Exact Solution of an One Dimensional Deterministic Sandpile Model

Using the transfer matrix method, we give the exact solution of a deterministic sandpile model for arbitrary $N$, where $N$ is the size of a single toppling. The one- and two-point functions are given in term of the eigenvalues of an $N \times N$ transfer matrix. All the n-point functions can be found in the same way. Application of this method to a more general class of models is discussed. We also present a quantitative description of the limit cycle (attractor) as a multifractal.Comment: need RevTeX; to appear in Physical Review E January 6, (1995

Variational Monte Carlo simulations using tensor-product projected states

We propose an efficient numerical method, which combines the advantages of recently developed tensor-network based methods and standard trial wave functions, to study the ground state properties of quantum many-body systems. In this approach, we apply a projector in the form of a tensor-product operator to an input wave function, such as a Jastrow-type or Hartree-Fock wave function, and optimize the tensor elements via variational Monte Carlo. The entanglement already contained in the input wave function can considerably reduce the bond dimensions compared to the regular tensor-product state representation. In particular, this allows us to also represent states that do not obey the area law of entanglement entropy. In addition, for fermionic systems, the fermion sign structure can be encoded in the input wave function. We show that the optimized states provide good approximations of the ground-state energy and correlation functions in the cases of two-dimensional bosonic and fermonic systems.Comment: 7 pages, 5 figures, published versio

Exactly solved Frenkel-Kontorova model with multiple subwells

[[abstract]]We exactly solve a class of Frenkel-Kontorova models with a periodic potential composed of piecewise convex parabolas having the same curvature. All rotationally ordered stable configurations can be depicted with appropriate phase parameters. The elements of a phase parameter are grouped into subcommensurate clusters. Phase transitions, manifested in the gap structure changes previously seen in numerical simulations, correspond to the splitting and merging of subcommensurate clusters with the appearance of incommensurate nonrecurrent rotationally ordered stable configurations. Through the notion of elementary phase shifts, all the possibilities for the existence of configurations degenerate with the ground state are scrutinized and the domains of stability in the phase diagram are characterized. At the boundaries of a domain of stability, nonrecurrent minimum energy configurations are degenerate with the ground state configurations and phase transitions occur.[[incitationindex]]SCI[[booktype]]紙

Variance and Passivity Constrained Fuzzy Control for Nonlinear Ship Steering Systems with State Multiplicative Noises

The variance and passivity constrained fuzzy control problem for the nonlinear ship steering systems with state multiplicative noises is investigated. The continuous-time Takagi-Sugeno fuzzy model is used to represent the nonlinear ship steering systems with state multiplicative noises. In order to simultaneously achieve variance, passivity, and stability performances, some sufficient conditions are derived based on the Lyapunov theory. Employing the matrix transformation technique, these sufficient conditions can be expressed in terms of linear matrix inequalities. By solving the corresponding linear matrix inequality conditions, a parallel distributed compensation based fuzzy controller can be obtained to guarantee the stability of the closed-loop nonlinear ship steering systems subject to variance and passivity performance constraints. Finally, a numerical simulation example is provided to illustrate the usefulness and applicability of the proposed multiple performance constrained fuzzy control method

Effects of natto extract on endothelial injury in a rat model

Vascular endothelial damage has been found to be associated with thrombus formation, which is considered to be a risk factor for cardiovascular disease. A diet of natto leads to a low prevalence of cardiovascular disease. The aim of the present study was to investigate the effects of natto extract on vascular endothelia damage with exposure to laser irradiation. Endothelial damage both in vitro and in vivo was induced by irradiation of rose bengal using a DPSS green laser. Cell viability was determined by MTS assay, and the intimal thickening was verified by a histological approach. The antioxidant content of natto extract was determined for the free radical scavenging activity. Endothelial cells were injured in the presence of rose bengal irradiated in a dose-dependent manner. Natto extract exhibits high levels of antioxidant activity compared with purified natto kinase. Apoptosis of laser-injured endothelial cells was significantly reduced in the presence of natto extract. Both the natto extract and natto kinase suppressed intimal thickening in rats with endothelial injury. The present findings suggest that natto extract suppresses vessel thickening as a synergic effect attributed to its antioxidant and anti-apoptosis properties