Mass Accretion During the Motion of Raindrops

Exploration of dynamics of raindrops is one of the simple yet most complicated mechanical problems. Mass accretion from moist air during the motion of raindrop through resistive medium holds an arbitrary power law equation. Its integral part is the change of shape, terminal motions and terminal solutions, etc. Classical Newtonian formalism is used to formulate a mathematical model of generalized first order differential equation. We have discussed about the terminal velocity of raindrop and its variation with the extensive use of python program and library. It is found that terminal velocity 𝐯𝐓𝐜𝛂𝛃 is achieved within 20 seconds where 𝛂=, 𝛃=(𝟎,𝟏) and 𝐧=𝟎,𝟏,𝟐,𝟑,𝟒,…. Its variations due to mass accretion roughly follows the earlier predicted range 𝐠/𝟕 to 𝐠/𝟑.

A Comprehensive Study of Mass Accretion and Atmospheric Effect of Raindrop

The mass accretion of a raindrop in different layers of the atmosphere is not dealt with so far. A comprehensive brief study of the motion of raindrops through the atmosphere (i) without mass accretion, (ii) with mass accretion and (iii) finally pressure variation in the atmosphere with altitude using Bernoulli’s equation is illustrated. Acquirement of mass from moist air is mass accretion and mass accretion during the motion of raindrop through resistive medium holds an arbitrary power-law equation. Bernoulli’s equation when applied to it, the generalized first-order differential equation is reduced to a polynomial equation. Results show a single intersecting point of approximate terminal velocity 1 m/s and mass 10-06 mg as illustrated. Terminal velocity is achieved within 25 sec. There is the approximate exponential growth of terminal velocity. An increase in momentum is due to mass accretion during motion. Various conditions of no mass accretion and mass accretion show the same result while for atmospheric effect using Bernoulli’s equation the first-order differential equation reduces to a polynomial equation.

The Rule of Law for All Sentient Animals

This paper argues for a theory of the rule of law that is inclusive of sentient non-human animals. It critiques the rule of law theories of Fuller, Waldron, and Allan, by showing that their theories presuppose that the legal subject is a person who can be guided by legal norms. This unduly excludes non-human animals, as well as certain humans who do not have rational capacities. If we view the basic idea of the rule of law as restraining arbitrary power, then rule of law theories need to give an account of who can be a potential victim of such power. Non-human animals and humans, whether endowed with rational capacities or not, can all be victims of arbitrary power. So, we need a new rule of law theory which is inclusive of all sentient animals, humans and non-human alike. This paper sets out such an inclusive theory.

Three-Port Series-Resonant DC/DC Converter for Automotive Charging Applications

In the energy distribution grid of electric vehicles (EVs), multiple different voltage potentials need to be interconnected, to allow arbitrary power flow between the various energy sources and the different electrical loads. However, between the different potentials, galvanic isolation is absolutely necessary, either due to safety reasons and/or due to different grounding schemes. This paper presents an isolated three-port DC/DC converter topology, which, in combination with an upstream PFC rectifier, can be used as combined EV charger for interconnecting the single-phase AC mains, the high-voltage (HV) battery and the low-voltage (LV) bus in EVs. The proposed topology comprises two synergetically controlled and magnetically coupled converter parts, namely, a series-resonant converter between the PFC-sided DC-link capacitor and the HV battery, as well as a phase-shifted full-bridge circuit equivalent in the LV port, and is mainly characterized by simplicity in terms of control and circuit complexity. For this converter, a simple soft switching modulation scheme is proposed and comprehensively analyzed, in consideration of all parasitic components of a real converter implementation. Based on this analysis, the design of a 3.6kW, 500V/ 500V/ 15V prototype is discussed, striving for the highest possible power density and as low as possible manufacturing costs, by using PCB-integrated windings for all magnetic components. The hardware demonstrator achieves a measured full-load efficiency in charge mode of 96.5% for nominal operating conditions and a power density of 16.4kW/L.

High-power ultrafast fiber lasers for materials processing

State-of-the-art fiber-laser systems can deliver femtosecond pulses at average powers beyond the kilowatt level and multi-mJ pulse energies by employing advanced large-mode-area fiber designs, chirped-pulse amplification, and the coherent combination of parallel fiber amplifiers. By using sophisticated coherent phase control, one or even several output ports can be modulated at virtually arbitrary power levels and switching speeds. In addition, an all-fiber setup for GHz-burst generation is described allowing to access an even wider range of laser parameters. The combination of all these approaches together with the robustness, efficiency, and excellent beam quality inherent to fiber-laser technology has the potential to strongly improve existing materials-processing applications.

Representative Democracy and Social Equality

When are inequalities in political power undemocratic, and why? While some writers condemn any inequalities in political power as a deviation from the ideal of democracy, this view is vulnerable to the simple objection that representative democracies concentrate political power in the hands of elected officials rather than distributing it equally among citizens, but they are no less democratic for it. Building on recent literature that interprets democracy as part of a broader vision of social equality, I argue that concentrations of political power are incompatible with democracy, and with a commitment to social equality more generally, when they consist in some having greater arbitrary power to influence decisions according to their idiosyncratic preferences. A novel account of the relationship between power and social status clarifies the role of social equality in the justification of democracy, including a representative democracy in which public officials have more political power than ordinary citizens.

Blow-up of solutions of semilinear wave equations in accelerated expanding Friedmann–Lemaître–Robertson–Walker spacetime

Consider a nonlinear wave equation for a massless scalar field with self-interaction in the spatially flat Friedmann–Lemaître–Robertson–Walker spacetimes. For the case of accelerated expansion, we show that the blow-up in a finite time occurs for the equation with arbitrary power nonlinearity as well as upper bounds of the lifespan of blow-up solutions. Comparing to the case of the Minkowski spacetime, we discuss how the scale factor affects the lifespan of blow-up solutions of the equation.

Applying Neo-Republican Theory to Welfare to Work Practices: Rules and Arbitrary Power in Mandatory Work Programmes in the Netherlands

Drawing on the neo-republican theory of non-domination and a qualitative case study conducted in three Dutch municipalities, this article explores the extent to which external rules are able to prevent arbitrary power in relationships between welfare officers and work supervisors, on the one hand, and welfare recipients participating in mandatory work programmes, on the other hand. It concludes that external rules were insufficiently implemented in the three municipalities in question. In addition, it found that rules cease to be capable of constraining arbitrary power where institutional contexts themselves are unpredictable and insecure. Under these conditions, welfare recipients may seek to avoid risks and act in accordance with the preferences (or their expectation of the preferences) of the welfare officer or work supervisor by playing the role of the ‘good recipient’ instead of relying on available rules of a protective nature or rules that enable them to have a say in their participation in mandatory work programmes.