13,013 research outputs found
Short timescale behavior of colliding heavy nuclei at intermediate energies
An Antisymmetrized Molecular Dynamics model is used to explore the collision
of Cd projectiles with Mo target nuclei at E/A=50 MeV over a
broad range in impact parameter. The atomic number (Z), velocity, and emission
pattern of the reaction products are examined as a function of the impact
parameter and the cluster recognition time. The non-central collisions are
found to be essentially binary in character resulting in the formation of an
excited projectile-like fragment (PLF) and target-like fragment (TLF).
The decay of these fragments occurs on a short timescale, 100t300
fm/c. The average excitation energy deduced for the PLF and TLF
`saturates for mid-central collisions, 3.5b6 fm, with its magnitude
depending on the cluster recognition time. For short cluster recognition times
(t=150 fm/c), an average excitation energy as high as 6 MeV is
predicted. Short timescale emission leads to a loss of initial correlations and
results in features such as an anisotropic emission pattern of both IMFs and
alpha particles emitted from the PLF and TLF in peripheral collisions.Comment: 19 pages, 17 figure
On the p-adic geometry of traces of singular moduli
The aim of this article is to show that p-adic geometry of modular curves is
useful in the study of p-adic properties of traces of singular moduli. In order
to do so, we partly answer a question by Ono. As our goal is just to illustrate
how p-adic geometry can be used in this context, we focus on a relatively
simple case, in the hope that others will try to obtain the strongest and most
general results. For example, for p=2, a result stronger than Thm.1 is proved
in [Boylan], and a result on some modular curves of genus zero can be found in
[Osburn] . It should be easy to apply our method, because of its local nature,
to modular curves of arbitrary level, as well as to Shimura curves.Comment: 3 pages, Late
Magnetic-Field Induced Gap in One-Dimensional Antiferromagnet KCuGaF
Magnetic susceptibility and specific heat measurements in magnetic fields
were performed on an one-dimensional antiferromagnet KCuGaF.
Exchange interaction was evaluated as K. However, no
magnetic ordering was observed down to 0.46 K. It was found that an applied
magnetic field induces a staggered magnetic susceptibility obeying the Curie
law and an excitation gap, both of which should be attributed to the
antisymmetric interaction of the Dzyaloshinsky-Moriya type and/or the staggered
-tensor. With increasing magnetic field , the gap increases almost in
proportion to .Comment: Submitted to Proceedings of Research in High Magnetic Fiel
Antisymmetrized molecular dynamics with quantum branching processes for collisions of heavy nuclei
Antisymmetrized molecular dynamics (AMD) with quantum branching processes is
reformulated so that it can be applicable to the collisions of heavy nuclei
such as Au + Au multifragmentation reactions. The quantum branching process due
to the wave packet diffusion effect is treated as a random term in a
Langevin-type equation of motion, whose numerical treatment is much easier than
the method of the previous papers. Furthermore a new approximation formula,
called the triple-loop approximation, is introduced in order to evaluate the
Hamiltonian in the equation of motion with much less computation time than the
exact calculation. A calculation is performed for the Au + Au central
collisions at 150 MeV/nucleon. The result shows that AMD almost reproduces the
copious fragment formation in this reaction.Comment: 24 pages, 5 figures embedde
Proof of the Umbral Moonshine Conjecture
The Umbral Moonshine Conjectures assert that there are infinite-dimensional
graded modules, for prescribed finite groups, whose McKay-Thompson series are
certain distinguished mock modular forms. Gannon has proved this for the
special case involving the largest sporadic simple Mathieu group. Here we
establish the existence of the umbral moonshine modules in the remaining 22
cases.Comment: 56 pages, to appear in Research in the Mathematical Science
Pariah moonshine
Finite simple groups are the building blocks of finite symmetry. The effort
to classify them precipitated the discovery of new examples, including the
monster, and six pariah groups which do not belong to any of the natural
families, and are not involved in the monster. It also precipitated monstrous
moonshine, which is an appearance of monster symmetry in number theory that
catalysed developments in mathematics and physics. Forty years ago the pioneers
of moonshine asked if there is anything similar for pariahs. Here we report on
a solution to this problem that reveals the O'Nan pariah group as a source of
hidden symmetry in quadratic forms and elliptic curves. Using this we prove
congruences for class numbers, and Selmer groups and Tate--Shafarevich groups
of elliptic curves. This demonstrates that pariah groups play a role in some of
the deepest problems in mathematics, and represents an appearance of pariah
groups in nature.Comment: 20 page
Antisymmetrized molecular dynamics of wave packets with stochastic incorporation of Vlasov equation
On the basis of the antisymmetrized molecular dynamics (AMD) of wave packets
for the quantum system, a novel model (called AMD-V) is constructed by the
stochastic incorporation of the diffusion and the deformation of wave packets
which is calculated by Vlasov equation without any restriction on the one-body
distribution. In other words, the stochastic branching process in molecular
dynamics is formulated so that the instantaneous time evolution of the averaged
one-body distribution is essentially equivalent to the solution of Vlasov
equation. Furthermore, as usual molecular dynamics, AMD-V keeps the many-body
correlation and can naturally describe the fluctuation among many channels of
the reaction. It is demonstrated that the newly introduced process of AMD-V has
drastic effects in heavy ion collisions of 40Ca + 40Ca at 35 MeV/nucleon,
especially on the fragmentation mechanism, and AMD-V reproduces the
fragmentation data very well. Discussions are given on the interrelation among
the frameworks of AMD, AMD-V and other microscopic models developed for the
nuclear dynamics.Comment: 26 pages, LaTeX with revtex and epsf, embedded postscript figure
Compatibility of localized wave packets and unrestricted single particle dynamics for cluster formation in nuclear collisions
Antisymmetrized molecular dynamics with quantum branching is generalized so
as to allow finite time duration of the unrestricted coherent mean field
propagation which is followed by the decoherence into wave packets. In this new
model, the wave packet shrinking by the mean field propagation is respected as
well as the diffusion, so that it predicts a one-body dynamics similar to that
in mean field models. The shrinking effect is expected to change the diffusion
property of nucleons in nuclear matter and the global one-body dynamics. The
central \xenon+\tin collisions at 50 MeV/nucleon are calculated by the models
with and without shrinking, and it is shown that the inclusion of the wave
packet shrinking has a large effect on the multifragmentation in a big
expanding system with a moderate expansion velocity.Comment: 16 pages, 7 figure
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