An interaction potential for heavy-ion scattering

The long-range part of the nucleus-nucleus interaction is taken to be given by folding the density distribution of one nucleus with the real part of the single-nucleon optical potential of the other. Analytic approximations are derived for the folded potential and its derivative in the case where the density distribution and single-nucleon optical potential have Saxon-Woods form factors of equal surface thickness. The approximations are generalised to the case of different surface thicknesses and are compared with a previous parametrisation due to Broglia and Winther. The variation with mass number of the central density of the Saxon-Woods matter distribution required to obtain the correct normalisation is shown to be large and an expression for the variation is given. Some calculations are performed on various elastic scattering data using the “quarter-point recipe” of Frahn's diffraction theory. The parameters required to fit the quarter-points of the elastic cross sections are shown to be consistent with their accepted values. It is shown, however, that the quarter-point recipe leads to a larger radius for ²⁰⁸Pb than for ²³²Th. The positions and heights of the pure Coulomb barrier (L = 0) are evaluated for various nuclei. The barrier radii are found to be sufficiently large to suggest that an interaction of the folded type should be reasonable in this region.     

Plane Symmetric Viscous Fluid Cosmological Models with Varying <Emphasis Type="Italic">Λ</Emphasis>-Term

Plane symmetric viscous fluid cosmological models of the universe with a variable cosmological term are investigated. The viscosity coefficient of bulk viscous fluid is assumed to be a power function of mass density whereas the coefficient of shear viscosity is to be proportional to rate of expansion in the model. We have also obtained a special model in which the shear viscosity is assumed to be zero. The cosmological constant Λ is found to be a decreasing function of time and a positive which is supported by results from recent supernovae Ia observations. Some physical and geometric properties of the models are also discussed.     

Numerical simulation of experiments on turbulent natural convection of heat generating liquid in cylindrical pool

Available experimental data on heat transfer of a melt with volumetric heat generation are analyzed in order to use them for validating the computer codes that describe a core catcher. The problem for CFD simulation of the experiments on heat transfer by laminar and turbulent natural convection is described. Information that can be obtained from experiments for verifying the models of convective heat transfer in a melt is analyzed. The effect of variable viscosity on the integral heat flux is discussed. Calculation results are represented and compared with experimental data on temperature distribution and integral heat transfer. The calculations are in good agreement with the experiment. The results are numerically extrapolated to the range of Rayleigh numbers up to 7 · 10¹⁶. It is concluded that the CFD calculations with the κ-ɛ turbulence model can be used in problems concerned with analysis of melt convection in a core catcher.     

Ground-state magnetovolume effects in alloys

We present a general theory for the magnetic contribution to the lattice parameters of ferromagnetic alloys of type A_χB_1?χ. This contribution is obtained as a function of χ. Calculations are given for the Fe-Co alloys and are in reasonable agreement with experiment. General trends in transition metal alloys are also found to be in agreement with the theory. The connection of the magnetovolume effect with the local moments on the various atoms is stressed. The effect is seen to be a sensitive probe of local magnetic order.     

The multiple scattering and N-body approaches to nuclear reactions

The relationship between conventional multiple scattering approaches and the recently developed N-body approaches to nuclear reactions is considered with a view towards elastic scattering applications. Connectivity expansions in the N-body approach and multiple scattering expansions in the Watson approach are developed by a common technique so that a comparison of the physical content of each can be made. In the N-body case this leads to a new derivation of the equations of Bencze, Redish, and Sloan in both particle-labelled and partition-labelled form and this yields new insight into the minimal dimensionality of these equations and into the role of channel coupling schemes within this formulation. The relative simplicity and generality with which these results are obtained is designed to be easily understood by those unfamiliar with N-body formalisms. The two approaches are contrasted first for the three-particle problem and subsequently for the many-body problem. We argue that a strict adherence to the connected-kernel property which is advantageous for the three-particle problem may not be so advantageous for the many-body elastic scattering problem. Undesirable physical characteristics of the connectivity expansion for elastic scattering are identified and their rectification is discussed. The off-shell transformation associated with the N-body approach is examined critically. The origin of the multiplicity of N-body coupling schemes is elucidated. It is shown that a modified concept of connectivity, called inclusive connectivity, can be introduced to guide expansions which can be truncated in a physically meaningful way. The inclusive connectivity expansion is seen to be identical to the spectator expansion for an elementary projectile but differs in the case of a composite projectile. Extant elastic scattering optical potential formulations based on the two concepts of connectivity are compared and contrasted. We show that connected kernel integral equations of the few-body type are required for computation of the individual low-order terms of the inclusive connectivity expansion of the optical potential.     

Intermittency and correlations in hadronic Z^0 decays

A multidimensional study of local multiplicity fluctuations and multiparticle correlations of hadrons produced in Z decays is performed. The study is based on the data sample of more than events recorded with the OPAL detector at LEP. The fluctuations and correlations are analysed in terms of the normalized scaled factorial moments and cumulants up to the fifth order. The moments are observed to have intermittency-like behaviour, which is found to be more pronounced with increasing dimension. The large data sample allows for the first time a study of the factorial cumulants in annihilation. The analysis of the cumulants shows the existence of genuine multiparticle correlations with a strong intermittency rise up to higher orders. These correlations are found to be stronger in higher dimensions. The decomposition of the factorial moments into lower-order correlations shows that the dynamical fluctuations have important contributions from genuine many-particle correlations. The Monte Carlo models Jetset 7.4 and Herwig 5.9 are found to reproduce the trend of the measured moments and cumulants but they underestimate the magnitudes. The results are found to be consistent with QCD jet formation dynamics, although additional contributions from other mechanisms cannot be excluded. Received: 8 February 1999 / Published online: 8 September 1999     

Stabilization of skyrmions via ϱ-mesons

It is shown that a skyrion can be stabilized by introducing ?-mesons into the chiral SU(2)_L × SU(2)_R lagrangian without higher-derivative terms like the Skyrme term. The ?-mesons are considered as dynamical gauge bosons associated with a hidden local symmetry of the non-linear sigma model. The lagrangian reduces to the Skyrme model in a limit of parameters. The Skyrmion mass M is found to be M = 1058 MeV when the parameters are fixed so as to satisfy the KSRF relation. It is also shown that a solition solution in a model with Ω-meson coupled with the baryonic current is a saddle-point solution.     

Banach spaces of weights on quasimanuals

Section 1 is a brief introduction. Section 2 contains the basic definitions of quasimanuals, weights, and operational logics. The linear spaceW of all weights on a quasimanualA is introduced and given a norm.W with this norm is seen to be a Banach space. The subspaceV ofW generated by the positive cone ofW is given the base norm and is also shown to be an Archimedian ordered Banach space with an additive norm. In Section 3 normal linear functionals onV ^* are defined in analogy with normal linear functionals onw ^* algebras. The spaceV is shown to be the set of normal functionals onV ^* and we showV to be the unique partially ordered Banach space with a closed generating cone which is predual toV ^*. Next, weakly compact subsets ofW are characterized in terms of eventwise convergence. This is the Hahn-Vitali-Saks theorem of classical measure theory in this noncommutative setting; several weak compactness results are drawn from this and compared with their classical counterparts. Section 4 introduces the ultraweak topology forV ^* in analogy with the same for the trace class operators on Hubert space. Here the condition for a compact base for the cone ofV is examined and shown to be a poor and unnecessary hypothesis in many circumstances. Many connections with the existent literature are made and throughout the paper there are many examples and open questions.     

A schematic model for monopole and quadrupole pairing in nuclei

A schematic Hamiltonian with a pairing interaction plus a quadrupole-quadrupole interaction between nucleons is presented. It is shown that all the states of the fermion system can be classified according to the number of nucleons u not coupled to coherent monopole or quadrupole pairs. The states with u = 0 are shown to have a one-to-one correspondence to the states of the interacting boson model. The spectra for these states are derived analytically for various limits of the pairing strength and the quadrupole strength. Analytical forms for the matrix elements of operators are derived for these limits. The operators in fermion space are mapped onto boson operators. The matrix elements of operators in the fermion space are shown to be equal to matrix elements of the boson operators multiplied by analytical Pauli factors which are state dependent. The two-nucleon transfer strength is calculated in two limits and is compared to experimental values.     

Aging kinetics of porous media due to freezing-thawing cycles

The two-dimensional Ausloos et al. model of fluid invasion, freezing and thawing in a porous medium is elaborated upon and investigated in order to take into account the pore volume redistribution and conservation during freezing. The results are qualitatively different from previous work, since the damaged pore sizes are found to be much less than the possible maximum value and is reached after a large number of invasion-freezing-thawing cycles, e.g. the material is “slowly damaged”. The pore size distribution is thus found in better agreement with expected practical findings. The successive invasion percolation clusters are still found to be self-avoiding with aging. The cluster size decreases with a power law as a function of invasion-frost-thaw iterations. The aging kinetics is also discussed through the normalized totally invaded pore volume. Received 24 September 1999 and Received in final form 5 January 2000     

Atomic N00N state generation in distant cavities by virtual excitations

A general scheme of generating N00N states of virtually-excited 2N atoms is proposed. The two cavities are fibre-connected with N atoms in each cavity. Although we focus on the case of N=2, the system can be extended to a few atoms with N>2. It is found that all 2N atoms can be entangled in the form of N00N states if the atoms in the first cavity are initially in the excited states and atoms in the second cavity are all in the ground states. The feasibility of the scheme is carefully discussed, it shows that the N00N state with a few atoms can be generated with good fidelity and the scheme is feasible in experiment.     

Linearized gravitation theory in macroscopic media

The refraction of gravitational waves is discussed by developing a macroscopic theory of gravitation along the lines of classical electromagnetism. It is shown that the linearized Bianchi identities may be expressed in a form which is suggestive of Maxwell's equations with magnetic monopoles. The medium is then assumed to be corpuscular in structure and it is shown how, on performing an averaging process on the field quantities, the Bianchi identities must be modified by the inclusion of polarization terms resulting from the induction of quadrupole moments on the individual “molecules”. A model of a medium whose molecules are harmonic oscillators is discussed and constitutive equations are derived. Gravitational waves are demonstrated to slow down in such a medium.     

Model studies of the interaction of h atoms with bcc iron

Ab initio/effective core potential cluster studies are reported for the interaction of H atoms with bcc iron. The calculations use a one-electron ECP based on the 4s¹3d⁷ state of the Fe atom. Two-fold and four-fold sites on the (100) surface as well as octahedral, tetrahedral, and trigonal interior sites were studied. Four-fold surface sites are found to be bound by ~1.5 eV with the H atom ~ 0.5a₀ above the surface. Penetration of the surface at a four-fold site involves movement toward a second layer atom and is expected to be unfavorable. Two-fold surface sites have small binding energies ～ 0.25 eV. Penetration of the surface at this site involves movement toward a tetrahedral interior site and is downhill in energy. Tetrahedral interior sites are found to be bound by ～1.3 eV and are a minimum on the potential energy surface. Octahedral sites are a maximum on the potential energy surface and are estimated to be ～ 0.2 eV higher (including lattice relaxation effects). Trigonal sites are found to be a saddle point connecting adjacent tetrahedral sites and this pathway leads to an estimated barrier to diffusion of ～ 0.1 eV (including lattice relaxation effects). The volume expansion for a H atom in a tetrahedral site is calculated to be 21%.     

Effect of varying two key parameters in simulating evacuation for a dormitory in China

Student dormitories are both living and resting areas for students in their spare time. There are many small rooms in the dormitories. And the students are distributed densely in the dormitories. High occupant density is the main characteristic of student dormitories. Once there is an accident, such as fire or earthquake, the losses will be cruel. Computer evacuation models developed overseas are commonly applied in working out safety management schemes. The average minimum widths of corridor and exit are the two key parameters affecting the evacuation for the dormitory. The effect of varying these two parameters will be studied in this paper by taking a dormitory in our university as an example. Evacuation performance is predicted with the software FDS + Evac. The default values in the software are used and adjusted through a field survey. The effect of varying either of the two parameters is discussed. It is found that the simulated results agree well with the experimental results. From our study it seems that the evacuation time is not in proportion to the evacuation distance. And we also named a phenomenon of “the closer is not the faster”. For the building researched in this article, a corridor width of 3 m is the most appropriate. And the suitable exit width of the dormitory for evacuation is about 2.5 to 3 m. The number of people has great influence on the walking speed of people. The purpose of this study is to optimize the building, and to make the building in favor of personnel evacuation. Then the damage could be minimized.     

Multicolor QCD as a dual-resonance theory

The quantum chromodynamics with massless quarks and an infinite number of colors is represented as a theory of the noninteracting mesons which lie on rising Regge trajectories. The perturbation theory for these trajectories is developed. The expansion parameter (effective coupling) is calculated and appears to be about $\text{1}\text{2}$. The expansion coefficients can also be calculated analytically as functions of spin and other quantum numbers. The calculations are carried through to the end in the zeroth and first order. The resulting trajectories look reasonable and are in qualitative agreement with experiment. The corrections from finite numbers of colors and from quark masses can also be found, but are not considered here.     

An investigation into the maximum entropy production principle in chaotic Rayleigh–Bénard convection

The hypothesis is made that the temperature and velocity fields in Rayleigh–Bénard convection can be expressed as a superposition of the active modes with time-dependent amplitudes, even in the chaotic regime. The maximum entropy production principle is interpreted as a variational principle in which the amplitudes of the modes are the variational degrees of freedom. For a given Rayleigh number, the maximum heat flow for any set of amplitudes is sought, subject only to the constraints that the energy equation be obeyed and the fluid be incompressible. The additional hypothesis is made that all temporal correlations between modes are zero, so that only the mean-squared amplitudes are optimising variables. The resulting maximal Nusselt number is close to experimental determinations. The Nusselt number would appear to be simply related to the number of active modes, in particular the number of distinct vertical modes. It is significant that reasonable results are obtained for the optimised Nusselt number in that the dynamics (the Navier–Stokes equation) is not used as a constraint. This suggests grounds for optimism that the maximum entropy production principle, interpreted in this variational manner, can provide a reasonable guide to the dynamic steady states of non-equilibrium systems whose detailed dynamics are unknown.     

Sticky spheres and related systems

Some properties of a system of hard-core particles with attractive wells in the Baxter sticky-sphere limit and a related limit are considered, as is the approach to these limits. A demonstration of the result of Stell and Williams that sticky spheres of equal diameter in the Baxter limit are not thermodynamically stable is given, and the way in which size polydispersity can be expected to restore thermodynamic stability is discussed. The implications of these results for the PY sticky-sphere approximation and recent sticky-sphere computer simulations are then examined. It is concluded that the Baxter PY sticky-sphere approximation for a monodisperse system may well be a reasonable one for a slightly polydisperse system of sticky spheres and that existing simulation results may also be relevant to such a system. How polydisperse a system must be in quantitative terms in order for the PY approximation to be useful remains to be seen, however. The question of whether the PY sticky-sphere approximation may prove to be useful and appropriate in describing monodisperse systems with pair potentials for which the attractive wells arenot extremely narrow is also considered; it is noted that firm evidence concerning this question also appears to be lacking. Implications for systems near, but not in, the limit of zero attractive-well width are also considered, especially in terms of the relative size of the well width and the degree of size polydispersity in the repulsive cores. The possible pertinence of such considerations to colloidal systems is observed. The importance of taking into consideration the extremely long equilibration times that can be expected for systems with very narrow attractive wells is also pointed out, in connection both with real colloidal systems and in computer simulations. It is further observed that in the Baxter limit sticky spheres described quantum mechanically are indistinguishable from hard spheres so described; near the zero-well-width limit, the quantal behavior hinges on the number of bound states and thus the well depth as well as the relative size of the de Broglie thermal wavelength and the well width. Related results and investigations relevant to the issues described above are cited.     

Theory of the optical properties of phonon systems with disordered force constants,with application to NH4Cl

A theory of systems with substitutional disorder is presented. The theory treats off-diagonal disorder and is thus suitable for application to systems with disordered force constants. An example of such a system, to which particular consideration is given, is NH₄Cl, which has a disordered phase in which the force constants between NH₄⁺ ions are disordered because there are two equally probable orientations of an NH₄⁺ ion within a unit cell. The effect of disorder, in particular the breakdown of k-conservation, on the optical properties of such systems is studied via a calculation of the single-particle Green's function. Both the optical absorption and Raman cross section are shown to be related to the self-energy of this Green's function, and expressions for these quantities are obtained which are exact to second order in the ratio of order-dependent to non order-dependent force constants. The major qualitative features of the expression for the Raman cross section are found to be in good agreement with existing Raman scattering data on NH₄Cl.     

Transmission properties in a one-dimensional finite extrinsic semiconductor InSb photonic crystal

The properties of wave transmission in a strongly dispersive semiconductor-dielectric photonic crystal (SDPC) are theoretically investigated. We consider a one-dimensional finite SDPC, air/(SD) ^N S/air, where, N is the stack number, S is an extrinsic semiconductor, n-type InSb (n-InSb), and D is a dielectric layer of SiO₂. Transmission peaks can be found in the frequency region where the real part of the complex permittivity of n-InSb is negative. The number of peaks is equal to the stack number N. The positions of peaks can be tuned by the thicknesses of S and D. The peaks are seen to be blue-shifted as the doping density increases, leading to a tunable filter. The locations of peaks are also strongly dependent on the incidence angle, but weakly dependent on the polarization of the incident wave. The results suggest that a tunable multichannel filter can be achieved by using such an SDPC. Filters with tunable and multichannel features are of technical use in photonic applications such as in the optical electronics and communications.     

Extremely high energy cosmic rays

The evidence for the existence of cosmic rays with energies in excess of 10²⁰ eV is now overwhelming. There is so far no indication of the GZK cutoff in the energy spectrum at 5 × 10¹⁹ eV. This conclusion is not firm for lack of statistics. A cutoff would be expected if the sources of the cosmic rays were distributed uniformly throughout the cosmos. The sources of cosmic rays with energy above the GZK cutoff must be at a distance ≤ 100 Mpc, and if they are protons they are very likely to point to these sources. There are no easy explanations how known astrophysical objects can accelerate protons (or atomic nuclei) to these energies. This difficulty has led to speculation that there may be exotic sources such as topological defects which produce these energetic cosmic rays directly along with a copious supply of neutrinos of similar energy. The fluxes of these cosmic rays is very low and large instruments are required to observe them even with modest statistics. One such instrument, the Pierre Auger Observatory, is described. It is designed for all-sky coverage and the construction of its southern site will begin in Argentina in 1999.