Analytical Series Research Articles

An analytical series solution to the steady laminar flow of a Newtonian fluid in a partially filled pipe, including the velocity distribution and the dip phenomenon

An analytical series solution to the steady laminar flow of a Newtonian fluid in a partially filled pipe, including the velocity distribution and the dip phenomenon

Effectiveness of nurse leader rounding and post-discharge telephone calls in patient satisfaction: a systematic review

Background Patients' satisfaction with hospital services is an important indicator in demonstrating that nursing care meets their expectations. Hospitals are responsible for providing safe and quality care to patients during their hospitalization and ensuring patients receive continued care post-discharge. Interventions such as nurse leader rounding and post-discharge telephone calls could potentially enhance patients' hospital stay, meeting their expectations and needs in a timely manner. Objectives The objective of this review was to synthesize the best available evidence on the effectiveness of nurse leader rounding and post-discharge telephone calls in patient satisfaction of nursing and hospital services. Inclusion criteria Types of participants The review included studies of adult patients (aged 18 years or older) who had been admitted to hospital. Studies undertaken in outpatient settings were excluded. Types of intervention(s) The interventions studied were nurse leader rounding and post-discharge telephone calls. There was no comparator. Types of studies This review considered studies with experimental designs, including randomized controlled trials, non-randomized controlled trials, quasi-experimental designs, and before and after studies. It also considered studies with analytical and descriptive epidemiological designs, including prospective and retrospective cohort studies, case control studies, analytical cross-sectional studies, case series, and individual case reports. Types of outcomes The primary outcome was patients' satisfaction with nursing and hospital services. Search strategy A search for published and unpublished English language studies from 2003 to 2013 was conducted in seven major electronic databases. They were Cochrane Central Register of Controlled Trials (CENTRAL), Scopus, Web of Science, MEDLINE, CINAHL, Embase, PsycINFO and Mednar. A three-step search strategy was used, developing MeSH terminology and keywords to search and retrieve all relevant literature for the review. Methodological quality Two reviewers appraised the methodological quality of the studies independently, using the Joanna Briggs Institute's standardized critical appraisal instruments. Data extraction Data was extracted from the studies using the standardized data extraction tool. The authors of primary studies were contacted for missing information or data. Data synthesis Statistical pooling was not possible due to the included studies being descriptive study design. Therefore, the data was presented in narrative summary. Results Three studies were included in the review. The evidence was weak to suggest that nurse leader rounding and post-discharge telephone calls were effective in enhancing patients' satisfaction. Conclusions The interventions on nurse leader rounding and post-discharge telephone calls had increased patients' satisfaction of nursing and hospital services. Implications for practice Hospitals could potentially use nurse leader rounding and post-discharge telephone calls to increase patients' satisfaction of nursing and hospital services. Implications for research Randomized controlled trials are needed to determine the effect of nurse leader rounding and post-discharge telephone calls on patients' satisfaction of nursing and hospital services.

АВТОМАТИЗАЦІЯ СИСТЕМИ ВНУТРІШНЬОЛАБОРАТОРНОГО КОНТРОЛЮ ЯКОСТІ

<p>Quality control system base d on the principles of standardi zation of all phases of laboratory testing and analysis of internal laboratory quality control and external quality assessment. For the detection accuracy of the results of laboratory tests, carried out internally between the laboratory and laboratory quality control. Under internal laboratory quality control we understand measurement results of each analysis in each anal ytical series rendered directly in the lab every day. The purpose of internal laboratory control - identifying and eliminating unacceptable deviations from standard perfor mance test in the laboratory, i.e. identifying and eliminating harmful analytical errors. The solutions to these problems by implementing automated systems - software that allows you to optimize analytical laboratory research stage of the procedure by automatically creating process control charts was shown.</p>

Solving the Bloch equation with periodic excitation using harmonic balancing: application to Rabi modulated excitation.

In waveform design for magnetic resonance applications, periodic continuous-wave excitation offers potential advantages that remain largely unexplored because of a lack of understanding of the Bloch equation with periodic continuous-wave excitations. Using harmonic balancing techniques the steady state solutions of the Bloch equation with periodic excitation can be effectively solved. Moreover, the convergence speed of the proposed series approximation is such that a few terms in the series expansion suffice to obtain a very accurate description of the steady state solution. The accuracy of the proposed analytic approximate series solution is verified using both a simulation study as well as experimental data derived from a spherical phantom with doped water under continuous-wave excitation. Typically a five term series suffices to achieve a relative error of less than one percent, allowing for a very effective and efficient analytical design process. The opportunities for Rabi frequency modulated continuous-wave form excitation are then explored, based on a comparison with steady state free precession pulse sequences.

The finite element discretized symplectic method for composite mode III cracks

A finite element discretized symplectic method is proposed to compute the stress intensity factors (SIFs) of interface cracks in multi-material composites subjected to anti-plane loading. The whole body is divided into a near field containing a crack to be solved analytically and a far field to be solved by conventional finite elements. In the near field, analytical series solutions are found by the Hamiltonian formulation. The unknown displacements of the densely populated finite elements are transformed to a handful of unknown coefficients of the series. After combining with the far field, the SIFs are actually the first few coefficients.

Analytical Solutions of Time Periodic Electroosmotic Flow in a Semicircular Microchannel

The time periodic electroosmotic flow of Newtonian fluids through a semicircular microchannel is studied under the Debye–Hückel approximation. Analytical series of solutions are found, and they consist of a time-dependent oscillating part and a time-dependent generating or transient part. Some new physical phenomena are found. The electroosmotic flow driven by an alternating electric field is not periodic in time, but quasi-periodic. There is a phase shift between voltage and flow, which is only dependent on the frequency of external electric field.

Reliability assessment of a standalone wind-conventional/energy storage system using probabilistic production simulation method

This paper presents a reliability evaluation technique for a small standalone system including wind and conventional resources integrated with an energy storage system. A battery bank is considered as the energy storage system. The focus in this analysis is on the effect of battery modeling and its performance on system reliability. In this way, this paper presents an accurate model for the electrochemical batteries, which takes into account all the influential characteristics of the battery related to reliability studies, such as depth of charge, efficiency of charge, and rate of discharge. The proposed reliability evaluation method is based on the combination of a probabilistic production simulation technique as an analytical method and time series technique, in the domain of adequacy studies. By using the probabilistic production simulation technique, not only can the reliability of wind-conventional resources be assessed, but the fuel consumption can also be analyzed. On the other hand, by using the time series approach, the time variation of wind speed and operating constraints of the battery bank can be considered in evaluating the reliability indices. In this paper, a typical lead--acid battery bank is used. It is shown how the accurate modeling of the battery bank can affect the reliability indices. Beneficial results are obtained for different operating strategies and wind penetrations and are then compared.

Application of discrete Fourier series to the stress analysis of shell structures

A method for the solution of problems associated with determination of the stress state of shells of revolution using a discrete Fourier-series method is proposed. In the present work the classical theory based on Kirchhoff-Lova hypotheses is used to describe the stress state of shells. The problem of determination of the stress state of a shell with variable parameters along a generatrix is reduced to the solution of the system of partial differential equations. Discrete Fourier series are the set of functions defined on a discrete set of points. This method allows one to reduce the dimension of the problem and to solve it by the numerical Godunov’s method of discrete orthogonalization. As the approach based on application of a discrete Fourier-series for the functions set on a discrete ensemble of points is used, the curvilinear grid with an equal step on a meridian is plotted on the shell surface. The circles obtained are broken into equal amounts. This yields a set of virtual shell elements. It is recognized that the value of distributed loads on this set of virtual elements is known. We suggest to approximate loads using a discrete Fourier series expansion in cosines and sines, which makes it possible to describe any asymmetric loading. Examples of application of analytical and discrete Fourier series to calculation of isotropic and the orthotrophic of shells are given. The errors in approximating the given functions are defined by discrete series. For all the problems the necessary number of harmonics is determined. On necessary retention of the quantity of summable harmonics, the approximating function describes rather precisely various external superficial loading modes. The approximation error obtained by the Fourier series expansion method proposed here is insignificant, and this provides a description of any asymmetric loading. Application of discrete Fourier series makes it possible to reduce the dimension of the problem and to determine the stress state of shells of revolution.

Thermal performance of a porus radial fin with natural convection and radiative heat losses

An analytic (series) solution is developed to describe the thermal performance of a porous radial fin with natural convection in the fluid saturating the fin and radiation heat loss from the top and bottom surfaces of the fin. The HAM results for the temperature distribution and base heat flux are compared with the direct numerical results and found to be very accurate.

The Nonlinear Hydroelastic Response of a Semi-Infinite Elastic Plate Floating on a Fluid due to Incident Progressive Waves

The nonlinear hydroelastic response of very large floating structures (VLFSs) or an ice sheet floating on the surface of deep water, idealized as a semi-infinite thin elastic plate, is investigated analytically in the case of nonlinear incident waves. Assuming that the fluid is inviscid and incompressible and the motion is irrotational, we consider incident progressive waves with a given angular frequency within the framework of potential flow theory. With the aid of the homotopy analysis method (HAM), the convergent analytical series solutions are derived by solving the simultaneous equations in which we apply a convergence-control parameter to obtain convergent solutions with relatively few terms. The clear calculation results are represented to show nonlinear wave-plate interaction. The effects of different physical parameters, including incident wave amplitude, Young’s modulus, the thickness and density of the plate on the wave scattering, and the hydroelastic response of the floating plate, are considered. We find that the variations of the plate stiffness, thickness, and density greatly change amount of wave energy which is reflected into the open water region and is transmitted into the plate-covered region. Further, the hydroelastic response of the plate also can be affected by the amplitude of incident wave.

Presence of Pressure Gradient on Laminar Boundary Layer over a Permeable Surface with Convective Boundary Condition

This paper concerns with pressure gradient on laminar thermal boundary layer over a permeable surface in a uniform stream of fluid with convective boundary condition. The analytical series solution is used to study the effects of Prandtl number (���� ), Suction or Injection parameter (�� ), and pressure gradient (��) on both velocity and temperature profiles in the boundary layer. The governing equations which are non-linear partial differential equations are reduced to ordinary differential equations by using similarity transformations. Homotopy Analysis Method (HAM) is used to obtain the solutions for velocity and temperature. The effects of various parameters of interest on the velocity and temperature distribution are discussed. We compared our numerical values obtained with previous published work in the literature and found to be in good agreement.

Differential Transform Method with Complex Transforms to Some Nonlinear Fractional Problems in Mathematical Physics

This paper witnesses the coupling of an analytical series expansion method which is called reduced differential transform with fractional complex transform. The proposed technique is applied on three mathematical models, namely, fractional Kaup-Kupershmidt equation, generalized fractional Drinfeld-Sokolov equations, and system of coupled fractional Sine-Gordon equations subject to the appropriate initial conditions which arise frequently in mathematical physics. The derivatives are defined in Jumarie’s sense. The accuracy, efficiency, and convergence of the proposed technique are demonstrated through the numerical examples. It is observed that the presented coupling is an alternative approach to overcome the demerit of complex calculation of fractional differential equations. The proposed technique is independent of complexities arising in the calculation of Lagrange multipliers, Adomian’s polynomials, linearization, discretization, perturbation, and unrealistic assumptions and hence gives the solution in the form of convergent power series with elegantly computed components. All the examples show that the proposed combination is a powerful mathematical tool to solve other nonlinear equations also.

Approximate Solution of Two-Dimensional Nonlinear Wave Equation by Optimal Homotopy Asymptotic Method

The two-dimensional nonlinear wave equations are considered. Solution to the problem is approximated by using optimal homotopy asymptotic method (OHAM). The residual and convergence of the proposed method to nonlinear wave equation are presented through graphs. The resultant analytic series solution of the two-dimensional nonlinear wave equation shows the effectiveness of the proposed method. The comparison of results has been made with the existing results available in the literature.

Non-Similar Flow of a Heated Vertical Plate in the Stagnation Region Due to Impulsive Motion with Radiation in a Porous Medium

The two-dimensional mixed convection flow near the stagnation point region in a fluid saturated porous medium along heated vertical plate with effect of buoyancy forces and thermal radiation investigated in this paper. This study gains importance when the buoyancy forces due to the temperature difference between the surface and the free stream become large. The governing coupled non-linear partial differential equations are solved approximate analytically. An analytical series solution has been obtained using Homotopy Analysis Method (HAM) for various values of physical parameters. The present results are compared for the special cases with the results available in the literature and found to be in excellent agreement. The effect of various physical parameters on velocity and temperature profiles as well as on the heat transfer and the shear stress rates.

Series solution to coupled nonlinear heat and moisture transfer in slabs with temperature-dependent diffusivities

Abstract The two-dimensional differential transform method (DTM) is applied to solve the one-dimensional coupled heat and moisture diffusion problem for a slab with temperature-dependent thermal and moisture diffusivities, which are expressed by a linear function and an exponential function of temperature, respectively. One surface of the slab is subjected to convective hygrothermal loading and the other has constant prescribed temperature and moisture. Approximate analytical (series) solutions for the temperature and moisture profiles in the slab are derived. The transformed functions included in the solutions are obtained through a simple recursive procedure. Numerical results for a slab subjected to a sudden change in surface temperature illustrate the effects of temperature-dependent diffusivities on the transient temperature and moisture profiles of the slab. The results indicate that the nonlinear effect originating from the varying moisture diffusivity is not negligible for resin composites. The DTMis a useful new analytical method for solving nonlinear coupled transient problems.

Diffusion–convection impedance using an efficient analytical approximation of the mass transfer function for a rotating disk

This article mainly focuses on analytical approximation of the mass transfer function for dissolved species reacting at the surface of a uniformly accessible rotating disk electrode. A new analytical expression is proposed for the mass transfer function, with direct application to the associated diffusion–convection impedance. Complex fitting of the impedance model to highly accurate benchmark data is performed to check the efficiency of analytical approximation. Comparison with previous analytical formulations and asymptotic series expansion of the diffusion–convection impedance is also presented.

Harmonic analysis for the characterization and correction of geometric distortion in MRI.

Magnetic resonance imaging (MRI) is gaining widespread use in radiation therapy planning, patient setup verification, and real-time guidance of radiation delivery. Successful implementation of these technologies relies on the development of simple and efficient methods to characterize and monitor the geometric distortions arising due to system imperfections and gradient nonlinearities. To this end, the authors present the theory and validation of a novel harmonic approach to the quantification of system-related distortions in MRI. The theory of spatial encoding in MRI is applied to demonstrate that the 3D distortion vector field (DVF) is given by the solution of a second-order boundary value problem (BVP). This BVP is comprised of Laplace's equation and a limited measurement of the distortion on the boundary of a specified region of interest (ROI). An analytical series expansion solving this BVP within a spherical ROI is obtained, and a statistical uncertainty analysis is performed to determine how random errors in the boundary measurements propagate to the ROI interior. This series expansion is then evaluated to obtain volumetric DVF mappings that are compared to reference data obtained on a 3 T full-body scanner. This validation is performed within two spheres of 20 cm diameter (one centered at the scanner origin and the other offset +3 cm along each of the transverse directions). Initially, a high-order mapping requiring measurements at 5810 boundary points is used. Then, after exploring the impact of the boundary sampling density and the effect of series truncation, a reduced-order mapping requiring measurements at 302 boundary points is evaluated. The volumetric DVF mappings obtained from the harmonic analysis are in good agreement with the reference data. Following distortion correction using the high-order mapping, the authors estimate a reduction in the mean distortion magnitude from 0.86 to 0.42 mm and from 0.93 to 0.39 mm within the central and offset ROIs, respectively. In addition, the fraction of points with a distortion magnitude greater than 1 mm is reduced from 35.6% to 2.8% and from 40.4% to 1.5%, respectively. Similarly, following correction using the reduced-order mapping, the mean distortion magnitude reduces to 0.45-0.42 mm within the central and offset ROIs, and the fraction of points with a distortion magnitude greater than 1 mm is reduced to 2.8% and 1.5%, respectively. A novel harmonic approach to the characterization of system-related distortions in MRI is presented. This method permits a complete and accurate mapping of the DVF within a specified ROI using a limited measurement of the distortion on the ROI boundary. This technique eliminates the requirement to exhaustively sample the DVF at a dense 3D array of points, thereby permitting the design of simple, inexpensive phantoms that may incorporate additional modules for auxiliary quality assurance objectives.

Hydromagnetic stagnation point flow of a micropolar viscoelastic fluid towards a stretching/shrinking sheet in the presence of heat generation

In this article, the boundary layer two-dimensional Hiemenz flow and heat transfer for a micropolar, viscoelastic electrically conducting fluid over a shrinking/stretching sheet with heat generation is investigated. The governing system of flow equations is first reduced to coupled nonlinear ordinary differential equations by means of similarity transformations. A purely analytical series solutions of these equations is obtained in which domain (0 ≤ η ≤ ∞) using an analytic technique, namely, the homotopy analysis method. The convergence of the series solutions is discussed explicitly. The influences of an emerging parameters on the fluid velocity, microrotation velocity and temperature field are shown graphically and discussed in detail. The comparison of present results with the existing results is also given and found in excellent agreement.

Closed-form solutions of transient electro-osmotic flow driven by AC electric field in a microannulus

The time-periodic electro-osmotic flow of Newtonian fluids through a microannulus is studied in the Debye-Hückel approximation. Analytical series solutions for velocity and flow rate are presented with the help of an integral transform. The expression for the distribution of the velocity profile consists of a time-dependent oscillating part and a time-dependent generating or transient one, and the normalized velocity function is independent of the Reynolds number, which is very different from previous results. Then the effects of the electrokinetic width K, the wall zeta potential ratio β, and the frequency of applied external electric field ω on the distribution of the velocity profiles and flow rates are discussed numerically and theoretically. Some new physical and chemical phenomena are found theoretically. We point out that the electro-osmotic flow driven by an alternating electric field is not periodic in time, but quasi-periodic. There is a phase shift between voltage and flow, which is only dependent on the frequency of the external electric field.

Electromagnetic induction in a conductive strip in a medium of contrasting conductivity: application to VLF and MT above molten dykes

Very low frequency (VLF) electromagnetic waves that penetrate con- ductive magma-filled dikes generate secondary fields on the surface that can be used to invert for dike properties. The model used for the interpretation calculates cur- rents induced in a conductive strip by an inducing field that decays exponentially with depth due to the conductivity of the surrounding medium. The differential equations are integrated to give an inhomogeneous Fredholm equation of the second kind with a kernel consisting of a modified Bessel function of the second kind. Numerical meth- ods are typically used to solve for the induced currents in the strip. In this paper we apply a modified Galerkin-Chebyshev method, which involves separating the kernel into source and field spectra and integrating the source terms to obtain a matrix equa- tion for the unknown coefficients. The incident wave is expressed as a Chebyshev series. The Modified Bessel function is separated into a logarithmic singularity and a non-singular remainder, both of which are expanded in complex Chebyshev polyno- mials. The Chebyshev coefficients for the remainder are evaluated using a fast Fourier transform, while the logarithmic term and incident field have analytic series. The deconvolution then involves a matrix inversion. The results depend on the ratio of strip-size to skin-depth. For infinite skin-depth and a singular conductivity distribu- tion given by � 0a / p a 2 z 2 (where � 0 is the conductance, a is the half-length, and z the distance from the center), Parker (2011) gives an analytic solution. We present a similar analytic series solution for the finite skin-depth case, where the size to skin depth ratio is small. Results are presented for different ratios of size to skin depth that can be compared with numerical solutions. We compare full-space and half-space solutions. A fit of the model to VLF data taken above a magma filled dikes in Hawaii