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Kink oscillations of curved coronal loops with the density varying along the loop are studied in the thin tube approximation. The equilibrium magnetic field is assumed to be potential, and the field potential and flux function are used as curvilinear coordinates. It is also assumed that the loop expansion is weak, and the solution to the problem is looked for in the form of power series with respect to the tube expansion parameter λ≪1. The main result of the study is that the eigenfrequencies of the vertical and horizontal tube oscillations are, in general, different, their difference being proportional to λ. As an example a simple equilibrium with the magnetic field magnitude exponentially decaying with the height is considered. The implication of the obtained results for the interpretation of observational data is discussed.

Context. Collective oscillations of two or more coronal magnetic loops are observed very often.

Aims.We explore the solar coronal heating enigma by an analytical and numerical study of the enhanced phase mixing of harmonic Alfvén waves propagating in gravitationally stratified coronal structures of varying magnetic field divergence.

Aims.We propose a model for rotating current patterns within radiopulsar polar cap accelerators which has observational consequences that mimic those which have been attributed to neutron star precession.

In the recent study of nine transversely oscillating coronal loops Verwichte et al. (2004) found that in two events the fundamental mode and the first overtone were observed simultaneously, and the ratio of their periods was different from two predicted by the uniform tube model. This observation inspired Andries et al. (2005a, ApJ, 624, L57) to use this ratio for determining the atmospheric scale height. When doing so these authors assumed that the loop has a semicircular shape. In our paper we address the question how strongly the method suggested by Andries et al. (2005a) depends on the assumed loop shape. We found that this dependence is fairly strong, so that observations of frequencies of the fundamental mode and first overtone have to be supplemented with observations of the loop shape.

Soon after coronal loop oscillations were observed by TRACE spacecraft for the first time in 1999, various theoretical models have been put forward to explain the rapid damping of the oscillations of these intriguing objects. Coronal loop oscillations are often interpreted as fast kink modes of a straight cylindrical magnetic flux tube with immovable edges modelling dense photospheric plasma at the ends of the loop. Taking this model as a basis we use cold plasma approximation and consider the tube to be thin to simplify the problem and be able to deal with it analytically. In its equilibrium state the tube is permeated by a homogeneous magnetic field directed along the tube axis. We include the effect of stratification in our model supposing that plasma density varies along the tube. There is also density inhomogeneity in the radial direction confined in a layer with thickness much smaller than the radius of the tube. Considering the system of linearized MHD equations we study the dependence of the spectrum of tube oscillations and its damping due to resonant absorption on the parameters of the unperturbed state. The implication of the obtained results on coronal seismology is discussed.

Context.The stability of parallel propagating circularly polarized Alfvén waves (pump waves) has been studied for more than four decades with the use of normal mode analysis. It is well known that the normal mode analysis does not answer the question if a pump wave looks stable or unstable in a particular reference frame. To answer this question it is necessary to find out if the instability is absolute or convective in this reference frame.

In this paper we present the results of the stability analysis of a simple shear flow of an incompressible fluid with a piecewise linear velocity profile in the presence of a magnetic field. In the flow, a finite transitional magnetic-free layer with a linear velocity profile is sandwiched by two semi-infinite regions. One of these regions is magnetic-free and the flow velocity in the region is constant. The other region is magnetic and the fluid in it is quiescent. The magnetic field is constant and parallel to the flow in the transitional layer. The fluid density is constant both in the magnetic as well as the magnetic-free regions, while it has a jump-type discontinuity at the boundary between the transitional layer and the magnetic region. The effect of gravity is included in the model, and it is assumed that the lighter fluid is overlaying the heavier one, thus no Rayleigh-Taylor instability is present. The dispersion equation governing the normal-mode stability of the flow is derived and its properties are analysed. We study stability of two cases: (i) magnetic-free flow in the presence of gravity, and (ii) magnetic flow without gravity. In the first case, the flow stability is controlled by the Rayleigh number, $R.$In the second case, the control parameter is the inverse squared Alfvénic Mach number, H. Stability of a particular monochromatic perturbation also depends on its dimensionless wavenumber α. We combine the analytical and numerical approaches to obtain the neutral stability curves in the $(\alpha,R)$-plane in the case of the magnetic-free flow, and in the $(\alpha,H)$-plane in the case of the magnetic flow. The dependence of the instability increment on Rin the first case, and on Hin the second case is treated. We apply the results of the analysis to the stability of a strongly subsonic portion of the heliopause. Our main conclusion is as follows: The inclusion of a transitional layer near the heliopause into the model increases by an order of magnitude the strength of the interstellar magnetic field required to stabilize this portion of the heliopause in comparison with the corresponding stabilizing strength of the magnetic field required when modelling the heliopause as a tangential discontinuity.

Motivated by recent Transition Region and Coronal Explorer (TRACE)observations of damped oscillations in coronal loops, Ruderman & Roberts ([CITE]), studied resonant damping of kink oscillations of thin straight magnetic tubes in a cold plasma. In their analysis, Ruderman & Roberts considered magnetic tubes with circular cross-sections. We extend their analysis for magnetic tubes with elliptic cross-sections. We find that there are two infinite sequences of the eigenfrequencies of the tube oscillations, $\{\omega_{nc}\}$and $\{\omega_{ns}\}$, $n = 1,2,\dots$. The eigenfrequencies $\{\omega_{nc}\}$and $\{\omega_{ns}\}$correspond to modes with $2n$nodes at the tube boundary. In particular, $\omega_{1c}$and $\omega_{1s}$correspond to two kink modes. These modes are linearly polarized in the direction of the large and small axis of the tube elliptic cross-section respectively. The sequence $\{\omega_{nc}\}$is monotonically growing and $\{\omega_{ns}\}$monotonically decreasing, and they both tend to $\omega_k$as $n\to \infty$, where $\omega_k$is the frequency of the kink mode of tubes with circular cross-sections. In particular, $\omega_{1c} < \omega_k < \omega_{1s}$. We calculate the decrements of the two kink modes and show that they are of the order of decrement of the kink mode of a tube with a circular cross-section.

In this paper, the extended state dependent Riccati equation (ESDRE) method is applied to robotic joint control. The control scheme compares the predicted reference state and the actual state, thus rapidly reducing the steady-state error, even in the presence of significant model uncertainties. The state dependent coefficient (SDC) model and the corresponding control law are formulated for the discrete state-space by linear interpolation among operating points. The approach is validated on a 1-DOF rigid robotic manipulator which major nonlinearities are the velocity dependent Stribeck friction and the position dependent gravity. Considering the relative weighting matrices as parameters of the underlying optimization problem by control design the state dependent feedback function is determined. The developed ESDRE control proves superior compared to the PID reference controller with auxiliary gravity compensator. Considering the robust performance and ease of implementation the proposed ESDRE scheme constitutes a serious competitor to the established model-based robot control strategies.

This paper contains the discussion inputs by the contributors of the special issue on the subject of rogue waves.

This paper contains the discussion inputs by the contributors of the special issue on the subject of rogue waves.

Abstract.: This paper contains the discussion inputs by the contributors of the special issue on the subject of rogue waves.

Aims. In the approximation of linear dissipative magnetohydrodynamics (MHD), it can be shown that driven MHD?waves in magnetic plasmas with high Reynolds number exhibit a near resonant behaviour if the frequency of the wave becomes equal to the local Alfv?n (or slow) frequency of a magnetic surface. This behaviour is confined to a thin region, known as the dissipative layer, which embraces the resonant magnetic surface. Although driven MHD?waves have small dimensionless amplitude far away from the resonant surface, this near-resonant behaviour in the dissipative layer may cause a breakdown of linear theory. Our aim is to study the nonlinear effects in Alfv?n dissipative layerMethods. In the present paper, the method of simplified matched asymptotic expansions developed for nonlinear slow resonant waves is used to describe nonlinear effects inside the Alfv?n dissipative layer.Results. The nonlinear corrections to resonant waves in the Alfv?n dissipative layer are derived, and it is proved that at the Alfv?n resonance (with isotropic/anisotropic dissipation) wave dynamics can be described by the linear theory with great accuracy.

Aims.We explore the solar coronal heating enigma by an analytical and numerical study of the enhanced phase mixing of harmonic Alfv?n waves propagating in gravitationally stratified coronal structures of varying magnetic field divergence.Methods.Corrected analytical solutions are derived to model the dissipation of Alfv?n waves propagating in divergent and stratified coronal structures. These analytical solutions are validated and further explored using a newly developed 2.5D visco-resistive linear MHD code.Results.Corrected analytical solutions describing the enhanced phase mixing of Alfv?n waves in divergent and stratified coronal structures are presented. These show that the enhanced phase mixing mechanism can dissipate Alfv?n waves at heights less than half that is predicted by the previous analytical solutions. In divergent and stratified coronal structures, the enhanced phase mixing effect occurs only when the ratio of the magnetic and density scale heights, Hb / H? < 2. The enhanced phase mixing of 0.1?Hz harmonic Alfv?n waves propagating in strongly divergent, Hb = 5?Mm, stratified coronal structures, H? = 50?Mm, can fulfill 100% of an active region heating requirement, by generating viscous heating fluxes of FH ?2100?J?m-2?s-1. The Alfv?n waves in this configuration are fully dissipated within 20?Mm, which is six times lower than would occur as a result of standard phase mixing in uniform magnetic fields. This results in the heating length scale, LH, defined as the height at which 95% of the Alfv?n wave poynting flux has dissipated, being lowered by a factor of six, to less than half of an active region density scale height. Using the corrected analytical solutions it was found that, for a given wave frequency, the generation of a heating length scale of LH ?50?Mm, by enhanced phase mixing in strongly divergent magnetic fields, requires a shear viscosity eight orders of magnitude lower, than required by standard phase mixing in uniform magnetic fields. It was also found that the enhanced phase mixing of observable, ??0.01?rads?s-1, Alfv?n waves, in strongly divergent magnetic fields, Hb = 5?Mm, can generate heating length scales within a density scale height, H? = 50?Mm, using classical Braginskii viscosity. It is therefore not necessary to invoke anomalous viscosity in corona, if phase mixing takes place in strongly divergent magnetic fields. This study shows that the importance of enhanced phase mixing as a mechanism for dissipating Alfv?n waves in the solar corona (a stratified and divergent medium), has been seriously underestimated.

We consider the stability of a compressible shear flow separating two streams of different speeds and temperatures. The velocity and temperature profiles in this mixing layer are hyperbolic tangents. The normal mode analysis of the flow stability reduces to an eigenvalue problem for the pressure perturbation. We briefly describe the numerical method that we used to solve this problem. Then, we introduce the notions of the absolute and convective instabilities and examine the effects of Mach number, and the velocity and temperature ratios of each stream on the transition between convective and absolute instabilities. Finally, we discuss the implication of the results presented in this paper for the heliopause stability. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

A three-dimensional pulsar magnetosphere model is used to study the geometry of outer magnetospheric gap accelerators, following seminal work of Romani and coworkers. The size of the outer gap is self-consistently limited by pair production from collisions of thermal photons from polar cap heating of backflow outer gap current with curvature photons emitted by gap-accelerated charged particles. In principle, there could be two topologically disconnected outer gaps. Conditions for local pair production such as local field line curvature, soft X-ray density, electric field, etc., support pair production insidean outer gap only between rin() (the radius of the null surface at azimuthal angle ) and rlim() ? 6rin(= 0) RL(the light cylinder radius). Secondary pairs, on the other hand, are produced almost everywhere outside the outer gap by collisions between curvature photons and synchrotron X-rays emitted by these secondary pairs. These processes produce a wide X-ray fan beam in the outgoing direction and a very narrow beam in the incoming direction for each outer gap. For pulsars with a large magnetic dipole inclination angle, part of the incoming ?-ray beam will be absorbed by the stellar magnetic field. If the surface magnetic field is dominated by a far off-center dipole moment (e.g., as in a proposed "plate tectonic" model), gravitational bending of photons from polar cap accelerators and their ultimate conversion into outflowing e±pairs can result in the quenching of one of these two outer gaps. Various emission morphologies for the pulsar (depending on magnetic inclination angle and viewing angle) are presented. Double-peak light curves with strong bridges are most common. From the three-dimensional structure of the outer gap and its local properties, we calculate phase-resolved spectra of gamma-ray pulsars and apply them to observed spectra of the Crab pulsar.

The nonlinear theory of driven magnetohydrodynamic (MHD) waves in resonant slow-wave layers developed by Ruderman et al. [Phys. Plasmas 4, 75 (1997)] is used to study the interaction of sound waves with a one-dimensional planar magnetic plasma configuration. The physical problem studied here is the same as that considered by Ruderman et al. [Phys. Plasmas 4, 91 (1997)]. The difference is in the description of the wave motion in the resonant layer. Ruderman et al. assumed that dissipation dominates non-linearity in the resonant layer and considered the nonlinear term in the governing equation for the wave motion in the resonant layer as a perturbation. In contrast, it is assumed in the present paper that nonlinearity dominates dissipation in the resonant layer. The solution to the governing equation for the wave motion in the resonant layer is obtained in the approximation of strong nonlinearity, and it is shown that the amplitude of the wave motion saturates when the Reynolds number tends to infinity. This solution is then used to derive the nonlinear connection formula that determines the jump across the resonant layer in the velocity component in the direction of inhomogeneity. The nonlinear connection formula is, in turn, used to obtain a nonlinear one- dimensional integral equation describing the outgoing sound wave, which appears owing to partial reflection of the incoming sound wave from the inhomogeneous plasma. The solution to this integral equation is obtained in the form of a sinusoidal wave under the assumption that an incoming sound wave contains the fundamental harmonic only. The coefficient of wave-energy absorption is calculated analytically in the long-wavelength approximation and numerically for arbitrary wavelengths.

The model of the solar wind interaction with interstellar medium suggested by Baranovet al. (1970) is developed. In this model (TSM) the presence of two shock waves is assumed, through which the solar wind and interstellar gas pass, the latter moving relative to the Sun at supersonic speed (20 km s-1).

The Benjamin-Ono equation is derived for long slow sausage waves propagating in a vertical magnetic slab embedded into a stratified atmosphere, provided that the slab thickness is much smaller than the scale height of the atmosphere. The soliton propagation in a nonstratified atmosphere is discussed. The approximate formulas describing the slow evolution of the amplitude and the length of a soliton propagating in a very weakly stratified atmosphere are obtained. The exact soliton-like solution for an atmosphere with a linearly growing temperature is found.

Models for the generation of the magnetic field depending on one and two Cartesian coordinates in an anisotropically conducting fluid are constructed. A similarity between the solutions and the known homopolar disk dynamo is noted.

The nonlinear stage of development of perturbations at a tangential magnetohydrodynamic discontinuity is investigated in the weakly subcritical and supercritical regimes. It is assumed that the fluid is incompressible and that the density and magnetic field, as well as the velocity, suffer a discontinuity. An equation describing the evolution of low-amplitude nonlinear perturbations is obtained. For periodic perturbations this equation reduces to an infinite system of ordinary differential equations for the amplitudes of the Fourier harmonics. The system is reduced to finite form by truncation and then integrated numerically. Calculations show that the evolution of an initially sinusoidal perturbation always ends with the appearance in the wave profile of an infinite derivative. This can take the form of either an infinitely sharp peak (knife-edge) or wave breaking.

An investigation is made into the propagation of long nonlinear weakly nonone-dimensional internal waves in an incompressible stratified fluid of infinite depth in the presence of a horizontal magnetic field. It is shown that such waves are described by an equation representing the extension of the Benjamin-Ono equation to the weakly nonone-dimensional case. The equation obtained differs from that obtained in [4], which is attributable to the anisotropy of the medium resulting from the presence of a magnetic field. The stability of a soliton with respect to flexural perturbations is investigated. A particular case of the variation of the density with height at constant Alfvén velocity is examined in detail.

Benjamin [1] and Davis and Acrivos [2] derived an equation for long steady nonlinear internal waves in an infinitely deep stratified fluid when the density varies only in a layer whose thickness is small compared with the characteristic perturbation length. Ono [3] generalized this equation to the unsteady case. The resulting equation was subsequently called the Benjamin—Ono equation. Steady solutions of this equation were found by Benjamin and Ono in the form of solitons and periodic waves. In the present paper it is shown that long nonlinear waves on shallow water in the presence of a horizontal magnetic field can also be described by the Benjamin—Ono equation, and not the Korteweg—de Vries equation [4], as in the case when there is no field. Moreover, in contrast to a soliton in a stratified fluid a soliton on shallow water in a horizontal magnetic field moves with a velocity less than the velocity of infinitely long perturbations of small amplitude. The dependence of the parameters of a soliton and a periodic wave on the intensity and direction of the unperturbed magnetic field is investigated.

The evolution of steady-state periodic solutions of the Korteweg-de Vries equation (the socalled cnoidal waves), propagating along the direction of the gravitational force with an arbitrary orientation of the magnetic field, is studied for plasma characterized by Hall dispersion and Joule dissipation, using the magnetohydrodynamic approximation. The wavelength is regarded as much shorter than the characteristic scale of the inhomogeneity. The dependence of the wave amplitude on the distance to the source of the wave is considered for various limiting cases. The behavior of the wave depends on the temperature distribution in the medium. In the particular case of an isothermal atmosphere, the problem is solved analytically for a cold plasma in the absence of dissipation. The amplitude of both fast and slow waves increases when the wave travels upward and diminishes when the wave travels downward. The nonlinearity of the wave (i.e., the parameter characterizing the deviation of the wave from sinusoidal form) diminishes in the case of fast magnetoacoustic waves when the wave travels upward and increases when the wave travels downward. The situation is reversed for slow magnetoacoustic waves.

The structure of the region of interaction between the solar wind and the interstellar medium in the two-shocks model (TSM), first suggested by Baranovet al. (1970), is numerically calculated.

Surface magnetohydrodynamic wave propagation on a magnetic interface in a cold plasma is studied. The anisotropic ion viscosity is taken into account. Only long waves damping weakly in a wave period are considered. The dispersion equation is obtained. This equation is shown always to have exactly one root if there is no viscosity. The dependences of phase velocity, penetration depth and damping decrement of waves on the parameters of undisturbed plasma and wave propagation direction are investigated. The resulting application for describing of surface wave damping in the solar corona is discussed.

The structure and stability of quasiparallel magnetohydrodynamic shock waves of small but finite amplitude are investigated. Only those waves whose propagation velocities are close to the Alfvén velocity are considered, i.e., fast shock waves in a medium in which the Alfvén velocity is greater than the speed of sound and slow shock waves in a medium in which the Alfvén velocity is less than the speed of sound and, moreover, intermediate (nonevolutionary) shock waves.

By analogy with the generalization obtained in [16] for the Korteweg-de Vries equation, the derivative nonlinear Schrödinger equation is extended to the weakly non-one-dimensional case. On the basis of the equation obtained the stability of solitons propagating at small angles to the undisturbed magnetic field relative to non-one-dimensional perturbations is investigated.

Abstract: It is proposed to consider the propagation of surface waves along a tangential magnetohydrodynamic discontinuity in the particular case where the fluid velocities on both sides of the interface are equal to zero. In [1] it was shown that waves called surface Alfvn waves may be propagated along the surface separating a semi-infinite region without a field from a region with a uniform magnetic field. The linear theory of surface Alfvn waves in a compressible medium was considered in [2]. In [3] the damping of surface Alfvn waves as a result of viscosity and heat conduction was investigated. The propagation of low-amplitude nonlinear surface Alfvn waves in an incompressible fluid in the absence of dissipative processes is described by the integrodifferential equation obtained in [4]. By means of a numerical solution of this equation it was shown that a perturbation initially in the form of a sinusoidal wave will break. The breaking time was determined. In this paper the equation derived in [4] is extended to the case of a viscous fluid. It is shown that the equation obtained does not have steady-state solutions. The propagation of periodic disturbances is investigated numerically.

An equation, analogous to the Khokhlov-Zabolotskaya equation, is derived for narrow beams of quasitransverse waves propagating at small angles to a magnetic field. The effect of diffraction on wave propagation is investigated in the linear approximation.

We have measured plasma and synovial fluid concentrations of meclofenamic acid at 2, 4, 8, and 12 h during steady-state administration (100 mg three times daily for 4–7 days). Paired plasma and synovial samples were obtained pre-treatment and at one of the above times in twelve patients with a diagnosis of rheumatoid arthritis. In addition, the extent of protein binding of meclofenamic acid was assessed in vitro in the pre-treatment plasma and synovial fluid specimens.

The resonant absorption of small amplitude surface Alfvén waves is studied in nonlinear incompressible MHD for a viscous and resistive plasma. The reductive perturbation method is used to obtain the equation that governs the spatial and temporal behaviour of small amplitude nonlinear surface Alfvén waves. Numerical solutions to this equation are obtained under the initial condition that att = 0 the spatial variation is purely sinusoidal. The numerical results show that nonlinearity accelerates the wave damping due to resonant absorption. Resonant absorption is a more efficient wave damping mechanism than can be anticipated on the basis of linear theory.

The propagation of nonlinear slow sausage small-amplitude waves in a magnetic slab in a magnetic environment is considered. The equation for surface waves that is allied form of the Benjamin-Ono equation and the equation for body waves that is allied form of the equation for body waves in the slab are derived with the use of the method of stretching variables. The solutions of the equation for surface waves in the form of solitary waves are obtained numerically.

The Hohlov-Zabolotskaja equation with an additional boundary condition is shown to describe long nonlinear small-amplitude fast sausage surface waves in a magnetic slab embedded in magnetic environment. It is proved that the obtained boundary problem has no solutions in the form of solitary waves. Approximate solution in the form of nonlinear stationary wave is found with the use of expansion in the power series of small amplitude. Second harmonic generation by a sinusoidal wave is studied. The law of energy conservation is obtained. Results of numerical computations are presented. They show that a sinusoidal disturbance does not overturn. The possibility of transmission of wave energy into corona along a magnetic slab is discussed in connection with these results.

An approximate equation describing long nonlinear slow body wave propagation in a magnetic slab in magnetic environments is derived. It is shown that this equation has no solutions in the form of solitary waves. Second-harmonic generation by a sinusoidal wave is studied. Results of numerical computations are presented. They show that a sinusoidal disturbance overturns, i.e., infinite gradients arise. An approximate formula for the overturning time is derived. The application of these results to the problem of coronal heating is discussed.

We estimate the partial cross section for the transfer of vibrational excitation energy between NO+ and N2 molecules to be about 10−16 cm2. This exceptionally large cross‐section depends upon both the near degeneracy of the N2 and NO+ vibrations and special features of the molecular orbits caused by the strong long range interaction between the NO+ Coulomb field and the highly polarizable N2. One consequence is that little NO+ vibational radiation (4.3 μ) should be associated with ionizing radiation in the atmosphere up to altitudes above 100 km despite copious NO+ production.

The paper considers the propagation of low-amplitude nonlinear waves over a surface of magnetic discontinuity. An equation for these waves is derived. The evolution of a sinusoidal perturbation is investigated. The discontinuity formation time is numerically determined.

In a magnetohydrodynamic approximation, an investigation is made of the propagation of waves in a plasma, whose characteristic frequency O is much less than the collision frequency of the electrons ?e-1. It is assumed that the magnetic field is sufficiently strong so that the equality Oe?e»1 will be satisfied, where Oe is the cyclotron frequency of the rotation of the electrons. With large magnetic Reynolds numbers (Rm»1), which are characteristic for many astrophysical problems, this latter condition leads to a need to take account of dispersion effects connected with Hall currents, in the absence of Joule dissipation. The dispersion equation for the propagation of small perturbations is analyzed in the limiting cases of weak dispersion and of a wave propagating along the magnetic field. In the case of weak dispersion, an equation is derived for nonlinear waves. The solutions are found in the form of stationary solitons. The region of such solutions is analyzed. A typical example of a medium with Hall dispersion is an interplanetary plasma, in which the parameter Oe?e is generally great.

The interaction of a boson field with a source is assumed to vanish outside of a radiusa; no special properties are assumed for this source within the radius. It is shown that with such a model for the interaction of pions or K-mesons with nucleons and hyperons, rigorous upper limits, depending only uponaand the particle masses, can be established for the renormalized coupling constantsg2Λ,g2pΣκ,g2pΛκ corresponding to the matrix elements for the processes π+Λ0↔Σ. $$\bar K$$ +p↔Σ and K-+p↔Λ0For the pion-nucleon interaction a maximumg2npπis found, above which there must exist a doubly charged state of the system π++p. Ifg2npπapproach infinity or ifaapproaches zero, it is proved that the neutron-proton mass difference goes to zero independently of other interactions or whether the bare masses are identical. Similar results hold for the mass difference of any baryon pair if they transform into each other by single boson emission or absorption. Finally a general class of field theory models, which will always have « ghosts », is described. Si assume die l’interazione di Un campo bosonico con una sorgente si annulli olte ii raggioa; entro tale raggio non si postulano speciali proprietá della sorgente. Si di mostra che, con tale modello, per l’interazione di pioni o mesoni K con nucleoni e ipe roni si possono porre per le costanti di accoppiamento rinormalizzateg2Λ,g2pΣκ eg2pΛκ corrispondenti agli elementi di matrice per i processi $$\bar K$$ rigorosi limiti superiori dipendenti soltanto daae dalle masse delle particelle. Per l’interazione pione-nucleone Si trova ung2npπmassimo, oltre il quale deve esistere uno stato del sistema π++p dotato di carica doppia. Si trova che se $$\bar K$$ +p↔Σ and K-+p↔Λ0tende all’infinita o seatende a zero, la differenza tra le masse del neutrone e del protone si aniiulla indipendentemente da altre interazioni o dal fatto che le masse nude siano identiche. Risultati simili valgono per la differenza fra le masse di qualsiasi Coppia di barioni so si trasformano l’una nell’altra con emissione o assorbimento di un singolo bosone. Finalmente Si descrive una classe generale di modelli di teorie di campo che debbono. sempre condurre a « fantasmi ».