Nonhomogeneous Part Research Articles

Reduced model and nonlinear analysis of localized instabilities of residually stressed cylinders under axial stretch

In this paper, we present a dimensional reduction to obtain a one-dimensional model to analyze localized necking or bulging in a residually stressed circular cylindrical solid. The nonlinear theory of elasticity is first specialized to obtain the equations governing the homogeneous deformation. Then, to analyze the nonhomogeneous part, we include higher-order correction terms of the axisymmetric displacement components leading to a three-dimensional form of the total potential energy functional. Details of the reduction to the one-dimensional form are given. We focus on a residually stressed Gent material and use numerical methods to solve the governing equations. Two loading conditions are considered. First, the residual stress is maintained constant, while the axial stretch is used as the loading parameter. Second, we keep the pre-stretch constant and monotonically increase the residual stress until bifurcation occurs. We specify initial conditions, find the critical values for localized bifurcation, and compute the change in radius during localized necking or bulging growth. Finally, we optimize material properties and use the one-dimensional model to simulate necking or bulging until the Maxwell values of stretch are reached.

Estimation of the solution of asymptotically observable linear completely regular differential-algebraic systems with delay

In the article, a problem of solution estimation for linear autonomous completely regular differential-algebraic systems with many commensurate delays is investigated. The class of completely regular differential-algebraic systems with delay under study includes the classes of linear systems of delayed and neutral types; in addition, the analysis of continuous-discrete systems is reduced to completely regular systems. For linear autonomous completely regular differential-algebraic systems with many commensurate delays, the property of asymptotic observability is determined, which are characterized by the fact that all solutions generating the same output signal are indistinguishable in the future. Conditions for asymptotic observability expressed in terms of the parameters of the original system are formulated and proved. For asymptotically observable systems, a solution estimation procedure is proposed, the implementation of which consists of the following steps. First, using the observed output, a linear autonomous non-homogeneous asymptotically observable retarded type system with a non-homogeneous part depending on the output is put in correspondence with the original system. The solution of the new system uniquely determines the solution of the original system. Then a transformation is constructed that reduces the matrices of the retarded type system to a certain form. After that, with the help of a finite chain of observers, the solution is evaluated. The results of the presented study are applicable to systems that do not have the property of final observability, which makes it possible to significantly reduce the requirements for observing organs when modeling the corresponding objects of the real world.

Solving Conformable Fractional Differential Equations with ``EJS Software and Visualization of Sub-diffusion Process

In this work, we numerically solve ordinary and conformable fractional differential equations using Easy Java Simulations software. Their solutions, including homogeneous and non-homogeneous parts, are compared in various time intervals. Using software’s visualization andsimulation features, we may better examine, compare, and evaluate solutions of analytical and numerical fractional differential equations. A kind of oscillatory behavior is seen in long enough times. In simulation of diffusion and sub-diffusion processes, two intriguing events have been observed.

On the Growth of Solutions of Nonhomogeneous Higher order Complex Linear Differential Equations

The nonhomogeneous higher order linear complex differential equation (HOLCDE) with meromorphic (or entire) functions is considered in this paper. The results are obtained by putting some conditions on the coefficients to prove that the hyper order of any nonzero solution of this equation equals the order of one of its coefficients in case the coefficients are meromorphic functions. In this case, the conditions were put are that the lower order of one of the coefficients dominates the maximum of the convergence exponent of the zeros sequence of it, the lower order of both of the other coefficients and the nonhomogeneous part and that the solution has infinite order. Whiles in case the coefficients are entire functions, any nonzero solution with finite order has hyper order equals to the lower order of one of its coefficients is proved. In this case, the condition that the lower order of one of the coefficients is greater than the maximum of the lower order of the other coefficients and the lower order of the nonhomogeneous part is assumed.

The Bessel function J 0 in fractional differential equations

Spherical Bessel functions have many important applications in engineering, optic and science. In this work, wich is a continuation of the error function in fractional differential equations, it is shown how solve the fractional differential equation where the nonhomogenous part is the function Bessel spherical J 0(x).

English

In this article, we prove that initial value problem associated to the non-homogeneous KdV-Kuramoto-Sivashinsky (KdV-K-S) equation in periodic Sobolev spaces has a local solution in with and the solution has continuous dependence with respect to the initial data and the non-homogeneous part of the problem. We do this in an intuitive way using Fourier theory and introducing a inspired by the work of Iorio [2] and Ayala and Romero [8]. Also, we prove the uniqueness solution of the homogeneous and non-homogeneous KdV-K-S equation, using its dissipative property, inspired by the work of Iorio [2] and Ayala and Romero [9].

A novel method with Newton polynomial-Chebyshev nodes for milling stability prediction

As the approximation orders enlarge, the numerical algorithms of milling stability prediction are becoming increasingly complex with more and more calculation time being consuming. Above all, the effects of convergence and accuracy do not continuously improve for the presence of Runge phenomenon. This paper suggests a novel predictive scheme immune from this undesirable effect based on the Newton polynomial-Chebyshev nodes. Firstly, the processing dynamics embracing the self-excited vibration is described as the state-space equation with a separate time delay. Then n-order Newton polynomial with linear sampling nodes is chosen to unfold the monolithic non-homogeneous part to estimate the continuous response into linear discrete map, which designates the state transition of the system within a single cutting period. Taking advantage of this closed-form map, two coefficients that have considerable coupled elements with each other are established to generate the transition matrix, and the stability limits is searched out depending on Floquet theory. A set of comparisons are conducted using the experimentally validated examples to determine the optimal approximated order with exhibiting the features of the proposed methods. It is also disclosed that there is an obvious Runge effect existing in the presented high-order methods, which seriously lowers the estimated accuracy. In the interests of eliminating this unwanted effect, a nonlinear sampling technique based on Chebyshev nodes is adopted to substitute for the origin uniform time joints to establish a novel transition matrix with fewer calculated loads for the milling stability prediction, and the verifications illuminate the reconstituted methods are of satisfactory performance. The proposed methods are beneficial for the path planers to avoid some unsuited parameters which cause the machining chatter.

Recovering a quasilinear conductivity from boundary measurements

We consider the Calderón type inverse problem of recovering an isotropic quasilinear conductivity from the Dirichlet-to-Neumann map when the conductivity depends on the solution and its gradient. We show that the conductivity can be recovered on an open subset of small gradients, hence extending a partial result of Muñoz and Uhlmann to all real analytic conductivities. We also recover non-analytic conductivities with additional growth assumptions along large gradients. Moreover, the results hold for non-homogeneous conductivities if the non-homogeneous part is assumed known.

O Caráter Essencial dos Corpos Homogêneos em Aristóteles

The present paper aims at examining the characteristics that determine the essential nature of the homogeneous bodies in Aristotle, from an analysis of Meteorology IV.12, which would at the same time establish a certain relationship with other treatises of natural philosophy and also in particular with books VII and VIII of Metaphysics. With this investigation, I will delineate a certain line of argument that goes against a reading perspective considered as traditional, with certain interpretive variants, according to which Aristotle would have adopted the idea of ​​a universal teleology, in the general sense that all natural bodies would be generated for a specific goal, or for a natural purpose. According to a certain view, linked to this perspective, the teleological character of functional type of vital activities, notably expressed by the compositional arrangement of the non-homogeneous parts in the living being's complexion, would be somehow involved in the constitution of the homogeneous bodies considered in themselves and for themselves. In contrast to such a view, I will examine, in a precise way, to what extent the homogeneous bodies would comprise a certain formal factor directly involved in the characterization of their constitutional particularities, taking into account a comparative examination with other kinds of natural compositions, namely, elemental aggregates and living organisms. Thus, through this examination, I will explore the question of whether, in function of this formal factor, such bodies could present some teleological character trait, distinct from the functional type, characteristic of organic-animate constitutions.

Comparison of efficiency among different techniques to avoid order reduction with Strang splitting

AbstractIn this article, we offer a comparison in terms of computational efficiency between two techniques to avoid order reduction when using Strang method to integrate nonlinear initial boundary value problems with time‐dependent boundary conditions. We see that it is important to consider an exponential method for the integration of the linear nonhomogeneous and stiff part in the technique by Einkemmer et al. so that the latter is comparable in efficiency with that suggested by Alonso et al. Some other advantages of the technique suggested by Alonso et al. are stated in the conclusions.

Spectroscopic ellipsometry studies of an electrochemically synthesized molecularly imprinted polymer for the detection of an aviation biokerosene contaminant

The present work reports the use of spectroscopic ellipsometry to study the properties of molecularly imprinted poly(ortho-phenylenediamine) film. This polymer was electrosynthesized by cyclic voltammetry and applied for the detection of hexahydrofarnesol, which is the main contaminant of aviation biokerosene. Ellipsometry was used to obtain the thickness of the polymeric film and to investigate the optical and dielectric properties of this material. The results obtained showed that the optical properties and dielectric constants of the molecularly imprinted polymer were sensitive to the presence or absence of the hexahydrofarnesol molecule. Detection studies for this molecule showed that the modified electrode responds linearly in two distinct concentration ranges: 5.0 × 10−8 to 1.3 × 10−7 mol L−1 and 3.0 × 10−7 to 1.5 × 10−6 mol L−1, with the first linear range presenting a sensitivity 27.3 times higher than the second range. This is in line with the behavior of the optical properties (refractive index and extinction coefficient) of the polymeric film, which pointed to the presence of a larger number of imprinted cavities in the non-homogeneous part of the polymer. Essentially, this study proved that, apart from measuring film thickness, spectroscopic ellipsometry is a powerful tool for the characterization of molecularly imprinted polymers.

(Keynote) Ellipsometric Study of a Molecularly Imprinted Polymer Modified Carbon Electrode for Detection of Hexahydrofarnesol

Molecularly imprinted polymers (MIPs) are highly selective synthetic materials for the detection of target compounds. In this work, the spectroscopic ellipsometry was used to study the properties of a molecularly imprinted poly(ortho-phenylenediamine) film. This device was electrosynthesized by cyclic voltammetry on a glassy carbon electrode and applied for hexahydrofarnesol detection, which is the main contaminant of aviation biokerosene. The ellipsometric parameters were used to obtain the thickness of this polymeric film and the values found are in agreement with the atomic force microscopy data. Ellipsometric modeling was performed using Forouhi-Bloomer and Lorentz models, which are used to describe amorphous carbon films. Ellipsometric analyzes showed that the optical properties, including refractive index and extinction coefficient, as well as the dielectric constants of this molecularly imprinted polymer are sensitive to the presence or absence of the hexahydrofarnesol molecule. This confirmed the formation of the imprinted cavities after the extraction process of the template molecule. In addition, the dielectric constants showed that the formation of imprinted cavities leads to increased conductivity of the poly(ortho-phenylenediamine) film. The equilibrium parameters between the imprinted cavities and the hexahydrofarnesol molecules, such as the affinity constant and dissociation constant, were determined by the Langmuir adsorption isotherm to be 2.1×107 and 4.7×10-8 mol L-1, respectively. These values indicate that the imprinted cavities have a high affinity to recognize hexahydrofarnesol molecules. Under optimized conditions, the hexahydrofarnesol detection study showed that the MIP-modified electrode has two linear concentration ranges: 5.0×10-8 to 1.3×10-7 mol L-1 (y = 71C + 9.9×10-6; R2 = 0.973) and 3.0×10-7 to 1.5×10-6 mol L-1 (y = 2.6C + 1.9×10-5; R2 = 0.987). The presence of two linear ranges in electrochemically synthesized MIPs is due to the distribution of the imprinted cavities on the polymer structure. This behavior is in agreement with the ellipsometric studies, which pointed to a larger number of imprinted cavities on the non-homogeneous part of the polymer film. This study proved that spectroscopic ellipsometry is a powerful tool for the characterization of molecularly imprinted polymers. Acknowledgments: The authors would like to thank Brazilian Agencies FAPESP (process 2017/23529-6), FINEP, CNPq, FAPERJ and CAPES for the financial support.

Pointwise Convergence of the Schrödinger Flow

Abstract In this paper we address the question of the pointwise almost everywhere limit of nonlinear Schrödinger flows to the initial data, in both the continuous and the periodic settings. Then we show how, in some cases, certain smoothing effects for the non-homogeneous part of the solution can be used to upgrade to a uniform convergence to zero of this part, and we discuss the sharpness of the results obtained. We also use randomization techniques to prove that with much less regularity of the initial data, both in continuous and the periodic settings, almost surely one obtains uniform convergence of the nonlinear solution to the initial data, hence showing how more generic results can be obtained.

Adaptive Exploration-based Whale Optimization for Image Segmentation Based on Variable Parametric Error

Image segmentation is the process of splitting an image into numerous segments. Its major purpose is to change or simplify the image, which could be more significant and simpler to examine. However, it does not execute well while segmenting complex images with non-homogeneous parts. In this paper, a hybrid image segmentation model with the aid of Active Contour and Graph cut techniques is proposed. Moreover, it extracts the mutual information from two adopted segmentation schemes, and subsequently, the high-intensity and low-intensity pixels of resultant images are grouped by Fuzzy Entropy Maximization (FEM) method. A modified optimization algorithm termed as Adaptive Exploration based Whale Optimization (AEW) is used for solving the FEM problem. The performance of the proposed Active contour Graph cut Fuzzy Entropy-based Segmentation(AGFES), (AEW-AGFES) is algorithmically analyzed in terms of various performance measures to substantiate its effectiveness.

Application of Dual Integral Equations in Heat Equation for Unbounded Plate

An analytical solution to a two-dimensional nonstationary nonhomogeneous heat equation in axially symmetrical cylindrical coordinates for an unbounded plate subjected to mixed boundary conditions of the first and second kinds has been obtained. The application of the Laplace transform (L-transform) and the separation of variables result in the solution to the initial mixed boundary-value problem as the solution to a pair of dual integral equations (DIEs) with an unknown function dependent on the L-transform parameter. The DIEs solution is proposed by using the known discontinuous integrals and an infinite series method. The Green’s function is used to determine the solution to the nonhomogeneous part of the problem.

An algebraic approach to on-line signal denoising and derivatives estimation

In this paper, a new algebraic approach to the on-line signal derivatives estimation is proposed. The proposed approach is based on the conversion of the truncated Taylor series expansion to the set of linearly independent equations regarding the signal derivatives. The nonhomogeneous parts of the obtained set of equations are convolution integrals, which can be transformed to the stable linear state-space filter realization. The proposed algebraic estimator provides stable convergence without the need for periodic re-initialization, as in the case of the conventional algebraic estimators. In contrast to the Taylor series-based tracking differentiators, the proposed estimator also provides an estimation of the arbitrary number of the higher-order signal derivatives. In addition, the tuning of the estimator parameters does not depends on the filter dimension. The efficiency of the proposed estimator is illustrated by the simulation examples and experimental results related to the monitoring of the surgical drilling process.

Effect of Proximity of Features on the Damage Threshold During Submicron Additive Manufacturing Via Two-Photon Polymerization

Two-photon polymerization (TPP) is a laser writing process that enables fabrication of millimeter scale three-dimensional (3D) structures with submicron features. In TPP, writing is achieved via nonlinear two-photon absorption that occurs at high laser intensities. Thus, it is essential to carefully select the incident power to prevent laser damage during polymerization. Currently, the feasible range of laser power is identified by writing small test patterns at varying power levels. Herein, we demonstrate that the results of these tests cannot be generalized, because the damage threshold power depends on the proximity of features and reduces by as much as 47% for overlapping features. We have identified that this reduction occurs primarily due to an increase in the single-photon absorptivity of the resin after curing. We have captured the damage from proximity effects via X-ray 3D computed tomography (CT) images of a nonhomogenous part that has varying feature density. Part damage manifests as internal spherical voids that arise due to boiling of the resist. We have empirically quantified this proximity effect by identifying the damage threshold power at different writing speeds and feature overlap spacings. In addition, we present a first-order analytical model that captures the scaling of this proximity effect. Based on this model and the experiments, we have identified that the proximity effect is more significant at high writing speeds; therefore, it adversely affects the scalability of manufacturing. The scaling laws and the empirical data generated here can be used to select the appropriate TPP writing parameters.

The Application of Quadratic Bezier Curve on Rotational and Symmetrical Lampshade

The procedure of constructing lampshade is through parameter merger and selection of Bezier surfaces shapeshifters; thus it producesperfect and varied sitting-lampshades.Constructing sitting-lamp shades requires the study of the physical (lighting) and geometryaspects. In terms of geometry, the existed sitting-lampshade creation models is generally monotonous and constructed from objects pieces. In line with these problems, this research is divided into four stages:First, preparing the data to build a sitting-lampshade. Second, technical studying to construct the symmetricity of the sitting-lamp shade shape.Third, constructing the parts of the sitting-lampshade, namely the base, the main part, the roof. Fourth, constructingthe complete sitting-lampshade. The results of this research to obtain the procedures of constructing the sitting-lampshade namely: First, dividing the major axis into three non-homogeneous sub segments.Second, constructing parts of the sitting-lampshade namely the base, the main part, and the roof by combining the sitting-lamp shade components from the geometrical objects deformation.Third, filling each sub segment of non-homogeneous parts with parts of the lampshade and creating the boundary curvesproducing a varied innovative symmetricalmodels of sitting-lampshade.

Bacterial anti-adhesive and pH-induced antibacterial agent releasing ultra-thin films of zwitterionic copolymer micelles

We report on preparation of substrates with dual function coatings, i.e. bacterial anti-adhesive and antibacterial agent releasing polymer films of zwitterionic block copolymer micelles (BCMs). BCMs were obtained by pH-induced self-assembly of poly[3-dimethyl (methacryloyloxyethyl) ammonium propane sulfonate-b-2-(diisopropylamino)ethyl methacrylate] (βPDMA-b-PDPA), resulting in BCMs with zwitterionic βPDMA-coronae and pH-responsive PDPA-core. These zwitterionic BCMs were then used as building blocks to construct mono- and multi-layer films. We found that the number of layers in the film was critical for the anti-adhesive property and 3-layer films were the most anti-adhesive against a model Gram-positive bacterium, Staphylococcus aureus. Antibacterial activity could be introduced to the films by loading Triclosan into βPDMA-b-PDPA micelles. Triclosan containing films were effective against Triclosan-sensitive Staphylococcus aureus specifically at moderately acidic conditions due to pH-induced disintegration of the micellar core blocks and release of Triclosan from the surface. Three-layer films also exhibited anti-adhesive property at physiological pH against a model Gram-negative bacterium, Escherichia coli. At moderately acidic pH, the coatings showed a contact antibacterial effect against an isolate of Escherichia coli with low sensitivity to Triclosan only when micellar cores were loaded with Triclosan. Such dual function films can be promising to combat biofouling at the non-homogeneous and/or defective parts of an anti-adhesive coating. Moreover, considering the moderately acidic conditions around an infection site, these multilayers can be advantageous due to their property of pH-induced antibacterial agent release. Statement of SignificanceThis study presents preparation of substrates with dual function ultra-thin coatings of zwitterionic block copolymer micelles which show bacterial anti-adhesive properties against a Gram-positive and a Gram-negative bacterium. Such coatings are also capable of releasing antibacterial compounds in response to pH changes. Films were prepared by self-assembly of polymers at the surface. Our findings showed that zwitterionic micellar coronae introduced bacterial anti-adhesive property to the films, whereas pH-responsive micellar cores enabled release of an antibacterial agent from the surface at acidic pH. Considering the moderately acidic conditions around an infection site, such multilayers can be promising for the coating of implants/medical devices.

A novel analytical-numerical solution for nonlinear time-dependent electro-thermo-mechanical creep behavior of rotating disk made of piezoelectric polymer

A new analytical-numerical method has been developed for electro-thermo-mechanical transient creep response of rotating disk made of nonlinear piezoelectric polymer. The viscoelastic properties are stress, temperature and time dependent. The disk has been placed in an axisymmetric distributed temperature field and is subjected to a centrifugal body force with free-free, free-fixed and fixed-free boundary conditions. The Burgers’ viscoelastic creep model for long time prediction has been employed. Using the potential-displacement equation, charge equation of electrostatics, strain-displacement equations, stress-strain relations and equilibrium equation, the constitutive differential equation in terms of displacement is obtained. The non-homogeneous part of which contains creep strains. An analytical solution for radial displacement in terms of creep strains has been performed. Then the stresses, strains and electric potentials are also derived in terms of creep-strains. Prandtl-Reuss relations and the material creep model are employed to obtain history of displacement, stresses, strains and electric potential. It is concluded that the displacement is increasing with time while effective stresses are decreasing. A significant redistribution occurs for the electric potential which is due to stress redistribution during the lifetime of the disk. The results are validated with ABAQUS software. The analytical-numerical method can be used to predict the history of displacement and stresses in all structures made of nonlinear viscoelastic material.