Generic Dynamics of 4-Dimensional C 2 Hamiltonian Systems

We study the dynamical behaviour of Hamiltonian flows defined on 4-dimensional compact symplectic manifolds. We find the existence of a C ²-residual set of Hamiltonians for which there is an open mod 0 dense set of regular energy surfaces each either being Anosov or having zero Lyapunov exponents almost everywhere. This is in the spirit of the Bochi-Mañé dichotomy for area-preserving diffeomorphisms on compact surfaces [2] and its continuous-time version for 3-dimensional volume-preserving flows [1].     

Structural considerations for elastic magnetic electron-nucleus scattering

To explain the form factors obtained by magnetic electron scattering on ¹⁷O it is clear that core polarization has to be taken into account. We discuss how this can be done by means of the Hartree-Fock theory. We note that projection from an intrinsic state of definite K gives an incorrect answer for weakly deformed systems such as ¹⁷O and we present an alternative procedure for extracting the moments. Using a purely velocity dependent Skyrme interaction (only t₀ and t₁ are non-zero) a Hartree-Fock calculation is carried out for the seventeen-nucleon system. The calculation leads to a suppression of the M3 form factor. It is emphasized that the suppression arises from the fact that not only is the ¹⁶O core deformed, but that spin-up particles have a different deformation than spin-down particles. This arises from the spin dependence of the interaction and from the Pauli principle. A peculiar feature with the interaction that is used is that the M5 form factor gets enhanced. This is attributed to the repulsive velocity dependent term in the interaction. The origin of the velocity dependence is discussed. The effect of the velocity dependence on the magnetic moment operator is also considered.     

General Volume-Preserving Mechanical Systems

We present the general form of equations that generate a volume-preserving flow on a symplectic manifold M, ) via the highest Euler–Lagrange cohomology. It is shown that for every volume-preserving flow there are some 2-forms that play a similar role to the Hamiltonian in Hamilton mechanics. The ordinary canonical equations are included as a special case with a 2-form 1/(n - 1)H, where H is the corresponding Hamiltonian.     

Random pseudofractal networks with competition

In this paper, we present a simple rule which assigns fitness to each edge to generate random pseudofractal networks (RPNs). This RPN model is both scale-free and small-world. We obtain the theoretical results that the power-law exponent is γ=2+1/(1+α) for the tunable parameter α>-1, and that the degree distribution is of an exponential form for others. Analytical results also show that an RPN has a large clustering coefficient and can process hierarchical structure as C(k)∼k^-1 that is in accordance with many real networks. And we prove that the mean distance L(N) scales slower logarithmically with network size N. In particular, we explain the effect of nodes with degree 2 on the clustering coefficient. These results agree with numerical simulations very well.     

High-mass diffraction and Regge behavior of total cross sections

We consider a modified two-component model of particle production in which diffractive excitation into high mass states gives a contribution to K^±p, π^±p and pp total cross sections of sufficient magnitude and with the proper associated threshold to be a possible explanation of deviations of σ_tot from Regge pole model fits at Serpukhov energies. We present tests of the model. for K⁺p scattering by extrapolating σ_tot to National Accelerator Laboratory energies and by calculating the high mass diffraction contribution to the forward peak in inclusive reactions. The consistency of this scheme is discussed in relation to the pomeron intercept and the form of the triple-pomeron coupling.     

Instabilities of massive scalar perturbations of a rotating black hole

We study the stability of a massive scalar field in the exterior metric of a rotating Kerr black hole. An argument based on energy conservation shows, under some strong technical assumptions, that unstable normal modes exist. These unstable modes can be interpreted as wave packets in bound, superradiant orbits. A JWKB estimate of the fastest growth rate gives 10^?7M^?1exp(?1.84Mμ) in the case Mμ ? 1, where M is the mass of the hole and μ is the mass of the field. The existence of unstable normal modes has significant implications for quantum particle creation by rotating black holes, which we attempt to assess.     

The linked dipole chain model for DIS

The Linked Dipole Chain Model provides an interpolation between the regions of high Q² (DGLAP) and low x moderate Q² (BFKL) in DIS. It is a reformulation and a generalization of the results obtained by Ciafaloni, Catani, Fiorani and Marchesini, and it gives a unified treatment of “normal DIS”, boson-gluon fusion events and hard subcollisions in resolved photon-proton scattering. Thus the formalism provides a complete picture which incorporates all hard or semihard hadronic interactions in a simple way, which is suitable for a Monte Carlo treatment of both structure functions and final state properties. We also discuss non-leading effects which significantly reduce the increase of the structure function for very small x-values.     

The deuteron wave function at short range and the triton

It is shown that if one assumes something between zero and the prediction of the scaling model with dipole fit for the neutron electric form factor, then a variety of short-range behaviour for the deuteron wave function is consistent with existing experimental data on the deuteron electric form factor. This still relatively wide latitude for the inner deuteron wave function, consistent with existing experimental electromagnetic data, gives rise to an off-shell variation of approximately 1.2 MeV in the triton binding energy with a fixed ¹S₀ interaction and a P_D varying from 4.5 to 6.5 %. Interactions with greater densities of matter at short range bind the triton more strongly and closer to the experimental value. An off-shell variation of 0.7 MeV is obtained with a fixed p_d and singlet interaction. However, a single measurement of the deuteron tensor polarization at about q² = 20 fm^?2 would severely restrict this variation.     

Entropy Bounds in R×S Geometries

Exact calculations are given for the Casimir energy for various fields in R×S³ geometry. The Green's function method naturally gives a result in a form convenient in the high-temperature limit, while the statistical-mechanical approach gives a form convenient for low temperatures. The equivalence of these two representations is demonstrated. Some discrepancies with previous work are noted. In no case, even for N=4 SUSY, is the ratio of entropy to energy found to be bounded. This deviation, however, occurs for low temperature, where the equilibrium approach may not be relevant. The same methods are used to calculate the energy and free energy for the transverse electric modes in a half-Einstein universe bounded by a perfectly conducting 2-sphere.     

Slow-roll freezing quintessence

We examine the evolution of quintessence models with potentials satisfying ²(V^′/V)?1 and V^″/V?1, in the case where the initial field velocity is nonzero. We derive an analytic approximation for the evolution of the equation of state parameter, w, for the quintessence field. We show that such models are characterized by an initial rapid freezing phase, in which the equation of state parameter w decreases with time, followed by slow thawing evolution, for which w increases with time. These models resemble constant-V models at early times but diverge at late times. Our analytic approximation gives results in excellent agreement with exact numerical evolution.     

Isovector kaon form factor in the dispersion theory and S-wave π K-scattering lengths

A one-dimensional integral representation for isovector kaon form factor is constructed within the dispersion theory in terms of the pion form factor and the backwardπK-scattering amplitude. The normalization condition for isovector kaon form factor at zero momentum transfer gives a sum rule for theπK-scattering amplitude, with the use of which difference between thes-waveπK-scattering lengths in triplet and singlet isospin states is estimated to bea ₀ ^3/2 - a ₀ ^1/2 ≈μ ^{? 1} whereμ is the pion mass. In agreement with the vector-meson-dominance model, deviations of the isovector kaon form factor from half of the pion form factor are found to be small.     

On the applicability of finite order perturbative QCD calculations of jet rates ine + e − annihilation

We have studied the measurement of α _s using exact second order QCD matrix element calculations of jet rates ine ⁺ e ^?→hadrons. We investigate the dependence of α _s (M _Z ² ), measured by experiments at theZ ⁰ resonance, on the choice of renormalisation scale in terms of the functional form of the three-jet matrix element. We find that only a restricted domain of the jet resolution parametery _c , $\Lambda _{\overline {MS} } $ , and scale gives a perturbation series which is well-behaved to second order, and that this domain is different for the various jet algorithms in current use.     

A Combined Study of the Pion’s Static Properties and form Factors

We study consistently the pion’s static observables and the elastic and γ* γ → π ⁰ transition form factors within a light-front model. Consistency requires that all calculations are performed within a given model with the same and single adjusted length or mass-scale parameter of the associated pion bound-state wave function. Our results agree well with all extent data including recent Belle data on the γ* γ → π ⁰ form factor at large q ², yet the BaBar data on this transition form factor resists a sensible comparison. We relax the initial constraint on the bound-state wave function and show the BaBar data can partially be accommodated. This, however, comes at the cost of a hard elastic form factor not in agreement with experiment. Moreover, the pion charge radius is about 40 % smaller than its experimentally determined value. It is argued that a decreasing charge radius produces an ever harder form factor with a bound-state amplitude difficultly reconcilable with soft QCD. We also discuss why vector dominance type models for the photon-quark vertex, based on analyticity and crossing symmetry, are unlikely to reproduce the litigious transition form factor data.     

A correlated majority model

We extend and solve analytically a bichromatic majority model including color correlation between nearest neighbor plaquettes. The behaviour of the one color, say black, dominant cluster size is studied as a function of the black concentration and the correlation degree. This mean value shows a divergence with a critical exponent v. We also define an order parameter m for the model whose critical exponent is β. We find v = β = 1 independent of the correlation degree. We present a Monte Carlo simulation of the process which gives a good agreement with the theoretical results.     

One-body dissipation and nuclear dynamics

We discuss recent developments in the “one-body” dissipation theory described in B?ocki et al. [Ann. Phys. (N.Y.)113 (1978), 330]. The principal new result is the derivation of the functional form of the dissipation expression (the Rayleigh Dissipation Function) for a finite idealized nucleus with a diffuse surface, in the form of an expansion in powers of the dimensionless ratio of the surface diffuseness to the size, R, of the system. The leading term in such an expansion is a surface contribution, of relative order R², in the form of the “Wall Formula” of B?ocki et al. The next is a curvature correction of order R. At the next level (R⁰) there are two higher order curvature corrections and a correction for the presence of gradients in the normal velocity field specifying the motion of the surface. For simple models of the nuclear surface profile we work out analytically the coefficients in the curvature and velocity-gradient correction terms. We compare the one-body dissipation theory formulated in this way with recent linear-response and Time-Dependent Hartree-Fock treatments of the nuclear problem. The principal theme that emerges from this study is the close analogy between the problem of the nuclear macroscopic dissipation function and the problem of the nuclear macroscopic potential energy.     

Calculated rotational transition probabilities for the A−X system of OH

Transition probabilities have been calculated as a function of vibrational and rotational level for the A²Σ⁺?X²π_i system of the hydroxyl molecule. The wavefunctions are obtained from RKR calculations. The electronic transition moment is constructed by adding a small hyperbolic tail at large internuclear distance r (taken from an ab initio calculation) to a linear form at small r; this linear form was validated in earlier studies by laser-excited fluorescence measurements, calculations, and an examination of literature data. The results show, as anticipated, a variation in transition probability with rotatinaal quantum number J, the degree of which varies with vibrational band. The widely used results of Anketell and Learner, based on an inferior form of the transition moment, are accurate to within about 10% for the range J = 0?20 within a given vibrational band, although not from band to band.     

Heterolayer mobility in the Bloch-Grüneisen range

It is shown that, for two-dimensional heterolayer conduction at low temperatures, the phonon-scattering contribution to the reciprocal of the ohmic mobility has a Bloch-Grüneisen regime, for low enough temperatures T, in which the deformation coupling gives a term proportional to T⁷ and (for polar semiconductors) piezoelectric coupling gives a term proportional to T⁵. It is pointed out that there could be an intermediate temperature range with a slower T dependence.     

Euler elasticae in the plane and the Whitney-Graustein theorem

In this paper, we study normal forms of plane curves and knots. We investigate the Euler functional E (the integral of the square of the curvature along the given curve) for closed plane curves, and introduce a closely related functional A, defined for polygonal curves in the plane ?² and its modified version A _R , defined for polygonal knots in Euclidean space ?³. For closed plane curves, we find the critical points of E and, among them, distinguish the minima of E, which give us the normal forms of plane curves. The minimization of the functional A for plane curves, implemented in a computer animation, gives a very visual approximation of the process of gradient descent along the Euler functional E and, thereby, illustrates the homotopy in the proof of the classical Whitney-Graustein theorem. In ?³, the minimization of A _R (implemented in a 3D animation) shows how classical knots (or more precisely thin knotted solid tori, which model resilient closed wire curves in space) are isotoped to normal forms.