Illusions of vision: Interpretation within the framework of a holographic model

Several illusions of vision are considered on the basis of a neurophysiological holographic model of visual perception at the level of the eye’s and the retina. It is suggested that the eye’s optical system forms a spatial spectrum of the observed object rather than its image on the retina. The spectrum is encoded by active anisotropic quasi-crystalline structures of rod rhodopsins and cone iodopsins, and a complex Fourier hologram of the observed object consisting of two quadrature components is recorded. The holographic hypothesis is confirmed by the results obtained by digital simulation.     

Super-transfer within the fragmentation theory of heavy-ion collisions

With the mass-asymmetry described by the dynamical collective fragmentation coordinateη, relevant collective potentials and mass parameters in heavy-ion fusion and collision processes calculated for the U-U system are considered and the structure of the collective Hamiltonian is examined. Conclusions on supertransfer leading to the eventual formation of superheavy elements are indicated.     

A framework for iterative analysis of non-classically damped dynamical systems

In this paper, we propose a general iterative framework to solve the dynamic problem for linear systems with non-classical viscous damping. A systematic approach is used to derive families of stationary iterative schemes that, as an instance of particular interest, decouple the equations of motion for numerical study of the system response. For such schemes, we present a detailed convergence analysis and propose several solution strategies suitable for a broad class of systems. These techniques are based on spectral analysis of particular iteration matrices arising in the derivation and aim at optimizing the convergence performance of the method. We demonstrate that the proposed systematic framework, based on a novel application of the homotopy analysis method, generalizes iterative schemes previously reported in the literature and, importantly, provides a unified perspective for the study of iterative solutions of dynamic problems. Further, we establish a connection between our results and the theory of iterative schemes for algebraic linear systems, thus providing insights on convergence results and applicability of the method. Numerical examples illustrate the effectiveness of the approach and indicate future research directions.     

Exact solution in the damped Cummings-Tavis model and entanglement

An exact analytical expression is found for the density matrix of a system composed of a photon mode and two two-level dipole-dipole interacting atoms in a cavity with losses. The behavior of the atom-atom entanglement has been investigated on the basis of the Peres-Horodecki criterion.     

Intramolecular association within the SAFT framework

A general theory for modelling intramolecular association within the SAFT framework is proposed. Sear and Jackson [Phys. Rev. E. 50 (1), 386 (1994)] and Ghonasgi and Chapman [J. Chem. Phys. 102 (6), 2585 (1995)] have previously extended SAFT to include intramolecular association for chains with two sites. We show that the resulting equations from the two approaches are equivalent, and use their work as a basis for developing a new general theory. The approach used by Ghonasgi and Chapman is based on mass balances and an infinite dilution result and provides the equations needed to determine the contribution to the Helmholtz free energy from association (inter- as well as intramolecularly) at equilibrium. Sear and Jackson rederived the contribution to the Helmholtz free energy from association from the theory by Wertheim [J. Stat. Phys. 42 (3–4), 459 (1986)] with inclusion of intramolecular association, and using this approach we obtain an expression for the Helmholtz free energy that is valid also at non-equilibrium states (with respect to hydrogen bonds), which is very useful when calculating derivatives.     

Quantisation of the string fragmentation model

We quantise the classical Artru-Mennessier string model with a Feynman sum over histories method. This procedure yields both propagation amplitudes and a Veneziano mass spectrum for mesons, with resonance poles for unstable states. Applied to the processe ⁺ e ^?→hadrons our amplitudes justify previous applications of string models and in particular the relative amplitudes for different string configurations are in agreement with a recent conjecture of Andersson and Hofmann which can account for the observed Bose-Einstein correlations ine ⁺ e ^? annihilation.     

A complex symplectic model for the damped oscillator

The linearly damped harmonic oscillator is described by a hamiltonian complex manifold. The master equation for the complex eigenstates of the quantized hamiltonian is found.     

A discrete model of damped acoustic metamaterials

For damped acoustic metamaterials, a discrete model is proposed in the form of a periodic structure with cells of the simplest type. The effective parameters of the model are determined by criteria based on the equality of dispersion of waves. The general properties of the model are studied. An example of one negative type of metamaterials is presented. The model is useful for analyzing wave properties and creating metamaterials with given acoustic properties.     

Calculations of the propagator within the tomographic-probability framework

We show that the ambiguity in choosing the tomographic propagator for an evolving linear quantum system is related to the homogeneity properties of the system symplectic tomogram. We study in detail an example of the driven harmonic oscillator. We prove that two formally different propagators of the quantum kinetic equation for the oscillator are identical on the domain of homogeneous tomographic probability distributions.     

On the core width and Peierls stress of bubble rafts dislocations within the framework of modified Peierls-Nabarro model

Using Foreman’s method, the core structure and Peierls stress of dislocations in bubble rafts have been investigated within the framework of the modified Peierls-Nabarro (P-N) model in which the discrete lattice effect is taken into account. The core width obtained from the modified P-N model is much wider than that from the P-N model owing to the discrete lattice effect. It is found that the core width of dislocation increases with a decrease of the bubble radius. The elastic strain energy associated with the discrete effect is considered while calculating the Peierls stress. The new expression of the Peierls stress obtained in this paper is not explicitly dependent on the particular form of the restoring force law, which is only related to the core structure parameter and can be used expediently to predict the Peierls stress of dislocations. The Peierls stress decreases rapidly with the decrease of the bubble radius.     

Evaluation of the single ionisation transition amplitude using the CDW-EIS model within the framework of the impact-parameter method

The continuum distorted-wave model with an eikonal initial state for ionisation is discussed within the framework of the impact-parameter method. Particular attention is paid to the surface term, which describes the transition by a distorting potential, and which has been omitted in all of the previous calculations performed using the model. However, this term is included in the transition amplitude in a recent application of the model based upon a quantum-mechanical treatment. The present study, in which the surface term is evaluated within the impact-parameter method, shows that this term does not contribute to the transition amplitude. In describing the electron-ejection mechanism for a p^±–H collision, the cross-sections evaluated using the impact-parameter model show numerical agreement with those determined in the quantum-mechanical version. This agreement indicates that the contribution of the surface term calculated in the wave treatment is negligible over the region in which the impact-parameter model is valid.     

A mechanical model for weakly damped solitons

A simple mechanical model permits to recover the main properties of adiabatically weakly damped solitons which may be described in terms of a particle in a potential well. The adiabatic damping rate and the tail amplitude are obtained. Three examples are chosen which cover a wide field of nonlinear physics.     

Bipartite entanglement within the framework of real and ideal lasers

We study the nonlocal correlations and quantum entanglement for two deformed bosonic fields of arbitrary deformation parameters, q ₁ and q ₂, prepared in an entanglement of deformed coherent states. As a measure of entanglement, we use the von Neumann entropy and investigate its behavior for different strength regimes of the optical fields. We find that the photon number can enhance the von Neumann entropy, and the deformation parameters can restrain the system entanglement.     

Analysis of transverse momentum distributions forpp interactions at 360 GeV/c in the framework of a quark-diquark fragmentation model

Using a quark-diquark fragmentation model, in which either the Field-Feynman or the Lund model is coupled with a quark-diquark distribution function, we study transverse momentum distributions,p _T, for the inclusive reactionspp→hadron +anything at 360 GeV/c. We find that a primordial mean transverse momentum 〈k _T〉?0.4 GeV/c can well reproduce thep _T ² distributions of charged hadrons, π⁰,K _s ⁰ , Λ⁰,K ^* and Σ^* and the Feynmanx?p _T correlations. We confirm that a diquark in a proton plays an important rôle in reproducing thex?p _T correlation of Λ⁰.     

Inclusive projectile fragmentation in the spectator model

Grazing-angle singles spectra for projectile fragments from nuclear collisions exhibit a broad peak centered near the beam velocity, suggesting that these observed fragments play only a “spectator” role in the reaction. Using only this spectator assumption (but not DWBA), we find that a “prior form” formulation of the reaction leads, via closure, to a 〈ψ∥W∥ψ〉-type estimate of the inclusive spectator spectrum, thus relating it to the reaction cross section for the “participant” with the target. We show explicitly that this expression includes an improved multi-channel version of the Udagawa-Tamura formula for the “breakup-fusion” or incomplete-fusion cross section, and identifies it as the fluctuation part of the participant-target reaction cross section. A Glauber-type estimate of the distorted wave functions which enter clearly shows how the width of the peak in the spectator spectrum arises from the “Fermi motion” within the projectile, as in the simpler Serber model, but is modified by the “overlap geometry” of the collision.