Ultimate Equilibrium Research Articles

Continuous chromatomembrane headspace analysis

A novel version of headspace analysis is substantiated by theory and experiment. The version assumes chromatomembrane extraction of the analyte components into a gas phase. The boundary conditions for the process of chromatomembrane gas extraction are established. Two modes are suggested for analysis with continuous extraction of analyte substances: the mode of ultimate equilibrium saturation and that of total isolation. The advantages of the method in the determination of traces of volatile substances are obvious from its comparison with traditional techniques based on stripping or membrane diffusion.

Elasto-plastic rotational capacity of welded symmetrical moment connections

A study is conducted on the moment-rotation characteristics of welded beam-to-column symmetrical moment connections. The study focuses on the effect of column axial load and beam depth on the moment-rotation behavior of the connection. Numerical experiments using nonlinear finite element analysis are conducted where a special incremental version of a deformation theory is incorporated into the formulation in order to yield information both at imminent buckling of the web and at ultimate elastic-plastic equilibrium load.

Non-local reaction-diffusion equations modelling predator-prey coevolution

In this paper we examine a prey-predator system with a characteristic of the predator subject to mutation. The ultimate equilibrium of the system is found by Maynard-Smith et al. by the so called ESS (Evolutionary Stable Strategy). Using a system of reaction-diffusion equations with non local terms, we conclude the ESS result for the diffusion coefficient tending to zero, without resorting to any optimization criterion.

Neutral buoyancy and the structure of mid‐ocean ridge magma reservoirs

The mechanical structure of the regions for shallow storage and lateral intrusion of mid‐ocean ridge basalt (MORB) is explored in part by examining the density range appropriate for picritic‐to‐tholeiitic liquids and liquid + crystal mixtures, and its relationship to the nonlinear density‐depth structure of the ridge. Magma density spans the range 2.6 to at least 2.82 Mg m−3 and incorporates the effects of fractional crystallization on the density evolution, the incorporation of olivine phenocrysts and the contributions of water in melt phase density reductions. The melt and melt + crystal density band crosses the in situ rock density curve over the ≈1 to ≈3 km depth interval beneath the volcanic surface. Within that averaged interval, picritic‐to‐tholeiitic melt and melt + crystal mixtures are in approximate mechanical equilibrium with their surroundings, and the interval is referred to as the MORB horizon of neutral buoyancy (HNB). The detailed locations of the transition regions between the negative and neutral buoyancy and between the neutral and positive buoyancy regimes are dependent on melt phase composition as well as the presence of suspended mineral phases and their identity. In the East Pacific Rise, the HNB has a 1:1 correspondence with the inferred location of the sheeted dike complex and the seismically detected minimum compressional wave velocity region. In ophiolite complexes the region corresponds to the sheeted dike complex and the uppermost isotropic gabbros. Above the HNB is the region of negative buoyancy (seafloor to an averaged ≈1 km depth) within which, negative buoyancy forces may induce the descent of nonvesiculated melt. This region corresponds to the pillow basalt ± sediment sequence. The region of positive buoyancy extends from ≈3 km to the depth of melt generation, and picritic melt ascends in dikes and veins of finite height ≈500 m to ≈11 km and relatively narrow width ≈20 mm to ≈100 cm. The finite strengths of high‐temperature fluid‐weakened rocks mandate finite height melt parcels along the ascent pathway. The magmatic source region is therefore never hydraulically connected with the surface nor with the near‐surface reservoir. Thus relatively locally integrated buoyancy has a natural role in the ascent of melt from the source region to the region of neutral buoyancy. During the final stages of magma ascent, hydrothermal fluid circulation enshrouds the HNB in a three‐dimensional envelope, as suggested by the depth extent of alteration mineralogy in ophiolite complexes. While hydrothermal cooling may play an important role in arresting the ascent of magma in very low spreading‐rate environments, gravitational equilibrium represents the effectively dominant theme in intermediate and high spreading‐rate regions such as the East Pacific Rise. Elastic crack penetration of rheological transition zones near the HNB identify modes of crack‐tip morphologic changes as a function of Young's modulus ratios (E2/E1) above and beneath the transition and affect the style of intrusion, while melt buoyancy determines the ultimate equilibrium resting place. Elastic crack stability considerations relate the vertical magma pressure gradients for tholeiitic (∇PT) and picritic (∇Pp) magmas to the vertically varying gradient in the horizontal stress component (∇σH) and suggest further subdivision into two horizons of neutral buoyancy: one for tholeiitic magma (HNBT), and one for the picritic liquid + olivine mixtures (HNBP). These intervals are very approximate but are estimated as ≈600 m to ≈1400 m and ≈1400 to ≈3000 m depth, respectively, beneath the East Pacific Rise axis. As oceanic lithosphere is created at the rise axis and spreads laterally, the horizons of negative buoyancy and neutral buoyancy ride with it and may continue to modulate the subsurface magma dynamics that influence off‐axis volcanism.

The size distribution of liquid droplets during their growth from a vapor

We consider a collection of droplets growing from a supersaturated vapor or from a gas mixture containing such a vapor. The evolution of the distribution function of their radii is calculated in a simple mean field approximation for the time regime starting well after nucleation and continuing well into the Ostwald ripening regime. Between the diffusion controlled regime and the Ostwald ripening regime one often observes a long “waiting period” during which the typical droplet size appears to grow slower than any power of the time (or at most with a very small power). The waiting period increases with decreasing initial width of the distribution and with a decreasing volume ratio of liquid and vapor in the ultimate equilibrium state. The waiting period is shown to be connected with the existence of an unstable fixed point in the evolution equation for the droplet size distribution, corresponding to equal size of all droplets. The dependence of the length of the waiting period on the parameters of the problem and its sensitivity to changes in the model are also discussed.

Competitive and noncompetitive reversible binding processes.

This work treats many-body aspects in an idealized class of reversible binding problems involving a static binding site with many diffusing point particles. In the noncompetitive limit, where no restriction exists on the number of simultaneously bound particles, the problem reduces to reversible aggregation. In the competitive limit, where only one particle may be simultaneously bound, it becomes a model for a pseudounimolecular reaction. The general formalism for both binding limits involves the exact microscopic hierarchy of diffusion equations for the N-body density functions. In the noncompetitive limit of independent particles, the hierarchy admits an analytical solution which may be viewed as a generalization of the Smoluchowski aggregation theory to the (idealized) reversible case. In the competitive limit, the hierarchy enables straightforward derivations of useful identities, determination of the ultimate equilibrium solution, and justification for approximations. In particular, the utility of a density-expansion, short-time approximation is investigated. The approximation relies on the ability to solve the hierarchy numerically for a small number of particles. This direct-propagation algorithm is described in the numerical section.

Dynamic competitive pricing strategies

Pricing decisions have long been of interest to researchers in the competitive strategy area. Static game theory models of competitive pricing commonly assume that rivals act with full information and full rationality. Such models imply that rivals immediately reach a Nash equilibrium. This implication is consistent neither with experimental research results nor with casual observation of real markets. We therefore relax the assumption of full information to investigate how competitors learn and update their marketing strategies over time, as well as to identify the ultimate equilibrium they reach. This dual focus on the learning process as well as its outcome is important to understanding how rivals compete over time. We find that the ultimate equilibrium takes some time to reach, and is neither the standard Nash solution nor a collusive one. These differences from the usual static game solutions suggest the value of models that better capture the incomplete information facing a firm in a competitive marketplace.

Is the concept of an Equilibrium Demand for Money Meaningful? A Reply to “Has the Demand for Money been Mislaid?”

In his latest paper, Basil Moore has clearly defined a central methodological difference between our two positions. I do, indeed, as he states, envisage economic units as having a demand in 'ultimate equilibrium' to hold some proportion of their total wealth portfolios in money balances, the proportion depending on [various well-known factors]. Moore argues that the concept of equilibrium is inadmissible in a monetary economy, since if we are in a certainty-equivalent world, we will not need money balances at all, while if there is uncertainty and changing expectations, you cannot ever reach afull equilibrium. While I accept that there is no clear role formoney in a certainty-equivalent Arrow-Debreu model, it does not seem to me that this prevents concepts of (partial) equilibrium, or balance, from being useful. Let me try one such thought experiment. The Central Bank decides, exogenously, to lower interest rates (because the stochastic error term in its reaction function shifts). In consequence, my aunt decides to borrow $10,000 to give me, her favorite nephew, the proceeds. Clearly, the increase in the supply of money is not independent of her demand function for loans, but the immediate cause of her decision was an exogenous policy change by the authorities. Why, then, is it illegitimate and misleading to analyze the effects of an increase in the supply of credit money, ceteris paribus? Is Moore arguing that there is no such thing as exogenous monetary policy decisions, or that they have no effect on the resulting volume of credit and money balances outstanding? Moore is, of course, absolutely correct that I will accept $10,000, or $1, or $100,000 from my aunt (kind aunt), but I do notnecessarily want

FAILURE OF THE KETY‐SCHMIDT NITROUS OXIDE METHOD FOR DETERMINATION OF MYOCARDIAL BLOOD FLOW

1. The reliability of the Kety-Schmidt nitrous oxide (N2O) blood-tissue equilibration method was examined in 50 studies of myocardial blood flow in seven conscious, unrestrained sheep using a newly developed carefully validated gas chromatographic assay for N2O. 2. In 10 studies the arterial and coronary sinus N2O blood concentration-time curves converged as expected at the end of the 10 min sampling period. In 14 studies they crossed over, and in 26 studies, the curves failed to converge. 3. A survey of the literature revealed that such results have been encountered previously but have not been accorded particular significance. An ultimate matching equilibrium between arterial and venous blood N2O concentration-time curves is, however, fundamental to the validity of the method. 4. The results indicate that the use of the Kety-Schmidt method with N2O as the indicator gas is invalid as applied to the measurement of myocardial blood flow in this preparation.

ANALYTICAL STUDY ON THE SHEAR CAPACITY OF REINFORCED CONCRETE BEAMS WITH WEB REINFORCEMENTS

The purpose of this study is theoretically to clarify the ultimate shear strengths and the deformations of reinforced concrete beams with web reinforcement, subjected to combined bending moment and shear. To achieve it, ultimate equilibrium method based on the energy principle is applied. The proposed equations which are derived by equilibrium condition of force and moment for the failure surface on the ultimate state are compared with test results and good agreement is noted. And, compatibility condition of strains on the shear element is considered to predict the failure mode of beams. Also, the interaction between bending moment and shear is proposed.

ANALYTICAL STUDY ON THE INTERACTION AMONG ULTIMATE STRENGTHS OF RC MEMBERS SUBJECTED TO FLEXURE-SHEAR AND AXIAL LOAD

The purpose of this study is theoretically to clarify the interaction among ultimate strengths of reinforced concrete members with web reinforcement, subjected to flexureshear and axial load simultaneously. Ultimate equilibrium method which is based on the energy principle is applied in order to evaluate the shear strength of RC member. The proposed equations are derived by equilibrium condition of force and moment for the failure surface on the ultimate state. And compatibility condition of strains on the shear element is considered to predict the failure mode of member. The interaction curves among three ultimate strengths -bending, shear, and axial capacities- are theoretically proposed. Furthermore, this study involves some significant considerations for the design method.

Finite amplitude and free vibrations of a body supported by incompressible, nonlinear viscoelastic shear mountings

A constitutive equation for an incompressible, isotropic, nonlinear viscoelastic solid of differential type, a class which includes the Voigt-Kelvin solid of classical linear viscoelasticity, is applied to study the quasi-static response of the material in a simple shearing deformation superimposed on a given static homogeneous strain. The Cauchy stress is determined and general relations that characterize creep and recovery phenomena are obtained. Specific equations are derived for a viscoelastic Mooney-Rivlin model. Then the finite amplitude, damped, free vibration of a rigid body supported symmetrically by viscoelastic Mooney-Rivlin shear mountings is examined, and solutions are given for heavily damped and lightly damped motions. The effects of the primary static deformation on creep and recovery phenomena of the shear blocks, and its effects on the frequency, damping, and logarithmic decrement characteristic of the motion are described analytically and illustrated graphically. Effects of the ultimate equilibrium shear induced by the load also are described. Universal frequency and damping relations for viscoelastic Mooney-Rivlin and neo-Hookean models are noted. It is shown that the primary homogeneous deformation plays an important role in determination of all aspects of the mechanical response. General equations for the exact solution of the problem for free vibrations of a load on nonlinear, perfectly elastic shear mountings also are provided.

Thermodynamic equilibrium limits of extremely small droplets in supersaturated vapour

A phenomenological thermodynamic description of equilibrium conditions between extremely small droplets and highly supersaturated vapour is presented with account taken of real gas properties and of the surface tension dependence on the droplet size. Spinodal conditions i.e. ultimate limit equilibrium conditions are examined and employed in derivation of equations describing dropletvapour equilibrium in the whole range of supersaturation states and droplet sizes. Calculation results of characteristic data are presented and discussed.

Analysis of winding stockroll potential

When a dielectric web is wound into a stockroll, the electrical potential of the stockroll can build to a very high value if the web carries a net electrical charge, such as from electrification by conveyance rollers. If the web has a somewhat conductive layer the stockroll potential will reach a limiting value due to conduction away from the stockroll. If the web has finite resistivity, a current will flow in the web, due to the potential gradient between the building stockroll and the last conveyance roller, and may be sufficient to limit the stockroll potential (SRP). The relationship between this limiting SRP and the conveyance parameters of web velocity, web conductivity, charge density on the moving web, and other parameters is discussed in terms of a model whose characteristics are derived and compared with measurements made on winding stockrolls in a laboratory. Experimental results that confirm the predictions of the model are presented. The level of net charge on the web before windup is found to influence the rate at which the equilibrium potential is approached, but does not affect the ultimate equilibrium potential of the stockroll.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

パルス応答解析と有限共振応答解析による損傷評価に関する研究 : 完全弾塑性型復元力特性をもつ1質点系について

The authors have presented Ultimate Response Analysis (U.R.A.) by which one can evaluate earthquake responses of structures according to the principle of the ultimate energy equilibrium. In this analysis, response behaviours of structures are classified into the following two extreme typical cases, i.e., monotonic and cyclic responses. The former is calculated by Pulse Response Analysis (P.R.A.) and the latter by Finite Resonance Response Analysis (F.R.R.A.). In this report, an evaluation method of damages of elasto-plastic structures by the U.R.A. is proposed from the comparison of the results of the U.R.A. with those of usual time-history dynamic earthquake response analysis (E.R.A.). The followings are concluded : (1) Damage factor (D_u) by U.R.A. based on the assumption in Sect. 4-3is safe side evaluation as compared with damage factor (D_e) by E.R.A. (cf. Sect. 4-5, Figs.10-13) (2) The damage duration for F.R.R.A. (t^p_<fr>) is given by Eq. (27) as the product of the duration of strong motion above 0.06g acceleration (T_<p6g>) and the duration ratio (t^p) given by Eq. (26). And the number of cyclic response times by F.R.R.A. (n_c) is given by Eq. (28) as the division of damage duration (t^p_<fr>) by the difference time (T_<eq>-T_e). (cf. Sect. 5-3, Fig.18) (3) The damage factor by U.R.A. (D_<fr>) is given by Eqs. (10)-(18). In this research, the authors have presented a method of the quantitative evaluation of damages by U.R.A.

On optimal plastic anisotropy

An approach is developed for the optimal design of a structure, based on optimization of the anisotropic plastic properties of materials. Problems of maximizing the ultimate plastic rupture load as a result of optimal orientation of the plastic anisotropy axes in the structure elements are formulated. Necessary conditions are presented for optimality in the three-dimensional problem of the theory of ultimate plastic equilibrium. Cases of the torsion and bending of plastic rods are considered. The bilateral achievable estimates of the ultimate loads are obtained. It is noted that the conditions for achieving the upper and lower bounds agree with the necessary optimality conditions. It is proved that the maximum ultimate load is realized in the case when the direction with the greatest yield point of the material agrees with the direction given by the tangential stress vector at the time of exhaustion of the carrying capacity.

パルス応答解析による1質点系の地震応答評価 : Bi-linear型復元力特性:完全弾塑性型と塑性劣化型について

The authors have presented Ultimate Response Analysis by which one can evaluate earthquake responses and seismic damages according to the principle of the ultimate energy equilibrium. In this analysis, the response behaviours of structures are classified into the two typical cases, i.e., cyclic responses and monotonic responses. The former is calculated by Finite Resonance Response Analysis and the latter by Pulse Response Analysis (velocity and acceleration pulses). In this report, the physical meanings of Pulse Response Analysis are examined essentially and it is proposed here a more accurate seismic analytical method, i.e., Ultimate Response Analysis in which the following are taken into account : (1) An equivalent amplitude ratio of input sine pulse wave to input rectangular pulse wave, (2) An equivalent amplification ratio of the duration of input rectangular pulse wave (t_P) to the period of in put spectrum (T), (3) The rule by which velocity or acceleration pulse is adopted in Pulse Response Analysis, (4) An initial velocity (V_0) by Finite Resonance Response Analysis The quantitative verification of the results of analysis are performed by means of statistical evaluations of earthquake inputs and responses. From this study, it is able to be concluded that Ultimate Response Analysis proposed here has a sufficient practical use.

Assessment of the parameters of decompressed rock mass in conditions of ultimate equilibrium determined by the Coulomb-Mohr hypothesis : Galczynski, S; Gergowicz, Z In: Application of Analytical Methods to Mining Geomechanics (paper to the Proceedings of the 7th Plenary Session of the International Bureau of Rock Mechanics, World Mining Congress, Katowice, 24–26 June 1981)P91–96. Publ Rotterdam: A. A. Balkema, 1982

Assessment of the parameters of decompressed rock mass in conditions of ultimate equilibrium determined by the Coulomb-Mohr hypothesis : Galczynski, S; Gergowicz, Z In: Application of Analytical Methods to Mining Geomechanics (paper to the Proceedings of the 7th Plenary Session of the International Bureau of Rock Mechanics, World Mining Congress, Katowice, 24–26 June 1981)P91–96. Publ Rotterdam: A. A. Balkema, 1982

Numerical solution of free-boundary problems in fluid mechanics. Part 1. The finite-difference technique

We present here a brief description of a numerical technique suitable for solving axisymmetric (or two-dimensional) free-boundary problems of fluid mechanics. The technique is based on a finite-difference solution of the equations of motion on an orthogonal curvilinear coordinate system, which is also constructed numerically and always adjusted so as to fit the current boundary shape. The overall solution is achieved via a global iterative process, with the condition of balance between total normal stress and the capillary pressure at the free boundary being used to drive the boundary shape to its ultimate equilibrium position.

J-Curves and Stability of the Foreign-Exchange Market

This paper considers certain aspects of the interactions of the exchange rate and current account during the adjustment of an open economy to an exogenous shock. Its special focus is on the character of the adjustment path when the current account reacts to an exchange-rate change in a delayed and staggered fashion - i.e., with a so-called J-curve response. The sudy is motivated by the frequent observation in recent populat accounts of exchange-market developments that some currencies -- such as the yen, for example -- have been especially volatile because of the presence of pronounced J-Curve effects. According to these accounts, transactors in the foreign presssures on the exchange rate in the same direction as that of the original shift. As a result, this perverse feedback between the exchange rate and current account will generate a movement of the exchange rate in the "wrong" direction, at least until lagged, stabilizing current-account reactions come into play. Some accounts have gone further to suggest that such a process may generate endogenous cycles that overshoot the ultimate equilibrium and may even give rise to a fundamentally unstable dynamic. In the latter case, some sort of intervention or other braking device is required to maintain the system within acceptable bounds.