The force, power and energy of the 100 meter sprint

At the 2008 Summer Olympics in Beijing, Usain Bolt broke the world record for the 100 m sprint. Just one year later, at the 2009 World Championships in Athletics in Berlin he broke it again. A few months after Beijing, Eriksen et al. studied Bolt's performance and predicted that Bolt could have run about one-tenth of a second faster, which was confirmed in Berlin. In this paper we extend the analysis of Eriksen et al. to model Bolt's velocity time-dependence for the Beijing 2008 and Berlin 2009 records. We deduce the maximum force, the maximum power, and the total mechanical energy produced by Bolt in both races. Surprisingly, we conclude that all of these values were smaller in 2009 than in 2008

A unified model for the long and high jump

A simple model based on the maximum energy that an athlete can produce in a small time interval is used to describe the high and long jump. Conservation of angular momentum is used to explain why an athlete should run horizontally to perform a vertical jump. Our results agree with world records.Comment: Accepted for publication in Am. J. Phy

Voluntary Public Unemployment Insurance

Voluntary public unemployment systems are limited to a handful of countries, including Finland, Sweden, and, more substantially, Denmark. A voluntary system has the positive feature of other user-cost schemes, potentially efficient targeting of services. This presumes rational behavior as well as reasonable risk rating of premiums and the absence of worker access to alternative social programs. Using a 10 per cent sample of the Danish population drawn from administrative data, we exploit the voluntary Danish system to explore the structure of unemployment insurance demand. The insurance take-up rate is surprisingly high, 80 percent in 1995, but varies systematically with economic incentives in a way that raises doubts about the targeting value of the current system. Political support for the Danish system may derive instead from the fact that a universal, compulsory system would generate rather modest additional net funds and with a twist--additional revenue would come disproportionately from low-wage workers.

Voluntary Public Unemployment Insurance

Voluntary public unemployment systems are limited to a handful of countries, including Finland, Sweden, and, more substantially, Denmark. A voluntary system has the positive feature of other user-cost schemes, potentially efficient targeting of services. This presumes rational behavior as well as reasonable risk rating of premiums and the absence of worker access to alternative social programs. Using a 10% sample of the Danish population drawn from administrative data, we exploit the voluntary Danish system to explore the structure of unemployment insurance demand. The insurance take-up rate is surprisingly high, 80 percent in 1995, but varies systematically with economic incentives in a way that raises doubts about the targeting value of the current system. Political support for the Danish system may derive instead from the fact that a universal, compulsory system would generate rather modest additional net funds and with a twist--additional revenue would come disproportionately from low-wage workers.

PPP Strikes Back: Aggregation and the Real Exchange Rate

We show the importance of a dynamic aggregation bias in accounting for the PPP puzzle. We prove that established time series and panel methods substantially exaggerate the persistence of real exchange rates because of heterogeneity in the dynamics of disaggregated relative prices. When heterogeneity is properly taken into account, estimates of the real exchange rate half-life fall dramatically, to little more than one year, or significantly below Rogoff's consensus view' of three to five years. We show corrected estimates are consistent with plausible nominal rigidities, thus, arguably, solving the puzzle. We also explain why traded goods prices account for the bulk of the persistence and volatility of the real exchange rate. The reason is that traded goods prices display dynamics that are more heterogeneous than non-traded ones.

PPP Strikes Back: Aggregation and the Real Exchange Rate

We show the importance of a dynamic aggregation bias in accounting for the PPP puzzle. We prove that established time series and panel methods substantially exaggerate the persistence of real exchange rates because of heterogeneity in the dynamics of disaggregated relative prices. When heterogeneity is properly taken into account, estimates of the real exchange rate half-life fall dramatically, to little more than one year, or significantly below Rogoff’s ‘consensus view’ of three to five years. We show that corrected estimates are consistent with plausible nominal rigidities, thus, arguably, solving the PPP puzzle.Real Exchange Rate Persistence, Purchasing Power Parity, Aggregation, Parameter Heterogeneity.

Variation in the seston C:N ratio of the Arctic Ocean and pan-Arctic shelves

Studying more than 3600 observations of particulate organic carbon (POC) and particulate organic nitrogen (PON), we evaluate the applicability of the classic Redfield C:N ratio (6.6) and the recently proposed Sterner ratio (8.3) for the Arctic Ocean and pan-Arctic shelves. The confidence intervals for C:N ranged from 6.43 to 8.82, while the average C:N ratio for all observations was 7.4. In general, neither the Redfield or Sterner ratios were applicable, with the Redfield ratio being too low and the Sterner ratio too high. On a regional basis, all northern high latitude regions had a C:N ratio significantly higher than the Redfield ratio, except the Arctic Ocean (6.6), Chukchi (6.4) and East Siberian (6.5) Seas. The latter two regions were influenced by nutrient-rich Pacific waters, and had a high fraction of autotrophic (i.e. algal-derived) material. The C:N ratios of the Laptev (7.9) and Kara (7.5) Seas were high, and had larger contributions of terrigenous material. The highest C:N ratios were in the North Water (8.7) and Northeast Water (8.0) polynyas, and these regions were more similar to the Sterner ratio. The C:N ratio varied between regions, and was significantly different between the Atlantic (6.7) and Arctic (7.9) influenced regions of the Barents Sea, while the Atlantic dominated regions (Norwegian, Greenland and Atlantic Barents Seas) were similar (6.7–7). All observations combined, and most individual regions, showed a pattern of decreasing C:N ratios with increasing seston concentrations. This meta-analysis has important implications for ecosystem modelling, as it demonstrated the striking temporal and spatial variability in C:N ratios and challenges the common assumption of a constant C:N ratio. The non-constant stoichiometry was believed to be caused by variable contributions of autotrophs, heterotrophs and detritus to seston, and a significant decrease in C:N ratios with increasing Chlorophyll a concentrations supports this view. This study adds support to the use of a power function model, where the exponent is system-specific, but we suggest a general Arctic relationship, where POC = 7.4 PON0.89

Understanding the tsunami with a simple model

In this paper, we use the approximation of shallow water waves (Margaritondo G 2005 Eur. J. Phys. 26 401) to understand the behaviour of a tsunami in a variable depth. We deduce the shallow water wave equation and the continuity equation that must be satisfied when a wave encounters a discontinuity in the sea depth. A short explanation about how the tsunami hit the west coast of India is given based on the refraction phenomenon. Our procedure also includes a simple numerical calculation suitable for undergraduate students in physics and engineering

Николай Николаевич Грицевич

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