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In today’s pulp and paper industry the Kraft process is the most common method for pulp production. This method uses sodium based chemicals (white liquor) in the cooking process to remove lignin from the wood chips and create pulp. The remains from this process is called black liquor and is being sent to a recycling system for the purpose of recovering the cooking chemicals. Evaporation of black liquor is a big part of this recycling, and the evaporation plant consists of many different tanks that stores black liquor. At Smurfit Kappa Piteå a model has previously been created for the purpose of production planning. In this work the opportunity to add a part that simulates how the liquor stock in the chemical recovery system will change based on the planned production was investigated. This was done by estimating the amount of dry black liquor in the tanks through inflows and outflows. A formula for the produced black liquor was also developed. The results showed that simulating tank levels separately was difficult as data was lacking in some key areas. The final model is therefore a simplified version that estimates the total amount of dry black liquor in the evaporation plant. It simulates the black liquor buffer based on the planed production and how it will change over five days. This could be done with an error smaller than 6%, compared to measurements from sensors in the black liquor tanks. Attempts were also made to create similar models for the rest of the chemical recovery system. It was concluded that information about the inflow of green and white liquor has to be further investigated in order to implement these in the production planning model.

Conductivity is an important parameter which has definite correlation with the amount of moisture present within the transformer insulation. However, in existing methods conductivity is usually estimated from time domain (PDC) measurement, which is inadvertently noise prone and time consuming. Considering this issue, in this article presents a novel technique for conductivity estimation for moisture sensing of oil-paper insulation using frequency domain spectroscopy measurement (FDS). To this end, FDS measurement of oil-paper insulation was performed from 50mHz to 1kHz to obtain the imaginary complex permittivity $\varepsilon ''$ ( $\omega$ ), which is a function of conductivity ( $\sigma$ ) as well as imaginary complex susceptibility $\chi ''$ ( $\omega$ ). From the knowledge of frequency variation of both $\sigma $ and $\chi ''$ ( $\omega$ ), we developed an electrical equivalent model of the insulation. The equivalent model parameters were optimized until $\varepsilon ''$ ( $\omega$ ) computed from the proposed model and that obtained from original FDS measurement were almost identical. The conductivity values obtained from the equivalent model showed good agreement when compared with PDC measurement. To validate the practicability of the proposed method, experiments were conducted on various test samples and also on a few real life transformers. Most importantly, the measurement time was found to be reduced by 78.5%, enabling diagnosis of transformer insulation at a significantly reduced time.

The variability and interdependence of local porosity and local mean geodesic tortuosity, which is a measure for the sinuosity of shortest transportation paths, is investigated at the example of the microstructure in sack paper. By means of statistical image analysis, these two morphological characteristics are computed for several cutouts of 3D image data obtained by X-ray microcomputed tomography. Considering cutouts of different sizes allows us to study the influence of the sample size on the local variability of the considered characteristics. Moreover, the interdependence between local porosity and local mean geodesic tortuosity is quantified by modeling their joint distribution parametrically using Archimedean copulas. It turns out that the family of Gumbel copulas is an appropriate model type, which is formally validated by a goodness of fit test. Besides mean geodesic tortuosity, we consider further related morphological characteristics, describing the sinuosity of those shortest transportation paths, whose minimum diameter exceeds a predefined threshold. Moreover, we show that the copula approach investigated in this paper can also be used to quantify the negative correlation between local porosity and these modified versions of local mean geodesic tortuosity. Our results elucidate the impact of local porosity on various kinds of morphological characteristics, which are not experimentally accessible and which are important for local air permeance – a key property of sack paper.

There is no simple definition of the slope for multicomponent systems because the vapour liquid equilibrium is represented by a surface (which lies in hyperspace for more than 3 compounds). Thus, for multicomponent systems any pseudo-binary method for estimating tray efficiencies and HETP must rely, in part, on an approximate method of estimating the slope. The objective of this paper is to present a new method of approximating the slope in multicomponent systems based on differentiation of the phase equilibrium surface with respect to the mole fraction of the design component, defined as that compound we seek to eliminate from the mixture in a particular section of the column. There is only one design compound per column section. The approach presented here can be easily applied to absorber and stripper columns, where the concept of key components is not applicable. Two analytical approximate methods of estimating the design slope are shown to be in good agreement with the rigorous calculation even in cases where the relative volatility is not constant. These simple approximations, which need nothing beyond what is readily available from any column simulation program are adequate for design and can be programmed easily in any spreadsheet.

This letter solves an open question of origami paper spring risen by Yoneda et al.(Phys. Rev. E 2019). By using both dimensional analysis and data fitting, a universal scaling law of a paper spring is formulated. The scaling law shows that origami spring force obeys power square law of spring extension, however strong nonlinear to the total twist angle. The study has also successfully generalized the scaling law from the Poisson ratio 0.3 to an arbitrary Poisson's ratio with the help of dimensional analysis., Comment: 3 pages, 3 figues and 1 table

In the Russian school, the total normalized gradient method belongs to the most wide‐spread of direct interpretation methods for potential field data. This method was also used and partly developed by many experts from abroad. The main advantage of the total normalized gradient method is its relative independence of parameters such as the expected differential density of interpreted structures. The method is built from a construction of a specially transformed field (total normalized gradient) on a section crossing the potential field sources. The special properties of this transformed field allow it to be used to detect the source positions. From the 1960s, the mathematical basis of the method underwent enormous development and several modifications of the method have been elaborated. The total normalized gradient operator itself represents a relatively complicated, non‐linear band‐pass filter in the spectral domain. The properties of this operator can be handled by means of several parameters that act to separate the information about field sources at different depth levels. In this contribution, we describe the development of the method from its very beginning (based mostly on qualitative interpretation of simple total normalized gradient sections) through to more recent numerical improvements to the method. These improvements include the quasi‐singular points method, which refines the filter properties of the total normalized gradient operator and defines an objective criteria (so called criterion ‘α’ and ‘Г') for the definition of source depths in the section. We end by describing possibilities for further development of the method in the future.

Paper (Maniar and Bhattacharyay, 2021) introduces a discrete random-walk (RW) model with a site dependent waiting time and an external force i.e. a site dependent drift. The RW is compared with a Smoluchowski equation in continuous space and time with space dependent diffusivity and space dependent damping. Using numerical simulations in Maniar and Bhattacharyay (2021) it is shown that the equilibrium distribution satisfies locally the Stokes–Einstein relation i.e. there is a constant temperature in the whole system. Here we show that the result can be recovered analytically with a continuous limit in the RW master equation. Moreover, we evidence that the RW model should be carefully defined in order to satisfy locally Stokes–Einstein relation, indeed a different definition of the discrete RW process describes a system that satisfies the Smoluchowski equation with constant damping, where the temperature is not uniform.

Paper board with bending stiffness is usually used as the substrates on cigarette package printing industry. The vibration of these paper boards in high speed affects the printing precision. The dynamic characteristics and stability of moving paper board with finite interior elastic point supports and elastic edges restrained are investigated. First, the energy function of the system is established by using the extended Hamilton’s principle; second, the dimensionless equations of motion for the moving paper board are obtained using the element-free Galerkin method. The equations of motion and the eigenvalue equations of the system are established. The relationship between the first three complex frequencies of the system and the moving speed is then obtained by the numerical calculation. The effects of the elastic point supports, the elastically restrained edges, and the dimensionless speed of the motion on the dynamic stability of the paper board are analyzed. The critical speed when the paper board is in a stable state under different conditions is obtained. The results improve the dynamic stability of the paper board in printing process and provide the theoretical basis for the optimization of printing equipment.

Kramers-Kronig function is treated as a universal relationship between the real and imaginary parts of a frequency domain response system. The present study aims at establishing this relationship’s specific implementation strategy in the field of frequency domain spectroscopy which is a promising insulation condition assessment method for power equipment. To achieve this, the physical meaning of dielectric material’s complex permittivity spectrum is discussed first, based on which Kramers-Kronig function’s role in the data processing is made clear. Further, the present study deduces a simplified formula from Kramers-Kronig function’s original form that is capable for oil-paper’s frequency domain spectrum data analysis. On this basis, an analysis model of real part and imaginary part of complex permittivity based on Kramers-Kronig relationship is established, and the mechanism analysis in the testing band is obtained. The result shows that a relaxation loss peak co-exists with AC conduction process in the low frequency range of oil-paper insulation’s frequency domain spectroscopy. Weight of each dielectric process is compared as well.

We discuss the recent paper by A. Dar\'os and L.K. Arruda (On the instability of elliptic traveling wave solutions of the modified Camassa-Holm equation, J. Diff. Equat., 266 (2019), 1946-1968). Our intention is to correct some imperfections left by the authors and present the orbital stability of periodic snoidal waves in the energy space., Comment: 10 pages and 2 figures

We realized a study of the shortest path fractal dimension in three dimensions for randomly crumpled paper balls. We took measurements between all possible combinations of pairs of points in crumpled and flat configurations, we found that a correlation between these distances exist, even more, such mean experimental value is dmin=1.2953±0.02 that coincides almost numerically with the very known 3D shortest path fractal dimension for percolation systems reported in computational simulations.

In the commented paper, the authors considered a two-dimensional airfoil with nonlinear stiffness and damping, and derived the amplitude modulation equation (AME) of the system limit cycle oscillation around its bifurcation. Based on the variation equation of the AME, they conducted the stability analysis. Unfortunately, the obtained variation equation associated with the AME is incorrect.

We develop a modal method for radially inhomogeneous waveguides. The formulation is derived with the two transverse components of the magnetic field. The algebraic eigensystem is solved by using Tchebycheff polynomials and a tau method.

The aim of this comment paper is to show that the paper (Pop et al., 2021) contains many serious errors.

It is shown that the solution to the steady flow of a Newtonian fluid in a pipe of equilateral triangular cross-section is wrong, for it is based on an inappropriate choice of a parameter and the incorrect use of trigonometry. Secondly, the assumption that the shear stresses in a steady flow in a pipe are given by the gradient of a scalar function is also incorrect, since it depends on the equality between directional and partial derivatives everywhere.

Frequency Dielectric Spectroscopy (FDS) Analysis has good application prospects in transformer insulation detection due to its non-destructive measurement and robustness against noise. Two steps are needed when analyzing transformer insulation using this method. The first step is to translate the dielectric spectroscopy of the major insulation of transformer to that of the oil-impregnated paper. Then based on dielectric spectroscopy, the aging degree and moisture content of the oil-impregnated paper are analyzed. Using a commonly used model named XY model, the complex permittivity of paper can be calculated by solving a quadratic equation. The equation has two solutions named solution1 and solution2 respectively. In this paper, the characteristics and distribution of the two solutions are studied. Firstly, the calculation process of translating dielectric spectroscopy of major insulation of transformer to oil-impregnated paper is introduced. For the cases of measured complex permittivity of oil-impregnated paper with different moisture content, the results show that the correct solution of most conditions is solution1. With the decline of moisture content of the paper, the range of frequency where solution2 is correct reduces. The calculated complex permittivity of oil-impregnated paper is decided by five variables. For universal cases, the variables’ influences on the distribution of the two solutions are studied. The results show that for all the situations, one and only one solution is in the first quadrant of the complex plane. Thus, the part of the two solutions in the first quadrant of the complex plane is the correct solution. Only when ω < 0.01 rad/s, part of the correct solutions become solution2 and enlarge with the decrease of ω. The increase of X and Y shrinks the outlines of the area which solution2 is correct and moves the outlines in the positive direction of X-axis.

A popular physics legend holds that scissors can cut paper with a speed faster than light. Here this counter-intuitive myth is investigated theoretically using four simple examples of scissors. For simplicity, all cases will involve a static lower scissors blade that remains horizontal just under the paper. In the first case, the upper blade will be considered perfectly rigid as it rotates around and through the paper, while in the second case, a rigid upper blade will drop down to cut the paper like a guillotine. In the third case, the paper is cut with a laser rotating with a constant angular speed that is pointed initially perpendicular to the paper at the closest point, while in the fourth case, the uniformly rotating laser is pointed initially parallel to the paper. Although details can be surprising and occasionally complex, all cases allow sections of the paper to be cut faster than light without violating special relativity. Therefore, the popular legend is confirmed, in theory, to be true., 6 pages, 9 figures, accepted for publication in Physics Education (un-copyedited version)

The diffusion of light within paper has an effect on the colors in a halftone image and must be taken into consideration in modeling halftone color. The diffusion can be accounted for by using the point spread function or equivalently the modulation transfer function (MTF) of the paper. A novel method of measurement of the paper's MTF, called the bar-target series expansion method, is proposed here. The experimental results of the method confirm that the shape of the MTF is an exponential function, which corresponds to a Lorentzian line spread function as predicted by the multiple-path model of reflection.

One of the simplest examples of a robust heteroclinic cycle involves three saddle equilibria: each one is unstable to the next in turn, and connections from one to the next occur within invariant subspaces. Such a situation can be described by a third-order ordinary differential equation (ODE), and typical trajectories approach each equilibrium point in turn, spending progressively longer to cycle around the three points but never stopping. This cycle has been invoked as a model of cyclic competition between populations adopting three strategies, characterised as Rock, Paper and Scissors. When spatial distribution and mobility of the populations is taken into account, waves of Rock can invade regions of Scissors, only to be invaded by Paper in turn. The dynamics is described by a set of partial differential equations (PDEs) that has travelling wave (in one dimension) and spiral (in two dimensions) solutions. In this paper, we explore how the robust heteroclinic cycle in the ODE manifests itself in the PDEs. Taking the wavespeed as a parameter, and moving into a travelling frame, the PDEs reduce to a sixth-order set of ODEs, in which travelling waves are created in a Hopf bifurcation and are destroyed in three different heteroclinic bifurcations, depending on parameters, as the travelling wave approaches the heteroclinic cycle. We explore the three different heteroclinic bifurcations, none of which have been observed in the context of robust heteroclinic cycles previously. These results are an important step towards a full understanding of the spiral patterns found in two dimensions, with possible application to travelling waves and spirals in other population dynamics models., Comment: 36 pages, 8 figures

After the reissue of Journal of Silk, the historical papers published can reflect the academic history of Chinese Textile and Apparel History research. The mathematical analysis of these papers is helpful to clarify the territory and important towns of the research on Chinese Textile and Apparel History. Through literature collation and mathematical analysis, the paper believes that: ① The changes in the types of historical papers in Journal of Silk, especially the decline in the amount of papers published by corporate personnel, indicate that the Journal has transformed from a journal that integrates education, academia, and training into an academic publication. ② For a long time, authors from Zhejiang and Jiangsu have published more than half of the papers. This phenomenon is related to the earliest research on historical theory in the two places, especially the Zhejiang Silk Institute of Technology, which was the first organization to engage in professional research on historical theory in China. ③ Authors in Zhejiang Province had the largest number of papers before 2003. But after 2004, authors in Jiangsu had the largest number of papers. And after 2004, authors in Shanghai had more papers published, which is related to the strengthening of relevant majors by Suzhou University, Jiangnan University and Donghua University. At the same time, the experience of Jiangnan University shows that restricting the graduation conditions for master's students is conducive to research in the field of Historical Theory.

This note is devoted to a small, but essential, extension of Theorem 2.1 of our recent paper (LeCrone et al. J Evolut Equ 14:509–533 2014). The improvement is explained in “The improvement” section and proved in “Proof of the main result” section. The importance of the extension is demonstrated in “Application to the Navier–Stokes equations” section with an application to the Navier–Stokes system in critical \(L_q\)-spaces.

In a recent paper, Zhu et al. used bender element-type ultrasonic actuator in order to generate S-waves transmission through mortar samples. New criteria for determining the initial and final setting are proposed. The developed methodology leads to the conclusion that these criteria are more reliable than previously published material. Several points would require further discussion, such as the consideration of the effect of temperature, the shear wave onset detection algorithm, or the curve fitting strategy. These considerations might undermine the reliability of the suggested method, and explain the divergence of results obtained in contrast with previously published material., SCOPUS: no.j, info:eu-repo/semantics/published

In (2012), Leonetti and Siepe [10] considered solutions to boundary value problems of some anisotropic elliptic equations of the type { ∑ i = 1 n D i ( a i ( x , D u ( x ) ) ) = 0 , x ∈ Ω , u ( x ) = θ ( x ) , x ∈ ∂ Ω . Under some suitable conditions, they obtained an integrability result, which shows that higher integrability of the boundary datum θ forces solutions u to have higher integrability as well. In the present paper, we consider K ψ , θ ( p i ) -obstacle problems of the nonhomogeneous anisotropic elliptic equations ∑ i = 1 n D i ( a i ( x , D u ( x ) ) ) = ∑ i = 1 n D i f i ( x ) under some controllable growth and monotonicity conditions. We obtain an integrability result, which can be regarded as a generalization of the result due to Leonetti and Siepe.

The objective of this contribution is to improve recent stability results for a system coupling ordinary differential equations to a vectorial transport partial differential equation by proposing a new structure of Lyapunov functional. Following the same process of most of the investigations in literature, that are based on an a priori selection of Lyapunov functionals and use the usual integral inequalities (Jensen, Wirtinger, Bessel...), we will present an efficient method to estimate the exponential decay rate of this coupled system leading to a tractable test expressed in terms of linear matrix inequalities. These LMI conditions stem from the new design of a candidate Lyapunov functional, but also the inherent properties of the Legendre polynomials, that are used to build a projection of the infinite dimensional part of the state of the system. Based on these polynomials and using the appropriate Bessel-Legendre inequality, we will prove an exponential stability result and in the end, we will show the efficiency of our approach on academic example.

A numerical model based on the Fokker-Planck equation for studying the orientation of paper fibers in a suspension is presented. The model is implemented in a finite volume framework. The rotational operators are discretized on a triangulated half sphere and the spatial operators are discretized on a Cartesian octree grid, where internal walls are handled with immersed boundary methods. Transient solutions of the two dimensional fiber orientation distribution are computed in the entire fluid domain. This is in contrast to earlier approaches that either only compute along streamlines or one dimensional projected orientations. The fibers are assumed to have negligible inertia and thus to follow the fluid perfectly and to be evenly distributed. A head-box geometry relevant for paper forming is used to exemplify the usefulness of the method. The influence of translational and rotational diffusion is included in the presented method.

This paper is an attempt to present the methodologically correct approach of the anisotropy-based theory for discrete-time systems with multiplicative noise. A formulation of sufficient conditions of boundedness of the anisotropic norm is the main goal of this paper. As it is shown, this problem can be reduced to the convex optimization problem. A simple numerical example to illustrate the solution procedure is given.

Let a(n) be the Fourier coefficient of a holomorphic cusp form on some discrete subgroup of \(SL_2({\mathbb R})\). This note is to refine a recent result of Hofmann and Kohnen on the non-positive (resp. non-negative) product of \(a(n)a(n+r)\) for a fixed positive integer r.

We describe a method to construct smooth and compactly supported solutions of 3D incompressible Euler equations and related models. The method is based on localizable Grad–Shafranov equations and is inspired by the recent result (Gavrilov in A steady Euler flow with compact support. Geom Funct Anal 29(1):90–197, [Gav19]).

In this note, we correct an error in our paper published in Communications in Nonlinear Science and Numerical Simulation in 2015 [5], in which the form of a Z2-equivariant cubic planar switching system is not correct. In this note, we add one more switching line and use the same equations given in [5] to construct a correct Z2-equivariant cubic system. Then, we prove that the new system can exhibit 15 limit cycles and therefore the conclusion given in [5] still holds.

In the past, partial discharge was considered as a completely random process, and various statistical spectra such as phase resolved partial discharge (PRPD) were constructed, but the accuracy still needs to be further improved. The chaos theory is introduced to research the development of partial-discharge defects of oil-paper insulation in transformer. The sphere-plate partial discharge model was constructed in the laboratory. And the data of the pulse discharge during the development of the pressboard from the initial discharge to the breakdown was obtained by the constant voltage method under six voltage levels. By constructing the discharge time series, the chaotic attractors are reconstructed in the phase space. And all the attractors of the samples under the six voltage levels satisfy the largest Lyapunov exponent λ 1 >0, the correlation dimension D is the fraction and the Kolmogorov entropy K 2 >0, indicating that the partial discharge is a deterministic chaotic process. It provides new research ideas for the diagnosis and prediction of the aging and the development of electrical branches for oil-paper insulation.

In Fritz John's famous paper (1979), he discovered that for the wave equation $\Box u=|u|^p$, where $1, Comment: 11 pages, 3 figures

The anisotropic norm of a linear discrete time invariant system is a measure of system output sensitivity to stationary Gaussian input disturbances with mean anisotropy bounded by some nonnegative parameter. The mean anisotropy characterizes the predictability (or coloredness) degree of stochastic signal. The anisotropic norm of a system is an induced norm, limiting cases of which are H 2 - and H ∞ -norms as a → 0 and a → ∞, respectively. In Vladimirov et al. (1996) a method for numerical computation of the anisotropic norm was proposed. This method involves cross-coupled Riccati and Lyapunov equations and associated special type equation. Another method for anisotropic norm computation via LMI-based approach was proposed in Tchaikovsky & Kurdyukov (2006). This paper develops a new method for getting the lower bound for anisotropic norm by linear algebra standard methods.