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Dimer models from mirror symmetry and quivering amoebae
Dimer models are 2-dimensional combinatorial systems that have been shown to encode the gauge groups, matter content and tree-level superpotential of the world-volume quiver gauge theories obtained by placing D3-branes at the tip of a singular toric Calabi-Yau cone. In particular the dimer graph is dual to the quiver graph. However, the string theoretic explanation of this was unclear. In this paper we use mirror symmetry to shed light on this: the dimer models live on a T^2 subspace of the T^3 fiber that is involved in mirror symmetry and is wrapped by D6-branes. These D6-branes are mirror to the D3-branes at the singular point, and geometrically encode the same quiver theory on their world-volume
Study of gossamer superconductivity and antiferromagnetism in the t-J-U model
The d-wave superconductivity (dSC) and antiferromagnetism are analytically
studied in a renormalized mean field theory for a two dimensional t-J model
plus an on-site repulsive Hubbard interaction . The purpose of introducing
the term is to partially impose the no double occupancy constraint by
employing the Gutzwiller approximation. The phase diagrams as functions of
doping and are studied. Using the standard value of and
in the large limit, we show that the antiferromagnetic (AF) order emerges
and coexists with the dSC in the underdoped region below the doping
. The dSC order parameter increases from zero as the doping
increases and reaches a maximum near the optimal doping . In
the small limit, only the dSC order survives while the AF order disappears.
As increased to a critical value, the AF order shows up and coexists with
the dSC in the underdoped regime. At half filing, the system is in the dSC
state for small and becomes an AF insulator for large . Within the
present mean field approach, We show that the ground state energy of the
coexistent state is always lower than that of the pure dSC state.Comment: 7 pages, 8 figure
On several families of elliptic curves with arbitrary large Selmer groups
In this paper, we calculate the Selmer groups
S^{(\phi)} (E / \Q) and S^{(\hat{\varphi})} (E^{\prime} / \Q) of elliptic
curves via descent theory
(see [S, Chapter X]), in particular, we obtain that the Selmer groups of
several families of such elliptic curves can be arbitrary large.Comment: 22 page
Global behavior of cosmological dynamics with interacting Veneziano ghost
In this paper, we shall study the dynamical behavior of the universe
accelerated by the so called Veneziano ghost dark energy component locally and
globally by using the linearization and nullcline method developed in this
paper. The energy density is generalized to be proportional to the Hawking
temperature defined on the trapping horizon instead of Hubble horizon of the
Friedmann-Robertson-Walker (FRW) universe. We also give a prediction of the
fate of the universe and present the bifurcation phenomenon of the dynamical
system of the universe. It seems that the universe could be dominated by dark
energy at present in some region of the parameter space.Comment: 8 pages, 7 figures, accepted for publication in JHE
Morphological instability, evolution, and scaling in strained epitaxial films: An amplitude equation analysis of the phase field crystal model
Morphological properties of strained epitaxial films are examined through a
mesoscopic approach developed to incorporate both the film crystalline
structure and standard continuum theory. Film surface profiles and properties,
such as surface energy, liquid-solid miscibility gap and interface thickness,
are determined as a function of misfit strains and film elastic modulus. We
analyze the stress-driven instability of film surface morphology that leads to
the formation of strained islands. We find a universal scaling relationship
between the island size and misfit strain which shows a crossover from the
well-known continuum elasticity result at the weak strain to a behavior
governed by a "perfect" lattice relaxation condition. The strain at which the
crossover occurs is shown to be a function of liquid-solid interfacial
thickness, and an asymmetry between tensile and compressive strains is
observed. The film instability is found to be accompanied by mode coupling of
the complex amplitudes of the surface morphological profile, a factor
associated with the crystalline nature of the strained film but absent in
conventional continuum theory.Comment: 16 pages, 10 figures; to be published in Phys. Rev.
Viscosity calculated in simulations of strongly-coupled dusty plasmas with gas friction
A two-dimensional strongly-coupled dusty plasma is modeled using Langevin and
frictionless molecular dynamical simulations. The static viscosity and
the wave-number-dependent viscosity are calculated from the
microscopic shear in the random motion of particles. A recently developed
method of calculating the wave-number-dependent viscosity is
validated by comparing the results of from the two simulations. It is
also verified that the Green-Kubo relation can still yield an accurate measure
of the static viscosity in the presence of a modest level of friction as
in dusty plasma experiments.Comment: 6 pages, 3 figures, Physics of Plasmas invited pape
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