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64 results

Page 1 of 4

  • Scale statistics of current sheets in relativistic collisionless plasma turbulence

  • Roberto F. Serrano, Joonas Nättilä, Vladimir Zhdankin
  • Journal:
    Journal of Plasma Physics / Volume 91 / Issue 2 / April 2025
    Published online by Cambridge University Press:
    31 March 2025, E50
    • Article
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      • Open access
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  • We analyse distributions of the spatial scales of coherent intermittent structures – current sheets – obtained from fully kinetic, two-dimensional simulations of relativistic turbulence in a collisionless pair plasma using unsupervised machine-learning data dissection. We find that the distribution functions of sheet length $\ell$ (longest scale of the analysed structure in the direction perpendicular to the dominant guide field) and curvature $r_c$ (radius of a circle fitted to the structures) can be well-approximated by power-law distributions, indicating self-similarity of the structures. The distribution for the sheet width $w$ (shortest scale of the structure) peaks at the kinetic scales and decays exponentially at larger values. The data shows little or no correlation between $w$ and $\ell$, as expected from theoretical considerations. The typical $r_c$ depends linearly on $\ell$, which indicates that the sheets all have a similar curvature relative to their sizes. We find a weak correlation between $r_c$ and $w$. Our results can be used to inform realistic magnetohydrodynamic subgrid models for plasma turbulence in high-energy astrophysics.

  • The Uses of Humour in Spanish Environmental Education: An Exploratory Qualitative Analysis of the Potentialities, Limitations and Good Practices of Humour

  • Jorge Alcántara-Manzanares, Silvia Medina Quintana, Roberto García-Morís, Miguel Jesús López Serrano
  • Journal:
    Australian Journal of Environmental Education / Volume 40 / Issue 5 / October 2024
    Published online by Cambridge University Press:
    21 October 2024, pp. 886-899
    • Article
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      • Open access
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  • This article is an exploratory analysis of the use of humour in Environmental Education, from the perspective of 10 Spanish specialists and educators. Research is carried out using a qualitative methodology through semistructured interviews and a focus group of specialists. The results point to a positive perception of the use of humour and the need for flexibility on the part of the educator to adapt to the particularities of the group and the topics addressed. The differences of opinion lie in the limitations in the use of humour as well as in the recommendations made by the specialists participating in the study, which, given their background, can be considered relevant to the use of humour for environmental education in the Spanish context.

A Short Course in Intermediate Microeconomics with Calculus
  • 2nd edition
  • Roberto Serrano, Allan M. Feldman
  • Published online:
    12 December 2018
    Print publication:
    13 September 2018
  • This second edition retains the positive features of being clearly written, well organized, and incorporating calculus in the text, while adding expanded coverage on game theory, experimental economics, and behavioural economics. It remains more focused and manageable than similar textbooks, and provides a concise yet comprehensive treatment of the core topics of microeconomics, including theories of the consumer and of the firm, market structure, partial and general equilibrium, and market failures caused by public goods, externalities and asymmetric information. The book includes helpful solved problems in all the substantive chapters, as well as over seventy new mathematical exercises and enhanced versions of the ones in the first edition. The authors make use of the book's full color with sharp and helpful graphs and illustrations. This mathematically rigorous textbook is meant for students at the intermediate level who have already had an introductory course in microeconomics, and a calculus course.

  • 4. - Demand Functions

  • from Part I. - Theory of the Consumer
  • Roberto Serrano, Brown University, Rhode Island, Allan M. Feldman, Brown University, Rhode Island
  • Book:
    A Short Course in Intermediate Microeconomics with Calculus
    Published online:
    12 December 2018
    Print publication:
    13 September 2018, pp 47-69

  • Summary

    We will start this chapter with a detailed study of individual demand functions. Each demand function depends on three independent variables. Because of this complication it would be impossible to graph them in the obvious way. Therefore we will look at how demand changes as we vary one independent variable at a time. This exercise is called comparative statics, because we are comparing the consumer’s optimal consumption of goods 1 and 2, as one of the exogenous variables—one of the prices, or income—changes from one level to another. From now on we shall concentrate on the demand function for just one of the goods, say, good 1. In Section 2 we will focus on demand as a function of income, holding prices constant. We will derive an Engel curve, a graph which shows the desired consumption of a good as a function of income. We will distinguish between normal goods (higher income results in higher consumption) and inferior goods (higher income results in lower consumption).

  • 8. - Theory of the Firm 1: The Single-Input Model

  • from Part II. - Theory of the Producer
  • Roberto Serrano, Brown University, Rhode Island, Allan M. Feldman, Brown University, Rhode Island
  • Book:
    A Short Course in Intermediate Microeconomics with Calculus
    Published online:
    12 December 2018
    Print publication:
    13 September 2018, pp 129-149

  • Summary

    Production is the transformation of inputs into outputs. The production process typically takes place within firms. They buy or hire various inputs, and combine them using available technology to produce various outputs, of goods and services. Then they sell the outputs they produce. For example, a firm that makes video games hires different kinds of labor (game experts, programmers, sales people, accountants, lawyers, and so on) and buys or rents various capital goods (office space, computer equipment, internet access, furniture, and so on) to make and market games. A farm, whose land and machinery are more or less fixed in the short term, employs labor to produce corn. In the farm example, it’s plausible to think of the production process as one that uses one input to produce one output. In this chapter, we will develop a simple production model with just one input and one output; we call it the single-input/single-output model. At the end of the chapter we will briefly describe a model with a single input and multiple outputs—most firms in reality have many outputs—and we will provide techniques for solving its profit maximization problem. Later, in the next chapter, we will move on to the case of the production of a single output with multiple inputs, the multiple-input/single-output model.

  • 12. - Monopoly and Monopolistic Competition

  • from Part III. - Partial Equilibrium: Market Structure
  • Roberto Serrano, Brown University, Rhode Island, Allan M. Feldman, Brown University, Rhode Island
  • Book:
    A Short Course in Intermediate Microeconomics with Calculus
    Published online:
    12 December 2018
    Print publication:
    13 September 2018, pp 212-234

  • Summary

    In the last chapter, we studied the behavior of competitive firms, that is, firms that take market prices as given and outside their control. Generally, such firms are small enough relative to their markets that their decisions have no effect on the market prices. Now we will study the polar opposite, the market in which only one firm supplies a particular good. This is called a monopoly market and the firm is a monopoly firm or monopolist. The word “monopoly” is from Greek, and means “one seller.” In the first part of this chapter, we will analyze the classical solution to the monopoly problem. Then we will consider various price discrimination techniques that monopolies can employ to increase their profits. At the end of the chapter, we will look at a special market structure, called monopolistic competition, in which there are many firms producing goods that are very similar, but not identical, such as different brands of laundry detergent.

  • 14. - Game Theory

  • from Part III. - Partial Equilibrium: Market Structure
  • Roberto Serrano, Brown University, Rhode Island, Allan M. Feldman, Brown University, Rhode Island
  • Book:
    A Short Course in Intermediate Microeconomics with Calculus
    Published online:
    12 December 2018
    Print publication:
    13 September 2018, pp 258-278

  • Summary

    This brief chapter is not meant to replace a formal course in game theory; it is only an introduction. The general emphasis is on how strategic behavior affects the interactions among rational players in a game. We will provide some basic definitions, and we will discuss a number of well-known simple examples. We will start with a description of the prisoners’ dilemma game, where we will introduce the idea of a dominant strategy equilibrium. Then we will describe the battle of the sexes game, and introduce the concept of Nash equilibrium. We will discuss the possibilities of there being multiple Nash equilibria, or no (pure-strategy) Nash equilibria, and we discuss the idea of mixed-strategy equilibria. We will then present an expanded battle of the sexes game, and we will see that in game theory, an expansion of choices may make players worse off instead of better off. Later on in the chapter, we will describe sequential move games, and we will briefly introduce threats. At the end of the chapter we will briefly discuss repeated games in the prisoners’ dilemma context, and tit for tat strategies.

  • 5. - Supply Functions for Labor and Savings

  • from Part I. - Theory of the Consumer
  • Roberto Serrano, Brown University, Rhode Island, Allan M. Feldman, Brown University, Rhode Island
  • Book:
    A Short Course in Intermediate Microeconomics with Calculus
    Published online:
    12 December 2018
    Print publication:
    13 September 2018, pp 70-93

  • Summary

    In the first part of this chapter we will study the decisions involving consumption and leisure, which are behind the supply of labor. We will model the standard budget constraint for the consumption/leisure choice, which involves the wage rate, consumption, and the time spent working versus the time spent on leisure. We will also model some special budget constraints, for example, involving non-labor income. We will analyze the effects of income taxation on the consumer’s labor/leisure choice. This analysis has some very interesting implications about the relative desirability of flat and progressive income taxes. We will then turn to the consumer’s decisions regarding the supply of savings. We will discuss borrowing and saving, and revisit intertemporal budget constraints like the ones introduced in Chapter 3. Savings flow through the financial system and end up (hopefully) as part of the capital used by firms to produce more goods and services. We will model the consumer’s savings decision, and show how the amount the consumer saves depends on the interest rate and the inflation rate, as well as on the timing of the consumer’s income stream.

  • 17. - Externalities

  • from Part V. - Market Failure
  • Roberto Serrano, Brown University, Rhode Island, Allan M. Feldman, Brown University, Rhode Island
  • Book:
    A Short Course in Intermediate Microeconomics with Calculus
    Published online:
    12 December 2018
    Print publication:
    13 September 2018, pp 329-350

  • Summary

    In this chapter, we will examine another very important kind of market failure, the kind produced by externalities. When we analyzed trade between two people, we assumed person i’s utility depended only on his bundle of goods, and not on person j’s. When we analyzed production by firms, we assumed that firm i’s costs and output depended only on its inputs, and not on the inputs or outputs of firm j. When we analyzed the interactions between firms and consumers, we assumed a consumer buying a firm’s output cared only about how much he consumed, and the price he paid. In this chapter we will analyze externalities. We will start with some examples. Then we will carefully describe how the market fails when externalities are present, and we will describe various possible remedies for the market failures created by externalities. The classical remedies for such market failures include Pigouvian taxes and subsidies, and Coasian legal remedies involving property rights. More modern remedies involve markets for pollution rights, including cap and trade markets.

  • 10. - Theory of the Firm 3: The Short-Run, Multiple-Input Model

  • from Part II. - Theory of the Producer
  • Roberto Serrano, Brown University, Rhode Island, Allan M. Feldman, Brown University, Rhode Island
  • Book:
    A Short Course in Intermediate Microeconomics with Calculus
    Published online:
    12 December 2018
    Print publication:
    13 September 2018, pp 154-186

  • Summary

    In this chapter we will develop our short run model. If there are n inputs, x1, x2, ... xn, with input prices w1, w2, ... wn, short run means that some of the inputs are fixed at non-zero levels, while others are variable. If the production function is y = f(x1, x2), with two inputs, short run means x2 is fixed at a non-zero level, while x1 is variable. One main implication should be immediately clear: in a short run model, the cost function has a non-zero fixed part. When there are just two inputs, this is w2 times the fixed quantity of input 2. When there are n inputs, this is the sum of the prices of the fixed inputs times the respective quantities of those inputs. Moreover, when there are just two inputs, one fixed and one variable, the short run model will be much like the Chapter 8 model, but with a fixed cost element attached; and if there are three or more inputs, with one or more fixed and two or more variable, the short run model will be much like the Chapter 9 model, but with the fixed cost element attached.

  • 15. - An Exchange Economy

  • from Part IV. - General Equilibrium
  • Roberto Serrano, Brown University, Rhode Island, Allan M. Feldman, Brown University, Rhode Island
  • Book:
    A Short Course in Intermediate Microeconomics with Calculus
    Published online:
    12 December 2018
    Print publication:
    13 September 2018, pp 281-305

  • Summary

    What economists call a pure exchange economy, or more simply an exchange economy, is a model of an economy with no production. Goods have already been produced, found, inherited, or endowed, and the only issue is how they should be distributed and consumed. Even though this model abstracts from production decisions, it illustrates important questions about the efficiency or inefficiency of allocations of goods among consumers, and provides important answers to those questions. In this chapter, we will start with a very simple model of an exchange economy, and we will discuss the Pareto optimality or Pareto efficiency for allocations of goods among consumers. Then we will turn to the role of markets, and discuss market or competitive equilibrium allocations. Finally we will discuss the extremely important connections between markets and efficiency in an exchange economy. These connections between markets and efficiency are among the most important results in economic theory, and are appropriately called the fundamental theorems of welfare economics.

  • 19. - Uncertainty and Expected Utility

  • from Part V. - Market Failure
  • Roberto Serrano, Brown University, Rhode Island, Allan M. Feldman, Brown University, Rhode Island
  • Book:
    A Short Course in Intermediate Microeconomics with Calculus
    Published online:
    12 December 2018
    Print publication:
    13 September 2018, pp 372-385

  • Summary

    In most of this book we have assumed perfect information. That is, we have assumed that every buyer and every seller of every good and service in the market has complete information about all the relevant facts. All the buyers and all the sellers know the market prices, and they all know the characteristics of the things being bought and sold. In the next two sections of this chapter we will lay out the basic model of consumer behavior under uncertainty, developed by John von Neumann (1903-1957) and Oskar Morgenstern (1902-1977). This model gives a utility function that can be used to analyze uncertainty. Then we will turn to some examples, which show how the von Neumann-Morgenstern utility function approach can be applied to consumers who want to reduce or avoid risk, and to consumers who like risk and want to increase it. The examples also show how people can trade risk in ways which make everybody better off.

  • 13. - Duopoly

  • from Part III. - Partial Equilibrium: Market Structure
  • Roberto Serrano, Brown University, Rhode Island, Allan M. Feldman, Brown University, Rhode Island
  • Book:
    A Short Course in Intermediate Microeconomics with Calculus
    Published online:
    12 December 2018
    Print publication:
    13 September 2018, pp 235-257

  • Summary

    In this chapter, we study market structures that lie between perfect competition and monopoly. As before we assume, at least in most of this chapter, that there is one homogeneous good which is the same no matter who makes it. We assume everyone has perfect information about the good and its price. In our discussion of monopoly, we assumed there were barriers to entry which preserved the monopolist’s position. In this chapter. we also assume there are barriers to entry which prevent other firms from entering the market. However, we now assume there are already two (or more) firms in the market. In this chapter, we assume that each firm takes into account how its own output, and its competitors’ outputs, affects the price, and through the price, its own profit. In this chapter, we will assume there are only two firms in the market. A market with just two firms is called a duopoly. Obviously a duopoly is the simplest sort of oligopoly, and many of the concepts and results that we will describe can be extended to the case of an oligopoly with more than two firms. Duopoly analysis by economists dates back to the 19th century.

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