Showing papers in "Lecture Notes in Physics in 1989"
266 citations
189 citations
TL;DR: The Cauchy problem for the nonlinear Schrodinger equation is solved in this article under the assumption that F is a C 1 -function (in the real sense) on C itself satisfying F(0)=0 and the growth condition |F'(ξ)≤const|ξ| p−1, where p 0 is a constant.
Abstract: The Cauchy problem for the nonlinear Schrodinger equation i∂ t u=Δu−F o u, u(0)=φ, on space domain R m , m≥1, is solved under the assumption that F is a C 1 -function (in the real sense)on C itself satisfying F(0)=0 and the growth condition |F'(ξ)≤const|ξ| p−1 , where p 0 On resout le probleme de Cauchy pour l'equation de Schrodinger non lineaire i∂ t u=Δu-F o u, u(0)=φ dans l'espace R m , m≥1, sous l'hypothese que la fonction F est C 1 (au sens reel) de C dans C, et satisfait F(0)=0 et la condition de croissance |F'(ξ)|≤const|ξ| P−1 avec p 0
171 citations
96 citations
TL;DR: In this article, the formation of dust from newly synthesized elements in the ejecta of SN 1987A was discovered photometrically through a precipitous fading in the UV and optical spectra with concomitant brightening in the IR.
Abstract: Work at ESO on the formation of dust from newly synthesized elements in the ejecta of SN 1987A began in late January when blue shifts of ≃ 600 km s-1 were found for various optical emission lines in spectra taken after September 1988. It was quickly realized that these shifts could be due to the attenuation of emission from the far, and therefore receding, side of the ejecta caused by dust within the ejecta. However, dust formation — if it occurred — was expected to be discovered photometrically through a precipitous fading in the UV and optical (DWEK [1], KOSAZA et al. [2]) with concomitant brightening in the IR. But no such fading had occurred and the brightening in the IR after day ≃ 450 (Smith et al. [3]) had been attributed to a thermal echo by pre-existing circumstellar dust, an interpretation apparently supported decisively by the measurement of a small, but finite angular size of ≃1.5 arcsec at 8-10µ (Roche et al. [4]).
80 citations
TL;DR: In this article, the authors consider a class of nonlinear equations with localized and dispersive solutions and show that for a ball in some Banach space of initial conditions, the asymptotic behavior (as t → ± ∞) of such states is given by a linear combination of a periodic (in time), localized (in space) solution (nonlinear bound state) of the equation and a purely dispersive part (with free dispersion).
Abstract: We consider a class of nonlinear equations with localized and dispersive solutions; we show that for a ball in some Banach space of initial conditions, the asymptotic behavior (as t → ±∞) of such states is given by a linear combination of a periodic (in time), localized (in space) solution (nonlinear bound state) of the equation and a purely dispersive part (with free dispersion). We also show that given data near a nonlinear bound state of the system, there is a nonlinear bound state of nearby energy and phase, such that the difference between the solution (adjusted by a phase) and the latter disperses to zero. It turns out that in general the time-period (and energy) of the localized part is different for t → ±∞from that for t → −∞.Moreover, the solution acquires an extra constant phase eiγ±.
66 citations
59 citations
TL;DR: In this article, the second moments of a two-dimensional density in conjugate coordinates are combined to form the emittance, which remains invariant under idealized beam transport, as will be implemented at the Brookhaven Accelerator Test Facility.
Abstract: We discuss experimental techniques for measurement of the density of beam particles in both the transverse and longitudinal phase space. The second moments of a two-dimensional density in conjugate coordinates are combined to form the emittance, which remains invariant under idealized beam transport. Four different methods of emittance measurement are presented, as will be implemented at the Brookhaven Accelerator Test Facility.
51 citations
47 citations
TL;DR: In this paper, the authors consider Riemann-problem based numerical techniques for two-phase reactive flows with moving boundaries and adopt a mixed hyperbolic-elliptic mathematical model.
Abstract: We consider Riemann-problem based (RPB) numerical techniques for two-phase reactive flows with moving boundaries. Given the still unresolved problem of hyperbolicity we adopt a mixed hyperbolic-elliptic mathematical model. A successful strategy consists of identifying two hyperbolic homogeneous systems, one for each phase. The remaining terms are regarded as (stiff) source terms. The associated Riemann problems are solved exactly and approximately. Two RPB methods are then used, namely Roe's method and a Weighted Average Flux Method (WAF) due to the author. Application of the technioues to a shock tube problem and a ballistics problem are carried out.
39 citations
TL;DR: In this paper, a Johnson-glass system is proposed and its absolute calibration derived based on the Bell model atmosphere fluxes for Alpha Lyrae, and the homogenized colors of the standard stars are used to derive intrinsic colors for stars with spectral types between B7V and M6V, and G7III and MSIII.
Abstract: The relations between colors of the JHKL systems of SAAO, ESO, CIT/CTIO, MSO, AAO and Arizona have been examined and linear relations derived to enable transformation between the J-K, J-H, H-K, and K-L colors in the different systems. A homogenized system, essentially the Johnson-Glass system is proposed and its absolute calibration derived based on the Bell model atmosphere fluxes for Alpha Lyrae. The homogenized colors of the standard stars were used to derive intrinsic colors for stars with spectral types between B7V and M6V, and G7III and MSIII. The JHKL passbands of the MSO IR system, derived from measured filter passbands and estimated atmospheric transmission values, were used to compute synthetic colors from relative absolute fluxes of some stars (including the sun). The reasonable agreement with the standardized JHKL colors indicates that these passbands can be adopted as representing the homogeneous system, and used to compute broad band IR colors from theoretical or observed fluxes. The passbands of other IR systems were similarly estimated from published data, and the synthetic colors were intercompared using black-body and stellar fluxes. These passbands were then adjusted in wavelength to produce agreement with the observed relations between different systems, enabling the effective wavelengths of the different natural systems to be established. Better effective wavelengths could be determined were spectrophotometry available for the very red stars with known broad band colors. The full text of this paper is published in Bessell and Brett (1988).
TL;DR: The Sobolev inequality on R n, n ≥ 3 is very important because it gives a lower bound for the kinetic energy in terms of an L P norm of f as mentioned in this paper.
Abstract: The Sobolev inequality on R n, n ≥ 3 is very important because it gives a lower bound for the kinetic energy \({\int {\left|
abla \right|} ^2}\) in terms of an L P norm of f. It is the following.
TL;DR: In this article, the authors describe a study of fuel-air mixing and reaction in a supersonic mixing layer and discuss several techniques that were applied for enhancing the mixing processes and overall combustion efficiency in the layer.
Abstract: Work has been underway for a number of years at the NASA Langley Research Center to develop a supersonic combustion ramjet or scramjet that is capable of propelling a vehicle at hypersonic speeds in the atmosphere or beyond. A recent part of that research has been directed toward the optimization of the scramjet combustor, and in particular the efficiency of fuel-air mixing and reaction in the engine. A supersonic, spatially developing and reacting mixing layer serves as an excellent physical model for the mixing and reaction processes that take place in a scramjet combustor, This paper describes a study of fuel-air mixing and reaction in a supersonic mixing layer and discusses several techniques that were applied for enhancing the mixing processes and the overall combustion efficiency in the layer. Based on the results of this study, an alternate fuel injector configuration was computationally designed, and that configuration significantly increased the amount of fuel-air mixing and combustion over a given combustor length that was achieved.
TL;DR: In this paper, the authors describe a class of stochastic processes, the so-called Levy processes (i.e. processes with stationary independent increments), and explain how they can be used in the study of relativistic operators and some abstract generalizations.
Abstract: Path integral methods for the investigation of the properties of Schrodinger operators go back to the pioneering works of Feynman and Kac. They have been successfully used for a long time but they have been restricted to nonrelativistic operators. We describe a class of stochastic processes, the so-called Levy processes (i.e. processes with stationary independent increments), and we explain how they can be used in the study of the relativistic operators and some of their abstract generalizations. We mimic the classical approach based on the use of Brownian motion and the Feynman-Kac's formula. We describe the class of potentials which can be handled by this approach, we discuss the regularity properties of the semigroups, the decay of the eigenfunctions and the existence of bound states. We also discuss some of the open problems which are naturally unravelled.
TL;DR: In this article, integrals and circulation theorems are deduced for inviscid fluids of grade n. A general classification of flows is given, and the thermodynamic form of the equation of motion is given.
Abstract: Fluids of grade n are continuous models for dynamic changes of phase which avoid the surfaces of discontinuity representing the capillary layers in liquid-vapour interfaces. We recall the thermodynamic form of the equation of motion for inviscid fluids of grade n [1]. First integrals and circulation theorems are deduced and a general classification of flows is given.
TL;DR: In this article, the random choice method was used to solve the Euler equation in a Lagrangian configuration with time-operator splitting to treat combustion chemistry, where the combustion reaction was assumed to be of simple irreversible Arrhenius type.
Abstract: Exothermically reactive gas flow in the region between a piston and a strong shock wave, (Mach 3.0), is modelled numerically using the Random Choice Method to solve the Euler equations. The numerical algorithm consists of the Random Choice scheme, formulated in a Lagrangian configuration, coupled with time-operator splitting to treat combustion chemistry. The combustion reaction is assumed to be of simple irreversible Arrhenius type. Numerical results show that ignition first occurs close to the piston face, and is followed by the formation of a compression pulse that finally contains a shock, an unsteady induction domain and a fast flame prior to transition of this system into a ZND-structured detonation.
TL;DR: In this paper, the authors examined the details of transition to detonation in a planar, one-dimensional configuration via a numerical simulation of the reactive Euler equations and observed that the eventual emergence of a ZND (Zeldovich, von Neumann, Doring) detonation is preceded by a rich sequence of events, including the creation of a localized thermal explosion, the birth of a supersonic reaction wave, and the appearance of a quasisteady weak detonation.
Abstract: Details of transition to detonation in a planar, one-dimensional configuration are examined via a numerical simulation of the reactive Euler equations. The initial state of the explosive is taken to involve a small temperature nonuniformity. It is observed that the eventual emergence of a ZND (Zeldovich, von Neumann, Doring) detonation is preceded by a rich sequence of events, including the creation of a localized thermal explosion, the birth of a supersonic reaction wave, and the appearance of a quasisteady weak detonation.
TL;DR: In this article, a complete set of newly measured radio continuum maps of the Orion Nebula at 20 and 2 cm is presented, and a detailed comparison with Hα images shows a very good match on all scale sizes.
Abstract: A complete set of newly measured radio continuum maps of the Orion Nebula at 20 and 2 cm is presented. The largest field covers a region of 2° × 2° with a resolution of 10', the smallest covers 3' × 3' field, centered on the peak, with a resolution of 0.1″. The lower resolution maps emphasise the extended emission of the diffuse ionized gas. As the resolution increases, the maps sample regions of higher emission measure. A detailed comparison with Hα images shows a very good match on all scale sizes. As the resolution becomes finer than 1″ a completely new aspect of the radio emission appears: a new class of weak, small diameter sources of high surface brightness are found. Many of these features are associated with stars
TL;DR: In this paper, the authors solve the 2-D thermo-diffusive model of premixed flames in the framework of Fourier Spectral Methods (FSM) and propose a particular treatment, simple to implement, that is applied to these quantities in order to transform them into the sum of a known profile and a periodic unknown.
Abstract: We solve the 2-D thermo-diffusive model of premixed flames in the framework of Fourier Spectral Methods. Although the temperature and concentration fields are not periodic in the direction perpendicular to the flame, we suggest a particular treatment, simple to implement, that is applied to these quantities in order to transform them into the sum of a known profile and a periodic unknown. This process also takes advantage of the fact that the physics of flames allows us to consider as periodic the higher derivatives. “Infinite” order convergence of Spectral Methods is thus recovered. This algorithm being very efficient, we can perform numerical simulation concerning the diffusive-thermal instability, far in the non-linear domain. Thus, at low Lewis number, we numerically observed, for the first time to our knowledge, a phenomenon of local extinction. This brings a plausible explanation to the presence of unburnt combustible in the lean hydrogen flame.
TL;DR: In this paper, the authors highlight the evidence for inflow of neutral gas toward the disk of the Galaxy and show that neutral gas may be a relatively important source of energy in localized regions of the outer Galaxy.
Abstract: I highlight the evidence for inflow of neutral gas toward the disk of the Galaxy. The Milky Way is accreting 0.2–0.5 M⊙/yr of extragalactic atomic hydrogen at very high velocities. The interaction of infalling clouds with galactic material produces large-scale disturbances in the interstellar medium. Although the injection of energy into the galactic disk by infalling neutral gas is only 1% of the energy from supernovae, the impinging of high velocity neutral gas may be a relatively important source of energy in localized regions of the outer Galaxy.
TL;DR: In this paper, a Burke-Schumann flame model is presented, where the initial flame is straight and passes through the vortex core, but not through the center of the vortex as in Marble's work.
Abstract: Marble's problem of a vortex winding up a diffusion flame sheet is simulated (Marble, 1985, with the effects of variable density and vorticity generation included. The initial flame is straight and passes through the vortex core, but not through the center of the vortex as in Marble's work. During the first eddy turn-over time, the swirling flow forms a flame tip region, and the amount of tip rotation around the vortex depends on the diffusion coefficient. During the next eddy turn-over time, the flame shape is quasi-steady with minor differences due to heat release and vorticity production over the parameter range examined. The gradient of mixture fraction at the flame sheet determines the amount of reaction in this Burke-Schumann flame model. This swirling flow maintains a uniform gradient along most of the flame surface, with the exception of a low-gradient region at the flame tip. If finite-rate chemistry is considered, then the tip region would likely be at higher temperature than the rest of the flame surface.
TL;DR: Rodriguez et al. as discussed by the authors studied a number of these disks to establish whether they have properties compatible with those attributed to the proto-solar nebula, in the early stages of evolution of our solar system.
Abstract: There is now a substantial body of evidence that disk-like structures of gas and dust surround many protostars and young stellar objects (e.g. Rodriguez, these proceedings). We are currently studying a number of these disks to establish whether they have properties compatible with those attributed to the proto-solar nebula, in the early stages of evolution of our solar system. The frequency with which such proto-planetary disks are associated with young stars is also being investigated.