Full Set Of Equations Research Articles

A Method for Determining Most Probable Errors in Nonlinear Lightwave Systems

We present a method for computing bit-error ratios in soliton-based lightwave systems. The method uses soliton perturbation theory and calculus of variations to find approximate versions of the most probable paths through sample space leading to errors, combined with importance-sampled Monte Carlo simulations of the full set of equations around these approximate paths to compute the actual error rates. As a specific example, the method is applied to a differential phase-shift-keyed lightwave system. For this example the method not only computes the bit-error ratio but also predicts the set of failure modes leading to large pulse distortions, thus illuminating the specific manner in which errors occur.

Solving a coupled field problem by eigenmode expansion and finite element method

The propagation of sound in fluids is governed by a set of coupled partial differential equations supplemented by an appropriate equation of state. In many cases of practical importance one restricts attention to the case of ideal fluids with vanishing transport coefficients. Then, the differential equations decouple and sound propagation can be described by the wave equation. However, when loss mechanisms are important, this is in general not possible and the full set of equations has to be considered. For photoacoustic cells, an alternative procedure has been used for the calculation of the photoacoustic signal of cylinder shaped cells. The method is based on an expansion of the sound pressure in terms of eigenmodes and the incorporation of loss through quality factors of various physical origins. In this paper, we demonstrate that the method can successfully be applied to photoacoustic cells of unconventional geometry using finite element analysis.

Structure and evolution of the solar coronal magnetic field

We review some of the results that we have obtained in the last decade on two problems related to the structure and evolution of the solar corona: How to reconstruct the magnetic field of an active region from its values measured at the photospheric level, and how to determine the evolution of the coronal field driven by the stressing of its footpoints on the photosphere and/or by flux emergence through that surface, our main goal being to elucidate the nature of the mechanisms triggering large scale eruptive processes like coronal mass ejections (CMEs). The first part of the paper is devoted to a first approach in which the coronal field is assumed to be force-free at any time (but during the late development of an eruptive event), its evolution being thus considered to be quasi-static. After presenting some general properties of this type of fields, we use this approximate model as a general framework for the reconstruction problem. To get a well posed problem, we introduce the Grad--Rubin formulation in which only a part of the photospheric data are taken into account. We present some mathematical results on this problem (existence and uniqueness of solutions), and report our method to treat it numerically in an efficient way. Thus we turn to the quasi-static boundary driven evolution problem. We find that a continuous injection of energy into a simple field (arcade or tube) by footpoints shearing leads in the ideal case to an expansion of the field which is at least as fast as at large time t, and to its eventual partial or total opening with the formation of a current sheet. The second part of the paper is concerned with a dynamic approach to the evolution problem. The full set of equations of the resistive magnetohydrodynamics is used and solved numerically in two different classes of models. In the first one, the evolution is driven by changing boundary conditions (describing shear, converging motions, flux cancellation, …) imposed at the photospheric level. In the second one, both the corona and the subphotospheric layer (top of the convection zone) are simultaneously considered, and the rising of a twisted tube below the photosphere and its emergence through that surface and subsequent evolution in the corona are followed. In all cases, a catastrophic behavior is found to follow a slow quasi-static phase. It is characterized by a rapid expansion of the field and a release of energy by reconnection. Moreover, a twisted flux rope is always observed to form during the evolution. Depending on the conditions, it is created either in equilibrium during the slow phase, then appearing as a favorable site for the support of a prominence, or during the global disruption phase. The energy of the configuration stays below that of the corresponding open field except when the driving of the evolution is ensured by flux cancellation on the boundary. In that case – to which we refer as the Flux Cancellation Model (FCM) of CME – the open field energy decreases up to a critical point at which it becomes close to the value of the magnetic energy of the configuration, and nonequilibrium sets in. The characteristics of the evolution in FCM are found to be similar in simple and complex topologies (in contrast, the Break Out Model of CME works only for a complex topology). However, when the topology is complex, there is a lowering of the confining effect of the overlying field, and the twisted rope is ejected at a faster rate.

Reliability of Steel Doweled Wood Connections Designed to ASCE 16-95

First-order reliability analyses were performed for wood connections, using bolts, nails, lag screws, and wood screws, including both wood and steel side plates, designed to ASCE 16-95. The reliability analyses were performed using the European yield model to determine the connection capacity. Using reasonable statistics for the random variables in the yield equations, a reliability index was determined for each of the possible failure modes for both single and double shear connections. Simple bounds were then determined for the reliability index of the series system consisting of multiple failure modes. These reliability analyses show that designs to ASCE 16-95 do not exhibit consistent reliability across the range of possible designs. One way to increase consistency is to use the full set of yield equations rather than the simplified set of design equations now present in ASCE 16-95 for most of the connectors. Other modifications may also be necessary since there are inconsistent reliability levels even for those connectors designed to the full set of equations.

Dx2-y2-STATE OF HIGH TEMPERATURE SUPERCONDUCTORS WITH A SMALL ADMIXTURE OF dxy-STATE

It is well known that most of the high temperature superconductors (at least hole-type) are in d-wave state. But it is still an unsolved problem whether it is a pure d-wave state or one has some kind of mixed state. Among the candidates for an admixture, there are s- and d-wave states. Existing experiments could not resolve this issue. New possibilities for experimental resolution of this problem are opened via recent observation of the collective modes in UBe 13 (heavy fermion superconductor) by microwave impedance technique experiments and in Sr 2 RuO 4 (high temperature superconductor) by ultrasound attenuation experiments. Some theoretical treatments show that the most likely state is a mixture of two d-wave states: dx2-y2 and dxy with a small admixture of former state. To create the theoretical basis for investigation of possible mixed superconducting state in unconventional superconductors by sound attenuation and microwave absorption experiments, I derive for the first time a full set of equations for collective modes spectrum in dx2-y2-state with small admixture of dxy state. These equations allow to calculate the whole collective mode spectrum in mixed dx2-y2+iεdxy state and distinguish this state from pure d-wave states (whose collective mode spectrum has been calculated earlier) by ultrasound attenuation and microwave absorption experiments.

Radiative Transfer in Obliquely Illuminated Accretion Disks

The illumination of an accretion disk around a black hole or neutron star by the central compact object or the disk itself often determines its spectrum, stability, and dynamics. The transport of radiation within the disk is, in general, a multidimensional, nonaxisymmetric problem, which is challenging to solve. Here I present a method of decomposing the radiative transfer equation that describes absorption, emission, and Compton scattering in an obliquely illuminated disk into a set of four one-dimensional transfer equations. I show that the exact calculation of the ionization balance and radiation heating of the accretion disk requires the solution of only one of the one-dimensional equations, which can be solved using existing numerical methods. I present a variant of the Feautrier method for solving the full set of equations, which accounts for the fact that the scattering kernels in the individual transfer equations are not forward-backward symmetric. I then apply this method in calculating the albedo of a cold, geometrically thin accretion disk.

Normal modes of deep atmospheres. II: f–F‐plane geometry

AbstractNumerical results have shown that, for a rotating spherical atmosphere with terrestrial parameters, making the shallow‐atmosphere approximation has only a very small impact on the frequency of linear, unforced normal modes, compared with those obtained from the full, unapproximated equations. In nearly all cases the normal‐mode frequencies are smaller in magnitude when the shallow‐atmosphere approximation is relaxed. Relaxing the approximation was also found to have only a small impact on the structures of normal modes, with the exception of long‐zonal‐wavelength internal acoustic modes. These results are particularly surprising in the tropics where the inclusion of the F = 2Ω cosϕ Coriolis terms (which are dropped in the shallow‐atmosphere approximation) might be expected to dominate the usual f=2Ωsinϕ Coriolis terms. The complexity of the full equations, however, prevents analysis of why this insensitivity to the extra terms arises.In this paper normal modes are examined under the f–F‐plane approximation and compared with those on the more usual f‐plane. The resulting equations are more amenable to analysis than the full equation set, and analytic expressions for the dispersion relation and for the normal‐mode structures are obtained for the particular case of an isothermal reference profile. This simplified geometry allows the effects of the F Coriolis terms to be examined while eliminating the geometrical effects of relaxing the shallow‐atmosphere approximation, giving some insight into the relative importance of the two types of effect as well as the physical mechanisms at work. The F Coriolis terms are found to be responsible for the structural changes to long‐zonal‐wavelength internal acoustic modes, and can also affect extremely shallow and extremely deep gravity modes. However, these terms are found to have only a small effect on normal‐mode frequencies, and geometrical effects, rather than these Coriolis terms, are responsible for the systematic reduction in the magnitude of normal‐mode frequencies in a deep spherical atmosphere.In planar geometry the inclusion of the F terms gives rise to a new kind of normal mode in addition to the usual Rossby, gravity, and acoustic modes. The new modes are inertial in character, have frequency very close to f, and have extremely strong vertical tilt. © Royal Meteorological Society, 2002. N. Wood's and A. Staniforth's contributions are Crown copyright.

Nonlinear ineraction of an annular electron beam with azimuthal surface waves

A nonlinear theory is developed that describes the interaction between an annular electron beam and an electromagnetic surface wave propagating strictly transverse to a constant external axial magnetic field in a cylindrical metal waveguide partially filled with a cold plasma. It is shown theoretically that surface waves with positive azimuthal mode numbers can be efficiently excited by an electron beam moving in the gap between the plasma column and the metal waveguide wall. Numerical simulations prove that, by applying a constant external electric field oriented along the waveguide radius, it is possible to increase the amplitude at which the surface waves saturate during the beam instability. The full set of equations consisting of the waveenvelope equation, the equation for the wave phase, and the equations of motion for the beam electrons is solved numerically in order to construct the phase diagrams of the beam electrons in momentum space and to determine their positions in coordinate space (in the radial variable-azimuthal angle plane).

Dynamic and steady state analysis of a three phase buck rectifier

Current source rectifiers among other alternatives, offer several advantages over line commutated rectifiers. Advantages include displacement power factor control and reduced line current harmonic distortion. This paper analyzes the current source rectifier (CSR) in transient and steady state, the models are developed in a synchronous reference frame. The load behavior is characterized for two load conditions, resistive load or, in general, increasing current for increasing voltage, and constant output power, decreasing output current for increasing voltage. Constant power operation can occur for a converter system supplying a pulse width modulation (PWM) inverter with high dynamics. Several static converter characteristics such as power factor, real and reactive power are analyzed for both types of load. Transient characteristics are analyzed for both types of load by exact small-signal model with full set of equations.

Electromagnetic dipole radiation of oscillating D-branes

I emphasize analogy between Dp-branes in string theories and solitons in gauge theories comparing their common properties and showing differences. In string theory we do not have the full set of equations which define the theory in all orders of coupling constant as it was in gauge theories, nevertheless such solutions have been found as solutions of low energy superstring effective action carrying the RR charges. The existence of dynamical RR charged extended objects in string theory has been deduced also by considering string theory with mixed boundary conditions, when type II closed superstring theory is enriched by open strings with Neumann boundary conditions on p + 1 directions and Dirichlet conditions on the remaining 9-p transverse directions. We will show that for certain excitations of the string/D3-brane system Neumann boundary conditions emerge from the Born-Infeld dynamics. Here the excitations which are coming down the string with a polarization along a direction parallel to the brane are almost completely reflected just as in the case of all-normal Dirichlet excitations considered by Callan and Maldacena, but now the end of the string moves freely on the 3-brane realizing Polchinski's open string Neumann boundary condition dynamically. In the low energy limit ω → 0, i.e. for wavelengths much larger than the string scale only a small fraction ∼ ω 4 of the energy escapes in the form of dipole radiation. The physical interpretation is that a string attached to the 3-brane manifests itself as an electric charge, and waves on the string cause the end point of the string to freely oscillate and produce e.m. dipole radiation in the asymptotic outer region. The magnitude of emitted power is in fact exactly equal to the one given by Thomson formula in electrodynamics.

Self-consistent estimates for the rate-dependentelastoplastic behaviour of polycrystalline materials

This paper aims at proving that, contrary to previous contributions to the subject, Hillsconception of the nonlinear self-consistent scheme, which has been applied in the past toelastoplasticity and to viscoplasticity, can still be adopted with success for elastoviscoplasticity.After a qualitative presentation of the main arguments for this statement, a new Hill-typeapproach is proposed for rate-dependent elastoplastic heterogeneous materials. The associatedlinearization procedure relies on an affine formulation instead of Hills incremental one and onthe use of the correspondence principle to solve the concentration problem; this problem isproved to reduce to a linear viscoelastic one with eigenstrain, i.e. to a linear thermoviscoelasticproblem. The full set of equations is reported for the case of the self-consistent scheme andillustrative applications are given for polycrystals: they are shown to be, as expected, alwayssofter than Kröner-type predictions and to take better into account the viscoelastic coupling andthe associated long range memory effect. In conclusion, the connection and differences betweenthe present approach and other ones already proposed for viscoplastic materials is emphasizedand the limits of Hills conception itself are acknowledged and discussed.

NON-ABELIAN DUAL MAPS IN PATH SPACE

We study an extension of the procedure to construct duality transformations among Abelian gauge theories to the non-Abelian case using a path space formulation. We define a pre-dual functional in path space and introduce a particular nonlocal map among Lie algebra valued one-form functionals which reduces to the ordinary Hodge-⋆ duality map of the Abelian theories. Further, we establish a full set of equations on path space representing the ordinary Yang–Mills equations and Bianchi identities of non-Abelian gauge theories of four-dimensional Euclidean space.

Complex vector model of the squirrel-cage induction machine including instantaneous rotor bar currents

In this paper, a new detailed mathematical derivation of the squirrel-cage induction machine d-q model is introduced. The model is based on coupled magnetic circuit theory and complex space-vector notation and takes into account the actual nonsinusoidal rotor bar distribution. It is shown for the first time that, given the structural symmetry of the induction machine, both stator and rotor circuits can be modeled by the simple set of only four coupled differential equations, i.e., the d-q model. More importantly, the number of equations does not depend on the number of rotor bars, and the model is valid even if the number of bars per pole is not an integer number. This enormous simplification is achieved without loss of generality nor loss of any information contained in the full set of equations, and it is valid for any operating condition. The actual n rotor bars and end-ring currents are fully included in the model, and they are obtained directly by using a simple vector transformation. In addition, the three-phase rotor equivalent parameters are obtained. Second-order effects, such as skin effect in the rotor bars, can be taken into account by simply modifying the bar and end-ring resistance values. An equivalent circuit based on the model is also derived.

Strings in Anisotropic Cosmological Spacetimes

We present a general method to reduce the full set of equations of motion and constraints in the conformal gauge for the bosonic string moving in a four-dimensional curved spacetime manifold with two spacelike Killing vector fields, to a set of six coupled first-order partial differential equations in six unknown functions. By an explicit transformation the constraints are solved identically and one ends up with only the equations of motion and integrability conditions. We apply the method to the family of inhomogeneous, non-singular cosmological models of Senovilla possessing two spacelike Killing vector fields, and show how one can extract classes of special exact solutions, even for this highly complicated metric. For the case of the same family of exact cosmological spacetimes, we give an explicit example, not previously encountered, where we have a direct and mutual transfer of energy between the string and the gravitational field.

Modeling and analysis of static and dynamic characteristics for buck-type three-phase PWM rectifier by circuit DQ transformation

The static and dynamic characteristics of buck-type three-phase pulse width modulation (PWM) rectifier are fully analyzed based on the DC and AC circuit models developed by the circuit DQ transformation. Various static power converter characteristics such as gain, real and reactive power, power factor and unity power factor conditions are completely analyzed. Transition characteristics are also analyzed by both exact small-signal models with full set of equations and simplified output models in explicit form. The usefulness of the models is verified through computer simulations and experiments with good agreement shown.

Simulation of transient pipeline flow by a reversed shock-tube technique

Standard shock-tube technology has been modified to provide a tool for the simulation of aspects of pipeline flow. It was found adaptable to investigation of transient behaviour in accelerating/expanding, uniform/stratified and outflowing/emerging situations. Concurrence between the nature of the flow field in such an experimental facility and the predictions from ideal, centred wave theory was investigated. The conservation equations, the equation of state and expressions for perfect gas properties provided a base for describing the full range of expansion flow properties for which solutions were obtained by the method of characteristics. Procedures and a full set of equations are described. Sensitive real influences were considered and critical conditions identified. Validation by reversed shock-tube experiments with air, conducted within limits set by the critical conditions, are discussed. In expanding and stratified flow from initial pressure across the shock-tube diaphragm in the range 2.0–8.0, representing expansion strengths in the range 0.3–0.7, excellent agreement with theoretical predictions was found for pressure variations and for predicted and recorded wave and particle velocities. Although the latter remained firmly in the subsonic range, it was shown that relatively high Reynolds numbers of 5–10 × 10 6 were achieved. The technique has wider applicability, of which the use for flame propagation studies in expanding flow is indicated.

Time evolution of nonequilibrium quasiparticle and phonon distributions in superconducting films

Superconducting tunneling junctions are promising candidates for low energy X-ray detectors. To fully exploit the possibilities of the high energy resolution it is necessary to understand the microscopic processes and to get a clear insight into the importance of the different loss mechanisms. The linearized coupled kinetic equations for the nonequilibrium quasiparticle f(ω, t) and phonon n(Ω, t) distributions were solved by Chang and Scalapino for the stationary case. The time evolution of the full set of equations was investigated later by Zehnder. In this work we report results of calculations for the time dependence of f(ω, t) and n(Ω, t) which were obtained in a more general approach. In particular, the volume expansion of the initial distribution created by the absorption process was considered by making the distribution functions space dependent and adding a diffusion term to the equations. Results for Nb are discussed in detail.

Protostar formation under two current carrying gas filaments collision

A model of protostar formation under two current carrying gas filaments collision is presented. The model implies MHD approach involving self-gravity and radiative cooling effects. We suppose that through the current carrying gas filament collision a magnetic field reconnection takes place. Using an appropriate self-consistent presentation for time and special dependences of physical quantities in MHD equations, we derive the full set of equations that describes time evolution of the physical quantities just after an occurrence of magnetic field reconnection. Numerical simulations reveal that the process consists of three main phases of evolution. The first is an appearance of preceding peaks in time profiles of density and temperature following by the next phase of depression of both temperature and density and the final fast condensation phase with either cooling or heating of matter depending on initial parameters of problem. Effects of initial conditions like as magnetic field strength, current strength, initial gravity energy, cooling time and a geometry of collision are investigated. Main conclusion is that protostar formation takes place within the time interval less than one free fall time and it is preceded by the appearance of dense and hot matter with lifetime much less than free fall time. The final temperature of the protostar depends on the physical conditions and mainly on the ratio between free fall time and cooling time in the colliding current carrying gas filaments.

Exciton transport in dynamically disordered molecular aggregates: influence on optical line shapes

For Frenkel excitons moving on a linear trimer we investigate the influence of dynamic disorder on their optical line shapes. The dynamic disorder models the influence of vibrational degrees of freedom and is taken into account by fluctuations of the local excitation energy and of the transfer matrix element between neighbouring molecules. The fluctuations are represented by dichotomic Markov processes with coloured noise. We obtain a closed set of equations of motion for the correlation functions determining the optical line shape which is solved exactly as well as using various approximations. The line shapes are discussed for various sets of the model parameters. Furthermore we show that slower fluctuations need higher approximations in our factorization scheme. The limit of static fluctuations can only be covered by the full set of equations.

Computer simulation of superplastic deformation

In this paper, a numerical procedure is described to simulate the grain structure evolution of fine grain materials during superplastic deformation. The basic assumption is that the dominant mechanism for the deformation of the material under mechanical loading is grain-boundary sliding accomodated by grain-boundary diffusion. At each time step, the full set of equations which control the grain-boundary diffusion process are solved by the numerical technique suggested by Cocks [1–2] with a further extension to the situation of grains with arbitrary sizes and shapes. The grain boundary network is updated according to grain velocities obtained from the numerical analysis. Any four-rayed grain boundary junction is supposed to be unstable. Therefore a vanishing grain-boundary will lead to either a “neighbour-switching” [3] or “grain vanishing” event. It is demonstrated that the computer simulation based on these few assumptions is able to capture the main characteristics of microstructural evolution in fine grain materials during superplastic deformation. Most importantly, the grain size increases slightly and the grain shape is essentially preserved, remaining equiaxed after a hundred percent elongation.