Convergence study and optimal weight functions of an explicit particle method for the incompressible Navier--Stokes equations

To increase the reliability of simulations by particle methods for incompressible viscous flow problems, convergence studies and improvements of accuracy are considered for a fully explicit particle method for incompressible Navier--Stokes equations. The explicit particle method is based on a penalty problem, which converges theoretically to the incompressible Navier--Stokes equations, and is discretized in space by generalized approximate operators defined as a wider class of approximate operators than those of the smoothed particle hydrodynamics (SPH) and moving particle semi-implicit (MPS) methods. By considering an analytical derivation of the explicit particle method and truncation error estimates of the generalized approximate operators, sufficient conditions of convergence are conjectured.Under these conditions, the convergence of the explicit particle method is confirmed by numerically comparing errors between exact and approximate solutions. Moreover, by focusing on the truncation errors of the generalized approximate operators, an optimal weight function is derived by reducing the truncation errors over general particle distributions. The effectiveness of the generalized approximate operators with the optimal weight functions is confirmed using numerical results of truncation errors and driven cavity flow. As an application for flow problems with free surface effects, the explicit particle method is applied to a dam break flow.Comment: 27 pages, 13 figure

Large-scale simulations of viscoelastic deformable multi-body systems using quadruple discrete element method on supercomputers

Contact problems among viscoelastic materials in the multibody system is one of the challenging topics in science and many engineering applications. We have developed an effective simulation method of combining QDEM (Quadruple Discrete Element Method) for the deformation analysis of structures with the DEM for the collisions among structures. However, it is still difficult to reproduce surface topography of structures because particles only set on four nodes of tetrahedrons in our current method. In this paper, QDEMSM (QDEM with Surface Modeling) is newly developed. Point-polygon collisions and line-line collisions are effectively coupled with QDEM. Our improved method was validated by several simulation results; domino simulations using the 40 pieces of shogi (= Japanese chess) were successfully carried out. It was also found the friction forces acted on the surface critically effected on the propagation speeds of contact forces. In parallel computing, by applying the space-filling curve to decomposition of the computational domain, we make it possible to contain the same number of nodes in each decomposed domain. Our parallel simulation code achieves a good weak scalability on the TSUBAME2.5 supercomputer

Two-parameter neutrino mass matrices with two texture zeros

We reanalyse Majorana-neutrino mass matrices M_nu with two texture zeros, by searching for viable hybrid textures in which the non-zero matrix elements of M_nu have simple ratios. Referring to the classification scheme of Frampton, Glashow and Marfatia, we find that the mass matrix denoted by A1 allows the ratios (M_nu)_{mu mu} : (Mnu)_{tau tau} = 1:1 and (M_nu)_{e tau} : (Mnu)_{mu tau} = 1:2. There are analogous ratios for texture A2. With these two hybrid textures, one obtains, for instance, good agreement with the data if one computes the three mixing angles in terms of the experimentally determined mass-squared differences Delta m^2_21 and Delta m^2_31. We could not find viable hybrid textures based on mass matrices different from those of cases A1 and A2.Comment: 10 pages, no figures, minor changes, some references adde

A skeleton structure of self-replicating dynamics

A skeleton dynamics for the self-replicating patterns (SRP) of reaction diffusion system is presented. Self­replicating dynamics can be regarded as a transient process from a localized trigger to a stable Turing pattern or oscillatory Turing pattern. It looks like a reverse process of usual coarsening phenomena, i.e., the number of unit localized pattern increases until the domain is filled by them completely. SRP was found in several chemical reaction models, for instance, the Gray-Scott model as well as in real experi­ments. The most difficult point to describe SRP lies in the fact that it is truly a transient phenomenon in the sense that it can be captured neither as a definite object in dynamical system theory like an attractor nor an orbit itinerating among saddle points in the phase space. To our knowledge, it is not known that what kind of dynamical framework is suitable to clarify the behavior of SRP. The aim is to give a new point of view to describe such a transient dynamics of SRP on a finite interval. Especially we concen­trate on the basic mechanism causing SRP from a bifurcational view point by employing a new model system and its finite-dimensional con:.partment model which shares common qualitative features with the Gray-Scott model. By a careful anatomy of global bifurcation diagrams, the skeleton dynamics of SRP comes from a hierarchy structure of the subcritical bifurcating loops of oscillatory branches of pulse type. It should be noted that these loops themselves do not constitute the skeleton dynamics of SRP, but the ruins of them do it. In other words, the aftereffect of the hierarchy structure manifests the dynamics of SRP. The most important ingredient of an organizing center from which the whole hierarchy structure of SRP emerges is Bogdanov-Takens-Turing singularity as well as the existence of stable equilibrium point, which indicates universality of the above structure in the class of nonlinearities sharing this character

Optical Versus Mid-Infrared Spectroscopic Classification of Ultraluminous Infrared Galaxies

The origin of huge infrared luminosities of ultraluminous infrared galaxies (ULIGs) is still in question. Recently, Genzel et al. made mid-infrared (MIR) spectroscopy of a large number of ULIGs and found that the major energy source in them is massive stars formed in the recent starburst activity; i.e., $\sim$ 70% -- 80% of the sample are predominantly powered by the starburst. However, it is known that previous optical spectroscopic observations showed that the majority of ULIGs are classified as Seyferts or LINERs (low-ionization nuclear emission-line regions). In order to reconcile this difference, we compare types of emission-line activity for a sample of ULIGs which have been observed in both optical and MIR. We confirm the results of previous studies that the majority of ULIGs classified as LINERs based on the optical emission-line diagnostics turn to be starburst-dominated galaxies based on the MIR ones. Since the MIR spectroscopy can probe more heavily-reddened, inner parts of the ULIGs, it is quite unlikely that the inner parts are powered by the starburst while the outer parts are powered by non-stellar ionization sources. The most probable resolution of this dilemma is that the optical emission-line nebulae with the LINER properties are powered predominantly by shock heating driven by the superwind activity; i.e., a blast wave driven by a collective effect of a large number of supernovae in the central region of galaxy mergers.Comment: 15 pages, 2 tables, and 3 eps figures. The Astrophysical Journal (Part 1), in pres

Dengue disease, basic reproduction number and control

Dengue is one of the major international public health concerns. Although progress is underway, developing a vaccine against the disease is challenging. Thus, the main approach to fight the disease is vector control. A model for the transmission of Dengue disease is presented. It consists of eight mutually exclusive compartments representing the human and vector dynamics. It also includes a control parameter (insecticide) in order to fight the mosquito. The model presents three possible equilibria: two disease-free equilibria (DFE) and another endemic equilibrium. It has been proved that a DFE is locally asymptotically stable, whenever a certain epidemiological threshold, known as the basic reproduction number, is less than one. We show that if we apply a minimum level of insecticide, it is possible to maintain the basic reproduction number below unity. A case study, using data of the outbreak that occurred in 2009 in Cape Verde, is presented.Comment: This is a preprint of a paper whose final and definitive form has appeared in International Journal of Computer Mathematics (2011), DOI: 10.1080/00207160.2011.55454

SO(10) GUT and Quark-Lepton Mass Matrices

The phenomenological model that all quark and lepton mass matrices have the same zero texture, namely their (1,1), (1,3) and (3,1) components are zeros, is discussed in the context of SO(10) Grand Unified Theories (GUTs). The mass matrices of type I for quarks are consistent with the experimental data in the quark sector. For the lepton sector, consistent fitting to the data of neutrino oscillation experiments force us to use the mass matrix for the charged leptons which is slightly deviated from type I. Given quark masses and charged lepton masses, the model includes 19 free parameters, whereas the SO(10) GUTs gives 16 constrained equations. Changing the remaining three parameters freely, we can fit all the entries of the CKM quark mixing matrix and the MNS lepton mixing matrix, and three neutrino masses consistently with the present experimental data.Comment: 32pp, REV TeX, 12 EPS Figure

A Multi-band Photometric Study of Tidal Debris in A Compact Group of Galaxies: Seyfert's Sextet

In order to investigate the properties of the prominent tidal debris feature extending to the northeast of the compact group of galaxies Seyfert's Sextet, we analyzed multi-band (U, B, V, VR, R, I, J, H and K') photometric imaging data and obtained the following results: 1) The radial surface brightness distribution of this tidal debris in Seyfert's Sextet (TDSS) in each band appears to be well approximated by an exponential profile. 2) The observed B-V color of TDSS is similar to those of dwarf elliptical galaxies in nearby clusters. 3) Comparing the spectral energy distribution (SED) of TDSS with theoretical photometric evolution models and with the SED of the stars in the outer part of HCG 79b, we find that its SED is comparable to that of a $\sim$ 10 Gyr-old stellar population with solar metallicity, similar to the stellar population in the outer part of HCG 79b. This suggests that TDSS consists of stars that may have been liberated from HCG 79b by strong galaxy interactions, not a pre-existing dwarf galaxy previously thought.Comment: 9 pages, included 6 figures (5 PS files and 6 EPS files), emulateapj LaTeX, Publications of the Astronomical Society of Japan, 2002, 54, No.1, in pres

Early Epidemiological Assessment of the Virulence of Emerging Infectious Diseases: A Case Study of an Influenza Pandemic

Background: The case fatality ratio (CFR), the ratio of deaths from an infectious disease to the number of cases, provides an assessment of virulence. Calculation of the ratio of the cumulative number of deaths to cases during the course of an epidemic tends to result in a biased CFR. The present study develops a simple method to obtain an unbiased estimate of confirmed CFR (cCFR), using only the confirmed cases as the denominator, at an early stage of epidemic, even when there have been only a few deaths. Methodology/Principal Findings: Our method adjusts the biased cCFR by a factor of underestimation which is informed by the time from symptom onset to death. We first examine the approach by analyzing an outbreak of severe acute respiratory syndrome in Hong Kong (2003) with known unbiased cCFR estimate, and then investigate published epidemiological datasets of novel swine-origin influenza A (H1N1) virus infection in the USA and Canada (2009). Because observation of a few deaths alone does not permit estimating the distribution of the time from onset to death, the uncertainty is addressed by means of sensitivity analysis. The maximum likelihood estimate of the unbiased cCFR for influenza may lie in the range of 0.16-4.48% within the assumed parameter space for a factor of underestimation. The estimates for influenza suggest that the virulence is comparable to the early estimate in Mexico. Even when there have been no deaths, our model permits estimating a conservative upper bound of the cCFR. Conclusions: Although one has to keep in mind that the cCFR for an entire population is vulnerable to its variations among sub-populations and underdiagnosis, our method is useful for assessing virulence at the early stage of an epidemic and for informing policy makers and the public. © 2009 Nishiura et al.published_or_final_versio