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  • Philip Morrison is Professor of Human Geography at Victoria University of Wellington, New Zealand. He holds degrees ... more
    (Philip Morrison is Professor of Human Geography at Victoria University of Wellington, New Zealand.&nbsp; He holds degrees from the University of Toronto and Victoria University of Wellington (VUW).&nbsp; He undertakes research into economic geography, labour and housing markets, inequality and subjective wellbeing.&nbsp; He also undertakes research into rural development in Sarawak, Malaysia.<br /><br />Philip has been an Urban Studies Fellow at the Centre for Urban Studies, University of Glasgow, Visiting Fellow at the University of Cambridge and the University of Melbourne and the University of Toronto,&nbsp; Institute of Southeast Asia Studies (ISEAS), and University of California, Los Angeles (UCLA), University of Queensland among others.&nbsp; <br /><br />He has held the Henry Lang Fellowship at the Institute of Policy Studies, VUW, and the Hodge Fellowship, Social Science Research Fund Committee and a Development Fellowship from the Association of Commonwealth Universities. <br /><br />He was awarded the Distinguished Geographer Medal by the New Zealand Geographical Society in 2013.<br /><br />For further details see:&nbsp; http://www.victoria.ac.nz/sgees/about/staff/philip-morrison)
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This article argues that the residential sorting process which confers advantages on those who can choose their residential environments may also deny such advantages to others. The policy question therefore is the degree to which... more
This article argues that the residential sorting process which confers advantages on those who can choose their residential environments may also deny such advantages to others. The policy question therefore is the degree to which residing in neighbourhoods with relatively high levels of deprivation lowers people’s prospects of social mobility.
The widespread international concern over the low average wellbeing of university students shows no sign of abating. Neglected in the debate is a recognition that wellbeing itself is multidimensional and not all components respond in the... more
The widespread international concern over the low average wellbeing of university students shows no sign of abating. Neglected in the debate is a recognition that wellbeing itself is multidimensional and not all components respond in the same way to external and internal pressures. We draw on a large sample survey of first year students who enrolled in a New Zealand university in 2019 and measure their wellbeing using the WHO-5 measuring instrument. Instead of modelling the index itself we address its five individual components. We apply the marginal (population-averages) model using the generalised estimating equation (GEE) method. As well as confirming earlier findings that students with poorer physical health and lower financial capacity experience lower levels of wellbeing, we document their uneven influence on the relative frequency with which the five individual components are experienced: being cheerful, calm, active, fresh and interested over the previous two teaching weeks.
One of the curious features of recent writing on income inequality is the scant attention paid to the geography of inequality, to the spatial separation of rich and poor. While it is recognised that social capital can be enhanced by... more
One of the curious features of recent writing on income inequality is the scant attention paid to the geography of inequality, to the spatial separation of rich and poor. While it is recognised that social capital can be enhanced by residential sorting into more homogeneous groups, there is longstanding concern that this same residential sorting may exacerbate existing inequality by inhibiting the social mobility of the poor (Turner and Fortuny, 2009).  The perspective I want to advance here differs from the standard ‘neighbourhood effects’ literature by focusing not on those living in poor neighbourhoods, but instead on the benefits residential sorting may yield for the rich – the way in which location decisions redistribute income to the upper end of the income distribution and hence further income (and wealth) inequality. 
On the eve of the lecture by the authors of The Spirit Level at the University of Auckland in May 2014, Tim Hazledine pointed to a 2006 international survey which found that  New Zealanders were less supportive of redistributing income... more
On the eve of the lecture by the authors of The Spirit Level at the University of Auckland in May 2014, Tim Hazledine pointed to a 2006 international survey which found that  New Zealanders were less supportive of redistributing income from the rich to the poor than people in most other nations in the survey. ‘I don’t think that leads to saying all is well’, Hazledine said. ‘I think inequality is a problem. But we have to understand why we tolerate it’; ‘We have to understand why we don’t have blood flowing in the streets’ (Collins, 2014).
The purpose of this overview is to take stock of the research into labour, employment and work undertaken in New Zealand as represented by this conference and to summarise as succinctly as possible the key points made in each paper.
Our understanding of people’s well-being was, until very recently, inferred from observable objective indicators such as their income and education. These measures were then aggregated to generate an average that characterized the city or... more
Our understanding of people’s well-being was, until very recently, inferred from observable objective indicators such as their income and education. These measures were then aggregated to generate an average that characterized the city or region. With the growing availability of sample survey data, we now have at our disposal an increasing range of subjective measures of well-being that capture quality of life assessments made by individuals themselves. It is these internal measures of subjective well-being from microdata that are now being widely used throughout the social sciences to study what we call well-being or “happiness.” Contemporary interest in subjective measures of well-being stems from a wish to supplement market-based criteria such as GDP per capita with other more direct measures of societal well-being. Subjective measures are particularly useful in areas where the distribution of outcomes is not easily identified using other, especially market, criteria. The effect of investment in public infrastructure or the provision of green space or in fostering community networks or in redeveloping neighborhoods can be captured in responses to questions on wellbeing, preferably over time. These subjective measures, which have been shown to be highly correlated with clinical and other assessments of well-being, are likely to be of particular interest in regional science because of the way changes to places result from, or generate, a range of positive or negative externalities.
Two quite distinct views on how metropolitan labour markets work have co-existed for over three decades. Both claim empirical support and, after a brief period of confrontation, they continue to co-exist today giving quite conflicting... more
Two quite distinct views on how metropolitan labour markets work have co-existed for over three decades. Both claim empirical support and, after a brief period of confrontation, they continue to co-exist today giving quite conflicting signals to policy-makers. According to the first model, the urban labour market consists of a number of spatially defined sub-markets so that local unemployment exists primarily because of deficiencies in highly localised demand for labour. By this argument, unemployment rates remain high in the absence of a renewed supply of appropriate jobs within short commuting distances of the jobless. The solution according to this model is to attract private- and public-sector production into such areas. In contrast, a second model views the city as a single market in which transactions between labour and capital take place regardless of the location of residence and employment sites. According to this perspective, the spatial incidence of unemployment simply re...
In most countries the taxi industry is highly regulated and in cases where deregulation has been attempted, positive outcomes have not always been evident. The taxi industry was one of the very last to be deregulated by the New Zealand... more
In most countries the taxi industry is highly regulated and in cases where deregulation has been attempted, positive outcomes have not always been evident. The taxi industry was one of the very last to be deregulated by the New Zealand government as part of its sweeping restructuring of the country&#39;s industry in the 1980s. The author looks at the impact of that 1989 Act. The 1989 legislation, which removed the quantitative controls (deregulation), has been followed by a tripling of the number of companies in the metropolitan centres and a massive increase in the number of taxi cabs. A much wider range of taxi services now exploit different market segments and offer a wider geographic coverage. These changes have been accompanied by a decline in fares in real, if not nominal, terms. As expected, the influx of new players has necessitated the imposition of additional quality controls. Customers have benefited from greater numbers of cabs, shorter waiting times, and a greater range...
Empirical support for models of internal labour migration are usually based on observed patterns of net flows into local labour markets with relatively low unemployment and relatively high real wages. The inference drawn from such... more
Empirical support for models of internal labour migration are usually based on observed patterns of net flows into local labour markets with relatively low unemployment and relatively high real wages. The inference drawn from such evidence is that internal migrants move to enhance returns to their labour. However, major surveys in the USA (Panel Study of Income Dynamics, and the Current Population Survey), the UK (British Household Panel Survey) and Australia (Household, Income and Labour Dynamics in Australia) all show that less than a third of internal migrants are motivated primarily by employment reasons. This paper explores this apparent disconnect between net flows and motives using the Survey of Dynamics of Motivation and Migration, which has recorded in detail the reasons why over 6000 individuals moved within New Zealand over the two-year period 2005 and 2006. The survey confirms that only a minority of working-age migrants move between local labour markets primarily for em...
This paper demonstrates that residential locations observed at one point in time influence socio-spatial mobility and hence neighbourhood outcomes arising from residential mobility. Using a unique survey of migration within New Zealand,... more
This paper demonstrates that residential locations observed at one point in time influence socio-spatial mobility and hence neighbourhood outcomes arising from residential mobility. Using a unique survey of migration within New Zealand, it illustrates the classic result that repeated observations regress towards the mean. According to this statistical property, those leaving the most and least deprived areas are observed moving up and down towards the mean level of neighbourhood quality. After addressing this statistical effect, it is shown that those leaving very deprived areas are less likely to upgrade their neighbourhood, particularly if they also report relatively low incomes. By contrast, the downward adjustment observed by those leaving areas of low deprivation approximate those expected on the basis of regression towards the mean.
Throughout Asia, the decline in the total fertility rate has been accompanied by a growth in the child deficit—the gap between the number of children people want as young adults and the number they end up having by middle age. In this... more
Throughout Asia, the decline in the total fertility rate has been accompanied by a growth in the child deficit—the gap between the number of children people want as young adults and the number they end up having by middle age. In this chapter, I argue that the internally constructed values which support the ideal family size change more slowly than the externally imposed instrumental values that condition the number actually born. In the Asian case, the gap between the actual and ideal number of children is a function of the close interrelationship between the decision to marry and the decision to have children. An increasing proportion of young women, in littoral Asia in particular, are deciding not to marry and the majority that do are postponing marriage and delaying the fewer children in order to continue to study and/or work in the expanding urban labour markets. Both decisions reflect a change in the relative value placed on motherhood and, by extension, the child. By contrast, countries of central and south Asia have seen little reduction in the proportion of women marrying and little evidence of postponing marriage. However, they too are postponing children within marriage and reducing their average family size. Empirical support for these associations is sought through successive World Values Surveys which ask questions about the ideal and the actual number of children. The results are compared across the sub-set of Asian countries for which responses are complete. A key finding is the negative relationship between the child deficit and the country’s total fertility rate. The latent, unfulfilled demand for children is, therefore, deepest and more widespread in those East and South-East Asian countries experiencing ultra-low fertility.
While most models of population migration assume that members of the labour force migrate to enhance returns to their labour, major surveys in the USA (PSID and CPS), in the UK (BHPS) and Australia (HILDA) all show that only around 10... more
While most models of population migration assume that members of the labour force migrate to enhance returns to their labour, major surveys in the USA (PSID and CPS), in the UK (BHPS) and Australia (HILDA) all show that only around 10 percent of all individuals who change residence are motivated primarily by employment reasons. Of those moving between local labour markets only about 30 percent say they are motivated by employment reasons. We explore this apparent paradox by drawing on evidence from the Dynamics of Motivation and Migration Survey (DMM), which recorded the reasons people of working age, changed their permanent residence in New Zealand over the two-year period 2005 and 2006. The need to solve the employment problem before moving means that reasons offered retrospectively for moving usually reflect a wish to adjust consumption even in the case of those moving between local labour markets. For most people of working age employment remains a necessary condition rather tha...
Urban pride is an individual and collective response to living in a given city. Unlike other emotions such as life satisfaction or happiness with which it is weakly positively correlated, pride involves stake holding; to be proud of... more
Urban pride is an individual and collective response to living in a given city. Unlike other emotions such as life satisfaction or happiness with which it is weakly positively correlated, pride involves stake holding; to be proud of something requires having an investment in its success emotionally, financially or culturally. For this study I specify a multilevel model based on responses to a five category survey question which asks residents how proud they are in the ‘look and feel of their city’. Responses to the 2008 survey are distributed over almost 6000 residents across 12 cities in New Zealand. Although the primary variation is among individuals, urban pride also varies by city and I show how differences in urban context affect the way different types of stake holding temper urban pride. JEL classification: R19, R590, I390, H890
This paper explores the way subjective well-being varies with age. It is motivated by the relatively high level of suicide among young adults in New Zealand compared to other new settler countries like Australia, Canada and the USA. Since... more
This paper explores the way subjective well-being varies with age. It is motivated by the relatively high level of suicide among young adults in New Zealand compared to other new settler countries like Australia, Canada and the USA. Since the Second World War age specific suicide rates of the young have increased in many countries while those of the old have fallen. This generational switch in age-specific suicide rates is believed to reflect an underlying shift in the distribution of subjective wellbeing away from the young towards the old. The time series measures of well-being necessary to test such a proposition are unavailable, however we can compare the size of the generation gap in New Zealand to that prevailing in comparable countries. Evidence from two World Values Surveys offers empirical support for the presence of a wider gap in wellbeing between the younger and older age groups in New Zealand eoffrey Rose (1995) argued that there is a link between the way measures of he...
The proposition that living in the largest urban agglomerations of an advanced economy reduces the average wellbeing of residents is known as the urban wellbeing paradox. Empirical tests using subjective wellbeing have produced mixed... more
The proposition that living in the largest urban agglomerations of an advanced economy reduces the average wellbeing of residents is known as the urban wellbeing paradox. Empirical tests using subjective wellbeing have produced mixed results and there are two reasons for being cautious. Firstly, the default reliance on the conditional mean can disguise uneven effects across the wellbeing distribution. Secondly, relying on respondents to define their settlement size does not ensure a consistent measure of the agglomeration. I therefore apply quantile regression to the life satisfaction and happiness measures of wellbeing as collected by the 2018 European Social Survey (ESS9) and employ a consistent local labour market-based definition of agglomeration—The Functional Urban Area (FUA). I compare three countries as proof of concept: one with a known strong negative (respondent defined) agglomeration effect (Austria), one with a slight negative effect (Czech Republic), and one where livi...
Blanchflower and Oswald argue in their 1994 book that there is a stable downward-sloping convex curve linking the level of pay to the local unemployment rate. They derived this so-called wage curve from measurements on individuals within... more
Blanchflower and Oswald argue in their 1994 book that there is a stable downward-sloping convex curve linking the level of pay to the local unemployment rate. They derived this so-called wage curve from measurements on individuals within regions (local labour markets) for several countries and periods. Other investigators have confirmed the robustness of this finding. In this paper we seek evidence for the wage curve in New Zealand drawing on data at the regional level by means of the /996 census of population and dwellings. New Zealand research is hampered by the inaccessibility of unit record data and the paper reports results based on publicly available grouped data. The results show that a cross-sectional wage curve does exist in New Zealand. The elasticity is in the range of-0.07 to -0.12, which is similar to results obtained for other countries. However, research to date has not been able to choose between competing explanations for this phenomenon. We argue that a better unde...
Pride in one’s city is an individual, and collective as well as institutional response to urban conditions which may be harnessed in support of expanding urban facilities and services. Pride is likely to be felt most keenly by those who... more
Pride in one’s city is an individual, and collective as well as institutional response to urban conditions which may be harnessed in support of expanding urban facilities and services. Pride is likely to be felt most keenly by those who have a stake in the city and for this reason anecdotal reporting of urban pride in the media is subject to likely bias in favour of vested interests.  In practice however we know very little about urban pride.  The vast literature on urbanism does not appear to have identified any role for urban pride let alone indicating which cities gather pride or who among its inhabitants exhibit such prideThis paper applies a multi-level statistical model to large random sample of residents in twelve New Zealand cities.  From the results we learn that, although financial stake holding is relevant,   urban pride is concentrated more broadly among those whose social and cultural identity is closely tied to the city. Where financial stake holding is most influentia...
Morrison P. S. Local expressions of subjective well-being: the New Zealand experience, Regional Studies. Students of regional science have been preoccupied with economic drivers while at the same time implicitly assuming that increasing... more
Morrison P. S. Local expressions of subjective well-being: the New Zealand experience, Regional Studies. Students of regional science have been preoccupied with economic drivers while at the same time implicitly assuming that increasing urban size and density raises local well-being. However, the geography of happiness may not mirror the geography of growth. Rather, there is a localization to the paradox
This paper explores the way subjective well-being varies with age. It is motivated by the relatively high level of suicide among young adults in New Zealand compared to other new settler countries like Australia, Canada and the USA. Since... more
This paper explores the way subjective well-being varies with age. It is motivated by the relatively high level of suicide among young adults in New Zealand compared to other new settler countries like Australia, Canada and the USA. Since the Second World War age specific suicide rates of the young have increased in many countries while those of the old have fallen. This generational switch in age-specific suicide rates is believed to reflect an underlying shift in the distribution of subjective wellbeing away from the young towards the old. The time series measures of well-being necessary to test such a proposition are unavailable, however we can compare the size of the generation gap in New Zealand to that prevailing in comparable countries. Evidence from two World Values Surveys offers empirical support for the presence of a wider gap in wellbeing between the younger and older age groups in New Zealand
Living in a country’s largest metropolitan centre has a negative effect on subjective well-being. Although documented in many developed economies, the reasons for this particular geography of well-being are still poorly understood.... more
Living in a country’s largest metropolitan centre has a negative effect on subjective well-being. Although documented in many developed economies, the reasons for this particular geography of well-being are still poorly understood. Meanwhile a separate body of research has shown that the holding of extrinsic or personally focused values is also associated with lower levels of subjective well-being. This paper demonstrates the link between the two. It draws on the European Social
Survey (ESS) 2012 to show how metropolitan residents in Finland are more likely to hold extrinsic values such as power and achievement.
KEYWORDS
human values; value dissonance; subjective well-being; life satisfaction; Finland
Research Interests:
Studies of internal migration ask who moves, why they move, and what are the consequences − to themselves, their origin, and their destination. By contrast, studies of those who stay for very long durations are less common, despite the... more
Studies of internal migration ask who moves, why they move, and what are the consequences − to themselves, their origin, and their destination. By contrast, studies of those who stay for very long durations are less common, despite the fact that most people move relatively infrequently. 
We argue that staying is the deominant, preferred state and that moving is simply an adjustment toward a desired state of stability (or equilibrium). The core of our argument, already recognized in the literature, is that migration is risky. However, we extend the argument to loss aversion as developed within prospect theory. Prospect theory posits that existing possessions, including the dwelling and existing commodities, are attributed a value well beyond their purchase price and that this extends the average period of staying among the loss-averse.
Applying prospect theory has several challenges, including measurement of the reference point and potential degrees of gain and loss households face in deciding to change residence, as well as their own degree of loss aversion. The growing number of large panel sets should make it possible to estimate the degree to which endowment effects are likely to extend durations of residence as predicted by prospect theory.
Rational expectations models of mobility focus on the changes in the level of consumption of residential services. By contrast, prospect theory focuses on potential gains and losses relative to the existing dwelling − the reference point. As we confront increasing durations of residence in contemporary society, an application of prospect
Abstract BACKGROUND Studies of internal migration ask who moves, why they move, and what are the consequences − to themselves, their origin, and their destination. By contrast, studies of those who stay for very long durations are less... more
Abstract
BACKGROUND
Studies of internal migration ask who moves, why they move, and what are the consequences − to themselves, their origin, and their destination. By contrast, studies of those who stay for very long durations are less common, despite the fact that most people move relatively infrequently.
OBJECTIVE
We argue that staying is the dominant, preferred state and that moving is simply an adjustment toward a desired state of stability (or equilibrium). The core of our argument, already recognized in the literature, is that migration is risky. However, we extend the argument to loss aversion as developed within prospect theory. Prospect theory posits that existing possessions, including the dwelling and existing commodities, are attributed a value well beyond their purchase price and that this extends the average period of staying among the loss-averse.
METHODS
Applying prospect theory has several challenges, including measurement of the reference point and potential degrees of gain and loss households face in deciding to change residence, as well as their own degree of loss aversion. The growing number of large panel sets should make it possible to estimate the degree to which endowment effects are likely to extend durations of residence as predicted by prospect theory.
CONCLUSIONS
Rational expectations models of mobility focus on the changes in the level of consumption of residential services. By contrast, prospect theory focuses on potential gains and losses relative to the existing dwelling − the reference point. As we confront increasing durations of residence in contemporary society, an application of prospect theory is likely to yield important advantages over existing models of mobility and staying.
Research Interests:
The energy-Casimir method is a technique which gives a sufficient condition for the stability of Hamiltonian systems by a constrained minimization of the energy. For example, in the 1--D Vlasov system one obtains the requirement of... more
The energy-Casimir method is a technique which gives a sufficient condition for the stability of Hamiltonian systems by a constrained minimization of the energy. For example, in the 1--D Vlasov system one obtains the requirement of monoticity in velocity of the distribution function.(Fjortoft, R., 1950, Geofys. Publ. 17), 1; Gardner, C. S., 1963, Phys. Fluids 6, 839; Fowler, K., 1963, J. Math Phys. 4, 559; Newcomb, W. A., in Appendix of Bernstein, I., 1958, Phys. Rev. 109, 10; Kruskal, M. D., and C. Oberman, 1958, Phys. Fluids 1, 275. We review the method of dynamical accessibility for directly imposing constraints,(Morrison, P. J., 1998, Rev. Mod. Phys. 70), 467. and consider examples: 2--D low-beta reduced MHD,(Strauss, H. R. 1977, Phys. Fluids 20), 1354. and 2--D compressible reduced MHD,(Hazeltine, R. D., M. Kotschenreuther, and P. J. Morrison, 1985, Phys. Fluids 28), 2466. a model that includes pressure, compressibility, and parallel velocity. Finally, we discuss the general problem of stability of Lie--Poisson systems with quadratic Hamiltonians.
Using the HiRes stereo fluorescence detectors, the three-dimensional geometry of an extensive air shower may be found without assuming the shower is traveling at c. Since speed is not a constraint, it can be measured. The method can be... more
Using the HiRes stereo fluorescence detectors, the three-dimensional geometry of an extensive air shower may be found without assuming the shower is traveling at c. Since speed is not a constraint, it can be measured. The method can be tested on pulsed "flashers" and lasers where the geometry (and speed) is known. A preliminary measurement of shower speeds will be presented. This technique is also sensitive to objects which do not travel at c.
The use of functional integrals for the evaluation of homogeneous turbulent fluid spectra dates to the early work of T. D. Lee and L. Onsager. For example, such statistical mechanics techniques have been applied to two-dimensional Euler... more
The use of functional integrals for the evaluation of homogeneous turbulent fluid spectra dates to the early work of T. D. Lee and L. Onsager. For example, such statistical mechanics techniques have been applied to two-dimensional Euler fluid equations(D. Montgomery and R. Kraichnan, Rep. Prog. Phys. 43), 35 (1979). by analyzing point vortices or, alternatively, by Fourier transforming the vorticity and treating the resulting Fourier amplitudes as particle degrees of freedom. We, however, obtain the turbulent fluctuation spectrum for a Vlasov plasma by expanding in the eigenfunctions of the continuous spectrum --- van Kampen modes. We calculate the functional integrals exactly obtaining a composite spectrum with screening and particle contributions. The methods employed are of general utility and can also be applied to inhomogeneous fluid systems such as shear flow in a channel.
Hamiltonian bifurcations in the context of noncanonical Hamiltonian matter models are described. First, a large class of 1 + 1 Hamiltonian multi-fluid models is considered. These models have linear dynamics with discrete spectra, when... more
Hamiltonian bifurcations in the context of noncanonical Hamiltonian matter models are described. First, a large class of 1 + 1 Hamiltonian multi-fluid models is considered. These models have linear dynamics with discrete spectra, when linearized about homogeneous equilibria, and these spectra have counterparts to the steady state and Hamiltonian Hopf bifurcations when equilibrium parameters are varied. Examples of fluid sound waves and plasma and gravitational streaming are treated in detail. Next, using these 1 + 1 examples as a guide, a large class of 2 + 1 Hamiltonian systems is introduced, and Hamiltonian bifurcations with continuous spectra are examined. It is shown how to attach a signature to such continuous spectra, which facilitates the description of the continuous Hamiltonian Hopf bifurcation. This chapter lays the groundwork for Kre\u{i}n-like theorems associated with the CHH bifurcation that are more rigorously discussed in our companion chapter \cite{chaptII}.
We discuss the pitch angle scattering of relativistic particles by self-generated hydromagnetic waves. We show that in a hot background plasma, because of the resonant damping of short wavelength waves by thermal protons, cosmic rays need... more
We discuss the pitch angle scattering of relativistic particles by self-generated hydromagnetic waves. We show that in a hot background plasma, because of the resonant damping of short wavelength waves by thermal protons, cosmic rays need not slow down to a mean streaming speed which is of order the Alfven speed. We also discuss the effects of a high cosmic
The technique was developed to determine the chemical composition, size, and number density distributions of multi-phase particulate and droplet samples. The method is based on measurements of the infrared emission and transmission of the... more
The technique was developed to determine the chemical composition, size, and number density distributions of multi-phase particulate and droplet samples. The method is based on measurements of the infrared emission and transmission of the sample using a Fourier Transform Infrared (FT-IR) spectrometer. The technique, called E/T FT-IR, is based on the discovery that for cold particles surrounded by hot walls, the infrared band structure of gas suspended particles appears in the emission spectra. Application of the E/T method is considered practical for the analysis of streams of particles where the particles are already suspended in a gas stream as a result of the process; otherwise, only when emissivities are required.
The only known exact solutions of the Euler equations for an asymmetric, self-gravitating mass are the Riemann ellipsoids. They are characterized by motions of uniform vorticity in a rotating reference frame, and are governed by a... more
The only known exact solutions of the Euler equations for an asymmetric, self-gravitating mass are the Riemann ellipsoids. They are characterized by motions of uniform vorticity in a rotating reference frame, and are governed by a finite-dimensional system, i.e., a system of ordinary differental equations. A noncanonical Hamiltonian description in terms of a finite number of moments of velocity and density was first written down by Rosensteel, for the case when the fluid is unconstrained by the assumption of incompressibility. We show that this system can be obtained systematically by a moment reduction from the compressible-fluid bracket. We then employ the Dirac- bracket procedure to incorporate the constraint of incompressibility in this finite-dimensional system and show that the resulting bracket precisely confirms the moment-reduction obtained directly from an incompressible-fluid bracket, as described in the companion paper.

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