Search

Purpose: The purpose of this paper is to study the aerodynamic characteristics and uplift force tendencies of pantographs within the operational height span of 1,600–2,980 mm, aiming to offer valuable insights for research concerning the adaptability of pantograph-catenary systems on double-stack high container transportation lines. Design/methodology/approach: Eight pantograph models were formulated based on lines with the contact wire of 6,680 mm in height. The aerodynamic calculations were carried out using the SST k-ω separated vortex model. A more improved aerodynamic uplift force method was also presented. The change rule of the aerodynamic uplift force under different working heights of the pantograph was analyzed according to the transfer coefficients of the aerodynamic forces and moments. Findings: The results show that the absolute values of the aerodynamic forces and moments of the upper and lower frame increase with the working height, whereas those of the collector head do not change. The absolute values of the transfer coefficients of the lower frame and link arm were significantly larger than those of the upper frame. Therefore, the absolute value of the aerodynamic uplift force increased and then decreased with the working height. The maximum value occurred at a working height of 2,400 mm. Originality/value: A new method for calculating the aerodynamic uplift force of pantographs is proposed. The specifical change rule of the aerodynamic uplift force of the pantograph on double-stack high container transportation lines was determined from the perspective of the transfer coefficients of the aerodynamic forces and moments. [ABSTRACT FROM AUTHOR]

This paper characterizes temporal and spatial changes of humidity in Poland during April--September in 1981-2020 and its decades. For this purpose, absolute values of climatic water balance (PEI) and its standardized values (SPEI) were used, based on data from the Institute of Meteorology and Water Management -- National Research Institute (IMWM-NRI). The PEI component, potential evaporation, was calculated using the Penman-Monteith method. The average PEI totals were found to be negative across most of Poland, with the lowest values below -250mm in the central part of the country. A particularly pronounced decrease in the PEI and the SPEI was noted during the decade 2011-2020. Temporal variability of the SPEI indicates that in the last two decades there has been a noticeable increase in moisture deficit. This is particularly noticeable from 2011-2020 when changes in the mean SPEI values were statistically significant (α = 0.05). During the period 1981-2020, the 6-month area-averaged PEI totals showed a negative trend (15 mm/decade). The minimum and maximum PEI values also showed negative trends. The rate of change of the minimum PEI values was almost 3 times higher than that of the maximum PEI values. The trends for the minimum PEI values are statistically significant (α = 0.05). After the year 2000, a higher prevalence of negative SPEI was found, as well as its intensity in the decade 2011-2020. All negative SPEI categories show positive trends. In contrast, positive SPEI categories are characterized by little or no negative trends, as in the case of extremely wet conditions. Frequency trends for all SPEI categories are not statistically significant at α = 0.05. [ABSTRACT FROM AUTHOR]

Purpose: The purpose of this paper is to simulate charge transport in monolayer graphene on a substrate made of hexagonal boron nitride (h-BN). This choice is motivated by the fact that h-BN is one of the most promising substrates on account of the reduced degradation of the velocity due to the remote impurities. Design/methodology/approach: The semiclassical Boltzmann equations for electrons in the monolayer graphene are numerically solved by an approach based on a discontinuous Galerkin (DG) method. Both the conduction and valence bands are included, and the inter-band scatterings are taken into account as well. Findings: The importance of the inter-band scatterings is accurately evaluated for several values of the Fermi energy, addressing the issue related to the validity of neglecting the generation-recombination terms. It is found out that the inclusion of the inter-band scatterings produces sizable variations in the average values, like the current density, at zero Fermi energy, whereas, as expected, the effect of the inter-band scattering becomes negligible by increasing the absolute value of the Fermi energy. Research limitations/implications: The correct evaluation of the influence of the inter-band scatterings on the electronic performances is deeply important not only from a theoretical point of view but also for the applications. In particular, it will be shown that the time necessary to reach the steady state is greatly affected by the inter-band scatterings, with not negligible consequences on the switching on/off processes of realistic devices. As a limitation of the present work, the proposed approach refers to the spatially homogeneous case. For the simulation of electron devices, non-homogenous numerical solutions are required. This last case will be tackled in a forthcoming paper. Originality/value: As observed in Majorana et al. (2019), the use of a Direct Simulation Monte Carlo (DSMC) approach, which properly describes the inter-band scatterings, is computationally very expensive because the valence band is highly populated and a huge number of particles is needed. Even by simulating holes instead of electrons does not overcome the problem because there is a certain degree of ambiguity in the generation and recombination terms of electron-hole pairs. The DG approach, used in this paper, does not suffer from the previous drawbacks and requires a reasonable computing effort. [ABSTRACT FROM AUTHOR]

This paper presents a mean absolute deviation (MAD)-based background timing-skew calibration technique for time-interleaved (TI) ADCs. It uses a single comparator-based window detector to select input samples near the zero crossing and computes their MAD value, which is used as an indicator for the timing skew. The proposed technique has low computation complexity, as it only requires taking absolute value and averaging. It also has a fast convergence speed when operating in the background with unknown random inputs, as the MAD value can be accurately estimated with a small number of samples. A prototype 10-bit 2-way TI-SAR ADC is built in 40-nm CMOS to verify the proposed technique. It achieves over 52 dB of SNDR over the entire Nyquist band. Operating at 600 MS/s, it consumes 4.7 mW, which translates to a Walden figure-of-merit of 24-fJ/conversion-step. [ABSTRACT FROM AUTHOR]

A quiz concerning questions for Joint Entrance Examination (JEE) is presented.

In this paper, we study the minimization problem of a non-convex sparsity-promoting penalty function, i.e., fraction function, in compressed sensing. First, we discuss the equivalence of $\ell _{0}$ minimization and fraction function minimization. It is proved that the optimal solution to fraction function minimization solves $\ell _{0}$ minimization and the optimal solution to the regularization problem also solves fraction function minimization if the certain conditions are satisfied, which is similar to the regularization problem in a convex optimization theory. Second, we study the properties of the optimal solution to the regularization problem, including the first-order and second-order optimality conditions and the lower and upper bounds of the absolute value for its nonzero entries. Finally, we derive the closed-form representation of the optimal solution to the regularization problem and propose an iterative $FP$ thresholding algorithm to solve the regularization problem. We also provide a series of experiments to assess the performance of the $FP$ algorithm, and the experimental results show that the $FP$ algorithm performs well in sparse signal recovery with and without measurement noise. [ABSTRACT FROM AUTHOR]

In this paper, the consensus problem is investigated for a class of nonaffine nonlinear multiagent systems (MASs) with actuator faults of partial loss of effectiveness fault and biased fault. To deal with the control difficulty caused by the nonaffine dynamics, a neural network (NN)-based adaptive consensus protocol is developed based on the Lyapunov analysis. The neuron input of the NN uses both the state information and the consensus error information. In addition, the negative feedback term of the NN weight update law is multiplied by an absolute value of the consensus error, which is helpful in improving the consensus accuracy. With the developed adaptive NN consensus protocol, semiglobal consensus with a bounded residual consensus error of the MAS is achieved, and the bounded NN weight matrix is guaranteed. Finally, simulation results show that the developed adaptive NN consensus protocol has advantages of fast convergence rate and good consensus accuracy and has the capability of rapid response with respect to the actuator faults. [ABSTRACT FROM AUTHOR]

This article discusses the topic of spotting outliers in calibration science, specifically in the context of cannabis analysis. Outliers are data points that are significantly different from the rest of the data set. The article explains how to spot outliers in concentration and spectral data, and discusses potential causes for these outliers, such as transcription errors, poorly made standards, sample problems, improperly measured absorbances, noise, instrument malfunction, impurities/interferents, and operator error. The article also provides guidelines for deciding whether to include or exclude outliers from a calibration. [Extracted from the article]

Orbit Angular Momentum (OAM) is a potential candidate for next-generation short-distance line-of-sight wireless communication, it is assumed that the channels associated with different OAM modes are orthogonal. When there are misalignments between transmitter and receiver arrays, the assumption is incorrect. In this paper, we propose the methods to estimate the array misalignment values in the OAM-based communication system for Uniform Circular Array (UCA) in transmitter and receiver. It is shown that, when the pilot signals are transmitted in a single or all OAM modes, the absolute value of the received signal can be approximated by the polynomial functions of misalignment angle. By solving these functions, the misalignment angle can be estimated. The proposed methods are theoretically analyzed and tested for OAM Index Modulation (OAM-IM)-based communication system, The obtained results indicate that the proposed methods improve the OAM-IM based communication system in the presence of array misalignments problem. [ABSTRACT FROM AUTHOR]

This paper discusses the finite-time synchronization (FTS) of fractional-order memristive neural networks (FMNNs) with time-varying delays. Firstly, based on Gronwall–Bellman inequality and the fractional-order derivative of the power function, two novel propositions on finite-time fractional functional differential inequality are built. Secondly, the feedback controller and intermittent controller designed in this paper are all delay-independent controllers, which can work even when the prior state cannot be measured or the specific time delay function is unknown. Thirdly, in addition to the traditional Lyapunov function with absolute value form, a more general and flexile Lyapunov function based on p-norm form is constructed to analyze the criteria of FTS. Meanwhile, an improved estimation of settling time of fractional system is given explicitly, which is more accurate and general than the existing results. Eventually, the validity of theoretical analysis is confirmed by numerical examples. [ABSTRACT FROM AUTHOR]

This paper investigates the stability and stabilizability of complex-valued memristive neural networks (CVMNNs) with random time-varying delays via non-fragile sampled-data control. Taking the influence of gain fluctuations into account, a non-fragile sampled-data controller is designed for CVMNNs. Compared with the existing control schemes, the one here is more applicable and can effectively save the communication resources. The assumption on activation functions of CVMNNs is relaxed by only needing the complex-valued activation functions satisfying the Lipschitz condition. By constructing a suitable Lyapunov–Krasovskii functional (LKF), new stability and stabilizability criteria are derived for CVMNNs. Different from the existing results with the maximum absolute values of memristive connection weights, our ones are based on the average values of the maximum and minimum of the memristive connection weights. Finally, numerical simulations are given to validate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

Markov Chain Monte Carlo methods become increasingly popular in applied mathematics as a tool for numerical integration with respect to complex and high-dimensional distributions. However, application of MCMC methods to heavy-tailed distributions and distributions with analytically intractable densities turns out to be rather problematic. In this paper, we propose a novel approach towards the use of MCMC algorithms for distributions with analytically known Fourier transforms and, in particular, heavy-tailed distributions. The main idea of the proposed approach is to use MCMC methods in Fourier domain to sample from a density proportional to the absolute value of the underlying characteristic function. A subsequent application of the Parseval's formula leads to an efficient algorithm for the computation of integrals with respect to the underlying density. We show that the resulting Markov chain in Fourier domain may be geometrically ergodic even in the case of heavy-tailed original distributions. We illustrate our approach by several numerical examples including multivariate elliptically contoured stable distributions. [ABSTRACT FROM AUTHOR]

This paper presents a new framework to solve the position tracking problem of a quadrotor helicopter. This algorithm consists of a cascade architecture which employs a measurement feedback nonlinear H ∞ algorithm in the outer-loop to track the reference trajectory via noisy measurements, and a state-feedback nonlinear H ∞ in the inner-loop to stabilize the attitude dynamics. The obtained structure for the outer-loop includes a robust controller-estimator combination which satisfies the stability and convergence of both parts. Analytical results show the asymptotic stability and output boundedness for both inner and outer loops and consequently the cascade system. The Monte-Carlo simulations are performed to numerically examine the robust performance and the region of attraction of the overall system. Different environmental disturbances and modeling uncertainties are considered in 1000 simulations to verify the robust performance and boundedness of all states. Moreover, to quantify the performance of the algorithm, two numerical indexes; Integrated Square error (ISE), and Integral of the Absolute value of the control Derivative (IADU) are suggested and utilized for statistical analysis of the state tracking performance and control effort, respectively. Finally, a Software-in-the-Loop (SIL) test is performed using PX4-FMU open source autopilot and Raspberry-Pi 3 as an auxiliary processor to show the capability of the algorithm for hardware implementation. [ABSTRACT FROM AUTHOR]

Dynamic time warping (DTW) is the most widely used method to evaluate the similarity between time series. However, the DTW distance only takes into account the difference in amplitude, but does not reflect the time distortion information between them. In this paper, we propose a novel time similarity metric, called the time distortion coefficient, based on the DTW warping path to quantify the time distortion between time series. It is able to characterize the type and degree of time distortion between two time series at each point. By summing the absolute values of the time distortion coefficients, the overall time distortion is introduced to quantify time distortion between two time series. For the Nearest Neighbor (NN) based time series classification, a fusional similarity measure combining the DTW distance and the overall time distortion measure is proposed, which is able to evaluate the similarity in both amplitude and time domains. The experimental results conducted on the UCR time series classification archive datasets demonstrate that the proposed fusional similarity measure can significantly improve the classification accuracy of the 1-NN classifier with only a small amount of additional computational cost compared to the DTW distance and other metrics. [ABSTRACT FROM AUTHOR]

This paper addresses the problems of finite-time dissipative analysis and control for discrete-time memristive neural networks (DMNNs). With the help of interval matrix method (IMM), the challenges posed by the mismatched state-dependent parameters of DMNNs can be solved, which is different from the maximal absolute value operation-based method (MAVOM) in most existing literature. Based on a discrete-time Lyapunov-Krasovskii functional (LKF) and some inequality techniques, several sufficient conditions are established for achieving both finite-time bounded (FTB) behavior and finite-time (Q , S , R) − γ dissipative (FTD). Moreover, the control gains are obtained by solving a series of linear matrix inequalities (LMIs) and convex optimization problems. Finally, the validity of our main findings and the superiority of the control strategies are verified through numerical simulations. • The model of discrete-time MNNs with time-varying delays is considered. • Interval matrix method is adopted to handle state-dependent switching parameters. • A new state feedback controller incorporating time-varying delays is designed. [ABSTRACT FROM AUTHOR]

When both an absolute value function and a cosine function are introduced for chaotic sequence generation, coexisting attractors with different polarities and locations could be extracted by the offset boosting of the initial condition, and thus a hyperchaotic map with distance-increasing coexisting attractors is constructed. It is found that this map has two controllers for rescaling the oscillation totally and partially. The digital circuit implementation shows good consistency with numerical simulation. Moreover, the parameter adaptation in the basic Pelican Optimization Algorithm (POA) is improved by the above-mentioned hyperchaotic map. Correspondingly, the Hyperchaotic Pelican Optimization Algorithm (HCPOA) is constructed, where the hyperchaotic sequences are employed as the sampling pool when random numbers are required in the basic POA. Furthermore, the impact of chaos regulation on the performance of HCPOA is investigated, and the indicators of HCPOA are analyzed by employing five benchmark functions, where the single attractor shows better performance than the double-cavity attractor. The methods of HCPOA proposed in this paper bring the chance to improve the quality of solutions and the ability to escape local optima. • The initially-controlled offset boosting gives birth to various regimes of double-cavity hyperchaotic attractors. And two control knobs are extracted for amplitude rescaling, including total and partial controllers. • An improved HyperChaotic Pelican Optimization Algorithm (HCPOA) is firstly developed by employing the hyperchaotic map, and the performance influenced by the chaotic property is exhaustively explored. • The performance criteria of HCPOA with various chaotic sequences associated with five benchmark functions are compared, indicating that the solution performance of the proposed algorithm can be modified flexibly by different initial conditions and amplitude. [ABSTRACT FROM AUTHOR]

In this paper, a new infrared and visible image fusion method based on saliency detection and LatLRR-FPDE is proposed to ensure the saliency of the fused target and improve the clarity of the texture detail information of the latent low-rank representation (LatLRR) fusion method. In the feature representation stage, source images are decomposed into low-rank and sparse parts based on LatLRR. Then Fourth order Partial Differential Equation (FPDE) is used to extract high-frequency detail information from the low-rank part. In the fusion decision stage, according to the characteristic difference of the decomposed sub-bands, a multi-scale fusion scheme is carried out using rules such as EM (expectation-maximization), average (AVG), and the maximum absolute value. To guarantee the integrity of thermal radiation features in the target area in fusion results, an infrared image saliency detection algorithm is proposed, which utilizes the fusion information obtained from the sparse and prior saliency feature. Specifically, the algorithm uses convex hull center prior and contrast prior to obtain the background-suppressed saliency map. Meanwhile, to make full use of the high-dimensional saliency features in the image decomposition stage, the prior saliency map and the sparse saliency map are fused to improve the accuracy of saliency detection without the demand to extract redundant feature, which largely increases time-efficiency of the model. Finally, infrared feature compensation is performed on the target region of the fused image based on the saliency mapping strategy to make the final fused image having a better infrared target feature representation. The experiments are based on registered public datasets and compared with various popular image fusion algorithms. The subjective and objective results show that the proposed algorithm can effectively keep the integrity of salient infrared features and has superior visual quality. [ABSTRACT FROM AUTHOR]

In this paper, we provide an answer to the following question: In the particular case of a non-differentiable likelihood, is the formula for the BIC model selection criterion the same? More precisely, we obtain the Laplace method for a sum-of-absolute-values function and we deduce that the usual BIC formula with penalty in l o g (n) remains the same in the context of a selection of explanatory variables by least absolute value regression. [ABSTRACT FROM AUTHOR]

The rate of convergence of the Gibbs sampler for the generalized one-dimensional Ising model is determined by the second largest eigenvalue of its transition matrix in absolute value denoted by β ∗. In this paper we generalize a bound for β ∗ from Shiu and Chen (2015) for the one-dimensional Ising model with two states to a multiple state situation. The method is based on Diaconis and Stroock bound for reversible Markov processes. The new bound presented in this paper improves Ingrassia's (1994) result. [ABSTRACT FROM AUTHOR]

The conception of extended fractal left- as well as right-side integral operators and the related Hermite–Hadamard's integral inequalities along with midpoint are proposed firstly in this paper. A midpoint-type integral identity in fractal domain, involving twice differentiable mappings, is then derived based on the introduced extended fractal integral operators for the objective of deriving fractal midpoint-type integral inequalities with the mappings whose second-order derivatives in absolute value are required to be generalized convex. Finally, a series of fractal outcomes regarding ɛ -type special means, moments of random variable and wave equations are acquired as applications, correspondingly. • The left- and right-sided extended fractal integral operators are introduced. • The fractal Hermite–Hadamard's integral inequality with midpoint is developed. • A series of midpoint-type integral inequalities are established in fractal domains. • Some interesting examples and applications are also given. [ABSTRACT FROM AUTHOR]

A patent application by HyperBio Biological Technology Co. Ltd. for a method and apparatus to analyze high-frequency QRS-complex data has been made available online. The invention aims to improve the efficiency of doctors in reading electrocardiograms by focusing on high-frequency QRS waveform data. The method involves acquiring, calculating, and analyzing data to provide cardiac health information based on lead positive index and waveform change shape index. The patent application outlines specific rules and categories for labeling attention levels corresponding to the high-frequency QRS waveform data. [Extracted from the article]

The massive Multiple-Input and Multiple-Output (MIMO) system is one of the technologies in 6-Generation (6G) communication networks. Omnidirectional or broad coverage precoding is used in massive MIMO to broadcast the common signals from public channels to all active and non-active users so that the radiation power of these signals is constant in all spatial directions. On the other hand, in large-scale array antennas, the presence of mutual coupling leads to deteriorating the performance of MIMO systems. In this paper, we propose omnidirectional precoding of the massive MIMO equipped with a Uniform Rectangular Array (URA) in presence of the mutual coupling. In the proposed method, omnidirectional transmission and maximum achievable ergodic rate conditions are developed for the case that mutual coupling exists, then an omnidirectional precoding matrix is designed to satisfy three constraints: 1) Omnidirectional transmission, 2) Equal average power transmission per antenna, and 3) Maximum achievable ergodic rate. For this purpose, we show that an omnidirectional matrix can be reconstructed using a pair of vectors with elements' absolute value equal to one that forms a Complementary Set (CS), and the Complete Complementary Codes (CCC) that satisfied some conditions. The intended CS is selected from the Golay sequence and the intended CCC is obtained by solving a gradient algorithm with projection on the Grassmann and Stiefel manifolds. Simulation results confirm the expected results. [ABSTRACT FROM AUTHOR]

With the successes of f(R) theory as a neutral modification of Einstein's general relativity (GR), we continue our study in this field and attempt to find general neutral and charged black hole (BH) solutions. In the previous papers [Phys. Rev. D 102, 124022 (2020); Phys. Lett. B 820, 136475 (2021)], we applied the field equation of the f(R) gravity to a spherically symmetric space-time ds²=-U(r)dt²+dr2V(r)+r²(dθ²+sin²θdϕ²) with unequal metric potentials U(r) and V(r) and with and without electric charge. Then we have obtained equations which include all the possible static solutions with spherical symmetry. To ensure the closed form of system of the resulting differential equations in order to obtain specific solutions, we assumed the derivative of the f(R) with respect to the scalar curvature R to have a form F1(r)=df(R(r))dR(r)=1-F0-(n-3)rn with a constant F0 and show that we can generate asymptotically GR BH solutions for n>2 but we show that the n=2 case is not allowed. This form of F1(r) could be the most acceptable physical form that we can generate from it physical metric potentials that can have a well-known asymptotic form and we obtain the metric of the Einstein general relativity in the limit of F0→n-3. We show that the form of the electric charge depends on n and that n≠2. Our study shows that the power n is sensitive and why we should exclude the case n=2 for the choice of F1(r) presented in this study. We also study the physics of these black hole solutions by calculating their thermodynamical quantities, like entropy, the Hawking temperature and Gibb's free energy, and derive the stability conditions by using geodesic deviations. In the standard Reissner-Nordström space-time which is the charged black hole solution in GR, there appear two black hole horizons, that is, inner horizon and outer horizon. When the radii of the two horizons coincide with each other, which is called the extremal limit, the absolute value of the charge equals to the mass and the Hawking temperature vanishes. In our model, however, the absolute value of the charge is not equal to the mass in the limit although the Hawking temperature vanishes. [ABSTRACT FROM AUTHOR]

In this paper we introduce the fractional dark energy model, in which the accelerated expansion of the Universe is driven by a nonrelativistic gas (composed by either fermions or bosons) with a noncanonical kinetic term. The kinetic energy is inversely proportional to the cube of the absolute value of the momentum for a fluid with an equation of state parameter equal to minus one, and whose corresponding energy density mimics the one of the cosmological constant. In the general case, the dark energy equation of state parameter (times three) is precisely the exponent of the momentum in the kinetic term. We show that this inverse momentum operator appears in fractional quantum mechanics and it is the inverse of the Riesz fractional derivative. The observed vacuum energy can be obtained through the integral of the Fermi-Dirac (or Bose-Einstein) distribution and the lowest allowed energy of the particles. Finally, a possible thermal production and fate of fractional dark energy is investigated. [ABSTRACT FROM AUTHOR]

In this article, by introducing a signed graph to describe the coopetition interactions among network nodes, the mathematical model of multiple memristor-based neural networks (MMNNs) with antagonistic interactions is established. Since the cooperative and competitive interactions coexist, the states of MMNNs cannot reach complete synchronization. Instead, they will reach the bipartite synchronization: all nodes’ states will reach an identical absolute value but opposite sign. To reach bipartite synchronization, two kinds of the novel node- and edge-based adaptive strategies are proposed, respectively. First, based on the global information of the network nodes, a node-based adaptive control strategy is constructed to solve the bipartite synchronization problem of MMNNs. Secondly, a local edge-based adaptive algorithm is proposed, where the weight values of edges between two nodes will change according to the designed adaptive law. Finally, two simulation examples validate the effectiveness of the proposed adaptive controllers and bipartite synchronization criteria. [ABSTRACT FROM AUTHOR]

The Colless index for bifurcating phylogenetic trees, introduced by Colless (1982), is defined as the sum, over all internal nodes v of the tree, of the absolute value of the difference of the sizes of the clades defined by the children of v. It is one of the most popular phylogenetic balance indices, because, in addition to measuring the balance of a tree in a very simple and intuitive way, it turns out to be one of the most powerful and discriminating phylogenetic shape indices. But it has some drawbacks. On the one hand, although its minimum value is reached at the so-called maximally balanced trees, it is almost always reached also at trees that are not maximally balanced. On the other hand, its definition as a sum of absolute values of differences makes it difficult to study analytically its distribution under probabilistic models of bifurcating phylogenetic trees. In this paper we show that if we replace in its definition the absolute values of the differences of clade sizes by the squares of these differences, all these drawbacks are overcome and the resulting index is still more powerful and discriminating than the original Colless index. • We define a modification of the classical Colless index for bifurcating trees. • Our Q-Colless index classifies as most balanced exactly the maximally balanced trees. • Our Q-Colless index has a larger resolutive power than the Colless index. • We give closed formulas for its first moments under the Yule and uniform models. [ABSTRACT FROM AUTHOR]

The paper shows how to use a genetic algorithm to design quasi one-dimensional structures with given properties. The superlattices were surrounded by water and made of epoxy resin and glass, with a layer thicknesses selected in such a way that a phononic bandgap occurs in the frequency range of acoustic waves. Multilayer transmission was calculated using the Transfer Matrix Method algorithm. In order to determine the optimal objective function for the genetic algorithm, the entire space of the possibility of the layers' distribution for a six-layer structure was analyzed. The spread of the transmission integral values even for the 6-layer structure was significant and ranged from 11.9% to 81.5%. Minimizing the value of the transmission integral as an objective function could lead to a large number of high transmission peaks with a small half width. It allowed the determining of the optimal objective functions for minimizing transmission in a given frequency range, and another allowing for its maximization. The phase diagram of the solution space for the transmission integral from the integral of the absolute value of the transmission functions derivative was determined. Transmission of the most and the least optimal six-layer structures was shown depending on the assumed objective function. Then, the analysis of fifteen and thirty-layer structures was carried out. From the dependence of the objective function values for the best individuals for each generation, it was determined that despite carrying out a thousand iterations, the stable state was determined before reaching 250 iterations of the algorithm, and thus the optimal structure was determined. The transmissions ratio of analyzed structures in the studied frequency range (up to 20 kHz) to full transmission (without structures) in this acoustic frequency range for the analyzed optimal 6, 15 and 30-layer structures were 16.78%, 9.6% and 4.41%, respectively. • The use of a genetic algorithm to optimize the structure was investigated. • It is necessary to select the objective function for the expected transmission. • The transmission depends on the amount of superlattice layers. • Increasing the number of layers reduces transmission. [ABSTRACT FROM AUTHOR]

In this paper, an analytical scheme [the generalized Sinh–Gordon equation method) with a new fractional operator (ABR fractional operator] is employed to find novel computational solutions of the nonlinear fractional Kolmogorov–Petrovskii–Piskunov (FKPP) equation. These solutions are used to evaluate the initial and boundary conditions under the numerical scheme (B-spline schemes) to get the numerical solutions of the same model. This equation describes the behavior of genetic models in the increase of microorganisms. Usually, it is used as a biological model to investigate the microbiological densities in bacteria cells as a result of diffusion mechanisms in terms of space–time. Some novel computational solutions are obtained, and the accuracy of them is investigated by calculating the absolute value of error between the obtained computational and numerical solutions. The comparison between the distinct types of obtained solutions is shown by calculating the absolute value of error. [ABSTRACT FROM AUTHOR]

This research paper investigates the analytical and numerical solutions of the generalized formula of Hirota-Satsuma coupled KdV system which is also known as the generalized KdV equation that is derived by R. Hirota and J. Satsuma. The modified Khater method and B-spline scheme are used to earn abundant of computational and approximate solutions on this model. This equation characterizes an interaction of two long undulations with diverse dispersion kinsmen. The comparison between our obtained computational and numerical solutions to clarify the convergence of solutions is explained and discussed. For more explanation of the model's physical properties, some of the obtained solutions are sketched in different types, and the comparison between the computational and numerical solutions are explained by showing the values of absolute error between them. The performance of both used method is effective, powerful, and shows its ability to apply to many nonlinear evolution equations. [ABSTRACT FROM AUTHOR]

In this paper we discuss the Casimir effect in a small cavity, freely falling from spatial infinity in spacetime geometry outside of a Schwarzschild black hole. Our main goal is to search for possible changes in the vacuum energy, as well as particle creation inside the falling cavity, with respect to a comoving observer. Working in the Lemaître chart and assuming a cavity size L much smaller than the Schwarzschild radius (L/rg≪1), we solve the Klein-Gordon equation for a massless scalar field confined within the cavity in the reference frame of the comoving observer. We follow Schwinger's proper time approach, evaluating the one-loop effective action for the field in the falling cavity hence evaluating the corrections to the vacuum energy. We find a small reduction in the absolute value of Casimir energy as the cavity approaches the black hole horizon due to the changing spacetime geometry. Since the spacetime geometry for the cavity changes dynamically, we further find the energy density of the created particles due to the dynamical Casimir effect. These dynamical contributions exactly match the deficit to the static Casimir energy. Combined, the observer measures a net increase in energy within the cavity as she falls. [ABSTRACT FROM AUTHOR]