Shell Amplitudes Research Articles

Pairwise Multiparticle States and the Monopole Unitarity Puzzle.

We suggest a novel resolution for a decades old mystery-what happens when a positron scatters off a minimal grand-unification-theory monopole in an s wave, a puzzle first discussed by Callan in 1983. Using the language of on shell amplitudes and pairwise helicity we suggest that the final state contains two up quarks and a down quark in an entangled "pairwise" multiparticle state-the only particle final state that satisfies angular momentum and gauge charge conservation. The cross section for this process is as large as in the original Rubakov-Callan effect, only suppressed by the QCD scale. The final state we find cannot be seen in Callan's truncated 2D theory, since our new pairwise state appears only in more than two dimensions.

Holographic thermalization in a top-down confining model

It is interesting to ask how a confinement scale affects the thermalization of strongly coupled gauge theories with gravity duals. We study this question for the AdS soliton model, which underlies top-down holographic models for Yang-Mills theory and QCD. Injecting energy via a homogeneous massless scalar source that is briefly turned on, our fully backreacted numerical analysis finds two regimes. Either a black brane forms, possibly after one or more bounces, after which the pressure components relax according to the lowest quasinormal mode. Or the scalar shell keeps scattering, in which case the pressure components oscillate and undergo modulation on time scales independent of the (small) shell amplitude. We show analytically that the scattering shell cannot relax to a homogeneous equilibrium state, and explain the modulation as due to a near-resonance between a normal mode frequency of the metric and the frequency with which the scalar shell oscillates.

Two, three, many body systems involving mesons

In this talk we show recent developments on few body systems involving mesons. We report on an approach to Faddeev equations using chiral unitary dynamics, where an explicit cancellation of the two body off shell amplitude with three body forces stemming from the same chiral Lagrangians takes place. This removal of the unphysical off shell part of the amplitudes is most welcome and renders the approach unambiguous, showing that only on shell two body amplitudes need to be used. Within this approach, systems of two mesons and one baryon are studied, reproducing properties of the low lying 1/2+ states. On the other hand we also report on multirho and K∗ multirho states which can be associated to known meson resonances of high spin.

MHV Lagrangian forN= 4 super Yang-Mills

Here we formulate two field redefinitions for N=4 Super Yang-Mills in light cone superspace that generates only MHV vertices in the new Lagrangian. After careful consideration of the S-matrix equivalence theorem, we see that only the canonical transformation gives the MHV Lagrangian that would correspond to the CSW expansion. Being in superspace, it is easier to analyse the equivalence theorem at loop level. We calculate the on shell amplitude for 4pt $(\bar{\Lambda}\bar{{\rm A}}\Lambda {\rm A})$ MHV in the new lagrangian and show that it reproduces the previously known form. We also briefly discuss the relationship with the off-shell continuation prescription of CSW.

Nonlinear free vibration of spherical shell panel using higher order shear deformation theory – A finite element approach

A nonlinear finite element model for geometrically large amplitude free vibration analysis of doubly curved composite spherical shell panel is presented using higher order shear deformation theory (HSDT). The nonlinearity is introduced in the Green–Lagrange sense. The governing equations of the vibrated shell panel are derived using the Variational approach. Frequency ratios (nonlinear frequency to linear frequency) of the spherical panels are determined as a function of shell amplitude ratio. The results are computed for different orthotropicity ratios, stacking sequences, thickness ratios, amplitude ratios and boundary conditions and also compared with those available in literature.

Oscillations of a cylinder liner of an internal combustion engine with a water cooling system caused by piston group impacts

The forced oscillations of a cylindrical shell surrounded by a liquid layer caused by impacts have been investigated based on the dynamic problem of hydroelasticity. The relationships describing the shell deflection, the pressure in the liquid layer, and the shell amplitude and phase frequency characteristics have been found. An example of calculation of the resonance frequencies of oscillations of a liner of an internal combustion engine with a water cooling system caused by piston group impacts is presented.

Temporal structures in shell models.

The intermittent dynamics of the turbulent Gledzer, Ohkitani, and Yamada shell-model is completely characterized by a single type of burstlike structure, which moves through the shells like a front. This temporal structure is described by the dynamics of the instantaneous configuration of the shell amplitudes, revealing an approximate chaotic attractor of the dynamics.

Hybrid finite element analysis of large amplitude vibration of orthotropic open and closed cylindrical shells subjected to a flowing fluid

A hybrid finite element method is developed to predict the influence of large amplitude vibration of orthotropic, circumferentially non-uniform open and closed cylindrical shells submerged and subjected to an internal and/or external fluid flow. The open shells are assumed to be freely simply supported along their curved edges and to have arbitrary straight edge boundary conditions. The method developed is a combination of thin shell theory, fluid theory and the finite element method. The solution is divided into three parts. In part one, the displacement functions are obtained from Sanders’ linear shell theory and the mass and linear stiffness matrices for an open shell element are obtained by the finite element procedure. In part two, the modal coefficients, derived from the Sanders–Koiter non-linear theory of thin shells, are obtained for these displacement functions. Expressions for the second and third order non-linear stiffness matrices of the open shell element are then determined through the finite element method. With the dynamic pressure of the moving fluid and the boundary condition of impermeability, we develop in the third part the mass and the stiffness matrices of a fluid finite element for the interaction shell–fluid system. The non-linear equation of motion is then solved by the fourth-order Runge–Kutta numerical method. The linear and non-linear natural frequency variations are determined as a function of shell amplitudes for different cases. Here the uncoupled non-linear system is solved. The complete solution of the coupled non-linear system will be treated in a future work.

Non-linear free vibration analysis of laminated orthotropic cylindrical shells

A method to predict the influence of geometric non-linearities on the natural frequencies of an empty laminated orthotropic cylindrical shell is presented in this paper. It is a hybrid of finite element and classical thin shell theories. Sanders—Koiter non-linear and strain-displacement relations are used. Displacement functions are evaluated using linearized equations of motion. Modal coefficients are then obtained for these displacement functions. Expressions for the mass, linear and non-linear stiffness matrices are derived through the finite element method (in terms of the elements of the elasticity matrix). The uncoupled equations are solved with the help of elliptic functions. The frequency variations are first determined as a function of shell amplitudes and then compared with the results in the literature.

NON-LINEAR DYNAMIC ANALYSIS OF ORTHOTROPIC OPEN CYLINDRICAL SHELLS SUBJECTED TO A FLOWING FLUID

A theory is presented to predict the influence of non-linearities associated with the wall of the shell and with the fluid flow on the dynamics of elastic, thin, orthotropic and non-uniform open cylindrical shells submerged and subjected simultaneously to an internal and external fluid. The open shells are assumed to be freely simply supported along their curved edges and to have arbitrary straight edge boundary conditions. The method developed is a hybrid of thin shell theory, fluid theory and the finite element method. The solution is divided into four parts. In part one, the displacement functions are obtained from Sander's linear shell theory and the mass and linear stiffness matrices for the empty shell are obtained by the finite element procedure. In part two, the modal coefficients derived from the Sanders–Koiter non-linear theory of thin shells are obtained for these displacement functions. Expressions for the second and third order non-linear stiffness matrices of the empty shell are then determined through the finite element method. In part three, a fluid finite element is developed; the model requires the use of a linear operator for the velocity potential and a linear boundary condition of impermeability. With the non-linear dynamic pressure, we develop in the fourth part three non-linear matrices for the fluid. The non-linear equation of motion is then solved by the fourth-order Runge–Kutta numerical method. The linear and non-linear natural frequency variations are determined as a function of shell amplitudes for different cases.

Off shell πN amplitude and the pp → ppπ0 reaction near threshold

We have used a conventional model for the pp → ppπ 0 reaction consisting of the Born term plus the s-wave rescattering term. As a novelty we have introduced the off shell dependence of the πN s-wave isoscalar amplitude. This amplitude is appreciably enhanced when one moves to the off shell situations met in the problem and, as a consequence, the pp → ppπ 0 cross section becomes considerably larger than with the use of the πN on shell amplitudes. Two different models for the off shell extrapolation found in the literature have been used and the cross sections obtained are large enough to account for the experimental data, although uncertainties remain due to the incomplete knowledge of the off shell extrapolation.

Anisotropy of the photoelectron mean free path and its influence on the EXAFS amplitude

The anisotropy of the inelastic mean free path (MFP) for electrons with energies between approximately 10-1000 eV has been studied for the first time in ReO3, NaWO3 and TiO crystals. The MFP was calculated within the one-plasmon and local density approximations from the imaginary part of the complex energy-dependent exchange and correlation potential of the Hedin-Lundqvist type. It is shown that the MFP in compounds with a highly anisotropic electron density distribution, such as ReO3 and NaWO3, differs in various crystallographic directions from the MFP calculated for the averaged electron density. In particular, it was found that in the ReO3 crystal, the MFP values in (100) directions coincide with those for a spherically averaged cluster potential and are approximately 1 AA smaller than in (110) and (111) directions. This result explains the variation of the outer shell amplitudes in the Re L3-edge EXAFS in ReO3.

Further results on multifractality in shell models

Very long integrations, involving hundreds of millions of time steps, have been performed for the Gledzer–Ohkitana–Yamada ‘‘shell model’’ of fully developed turbulence, thereby allowing the computation of essentially noise-free structure functions at all inertial- and dissipation-range scales. Previously reported results by Jensen et al. [Phys. Rev. A 43, 798 (1991)] on the multifractal behavior of this model are confirmed. Oscillations in the structure functions are found to be genuine. An exact relation for certain cubic moments, equivalent to Kolmogorov’s four-fifth law, is derived and tested. The third-order structure function, here defined in terms of the third moment of shell amplitudes, is not directly determined by this relation and need not have its exponent equal to one. Significant discrepancies are actually found when the ratio between successive shell wave numbers is less than two.

Extended X-Ray Absorption Fine Structure study of Potassium Niobate

AbstractExtended x-ray absorption fine structure (EXAFS) of potassium niobate (KnbO3 ) was measured at the K edge of Nb, at various temperatures to include all phases of the material. The first shell data were analyzed to determine the distances between the niobium atom and its oxygen neighbors. The single shell amplitude almost vanishes around k-7.5 A−1 at all temperatures, suggesting two distances with a separation of about 0.21 A. Nonlinear fitting was used to determine the structure more carefully and the data at all temperatures can be fit reasonably well with two Nb-O ditances. This is in disagreement with the displacive model which implies only one Nb-O distance in the cubic phase. This result suggests that the niobium atom is displaced along the (111) direction relative to the oxygen atom in all phases. Thus, the transitions are not displacive, but have a strong order-disorder character.

Exact three-dimensional reduction of the Bethe-Salpeter equation

The partial-wave Bethe-Salpeter equation in the ladder approximation is converted into a set of two one-dimensional equations. The resulting reduced equations determine two off-energy-shell, on-mass-shell amplitudes, one for the scattering of two positive-energy and the other for two negative-energy particles. The connection between the potentials of the reduced equations and the many-particle intermediate states is displayed by their series expansion. Two versions of the equations which are convenient for numerical computations are also obtained, and one of them is a one-channel equation which involves only the physical amplitude for the scattering of two positive-energy particles. The potentials are determined by auxiliary equations which are two dimensional but nonsingular and exactly solvable by standard numerical methods. One of the results of the derivation of the reduced equations is a set of reduction relations which express the off-mass-shell amplitude as a functional of a restricted shell amplitude.

Impact Parameter Representation for Forward and Backward Scattering of Two Particles

The Lippman–Schwinger equation is solved to obtain an impact parameter representation for the forward and backward scattering. The Blankenbecler and Goldberger type amplitude is obtained in the high energy limit without any angular restriction. Then, the off energy shell amplitude in the forward and backward cone is obtained, which reduces to Glauber form on the energy shell. Finally, unitarity restriction and the scope of the formalism are discussed.

Mandelstam representation in potential scattering

A new simplified proof of the Mandelstam representation in potential scattering is given. It is stressed that only on the mass shell amplitudes are needed throughout the proof.