19,252 research outputs found
Renormalized kinetic theory of classical fluids in and out of equilibrium
We present a theory for the construction of renormalized kinetic equations to
describe the dynamics of classical systems of particles in or out of
equilibrium. A closed, self-consistent set of evolution equations is derived
for the single-particle phase-space distribution function , the correlation
function , the retarded and advanced density response
functions to an external potential , and
the associated memory functions . The basis of the theory is an
effective action functional of external potentials that
contains all information about the dynamical properties of the system. In
particular, its functional derivatives generate successively the
single-particle phase-space density and all the correlation and density
response functions, which are coupled through an infinite hierarchy of
evolution equations. Traditional renormalization techniques are then used to
perform the closure of the hierarchy through memory functions. The latter
satisfy functional equations that can be used to devise systematic
approximations. The present formulation can be equally regarded as (i) a
generalization to dynamical problems of the density functional theory of fluids
in equilibrium and (ii) as the classical mechanical counterpart of the theory
of non-equilibrium Green's functions in quantum field theory. It unifies and
encompasses previous results for classical Hamiltonian systems with any initial
conditions. For equilibrium states, the theory reduces to the equilibrium
memory function approach. For non-equilibrium fluids, popular closures (e.g.
Landau, Boltzmann, Lenard-Balescu) are simply recovered and we discuss the
correspondence with the seminal approaches of Martin-Siggia-Rose and of
Rose.and we discuss the correspondence with the seminal approaches of
Martin-Siggia-Rose and of Rose.Comment: 63 pages, 10 figure
Shell structure of superheavy nuclei in self-consistent mean-field models
We study the extrapolation of nuclear shell structure to the region of
superheavy nuclei in self-consistent mean-field models -- the
Skyrme-Hartree-Fock approach and the relativistic mean-field model -- using a
large number of parameterizations. Results obtained with the Folded-Yukawa
potential are shown for comparison. We focus on differences in the isospin
dependence of the spin-orbit interaction and the effective mass between the
models and their influence on single-particle spectra. While all relativistic
models give a reasonable description of spin-orbit splittings, all
non-relativistic models show a wrong trend with mass number. The spin-orbit
splitting of heavy nuclei might be overestimated by 40%-80%. Spherical
doubly-magic superheavy nuclei are found at (Z=114,N=184), (Z=120,N=172) or
(Z=126,N=184) depending on the parameterization. The Z=114 proton shell
closure, which is related to a large spin-orbit splitting of proton 2f states,
is predicted only by forces which by far overestimate the proton spin-orbit
splitting in Pb208. The Z=120 and N=172 shell closures predicted by the
relativistic models and some Skyrme interactions are found to be related to a
central depression of the nuclear density distribution. This effect cannot
appear in macroscopic-microscopic models which have a limited freedom for the
density distribution only. In summary, our findings give a strong argument for
(Z=120,N=172) to be the next spherical doubly-magic superheavy nucleus.Comment: 22 pages REVTeX, 16 eps figures, accepted for publication in Phys.
Rev.
Shell structure of superheavy nuclei in self-consistent mean-field models
We study the extrapolation of nuclear shell structure to the region of superheavy nuclei in self-consistent mean-field models—the Skyrme-Hartree-Fock approach and the relativistic mean-field model—using a large number of parametrizations which give similar results for stable nuclei but differ in detail. Results obtained with the folded-Yukawa potential which is widely used in macroscopic-macroscopic models are shown for comparison. We focus on differences in the isospin dependence of the spin-orbit interaction and the effective mass between the models and their influence on single-particle spectra. The predictive power of the mean-field models concerning single-particle spectra is discussed for the examples of 208Pb and the spin-orbit splittings of selected neutron and proton levels in 16O, 132Sn, and 208Pb. While all relativistic models give a reasonable description of spin-orbit splittings, all Skyrme interactions show a wrong trend with mass number. The spin-orbit splitting of heavy nuclei might be overestimated by 40%–80%, which exposes a fundamental deficiency of the current nonrelativistic models. In most cases the occurrence of spherical shell closures is found to be nucleon-number dependent. Spherical doubly magic superheavy nuclei are found at 184298114, 172292120, or 184310126 depending on the parametrization. The Z=114 proton shell closure, which is related to a large spin-orbit splitting of proton 2f states, is predicted only by forces which by far overestimate the proton spin-orbit splitting in 208Pb. The Z=120 and N=172 shell closures predicted by the relativistic models and some Skyrme interactions are found to be related to a central depression of the nuclear density distribution. This effect cannot appear in macroscopic-microscopic models or semiclassical approaches like the extended Thomas-Fermi-Strutinski integral approach which have a limited freedom for the density distribution only. In summary, our findings give a strong argument for 172292120 to be the next spherical doubly magic superheavy nucleus
Liveness-Based Garbage Collection for Lazy Languages
We consider the problem of reducing the memory required to run lazy
first-order functional programs. Our approach is to analyze programs for
liveness of heap-allocated data. The result of the analysis is used to preserve
only live data---a subset of reachable data---during garbage collection. The
result is an increase in the garbage reclaimed and a reduction in the peak
memory requirement of programs. While this technique has already been shown to
yield benefits for eager first-order languages, the lack of a statically
determinable execution order and the presence of closures pose new challenges
for lazy languages. These require changes both in the liveness analysis itself
and in the design of the garbage collector.
To show the effectiveness of our method, we implemented a copying collector
that uses the results of the liveness analysis to preserve live objects, both
evaluated (i.e., in WHNF) and closures. Our experiments confirm that for
programs running with a liveness-based garbage collector, there is a
significant decrease in peak memory requirements. In addition, a sizable
reduction in the number of collections ensures that in spite of using a more
complex garbage collector, the execution times of programs running with
liveness and reachability-based collectors remain comparable
Superheavy nuclei in relativistic effective Lagrangian model
Isotopic and isotonic chains of superheavy nuclei are analyzed to search for
spherical double shell closures beyond Z=82 and N=126 within the new effective
field theory model of Furnstahl, Serot, and Tang for the relativistic nuclear
many-body problem. We take into account several indicators to identify the
occurrence of possible shell closures, such as two-nucleon separation energies,
two-nucleon shell gaps, average pairing gaps, and the shell correction energy.
The effective Lagrangian model predicts N=172 and Z=120 and N=258 and Z=120 as
spherical doubly magic superheavy nuclei, whereas N=184 and Z=114 show some
magic character depending on the parameter set. The magicity of a particular
neutron (proton) number in the analyzed mass region is found to depend on the
number of protons (neutrons) present in the nucleus.Comment: 26 pages, REVTeX, 10 ps figures; changed conten
Superheavy nuclei in relativistic effective Lagrangian model
Isotopic and isotonic chains of superheavy nuclei are analyzed to search for
spherical double shell closures beyond Z=82 and N=126 within the new effective
field theory model of Furnstahl, Serot, and Tang for the relativistic nuclear
many-body problem. We take into account several indicators to identify the
occurrence of possible shell closures, such as two-nucleon separation energies,
two-nucleon shell gaps, average pairing gaps, and the shell correction energy.
The effective Lagrangian model predicts N=172 and Z=120 and N=258 and Z=120 as
spherical doubly magic superheavy nuclei, whereas N=184 and Z=114 show some
magic character depending on the parameter set. The magicity of a particular
neutron (proton) number in the analyzed mass region is found to depend on the
number of protons (neutrons) present in the nucleus.Comment: 26 pages, REVTeX, 10 ps figures; changed conten
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