Interior Boundaries for Degenerate Elliptic Equations of Second Order Some Theory and Numerical Observations

2010 Mathematics Subject Classification: Primary 35J70; Secondary 35J15, 35D05.

Spontaneous order and social norms. Hayek’s theory of socio-cultural evolution

Hayek’s theory of socio-cultural evolution is a generalization of his theory on spontaneous market order. Hayek explains both the emergence of market and social institutions serving as a social basis for that order within the framework of a unified evolutionary logic. This logic interprets the emergence and survival of spontaneous order and group-level rules of conduct as an unintended consequence of human action. In order to explain the emergence of social norms exclusively on the basis of methodological individualism, one would have to give up an exclusively evolutionary explanation of these norms. Since Hayek applies the invisible-hand explanation to the investigation of social norms, he combines the position of methodological individualism with functionalist-evolutionary arguments in his analysis. Hayek’s theory of socio-cultural evolution represents a theory in the framework of which methodological individualism and functionalism do not crowd out but complement each other.

Spontaneous order and social norms. Hayek’s theory of socio-cultural evolution

Hayek's theory of socio-cultural evolution is a generalization of his theory on spontaneous market order. Hayek explains both the emergence of market and social institutions serving as a social basis for that order within the framework of a unified evolutionary logic. This logic interprets the emergence and survival of spontaneous order and group-level rules of conduct as an unintended consequence of human action. In order to explain the emergence of social norms exclusively on the basis of methodological individualism, one would have to give up an exclusively evolutionary explanation of these norms. Since Hayek applies the invisiblehand explanation to the investigation of social norms, he combines the position of methodological individualism with functionalist-evolutionary arguments in his analysis. Hayek's theory of socio-cultural evolution represents a theory in the framework of which methodological individualism and functionalism do not crowd out but complement each other.

Piaci rend és társadalmi normák. Hayek elmélete a társadalmi evolúcióról (Market order and social norms Hayek's theory of social evolution)

A hayeki szociokulturális evolúció elmélete a piaci rend elemzésének általánosítása. Hayek mind a piaci rend, mind a piaci rend alapzatául szolgáló társadalmi intézmények kialakulását és működését azonos logika alapján magyarázza. Ez a logika az egyéni cselekvések nem szándékolt következményeként értelmezi a spontán rend és a csoportszintű magatartásszabályok kialakulását és fennmaradását. A társadalmi normák magyarázatában a módszertani individualizmus elveinek érvényesítéséért az evolucionista perspektíva feladásával kellene fizetni. Hayek azonban a társadalmi normák magyarázatára is az evolucionista megközelítést alkalmazza, ezért egészíti ki a módszertani individualista megközelítést funkcionalista-evolucionista érvekkel. A szociokulturális evolúció hayeki elmélete példa arra, hogy a módszertani individualizmusra épülő magyarázat és a funkcionalista érvelés nem kiszorítja, hanem kiegészíti egymást. _____ Hayek's theory of socio-cultural evolution is a generalization of his theory of market order. He explains in the same way the development and operation of market order and those of the social institutions on which market order is based. This logic interprets the development and persistence of spontaneous order and group-level behaviour rules as an unintentional consequence of individual actions. In his explanation of social norms, enforcement of the principles of methodological individualism has to be paid for by abandoning the evolutionist perspective. But Hayek also employs an evolutionist approach in his explanation of social norms, and so he augments his methodological individualist approach with some functionalist-cum-evolutionist arguments. Hayek's theory of sociocultural evolution, for instance, exemplifies how an explanation resting on methodological individualism and a functionalist argument can complement, not preclude each other.

Quantum transition state theory and solving a first order master equation for complex reactions numerically

The field of chemical kinetics is an exciting and active field. The prevailing theories make a number of simplifying assumptions that do not always hold in actual cases. Another current problem concerns a development of efficient numerical algorithms for solving the master equations that arise in the description of complex reactions. The objective of the present work is to furnish a completely general and exact theory of reaction rates, in a form reminiscent of transition state theory, valid for all fluid phases and also to develop a computer program that can solve complex reactions by finding the concentrations of all participating substances as a function of time. To do so, the full quantum scattering theory is used for deriving the exact rate law, and then the resulting cumulative reaction probability is put into several equivalent forms that take into account all relativistic effects if applicable, including one that is strongly reminiscent of transition state theory, but includes corrections from scattering theory. Then two programs, one for solving complex reactions, the other for solving first order linear kinetic master equations to solve them, have been developed and tested for simple applications.

Reverse-flow integral methods for second-order supersonic flow theory,

"CM-1033."

Foundational, First-Order, and Second-Order Classification Theory

Both basic and applied research on the construction, implementation, maintenance, and evaluation of classification schemes is called classification theory. If we employ Ritzer’s metatheoretical method of analysis on the over one-hundred year-old body of literature, we can see categories of theory emerge. This paper looks at one particular part of knowledge organization work, namely classification theory, and asks 1) what are the contours of this intellectual space, and, 2) what have we produced in the theoretical reflection on con- structing, implementing, and evaluating classification schemes? The preliminary findings from this work are that classification theory can be separated into three kinds: foundational classification theory, first-order classification theory, and second-order classification theory, each with its own concerns and objects of study.

Density functional theory study of Fe(3)Ga

First-principles scalar relativistic calculations in supercells of 16 atoms are used to represent disordered B2 ordering of Fe(3)Ga in order to observe the effect of Ga-Ga pairs on the electronic structure of this alloy. From a comparison with pure bcc Fe it is observed that the energy position and occupation of e(g) and t(2g) states are largely affected by the Ga-Ga pairs and strengthened intraplane interactions takes place. The results show that a larger hybridization of the conduction band is in the source of the magnetostriction enhancement experimentally observed in Galfenol. (C) 2011 American Institute of Physics. [doi:10.1063/1.3525609]

Decision theory applied to image quality control in radiology

Background: The present work aims at the application of the decision theory to radiological image quality control ( QC) in diagnostic routine. The main problem addressed in the framework of decision theory is to accept or reject a film lot of a radiology service. The probability of each decision of a determined set of variables was obtained from the selected films. Methods: Based on a radiology service routine a decision probability function was determined for each considered group of combination characteristics. These characteristics were related to the film quality control. These parameters were also framed in a set of 8 possibilities, resulting in 256 possible decision rules. In order to determine a general utility application function to access the decision risk, we have used a simple unique parameter called r. The payoffs chosen were: diagnostic's result (correct/incorrect), cost (high/low), and patient satisfaction (yes/no) resulting in eight possible combinations. Results: Depending on the value of r, more or less risk will occur related to the decision-making. The utility function was evaluated in order to determine the probability of a decision. The decision was made with patients or administrators' opinions from a radiology service center. Conclusion: The model is a formal quantitative approach to make a decision related to the medical imaging quality, providing an instrument to discriminate what is really necessary to accept or reject a film or a film lot. The method presented herein can help to access the risk level of an incorrect radiological diagnosis decision.

Pressure of massless hot scalar theory in the boundary effective theory framework

We use the boundary effective theory approach to thermal field theory in order to calculate the pressure of a system of massless scalar fields with quartic interaction. The method naturally separates the infrared physics, and is essentially nonperturbative. To lowest order, the main ingredient is the solution of the free Euler-Lagrange equation with nontrivial (time) boundary conditions. We derive a resummed pressure, which is in good agreement with recent calculations found in the literature, following a very direct and compact procedure.

Finiteness of the noncommutative supersymmetric Maxwell-Chern-Simons theory

Within the superfield approach, we prove the absence of UV/IR mixing in the three-dimensional noncommutative supersymmetric Maxwell-Chern-Simons theory at any loop order and demonstrate its finiteness in one, three, and higher loop orders.

SYNCHRONIZATION OF A CLASS OF SECOND-ORDER NONLINEAR SYSTEMS

The asymptotic behavior of a class of coupled second-order nonlinear dynamical systems is studied in this paper. Using very mild assumptions on the vector-field, conditions on the coupling parameters that guarantee synchronization are provided. The proposed result does not require solutions to be ultimately bounded in order to prove synchronization, therefore it can be used to study coupled systems that do not globally synchronize, including synchronization of unbounded solutions. In this case, estimates of the synchronization region are obtained. Synchronization of two-coupled nonlinear pendulums and two-coupled Duffing systems are studied to illustrate the application of the proposed theory.

Enhanced aeroelastic energy harvesting by exploiting combined nonlinearities: theory and experiment

Converting aeroelastic vibrations into electricity for low power generation has received growing attention over the past few years. In addition to potential applications for aerospace structures, the goal is to develop alternative and scalable configurations for wind energy harvesting to use in wireless electronic systems. This paper presents modeling and experiments of aeroelastic energy harvesting using piezoelectric transduction with a focus on exploiting combined nonlinearities. An airfoil with plunge and pitch degrees of freedom (DOF) is investigated. Piezoelectric coupling is introduced to the plunge DOF while nonlinearities are introduced through the pitch DOF. A state-space model is presented and employed for the simulations of the piezoaeroelastic generator. A two-state approximation to Theodorsen aerodynamics is used in order to determine the unsteady aerodynamic loads. Three case studies are presented. First the interaction between piezoelectric power generation and linear aeroelastic behavior of a typical section is investigated for a set of resistive loads. Model predictions are compared to experimental data obtained from the wind tunnel tests at the flutter boundary. In the second case study, free play nonlinearity is added to the pitch DOF and it is shown that nonlinear limit-cycle oscillations can be obtained not only above but also below the linear flutter speed. The experimental results are successfully predicted by the model simulations. Finally, the combination of cubic hardening stiffness and free play nonlinearities is considered in the pitch DOF. The nonlinear piezoaeroelastic response is investigated for different values of the nonlinear-to-linear stiffness ratio. The free play nonlinearity reduces the cut-in speed while the hardening stiffness helps in obtaining persistent oscillations of acceptable amplitude over a wider range of airflow speeds. Such nonlinearities can be introduced to aeroelastic energy harvesters (exploiting piezoelectric or other transduction mechanisms) for performance enhancement.

Verification of a mixed high-order accurate DNS code for laminar turbulent transition by the method of manufactured solutions

This paper presents results on a verification test of a Direct Numerical Simulation code of mixed high-order of accuracy using the method of manufactured solutions (MMS). This test is based on the formulation of an analytical solution for the Navier-Stokes equations modified by the addition of a source term. The present numerical code was aimed at simulating the temporal evolution of instability waves in a plane Poiseuille flow. The governing equations were solved in a vorticity-velocity formulation for a two-dimensional incompressible flow. The code employed two different numerical schemes. One used mixed high-order compact and non-compact finite-differences from fourth-order to sixth-order of accuracy. The other scheme used spectral methods instead of finite-difference methods for the streamwise direction, which was periodic. In the present test, particular attention was paid to the boundary conditions of the physical problem of interest. Indeed, the verification procedure using MMS can be more demanding than the often used comparison with Linear Stability Theory. That is particularly because in the latter test no attention is paid to the nonlinear terms. For the present verification test, it was possible to manufacture an analytical solution that reproduced some aspects of an instability wave in a nonlinear stage. Although the results of the verification by MMS for this mixed-order numerical scheme had to be interpreted with care, the test was very useful as it gave confidence that the code was free of programming errors. Copyright (C) 2009 John Wiley & Sons, Ltd.