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Akira Ishii

Publications and source records attributed to Akira Ishii.

At least 37 records · Page 2Linked to original sources
arXiv2013

Dimer models and the special McKay correspondence

We study the behavior of a dimer model under the operation of removing a corner from the lattice polygon and taking the convex hull of the rest. This refines an operation of Gulotta, and the special McKay correspondence plays an essential role in this refinement. As a corollary, we show that for any lattice polygon, there is a dimer model such that the derived category of finitely-generated modules over the path algebra of the corresponding quiver with relations is equivalent to the derived category of coherent sheaves on a toric Calabi-Yau 3-fold determined by the lattice polygon. Our proof is based on a detailed study of relationship between combinatorics of dimer models and geometry of moduli spaces, and does not depend on the result of math/9908027.

math.AG↗
arXiv2013

Dimer models and crepant resolutions

We study variations of tautological bundles on moduli spaces of representations of quivers with relations associated with dimer models under a change of stability parameters. We prove that if the tautological bundle induces a derived equivalence for some stability parameter, then the same holds for any generic stability parameter, and any projective crepant resolution can be obtained as the moduli space for some stability parameter. This result is used in 0905.0059 to prove the abelian McKay correspondence without using the result of math/9908027.

math.AG↗
arXiv2012

On G/N-Hilb of N-Hilb

In this paper we consider the iterated G-equivariant Hilbert scheme G/N-Hilb(N-Hilb) and prove that G/N-Hilb(N-Hilb(C^3)) is a crepant resolution of C^3/G isomorphic to the moduli space of θ-stable representations of the McKay quiver for certain stability condition θ. We provide several explicit examples to illustrate this construction. We also consider the problem of when G/N-Hilb(N-Hilb) is isomorphic to G-Hilb showing the fact that these spaces are most of the times different.

math.AG↗
arXiv2011

Mathematical model for hit phenomena as stochastic process of interactions of human interactions

Mathematical model for hit phenomena in entertainments in the society is presented as stochastic process of interactions of human dynamics. The model use only the time distribution of advertisement budget as input and the words of mouth (WOM) as posting in the social network system is used as the data to compare with the calculated results. The unit of time is daily. The WOM distribution in time is found to be very close to the residue distribution in time. The calculations for Japanese motion picture market due to the mathematical model agree very well with the actual residue distribution in time.

physics.soc-ph↗
arXiv2011

Revenue Prediction of Local Event using Mathematical Model of Hit Phenomena

Theoretical approach to investigate human-human interaction in society performed using a many-body theory including human-human interaction. The advertisement is treated as an external force. The word of mouth (WOM) effect is included as a two-body interaction between humans. The rumor effect is included as a three-body interaction between humans. The parameters to define the strength of human interactions are assumed to be constant values. The calculated result explained well the two local events "Mizuki-Shigeru Road in Sakaiminato" and "the sculpture festival at Tottori" in Japan.

physics.soc-ph↗
arXiv2011

Dimer models and exceptional collections

We construct a full strong exceptional collection consisting of line bundles on any two-dimensional smooth toric weak Fano stack. The total endomorphism algebra of the resulting collection is isomorphic to the path algebra of a quiver with relations associated with a dimer model and a perfect matching on it.

math.AG↗
arXiv2010

A note on consistency conditions on dimer models

We show that for a non-degenerate dimer model, both the first consistency condition of Mozgovoy and Reineke and the properly-orderedness condition of Gulotta are equivalent to a condition on zigzag paths, which goes back to Hanany and Vegh. The last condition is used in arXiv:0905.0059 to study the behavior of a dimer model under the operation of removing a vertex from the lattice polygon and taking the convex hull of the rest.

math.AG↗
arXiv2010

Mathematical Model for Hit Phenomena

The mathematical model for hit phenomena in entertainments is presented as a nonlinear, dynamical and non-equilibrium phenomena. The purchase intention for each person is introduced and direct and indirect communications are expressed as two-body and three-body interaction in our model. The mathematical model is expressed as coupled nonlinear differential equations. The important factor in the model is the decay time of rumor for the hit. The calculated results agree very well with revenues of recent 25 movies.

physics.soc-ph↗
arXiv2010

Stability conditions on $A_n$-singularities

We study the spaces of locally-finite stability conditions on the derived categories of coherent sheaves on the minimal resolutions of $A_n$-singularities supported at the exceptional sets. Our main theorem is that they are connected and simply-connected. The proof is based on the study of spherical objects in math.AG/0409151 and the homological mirror symmetry for $A_n$-singularities.

math.AG↗
arXiv2009

A hierarchical research by large-scale and ab initio electronic structure theories -- Si and Ge cleavage and stepped (111)-2x1 surfaces --

The ab initio calculation with the density functional theory and plane-wave bases is carried out for stepped Si(111)-2x1 surfaces that were predicted in a cleavage simulation by the large-scale (order-N) electronic structure theory (T. Hoshi, Y. Iguchi and T. Fujiwara, Phys. Rev. B72 (2005) 075323). The present ab initio calculation confirms the predicted stepped structure and its bias-dependent STM image. Moreover, two (meta)stable step-edge structures are found and compared. The investigation is carried out also for Ge(111)-2x1 surfaces, so as to construct a common understanding among elements. The present study demonstrates the general importance of the hierarchical research between large-scale and ab initio electronic structure theories.

cond-mat.mtrl-sci↗
arXiv2008

On moduli spaces of quiver representations associated with dimer models

We give a sufficient condition for the moduli space of quiver representations associated with a dimer model to be smooth for a general stability parameter. We also show that the moduli space in this case is a crepant resolution of the toric variety determined by the Newton polygon of the characteristic polynomial.

math.AG↗
arXiv2007

DFT calculation for adatom adsorption on graphene sheet as a prototype of carbon nano tube functionalization

DFT calculation of various atomic species on graphene sheet is investigated as prototypes for formation of nano-structures on carbon nanotube (CNT) wall. We investigate computationally adsorption energies and adsorption sites on graphene sheet for a lot of atomic species including transition metals, noble metals, nitrogen and oxygen, using the DFT calculation as a prototype for CNT. The suitable atomic species can be chosen as each application from those results. The calculated results show us that Mo and Ru are bounded strongly on graphene sheet with large diffusion barrier energy. On the other hand, some atomic species has large binding energies with small diffusion barrier energies

cond-mat.mtrl-sci↗
arXiv2006

Growth mechanisms of GaN on the O-terminated ZnO(000-1) surfaces

We have investigated the stability of the 1ML-GaN on the O-polarity ZnO(000-1) interface structure using the first-principles calculation. We have found in our calculated results that the most stable structure for the 1ML-GaN on the O-polarity ZnO(000-1) interface has the N-polarity. However, we have found that the results of the adatom dynamics on the O-terminated ZnO(000-1) surface shows the Ga-polarity. We find that the key to change the polarity of GaN crystal grown on the O-terminated ZnO(000-1) surface is the growth temperature. We have suggested that the optimized initial growth condition for the growth of the Ga-polarity GaN crystal on the O-terminated ZnO(000-1) surface is under the suitable low temperature and the stoichiometric growth condition. Experimental observations show that GaN grown on ZnO(000-1) by PLD at substrate temperatures below 300C has Ga-polarity, which is quite consistent with the theoretical calculations

cond-mat.mtrl-sci↗
arXiv2005

The kinetic Monte Carlo Simulation scheme of the homoepicaxial growth of GaAs(001) for heterostructural growth on GaAs(001) substrate

The simulation scheme for heterostructural growth of compound semiconductors is presented based on the kinetic Monte Carlo method. The sheme is designed as simple as possible in order to apply it for any heteroepitaxial growth on GaAs(001) substrate. The parameters used in the simulation are determined with the first-principles calculation to reproduce experimental RHEED intensity curves for homoepitaxial growth of GaAs(001).

cond-mat.mtrl-sci↗
arXiv2003

Flops of G-Hilb and equivalences of derived categories by variation of GIT quotient

For a finite subgroup G in SL(3,C), Bridgeland, King and Reid proved that the moduli space of G-clusters is a crepant resolution of the quotient C^3/G. This paper considers the moduli spaces M_θ, introduced by Kronheimer and further studied by Sardo Infirri, which coincide with G-Hilb for a particular choice of the GIT parameter θ. For G Abelian, we prove that every projective crepant resolution of C^3/G is isomorphic to M_θfor some parameter θ. The key step is the description of GIT chambers in terms of the K-theory of the moduli space via the appropriate Fourier--Mukai transform. We also uncover explicit equivalences between the derived categories of moduli M_θfor parameters lying in adjacent GIT chambers.

math.AG↗
arXiv2002

d-like Symmetry of the Order Parameter and Intrinsic Josephson Effects in Bi2212 Cross-Whisker Junctions

An intrinsic tunnel junction was made using two Bi-2212 single crystal whiskers. The two whiskers with a cross-angle were overlaid at their c-planes and connected by annealing. The angular dependence of the critical current density along the c-axis is of the d-wave symmetry. However, the angular dependence is much stronger than that of the conventional d-wave. Furthermore, the current vs. voltage characteristics of the cross-whiskers junctions show a multiple-branch structure at any cross-angle, indicating the formation of the intrinsic Josephson junction array.

cond-mat.supr-con↗