Renormalization and Essential Singularity

In usual dimensional counting, momentum has dimension one. But a function f(x), when differentiated n times, does not always behave like one with its power smaller by n. This inevitable uncertainty may be essential in general theory of renormalization, including quantum gravity. As an example, we classify possible singularities of a potential for the Schr\"{o}dinger equation, assuming that the potential V has at least one $C^2$ class eigen function. The result crucially depends on the analytic property of the eigen function near its 0 point.Comment: 12 pages, no figures, PTPTeX with amsfonts. 2 pages added for detail

Numerical simulation of steady supersonic flow

A noniterative, implicit, space-marching, finite-difference algorithm was developed for the steady thin-layer Navier-Stokes equations in conservation-law form. The numerical algorithm is applicable to steady supersonic viscous flow over bodies of arbitrary shape. In addition, the same code can be used to compute supersonic inviscid flow or three-dimensional boundary layers. Computed results from two-dimensional and three-dimensional versions of the numerical algorithm are in good agreement with those obtained from more costly time-marching techniques

Aerodynamic characteristics of the standard dynamics model in coning motion at Mach 0.6

A wind tunnel test was conducted on the Standard Dynamics Model (a simplified generic fighter aircraft shape) undergoing coning motion at Mach 0.6. Six component force and moment data are presented for a range of angle of attack, sideslip, and coning rates. At the relatively low non-dimensional coning rate employed (omega b/2V less than or equal to 0.04), the lateral aerodynamic characteristics generally show a linear variation with coning rate

On the formulation of the aerodynamic characteristics in aircraft dynamics

The theory of functionals is used to reformulate the notions of aerodynamic indicial functions and superposition. Integral forms for the aerodynamic response to arbitrary motions are derived that are free of dependence on a linearity assumption. Simplifications of the integral forms lead to practicable nonlinear generalizations of the linear superpositions and stability derivative formulations. Applied to arbitrary nonplanar motions, the generalization yields a form for the aerodynamic response that can be compounded of the contributions from a limited number of well-defined characteristic motions, in principle reproducible in the wind tunnel. Further generalizations that would enable the consideration of random fluctuations and multivalued aerodynamic responses are indicated

Regional integration as diplomacy

Regional integration agreements (RIAs) are examples of second best and have an ambiguous impact on welfare, contend the authors. They build a model in which RIAs unambiguously raise welfare by correcting for externalities. It assumes that trade between neighboring countries increases trust between them and reduces the likelihood of conflict. The optimum intervention in that case is a subsidy on imports from the neighbor. The authors show that an equivalent solution is for the neighboring countries to tax imports fromthe rest of the world -that is, to form an RIA- together with imposing some domestic taxes. In fact, security threats have moved neighboring countries to form RIAs. Examples include the creation of the European Coal and Steel Community (1951) and the European Economic Community (1957) to reduce the threat of war in Europe, as well as various RIAs among developing countries. The authors show, among other things, that: 1) the optimum tariffs on imports from the rest of the world are likely to decline over time; 2) deep integration implies lower optimum external tariffs if it is exogenous; 3) but if deep integration is endogenous, it implies higher optimum external tariffs before it occurs and lower ones thereafter; and 4) enlargement of a bloc (in terms of symmetric countries) has an ambiguous impact on external tariffs but improves welfare, and some form of domino effect exists in the sense that enlargement increases the incentive for nonmembers to seek accession. Although externalities associated with security matters imply that an RIA may maximize welfare, this model suggests that the RIA is a transitory arrangement in the sense that optimum trade preferences are highest at the time the RIA is formed (when security is low) and tend to decline over time. In other words, the RIA's external trade policy becomes increasingly open over time (as well as following deep integration).Rules of Origin,Environmental Economics&Policies,Economic Theory&Research,Payment Systems&Infrastructure,Trade Policy,Trade Policy,Environmental Economics&Policies,Economic Theory&Research,TF054105-DONOR FUNDED OPERATION ADMINISTRATION FEE INCOME AND EXPENSE ACCOUNT,Trade and Regional Integration

Regional cooperation, and the role of international organizations and regional integration

The authors examine regional cooperation among neighboring countries in the area of regional public goods. These public goods include water basins (such as lakes, rivers, and underground water), infrastructure (such as roads, railways, and dams), energy, and the environment. Their analysis focuses on developing countries and the potentially beneficial role that international organizations and regional integration may play in bringing the relevant countries to a cooperative equilibrium. A major problem in reaching a cooperative solution is likely tobe the lack of trust. If neighboring countries do not trust each other because of past problems, they may fail to reach a cooperative solution as each tries to maximize its gain from the regional public good. These strategies typically do not account for spillover effects and ultimately leads to losses for all parties. Other constraints on reaching a cooperative solution are its complexity and the financial requirements. Two types of institutions may help resolve some or all of these problems. International organizations can help with trust, expertise, and financing. The United Nations and the World Bank have been involved in a number of such projects in Africa, Asia, and elsewhere, and have been successful in helping parties reach cooperative solutions. Regional integration agreements, though not necessary for regional cooperation, may also be helpful by embedding the negotiations on regional cooperation in a broader institutional framework. The authors examine these issues with the support of both analysis and a number of case studies.Environmental Economics&Policies,Water and Industry,Decentralization,Water Conservation,Common Property Resource Development,Water Supply and Sanitation Governance and Institutions,Water and Industry,Water Conservation,Environmental Economics&Policies,Common Property Resource Development

Application of CFD techniques toward the validation of nonlinear aerodynamic models

Applications of Computational fluid dynamics (CFD) methods to determine the regimes of applicability of nonlinear models describing the unsteady aerodynamic responses to aircraft flight motions are described. The potential advantages of computational methods over experimental methods are discussed and the concepts underlying mathematical modeling are reviewed. The economic and conceptual advantages of the modeling procedure over coupled, simultaneous solutions of the gasdynamic equations and the vehicle's kinematic equations of motion are discussed. The modeling approach, when valid, eliminates the need for costly repetitive computation of flow field solutions. For the test cases considered, the aerodynamic modeling approach is shown to be valid

The role of time-history effects in the formulation of the aerodynamics of aircraft dynamics

The scope of any aerodynamic formulation proposing to embrace a range of possible maneuvers is shown to be determined principally by the extent to which the aerodynamic indicial response is allowed to depend on the past motion. Starting from the linearized formulation, in which the indicial response is independent of the past motion, two successively more comprehensive statements about the dependence on the past motion are assigned to the indicial response: (1) dependence only on the recent past and (2) dependence additionally on a characteristic feature of the distant past. The first enables the rational introduction of nonlinear effects and accommodates a description of the rate dependent aerodynamic phenomena characteristic of airfoils in low speed dynamic stall; the second permits a description of the double valued aerodynamic behavior characteristic of certain kinds of aircraft stall. An aerodynamic formulation based on the second statement, automatically embracing the first, may be sufficiently comprehensive to include a large part of the aircraft's possible maneuvers. The results suggest a favorable conclusion regarding the role of dynamic stability experiments in flight dynamics studies

Towards reliable calculations of the correlation function

The correlation function of two identical pions interacting via Coulomb potential is computed for a general case of anisotropic particle's source of finite life time. The effect of halo is taken into account as an additional particle's source of large spatial extension. Due to the Coulomb interaction, the effect of halo is not limited to very small relative momenta but it influences the correlation function in a relatively large domain. The relativistic effects are discussed in detail and it is argued that the calculations have to be performed in the center-of-mass frame of particle's pair where the (nonrelativistic) wave function of particle's relative motion is meaningful. The Bowler-Sinyukov procedure to remove the Coulomb interaction is tested and it is shown to significantly underestimate the source's life time.Comment: 18 pages, presented at XIth International Workshop on Correlation and Fluctuation in Multiparticle Production, Hangzhou, China, November 21-24, 200

Investigation of the utility of mean square approximation systems and in system response predictions

A method is presented for estimating the variability of a system's natural frequencies arising from the variability of the system's parameters. The only information required to obtain the estimates is the member variability, in the form of second order properties, and the natural frequencies and mode shapes of the mean system. Several examples are worked out in detail to illustrate how the method is applied