of the time-dependent multigroup diffusion equations within TRANSFUSION is performed at the present stage of development by using a backward difference scheme for the time variable, leading to a rearrangement of FENDER by adding a new loop over time steps. The code retains the multigroup coupled neutron-gamma features of FENDER, and provides a consistent two-, and quasi three-dimensional numerical solution of both static and time-dependent multigroup diffusion equations. (orig./DG)

International Nuclear Information System (INIS)

We study the thermodynamics of a one-dimensional attractive Fermi gas (the Gaudin-Yang model) with spin imbalance. The exact solution has been known from the thermodynamic Bethe ansatz for decades, but it involves an infinite number of coupled nonlinear integral equations whose physics is difficult to extract. Here the solution is analytically reduced to a simple, powerful set of four algebraic equations. The simplified equations become universal and exact in the experimental regime of strong interaction and relatively low temperature. Using the new formulation, we discuss the qualitative features of finite-temperature crossover and make quantitative predictions on the density profiles in traps. We propose a practical two-stage scheme to achieve accurate thermometry for a trapped spin-imbalanced Fermi gas.

British Library Electronic Table of Contents (United Kingdom)

In this paper, the unsteady MHD free convection heat and mass transfer of viscous fluid flowing through a Darcian porous regime adjacent to a moving vertical semi-infinite plate under Soret and Dufour effect have been examined. Viscous dissipation effects are included in the energy equation. A uniform magnetic field is applied transversely to the direction of the flow. The differential equations governing the problem have been transformed by a similarity transformation into a system of non-dimensional differential equations which are solved numerically by element free Galerkin method. The influence of Grashof number (Gr), magnetic parameter (M), heat absorption parameter (Q), permeability parameter (K), Schmidt number (Sc), Soret number (Sr), and Dufour number (Du) on the velocity, tempera...

International Nuclear Information System (INIS)

A nodal integral method is derived for the monoenergetic, steady-state, fixed source neutron diffusion equation in hexagonal geometry based on a coordinate transformation that maps a parallelogram into a rectangle. The new hexagonal nodal diffusion method is implemented in the computer code HND where the discrete-variable equations are solved via an iterative scheme. Because the new method's equations are derived for a rhombus, they can be solved on a sequence of embedded meshes to study the method's error order. Indeed a preliminary numerical error analysis reveals a second-order error in the mesh size, and comparison with finite difference results obtained with the finite difference based BOLD-VENTURE code indicate the superior accuracy of our new nodal method.

CERN Document Server

This contribution deals with identification of fractional-order dynamical systems. System identification, which refers to estimation of process parameters, is a necessity in control theory. Real processes are usually of fractional order as opposed to the ideal integral order models. A simple and elegant scheme of estimating the parameters for such a fractional order process is proposed. This method employs fractional calculus theory to find equations relating the parameters that are to be estimated, and then estimates the process parameters after solving the simultaneous equations. The said simultaneous equations are generated and updated using particle swarm optimization (PSO) technique, the fitness function being the sum of squared deviations from the actual set of observations. The data used for the calculations are intentionally corrupted to simulate real-life conditions. Results show that the proposed scheme offers a ...

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A non-linear analysis of a Cerenkov maser is presented. The system consists of a ring configuration of a cylindrical waveguide filled with a dielectric material. A single transverse-magnetic mode is assumed to propagate in the system. A low-density pencil electron beam travels in part of the ring, confined by a strong axial magnetic field. Using the single-particle description for the beam and the wave equation for the field, we obtain a set of two coupled non-linear differential equations describing the slowly varying amplitude and phase of the electromagnetic mode. The gain per path is assumed to be small and the spatial growth of the field is neglected. The resulting time dependent amplitude includes the exponential gain of the linear stage and the saturation to its maximum value. The time dependent frequency is also calculated. The two equations are combined to a single Van Der Pol equation with a ...

International Nuclear Information System (INIS)

Determination of the specific surface of uranium oxides: UO_2 and U_3O_8 using a simplified equation derived from the Brunauer, Emmett and Teller theory. The method is suitable for samples having a surface between 6 to 50 m"2.

CERN Document Server

We solve the loop equations of the $\\beta$-ensemble model analogously to the solution found for the Hermitian matrices $\\beta=1$. For \\beta=1$, the solution was expressed using the algebraic spectral curve of equation $y^2=U(x)$. For arbitrary $\\beta$, the spectral curve converts into a Schr\\"odinger equation $((\\hbar\\partial)^2-U(x))\\psi(x)=0$ with $\\hbar\\propto (\\sqrt\\beta-1/\\sqrt\\beta)/N$. This paper is similar to the sister paper~I, in particular, all the main ingredients specific for the algebraic solution of the problem remain the same, but here we present the second approach to finding a solution of loop equations using sectorwise definition of resolvents. Being technically more involved, it allows defining consistently the B-cycle structure of the obtained quantum algebraic curve (a D-module of the form $y^2-U(x)$, where $[y,x]=\\hbar$) and to construct explicitly the correlation ...

International Nuclear Information System (INIS)

An exact cosmological solution of Einstein's equations which has time-dependent rotation is presented. The t-constant sections are of Bianchi type II. The source of this geometry is a fluid which has not been thermalized. (Author).

CERN Document Server

We show that, in addition to radiation travelling at the speed of light, QED theory predicts a second type of radiation with an infinite velocity. We also show that charge, as it appears in the Dirac equation, may have a triune nature.

Science.gov (United States)

In order to reduce the air concentration of (sup 3)H in the reactor buiIding of Wolsung Heavy Water Reactor, a computer code for estimation of adsorption behavior was programmed based on an equation derived for analysis of water vapor adsorption, and a ba...

Science.gov (United States)

A certain model of one-dimensional detonation waves leads to a Stefan problem: the unknown f satisfies Burgers equations on the two sides of a moving discontinuity at which it is given (f, say) and the jump in it derivative (corresponding to the exothermi...

International Nuclear Information System (INIS)

The numerical calculation of oscillatory wavefunctions occurring in the theory of electron scattering from positive ions is considered, the aim being to develop methods for evaluating the oscillatory solutions using a logarithmic grid. Thus, the permitted step-size for the solution depends only upon the potential, enabling calculations at different energies to be performed using the same discretisation. Two similar generalisations of the W.K.B. transformation for second order ordinary differential equations are made and applied to the radial Dirac equations. Iterative schemes for the solution of the resulting non-linear amplitude equations are discussed, one for use in the asymptotic region and the other a Newton scheme for continuing the solution closer to the origin. Using these techniques a reliable and efficient program for calculating relativistic scattering phase shifts from ionic potentials has been written. ...

UK PubMed Central (United Kingdom)

Background. Detection of subjects with early chronic kidney disease (CKD) is important because some will progress up to stage 5 CKD, and most are at high risk of cardiovascular morbidity...Full Text Available

British Library Electronic Table of Contents (United Kingdom)

We study a rapidly convergent modification of a two-sided method for the approximate integration of a boundary-value problem with parameters in boundary conditions for a system of quasilinear second-order differential equations.

International Nuclear Information System (INIS)

The B test series from the course of ISP Nr. 43 was analysed. The boundary conditions measured include the initial temperature of the primary system, the front/slug injection flowrate and temperature, and the pressure drop across the core. Temperature data were collected at 185 thermocouple positions in the downcomer and 38 positions in the lower plenum. The frequency of data acquisition for code predictions was set to 2 Hz, which corresponds to the acquisition frequency of the two experimental setups. Calculations were performed using the FLUENT Computational Fluid Dynamics (CFD) code. This program is based on the finite volume method, The computational mesh was generated by the pre-processor - GAMBIT program. FLUENT uses a control-volume-based technique to convert the governing equations to algebraic equations, which can be solved numerically. This control volume technique consists of integrating the governing equations ...

CERN Document Server

The methods of statistical dynamics are applied to a fluid with 5 conserved fields (the mass, the energy, and the three components of momentum) moving in a given external potential. When the potential is zero, we recover a previously derived system of parabolic differential equations, called "corrections to fluid dynamics".

CERN Document Server

We show the existence of global-in-time weak solutions to a general class of coupled FENE-type bead-spring chain models that arise from the kinetic theory of dilute solutions of polymeric liquids with noninteracting polymer chains. The class of models involves the unsteady incompressible Navier-Stokes equations in a bounded domain in two or three space dimensions for the velocity and the pressure of the fluid, with an elastic extra-stress tensor appearing on the right-hand side in the momentum equation. The extra-stress tensor stems from the random movement of the polymer chains and is defined by the Kramers expression through the associated probability density function that satisfies a Fokker-Planck-type parabolic equation, a crucial feature of which is the presence of a center-of-mass diffusion term. We require no structural assumptions on the drag term in the Fokker-Planck equation; in particular, ...

UK PubMed Central (United Kingdom)

We introduce in this paper a new method for reducing neurodynamical data to an effective diffusion equation, either experimentally or using simulations of biophysically detailed models. The dimensionality...Full Text Available

Energy Technology Data Exchange (ETDEWEB)

It is urged that the lesson of gauge invariance in quantum electrodynamics implies the irrelevance of `Schwinger term` difficulties in current algebra. The divergence equations of Veltman form the basis of a gauge-variation formalism in which these questions are avoided. (author). 9 refs.

Energy Technology Data Exchange (ETDEWEB)

A new energy concept known as centrifugal potential energy was discussed. This new energy concept is capable of increasing the pressure, temperature and enthalpy of a fluid, without having to apply work or heat transfer to the fluid. It occurs through a change in the centrifugal potential energy of the flowing fluid in a rotating frame of reference or a centrifugal force field, where work is performed internally by the centrifugal weight of the fluid. This energy concept has resulted in new energy equations, such as the Rotational Frame Bernoulli's Equation for liquids and the Rotational Frame Steady-Flow Energy Equation for gases. Applications of these equations have been incorporated into the design of centrifugal field pumps and compressors. Rather than compressing a fluid with a physical load transfer, these devices can compress a fluid via the effect of centrifugal force applied to the ...

Science.gov (United States)

This paper describes the development of an interactive internet-based cost-estimating tool for commonly used urban storm runoff best management practices (BMP), including: retention and detention ponds, grassed swales, and constructed wetlands. The paper presents the cost data, c...

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A numerical model of multiphase air-water flow and contaminant transport in the unsaturated zone is presented. The multiphase flow equations are solved using the two-pressure, mixed form of the equations with a modified Picard linearization of the equations and a finite element spatial approximation. A volatile contaminant is assumed to be transported in either phase, or in both phases simultaneously. The contaminant partitions between phases with an equilibrium distribution given by Henry`s Law or via kinetic mass transfer. The transport equations are solved using a Galerkin finite element method with reduced integration to lump the resultant matrices. The numerical model is applied to published experimental studies to examine the behavior of the air phase and associated contaminant movement under water infiltration. The model is also used to evaluate a hypothetical design for a low-level radioactive ...

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A stable, accurate, and efficient implementation of MacCormack's explicit algorithm for the Parabolized Navier-Stokes equations is demonstrated. The familiar problem of decoding the conservative axial flux vector is solved, resulting in accurate, smooth dependent variable profiles through the viscous-layer sonic line. Source terms due to transformation of the parabolized governing equations into the computational plane and the equations into the computational plane and the resulting metric differencing have been identified and eliminated through inclusion of appropriate geometric conservation law terms. Test cases computed include two- and three-dimensional supersonic and hypersonic flow at laminar and turbulent Reynolds numbers. The computed results demonstrate very good agreement with experiment and with solutions of the full Navier-Stokes equations. Computational times required for the ...

Science.gov (United States)

Wood, R. A.; and Ogden, H. R.: The All-Beta Titanium Alloy (Ti-13V-llCr-3Al). DMIC Rept. 110 (ASTIA AD 214002), Battelle Mem. Inst., Apr. 17, 1959. 22. White ...

Science.gov (United States)

An exact solution method for the free vibration problem of thin circular cylindrical shells is presented. The differential equations of motion are solved directly with the use of simple Fourier series as the modal displacement functions. Stokes' transformation is exploited to obtain correct series expressions for the derivatives of the Fourier series. From this method an explicit expression of the exact frequency equation can be obtained for any kind of boundary conditions. The accuracy of the present method is checked against available data. The proposed method is then used to find the modal characteristics of the thermal liner of the Fast Test Reactor (FTR). The numerical results obtained are compared with finite element method solutions. (auth)

International Nuclear Information System (INIS)

In terms of Berezins's theory of symbols of operators, the integral formulation is suggested for the free differential algebra which gives rise to consistent equations of motion of interacting massless fields of all spins 0#<=#s<#infinity# in the frameworks of gravity. In the first nontrivial order of the expansion in powers of curvatures, Frobenius consistency conditions for higher-spin equations of motion are shown to reduce to the simple geometrical fast that there are two ways for splitting any quadrangle in two triangles. To clarify our construction, we illustrate how it works in the simplest case of pure gravity. (orig.).

International Nuclear Information System (INIS)

Muonic-atom energy levels and wave functions are calculated. The results are corrected for nearly all important static effects, including finite nuclear size as produced by a user-specified nuclear charge distribution. Fourth-order Runge-Kutta integration of the radial Dirac equations, with the secant method determining the eigenvalues. Corrections are either included as potentials in the Dirac equations or computed as first-order perturbations. The code assumes spherical symmetry, so that effects of nuclear deformation may be treated only as static first-order perturbations. Dynamic muon-electron and muon-nuclear effects are neglected (the latter are calculated by RURP). (Auth.).

CERN Document Server

We present a dynamical spectral model for Large Eddy Simulation of the incompressible magnetohydrodynamic (MHD) equations based on the Eddy Damped Quasi Normal Markovian approximation. This model extends classical spectral Large Eddy Simulations for the Navier-Stokes equations to incorporate general (non Kolmogorovian) spectra as well as eddy noise. We derive the model for MHD and show that introducing a new eddy-damping time for the dynamics of spectral tensors in the absence of equipartition between the velocity and magnetic fields leads to better agreement with direct numerical simulations, an important point for dynamo computations.

Science.gov (United States)

A general model for the dissolution of particles in multi-component alloys is proposed and analyzed. The model is based on diffusion equations with cross-terms for the several species, combined with a Stefan condition as the equation of motion of the interface between the particle and diffusive phase. Several numerical schemes for the solution of the Stefan problem are proposed and compared. It turns out that diagonalization is useful for numerical purposes. However, for the case of position-dependent diffusion coefficients one has to use a different scheme. Here, we analyze stability and workload of several time integration methods.

British Library Electronic Table of Contents (United Kingdom)

Asymptotic and numerical analysis of relaxation self-oscillations in a three-dimensional system of Volterra ordinary differential equations that models the well-known Belousov reaction is carried out. A numerical study of the corresponding distributed model-the parabolic system obtained from the original system of ordinary differential equations with the diffusive terms taken into account subject to the zero Neumann boundary conditions at the endpoints of a finite interval is attempted. It is shown that, when the diffusion coefficients are proportionally decreased while the other parameters remain intact, the distributed model exhibits the diffusion chaos phenomenon; that is, chaotic attractors of arbitrarily high dimension emerge.

Energy Technology Data Exchange (ETDEWEB)

A simplified approach has been proposed to model the drying of capillary-porous materials with small geometric parameters for practical purposes. Luikov`s theory of mass and heat transfer for capillary-porous bodies was applied to drying of biological materials and it was shown that the thermo diffusion effect can be neglected if the thermal gradient remains small during the whole period of drying. The resulting simplified equations can then be solved using available mathematical software. The simplified equations were applied to drying of wood and a peanut pod

CERN Document Server

We investigate stability properties of indirectly damped systems of evolution equations in Hilbert spaces, under new compatibility assumptions. We prove polynomial decay for the energy of solutions and optimize our results by interpolation techniques, obtaining a full range of power-like decay rates. In particular, we give explicit estimates with respect to the initial data. We discuss several applications to hyperbolic systems with {\\em hybrid} boundary conditions, including the coupling of two wave equations subject to Dirichlet and Robin type boundary conditions, respectively.

International Nuclear Information System (INIS)

The entrainment flow rate distribution, the gas velocity profile, and the concentration profile of droplets across the channel cross section in fully developed region of a horizontal rectangular channel of 150 mm width and 50 mm height were measured. The concentration profile of droplets was expressed by a simple equation based on a constant diffusion coefficient model. From this equation the effects of gravity and turbulent diffusion of droplets on the concentration profile were evaluated. The characteristic mean settling velocity of a group of droplets with various diameters was derived, and using this value the mean diffusion coefficient of the group of droplets was obtained. (author).

DEFF Research Database (Denmark)

A simple closed-form equation to calculate the envelope correlation between any two receiver or transmitter antennas in a multi-input multi-output (MIMO) system of an arbitrary number of elements is derived. The equation uses the scattering parameters obtained at the antenna feed point to calculate the envelope correlation coefficient. This approach has the advantage that it does not require knowledge of the antenna radiation pattern. Numerical data that include conductor and permittivity loss are shown to validate the approach. Using the scattering parameters for calculating the envelope correlation is less laborious and relatively cheaper, as compared to the radiation pattern approach.

British Library Electronic Table of Contents (United Kingdom)

The present contribution deals with the thermophoresis particle deposition and thermal radiation effects on the flow, heat and mass transfer characteristics in a viscous fluid over a semi-infinite vertical porous plate. The governing boundary layer equations are written into a dimensionless form by similarity transformations. The transformed coupled nonlinear ordinary differential equations are solved numerically by means of the fourth-order Runge?Kutta method with a shooting technique. The effects of different parameters on the dimensionless velocity, temperature, and concentration profiles are shown graphically. In addition, results for the local skin-friction coefficient, the local Nusselt number, and the local Sherwood number are tabulated and discussed.

CERN Document Server

We find a large family of solutions to the Dirac equation on a manifold of $G_2$ holonomy asymptotic to a cone over $S^3 \\times S^3$, including all radial solutions. The behaviour of these solutions is studied as the manifold developes a conical singularity. None of the solutions found are both localised and square integrable at the origin. This result suggests that M-theory on the conifold over $S^3\\times S^3$ does not produce a chiral theory. The approach here is complementary to previous analyses using dualities and anomaly cancellation which found chiral fermions on all known $G_2$ conifolds except that over $S^3\\times S^3$.

International Nuclear Information System (INIS)

Burnout data with low pressure Freon-113 for even- and odd- numbered peripheral rod clusters with relatively large spacings were used to derive equations in terms of dimensionless parameters suggested by Barnett. The equations which are for three different flow regimes for each rod geometry (even or odd) were found to predict burnout data with maximum RMS deviation being 3.8%. (author). 11 figs., 3 tabs., 15 refs.

Energy Technology Data Exchange (ETDEWEB)

Diffusion of radon in a bed of activated charcoal is described by diffusion equations. An analytical solution of these equations is presented for the case of constant radon concentration in the atmosphere. The solutions are given separately for short term and long term exposure. An analytical form of the calibration constant f for long term exposure and constant radon concentration in air, was found. A numerical method and computer code based on the method of finite elements is developed for the case of variable radon concentration in air. This program simulates radon adsorption by the activated charcoal bed, enabling determination of sensitivity. The dependence of sensitivity on different parameters, such as temperature, thickness of the charcoal, etc. was studied using this program. (orig.) 10 refs.

CERN Document Server

We propose a numerical method for resummation of perturbative series, which is based on the stochastic perturbative solution of Schwinger-Dyson equations. The method stochastically estimates the coefficients of perturbative series, and incorporates Borel resummation in a natural way. Similarly to the "worm" algorithm, the method samples open Feynman diagrams, but with an arbitrary number of external legs. As a test of our numerical algorithm, we study the scale dependence of the renormalized coupling constant in a theory of one-component scalar field with quartic interaction. We confirm the triviality of this theory in four and five space-time dimensions, and the instability of the trivial fixed point in three dimensions.

International Nuclear Information System (INIS)

British Nuclear Fuels plc owns and operates the near-surface Drigg disposal facility for low level radioactive waste. The long-term performance of the site is modelled by a suite of computer codes called MONDRIAN. One of the modules of MONDRIAN deals with the transport of radionuclides through the environment, and this paper reports on the current status of this module (BIOS). We derive the basic set of working equations from first principles and show clearly how the approximate nature of the final equations is arrived at. This is done by an averaging process leading to compartments, in and out of which radionuclides, solids and water can flow. The equations allow radioactive decay chains and an arbitrary number of compartments. There is also the facility to deal with changes in the rate coefficients, thereby simulating different environmental states. It is also possible to include the creation of new compartments arising ...

Energy Technology Data Exchange (ETDEWEB)

The high energy limit of Quantum Chromodynamics is one of the most fascinating areas in the theory of strong interactions. Over a decade ago the HERA experiment at DESY in Hamburg provided strong evidence for the rise of the proton structure function at small values of the Bjorken variable x. This behavior can be explained as an increase of the gluon density of the proton with energy or correspondingly with smaller values of x. This increase can be attributed on the other hand to the large probability of gluon splitting in QCD. The natural framework for describing the gluon dynamics at small x is the Balitskii-Fadin-Kuraev-Lipatov formalism developed some 30 years ago. It predicts that the gluon density grows very fast with increasing energy, as a power with a large intercept. This increase has to be tamed in order to satisfy the unitarily bound. Over two decades ago, Gribov, Levin and Ryskin proposed the mechanism called the parton saturation, which slows down the fast rise of the ...

Energy Technology Data Exchange (ETDEWEB)

For an electron storage ring the beam size evaluation including beam-beam interaction gives an example of such a problem. Another good example is finding the beam size for a nonlinear machine. The present work gives a way to solve some of these problems, at least in principle. The approach described here is an application of the well known Green's function method, which in this case is applied to the Fokker-Planck equation governing the distribution function in the phase space of particle motion. The new step made in this paper is to consider the particle motion in two degrees of freedom rather than in one dimension, a characteristic of all the previous work. This step seems to be necessary for an adequate description of the problem, at least for the class of problems which are considered below. This work consists of the formal solution of the Fokker-Planck equation in terms of its Green's function and describing the ...

International Nuclear Information System (INIS)

Full text: In case of lanthanide (Ln) compounds the bis(trimethylsilyl)amido (btmsa) ligand is considered as a steric and electronic equivalent of the bis(trimethylsilyl)methanido (btmsm) group . Because of their extreme air and moisture sensitivity the chemistry of Ln(btmsm)_3 is very poor, whereas that of comparatively stable Ln(btmsa)_3 is much more developed. As we wish to extend the chemistry of Ln(btmsm)_3 and plan to derive and to parameterize the crystal field (CF) splitting patterns of the target molecules, it is recommended to study in advance the electronic structures of the corresponding compounds derived from Ln(btmsa)_3 . Beside (btmsa)_3 Nd(m-Cl)Li(THF)_3 a number of mono base adducts [(btmsa)_3 Ln.B] with sterically less demanding bases such as OPPh_3 , NCtBu or CNtBu have been described and were partly structurally characterized. Considering only the immediately coordinating atoms, the effective CF is of C_3_v symmetry. According to recent spectroscopic investigations, ...

Energy Technology Data Exchange (ETDEWEB)

The detailed features of the calculated energy-level schemes and of thesingle-particle, orbit-occupancy properties of the low-lying levels of the/ital N/=50 isotones /sup 80/Zn, /sup 81/Ga,/sup 82/Ge, /sup 83/As, /sup 84/Se,/sup 85/Br, /sup 86/Kr, and /sup 87/Rb arepresented and discussed. These results are obtained with a new effectiveHamiltonian operator obtained empirically from an iterative fit to experimentalenergies taken from all experimentally studied (/ital A/=82--96)/ital N/=50 nuclei. The model space for the calculations consists ofactive 0/ital f//sub 5/2/, 1/ital p//sub 3/2/,1/ital p//sub 1/2/, and 0/ital g//sub 9/2/ proton orbits relativeto a nominal /sup 78/Ni core. This space is truncated internally byrestricting the number of particles excited from the negative-parity orbitsinto the /ital g//sub 9/2/ orbit to be no greater than four. The typicalstructures predicted for these lighter /ital N/=50 isotones are found tobe dominated by well-mixed ...

Energy Technology Data Exchange (ETDEWEB)

An analysis of the energy level structure of Cr{sup 3+} ions in Cs{sub 2}NaAlF{sub 6} crystal is performed using the exchange charge model (ECM) together with the crystal field analysis/microscopic spin Hamiltonian (CFA/MSH) computer package. Utilizing the crystal structure data, our approach enables modelling of the crystal field parameters (CFPs) and thus the energy level structure for Cr{sup 3+} ions at the two crystallographically inequivalent sites in Cs{sub 2}NaAlF{sub 6}. Using the ECM initial adjustment procedure, the CFPs are calculated in the crystallographic axis system centred at the Cr{sup 3+} ion at each site. Additionally the CFPs are also calculated using the superposition model (SPM). The ECM and SPM predicted CFP values match very well. Consideration of the symmetry aspects for the so-obtained CFP datasets reveals that the latter axis system matches the symmetry-adapted axis system related directly to the six Cr-F bonds well. Using the ECM ...

Energy Technology Data Exchange (ETDEWEB)

An interfacial shear stress equation in the dispersed-annular two-phase flow regime has been developed, which is based on a three-fluid model consisting of a liquid film on a rod, vapor and entrained liquid associated with a vapor flow. It is an extension of J.G.M. Andersen's procedure that provides a two-fluid interfacial shear stress equation using the drift flux parameters C{sub 0} and V{sub gj}. This interfacial shear stress equation can take into account a phase and velocity distribution through an equivalence between the drift flux parameters and the interfacial shear stress. Using the three-fluid subchannel analysis code TEMPO with the three-fluid interfacial shear stress model the capability of a three-fluid calculation using the drift flux parameters C{sub 0} and V{sub gj} that reproduce a measured void fraction is demonstrated. A comparison was made with advanced X-ray computed tomography (CT) void ...

CERN Document Server

In this paper, we prove a uniqueness result in the inverse problem of determining several non-constant coefficients of one-dimensional reaction-diffusion equations. Such reaction-diffusion equations include the classical model of Kolmogorov, Petrovsky and Piskunov as well as more sophisticated models from biology. When the reaction term contains an unknown polynomial part of degree $N,$ with non-constant coefficients $\\mu_k(x),$ our result gives a sufficient condition for the uniqueness of the determination of this polynomial part. This sufficient condition only involves pointwise measurements of the solution $u$ of the reaction-diffusion equation and of its spatial derivative $\\partial u / \\partial x$ at a single point $x_0,$ during a time interval $(0,\\epsilon).$ In addition to this uniqueness result, we give several counter-examples to uniqueness, which emphasize the optimality of our assumptions. Finally, in the ...