Basic Definitions and Equations

Dissipation mechanics and exact solutions for nonlinear equations of dissipative type—Principle and application of dissipation mechanics (I)

Failure probability of welds by stress corrosion cracking (SCC) in austenitic stainless steel piping is analyzed by probabilistic fracture mechanics (PFM) approach based on an electro-chemical crack growth model named FRI model[1] through which a basic equation is derived. Introducing the relation among dK/dt, da/dt and dK/da (K: stress intensity factor, a: crack depth and t: time) into the basic equation, modified basic equation is derived which can give da/dt in explicit form in contrast to the fact that the basic equation is transcendental and can be solved only numerically by iterative method. From numerical evaluation of K distribution at a crack tip under bending stress, it is realized that there exists a relation between a and K and it can be expressed approximately by quadratic function, i.e. K=Km{1−(a−am)2/am2}. By examining K as function of a, am is proved to be a linear function of membrane stress to bending stress ratio. These findings are incorporated into the modified basic equation which is shown to be able to calculate da/dt without instability and needs no iteration. Stratified Monte-Carlo method is introduced which defines two dimensional sampling space composed of a/c (c is crack length at surface) ranging from 0 to 1 and K from 0 to Kw which has to be defined referring to KSCC. Log-normal distributions are anticipated for a/c and K probability distributions. The median of K is decided referring to median of a in Bru¨ckner model. Parameter surveys for cumulative failure probability (CFP) performed with the basic equation and the modified basic equation give very close results. In this study, the residual stress distribution generated by residual stress at welding is anticipated to be tensile on inner surface and compressive on outer surface like bending stress distribution. Therefore the simulation is performed under bending dominative condition. The modified basic equation is proved to need about 1/2 calculation time of needed by the original basic equation in the CFP simulation.

Investigation of calibration equations for NTC thermistors utilized in the deep-ocean temperature range

Heuristic hypothesis on the relation between cosmology and elementary particles

The steady state in the GAMMA10 tandem mirror, in which radial transport due to flute mode turbulence is balanced by plasma heating and production, is investigated. The basic equations used here exclude the Alfvén and acoustic modes, which are unnecessary for transport due to the flute modes. The basic equations can be applied to the magnetic divertor if the system is assumed to be axisymmetric. High-pressure effects in non-axisymmetric magnetic fields in GAMMA10 are taken into the magnetic specific volume. Numerical calculation is performed to investigate the transport process due to flute mode fluctuations. Mild plasma heating with production leads the system to a steady state, whereas strong heating with production leads the system into sawtooth-like oscillation due to strong flute mode turbulence.

The structure of a stationary accretion disk surrounding a black hole is studied by means of newly developed basic equations. The basic equations are derived under the assumption that the vertical distribution of disk matter is given by a polytrope. For a Keplerian accretion disk, basic equations reduce to a differential equation of the first order. We have found that solutions of an optically thick accretion disk converge to a limiting value, irrespective of the outer boundary condition. This gives the happy consequence that the inner structure of an optically thick accretion disk is determined irrespective of the outer boundary condition. On the contrary, an optically thin accretion disk shows bimodal behavior, that is, two physically distinct states exist depending on the outer boundary condition imposed at the outer edge of the accretion disk.

Abstract: Climate change like relative humidity can cause various negative impacts on water resources system, ecosystem, etc. To deal with these effects, it is necessary to study the climate change. There are various ways to study climate change in which one of the ways is the study of downscaling. Downscaling is the procedure in which prediction of information is done for local scale area from the available information of a large-scale area. In the downscaling of climatic variables, General Circulation Model (GCM) plays an important role. GCM gives larger scale climatic variables. With the help of this downscaling, we can predict different climatic variables such as temperature, for future time period over the selected area. To perform this downscaling there are different ways, we can classify it as statistical downscaling and dynamical downscaling. In statistical downscaling, we can find relation between predictand and predictors and this statistical relation we use for the future prediction of the selected climatic variable. In dynamical downscaling, we use Regional Climatic Model (RCM), and with the help of this, we carry out downscaling procedure. In this study, statistical downscaling has studied for temperature parameter such as relative humidity by considering the basic equation given by Wilby in (Inter-research). The study area selected for this research is jalna district Maharashtra State, India (Latitude: 19° .8347r, Longitude: 75° .8816r). In this study, in the first step, statistical downscaling has been done with the help of statistical downscaling model (SDSM) software by using HadCM3 GCM with A2a and B2a scenarios for temperature parameter for the future time period up to 2099. In second step, the Statistical downscaling performed by using basic equation given by Wilby Temperature values predicted up to 2099. These results are considered with three different series such as 2020s, 2050s, and 2080s. Downscaled results of temperature parameter by “SDSM” model were compared for future series. After study of these results, it is concluded that SDSM gives higher value of temperature changes in jalna district marathwada region. Key Words: Climate change Impact, possible future series, SDSM, HadCM3, A2a, B2a, relative humidity

Chapter 8 - Basic Equations and Solution Procedure

In this paper a frequency response analysis of a hydraulic feed system of machine-tool is described and a method to improve the dynamic characteristics of the system is developed. From the basic equations given in the previous paper, a transfer function of the table motion is introduced. The experimental analysis for the frequency response gives a good agreement with the theoretical analysis and from this result it is made clear that the basic equations are also valid for the frequency response. The frequency response obtained indicates that the dynamic behaviour at the table characteristic frequency region is the most important problem in the hydraulic feed system. Considering this result, a method in which the internal leakage in the cylinder is used to improve the dynamic bahaviour at the table characteristic frequency region is discussed both experimentally and theoretically. The result obtained indicates that this method is effective for the purpose.

Basic equations, theory and principle of computational stock market (III)—basic theories

As seen in the previous chapter, the basic equations are rather intricate and nonlinear (due to convective inertia terms). It is therefore useful to start by discussing assumptions involved, boundary conditions, and possible simplifying assumptions.

Chapter 1 - BASIC EQUATIONS

Simple, reliable basic equation for proton-reaction analysis of biological materials

19 - Viscous and Non-Newtonian Flows

Studies of the pressure-dissociation of several amyloid or amyloid-like fibrils have shown that the fibril state is considerably voluminous. Quantitative characterization of the protein fibrillation reaction with respect to volumetric parameters is necessary to elucidate mechanisms of amyloid fibrillation in molecular terms such as protein cavity and hydration. Here we discuss, firstly, basic equations in statics and kinetics of protein polymerization as employed to obtain thermodynamic, volumetric, and kinetic parameters. Equilibrium treatment of the reactions with the scheme such as one-step polymerization, linear-association polymerization, or nucleation-dependent polymerization, and kinetic treatment of seeded linear-polymerization or spontaneous nucleation-elongation polymerization are described. In particular we will detail kinetics of the dissociation of fibrils which have been produced under the linear-association mechanism and therefore the length-distribution of which conforms to a geometric sequence in the degree of polymerization with a common ratio r, which is less than, and usually very close to, unity. In this case, an observed macroscopic rate of dissociation is shown to be a product of the microscopic elementary dissociation rate constant and a factor (1-r), extremely reduced compared with the intrinsic elementary rate. Secondly, we discuss protein conformational states in fibrillogenesis with molecular and volumetric observations reported, such as the unfolded state responsible for the association with seeds and the extension of amyloid fibrils, the transition state in which protein cavity formation and dehydration occur to intermediate levels, and the fibril state in which they occur to final respective levels which, in some cases, depend on the maturity of the fibril.