Analytical Formulas Research Articles

Direct Current Motor Velocity Control With Integral Retarded Controller Under Unintentional Delay

Abstract Delay-based controllers have been recently revisited over proportional-integral-derivative (PID) controllers, with promising analytical tuning formulae and capabilities to effectively control plants with noisy measurements even without low-pass filters. One such controller is the integral retarded (IR) controller, which utilizes an intentional delay to reduce actuator chattering against noisy measurements while its integral part achieves zero steady-state error for set-point regulation of Type-0 open-loop systems. However, measurements can be unintentionally delayed in many applications. The integral retarded framework for such cases has not been studied in the literature. Here, we provide new analytical tuning rules of the controller in such cases, as well as validations through simulations and a direct current (DC) motor velocity control hardware experiment.

Analytical Study on the Buckling of Cylindrical Shells With Circumferential Thickness Variation Under Varying External Pressure

Abstract In this article, the analytical buckling load coefficient formula for a cylinder with circumferential thickness variation subjected to varying external pressure is established for the first time by developing a quadratic perturbation method. Based on the presented formula, some specific examples that consider either circumferential shell thickness variation or varying lateral pressure are studied and compared with those in the published literature. First, classical cosine thickness variation is analyzed. The computed results of buckling load coefficients indicate that most of differences between the proposed formula and finite element (FE) analyses in previous literature are less than 5%. Second, wind-type pressure load is discussed, and the maximum difference of predicted buckling load coefficients between our formula and results in published article is 2.3%. Third, both circumferential thickness variation and linear liquid pressure are analyzed by the proposed analytical formula and validated by the Galerkin method when both thickness and load variations are small. Therefore, accuracy and reliability of the established formula are validated. For the purpose of engineering application, buckling of a circular shell with local circumferential thickness variation due to weld shrinkage under wind-type pressure is analytically investigated. The effects of thickness variation amplitude, load parameter, half angle of thickness variation, and shell dimensions on buckling load coefficients are studied in detail.

Analytical and experimental evaluation of two-layered unsaturated sand bearing capacity

Pavement design methods based on principles of unsaturated soil mechanics take into account high soil shear strength due to matric suction resulting in more economical design especially in long roads. In this study, the bearing capacity of two-layer unsaturated sand was investigated using both analytical and experimental methods. At first, using the limit equilibrium method an analytical formula was proposed to determine the bearing capacity of two-layer unsaturated sand in which linear suction profile was considered in soil layers. It should be considered that the constant matric suction distribution assumed by the previous researchers does not show the real profile of matric suction within the soil, sometimes resulting in miscalculated unsaturated bearing capacity. Also, the bearing capacity of two-layer unsaturated poorly graded sand was investigated experimentally in different suctions by a special unsaturated chamber apparatus (UCA) designed for this purpose. The results show more than double increase of unsaturated soil bearing capacity with Sr = 25% compared to saturated soil. The formation of failure wedges in all experiments was investigated by image processing. An acceptable agreement was obtained between the theoretical and experimental bearing capacity results.

Stiffness of Loaded Face of Steel Rectangular Hollow Section Columns with and without Concrete Infill in Beam-column Endplate Connections

This paper presents a new analytical approach for calculating the stiffness of the loaded face of a rectangular hollow section RHS column in beam-column connections with and without concrete infill, as well as with flush and extended endplates, to determine the behavior curve of these types of connections. The approach, based on Eurocode 03's component method, offers efficient analytical formulas for accurately determining the loaded face's stiffness. A comparison with existing methods demonstrates its remarkable simplicity and efficiency, allowing a simple beam model to represent the RHS column's behavior with all relevant parameters considered. Comparison of the new approach to existing ones from the literature demonstrates their reliability and efficiency. Furthermore, when compared to 32 experimental tests presenting nearly the entire range of probable connection configurations, as well as attachment techniques commonly used in construction practice, the margin of error does not exceed 12 percent on average and a maximum of less than 25 percent.

USE OF GROUP POISSON FLOW IN SIMULATION MODELING OF MODERN VIDEO TRAFFIC

The possibility of using a group Poisson flow for simulation modeling of modern video traffic is considered in relation to the approximation of the first and second order statistical characteristics of the queue created by the traffic in the transmission buffer. A method is proposed for determining the parameters of an approximating group Poisson flow, which consists of simultaneously minimizing the deviation of the dependencies of the mathematical expectation of the queue and the dispersion of the queue on the channel load, calculated using the formulas for the approximating flow, from similar dependencies of real traffic. As analytical formulas for the mathematical expectation and queue dispersion, formulas obtained using the interval method for a queuing system with one device and constant service time are used. The quality of the approximation is checked by simulation of the passage of a group Poisson flow with calculated parameters through a given queuing system.

How Does the Inner Retinal Network Shape the Ganglion Cells Receptive Field? A Computational Study.

We consider a model of basic inner retinal connectivity where bipolar and amacrine cells interconnect and both cell types project onto ganglion cells, modulating their response output to the brain visual areas. We derive an analytical formula for the spatiotemporal response of retinal ganglion cells to stimuli, taking into account the effects of amacrine cells inhibition. This analysis reveals two important functional parameters of the network: (1) the intensity of the interactions between bipolar and amacrine cells and (2) the characteristic timescale of these responses. Both parameters have a profound combined impact on the spatiotemporal features of retinal ganglion cells' responses to light. The validity of the model is confirmed by faithfully reproducing pharmacogenetic experimental results obtained by stimulating excitatory DREADDs (Designer Receptors Exclusively Activated by Designer Drugs) expressed on ganglion cells and amacrine cells' subclasses, thereby modifying the inner retinal network activity to visual stimuli in a complex, entangled manner. Our mathematical model allows us to explore and decipher these complex effects in a manner that would not be feasible experimentally and provides novel insights in retinal dynamics.

Twisted splitting and propagation factor of superimposed twisted Hermite-Gaussian Schell-model beams in turbulent atmosphere

We believe this to be a new superposition twisted Hermite-Gaussian Schell-model (STHGSM) beam hat is proposed. Analytic formulas for the intensity distribution and propagation factor of the STHGSM beam in non-Kolmogorov turbulence are derived by utilizing the generalized Huygens-Fresnel principle (HFP) and the Wigner function. The evolution characteristics of STHGSM beams propagating are numerically calculated and analyzed. Our findings indicate that the light intensity of the STHGSM beam gradually undergoes splitting and rotation around the axis during propagation through non-Kolmogorov turbulence, eventually evolving into a diagonal lobe shape at a certain distance of transmission. The anti-turbulence capability of the beam strengthens with higher beam order or twist factor values.

A numerical investigation into the equivalent parameters of a compressible soil treated by stone columns

A series of triaxial test simulations are adopted to estimate the equivalent strength parameters for compressible soil samples reinforced with stone columns. The simulations utilize the finite difference code, Fast Lagrangian Analysis of Continua in three dimensions FLAC3D. An elasto-plastic model is applied to utilize a Mohr-Coulomb yield criterion. The equivalent strength parameters are estimated using newly proposed formulas for geo-composite materials. The researchers compare the obtained results to the analytical formulas proposed in the literature. Additionally, the equivalent parameters are used in equivalent area models. This study investigates the effect of the replacement area ratio. This study offers two applications. Firstly, it evaluates the safety factor of embankments constructed on compressible soil improved with stone columns. Secondly, it estimates the bearing capacity of strip footings on compressible soil treated with stone columns. In all applications, both individual column and equivalent area models are considered. The proposed equations for the equivalent elastic parameters (E, ν) and the mechanical properties, equivalent cohesion, and internal frictional angle (c and φ) give results that agree with the solutions reported in the existing literature.

Four-wave mixing induced general localized waves for a coupled generalized nonlinear Schrödinger system

In this paper, we investigate the general localized waves on the nonvanishing background for a coupled generalized nonlinear Schrödinger system with four wave mixing (FWM) effect. Using a uniform Darboux transformation, we construct a unified analytical solution formula which can be used not only to generate some reported localized waves, but also to yield some new results. Based on whether the relative wave vector of the two seed continuous-waves is zero, we respectively obtained various localized waves on the plane wave and periodic backgrounds, including bright/dark solitons, breathers, and rogue waves. Especially, we assort these localized waves and provide detailed parameter conditions for generating them, and find that the FWM term b plays a decisive role in generating the periodic background for those localized waves. In addition, interaction dynamics of the hybrid localized waves on both the plane wave and periodic backgrounds composed of the bright/dark soliton, breather and rogue wave are analyzed. We expect that these results will shed light on the understanding of localized waves on the periodic background owing to the interference of multiple continuous-wave fields.

Nonlocal Massive Gravity from Einstein Gravity.

We present a top-down construction of a three-dimensional nonlocal theory of massive gravity. This "nonlocal massive gravity" (NLMG) is obtained as the gravitational theory induced by Einstein gravity on a brane inserted in anti-de Sitter space modified by an overall minus sign. The theory involves an infinite series of increasingly complicated higher-derivative corrections to the Einstein-Hilbert action, with the quadratic term coinciding with new massive gravity. We obtain an analytic formula for the quadratic action of NLMG and show that its linearized spectrum consists of an infinite tower of positive-energy massive spin-2 modes. We compute the Newtonian potential and show that the introduction of the infinite series of terms makes it behave as ∼1/r at short distances, as opposed to the logarithmic behavior encountered when the series is truncated at any finite order. We use this and input from brane-world holography to argue that the theory may contain asymptotically flat black hole solutions.

A dynamic sliding model of hard spherical surfaces on a flat soft plane

This study proposes a dynamic sliding model of hard spherical surfaces on a flat soft plane. For the sphere sliding at velocity v, the dynamic frictional force was described as Fd = λAv using a surface parameter λ and the contact area A. The compressive force was expressed as Pd = λ'A'v using a surface parameter λ' and the sectional area A'. An analytical formula for the sliding motion was derived considering Fd and the drag force Df associated with Pd. The model was validated by comparing the experimental velocities of stainless steel spherical surfaces on a flat polypropylene plate. The model showed all the dominant aspects of the measured velocities during the sliding process.

A Two-Temperature Nonlocal Poro-Thermoelastic Solid Via Higher-Order Time-Derivatives Model with Phase Lag

Abstract Purpose The present study has depicted the effect of gravitational on a two-temperature nonlocal poro-thermoelastic solid. Methods The multi-phase-lag model and fractional derivatives are used to tackle the issue. Through normal mode analysis, analytical formulas for the variable fields are derived. Using appropriate boundary conditions, the physical fields are calculated and the numerical computations have been carried out with the help of MATLAB programming. Results Through a careful comparison of the numerical data, the impacts of gravity, fractional derivative order, and locatiy on the behavior of physical fields are described. Conclusion Physical variables are affected by nonlocal thermoelasticity, fractional derivative order as well as the gravity field.

Investigation of Physical Properties of Nanostructured Selenium-Based Compound Semiconductors

The study of physical properties of compound semiconductors plays a vital role in the device fabrication point of view. Different investigations suggest that one can tune these properties by impurity dopants, irradiation techniques, adopting different synthesis techniques, etc. In this study, the physical properties of nanostructured thin films of Se–S compound were tuned by different Hg dopant concentrations. X-ray diffraction spectra clarify the preferred crystallite growth occurs in the cubic phase of the corresponding Bravi’s crystal system. The particle size calculated from Bragg’s reflection spectra by using Scherrer’s analytical formula illustrates an enhancement of crystallite size in highly concentrated Hg-doped sample. Similar consequences are found in surface morphological micrographs. The optical band gap reduced from 1.65[Formula: see text]eV to 1.54[Formula: see text]eV on increasing the doping concentration of Hg, according to the computed optical parameters using optical transmission spectra in the wavelength range 200–1100[Formula: see text]nm. The thin-film refractive index dispersion data fits well in accordance with the single oscillator model. Investigation of electrical properties tells that there is significant improvement in electrical conductivity in highly concentrated Hg-doped samples. Therefore, the apparent tuning as observed in the physical properties of the investigated material may have practical uses in industry for a variety of optoelectronic devices.

Pricing derivatives on foreign assets using Markov-modulated cojump-diffusion dynamics

In this study, cross-currency derivatives pricing under stochastic interest rates is analyzed when Markov-modulated cojump-diffusion dynamics with both idiosyncratic and simultaneous jumps drive the underlying foreign equity price and foreign exchange rate processes. More specifically, the noise dynamics of these two assets are captured by the correlated Wiener processes, and the two types of jump events are described as two independent compound Poisson processes with log-normal jump amplitudes. Cojumping addresses the correlation between these two asset price jumps. In an incomplete market setting, the dynamic Esscher transform approach is applied to determine a pricing kernel. According to the resulting dynamics, explicit analytical formulas for evaluating values of European foreign equity call options are provided. Numerical experiments are also described.

Testing analytical methods to derive the cosmic-ray ionisation rate in cold regions via synthetic observations

Context. Cosmic rays (CRs) heavily impact the chemistry and physics of cold and dense star-forming regions. However, the characterisation of their ionisation rate continues to pose a challenge from the observational point of view. Aims. In the past, a few analytical formulas have been proposed to infer the cosmic-ray ionisation rate, ζ2, from molecular line observations. These have been derived from the chemical kinetics of the involved species, but they have not yet been validated using synthetic data processed with a standard observative pipeline. In this work, we aim to bridge this gap. Methods. We performed a radiative transfer on a set of three-dimensional magneto-hydrodynamical simulations of prestellar cores, exploring different initial ζ2, evolutionary stages, types of radiative transfer (for instance assuming local-thermodynamic-equilibrium conditions), and telescope responses. We then computed the column densities of the involved tracers to determine ζ2, employing a recently proposed method based on the detection of H2D+. We compared this approach with a previous method, based on more common tracers. Both approaches are commonly used. Results. Our results confirm that the equation based on the detection of H2D+ accurately retrieves the actual ζ2 within a factor of two to three in the physical conditions explored in our tests. Since we have also explored a non-local thermodynamic equilibrium (non-LTE) radiative transfer, this work indirectly offers insights into the excitation temperatures of common transitions at moderate volume densities (n ≈ 105 cm−3). We also performed a few tests using a previous methodology that is independent of H2D+, which overestimates the actual ζ2 by at least two orders of magnitude. We considered a new derivation of this method, however, we found that it still leads to high over-estimations. Conclusions. The method based on H2D+ is further validated in this work and demonstrates a reliable method for estimating ζ2 in cold and dense gas. On the contrary, the former analytical equation, as already pointed out by its authors, has no global domain of application. Thus, we find that it ought to be employed with caution.

Implementation of modified cam–clay model using closest point projection method under Cartesian coordinate system

The modified Cam–Clay model is an elastoplastic soil model that holds a prominent position in civil engineering for its precise depiction of varied soil behaviors. Despite extensive examination of its numerical processes, the predominant focus on stress integration algorithms within the triaxial stress space presents challenges for individuals less acquainted with geotechnical science. In response to this, the present study derived the stress integration equations for the modified Cam–Clay model within the Cartesian coordinate system employing the closest point projection method. Subsequently, a finite element program was developed incorporating the derived integration process. This study computed and compared the consolidation processes under both drained and undrained conditions for cubic soil samples with various over-consolidation ratios using the developed program, ABAQUS, and analytical formulas. The findings demonstrate that equations integrated within the Cartesian coordinate system offer ease of understanding and programming. The feasibility, accuracy, and stability of the closest point projection method have been validated. Comparative analysis of soil samples across various over-consolidation ratios indicated a reduction in failure stress with an increase in over-consolidation ratio, indicating a higher propensity for failure under undrained conditions than under the drained conditions.

Optimal cut-off frequency and controller gain of an integrated skyhook active isolation

Vibration isolation is a crucial technology in precision manufacturing. With the rapid development of smart sensors, smart actuators, and microprocessors, active vibration isolation has emerged as a viable approach to improve the performance of manufacturing equipment. In integrated skyhook active vibration isolation, the cut-off frequency limits the controller gain. Base on the repeated poles technique, this paper reveals the simple analytical forms of the optimal cut-off frequency and controller gain of the integrated skyhook active isolation. The analytical formula is useful in the design of active isolation. Numerical calculations are performed to show the good performance of the optimal design. An experiment is carried out to show the existence of the optimal controller gain.

Simulating the tidal disruption of stars by stellar-mass black holes using moving-mesh hydrodynamics

In the centers of dense star clusters, close encounters between stars and compact objects are likely to occur. We studied tidal disruption events of main-sequence (MS) stars by stellar-mass black holes (termed μTDEs), which can shed light on the processes occurring in these clusters, including being an avenue in the mass growth of stellar-mass BHs. Using the moving-mesh hydrodynamics code AREPO, we performed a suite of 58 hydrodynamics simulations of partial μTDEs of realistic, MESA-generated MS stars by varying the initial mass of the star (0.5 M⊙ and 1 M⊙), the age of the star (zero-age, middle-age and terminal-age), the mass of the black hole (10 M⊙ and 40 M⊙), and the impact parameter (yielding almost no mass loss to full disruption). We then examined the dependence of the masses, spins, and orbital parameters of the partially disrupted remnant on the initial encounter parameters. We find that the mass lost from a star decreases roughly exponentially with increasing approach distance and that a 1 M⊙ star loses less mass than a 0.5 M⊙ one. Moreover, a more evolved star is less susceptible to mass loss. Tidal torques at the closest approach spin up the remnant very close to break-up velocity when the impact parameter is low. The remnant star can be bound (eccentric) or unbound (hyperbolic) to the black hole; hyperbolic orbits occur when the star’s central density concentration is relatively low and the black-hole-star mass ratio is high, which is the case for the disruption of a 0.5 M⊙ star. Finally, we provide best-fit analytical formulae for the aforementioned range of parameters that can be incorporated into cluster codes to model star-black-hole interaction more accurately.

Eclipse-timing study of new hierarchical triple star candidates in the northern continuous viewing zone of TESS

Aims. We compiled a list of more than 3500 eclipsing binaries located in and near the northern continuous viewing zone (NCVZ) of the TESS space telescope that have sufficient TESS photometry to search for additional hidden components in these systems. In addition to discovering their hierarchical nature, we also determined their orbital parameters and analyzed their distributions. Methods. We obtained the TESS light curves of all targets in an automated way by applying convolution-aided differential photometry on the TESS full-frame images from all available sectors up to sector 60. Using a new self-developed Python GUI, we visually confirmed all of these light curves, determined the eclipsing periods of the objects, and calculated their eclipse-timing variations (ETVs). The ETV curves were used in order to search for nonlinear variations that could be attributed to a light travel-time effect (LTTE) or dynamical perturbations caused by additional components in these systems. We preselected 351 such candidates and modeled their ETVs with the analytic formulae of pure LTTE or with a combination of LTTE and dynamical perturbations. Results. We were able to fit a model solution for the ETVs of 135 hierarchical triple candidates, 10 systems of which were known from the literature, and the remaining 125 systems are new discoveries. These systems include some more noteworthy ones, such as five tight triples that are very close to their dynamical stability limit with a period ratio lower than 20, and three newly discovered triply eclipsing triples. We point out that dynamical perturbations occur in GZ Dra, which we found to be a triple, and that the system is one of the most strongly inclined systems known in the literature, with im = 58° ±7°. We also compared the distributions of some orbital parameters from our solutions with those from a previous Kepler sample. Finally, we verified the correlations between the available parameters for systems that have Gaia non-single star orbital solutions with those from our ETV solutions.

Investigating the impact of applied magnetic field and current on anode power deposition in AF-MPDT

The high temperature superconductors enhanced magnetoplasmadynamic thruster is a promising device for various space mission scenarios. However, a critical issue hindering the enhancement of the thruster’s performance is the problem of anode power deposition. Previous studies have identified the anode fall voltage as a major contributor to this power deposition. This paper introduces an approximate analytical formula for calculating anode power deposition resulting from anode fall voltage. The paper further analyzes and calculates the variation of anode fall voltage with an applied magnetic field and discharge current. The findings reveal a direct correlation between applied magnetic field and both anode fall voltage and power, indicating an increase with higher magnetic field values. In contrast, while the anode fall voltage experiences a slight decline with increased discharge current, the anode power deposition remains elevated due to the transition from field ionization to thermal ionization. To gain a comprehensive understanding of anode power deposition, an experiment was conducted to obtain measurements under different operating conditions, involving varying levels of applied magnetic field and discharge current. The experimental results align with the theoretical predictions. These insights have the potential to serve as a valuable reference for enhancing the efficiency of magnetoplasmadynamic thrusters, bringing us closer to unlocking the full potential of these remarkable propulsion systems in the realm of space exploration.