Simple Theoretical Derivation Research Articles

Pareto-like sequential sampling heuristic for global optimisation

In this paper, we propose a simple global optimisation algorithm inspired by Pareto’s principle. This algorithm samples most of its solutions within prominent search domains and is equipped with a self-adaptive mechanism to control the dynamic tightening of the prominent domains while the greediness of the algorithm increases over time (iterations). Unlike traditional metaheuristics, the proposed method has no direct mutation- or crossover-like operations. It depends solely on the sequential random sampling that can be used in diversification and intensification processes while keeping the information-flow between generations and the structural bias at a minimum. By using a simple topology, the algorithm avoids premature convergence by sampling new solutions every generation. A simple theoretical derivation revealed that the exploration of this approach is unbiased and the rate of the diversification is constant during the runtime. The trade-off balance between the diversification and the intensification is explained theoretically and experimentally. This proposed approach has been benchmarked against standard optimisation problems as well as a selected set of simple and complex engineering applications. We used 26 standard benchmarks with different properties that cover most of the optimisation problems’ nature, three traditional engineering problems, and one real complex engineering problem from the state-of-the-art literature. The algorithm performs well in finding global minima for nonconvex and multimodal functions, especially with high dimensional problems and it was found very competitive in comparison with the recent algorithmic proposals. Moreover, the algorithm outperforms and scales better than recent algorithms when it is benchmarked under a limited number of iterations for the composite CEC2017 problems. The design of this algorithm is kept simple so it can be easily coupled or hybridised with other search paradigms. The code of the algorithm is provided in C++14, Python3.7, and Octave (Matlab).

The Risk-Free Asset Implied by the Market: Medium-Term Bonds instead of Short-Term Bills

In empirical tests of the capital asset pricing model, the theoretical risk-free asset is typically assumed to be 1-month Treasury bills. This article examines the implications of a misspecified risk-free asset—that is, the possibility that the true risk-free asset is a longer-maturity Treasury bond. A simple theoretical derivation leads to the testable prediction that low-beta (high-beta) stocks should then exhibit positive (negative) bond betas. The author finds strong empirical confirmation for these predictions. The market-implied risk-free asset can be pinpointed at medium-term (5-year) bonds. Concrete implications of this finding are a lower equity risk premium and a less steep security market line. TOPICS:Portfolio theory, portfolio construction, derivatives Key Findings • In empirical tests of the capital asset pricing model, the theoretical risk-free asset is typically assumed to be 1-month Treasury bills. This article examines the implications of a misspecified risk-free asset—that is, the possibility that the true risk-free asset is a longer-maturity Treasury bond. • A simple theoretical derivation leads to the testable prediction that low-beta (high-beta) stocks should then exhibit positive (negative) bond betas. • The author finds strong empirical confirmation for these predictions and can pinpoint the market-implied risk-free asset at medium-term (5-year) bonds. Concrete implications of this finding are a lower equity risk premium and a less steep security market line.

Metal-hydride hydrogen compressors for laboratory use

The development of commercial applications of hydrogen at high pressure (300–700 + bar), for example in fuel cell vehicles and associated filling stations, necessitates the study of hydrogen capacity, and the safety of materials at pressures well above that of standard pressurised cylinders employed in research laboratories. This, in turn, requires laboratory instruments to have some mechanism for hydrogen compression as part of their operation. In this study, the use of metal-hydride compressors for laboratory applications is explored and evaluated. The reduced operating requirements of laboratory instruments, relative to industrial compressors, and the ready availability of laboratory heating and cooling methods, allows the use of relatively simple, single-stage metal-hydride compressors. A simple theoretical derivation enables the determination of the size and amount of hydrogen storage alloy required for a desired pressure, given the experimental volume to be pressurised. Practical requirements, both in terms of the hydrogen storage alloy, and of the pressure vessel, are discussed. Examples of working compressors for both manual operation to 1000 bar, and automated operation to 100 bar, under computer control, are also given.

The Risk-Free Asset Implied by the Market: Medium-Term Bonds instead of Short-Term Bills

In empirical tests of the CAPM, the theoretical risk-free asset is typically assumed to be 1-month Treasury bills. This paper examines the implications of a mis-specified risk-free asset, i.e. the possibility that the ‘true’ risk-free asset is a longer-maturity Treasury bond. A simple theoretical derivation leads to the testable prediction that low-beta (high-beta) stocks should then exhibit positive (negative) bond betas. We find strong empirical confirmation for these predictions. The market-implied risk-free asset can be pinpointed at medium-term (5-year) bonds. Concrete implications of this finding are a lower equity risk premium and a less steep security market line.

Nonresonant energy transfers independent on the phonon densities in polyatomic liquids.

Energy-gap-dependent vibrational-energy transfers among the nitrile stretches of KSCN/KS(13)CN/KS(13)C(15)N in D2O, DMF, and formamide liquid solutions at room temperature were measured by the vibrational-energy-exchange method. The energy transfers are slower with a larger energy donor/acceptor gap, independent of the calculated instantaneous normal mode ("phonons" in liquids) densities or the terahertz absorption spectra. The energy-gap dependences of the nonresonant energy transfers cannot be described by phonon compensation mechanisms with the assumption that phonons are the instantaneous normal modes of the liquids. Instead, the experimental energy-gap dependences can be quantitatively reproduced by the dephasing mechanism. A simple theoretical derivation shows that the fast molecular motions in liquids randomize the modulations on the energy donor and acceptor by phonons and diminish the phonon compensation efficiency on energy transfer. Estimations based on the theoretical derivations suggest that, for most nonresonant intermolecular vibrational-energy transfers in liquids with energy gaps smaller than the thermal energy, the dephasing mechanism dominates the energy-transfer process.

Dry particle coating for improving the flowability of cohesive powders

Several dry processing techniques are used to coat cohesive cornstarch powder with different size silica particles. For nanosized silica guest particles, FESEM images show that both the magnetic assisted impaction coater (MAIC) and the hybridizer (HB) produce particles that are significantly more uniformly coated than using either a V-shape blender or simple hand mixing. Image analysis confirms that MAIC and HB provide higher surface coverage for the amount of guest material (flow aid) used. The improvement in flowablity of coated cornstarch is determined from angle of repose measurements using a Hosokawa powder tester. These measurements show that nanosized silica provides the best flowability enhancement, whereas mono-dispersed 500-nm silica does not improve the flow properties of cornstarch at all. This observation agrees with a simple theoretical derivation based on the original Rumpf model, which shows that the flowability improvement is inversely proportional to the guest particle size for a given host particle size or size of surface asperities. Experimental results also indicate that surface-treated hydrophobic silica is more effective in improving the flowability of cornstarch particles than untreated hydrophilic silica. An increase in processing time using MAIC and the V-blender also improves the flowability of the cornstarch since the guest particles are more deagglomerated and better dispersed, the longer the processing time.

Spin waves in a periodically layered magnetic nanowire

We report a simple theoretical derivation of the spectrum and damping of spin waves in a cylindrical periodically structured magnetic nanowire (cylindrical magnonic crystal) in the “effective-medium” approximation. The dependence of the “effective” magnetic parameters upon the individual layer parameters is shown to be different from the arithmetic average over the volume of the superlattice. The formulas that are obtained can be applied firstly in the description of spin-wave dispersion in the first allowed band of the structure and secondly in the design of a magnonic crystal with band gaps in an arbitrary part of the spin-wave spectrum.

Characterization of traveling waves and analytical estimation of pollutant removal in one‐dimensional subsurface bioremediation modeling

We study the behavior of solute fronts for an in situ bioremediation scenario in which a sorbing substrate is degraded by indigenous microorganisms in the presence of an injected nonsorbing electron acceptor. The fronts behave as traveling waves, which leads to a simple theoretical derivation of the long‐term degradation rate of the organic pollutant (substrate). The long‐term degradation rate is dependent upon input and background solute concentrations, the flow velocity, and the sorption and stoichiometric coefficients, but it does not depend upon dispersion and microbial kinetic parameters. Numerical simulations show that the analytical method is valid for predicting the long‐term degradation rate, although the front velocity and shape exhibit oscillatory behavior under some conditions. Numerical simulations also show that traveling wave conditions are established only after an initial phase in which substrate degradation is strongly dependent upon microbial kinetic parameters.

Simple derivation of the thermal noise formula using window-limited Fourier transforms and other conundrums

A simple theoretical derivation for obtaining the Johnson thermal noise formula using window-limited Fourier transforms is presented in detail for the first time, utilizing the well-known energy theorems. In the literature, a diverse range of alternative methods already exist, and the pedagogical value of the Fourier transform approach illustrates useful mathematical principles, taught at the undergraduate level, naturally highlighting a number of physical assumptions that are not always clearly dealt with. We also proceed to survey a number of misconceptions, problems, surprises, and conundrums concerning thermal noise.

Variation in Crop Radiation‐Use Efficiency with Increased Diffuse Radiation

Radiation‐use efficiency (RUE; grams of biomass accumulated, divided by total solar radiation intercepted) has proven to be a useful variable for quantifying biomass accumulation by crops. Experimental results and theoretical analysis indicate that differences in RUE exist among species, but that RUE for unstressed conditions is relatively stable within a species. A departure from the general conclusion is that high values of RUE have been reported for conditions where the diffuse proportion of the total radiation is commonly large (e.g., glasshouse‐grown plants). In this paper, a simple theoretical derivation of RUE was examined to quantify potential responses in RUE to variation in the fraction of diffuse radiation. To simulate natural conditions, the absolute amount of incident diffuse radiation was held constant and the amount of the direct radiation component was varied so that both the fraction of diffuse radiation and total radiation were varied. The estimates of RUE for soybean [Glycine max (L.) Merr.] and maize (Zea mays L.) increased as the fraction of diffuse radiation increased and the total radiation decreased. These results indicate that plants grown in glasshouses or in other locations with large fractions of diffuse radiation are likely to have greater radiation‐use efficiency than observed under primarily direct radiation.

Maximum achievable crosstalk isolation in full-duplex single-strand fiber-optic systems

A simple theoretical derivation of the maximum cross-talk isolation achievable in full-duplex single-strand multi-mode fiber-optic systems operating at a single wavelength is performed. For a commercial fiber of 1 km length with a total attanuation of 8 dB/km and a NA of 0.16, the measured cross-talk isolation was 42 dB for a single 130 ns, 0.9 μm pulse in agreement with the theory.

Hard core phonon frequency at transition temperature

A simple theoretical derivation is given to show that one may expect a hard core for the phonon frequency at the transition temperature. This approach implies that the frequency of the phonon will follow ω ∝ {[1 + γ(T − T C )] V 0} 1 2 instead of that predicted by soft mode theory. Our expression should be valid whenever a Brownian sublattice exists in the crystal.

Attenuation in Shock Tubes

Simple theoretical derivation is given of the empirical formula of Emrich and Wheeler which enables one to calculate the shock wave attenuation due to boundary layer effect from the initial pressure conditions in a shock tube.

Input Resistance of Vacuum Tubes as Ultra-High-Frequency Amplifiers

Vacuum tubes which when operated as voltage amplifiers at low frequency require no measurable grid input power have been found to take very serious amounts of power at ultra-high frequencies. The grid input conductance is shown to be very accurately represented for electrodes of any shape by the expression g <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">g</inf> = Ks <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</inf> f <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> τ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> where g <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">g</inf> is the input conductance, S <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</inf> the grid-plate transconductance, f the frequency, and τ the electron transit time. K is a parameter which is a function of the geometry of the tube and the voltage distribution. A physical picture of the effect, a simple theoretical derivation, and experimental proof with conventional tubes are given. The magnitude of g <inf xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">g</inf> is such that it is the principal limitation for amplifiers at frequencies of the order of 100 megacycles, and it seriously affects the amplification at frequencies as low as fifteen megacycles. The input resistance of a typical commercial tube, the RCA-57, is approximately 20,000 ohms at thirty megacycles. Other commercial tubes, being of the same general construction and size, have input resistances of the same order. The use of very small tubes, such as the RCA-954, with correspondingly short transit times is shown to be a practical means of increasing the amlplification obtainable with conventional circuits. Input capacity variation with frequency is found to be negligible with the RCA-57 even up to eighty megacycles and higher.