4,765 research outputs found
The Inhomogeneous Phase of Dense Skyrmion Matter
It was predicted qualitatively in ref.[1] that skyrmion matter at low density
is stable in an inhomogeneous phase where skyrmions condensate into lumps while
the remaining space is mostly empty. The aim of this paper is to proof
quantitatively this prediction. In order to construct an inhomogeneous medium
we distort the original FCC crystal to produce a phase of planar structures
made of skyrmions. We implement mathematically these planar structures by means
of the 't Hooft instanton solution using the Atiyah-Manton ansatz. The results
of our calculation of the average density and energy confirm the prediction
suggesting that the phase diagram of the dense skyrmion matter is a lot more
complex than a simple phase transition from the skyrmion FCC crystal lattice to
the half-skyrmion CC one. Our results show that skyrmion matter shares common
properties with standard nuclear matter developing a skin and leading to a
binding energy equation which resembles the Weiszaecker mass formula.Comment: 8 figures, 14 page
Development of Three-Dimensional Parallel Code to Study the Motions of Particles in a Fluid Using Lattice Boltzmann Method
Department of Mechanical EngineeringThe three-dimensional parallel code is developed for the lattice Boltzmann method. It is to simulate multiphase flows containing particles. The code is the combination of the two models, the Shan-Chan multiphase model for a viscous fluid, the pseudo-solid model for particles. The difficulties in implementing the methods and some possible optimization techniques are suggested. This code can be used to simulate the dynamics of the self-assembly driven by evaporation and any multiphase flow with different sizes of particles.ope
The structure of gauge-invariant ideals of labelled graph -algebras
In this paper, we consider the gauge-invariant ideal structure of a
-algebra associated to a set-finite,
receiver set-finite and weakly left-resolving labelled space
, where is a labelling map assigning
an alphabet to each edge of the directed graph with no sinks. Under the
assumption that an accommodating set is closed under taking
relative complement, it is obtained that there is a one to one correspondence
between the set of all hereditary saturated subsets of and the
gauge-invariant ideals of . For this, we
introduce a quotient labelled space arising
from an equivalence relation on and show the existence
of the -algebra generated by a
universal representation of . Also the
gauge-invariant uniqueness theorem for is
obtained.
For simple labelled graph -algebras
, where is the
smallest accommodating set containing all the generalized vertices, it is
observed that if for each vertex of , a generalized vertex is
finite for some , then is simple if
and only if is strongly cofinal and
disagreeable. This is done by examining the merged labelled graph
of and the common properties that
and
share
Logarithmic base change theorem and smooth descent of positivity of log canonical divisor
We prove a logarithmic base change theorem for pushforwards of
pluri-canonical bundles and use it to deduce that positivity properties of log
canonical divisors descend via smooth projective morphisms. As an application,
for a surjective morphism with and big, we
prove is of log general type, where is the
discriminant locus. In particular, when we have and , generalizing the case
proved by Viehweg-Zuo. In addition, we prove Popa's conjecture on the
superadditivity of the logarithmic Kodaira dimension of smooth algebraic fiber
spaces over bases of dimension at most three and analyze related problems.Comment: 30 pages; v.2: a few new results on the superadditivity and the
descent of effectivity added; v.3: small expository change
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