Simple Law Research Articles

A Simple Law for the Distribution of Long-Term Profit: The Empirical Regularity Behind the 1% of Firms That Capture 73% of Value

A Simple Law for the Distribution of Long-Term Profit: The Empirical Regularity Behind the 1% of Firms That Capture 73% of Value

Phonon growth characteristics in one-dimensional cylindrical quantum wires at low lattice temperatures

The phonon growth characteristics in a cylindrical quantum wire structure has been theoretically analysed here under the condition of low lattice temperature. The present theory takes into account the effects of finite barrier height, energy band non-parabolicity of the material and the non-zero values of the transverse components of the phonon wave vector. At the low lattice temperatures again, the interaction of the non-equilibrium electrons with acoustic phonons becomes inelastic and consequently the phonon distribution cannot be approximated by the simple equipartition law. Hence the full form of the Bose-Einstein distribution for the phonon ensemble is taken into consideration. The numerical results that follow from the present theory for the wire samples of GaAs/Ga0.7Al0.3As and Ga0.47In0.53As/InP turn out to be quite different from what follows in the traditional simplified framework.

Fish couple forecasting with feedback control to chase and capture moving prey.

Predator-prey interactions are fundamental to ecological and evolutionary dynamics. Yet, predicting the outcome of such interactions-whether predators intercept prey or fail to do so-remains a challenge. An emerging hypothesis holds that interception trajectories of diverse predator species can be described by simple feedback control laws that map sensory inputs to motor outputs. This form of feedback control is widely used in engineered systems but suffers from degraded performance in the presence of processing delays such as those found in biological brains. We tested whether delay-uncompensated feedback control could explain predator pursuit manoeuvres using a novel experimental system to present hunting fish with virtual targets that manoeuvred in ways that push the limits of this type of control. We found that predator behaviour cannot be explained by delay-uncompensated feedback control, but is instead consistent with a pursuit algorithm that combines short-term forecasting of self-motion and prey motion with feedback control. This model predicts both predator interception trajectories and whether predators capture or fail to capture prey on a trial-by-trial basis. Our results demonstrate how animals can combine short-term forecasting with feedback control to generate robust flexible behaviours in the face of significant processing delays.

Information-theoretic measures and Compton profile of H atom under finite oscillator potential

Information-theoretic measures for nl (2L) states of a H atom (with n=1−10 and l=0−2 , where n and l denote principal and angular momentum quantum numbers) have been investigated within a quantum dot by utilizing the Ritz variational principle, with the help of a Slater-type basis set. A well-established two-parameter (depth and width) model of finite oscillator potential is used to simulate the dot environment. The variationally optimized position (r)-space wave function is utilized to determine the momentum (p)-space wave function, leading to the generation of p-space radial density distribution. We explore the impact of cavity parameters on quantum information theoretic measures, such as Shannon (S) and Fisher information (I) entropy, in the ground as well as the excited state. The results of S were also used to test the Bialynicki–Birula–Mycielski inequality, related to the entropic uncertainty principle for the confined H atom. Some simple new fitting laws pertaining to S and I have been proposed. Furthermore, the p-space radial density is employed to derive the Compton profile of the confined H atom. Possible tunability of S,I and Compton profiles with respect to the parameters is noted.

Propulsive performance of a heaving and pitching foil with large amplitudes in unsteady ground effect

To reveal the effect of ground on the force behavior, propulsion performance, and vortex dynamics of a flapping foil, we numerically study a flapping foil actuated by combined heaving and pitching motions with large amplitudes near a solid ground surface. The instantaneous forces in both streamwise and cross-stream directions undergo a sudden drop during upstroke in close ground effect. The time-averaged thrust is enhanced by the ground but varies non-monotonically with ground distance at high foil oscillating frequencies. Three force regimes are identified in lift production, giving rise to two equilibrium altitudes of zero lift, one stable and another unstable. Moreover, we propose a simple scaling law model by a path-length-based Strouhal number and ground effect for thrust and power performance of a large-amplitude flapping foil. The results of the model are consistent with numerical results and previous experimental studies. The vortex dynamics in the wake structure are largely affected by ground proximity; in particular, the formed vortex pairs and their orientations are sensitive to their initial relative positions. Different sources and mechanisms of satellite vortex formation are then discussed. The ground exerts little effect on the phase angles that optimize the propulsive efficiency. This study is expected to provide new insights into the development and maneuvering of flapping foil-based propulsive systems.

Principle of corresponding states of particle gases for passenger flights

Passenger flight delays in civil aviation systems cause much harm to people’s daily lives. Recent works confirmed that the simple laws of delays emerge from the complex interactions of the systems’ elements, the patterns of which can be traced by the actual operations of passenger flights. Figuring out the underlying mechanism of the collective behaviours of flights is required to capture the law of delays, and to alleviate them. In the present work, based on the historical records of the United States from 1995 to 2020, we propose state equations to describe the motion of Arrival/Departure(AD) type flights by considering the attractions from airports and air routes together with the repulsions between flights. We erect the universal gaseous constant R by removing the intercepts representing the systemic errors. With the linear relationship between the number of air routes and the mole number, we calculate the critical thermodynamic quantities. Introducing the reduced ones with them, we generalize the principle of corresponding states of passenger flight particle gases. According to it, we think increasing the number of AD type flights between airports would be a proper strategy for alleviating flight delays. We hope the general ideas presented here can stimulate much more work in civil aviation and be used to solve practical problems in other fields.

Trajectory Tracking with Obstacle Avoidance for Nonholonomic Mobile Robots with Diamond-Shaped Velocity Constraints and Output Performance Specifications.

In this paper, we address the trajectory-/target-tracking and obstacle-avoidance problem for nonholonomic mobile robots subjected to diamond-shaped velocity constraints and predefined output performance specifications. The proposed scheme leverages the adaptive performance control to dynamically adjust the user-defined output performance specifications, ensuring compliance with input and safety constraints. A key feature of this approach is the integration of multiple constraints into a single adaptive performance function, governed by a simple adaptive law. Additionally, we introduce a robust velocity estimator with a priori-determined performance attributes to reconstruct the unmeasured trajectory/target velocity. Finally, we validate the effectiveness and robustness of the proposed control scheme, through extensive simulations and a real-world experiment.

Large-amplitude internal waves and turbulent mixing in three-layer flows under a rigid lid

We consider a nonlinear long-wave Boussinesq-type model describing the propagation of breaking internal solitary waves in a three-layer flow between two rigid boundaries. The Green–Naghdi-type equations govern the fluid flow in the top and bottom homogeneous layers. In the intermediate hydrostatic layer, the fluid is non-homogeneous, and its flow is described by the depth-averaged shallow water equations for shear flows. The velocity shear in the outer layers can lead to the development of the Kelvin–Helmholtz instability and turbulent mixing. To take this into account, we propose a simple law of vertical mixing, which governs the interaction of these layers. Stationary solutions and non-stationary calculations show the effect of mixing (or breaking) for waves of sufficiently large amplitude. We construct steady-state soliton-like solutions of the three-layer model adjacent to a given constant flow. The obtained theoretical profiles of breaking solitary waves are consistent with laboratory experiments.

Oxidation Driven Damage on SiC/BN/SiC Ceramic Matrix Composite Aero-Engine Structures: An Iterative Computational Framework.

Ceramic matrix composites (CMCs) could be a game changer in the aero-engine industry. Their density is circa one-third of their metallic counterpart. CMCs, furthermore, offer increased strength and greater capability at very high temperatures. This would allow for a reduction in cooling and an increased engine performance. Some challenges, besides the complexity of the manufacturing process, however, remain for the structural integrity of this technology. CMCs are inherently brittle; furthermore, they tend to oxidise when attacked by water or oxygen, and their constituents become brittle and more prone to failure. There are two main points of novelty proposed by this work. The first one is to model and reproduce recent oxidation experimental data with a simple Fick's law implemented in Abaqus. The parameters of this modelling are a powerful tool for the design of such material systems. The second aspect consists in the development of a new computational framework for iteratively calculating oxygen diffusion and stiffness degradation of the material. Oxidation and stiffness degradation are in fact coupled phenomena. The crack (or microcracking) opening, the function of applied stress, accelerates oxygen diffusion whilst the oxidation diffusion itself contributes to embrittlement and then damage introduction in the material system.

Analysis of Power-Maximizing Region 2 Controllers for Wind and Marine Turbines

Wind and marine energy are rapidly growing and complementary technologies that share some techniques for simplified modeling and control, particularly in below-rated flow speeds. A turbine operator has several choices of controller for maximizing power in Region 2. The simple and ubiquitous KΩ2 control law is often effective but limited in its flexibility. Alternative controllers use reference tracking to split the control objectives into a low-bandwidth optimal tip-speed ratio tracking loop to maximize steady-state power and a higher-bandwidth proportional-integral control loop to reject inflow turbulence. Several options exist for identifying the slowly varying optimal set point during operation, based on estimating the inflow velocity or filtering the power or torque signals. This study compares the trade-offs between performance and other design priorities for a few choices of reference-tracking controller in the literature for reference wind and marine turbines. Analysis is performed in the frequency domain using the linearization of each controller, and the impact of turbulent disturbances on the closed-loop system is described. The controllers are simulated in OpenFAST to analyze their performance with higher-order nonlinear turbine dynamics.

Estimation of Crosswind Disturbances for a Vehicle by LPV‐MHE and its Application to Disturbance Cancellation

Crosswinds and transverse slopes of the road surface affect the motion of a ground vehicle as disturbances. The objective of this paper is to develop a method for estimating crosswind disturbances and lateral force disturbances caused by transverse slopes of the road surface under the variation of the vehicle speed. Firstly, a dynamical model of a vehicle is described as a Linear Parameter‐Varying (LPV) system in which the value of the coefficient matrices vary with the vehicle velocity. Then, an algorithm to estimate the disturbance is derived based on Moving Horizon Estimation (MHE) and applied to the derived LPV system. Furthermore, a simple control law which counteracts the effects of the disturbances on the lateral velocity and the yaw rate in steady‐state based on the estimates of the disturbances is presented. The effectiveness of the proposed method is demonstrated by a numerical example. © 2024 The Author(s). IEEJ Transactions on Electrical and Electronic Engineering published by Institute of Electrical Engineers of Japan and Wiley Periodicals LLC.

WITHDRAWN: Kinetics and mechanism of the reactions of alkanediamine-linked dinuclear platinum(II) complexes with some biorelevant-nucleophiles

The kinetics and mechanism of substitition reactions of dinuclear platinum(II) complexes of the general formula [{Pt(H2O)}2(N,N,N′,N′-tetrakis(2-pyridylmethyl)-N(CH2)n-N](ClO4)4,viz., n = 2 (PtEn); 3 (PtProp); 6 (PtHex); 8 (PtOct) and 10 (PtDec) were investigated in 0.10 M aqueous perchloric acid medium as a function of concentration of l-glutathione (Glu) and dl-penicilliamine (Pen) nucleophiles and temperature under pseudo first-order conditions using UV–visible spectrophotometry. The reactivity data of the dinuclear Pt(II) complexes were compared with those of their mononuclear analogues of the form [Pt(H2O)(N,N-bis(2-pyridylmethyl)-N(CH2)n-CH3](ClO4)2, n = 1 (Ptbpea); 2 (Ptbppa); 5 (Ptbpha) and 9 (Ptbpda) under the same experimental conditions. The observed rate constants for the substitution of the aqua ligands follow the simple rate law: kobs = k2[Nu]. The reactivity of the complexes increases as the chain length of the linker or tail increases except Prop which showed a higher reactivity towards the nucleophiles than the rest of the complexes. The overall trend of reactivity for the dinuclear platinum(II) complexes is PtEn < PtHex < PtOct < PtDec < PtProp. The reactivity of the mononuclear complexes follows the same trend as the dinuclears and increases in the order Ptbpea < Ptbppa < Ptbpha < Ptbpda. In all cases, the mononuclear complexes are more reactive than their dinuclear analogues, which is an indication of the steric retardation on the rate of substitution due to the conformations of the dinuclear platinum(II) complexes. Glu was found to be a better nucleophile than Pen. The relatively small and positive values for the enthalpy of activation, negative values for entropy of activation and the dependence of the second-order rate constants on the concentration of entering nucleophiles supports an associatively activated mechanism.

On the development and analysis of coupled surface–subsurface models of catchments. Part 3. Analytical solutions and scaling laws

The objective of this three-part work is to formulate and rigorously analyse a number of reduced mathematical models that are nevertheless capable of describing the hydrology at the scale of a river basin (i.e. catchment). Coupled surface and subsurface flows are considered. In this third part, we focus on the development of analytical solutions and scaling laws for a benchmark catchment model that models the river flow (runoff) generated during a single rainfall. We demonstrate that for catchments characterised by a shallow impenetrable bedrock, the shallow-water approximation allows a reduction of the governing formulation to a coupled system of one-dimensional time-dependent equations for the surface and subsurface flows. Asymptotic analysis is used to derive semi-analytical solutions for the model. We provide simple asymptotic scaling laws describing the peak flow formation, and demonstrate its accuracy through a comparison with the two-dimensional model developed in Part 2. These scaling laws can be used as an analytical benchmark for assessing the validity of other physical, conceptual or statistical models of catchments.

Study on the self-adaptive process of droplet traffic to a perturbation of flow resistance at the arms of a micro-T-junction

The response of the water–oil droplet flow to a perturbation of flow resistance added at the arms of a bypassed micro-T-junction is studied through a numerical method. The capillary number of the continuous flow varies between 0.007 and 0.034. Once an additional flow resistance is introduced at the arms of the T-junction, the flow self-adapts to the perturbation and droplets show complex dynamics at the junction, including splitting, merging, and reshaping. During the self-adaptive process, the instantaneous splitting ratios of the dispersed flow show positive correlations with that of the continuous flow. The correlation coefficient reduces as the increase in the amplitude of the perturbation. The ensemble splitting ratios of them, however, are independent. It shows a rather simple law that the ensemble splitting ratios of oil anchor at around a constant value while the corresponding parameter of water varies from 0 to 1. It illustrates that the droplet flow splitting at a T-junction resembles a resilient system, the stiffness of which depends on the capillary number of the flow. The energy loss of the system induced by a perturbation of the flow resistance is self-reduced by just redistributing of droplets into the two arms.

Non-Maxwellian electron effects on the macroscopic response of a Hall thruster discharge from an axial–radial kinetic model

A 2D axial–radial particle-in-cell (PIC) model of a Hall thruster discharge has been developed to analyze (mainly) the fluid equations satisfied by the azimuthally-averaged slow dynamics of electrons. Their weak collisionality together with a strong interaction with the thruster walls lead to a non-Maxwellian velocity distribution function (VDF). Consequently, the resulting macroscopic response differs from a conventional collisional fluid. First, the gyrotropic (diagonal) part of the pressure tensor is anisotropic. Second, its gyroviscous part, although small, is relevant in the azimuthal momentum balance, where the dominant contributions are orders of magnitude lower than in the axial momentum balance. Third, the heat flux vector does not satisfy simple laws, although convective and conductive behaviors can be identified for the parallel and perpendicular components, respectively. And fourth, the electron wall interaction parameters can differ largely from the classical sheath theory, based on near Maxwellian VDF. Furthermore, these effects behave differently in the near-anode and near-exit regions of the channel. Still, the profiles of basic plasma magnitudes agree well with those of 1D axial fluid models. To facilitate the interpretation of the plasma response, a quasiplanar geometry, a purely-radial magnetic field, and a simple empirical model of cross-field transport were used; but realistic configurations and a more elaborate anomalous diffusion formulation can be incorporated. Computational time was controlled by using an augmented vacuum permittivity and a stationary depletion law for neutrals.

Mortgages with non-random time-varying interest rates

AbstractHere we introduce an “alternative” version of the standard traditional amortization plan, where sequences of non-random time-varying periodic interest rates replace the usual constant periodic effective rate, while preserving all the other classical rules. In particular, we use two of these sequences coherently generated by two different specific hyperbolic instantaneous intensity functions. We found that the two standard amortization plans obtained through this approach match perfectly with the two main amortization plans recently proposed under the simple capitalization law. This matching provides thus a clear link between the traditional scheme and the new wave of proposals in simple regime.

Optimal guidance laws for diffractive solar sails with Littrow transmission grating

The use of advanced and highly engineered membrane films in solar sail design enables the thrust vector to achieve some specific characteristics that are capable of affecting the performance of a sail-based spacecraft trajectory in a transfer mission scenario. In this field, the recently proposed diffractive sail uses metamaterial films to coat the very thin sail membrane as a potential and effective (in some mission scenarios) alternative to the more common metallic reflective coating. The purpose of this work is to study the optimal guidance law, as a function of sail pitch angle, of a diffractive sailcraft with a Littrow transmission grating film in a typical two-dimensional heliocentric transfer. In particular, the optimal steering law is obtained through a classical indirect approach, depending on the characteristics of Lawden's primer vector, either in exact (by numerical simulation) or approximate (by analytical means) form. The performance of a diffractive sailcraft with a Littrow transmission grating film is then analyzed in a number of potential mission scenarios such as, for example, a phasing in a circular orbit, an interplanetary transfer between coplanar Keplerian trajectories, a circular orbit flip maneuver, and an escape from the Solar System. Simulation results indicate that this specific diffractive sailcraft is potentially capable of executing a typical solar sail-based mission scenario with a simple steering law.

Multiplicative Renormalization of Stochastic Differential Equations for the Abelian Sandpile Model

The long-term, large-scale behavior in a problem of stochastic nonlinear dynamics corresponding to the Abelian sandpile model is studied with the use of the quantum-field theory renormalization group approach. We prove the multiplicative renormalization of the model including an infinite number of coupling parameters, calculate an infinite number of renormalization constants, identify a plane of fixed points in the infinite dimensional space of coupling parameters, discuss their stability and critical scaling in the model, and formulate a simple law relating the asymptotic size of an avalanche to a model exponent quantifying the time-scale separation between the slow energy injection and fast avalanche relaxation processes.

Revealing the mechanism and scaling laws behind equilibrium altitudes of near-ground pitching hydrofoils

A classic lift decomposition (Von Kármán &amp; Sears, J. Aeronaut. Sci., vol. 5, 1938, pp. 379–390) is conducted on potential flow simulations of a near-ground pitching hydrofoil. It is discovered that previously observed stable and unstable equilibrium altitudes are generated by a balance between positive wake-induced lift and negative quasi-steady lift while the added mass lift does not play a role. Using both simulations and experiments, detailed analyses of each lift component's near-ground behaviour provide further physical insights. When applied to three-dimensional pitching hydrofoils the lift decomposition reveals that the disappearance of equilibrium altitudes for ${A{\kern-4pt}R}\ {\rm (aspect\ ratio)} &lt;1.5$ occurs due to the magnitude of the quasi-steady lift outweighing the magnitude of the wake-induced lift at all ground distances. Scaling laws for the quasi-steady lift, wake-induced lift and the stable equilibrium altitude are discovered. A simple scaling law for the lift of a steady foil in ground effect is derived. This scaling shows that both circulation enhancement and the velocity induced at a foil's leading edge by the bound vortex of its ground image foil are the essential physics to understand steady ground effect. The scaling laws for unsteady pitching foils can predict the equilibrium altitude to within $20\,\%$ of its value when $St\ {\rm (Strouhal\ number)} &lt; 0.45$ . For $St \ge 0.45$ there is a wake instability effect, not accounted for in the scaling relations, that significantly alters the wake-induced lift. These results not only provide key physical insights and scaling laws for steady and unsteady ground effects, but also for two schooling hydrofoils in a side-by-side formation with an out-of-phase synchronization.

Multi-scale spallation model for single-crystal ductile metals incorporating microscopic mechanism of void nucleation

Spall strength characterizes the tensile performance of materials under high strain rates. However, theoretical prediction of the spall strength has long been a big challenge since it involves information on the damage evolution at multiple length scales. In this work, a multi-scale model is proposed for the spallation of single-crystal ductile metals, which includes both a microscopic model of damage nucleation and an effective correlation between the microscopic physical mechanisms and the macroscopic mechanical behaviors. An energy criterion to predict the threshold stress for damage nucleation is firstly proposed based on a near-realistic three-dimensional configuration of dislocation emission. The statistical characteristics of the damage nucleation threshold are analyzed, based on which a multi-scale spall model is proposed to couple the physical essence at the micro-scale to the macro-scale, revealing the influences of temperature, vacancy concentration, and strain rate on spall strength. An approximate form of the multi-scale model is proposed by dimensional analysis and reasonable approximation, which is consistent with the empirical model summarized from experimental results, and further deduced to a simple scaling law that predicts the transition in the strain rate-sensitivity of spall strength.