Numerical investigations of mechanical stress caused in dendrite by melt convection and gravity

In order to investigate the effects of stress around dendrite neck cased by the convection and gravity on the dendrite fragmentation, the novel numerical model, where phase-field method, Navier-Stokes equations and finite element method are continuously and independently employed, has been developed. By applying the model to the dendritic solidification of Al-Si alloy, the maximum stress variations by melt convection and gravity with dendrite growth were evaluated

Nonmagnetic Insulating States near the Mott Transitions on Lattices with Geometrical Frustration and Implications for κ\kappa-(ET)2_2Cu2(CN)3_2(CN)_3

We study phase diagrams of the Hubbard model on anisotropic triangular lattices, which also represents a model for $\kappa$-type BEDT-TTF compounds. In contrast with mean-field predictions, path-integral renormalization group calculations show a universal presence of nonmagnetic insulator sandwitched by antiferromagnetic insulator and paramagnetic metals. The nonmagnetic phase does not show a simple translational symmetry breakings such as flux phases, implying a genuine Mott insulator. We discuss possible relevance on the nonmagnetic insulating phase found in $\kappa$-(ET)$_2$Cu$_2(CN)_3$.Comment: 4pages including 7 figure

Kernels for graphs

This chapter contains sections titled: Introduction, Label Sequence Kernel between Labeled Graphs, Experiments, Related Works, Conclusion

A Hamiltonian-based solution to the mixed sensitivity optimization problem for stable pseudorational plants

This paper considers the mixed sensitivity optimization problem for a class of infinite-dimensional stable plants. This problem is reducible to a two- or one-block H∞ control problem with structured weighting functions. We first show that these weighting functions violate the genericity assumptions of existing Hamiltonian-based solutions such as the well-known Zhou-Khargonekar formula. Then, we derive a new closed form formula for the computation of the optimal performance level, when the underlying plant structure is specified by a pseudorational transfer function. © 2005 Elsevier B.V. All rights reserved

Parameterization of suboptimal solutions of the Nehari problem for infinite-dimensional systems

The Nehari problem plays an important role in H∞ control theory. It is well known that H∞ control problem can be reduced to solving this problem. This note gives a parameterization of all suboptimal solutions of the Nehari problem for a class of infinite-dimensional systems. Many earlier solutions of this problem are seen to be special cases of this new parameterization. It is also shown that for finite impulse response systems this parameterization takes a particularly simple form. ©2007 IEEE

Thermodynamic Relations in Correlated Systems

Several useful thermodynamic relations are derived for metal-insulator transitions, as generalizations of the Clausius-Clapeyron and Eherenfest theorems. These relations hold in any spatial dimensions and at any temperatures. First, they relate several thermodynamic quantities to the slope of the metal-insulator phase boundary drawn in the plane of the chemical potential and the Coulomb interaction in the phase diagram of the Hubbard model. The relations impose constraints on the critical properties of the Mott transition. These thermodynamic relations are indeed confirmed to be satisfied in the cases of the one- and two-dimensional Hubbard models. One of these relations yields that at the continuous Mott transition with a diverging charge compressibility, the doublon susceptibility also diverges. The constraints on the shapes of the phase boundary containing a first-order metal-insulator transition at finite temperatures are clarified based on the thermodynamic relations. For example, the first-order phase boundary is parallel to the temperature axis asymptotically in the zero temperature limit. The applicability of the thermodynamic relations are not restricted only to the metal-insulator transition of the Hubbard model, but also hold in correlated systems with any types of phases in general. We demonstrate such examples in an extended Hubbard model with intersite Coulomb repulsion containing the charge order phase.Comment: 10 pages, 9 figure

First-Principles Computation of YVO3; Combining Path-Integral Renormalization Group with Density-Functional Approach

We investigate the electronic structure of the transition-metal oxide YVO3 by a hybrid first-principles scheme. The density-functional theory with the local-density-approximation by using the local muffin-tin orbital basis is applied to derive the whole band structure. The electron degrees of freedom far from the Fermi level are eliminated by a downfolding procedure leaving only the V 3d t2g Wannier band as the low-energy degrees of freedom, for which a low-energy effective model is constructed. This low-energy effective Hamiltonian is solved exactly by the path-integral renormalization group method. It is shown that the ground state has the G-type spin and the C-type orbital ordering in agreement with experimental indications. The indirect charge gap is estimated to be around 0.7 eV, which prominently improves the previous estimates by other conventional methods

Quantum Mott Transition and Multi-Furcating Criticality

Phenomenological theory of the Mott transition is presented. When the critical temperature of the Mott transition is much higher than the quantum degeneracy temperature, the transition is essentially described by the Ising universality class. Below the critical temperature, phase separation or first-order transition occurs. However, if the critical point is involved in the Fermi degeneracy region, a marginal quantum critical point appears at zero temperature. The originally single Mott critical point generates subsequent many unstable fixed points through various Fermi surface instabilities induced by the Mott criticality characterized by the diverging charge susceptibility or doublon susceptibility. This occurs in marginal quantum-critical region. Charge, magnetic and superconducting instabilitites compete severely under these critical charge fluctuations. The quantum Mott transition triggers multi-furcating criticality, which goes beyond the conventional concept of multicriticality in quantum phase transitions. Near the quantum Mott transition, the criticality generically drives growth of inhomogeneous structure in the momentum space with singular points of flat dispersion on the Fermi surface. The singular points determine the quantum dynamics of the Mott transition by the dynamical exponent $z=4$. We argue that many of filling-control Mott transitions are classified to this category. Recent numerical results as well as experimental results on strongly correlated systems including transition metal oxides, organic materials and $^3$He layer adsorbed on a substrate are consistently analyzed especially in two-dimensional systems.Comment: 28 pages including 2 figure

What is Minimal Model of 3He Adsorbed on Graphite? -Importance of Density Fluctuations in 4/7 Registered Solid -

We show theoretically that the second layer of 3He adsorbed on graphite and solidified at 4/7 of the first-layer density is close to the fluid-solid boundary with substantial density fluctuations on the third layer. The solid shows a translational symmetry breaking as in charge-ordered insulators of electronic systems. We construct a minimal model beyond the multiple-exchange Heisenberg model. An unexpectedly large magnetic field required for the measured saturation of magnetization is well explained by the density fluctuations. The emergence of quantum spin liquid is understood from the same mechanism as in the Hubbard model and in \kappa-(ET)_2Cu_2(CN)_3 near the Mott transitions.Comment: 9 pages, 5 figure