Journal articles: 'Hyperbolic Cosine Model'

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Pourhassan, B., and J. Naji. "Tachyonic matter cosmology with exponential and hyperbolic potentials." International Journal of Modern Physics D 26, no. 02 (February 2017): 1750012. http://dx.doi.org/10.1142/s0218271817500122.

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In this paper, we consider tachyonic matter in spatially flat Friedmann–Robertson–Walker (FRW) universe, and obtain behavior of some important cosmological parameters for two special cases of potentials. First, we assume the exponential potential and then consider hyperbolic cosine type potential. In both cases, we obtain behavior of the Hubble, deceleration and EoS parameters. Comparison with observational data suggest the model with hyperbolic cosine type scalar field potentials has good model to describe universe.

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Navó, G., and E. Elizalde. "Stability of hyperbolic and matter-dominated bounce cosmologies from F(R,𝒢)modified gravity at late evolution stages." International Journal of Geometric Methods in Modern Physics 17, no. 11 (August 26, 2020): 2050162. http://dx.doi.org/10.1142/s0219887820501625.

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The stability of two different bounce scenarios from [Formula: see text] modified gravity at later times is studied, namely a hyperbolic cosine bounce model and a matter-dominated one. After describing the main characteristics of [Formula: see text] modified gravity, the two different bounce scenarios stemming from this theory are reconstructed and their stability at late stages is discussed. The stability of the hyperbolic cosine model is proven, while the concrete matter-bounce model here chosen does not seem to accomplish the necessary conditions to be stable at later times.

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Abuelma'atti, Muhammad Taher. "Modelling of Nonuniform RC Structures for Computer Aided Design." Active and Passive Electronic Components 16, no. 2 (1994): 89–95. http://dx.doi.org/10.1155/1994/48291.

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A simple model for nonuniform distributed RC structures is presented. The model consists of three passive elements only and can be used for modelling nonuniform distributed RC structures involving exponential, hyperbolic sine squared, hyperbolic cosine squared and square taper geometries. The model can be easily implemented for computer-aided analysis and design of circuits and systems comprising nonuniform distributed RC structures.

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Dimitrijevic, Dragoljub, Goran Djordjevic, Milan Milosevic, and Marko Stojanovic. "Attractor behaviour of holographic inflation model for inverse cosine hyperbolic potential." Facta universitatis - series: Physics, Chemistry and Technology 18, no. 1 (2020): 65–73. http://dx.doi.org/10.2298/fupct2001065d.

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We study a model of tachyon inflation and its attractor solution in the framework of holographic cosmology. The model is based on a holographic braneworld scenario with a D3-brane located at the holographic boundary of an asymptotic ADS5 bulk. The tachyon field that drives inflation is represented by a Dirac-Born-Infeld (DBI) action on the brane. We examine the attractor trajectory in the phase space of the tachyon field for the case of inverse cosine hyperbolic tachyon potential.

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Joo, Seang-Hwane, Seokjoon Chun, Stephen Stark, and Olexander S. Chernyshenko. "Item Parameter Estimation With the General Hyperbolic Cosine Ideal Point IRT Model." Applied Psychological Measurement 43, no. 1 (April 26, 2018): 18–33. http://dx.doi.org/10.1177/0146621618758697.

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Over the last decade, researchers have come to recognize the benefits of ideal point item response theory (IRT) models for noncognitive measurement. Although most applied studies have utilized the Generalized Graded Unfolding Model (GGUM), many others have been developed. Most notably, David Andrich and colleagues published a series of papers comparing dominance and ideal point measurement perspectives, and they proposed ideal point models for dichotomous and polytomous single-stimulus responses, known as the Hyperbolic Cosine Model (HCM) and the General Hyperbolic Cosine Model (GHCM), respectively. These models have item response functions resembling the GGUM and its more constrained forms, but they are mathematically simpler. Despite the apparent impact of Andrich’s work on ensuing investigations, the HCM and GHCM have been largely overlooked by applied researchers. This may stem from questions about the compatibility of the parameter metric with other ideal point estimation and model-data fit software or seemingly unrealistic parameter estimates sometimes produced by the original joint maximum likelihood (JML) estimation software. Given the growing list of ideal point applications and variations in sample and scale characteristics, the authors believe these HCMs warrant renewed consideration. To address this need and overcome potential JML estimation difficulties, this study developed a marginal maximum likelihood (MML) estimation algorithm for the GHCM and explored parameter estimation requirements in a Monte Carlo study manipulating sample size, scale length, and data types. The authors found a sample size of 400 was adequate for parameter estimation and, in accordance with GGUM studies, estimation was superior in polytomous conditions.

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Andrich, David, and Guanzhong Luo. "A Hyperbolic Cosine Latent Trait Model For Unfolding Dichotomous Single-Stimulus Responses." Applied Psychological Measurement 17, no. 3 (September 1993): 253–76. http://dx.doi.org/10.1177/014662169301700307.

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Ghosh, U., T. Das, and S. Sarkar. "Homotopy Analysis Method and Time-fractional NLSE with Double Cosine, Morse, and New Hyperbolic Potential Traps." Nelineinaya Dinamika 18, no. 2 (2022): 309–28. http://dx.doi.org/10.20537/nd220211.

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A brief outline of the derivation of the time-fractional nonlinear Schrödinger equation (NLSE) is furnished. The homotopy analysis method (HAM) is applied to study time-fractional NLSE with three separate trapping potential models that we believe have not been investigated yet. The first potential is a double cosine potential $[V(x)=V_{1}\cos x+V_{2}\cos 2x]$, the second one is the Morse potential $[V(x)=V_{1}e^{-2\beta x}+V_{2}e^{-\beta x}]$, and a hyperbolic potential $[V(x)=V_{0}\tanh(x)\sech(x)]$ is taken as the third model. The fractional derivatives and integrals are described in the Caputo and Riemann Liouville sense, respectively. The solutions are given in the form of convergent series with easily computable components. A physical analysis with graphical representations explicitly reveals that HAM is effective and convenient for solving nonlinear differential equations of fractional order.

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AOKI, S., H. HIROSE, and Y. KIKUKAWA. "CHARGED FERMION STATES IN THE QUENCHED U(1) CHIRAL WILSON–YUKAWA MODEL." International Journal of Modern Physics A 09, no. 23 (September 20, 1994): 4129–48. http://dx.doi.org/10.1142/s0217751x94001679.

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The property of charged fermion states is investigated in the quenched U(1) chiral Wilson–Yukawa model. Fitting the charged fermion propagator with a single hyperbolic cosine does not yield reliable results. On the other hand the behavior of the propagator including large lattice size dependence is well described by the large Wilson–Yukawa coupling expansion, providing strong evidence that no charged fermion state exists as an asymptotic particle in this model.

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Andrich, David, and Guanzhong Luo. "A Law of Comparative Preference: Distinctions Between Models of Personal Preference and Impersonal Judgment in Pair Comparison Designs." Applied Psychological Measurement 43, no. 3 (November 2, 2017): 181–94. http://dx.doi.org/10.1177/0146621617738014.

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The pair comparison design for distinguishing between stimuli located on the same natural or hypothesized linear continuum is used both when the response is a personal preference and when it is an impersonal judgment. Appropriate models which complement the different responses have been proposed. However, the models most appropriate for impersonal judgments have also been described as modeling choice, which may imply personal preference. This leads to potential confusion in interpretation of scale estimates of the stimuli, in particular whether they reflect a substantive order on the variable or reflect a characteristic of the sample which is different from the substantive order on the variable. Using Thurstone’s concept of a discriminal response when a person engages with each stimulus, this article explains the overlapping and distinctive relationships between models for pair comparison designs when used for preference and judgment. In doing so, it exploits the properties of the relatively new hyperbolic cosine model which is not only appropriate for modeling personal preferences but has an explicit mathematical relationship with models for impersonal judgments. The hyperbolic cosine model is shown to be a special case of a more general form, referred to in parallel with Thurstone’s Law of Comparative Judgment, as a specific law of comparative preference. Analyses of two real data sets illustrate the differences between the models most appropriate for personal preferences and impersonal judgments in a pair comparison design.

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Salim, Abdulghafoor, and Anas Youns Abdullah. "Studying the Stability of a Non-linear Autoregressive Model (Polynomial with Hyperbolic Cosine Function)." AL-Rafidain Journal of Computer Sciences and Mathematics 11, no. 1 (July 1, 2014): 81–91. http://dx.doi.org/10.33899/csmj.2014.163733.

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Abdullah, Faizal Ade Rahmahuddin, and Elvi Syukrina Erianto. "Modeling a Wave on Mild Sloping Bottom Topography and Its Dispersion Relation Approximation." KUBIK: Jurnal Publikasi Ilmiah Matematika 7, no. 1 (September 30, 2022): 1–10. http://dx.doi.org/10.15575/kubik.v7i1.18419.

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Linear wave theory is a simple theory that researchers and engineers often use to study a wave in deep, intermediate, and shallow water regions. Many researchers mostly used it over the horizontal flat seabed, but in actual conditions, sloping seabed always exists, although mild. In this research, we try to model a wave over a mild sloping seabed by linear wave theory and analyze the influence of the seabed’s slope on the solution of the model. The model is constructed from Laplace and Bernoulli equations together with kinematic and dynamic boundary conditions. We used the result of the analytical solution to find the relation between propagation speed, wavelength, and bed slope through the dispersion relation. Because of the difference in fluid dispersive character for each water region, we also determined dispersion relation approximation by modifying the hyperbolic tangent form into hyperbolic sine-cosine and exponential form, then approximated it with Padé approximant. As the final result, exponential form modification with Padé approximant had the best agreement to exact dispersion relation equation then direct hyperbolic tangent form.

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Andrich, David. "A hyperbolic cosine latent trait model for unfolding polytomous responses: Reconciling Thurstone and Likert methodologies." British Journal of Mathematical and Statistical Psychology 49, no. 2 (November 1996): 347–65. http://dx.doi.org/10.1111/j.2044-8317.1996.tb01093.x.

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Luo, Guanzhong. "A Joint Maximum Likelihood Estimation Procedure for the Hyperbolic Cosine Model for Single-Stimulus Responses." Applied Psychological Measurement 24, no. 1 (March 2000): 33–49. http://dx.doi.org/10.1177/01466216000241002.

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KLOPMAN, GERT, BRENNY VAN GROESEN, and MAARTEN W. DINGEMANS. "A variational approach to Boussinesq modelling of fully nonlinear water waves." Journal of Fluid Mechanics 657 (August 3, 2010): 36–63. http://dx.doi.org/10.1017/s0022112010001345.

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In this paper we present a new method to derive Boussinesq-type equations from a variational principle. These equations are valid for nonlinear surface-water waves propagating over bathymetry. The vertical structure of the flow, required in the Hamiltonian, is approximated by a (series of) vertical shape functions associated with unknown parameter(s). It is not necessary to make approximations with respect to the nonlinearity of the waves. The resulting approximate Hamiltonian is positive definite, contributing to the good dynamical behaviour of the resulting equations. The resulting flow equations consist of temporal equations for the surface elevation and potential, as well as a (set of) elliptic equations for some auxiliary parameter(s). All equations only contain low-order spatial derivatives and no mixed time–space derivatives. Since one of the parameters, the surface potential, can be associated with a uniform shape function, the resulting equations are very well suited for wave–current interacting flows.The variational method is applied to two simple models, one with a parabolic vertical shape function and the other with a hyperbolic-cosine vertical structure. For both, as well as the general series model, the flow equations are derived. Linear dispersion and shoaling are studied using the average Lagrangian. The model with a parabolic vertical shape function has improved frequency dispersion, as compared to classical Boussinesq models. The model with a hyperbolic-cosine vertical structure can be made to have exact phase and group velocity, as well as shoaling, for a certain frequency.For the model with a parabolic vertical structure, numerical computations are done with a one-dimensional pseudo-spectral code. These show the nonlinear capabilities for periodic waves over a horizontal bed and an underwater bar. Further some long-distance computations for soliton wave groups over bathymetry are presented.

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Wang, Jue, George Engelhard, and Edward W. Wolfe. "Evaluating Rater Accuracy in Rater-Mediated Assessments Using an Unfolding Model." Educational and Psychological Measurement 76, no. 6 (July 20, 2016): 1005–25. http://dx.doi.org/10.1177/0013164415621606.

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The number of performance assessments continues to increase around the world, and it is important to explore new methods for evaluating the quality of ratings obtained from raters. This study describes an unfolding model for examining rater accuracy. Accuracy is defined as the difference between observed and expert ratings. Dichotomous accuracy ratings (0 = inaccurate, 1 = accurate) are unfolded into three latent categories: inaccurate below expert ratings, accurate ratings, and inaccurate above expert ratings. The hyperbolic cosine model (HCM) is used to examine dichotomous accuracy ratings from a statewide writing assessment. This study suggests that HCM is a promising approach for examining rater accuracy, and that the HCM can provide a useful interpretive framework for evaluating the quality of ratings obtained within the context of rater-mediated assessments.

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Doncov, Nebojsa, Tatjana Asenov, Zoran Stankovic, John Paul, and Bratislav Milovanovic. "TLM Z-transform method modelling of Lossy Grin MTM with different refractive index profiles." Facta universitatis - series: Electronics and Energetics 25, no. 2 (2012): 103–12. http://dx.doi.org/10.2298/fuee1202103d.

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In this paper, a numerical three-dimensional (3D) model of electromagnetic lefthanded metamaterials (LH MTM) is applied for the modelling of composite right-left handed (RH/LH) structures with a graded refractive index profile commonly named GRIN MTM. The core of this model is Transmission Line Matrix (TLM) Z-transform method that incorporates the Drude function to account for dispersive LH MTM properties in the time-domain. Lossy GRIN slabs with abrupt, hyperbolic tangent, cosine, and linear refractive index profiles have been considered. The accuracy, efficiency and stability of the proposed approach are verified using analytical solution.

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Shim, Sang Oh, Tae Hwa Jung, Sang Chul Kim, and Ki Chan Kim. "Finite Element Model for Laplace Equation." Applied Mechanics and Materials 267 (December 2012): 9–12. http://dx.doi.org/10.4028/www.scientific.net/amm.267.9.

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The mild-slope equation has widely been used for calculation of shallow water wave transformation. Recently, its extended version was introduced, which is capable of modeling wave transformation on rapidly varying topography. These equations were derived by integrating the Laplace equation vertically. Here, we develop a finite element model to solve the Laplace equation directly while keeping the same computational efficiency as the mild-slope equation. This model assumes the vertical variation of the wave potential as a cosine hyperbolic function as done in the derivation of the mild-slope equation, and the Galerkin method is used to discretize it. The computational domain is discretized with proper finite elements, while the radiation condition at infinity is treated by introducing the concept of an infinite element. The upper boundary condition can be either free surface or a solid structure. The applicability of the developed model is verified through example analyses of two-dimensional wave reflection and transmission. Analysis is also made for the case where a solid structure is floated near the still water level.

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Atlas, Glen, John K.-J. Li, Shawn Amin, and Robert G. Hahn. "Development and Retrospective Clinical Assessment of a Patient-Specific Closed-Form Integro-Differential Equation Model of Plasma Dilution." Biomedical Engineering and Computational Biology 8 (January 1, 2017): 117959721773030. http://dx.doi.org/10.1177/1179597217730305.

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A closed-form integro-differential equation (IDE) model of plasma dilution (PD) has been derived which represents both the intravenous (IV) infusion of crystalloid and the postinfusion period. Specifically, PD is mathematically represented using a combination of constant ratio, differential, and integral components. Furthermore, this model has successfully been applied to preexisting data, from a prior human study, in which crystalloid was infused for a period of 30 minutes at the beginning of thyroid surgery. Using Euler’s formula and a Laplace transform solution to the IDE, patients could be divided into two distinct groups based on their response to PD during the infusion period. Explicitly, Group 1 patients had an infusion-based PD response which was modeled using an exponentially decaying hyperbolic sine function, whereas Group 2 patients had an infusion-based PD response which was modeled using an exponentially decaying trigonometric sine function. Both Group 1 and Group 2 patients had postinfusion PD responses which were modeled using the same combination of hyperbolic sine and hyperbolic cosine functions. Statistically significant differences, between Groups 1 and 2, were noted with respect to the area under their PD curves during both the infusion and postinfusion periods. Specifically, Group 2 patients exhibited a response to PD which was most likely consistent with a preoperative hypovolemia. Overall, this IDE model of PD appears to be highly “adaptable” and successfully fits clinically-obtained human data on a patient-specific basis, during both the infusion and postinfusion periods. In addition, patient-specific IDE modeling of PD may be a useful adjunct in perioperative fluid management and in assessing clinical volume kinetics, of crystalloid solutions, in real time.

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Dutta, Jaideep, and Balaram Kundu. "Two-dimensional hybrid analytical approach for the investigation of thermal aspects in human tissue undergoing regional hyperthermia therapy." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 234, no. 20 (April 22, 2020): 3951–66. http://dx.doi.org/10.1177/0954406220919460.

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The formation of the present work is based on the development of the exact analytical solution of two-dimensional temperature response by employing the hyperbolic heat conduction bioheat model in a single-layered human skin tissue subjected to the regional hyperthermia therapy (RHT) for cancer treatment. The mathematical approach has been utilized as a hybrid form of ‘separation of variables’ and ‘finite integral transform’ method. Three kinds of surface heat fluxes (constant, sinusoidal and cosine) have been employed as an external heat source on the therapeutic surface of the square-shaped skin tissue of 100 mm × 100 mm. An innovative form of initial condition (spatially dependent) has been implemented in the present mathematical formulation as skin tissues are highly non-homogeneous and non-uniform in structure. The present research outcome indicates that cosine heat flux would be a suitable alternative for the sinusoidal heat flux. The impact of the relaxation time lag has been clearly noted in the thermal response with the waveform-like behaviour and it justifies the postulate of hyperbolic heat conduction. The two-dimensional temperature of the skin tissue has been observed in the range of 48.1 ℃–40 ℃ (in decreasing order). Estimated peak temperatures are in the proposed spectrum of hyperthermia therapy for an exposure time of 100 s, and this fact is true in an agreement with the medical protocol of the cancer treatment. The accuracy of the mathematical modelling and in-house computer codes are justified with the published numerical models and the maximum deviation of the thermal response has been noticed in order of 1.5–3%. The two-dimensional surface thermal contours have provided a glimpse of heat flow in the physical domain of skin tissue under different heating conditions and this research output may be beneficial to establish the theoretical standard of the regional hyperthermia treatment for cancer eradication.

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McGrane, Joshua A. "The Bipolarity of Attitudes: Unfolding the Implications of Ambivalence." Applied Psychological Measurement 43, no. 3 (March 26, 2018): 211–25. http://dx.doi.org/10.1177/0146621618762741.

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Recently, some attitude researchers have argued that the traditional bipolar model of attitudes should be replaced, claiming that a bivariate model is superior in several ways, foremost of which is its ability to account for ambivalent attitudes. This study argues that ambivalence is not at odds with bipolarity per se, but rather the conventional view of bipolarity, and that the psychometric evidence supporting a bivariate interpretation has been flawed. To demonstrate this, a scale developed out of the bivariate approach was examined using a unidimensional unfolding item response theory model: general hyperbolic cosine model for polytomous responses. The results were consistent with a bipolar interpretation, providing support for the argument that ambivalent evaluations are the correct middle-point of a bipolar evaluative dimension. Thus, it is argued that attitudinal ambivalence does not necessitate moving beyond bipolarity, but rather, moving beyond the conventional conceptualization and assessment of attitudes.

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Qian, Kaihuan, and Xiaohua Zhou. "Weighted Log-Rank Test for Clinical Trials with Delayed Treatment Effect Based on a Novel Hazard Function Family." Mathematics 10, no. 15 (July 25, 2022): 2573. http://dx.doi.org/10.3390/math10152573.

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In clinical trials with delayed treatment effect, the standard log-rank method in testing the difference between survival functions may have problems, including low power and poor robustness, so the method of weighted log-rank test (WLRT) is developed to improve the test performance. In this paper, a hyperbolic-cosine-shaped (CH) hazard function family model is proposed to simulate delayed treatment effect scenarios. Then, based on Fleming and Harrington’s method, this paper derives the corresponding weight function and its regular corrections, which are powerful in test, theoretically. Alternative methods of parameters selection based on potential information are also developed. Further, the simulation study is conducted to compare the power performance between CH WLRT, classical WLRT, modest weighted log-rank test and WLRT with logistic-type weight function under different hazard scenarios and simulation settings. The results indicate that the CH statistics are powerful and robust in testing the late difference, so the CH test is useful and meaningful in practice.

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Reza, Selim, Marta Campos Ferreira, José J. M. Machado, and João Manuel R. S. Tavares. "Traffic State Prediction Using One-Dimensional Convolution Neural Networks and Long Short-Term Memory." Applied Sciences 12, no. 10 (May 19, 2022): 5149. http://dx.doi.org/10.3390/app12105149.

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Traffic prediction is a vitally important keystone of an intelligent transportation system (ITS). It aims to improve travel route selection, reduce overall carbon emissions, mitigate congestion, and enhance safety. However, efficiently modelling traffic flow is challenging due to its dynamic and non-linear behaviour. With the availability of a vast number of data samples, deep neural network-based models are best suited to solve these challenges. However, conventional network-based models lack robustness and accuracy because of their incapability to capture traffic’s spatial and temporal correlations. Besides, they usually require data from adjacent roads to achieve accurate predictions. Hence, this article presents a one-dimensional (1D) convolution neural network (CNN) and long short-term memory (LSTM)-based traffic state prediction model, which was evaluated using the Zenodo and PeMS datasets. The model used three stacked layers of 1D CNN, and LSTM with a logarithmic hyperbolic cosine loss function. The 1D CNN layers extract the features from the data, and the goodness of the LSTM is used to remember the past events to leverage them for the learnt features for traffic state prediction. A comparative performance analysis of the proposed model against support vector regression, standard LSTM, gated recurrent units (GRUs), and CNN and GRU-based models under the same conditions is also presented. The results demonstrate very encouraging performance of the proposed model, improving the mean absolute error, root mean squared error, mean percentage absolute error, and coefficient of determination scores by a mean of 16.97%, 52.1%, 54.15%, and 7.87%, respectively, relative to the baselines under comparison.

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Kalafi, Elham Yousef, Ata Jodeiri, Seyed Kamaledin Setarehdan, Ng Wei Lin, Kartini Rahmat, Nur Aishah Taib, Mogana Darshini Ganggayah, and Sarinder Kaur Dhillon. "Classification of Breast Cancer Lesions in Ultrasound Images by Using Attention Layer and Loss Ensemble in Deep Convolutional Neural Networks." Diagnostics 11, no. 10 (October 9, 2021): 1859. http://dx.doi.org/10.3390/diagnostics11101859.

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The reliable classification of benign and malignant lesions in breast ultrasound images can provide an effective and relatively low-cost method for the early diagnosis of breast cancer. The accuracy of the diagnosis is, however, highly dependent on the quality of the ultrasound systems and the experience of the users (radiologists). The use of deep convolutional neural network approaches has provided solutions for the efficient analysis of breast ultrasound images. In this study, we propose a new framework for the classification of breast cancer lesions with an attention module in a modified VGG16 architecture. The adopted attention mechanism enhances the feature discrimination between the background and targeted lesions in ultrasound. We also propose a new ensembled loss function, which is a combination of binary cross-entropy and the logarithm of the hyperbolic cosine loss, to improve the model discrepancy between classified lesions and their labels. This combined loss function optimizes the network more quickly. The proposed model outperformed other modified VGG16 architectures, with an accuracy of 93%, and also, the results are competitive with those of other state-of-the-art frameworks for the classification of breast cancer lesions. Our experimental results show that the choice of loss function is highly important and plays a key role in breast lesion classification tasks. Additionally, by adding an attention block, we could improve the performance of the model.

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Montoya, Oscar Danilo, Luis Fernando Grisales-Noreña, and Jesús C. Hernández. "A Recursive Conic Approximation for Solving the Optimal Power Flow Problem in Bipolar Direct Current Grids." Energies 16, no. 4 (February 9, 2023): 1729. http://dx.doi.org/10.3390/en16041729.

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This paper proposes a recursive conic approximation methodology to deal with the optimal power flow (OPF) problem in unbalanced bipolar DC networks. The OPF problem is formulated through a nonlinear programming (NLP) representation, where the objective function corresponds to the minimization of the expected grid power losses for a particular load scenario. The NLP formulation has a non-convex structure due to the hyperbolic equality constraints that define the current injection/absorption in the constant power terminals as a function of the powers and voltages. To obtain an approximate convex model that represents the OPF problem in bipolar asymmetric distribution networks, the conic relation associated with the product of two positive variables is applied to all nodes with constant power loads. In the case of nodes with dispersed generation, a direct replacement of the voltage variables for their expected operating point is used. An iterative solution procedure is implemented in order to minimize the error introduced by the voltage linearization in the dispersed generation sources. The 21-bus grid is employed for all numerical validations. To validate the effectiveness of the proposed conic model, the power flow problem is solved, considering that the neutral wire is floating and grounded, and obtaining the same numerical results as the traditional power flow methods (successive approximations, triangular-based, and Taylor-based approaches): expected power losses of 95.4237 and 91.2701 kW, respectively. To validate the effectiveness of the proposed convex model for solving the OPF problem, three combinatorial optimization methods are implemented: the sine-cosine algorithm (SCA), the black-hole optimizer (BHO), and the vortex search algorithm (VSA). Numerical results show that the proposed convex model finds the global optimal solution with a value of 22.985 kW, followed by the VSA with a value of 22.986 kW. At the same time, the BHO and SCA are stuck in locally optimal solutions (23.066 and 23.054 kW, respectively). All simulations were carried out in a MATLAB programming environment.

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Stavek, Jiri. "Super-Elastic Double-Helix Model of Photon. Huygens-de Broglie Particle on the Helical Path Guided by the Newton-Bohm Entangled Helical Evolute. Quantum of Magnetic Flux Based on the Mathematical Beauty of Newton, Lorentz, Einstein, Dirac, Gell-Mann, Schw." Applied Physics Research 11, no. 4 (July 15, 2019): 40. http://dx.doi.org/10.5539/apr.v11n4p40.

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In our approach we have combined knowledge of Old Masters (working in this field before the year 1905), New Masters (working in this field after the year 1905) and Dissidents under the guidance of Louis de Broglie and David Bohm. In our model the photon is represented as the Huygens-de Broglie’s particle on the helical path (full wave) guided by the Newton-Bohm entangled evolute (empty wave). We have formulated the concept of the Super-Elastic Photon WAVE based on the Great Works of Weber, Abbe, Voigt and Einstein. This model works with the longitudinal elasticity of that WAVE that was already very well tested experimentally. Newly, we propose to test the elastic amplitude of this WAVE for the case of the Doppler’s redshift, the Doppler’s blueshift, and the Zwicky’s redshift. We have newly used the concept of the Lorentz’ force for the description of the photon acting force and the fermion reacting force. In this model the Lorentz’ factors γ and γ3 do not describe the “transverse mass of fermions” and longitudinal mass of fermions” but the “reacting transverse force of fermions” and the “reacting longitudinal force of fermions”. (The mass of photons and fermions does not change with their speed). It is very well-known that the cylindrical helix observed from different angles forms shadows in the Plato’s Cave as circle, sine, cosine, trochoid, cochleoid, hyperbolic spiral. Therefore, the resulting shape depends on the observer position in the Plato’s Cave-this is the famous Rashomon effect between observers. Based on the Newton-Bohm helical evolute and the Huygens-de Broglie helical path of the particle we have derived interesting formula known as the quantum of the magnetic flux. When we work further with this concept based on the Mathematical Beauty developed by Dirac, Gell-Mann, Schwinger, Polchinski, Witten and many others, we will obtain possible properties of the magnetic monopole. This photon quantum of the magnetic flux can be experimentally evaluated in the known tests with superconductors and micro-WAVES and infrared-WAVES. Can it be that Nature cleverly works with the magnetic monopole hidden in plain sight? We want to pass this concept into the hands of Readers of this Journal better educated in the Mathematics and Physics.

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Andrich, David. "Hyperbolic Cosine Latent Trait Models for Unfolding Direct Responses and Pairwise Preferences." Applied Psychological Measurement 19, no. 3 (September 1995): 269–90. http://dx.doi.org/10.1177/014662169501900306.

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Sabi’u, Jamilu, Hadi Rezazadeh, Rodica Cimpoiasu, and Radu Constantinescu. "Traveling wave solutions of the generalized Rosenau–Kawahara-RLW equation via the sine–cosine method and a generalized auxiliary equation method." International Journal of Nonlinear Sciences and Numerical Simulation 23, no. 3-4 (November 29, 2021): 539–51. http://dx.doi.org/10.1515/ijnsns-2019-0206.

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Abstract In this paper, we have approached a complicated nonlinear wave equation which links the Rosenau–Kawahara equation to the regularized long wave (RLW) equation. Taking advantages from the sine–cosine method as well as from the generalized auxiliary equation method, we have successfully reached to three types of traveling wave solutions: periodic, hyperbolic and exponential ones. Our results do constitute themselves as a challenge to apply the mentioned techniques in order to solve other generalized dynamical models, for example, the ones which involve phenomena such as a fully nonlinear dispersion and a fully nonlinear convection.

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Tsvankin, Ilya. "Normal moveout from dipping reflectors in anisotropic media." GEOPHYSICS 60, no. 1 (January 1995): 268–84. http://dx.doi.org/10.1190/1.1443755.

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Description of reflection moveout from dipping interfaces is important in developing seismic processing methods for anisotropic media, as well as in the inversion of reflection data. Here, I present a concise analytic expression for normal‐moveout (NMO) velocities valid for a wide range of homogeneous anisotropic models including transverse isotropy with a tilted in‐plane symmetry axis and symmetry planes in orthorhombic media. In transversely isotropic media, NMO velocity for quasi‐P‐waves may deviate substantially from the isotropic cosine‐of‐dip dependence used in conventional constant‐velocity dip‐moveout (DMO) algorithms. However, numerical studies of NMO velocities have revealed no apparent correlation between the conventional measures of anisotropy and errors in the cosine‐of‐dip DMO correction (“DMO errors”). The analytic treatment developed here shows that for transverse isotropy with a vertical symmetry axis, the magnitude of DMO errors is dependent primarily on the difference between Thomsen parameters ε and δ. For the most common case, ε − δ > 0, the cosine‐of‐dip–corrected moveout velocity remains significantly larger than the moveout velocity for a horizontal reflector. DMO errors at a dip of 45 degrees may exceed 20–25 percent, even for weak anisotropy. By comparing analytically derived NMO velocities with moveout velocities calculated on finite spreads, I analyze anisotropy‐induced deviations from hyperbolic moveout for dipping reflectors. For transversely isotropic media with a vertical velocity gradient and typical (positive) values of the difference ε − δ, inhomogeneity tends to reduce (sometimes significantly) the influence of anisotropy on the dip dependence of moveout velocity.

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29

Akhtar, J., K. U. Tariq, M. M. A. Khater, A. Houwe, and M. Inc. "A variety of exact solutions for fractional (2+1)-dimensional Heisenberg ferromagnetic spin chain in the semi classical limit." Revista Mexicana de Física 67, no. 4 Jul-Aug (May 26, 2021): 040701. http://dx.doi.org/10.31349/revmexfis.67.040701.

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This paper investigates exact voyaging (2 + 1) dimensional Heisenberg ferromagnetic spin chain solutions with conformable fractional derivatives, an important family of nonlinear equations from Schrödinger (NLSE) for the construction of hyperbolic, trigonometric and complex function solutions. The detailed rational sine-cosine system and rational sinh-cosh system were used to locate dim, special and periodic wave solutions successfully. These findings suggest that the proposed approaches may be useful to investigate a range of solutions inside a repository of applied sciences and engineering, with success, quality, and trust. In addition, graphical representations and physical expresses of such solutions are represented by a set of the required values of the parameters involved. The methods are essentially adequate and can be extended to different dynamic models that create the nonlinear processes in today’s research.

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Zhang, Zhiwei, Rajendra Singh, and Ashley R. Crowther. "Limitations of Smoothening Functions for Automotive Vibro-Impact Problems." Shock and Vibration 18, no. 1-2 (2011): 397–406. http://dx.doi.org/10.1155/2011/102720.

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Nonlinear torsional models are used to analyze automotive transmission rattle problems and find solutions to reduce noise, vibration and dynamic loads. The torsional stiffness and inertial distribution of such systems show that the underlying mathematical problem is numerically stiff. In addition, the clearance nonlinearities in the gear meshes introduce discontinuous functions. Both factors affect the efficacy of time domain integration and smoothening functions are widely used to overcome computational difficulties and improve the simulation. In this paper, alternate smoothening functions are studied for their influence on the numerical solutions and their impact on global convergence and computation times. In particular, four smoothening functions (arctan, hyperbolic-cosine, hyperbolic-tan and quintic-spline) are applied to a five-degree-of-freedom generic torsional system with two backlash (clearance) elements. Each function is assessed via a global convergence metric across an excitation map (a design of experiment). Regions of the excitation map, along with multiple solutions, are studied and the implications to assessing convergence are critically examined. It is observed that smoothening functions do not lead to better convergence in many cases. The smoothening parameter needs to be carefully selected, or over-smoothened solutions may be found. The system studied is representative of a typical automotive rattle problem and it was found that benefits were limited from applying such smoothening functions.

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Wang, Jue, George Engelhard, and Trenton Combs. "Exploring difficult-to-score essays with a hyperbolic cosine accuracy model and Coh-Metrix indices." Journal of Experimental Education, November 2, 2021, 1–20. http://dx.doi.org/10.1080/00220973.2021.1993774.

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Konik, Robert, Márton Lájer, and Giuseppe Mussardo. "Approaching the self-dual point of the sinh-Gordon model." Journal of High Energy Physics 2021, no. 1 (January 2021). http://dx.doi.org/10.1007/jhep01(2021)014.

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Abstract One of the most striking but mysterious properties of the sinh-Gordon model (ShG) is the b → 1/b self-duality of its S-matrix, of which there is no trace in its Lagrangian formulation. Here b is the coupling appearing in the model’s eponymous hyperbolic cosine present in its Lagrangian, cosh(bϕ). In this paper we develop truncated spectrum methods (TSMs) for studying the sinh-Gordon model at a finite volume as we vary the coupling constant. We obtain the expected results for b ≪ 1 and intermediate values of b, but as the self-dual point b = 1 is approached, the basic application of the TSM to the ShG breaks down. We find that the TSM gives results with a strong cutoff Ec dependence, which disappears according only to a very slow power law in Ec. Standard renormalization group strategies — whether they be numerical or analytic — also fail to improve upon matters here. We thus explore three strategies to address the basic limitations of the TSM in the vicinity of b = 1. In the first, we focus on the small-volume spectrum. We attempt to understand how much of the physics of the ShG is encoded in the zero mode part of its Hamiltonian, in essence how ‘quantum mechanical’ vs ‘quantum field theoretic’ the problem is. In the second, we identify the divergencies present in perturbation theory and perform their resummation using a supra-Borel approximate. In the third approach, we use the exact form factors of the model to treat the ShG at one value of b as a perturbation of a ShG at a different coupling. In the light of this work, we argue that the strong coupling phase b > 1 of the Lagrangian formulation of model may be different from what is naïvely inferred from its S-matrix. In particular, we present an argument that the theory is massless for b > 1.

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Mohammed, Wael W., Hijaz Ahmad, Hamid Boulares, Fathi Khelifi, and Mahmoud El-Morshedy. "Exact solutions of Hirota–Maccari system forced by multiplicative noise in the Itô sense." Journal of Low Frequency Noise, Vibration and Active Control, June 24, 2021, 146134842110281. http://dx.doi.org/10.1177/14613484211028100.

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In this article, the stochastic Hirota–Maccari system forced in the Itô sense by multiplicative noise is considered. We just use the He’s semi-inverse method, sine–cosine method, and Riccati–Bernoulli sub-ODE method to get new stochastic solutions which are hyperbolic, trigonometric, and rational. The major benefit of these three approaches is that they can be used to solve similar models. Furthermore, we plot 3D surfaces of analytical solutions obtained in this article by using MATLAB to illustrate the effect of multiplicative noise on the exact solution of the Hirota–Maccari method.

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Bhargava, Parth, Sayantan Choudhury, Satyaki Chowdhury, Anurag Mishara, Sachin Panneer Selvam, Sudhakar Panda, and Gabriel D. Pasquino. "Quantum aspects of chaos and complexity from bouncing cosmology: A study with two-mode single field squeezed state formalism." SciPost Physics Core 4, no. 4 (October 7, 2021). http://dx.doi.org/10.21468/scipostphyscore.4.4.026.

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Circuit Complexity, a well known computational technique has recently become the backbone of the physics community to probe the chaotic behaviour and random quantum fluctuations of quantum fields. This paper is devoted to the study of out-of-equilibrium aspects and quantum chaos appearing in the universe from the paradigm of two well known bouncing cosmological solutions viz. Cosine hyperbolic and Exponential models of scale factors. Besides circuit complexity, we use the Out-of-Time Ordered correlation (OTOC) functions for probing the random behaviour of the universe both at early and the late times. In particular, we use the techniques of well known two-mode squeezed state formalism in cosmological perturbation theory as a key ingredient for the purpose of our computation. To give an appropriate theoretical interpretation that is consistent with the observational perspective we use the scale factor and the number of e-foldings as a dynamical variable instead of conformal time for this computation. From this study, we found that the period of post bounce is the most interesting one. Though it may not be immediately visible but an exponential rise can be seen in the complexity once the post bounce feature is extrapolated to the present time scales. We also find within the very small acceptable error range a universal connecting relation between Complexity computed from two different kinds of cost functionals-linearly weighted and geodesic weighted with the OTOC. Furthermore, from the complexity computation obtained from both the cosmological models under consideration and also using the well known Maldacena (M) Shenker (S) Stanford (S) bound on quantum Lyapunov exponent, \lambda\leq 2\pi/\betaλ≤2π/β for the saturation of chaos, we estimate the lower bound on the equilibrium temperature of our universe at the late time scale. Finally, we provide a rough estimation of the scrambling time scale in terms of the conformal time.

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Journal articles on the topic 'Hyperbolic Cosine Model'

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