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The combustion behavior of energetic materials (e.g., solid propellants) has long been of interest in the fields of propulsion and pyrotechnics. In many such applications, it is becoming increasingly clear that two-phase flow effects play an important role, especially since, during combustion, most homogeneous solid propellants develop thin multi-phase layers at their surfaces in which finite-rate exothermic reactions occur. In addition, there is a growing interest in the behavior of porous energetic solids, since even initially dense materials can develop significant void fractions if, at any time, they are exposed to abnormal thermal environments. The deflagration characteristics of such ``damaged`` materials may then differ significantly from those of the pristine material due, at least in part, to gas flow in the solid/gas preheat region. The presence of gas in the porous solid in turn results in a more pronounced two-phase effect in the multi-phase surface layer, such as in the liquid melt region of nitramine propellants, which thus tend to exhibit extensive bubbling in an exothermic foam layer. The present analysis is largely applicable to this latter class of propellants.

Do economies and markets make remediable errors in the choice of products? Does the economy "lock-in" to these incorrect choices even when the knowledge that these choices are incorrect is readily available? The literature of path dependence may be understood to argue that these lock-ins and errors occur, even in a world characterized by voluntary decisions and individually maximizing behavior. In this article, we examine path dependence and illustrate three different forms of the term, each having a different implication regarding market errors and lock-in. Two of these meanings are common in the economy but provide no support for the claims that remediable errors occur. The third meaning, which does imply irremediable error, we show to be based on highly restrictive and implausible assumptions. The analysis is illustrated by examining the market's choice of video-recorder formats. Path dependence has been offered as an alternative analytical perspective for economics, a revolutionary reformulation of the neoclassical paradigm. Brian Arthur, a leading figure in this literature, distinguishes between "conventional economics," which largely avoids increasing returns or path dependence, and the new "positive feedback economics," which embraces them (Arthur, 1990: 99). Before we stroll too far along the path dependence path, however, it makes sense to stop, take stock, and figure out where that path is leading us. The claim for path dependence is that a minor or fleeting advantage or a seemingly inconsequential lead for some technology, product, or standard can have important and irreversible influences on the ultimate market allocation of resources, even in a world characterized by voluntary decisions and individually maximizing behavior. The path dependence literature comes to us accompanied and motivated by amathematical literature of nonlinear dynamic models, known as chaos or complexity models, for which a key finding is "sensitive dependence

The combustion of solids and high-density fluids, such as the combustion synthesis of refractory materials or the high-pressure oxidation of organic compounds in supercritical water, is often characterized by a highly temperature-dependent mass diffusivity. In particular, the case of an Arrhenius dependence of this quantity on temperature is considered, where the activation energy of reactant diffusion is of the same order as that of the overall chemical reaction. Exploiting the asymptotic limit of large activation energies, it is shown that reactant diffusion becomes significant in the thin reaction zone, where a balance among convection, reaction, and diffusion is maintained. Relative to the case of either a zero or constant mass diffusion coefficient, this leads to modifications in the steady, planar flame-speed eigenvalue. A new asymptotic model is then derived that predicts corresponding shifts in the neutral stability boundary that marks the transition from steady to nonsteady modes of flame propagation.

Background Earlier studies have successfully demonstrated that medical students can achieve success in core clinical rotations with long term attachments in small groups to rural general / family practices. Methods In this study, three students from a class of 226 volunteered for this 1-year pilot program, conducted by the University of Queensland in 2004, for medical students in the 3rd year of a 4-year graduate entry medical course. Each student was based with a private solo general practitioner in a different rural town between 170 and 270 km from the nearest teaching hospital. Each was in a relatively isolated rural setting, rated 5 or 6 on the RRMA scale (Rural, Remote, Metropolitan Classification: capital city = 1, other metropolitan = 2, large regional city = 3, most remote community = 7). The rural towns had populations respectively of 500, 2000 and 10,000. One practice also had a General Practice registrar. Only one of the locations had doctors in the same town but outside the teaching practice, while all had other doctors within the same area. All 3 supervisors had hospital admitting rights to a hospital within their town. The core clinical rotations of medicine, surgery, mental health, general practice and rural health were primarily conducted within these rural communities, with the student based in their own consulting room at the general practitioner (GP) supervisor's surgery. The primary teacher was the GP supervisor, with additional learning opportunities provided by visiting specialists, teleconferences and university websites. At times, especially during medicine and surgery terms, each student would return to the teaching hospital for additional learning opportunities. Results All students successfully completed the year. There were no statistical differences in marks at summative assessment in each of the five core rotations between the students in this pilot and their peers at the metropolitan or rural hospital based clinical schools. Conclusion The results suggest that isolated rural general practice could provide a more substantial role in medical student education.

The leading-order fluid motions and frequencies in resonance tubes coupled to a combustion-driven flow source, such as occurs in various types of pulse combustors, are usually strongly related to those predicted by linear acoustics. However, in order to determine the amplitudes of the infinite number of classical acoustic modes predicted by linear theory alone, and hence the complete solution, a nonlinear analysis is required. In the present work, we adopt a formal perturbation approach based on the smallness of the mean-flow Mach number which, as a consequence of solvability conditions at higher orders in the analysis, results in an infinitely coupled system of nonlinear evolution equations for the amplitudes of the linear acoustic modes

A vectorized separation of variables approach is applied to a coupled pair of parabolic partial differential equations describing the degradation of a thermocline in a packed bed thermal storage tank. The time-dependent quasi-one-dimensional model includes the effects of finite tank length, thermal conduction in the direction parallel to the tank walls, and heat transfer between the fluid and solid components of the bed. For certain classes of boundary conditions, the analysis leads to an eigenvalue problem for the spatial dependence of the fluid and solid temperatures in the bed. The eigenvalues and corresponding eigenfunctions are readily calculated, and completeness of the eigenfunctions follows from a transformation to an integral equation by the construction of a Green’s tensor function. The method is illustrated by an example which arises in the analysis of the thermal storage subsystem of a central solar receiver power plant.

We consider premixed flame propagation in long rectangular channels. A steadily propagating planar flame is stable for Lewis numbers less than a critical value. For Lewis numbers exceeding this critical value a sequence of primary bifurcation states, corresponding to time-periodic pulsating cellular flames, emanates from the steadily propagating solution. We analyze the problem in a neighborhood of a multiple primary bifurcation point. By varying the channel dimensions, we split the multiple bifurcation point and show that a stable quasi-periodic pulsating flame can arise as a secondary bifurcation from one of the primary bifurcation states. We also exhibit the phenomenon of mode-jumping, in which there is an exchange of stability between two primary states.

A dynamic model of liquid propellant combustion is introduced which generalizes the classical models of Landau [ Acta Physicochim . 19:77–85 (1944)] and Levich [ Dokl. Akad. Nauk SSSR 109:975–978 (1956)]. These earlier studies assumed that the liquid/gas interface propagated normal to itself with constant velocity, and showed that steady, planar burning was intrinsically unstable unless gravitational effects, coupled with either the effects due to surface tension or (liquid) viscosity, were sufficiently strong. In contrast, the present model assumes a more general pyrolysis burning rate law, and preliminary results reported in Part I [ Twenty-Second Symposium (International) on Combustion , 1988] indicate that the resulting coupling of the temperature field can render steady, planar burning stable with respect to hydrodynamic (Landau) instability even in the absence of gravity and surface tension. At the same time, a new type of reactive/diffusive pulsating instability appears for sufficiently large values of a temperature sensitivity parameter. In Part II, a complete linear stability analysis of both hydrodynamic and reactive/diffusive instabilities in the limit of zero viscosity is presented, allowing for a pressure, as well as a temperature, dependence in the burning rate law, and nonzero gravity and surface tension. The results indicate still more types of hydrodynamic and reactive/diffusive instability phenomena, as well as a stable parameter region for steady, planar deflagration.

The steady propagation of a planar flame through a premixed combustible mixture is studied for the case in which the mixture contains two distinct fuels which compete for available oxidizer. It is assumed that sufficient oxidizer is present in the unburned mixture to allow for eventual complete burning of both fuels. Employing the method of matched asymptotic expansions to derive a solution for large activation energies, the propagation velocity U and the effective separation distance H between the points where the two chemical reactions go to completion are determined as functions of standard flame parameters. The analysis extends a recent study by Margolis and Matkowsky (1982a) to include the effects of stoichiometry on flame propagation with multiple fuels.

The one-dimensional, time-dependent, multicomponent premixed laminar flame is solved via a highly accurate method of lines approach. The neglect of pressure variations and viscous dissipation and the use of a Lagrangian spatial coordinate reduce the problem to a system of parabolic partial differential equations for the species concentrations and the temperature. Introducing an appropriate B-spline (finite element) basis for the spatial variation and imposing collocation and boundary conditions on the time-dependent coefficients produce a stiff ordinary initial value problem which can be solved by standard techniques. Physical results of special interest include the transient and steady-state profiles of fluid velocity, temperature, and species concentrations through the reaction zone and the upstream velocity (flame speed) of the combustible mixture required to asymptotically stabilize the flame. The analysis is illustrated for the case of an ozone decomposition flame and a comparison with other theoretical predictions shows that the use of less accurate methods can result in significant errors in the predicted values of minor species profiles and the flame speed.

A one-dimensional, steady, non-adiabatic, premixed laminar flame is assumed semi-infinite with the burner at the origin, and the investigation centers on the asymptotic behavior of the temperature and species mass fractions in the burned region near infinity. After a consideration of the generalNN-species problem, specific results are obtained for the global two-step reactionvrR→μiI{v_r}R \to {\mu _i}I,vrI→μpP{v_r}I \to {\mu _p}P, whereRR,II,PPdenote reactant, intermediate, and product species, respectively, andvr{v_r},vi{v_i},μi{\mu _i},μp{\mu _p}are stoichiometric coefficients. Assuming Arrhenius kinetics, it is shown that the classical linearized asymptotic theory is not applicable unlessvr=vi=1{v_r} = {v_i} = 1, in which case the approach to burned equilibrium is an exponential decay. Consequently, a nonlinear theory applicable to arbitraryvr{v_r}andvi{v_i}is presented which shows that in general the asymptotic decay is algebraic. It is further shown that boundedness of the solution at infinity permits the arbitrary specification of only three boundary conditions on the original sixth-order differential system. This result is illustrated by a comprehensive analytical example and the computational implications for the generalNN-species problem are discussed.

THE efficiency paradigm of wealth maximization has provided a coherent framework for understanding many aspects of the law. Unfortunately, that understanding can be hampered by a failure to specify precisely what is meant by efficiency. In the absence of a clear definition, confusion is likely. This confusion is important. A faulty definition of efficiency will lead to a faulty analysis, which could exclude key features of the social situation that must be accounted for in any assessment of the legal setting. In this paper, I seek to identify two closely related definitions of wealth maximization. I show how they differ and why the second definition is superior in connection with a number of plausible illustrations where the choice between the definitions leads to a difference in outcome. To the extent that writers in this field state explicitly what they mean by wealth maximization, they usually echo the definition that Posner offers in his textbook: "Efficiency means exploiting economic resources in such a way that value-human satisfaction as measured by aggregate willingness to pay for goods and services-is maximized."' There is, however, an ambiguity in considering willingness to pay: what shall we assume about the cost of expressing that willingness? For example, suppose I have a neighbor who keeps a messy yard, and suppose further that I would be willing to pay $200 to have him clean up his property. Unfortunately, the cost of expressing this concern and specifying a contract is

Abstract— We derive a model which describes the dynamics ofa multiphase system consisting ofa gas flame attached to a pyrolyzing solid or liquid propellant. We consider the case in which the multiphase ftame, which includes the propellant interface, the preheat zone and the gas- phase reaction zone, is thin compared to some characteristic hydrodynamic length. An asymptotic analysis of the inner structure then yields jump conditions on the fluid and transport variables across the multiphase flame, which is treated as a surface of discontinuity separating the unburned condensed-phase propellant from the burned gas. The resulting model, which describes the evolution of this surface, is then used to investigate the hydrodynamic (Landau) stability of propellant deftagration. In particular, it is shown that this type of instability is completely suppressed for solid propellants, whereas for liquid propellants. a cellular instability arises which is similar to that which occurs in premixed flame propaga...

We derive a nonlinear evolution equation and associated boundary conditions which, under certain circumstances, describe downward adiabatic flame propagation in long, vertical channels. We analyze this problem for the case of axial symmetry and show that there exist two critical parameters, the channel radius R and a gravitational acceleration parameter G, which determine the stability and bifurcation characteristics of the flame. In particular, we show that there exist discrete critical points in the $(G,R)$ plane at which either one or three solutions corresponding to bimodal cellular flames bifurcate from the basic planar solution. We perform a nonlinear stability and bifurcation analysis in arbitrary neighborhoods of these critical points and show that either zero, one or two of the branches are stable, and the remaining branches are unstable. We thus describe new stable modes of cellular flame propagation.

A nonlinear response theory is employed to obtain the modification of the mean burning rate of a nonhomogeneous solid propellant. Although the methods used here are quite general, attention is focused on the interaction between the three-dimensional structure of the deflagration and the constitutive model. Based on a calculation of the mean burning rate as a function of the correlation length of a random nonhomogeneity, it is shown that the mean burning rate is greater than that of homogeneous burning for small correlation lengths, and is less for larger correlation lengths. Thus, this study indicates that a solid composed of particles of two different propellants would burn more slowly than their mean rate if the size of the particles were large, and more quickly if their size were small. As many of the methods used here are new to this application, some comment is also made on the utility of this approach in computing mean burning rate statistics for random media.

We employ a nonlinear stability analysis in the neighborhood of a multiple bifurcation point to describe the interaction of pulsating and spinning modes of condensed phase combustion. Such phenomena occur in the synthesis of refractory materials. In particular, we consider the propagation of combustion waves in a long thermally insulated cylindrical sample and show that steady, planar combustion is stable for a modified activation energy/melting parameter less than a critical value. Above this critical value primary bifurcation states, corresponding to time-periodic pulsating and spinning modes of combustion, emanate from the steadily propagating solution. By varying the sample radius, we split a multiple bifurcation point to obtain bifurcation diagrams which exhibit secondary, tertiary, and quaternary branching to various types of quasi-periodic combustion waves.

The one-dimensional stability of an isobaric burner-stabilized premixed flame is investigated for arbitrary Lewis number and stoichiometry in the asymptotic limit of large activation energy. Assuming a one-step irreversible chemical reaction in which fuel and oxidizer react to form a product, a linear stability analysis is Used to calculate the neutral stability boundary in Lewis number-activation energy space as a function of incoming flow velocity (or equivalently, the burned temperature) The major result is that although a steady-state adiabatic flame is likely to be stable for typical parameter values, a value of the incoming flow velocity sufficiently less than the adiabatic flame speed is destabilizing to the extent that the unstable region becomes feasible for many flames. Consequently, if all other parameters are fixed, there exists for such flames a critical value of the incoming flow velocity at which the time-asymptotic solution to the time-dependent problem bifurcates from the nontriv...

In a classical study of liquid propellant combustion. Landau 1 introduced a simple model in which the liquid/gas interface was assumed to propagate normal to itself with constant velocity. Such a model, applied to the problem of premixed flame propagation, introduced the phenomenon of hydrodynamic flame instability, in which steady, planar deflagration was unstable to steady, but nonplanar (cellular), disturbances. For the case of liquid propellants, it was shown that the inclusion of gravitational and surface tension effects could supress this phenomenon, whereas a later study due to Levich 2 showed that the coupling of gravitational and viscous effects could produce a similar result. In the present work, we show that the assumption of a more realistic pyrolysis burning-rate law, which couples the temperature field to the problem, also is stabilizing with respect to hydrodynamic instability. In addition, this model admits a pulsating type of instability associated with the thermal sensitivity of the chemical reaction, analogous to that which exists for solid propellant combustion and the combustion synthesis of refractory materials. These results parallel recent developments in flame theory, which also suggest that the dynamic coupling of the burning rate with local conditions at the flame front can suppress Landau instability. In addition, however, the present work presents a closed-form expression for the dispersion relation, and predicts regions of stability for steady, planar burning with to both hydrodynamic and reactive/diffusive instabilities.

Combustible mixtures under supercritical pressures and temperatures are capable of supporting a self-propagating flame under certain conditions. We consider the multiplicity and stability of such flames in a nonadiabatic tubular reactor as a function of inflow velocity, inlet and volumetric heat loss parameters, reactor length, and overall activation energy. We find that a steady, planar flame can only exist within certain parameter ranges, and that there are both high- and low-temperature solutions which correspond to a given flame position within the reactor. In addition, a linear stability analysis shows that for sufficiently large values of the overall activation energy, the high-temperature solution is unstable to disturbances which correspond to nonsteady, nonplanar supercritical flames. Consequently, we show that for typical values of this parameter, the basic solution branch representing high-temperature, steady combustion is stable when the flame lies well within the reactor, but it lose...

The USA and Canada are each considering measures to reduce general exposure to asbestos. Product bans and workplace exposure rules may each reduce general exposure by reducing domestic asbestos demand. The effectiveness of demand-reducing measures will depend upon the elasticity of asbestos supply to the domestic market. This paper provides calculations of this elasticity for three fibre grade groupings, using a framework that recognizes international trade in asbestos and the joint product nature of most asbestos fibre production. The results suggest that reductions in North American demand result in relatively substantial changes in asbestos use but very small changes in price.

We employ a nonlinear stability analysis to describe the bifurcation of pulsating and spinning modes of combustion in condensed media. We adopt the two-phase model of Margolis (1983) in which the modified nondimensional activation energy Δ of the reaction is large, but finite, and in which the limiting component of the mixture melts during the reaction process, as characterized by a nondimensional melting parameter M. We identify several types of non-steady solution branches which bifurcate from the steady palanar solution and show that they are supercritical and stable only for certain realistic ranges of M. For example, the spinning modes, though supercritical and stable for a range of M > 0, are subcritical and unstable for M = 0.

Steady, planar propagation of a condensed phase reaction front is unstable to disturbances corresponding to pulsating and spinning waves for sufficiently large values of a parameter related to the activation energy. This paper considers the nonlinear evolution equations for the amplitudes of the pulsating and spinning waves in a neighborhood of a double eigenvalue of the problem linearized about the steady, planar solution. In particular, near a degenerate Hopf bifurcation point, closed branches of solutions which represent new quasi-periodic modes of combustion are described.

The reaction rate of a heterogeneous, or diffusion-limited, reaction in a solid combustible mixture, sub seq uent to melting of one of the reactants, is proportional to exp[ - m(1- Y)](l- y)-n exp( - [etilde]/[ttilde]), where Y is the unreacted fraction and r is the temperature. We exploit the largeness of the activation energy Eto derive an asymptotic model for the propagation of a reaction front through such a mixture. The analysis parallels a similar study of homogeneous condensed combustion (Margolis, 1983), in which the reaction rate both before and after melting is proportional to Y exp( - [etilde]/[ttilde]). We derive formulas for the propagation speed of a steady planar reaction front, as well as present the asymptotic model for nonsteady, non planar combustion. This model is identical in form to that obtained from a special limiting case of the homogeneous problem. Thus, the well-known loss of stability of the stead y planar solution for sufficiently large values of a modified activation...

The steady propagation of a flame through a premixed combustible mixture is studied for the case in which the mixture consists of two distinct fuels. The overall chemical reaction mechanism is represented by $A + \nu_A O \to \mu _A P,B + \nu_B O \to \mu _B Q$, where A and B denote the fuels, O is the oxidizer, P and Q are the corresponding products, and $\nu_A ,\mu _A ,\nu_B ,\mu _B $, are stoichiometric coefficients. We employ the method of matched asymptotic expansions to derive a solution for large activation energies, in which case both chemical reactions are confined to a thin layer. The (small) separation distance H between the points where the two reactions go to completion and the propagation velocity U are determined as functions of such quantities as Lewis numbers, activation energies, Damkohler numbers and heat release fractions. The formula for H represents a relative measure of the flame thickness in terms of standard parameters, while that for U determines the role of each reaction in the ov...

Steady and pulsating modes of flame propagation through a premixed combustible mixture are studied for the case in which the flame is characterized by the sequential production and depletion of a significant intermediate species. We employ the method of matched asymptotic expansions to derive a model valid for large activation energies, and show that the pulsating solution is the result of a supercritical Hopf bifurcation from the steadily propagating solution (which becomes unstable). Through a nonlinear bifurcation analysis, we calculate the pulsation amplitude and other characteristics of the flame along the bifurcated branch. It is shown that the average thickness of the pulsating flame, by which we mean the average effective separation distance between production and depletion of the intermediate species, is greater than that predicted by a steady-state theory. In addition, we find that the mean propagation speed is less than that of the steadily propagating solution, but that the instantane...

We consider nonadiabatic premixed flame propagation in a long cylindrical channel. A steadily propagating planar flame exists for heat losses below a critical value. It is stable provided that the Lewis number and the volumetric heat loss coefficient are sufficiently small. At critical values of these parameters, bifurcated states, corresponding to time-periodic pulsating cellular flames, emanate from the steadily propagating solution. We analyze the problem in a neighborhood of a multiple primary bifurcation point. By varying the radius of the channel, we split the multiple bifurcation point and show that various types of stable periodic and quasi-periodic pulsating flames can arise as secondary, tertiary, and quaternary bifurcations. Our analysis describes several types of spinning and pulsating flame propagation which have been experimentally observed in nonadiabatic flames, and also describes additional quasi-periodic modes of burning which have yet to be documented experimentally.

Theoretical analyses are developed for the deflagration of solids such as nitramines that experience exothermic reactions in liquid layers at their surfaces. Relative motion of gas and liquid in a two-phase region at the surface is considered, with influences of pressure gradients and of surface-tension gradients taken into account for the drops and bubbles. It is shown that these influences tend to produce gas velocities in excess of liquid velocities. Burning-rate expressions are derived by activation-energy asymptotics, with special attention paid to the role of interphase heat transfer.

A method for predicting the steady-state structure and propagation velocity of an infinite, exothermic alloying process is presented. It is assumed that two unreacted solid-phase metals, one of which is assumed to be in a combined state with a gaseous species, are premixed in stoichiometric proportions. It is also assumed that the propagation of the reaction is limited not only by thermal and mass diffusion, but also by the need for the gaseous species to be completely driven off before the two metals can react. The governing ordinary differential system possesses an equilibrium point in the burned region at infinity, and an asymptotic analysis in this region shows the structure of the equilibrium point to be that of a saddle point. The unknown eigenvalue V ∗ , the velocity of propagation of the reaction, is then uniquely determined from the requirement that the solution be bounded at infinity. The method is illustrated by considering both an idealized analytical example and a more realistic model requiring a numerical algorithm suggested by the analysis.

The steady propagation of a flame through a premixed combustible mixture is studied for the case in which the flame is characterized by the production and depletion of a significant intermediate species. The overall chemical reaction mechanism is of the sequential type and is represented by $A + \nu_A O \to \mu _I I,I + \nu_1 O \to \mu _p P$, where A is the fuel, O is the oxidizer, I is the intermediate species, P is the product, and $\nu _A ,\mu _I ,\nu_I ,\mu _p $ are stoichiometric coefficients. We employ the method of matched asymptotic expansions to derive a solution for large activation energies, in which case both chemical reactions are confined to a thin layer. The (small) separation distance H between the points where the two reactions go to completion and the propagation velocity U play the role of eigenvalues and are determined as functions of standard flame parameters. The formula for H also represents the effective spatial distance between production and depletion of the intermediate species ...

A multidimensional, time-dependent model of the thermocline degradation in a packed bed thermal storage tank is presented. The formulation includes the effects of finite tank length, multidimensional thermal conduction, heat transfer between the fluid and solid portions of the bed, and heat losses across all tank surfaces. The technique used to solve the coupled pair of parabolic partial differential equations describing the degradation of the thermocline is based on a vectorized separation of variables approach. Assuming cylindrical geometry, the analysis leads to separate eigenvalue problems for the radial, angular, and axial spatial dependencies of the fluid and solid temperatures in the bed. The eigenvalues are readily calculated and the corresponding eigenfunctions are shown to form a complete set of spatial basis functions for the solution space. The method and results are illustrated by several examples.

Intrinsic instability in the steady, planar deflagration of a homogeneous solid propellant is considered through an asymptotic analysis for large values of nondimensional overall activation energies for the surface pyrolysis and gas-phase combustion processes. It is shown that the previously known pulsating instability is essentially connected with condensed-phase pyrolysis, and that new instability phenomena, which are associated with intrinsic gas-flame instability and which are sensitive to the value of the gas-phase Lewis number and to the distance of the gas flame from the propellant surface, arise. These results are obtained by relaxing the usual assumptions of quasi-steadiness and quasi-planarity for the gas phase, so that the coupling of intrinsic diffusional/thermal instabilities in the gas and solid phases becomes an integral feature of the model. The steady, planar deflagration thus may be unstable not only to pulsating disturbances, but also to (time-independent, nonplanar) cellular p...

We analyze the steady-state structure of a l1ame stabilized on a burner which is fed by a nonuniform mixture. Our diffusional-thermal model is based on the assumption of large overall activation energy, and the nonuniformity in the feed is treated as a perturbation of the uniform case. The flame shape for a given inflow enthalpy profile depends on Lewis number, inflow velocity, and conductance of the burner, and for sufficiently small Lewis number, we exhibit the onset of cellular flame formation. Unlike previously encountered flame instabilities, the transition to a cellular name occurs here in a gradual, rather than an abrupt, fashion through an "imperfect bifurcation."

The effects of selective diffusion, or multiple Lewis numbers, on the one-dimensional stability of an isobaric burner-stabilized premixed flame is investigated for arbitrary stoichiometry and reaction order in the asymptotic limit of large activation energy. Utilizing a global reaction model of the form νfF+νoO→νpP, the author has recently shown that, unlike most adiabatic flames, many burner-stabilized flames are unstable to arbitrarily small “normal mode” disturbances under easily achievable conditions. In particular, when certain parameters pass through critical values, the nontrivial steady-state solution undergoes a supercritical Hopf bifurcation to a pulsating, or time-oscillating, solution branch. In the present work, the previous restrictive assumption that Lef=Leo is relaxed to allow for unequal diffusion of fuel and oxidizer. This results in a number of interesting and significant effects (which are absent when Lef=Leo) on the location of the stability boundary in parameter space and which are particularly relevant for complex hydrocarbon flames, where the heavier hydrocarbon fuel may have a significantly higher Lewis number than the oxidizing species. The bifurcation phenomenon is illustrated by a computer-generated movie which shows the transient response of a realistic H2/O2 flame when parameter values lie on either side of the neutral stability boundary.

Abstract–We review recent analytical results in the theory of transition from laminar to turbulent premixed Rame propagation. We exploit the fact that the overall activation energy is large to formally derive dynamical flame sheet models, which are then used to predict instability thresholds as functions of the various parameters in the problem, at which steps in the transition occur. Employing perturbation techniques, we then describe bifurcations from a steady, planar flame to both pulsating and cellular modes of propagation. These nonsteady, nonplanar propagation modes represent intermediate stages in the evolution from laminar to turbulent combustion.

We present a model for nonhomogeneous solid propellant combustion that treats the nonhomogeneity as a small random perturbation of a homogeneous deflagration. Our model is based on our previous work (Margolis and Armstrong, 1986) and, unlike most previous models which are quasi-steady and one dimensional, allows for a fully nonsteady, multidimensional response of the deflagration to both spatial and temporal nonhomogeneities. In one calculation, we assume a random spatial distribution for the solid pyrolysis rate coefficient and obtain fluctuation statistics for the burning propellant in terms of the statistics of the random propellant medium. In another calculation, we obtain the burning rate response to a deterministic external pressure fluctuation. Our results are particularly applicable to nitrocellulose/nitroglycerin propellants, which are typically “almost” homogeneous.

New multi-programmable pacemakers frequently employ complementary metal oxide semiconductors (CMOS). This circuitry appears more sensitive to the effects of ionizing radiation when compared to the semiconductor circuits used in older pacemakers. A case of radiation induced runaway pacemaker in a CMOS device is described. Because of this and other recent reports of radiation therapy-induced CMOS type pacemaker failure, these pacemakers should not be irradiated. If necessary, the pacemaker can be shielded or moved to a site which can be shielded before institution of radiation therapy. This is done to prevent damage to the CMOS circuit and the life threatening arrythmias which may result from such damage.

A computer program is described which simulates the growth and DNA replication processes in bacteria. The program is based on a particular model of DNA replication and its coordination with cell division ( 2, 5, 7 ). Results of our studies indicate that the model is consistent with a number of experimental results. We have also investigated some apparently inconsistent results and have shown how these too may be explained by the model when actual experimental conditions are simulated.

The notion and interpretation of path dependence have been discussed and utilized in various social sciences during the last two decades. This innovative book provides significant new insights onto how the different applications of path dependence have developed and evolved. The authors suggest that there has been a definite evolution from applications of path dependence in the history of technology towards other fields of social science. They also discuss the various definitions of path dependence (strong or weak) and explore the potential applications of path dependence in new areas such as political economy and economic geography.

This paper identifies the latent opportunities and challenges inherent in the formative stages of a project that was resumed after partial completion by other on-the-ground research teams.Grounded theory methods were used to analyse project documentation from previous research teams and to generate new process-oriented data.The intention of all research teams was moving towards Engaging in Community-Based Participatory Research; this was conceptually identified as the core category. The social process involved in achieving community engagement practice was named Coming to an Ethics of Practice. Four different facets comprised the core category: Developing meaningful relationships; being reflective; recognising difference; and making research relevant.To achieve mutually beneficial outcomes, researchers conducting community-based research with Aboriginal people must implement strengths-based approaches to realise ethically sound research; prioritise the relevance of the research to the daily lives, needs and aspirations of those with whom they work; and in doing so, remain cognisant of their own philosophical position and context in which the research is located.

Featuring expert contributors from around the world, this book offers insight into the vital theoretical and practical aspects of the economics of copyright. Topics discussed include fair use, performers’ rights, copyright and trade, online music streaming, internet piracy, copyright and visual art markets, and open source publishing. In addition to in-depth coverage of these timely topics, the authors also offer insightful predictions and policy recommendations for the future.

Recent years have seen the development of new theories of market failure based on asymmetric information and network effects. According to the new paradigm, we can expect substantial failure in the markets for labor, credit, insurance, software, new technologies and even used cars, to give but a few examples. This volume brings together the key papers on the subject, including classic papers by Joseph Stiglitz, George Akerlof and Paul David. The book provides powerful theoretical and empirical rebuttals challenging the assumptions of these new models and questioning the usual policy conclusions. It goes on to demonstrate how an examination of real markets and careful experimental studies are unable to verify the new theories. New frontiers for research are also suggested.

More than three-quarters of Australia is classified as geographically remote. Remote areas are characterised by geographic isolation, cultural diversity, socioeconomic inequality, resource inequity, Indigenous health inequality, and a full range of extreme climatic conditions. Although several descriptive definitions have been developed for "remote health" and "remote practice", definitions of "remote medical practice" or "remote medicine" have not been previously published. In 2007, a working group of doctors and academics with experience in remote medicine was formed to develop the first advanced specialised remote medicine curriculum for remote doctors undertaking training with the Australian College of Rural and Remote Medicine. The first step was to define remote medical practice. Remote medical practice has eight key features: employment rather than private practice, isolation, use of telehealth, increased clinical acumen, extended practice, cross-cultural setting, multidisciplinary practice, and an emphasis on public health and personal security. From these eight features, we developed the first working definition of remote medical practice in the Australian context. Our definition will assist policymakers, medical colleges, standard setters, and educators to develop programs and resources for the future remote medical workforce.

A model is presented for flame propagation though a condensed combustible mixture in which the limiting component of the mixture melts during the reaction process. An asymptotic analysis, valid for large activation energies, is employed to derive a two-term expansion for the steady, planar adiabatic flame speed. A linear stability analysis is then used to show that for sufficiently large values of the activation energy and/or a special group of melting parameters, the steady, planar solution loses stability to various types of planar and nonplanar pulsating modes. The effect of melting is found to be destabilizing in the sense that these pulsating modes occur for lower values of the activation energy than would be the case for strictly solid fuel combustion. 1. Introduction. The propagation of reaction fronts in condensed phase combus- tion occurs in various metallurgical and pyrotechnical applications. In exothermic metal alloying processes, for example, two metals are ground into a fine powdered mixture. When ignited, a reaction front is established which propagates through the mixture, converting the metal reactants into an alloy product. Although this phenomenon is often referred to as solid fuel combustion, melting of at least one of the reactants is thought to be necessary in order to sustain the combustion process (cf. Hardt and Phung (1973)). An obvious explanation for this is that microscopic species diffusion, which determines the local reaction rate, is small when both reactants are solid due to the limited amount of surface-to-surface contact between the solid particles. When one of the reactants melts, the melted reactant can coat the unmelted particles, thereby significantly increasing the local reaction rate. One fascinating feature of condensed phase combustion is the confirmed existence of nonsteady, nonplanar modes of propagation of the reaction front. Experimental studies due to Merzhanov et al. (1973) and Maksimov et al. (1979) show that in addition to the usual steady, planar mode of propagation, there exist parameter regimes for which "auto-oscillatory" and spinning combustion fronts are observed. In the former case, the reaction front propagates in a pulsating fashion and the burned samples have a layered appearance. In the latter situation, the front has a nonuniform structure in which one or more hot spots are observed to rotate about the surface of the cylindrical fuel sample as the front propagates. Numerical predictions of these phenomena in condensed single-phase systems (i.e., no melting) have been reported by Shkadinsky et al. (1971) and Ivleva et al. (1978). The former paper showed that the activation energy is a critical parameter in determining the transition between the steadily propagating and pulsating solutions. In addition, due to what appears to be secondary and higher order bifurcations, the pulsating modes can be multiply periodic. That is, a complete cycle can consist of several pulsations. A similar phenomenon in gaseous combustion was predicted by Margolis (1980). The nature and transition characteristics of these various modes of propagation have been greatly clarified by several recent analytical studies (Matkowsky and Sivashinsky (1978), Sivashinsky (1981), Kaper, Leaf and Matkowsky (1982)). Using a single-phase model suggested by the asymptotic (large activation energy) models derived for gaseous flames (Sivashinsky (1977), Matkowsky and Sivashinsky (1979))

Approximate solutions of nonlinear boundary‐value problems arising in inviscid stratified shear fluid flows over relatively small obstacles are considered. The presence of a critical layer in the flow field leads to a failure of the linear theory, necessitating the derivation of a nonlinear critical layer equation. The solution of this second‐order differential equation for the horizontal velocity is found to be discontinuous along the streamline which passes through the upstream critical point. In the analysis, three constants of motion along a streamline are used to study flows involving slip and split streamlines emanating from this point. The matching of the critical layer (inner) and the linearized outer solutions is discussed and some examples of steady flows over an obstacle and waves propagating with constant speed are given.

The excess-capacity theorem pertaining to monopolistic competition implies a trade-off between variety and cost. This article shows that the excess-capacity theorem does not hold if firms market several products under a single brand name and if marketing efforts spill over from one product to another. The argument of the article requires that selling efforts not be prejudged to be wasteful or redundant, a position adopted and defended in Harold Demsetz's writing on monopolistic competition. Within that framework, the article constructs a counterexample to the excess-capacity theorem. Copyright 1989 by the University of Chicago.