Nonuniform Part Research Articles

Adaptive integer arithmetic coding with RLE-transform

The paper proposes a method of multilevel selective processing to increase the availability of information about critical infrastructure objects with a given level of reliability and confidentiality. This technology is based on the identification of key information at several stages of processing and adaptation of the RLE algorithm and integral arithmetic coding into a new input data structure. Thus, the last stage of processing video data by the proposed approach is considered, which is aimed at reducing the volume with the following features: further development of the method of linearization of two-dimensional transforms based on zig-zag scanning is obtained. The differences of the method lie in carrying out the vector intertransform zigzag linearization taking into account the selection of spectral components, which is defined as complementary. For the first time, a method of decomposition of a linearized transform based on the definition of a threshold has been developed. Characteristic features of the method: the threshold is found taking into account the presence in the group of different types of transformants to determine the total uneven number of non-equilibrium complementary components; the integral arithmetic coding has been improved based on taking into account the frequencies of dictionary elements (two-dictionary integral arithmetic coding). Distinctive features of the method: determination of the current code components by the decomposed working interval, depending on the capacity of the dictionaries of significant elements and the number of repetitions. This allows additionally taking into account the statistical features of the components of the RLE-structured linearized transform and reducing the length of the arithmetic code; For the first time, a transformant compression technology was created based on the reduction of various types of redundancy in groups of transformants. Characteristic features of the technology: RLE-structuring of the non-uniform complementary part of the group of transforms after their vector linearization and decomposing; the formation of two arithmetic codes according to two dictionary principles of uneven division of the working interval, depending on the type of transformants in the group.

A Comprehensive Study of Auxiliary Arrangements for Attaining Omnidirectionality in Additive Manufacturing Machine Tools

AbstractAnisotropy and omnidirectionality are the two most significant impediments to the growth of additive manufacturing (AM). While anisotropy is a property of the part, omnidirectionality is a characteristic of the machine tool. Omnidirectionality, implying invariance in AM processes with the goal of minimizing variations in material and geometric properties of the as-built parts, is often ignored during systems and process design. Disregard to directional sensitivity, which in some cases are inherent to the process (and/ or system), inadvertently changes the process parameter in-situ consequently, producing parts with non-uniform and often erratic properties. AM, attributing to its sheer number of processing variables, is especially susceptible to this subtle, yet significant system property. While some AM platforms, due to their nature of part production, are inherently omnidirectional, others require additional setup to ensure the same. Having an omnidirectional AM platform ensures that the parts are fabricated with process variables that are equally sensitive in all directions. In most AM systems, given a fixed set of process parameters, the spatial orientation of fusion (or joining) source vector, feedstock-delivery vector, and travel direction vector relative to each other governs omnidirectionality. Inconsistency or change in orientation of these three vectors results in non-uniform part properties and variations in geometric dimensions. Therefore, AM systems have to be omnidirectional to improve part performance and promote industrial acceptance. This paper, through a formal definition of omnidirectionality, analyses these three vectors individually along with their interplay with other process parameters and design variables.

Coulomb law in the nonuniform Euler–Heisenberg theory

We consider the nonlinear classical field theory which results from adding to the Maxwell’s Lagrangian the contributions from the weak-field Euler–Heisenberg Lagrangian and a nonuniform part which involves derivatives of the electric and magnetic fields. We focus on the electrostatic case where the magnetic field is set to zero, and we derive the modified Gauss law, resulting in a higher-order differential equation. This equation gives the electric field produced by stationary charges in the higher-order nonlinear electrodynamics. Specializing for the case of a point charge, we investigate the solutions of the modified Gauss law and calculate the correction to the Coulomb law.

Resonant absorption: Transformation of compressive motions into vortical motions

This paper investigates the changes in spatial properties when magnetohydrodynamic (MHD) waves undergo resonant damping in the Alfvén continuum. The analysis is carried out for a 1D cylindrical pressure-less plasma with a straight magnetic field. The effect of the damping on the spatial wave variables is determined by using complex frequencies that arise as a result of the resonant damping. Compression and vorticity are used to characterise the spatial evolution of the MHD wave. The most striking result is the huge spatial variation in the vorticity component parallel to the magnetic field. Parallel vorticity vanishes in the uniform part of the equilibrium. However, when the MHD wave moves into the non-uniform part, parallel vorticity explodes to values that are orders of magnitude higher than those attained by the transverse components in planes normal to the straight magnetic field. In the non-uniform part of the equilibrium plasma, the MHD wave is controlled by parallel vorticity and resembles an Alfvén wave, with the unfamiliar property that it has pressure variations even in the linear regime.

Quantitative assessment of microcalcification cluster image quality in digital breast tomosynthesis, 2-dimensional and synthetic mammography.

Quantitative assessment of microcalcification (MC) cluster image quality is presented, in terms of cluster signal-difference-to-noise ratio (SDNR) intercomparison among digital breast tomosynthesis (DBT) and 2-dimensional (2D) and synthetic-2-dimensional (s2D) mammography. A phantom that provides realistic appearance of MC clusters located in uniform and nonuniform background was imaged in 2D and DBT, considering various scattering conditions. MC cluster SDNR differentiation is investigated with respect to MC particle size (uniform background) and surrounding parenchyma density (nonuniform background). An accurate MC cluster segmentation method was used to delineate individual MC particles and estimate MC cluster SDNR. Analysis of the uniform part of the phantom indicated higher performance of DBT and 2D over s2D for the smallest cluster size (106-177 μm), no difference among mammographic modes for the largest MC cluster (224-354 μm), and enhanced role of 2D for decreasing cluster size and increasing scattering. Analysis of the nonuniform part of the phantom indicated DBT performed better than 2D and s2D in case of dense parenchyma pattern, while 2D and s2D did not differ across parenchyma density patterns and scattering conditions. The presented MC cluster SDNR analysis was capable of revealing subtle differences among mammographic modes and suggests a methodology for clinical image quality assessment. Graphical abstract.

Post-laser in-situ keratomileuses effects on visual field in myopia and myopic astigmatism

BackgroundThe suction used during the laser insitu keratomileusis (LASIK) procedure necessary for cutting of the cornea by an oscillating blade induces an increase of intraocular pressure (IOP) to approximately 60 mm Hg or even more. This acute increase in IOP during LASIK may endanger the blood flow within the retinal vessels and induce visual field (VF) depression. PurposeTo identify the effect of LASIK on the visual field parameters. SettingsProspective interventional case series study performed in ELNOOR ophthalmology center. From October 2015 to October 2016. MethodsProspective interventional case series study including patients with myopia and myopic astigmatism who were deemed candidates for LASIK correction. All recruited patients underwent visual field examination immediately before,1 week and 3 months post LASIK using Humphrey 750 Visual Field Analyzer (Zeiss Humphrey Systems, San Leandro, CA, USA), with a white-on-white Swedish Interactive Threshold (SITA). LASIK procedure was done using Allegretto device (wave light EX500, ALCON, Fort Worth, TX, USA) and Moria microkeratome (MM2). Results60 eyes of 30 patients were included in our study. Mean age was 28 + 5.6 years (range20-41), mean spherical equivalent (S.E) was -6.1 + 3.2 D (Range -1.4 to -15.1D), mean axial length was 23.5 + 1.5mm (Range 21-26.3mm). Humphrey global indexes included MD and PSD. The MD index estimates the uniform part of VF deviation, while the PSD index estimates the non-uniform part of VF deviation, reflecting the amount of localized depression of the VF. We found that (MD) shows slight decrease 1-week postoperative which is statistically significant, then improved 3 months postoperative with no statistical significant difference between preoperative and 3 months postoperative values. As regards PSD we found that there is no statistical difference between preoperative,1 week and 3 months postoperative. ConclusionThe surgery of LASIK is safe and efficient, but surgeons should choose effective and safe suction mode, shorten the suction time and exclude potential retinopathy and preexisting glaucoma before surgery to improve the safety and efficacy. We found that LASIK procedure has no significant effect on visual field parameters, except for diffuse depression that occurs in the first week postoperative.

Normal forms via nonuniform hyperbolicity

We develop a normal form theory for a nonautonomous dynamics xm+1=Amxm+fm(xm) with discrete time, based on the nonuniform spectrum of the sequence of matrices Am. In particular, we show that any nonresonant terms of the perturbations fm can be eliminated through an appropriate coordinate change, with the resonances expressed in terms of the connected components of the nonuniform spectrum. The latter is defined in terms of the notion of a nonuniform exponential dichotomy with a small nonuniform part, which is ubiquitous in the context of ergodic theory. We first make a preparation of the linear part of the dynamics that is of independent interest: we show that any sequence of matrices with a bounded nonuniform spectrum can be reduced to a sequence of matrices in block form via a Lyapunov coordinate change. This allows maintaining the Lyapunov exponents as well as the nonuniform spectrum. As further developments, we describe normal form theories in two additional contexts: we consider nonuniformly hyperbolic cocycles over a diffeomorphism of a compact manifold as well as perturbations fm of a sequence of compact linear operators Am on a Banach space. The latter includes the particular case of a sequence of matrices that need not be invertible.

Nonuniform spectrum on Banach spaces

For a sequence of bounded linear operators acting on a Banach space, we consider the notion of nonuniform spectrum. This is defined in terms of the existence of nonuniform exponential dichotomies with an arbitrarily small nonuniform part and can be seen as a nonuniform version of the spectrum introduced by Sacker and Sell in the case of a single trajectory, although now in the infinite-dimensional setting. We give a complete characterization of all possible forms of the nonuniform spectrum for sequences of compact linear operators and, more generally, for sequences of bounded linear operators satisfying a certain asymptotic compactness. Moreover, we provide explicit examples of sequences of compact linear operators acting on the l2 space of sequences of real numbers for all the possible forms of the nonuniform spectrum. As nontrivial applications, we show that the nonuniform spectrum of a Lyapunov regular sequence is the set of Lyapunov exponents and that the asymptotic behavior persists under sufficiently small nonlinear perturbations, in the sense that the lower and upper Lyapunov exponents of the perturbed dynamics belong to a connected component of the nonuniform spectrum. Finally, we obtain appropriate versions of the results for nonuniformly hyperbolic cocycles.

Strong nonuniform spectrum for arbitrary growth rates

We consider the notion of strong nonuniform spectrum for a nonautonomous dynamics with discrete time obtained from a sequence of matrices, which is defined in terms of the existence of strong nonuniform exponential dichotomies with an arbitrarily small nonuniform part. The latter exponential dichotomies are ubiquitous in the context of ergodic theory and correspond to have both lower and upper bounds along the stable and unstable directions, besides possibly a nonuniform conditional stability although with an arbitrarily small exponential dependence on the initial time. Moreover, we consider arbitrary growth rates instead of only the usual exponential rates. We give a complete characterization of the possible strong nonuniform spectra and for a Lyapunov regular trajectory, we show that the spectrum is the set of Lyapunov exponents. In addition, we provide explicit examples of nonautonomous dynamics for all possible strong nonuniform spectra. A remarkable consequence of our results is that for a sequence of matrices [Formula: see text], either [Formula: see text] does not admit a strong exponential dichotomy for any [Formula: see text], or if [Formula: see text] admits an exponential dichotomy for some [Formula: see text], then it also admits a strong exponential dichotomy for that [Formula: see text]. We emphasize that this result is not in the literature even in the special case of uniform exponential dichotomies.

NON‐UNIFORM TRICHOTOMIES AND ARBITRARY GROWTH RATES

For a non-autonomous dynamics defined by a sequence of matrices, we consider the notion of a non-uniform exponential trichotomy for an arbitrary growth rate (this means that there may exist contracting, expanding and neutral directions with an arbitrary fixed growth rate). The purpose of our work is two-fold: to use a regularity coefficient in order to show that these trichotomies occur naturally and to provide several alternative characterizations of those for which the non-uniform part is arbitrarily small. This includes characterizations in terms of the growth rate of volumes and of the Lyapunov exponents of the dynamics and its adjoint. We also obtain sharp lower and upper bounds for the regularity coefficient.

Reverse engineering of B-pillar with 3D optical scanning for manufacturing of non-uniform thickness part

This paper presents reverse engineering (RE) of a complex automobile structural part, B-pillar. As a major part of the automobile body-in white (BiW), B-pillar has substantial opportunity for weight reduction by introducing variable thickness across its sections. To leverage such potential, an existing B-pillar was reverse engineered with a 3D optical scanner and computer aided design (CAD) application. First, digital data (i.e. in meshes) of exiting B-pillar was obtained by the scanner, and subsequently, this information was utilized in developing a complete 3D CAD model. CATIA V5 was used in the modeling where some of the essential work benches were “Digitized Shape Editor”, “Quick Surface Reconstruction”, “Wireframe and Surface Design”, “Freestyle”, “Generation Shape Design” and “Part design”. In the final CAD design, five different thicknesses were incorporated successfully in order to get a B-pillar with non-uniform sections. This research opened opportunities for thickness optimization and mold tooling design in real time manufacturing.

Nonuniform Spectrum on the Half Line and Perturbations

For a one-sided nonautonomous dynamics defined by a sequence of invertible matrices, we develop a spectral theory (in the sense of Sacker and Sell) for the notion of a nonuniform exponential dichotomy with an arbitrarily small nonuniform part. We emphasize that this notion is ubiquitous in the context of ergodic theory, unlike the notion of a uniform exponential dichotomy. In particular, we show that each Lyapunov exponent belongs to one interval of the spectrum. We also consider a class of sufficiently small nonlinear perturbations of a linear dynamics satisfying a nonuniform bounded growth condition and we show that each solution is either eventually zero or the Lyapunov exponents belong to one interval of the spectrum.

Coherent Light induced in Optical Fiber by a Charged Particle

Coherent light production in an optical fiber by a charged particle (named PIGL, for particle-induced guided, light) is reviewed. From the microscopic point of view, light is emitted by transient electric dipoles induced in the fiber medium by the Coulomb field of the particle. The phenomenon can also considered as the capture of virtual photons of the particle field by the fiber. Two types of captures are distinguished. Type-I takes place in a uniform part of the fiber; then the photon keeps its longitudinal momentum pz. Type-II takes place near an end or in a non-uniform part of the fiber; then pz is not conserved. Type-I PIGL is not affected by background lights external to the fiber. At grazing incidence it becomes nearly monochromatic. Its circular polarization depends on the angular momentum of the particle about the fiber and on the relative velocity between the particle and the guided wave. A general formula for the yield of Type-II radiation, based on the reciprocity theorem, is proposed. This radiation can be assisted by metallic objects stuck to the fiber, via plasmon excitation. A periodic structure leads to a guided Smith-Purcell radiation. Applications of PIGL in beam diagnostics are considered.

A Non-Uniform Bound of the Remainder Term in the Central Limit Theorem for Bernoulli Random Variables

A bound for the remainder in the Esseen expansion is obtained in the case of Bernoulli random variables. The bound consists of two parts, uniform and non-uniform. The uniform part depends only on n and p, and the non-uniform part depends also on x. This bound is compared with other known bounds. It is shown how this result can be applied to the problem of the absolute constant in the Berry–Esseen inequality.

Lyapunov’s coefficient of regularity and nonuniform hyperbolicity

For a nonautonomous dynamics with discrete time defined by a sequence of matrices, we obtain sharp lower and upper bounds for the Lyapunov coefficient of regularity. This has the advantage of avoiding considering the adjoint dynamics (in contrast to what happens with the regularity coefficients considered by Perron and Grobman). We also show that the dynamics can always be reduced to one defined by upper triangular matrices with the additional properties that the canonical basis is normal and ordered. Moreover, we show in a simpler manner that the Lyapunov coefficient of regularity is related to the notion of nonuniform hyperbolicity, more precisely to the nonuniform part of a nonuniform exponential contraction or a nonuniform exponential dichotomy. Finally, as an application of this relation, we show that from the point of view of ergodic theory, for almost all trajectories with negative Lyapunov exponents the nonuniformity can be made arbitrarily small.

Turbulence attenuation in particle-laden flow in smooth and rough channels

Results of point-particle direct numerical simulations of downward gas–solid flow in smooth and rough vertical channels are presented. Two-way coupling and inter-particle collisions are included. The rough walls are shaped as fixed layers of tiny spherical particles with diameter much smaller than the viscous wall unit. The turbulence attenuation induced by the free solid particles in the gas flow is shown to be enhanced with increasing wall roughness. The so-called feedback force, the force exerted by the free particles on the gas, is decomposed into three contributions: the domain average of the mean feedback force, the non-uniform part of the mean feedback force and the fluctuating part of the feedback force. Since the non-uniformity of the mean feedback force increases with wall roughness, the effect of the non-uniform part of the mean feedback force is investigated in detail. For both smooth and rough walls, the non-uniform part of the mean feedback force is shown to contribute significantly to the particle-induced turbulence attenuation.

Non-zero Lyapunov exponents and Lyapunov's coefficient of regularity for flows

We obtain sharp lower and upper bounds for the Lyapunov coefficient of regularity defined by the solutions of a non-autonomous linear equation. We also show that the dynamics can always be reduced to one defined by an upper triangular coefficient matrix with the property that the canonical basis is normal. The bounds are then used to show in a simple manner that the coefficient of regularity is related to the notion of non-uniform hyperbolicity, more precisely to the non-uniform part of a non-uniform exponential contraction or dichotomy. As an application, we show that for almost all trajectories of a measure-preserving flow with negative Lyapunov exponents, the non-uniformity can be made arbitrarily small.

Topological conjugacies and behavior at infinity

We obtain a version of the Grobman--Hartman theorem in Banachspaces for perturbations of a nonuniform exponential contraction, both for discrete and continuous time. More precisely, we consider the general case of an exponential contraction with an arbitrary nonuniform part and obtained from a nonautonomous dynamics, and we establish the existence of Hölder continuous conjugacies between an exponential contraction and any sufficiently small perturbation. As a nontrivial application, we describe the asymptotic behavior of the topological conjugacies in terms of the perturbations: namely, we show that for perturbations growing in a certain controlled manner the conjugacies approach zero at infinity and that when the perturbations decay exponentially at infinity the conjugacies have the same exponential behavior.

Stable Manifolds and Nonuniform Hyperbolicity: Optimal Estimates

We establish the existence of invariant stable manifolds for C 1 perturbations of a nonuniform exponential dichotomy with an arbitrary nonuniform part. We consider the general case of sequences of maps, which corresponds to a nonautonomous dynamics with discrete time. We also obtain optimal estimates for the decay of trajectories along the stable manifolds. The optimal C 1 smoothness of the invariant manifolds is obtained using an invariant family of cones.

FRINGE WAVES IN AN IMPEDANCE HALF-PLANE

The uniform expressions of scalar fringe waves which are based on the physical theory of difiraction (PTD) were obtained for the impedance half plane in terms of the Fresnel integrals. Asymptotic and uniform forms of the fringe flelds were compared. The radiated flelds of the fringe expressions were analyzed numerically. Physical optics (PO) is based on the integration of surface currents which are induced by the incident flelds. This concept is valid and accurate for metallic scatterer surfaces and gives exact geometric optics (GO) waves in the high frequencies. There are lots of studies in the literature about the application of the PO method (1{3). The edge difiracted flelds which are found from the contribution of the PO surface integral are not correct. In addition PO currents just consider the illuminated part of the scatterer and ignore the shadow regions. The physical theory of difiraction (PTD) method was proposed by Uflmtsev to overcome the flrst defeat (4). The PTD consists of two main parts. The flrst part is the uniform part which is obtained from the PO and the second part is the contribution of the non-uniform or fringe part. The fringe part is the result of the fringe currents. It is pointed out that the fringe currents are obtained by dividing the induced surface currents into two parts. The flelds, radiated by the fringe currents, can be found by subtracting of uniform part from the exact solution. The method is widely used in the literature for investigation of the scattering problems (5{8). Using the uniform fringe flelds instead of the non-uniform version is more reliable. Non- uniform fringe flelds can be obtained by the subtraction of asymptotic